Weitao Yang

A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTDensity functional approach to the frontier-electron theory of chemical reactivityRobert G. Parr and Weitao YangCite this: J. Am. Chem. Soc. 1984, 106, 14, 4049–4050Publication Date (Print):July 1, 1984Publication History Published online1 May 2002Published inissue 1 July 1984https://doi.org/10.1021/ja00326a036Request reuse permissionsArticle Views4598Altmetric-Citations2696LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (275 KB) Get e-Alertsclose Get e-Alerts

Noncovalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these noncovalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define noncovalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their vdW radii. We recently developed an alternative perspective, derived from the electronic density: the non-covalent interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of noncovalent interactions is of great potential value. Here, we describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical as well as promolecular densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/∼yang/software.htm.

A Comment on the Letter by John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). The authors of the Letter offer a Reply.Received 2 June 1997DOI:https://doi.org/10.1103/PhysRevLett.80.890©1998 American Physical Society

Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, for many predicted properties, there are spectacular failures that can be traced to the delocalization error and static correlation error of commonly used approximations. These errors can be characterized and understood through the perspective of fractional charges and fractional spins introduced recently. Reducing these errors will open new frontiers for applications of density functional theory.

ADVERTISEMENT RETURN TO ISSUEPREVReviewNEXTChallenges for Density Functional TheoryAron J. Cohen*, Paula Mori-Sánchez*, and Weitao YangView Author Information Department of Chemistry, Lensfield Road, University of Cambridge, Cambridge, CB2 1EW, United Kingdom Departamento de Química, Universidad Autónoma de Madrid, 28049 Madrid, Spain Department of Chemistry, French Family Science Center, Duke University, Durham, North Carolina, 27708, United States*E-mail: [email protected], [email protected] and [email protected]Cite this: Chem. Rev. 2012, 112, 1, 289–320Publication Date (Web):December 22, 2011Publication History Received5 April 2011Published online22 December 2011Published inissue 11 January 2012https://doi.org/10.1021/cr200107zCopyright © 2011 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views26030Altmetric-Citations1549LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (5 MB) Get e-AlertsSUBJECTS:Density functional theory,Electrical energy,Energy,Molecules,Quantum mechanics Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe use of global and local molecular parameters for the analysis of the gas-phase basicity of aminesWeitao. Yang and Wilfried J. MortierCite this: J. Am. Chem. Soc. 1986, 108, 19, 5708–5711Publication Date (Print):September 1, 1986Publication History Published online1 May 2002Published inissue 1 September 1986https://doi.org/10.1021/ja00279a008RIGHTS & PERMISSIONSArticle Views2195Altmetric-Citations1355LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (542 KB) Get e-Alerts Get e-Alerts

The concepts of hardness eta = (2E/N2)nu and fukui function f(r) = [rho (r)/N]nu, which have recently been associated with the theory of chemical reactivity in molecules, are extended to the theory of metals. It is shown that at T = 0, 1/eta = g(epsilon F) and f(r) = g(epsilon F, r)/g(epsilon F), where g(epsilon F), and g(epsilon F, r) are the density of states and the local density of states, at the Fermi energy epsilon F. Softness S and local softness s(r) are defined as 1/eta and Sf(r), respectively, and it is shown that (formula; see text) where the averages are over a grand canonical ensemble. It is pointed out that the postulate that f(r) or g(epsilon F, r) determines site selectivity for metals in chemisorption and catalysis is synonymous with the recent argument by Falicov and Somorjai [Falicov, L. M. & Somorjai, G. A. (1985) Proc. Natl. Acad. Sci. USA 82, 2207-2211] that such selectivity is determined by low-energy density fluctuations.

The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory.

A new approach for the study of ground states of many-electron systems is developed via direct calculation of the density in density-functional theory. Not using the Kohn-Sham equations, the method divides a system into subsystems in physical space and determines the density for each subsystem. The method is demonstrated with calculations for the nitrogen molecule, which is divided into two atomic subsystems. We expect this approach to enable calcultions for large molecules beyond the reach of conventional methods.

Recent fundamental advances in the density-functional theory of electronic structure are summarized. Emphasis is given to four aspects of the subject: (a) tests of functionals, (b) new methods for determining accurate exchange-correlation functionals, (c) linear scaling methods, and (d) developments in the description of chemical reactivity.

An empirical method has been designed to account for the van der Waals interactions in practical molecular calculations with density functional theory. For each atom pair separated at a distance R, the method adds to the density functional electronic structure calculations an additional attraction energy EvdW=−fd(R)C6R−6, where fd(R) is the damping function which equals to one at large value of R and zero at small value of R. The coefficients C6 for pair interactions between hydrogen, carbon, nitrogen, and oxygen atoms have been developed in this work by a least-square fitting to the molecular C6 coefficients obtained from the dipole oscillator strength distribution method by Meath and co-workers. Two forms of the damping functions have been studied, with one dropping to zero at short distances much faster than the other. Four density functionals have been examined: Becke’s three parameter hybrid functional with the Lee-Yang-Parr correlation functional, Becke’s 1988 exchange functional with the LYP correlation functional, Becke’s 1988 exchange functional with Perdew and Wang’s 1991 (PW91) correlation functional, and PW91 exchange and correlation functional. The method has been applied to three systems where the van der Waals attractions are known to be important: rare-gas diatomic molecules, stacking of base pairs and polyalanines’ conformation stabilities. The results show that this empirical method, with the damping function dropping to zero smoothly, provides a significant correction to both of the Becke’s hybrid functional and the PW91 exchange and correlation functional. Results are comparable to the corresponding second-order Møller-Plesset calculations in many cases.

MoS2 presents a promising low-cost catalyst for the hydrogen evolution reaction (HER), but the understanding about its active sites has remained limited. Here we present an unambiguous study of the catalytic activities of all possible reaction sites of MoS2, including edge sites, sulfur vacancies, and grain boundaries. We demonstrate that, in addition to the well-known catalytically active edge sites, sulfur vacancies provide another major active site for the HER, while the catalytic activity of grain boundaries is much weaker. The intrinsic turnover frequencies (Tafel slopes) of the edge sites, sulfur vacancies, and grain boundaries are estimated to be 7.5 s-1 (65-75 mV/dec), 3.2 s-1 (65-85 mV/dec), and 0.1 s-1 (120-160 mV/dec), respectively. We also demonstrate that the catalytic activity of sulfur vacancies strongly depends on the density of the vacancies and the local crystalline structure in proximity to the vacancies. Unlike edge sites, whose catalytic activity linearly depends on the length, sulfur vacancies show optimal catalytic activities when the vacancy density is in the range of 7-10%, and the number of sulfur vacancies in high crystalline quality MoS2 is higher than that in low crystalline quality MoS2, which may be related with the proximity of different local crystalline structures to the vacancies.

The quantitative correlation of the catalytic activity with microscopic structure of heterogeneous catalysts is a major challenge for the field of catalysis science. It requests synergistic capabilities to tailor the structure with atomic scale precision and to control the catalytic reaction to proceed through well-defined pathways. Here we leverage on the controlled growth of MoS2 atomically thin films to demonstrate that the catalytic activity of MoS2 for the hydrogen evolution reaction decreases by a factor of ~4.47 for the addition of every one more layer. Similar layer dependence is also found in edge-riched MoS2 pyramid platelets. This layer-dependent electrocatalysis can be correlated to the hopping of electrons in the vertical direction of MoS2 layers over an interlayer potential barrier, which is found to be 0.119V and consistent with theoretical calculations. Our results point out that increasing the hopping efficiency of electrons in the vertical direction is a key for the development of high-efficiency two-dimensional material catalysts.

One of the most important challenges in density functional theory (DFT) is the proper description of fractional charge systems relating to the self-interaction error (SIE). Traditionally, the SIE has been formulated as a one-electron problem, which has been addressed in several recent functionals. However, these recent one-electron SIE-free functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the many-electron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from many-electron SIE. Finally, we give a SIE classification of density functionals.

The difficulty of widely used density functionals in describing the dissociation behavior of some homonuclear and heteronuclear diatomic radicals is analyzed. It is shown that the self-interaction error of these functionals accounts for the problem—it is much larger for a system with a noninteger number of electrons than a system with an integer number of electrons. We find the condition for the erroneous dissociation behavior described by approximate density functionals: when the ionization energy of one dissociation partner differs from the electron affinity of the other partner by a small amount, the self-interaction error will lead to wrong dissociation limit. Systems with a noninteger number of electrons and hence the large amount of self-interaction error in approximate density functionals arise also in the transition states of some chemical reactions and in some charge-transfer complexes. In the course of analysis, we derive a scaling relation necessary for an exchange-correlation functional to be self-interaction free.

The calculation of the band gap by density-functional theory (DFT) is examined by considering the behavior of the energy as a function of number of electrons. It is explained that the incorrect band-gap prediction with most approximate functionals originates mainly from errors in describing systems with fractional charges. Formulas for the energy derivatives with respect to number of electrons are derived, which clarify the role of optimized effective potentials in prediction of the band gap. Calculations with a recent functional that has much improved behavior for fractional charges give a good prediction of the energy gap and also ${\ensuremath{\epsilon}}_{\mathrm{HOMO}}\ensuremath{\simeq}\ensuremath{-}I$ for finite systems. Our results indicate that it is possible, within DFT, to have a functional whose eigenvalues or derivatives accurately predict the band gap.

A density matrix divide-and-conquer method is proposed for electronic structure calculation of large molecules. It is based on partition of density matrix and thus applicable to both density-functional and Hartree–Fock method. Compared to the original formulation with electron density, the present method is more efficient and as accurate.

A major challenge for combined quantum mechanical and molecular mechanical methods (QM/MM) to study large molecules is how to treat the QM/MM boundary that bisects some covalent bonds. Here a pseudobond approach has been developed to solve this problem for ab initio QM/MM calculations: a one-free-valence atom with an effective core potential is constructed to replace the boundary atom of the environment part and to form a pseudobond with the boundary atom of the active part. This pseudobond, which is described only by the QM method, is designed to mimic the original bond with similar bond length and strength, and similar effects on the rest of the active part. With this pseudobond approach, some well-known deficiencies of the link atom approach have been circumvented and a well-defined potential energy surface of the whole QM/MM system has been provided. The construction of the effective core potential for the pseudobond is independent of the molecular mechanical force field and the same effective core potential is applicable to both Hartree–Fock and density functional methods. Tests on a series of molecules yield very good structural, electronic, and energetic results in comparison with the corresponding full ab initio quantum mechanical calculations.

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The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. But the gap in the band-structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density functional theory. Here we give a simple proof of a new theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from meta-generalized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

A new practical approach to studying enzyme reactions by combining ab initio QM/MM calculations with free energy perturbation is presented. An efficient iterative optimization procedure has been developed to determine optimized structures and minimum energy paths for a system with thousands of atoms on the ab initio QM/MM potential: the small QM sub-system is optimized using a quasi-Newton minimizer in redundant internal coordinates with ab initio QM/MM calculations, while the large MM sub-system is minimized by the truncated Newton method in Cartesian coordinates with only molecular mechanical calculations. The above two optimization procedures are performed iteratively until they converge. With the determined minimum energy paths, free energy perturbation calculations are carried out to determine the change in free energy along the reaction coordinate. Critical to the success of the iterative optimization procedure and the free energy calculations is the smooth connection between the QM and MM regions provided by a recently proposed pseudobond QM/MM approach [J. Chem. Phys. 110, 46 (1999)]. The methods have been demonstrated by studying the initial proton transfer step in the reaction catalyzed by the enzyme triosephosphate isomerase (TIM).

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.

Combined quantum mechanics/molecular mechanics (QM/MM) methods provide an accurate and efficient energetic description of complex chemical and biological systems, leading to significant advances in the understanding of chemical reactions in solution and in enzymes. Here we review progress in QM/MM methodology and applications, focusing on ab initio QM-based approaches. Ab initio QM/MM methods capitalize on the accuracy and reliability of the associated quantum-mechanical approaches, however, at a much higher computational cost compared with semiempirical quantum-mechanical approaches. Thus reaction-path and activation free-energy calculations based on ab initio QM/MM methods encounter unique challenges in simulation timescales and phase-space sampling. This review features recent developments overcoming these challenges and enabling accurate free-energy determination for reaction processes in solution and in enzymes, along with applications.

Photocatalysis has not found widespread industrial adoption, in spite of decades of active research, because the challenges associated with catalyst illumination and turnover outweigh the touted advantages of replacing heat with light. A demonstration that light can control product selectivity in complex chemical reactions could prove to be transformative. Here, we show how the recently demonstrated plasmonic behaviour of rhodium nanoparticles profoundly improves their already excellent catalytic properties by simultaneously reducing the activation energy and selectively producing a desired but kinetically unfavourable product for the important carbon dioxide hydrogenation reaction. Methane is almost exclusively produced when rhodium nanoparticles are mildly illuminated as hot electrons are injected into the anti-bonding orbital of a critical intermediate, while carbon monoxide and methane are equally produced without illumination. The reduced activation energy and super-linear dependence on light intensity cause the unheated photocatalytic methane production rate to exceed the thermocatalytic rate at 350 °C.

Herein, we investigated a series of fullerene-free organic solar cells (OSCs) based on six different donor:acceptor (D:A) blends with varied highest occupied molecular orbital (HOMO) offsets from −0.05 to 0.21 eV. First, to verify the energetic compatibility of a specific D:A pair, especially for HOMO offsets, we established a simple method to estimate the hole transfer tendencies between D and A by using bilayer hole-only devices. It reveals that the asymmetrical diode effect of the bilayer hole-only devices can correlate with the FF and Jsc of the relevant OSCs. Second, to find out whether HOMO offset is the main restriction of hole transfer, we measured transient absorption spectra and examined the hole transfer behavior in the blends, revealing that the occurrence of hole transfer is independent of the HOMO offsets and ultrafast in the time scale of ≤4.6 ps for those blends with ≥0 eV HOMO offsets. In contrast, a negative HOMO offset can significantly slow down the hole transfer with a half-time of ∼400 ps. Furthermore, we compare the device parameters under varied light intensities and discover that the bimolecular recombination should be one of the main restrictions for high device performance. Surprisingly, small HOMO offsets of 0 and 0.06 eV can also enable high PCEs of 10.42% and 11.75% for blend 2 (PTQ10:HC-PCIC) and blend 3 (PBDB-TF:HC-PCIC), respectively. Overall, our work demonstrates not only the validity of high-performance OSCs operating at the near zero HOMO offsets but also the charge dynamic insights of these blends, which will help gain understanding on the further improvement of OSCs.

Hydrogen bonds are of crucial relevance to many problems in chemistry, biology, and materials science. The recently developed NCI (noncovalent interactions) index enables real-space visualization of both attractive (van der Waals and hydrogen-bonding) and repulsive (steric) interactions based on properties of the electron density. It is thus an optimal index to describe the interplay of stabilizing and destabilizing contributions that determine stable minima on hydrogen-bonding potential-energy surfaces (PESs). In the framework of density-functional theory, energetics are completely determined by the electron density. Consequently, NCI will be shown to allow quantitative treatment of hydrogen-bond energetics. The evolution of NCI regions along a PES follows a well-behaved pattern which, upon integration of the electron density, is capable of mimicking conventional hydrogen-bond interatomic potentials.

Abstract Increasing the power conversion efficiency (PCE) of the two‐dimensional (2D) perovskite‐based solar cells (PVSCs) is really a challenge. Vertical orientation of the 2D perovskite film is an efficient strategy to elevate the PCE. In this work, vertically orientated highly crystalline 2D (PEA) 2 (MA) n–1 Pb n I 3n+1 (PEA= phenylethylammonium, MA = methylammonium, n = 3, 4, 5) films are fabricated with the assistance of an ammonium thiocyanate (NH 4 SCN) additive by a one‐step spin‐coating method. Planar‐structured PVSCs with the device structure of indium tin oxide (ITO)/poly(3,4‐ethylenedioxythiophene):poly(styrenesulfonate)/(PEA) 2 (MA) n–1 Pb n I 3n+1 /[6,6]‐phenyl‐C61‐butyric acid methyl ester/bahocuproine/Ag are fabricated. The PCE of the PVSCs is boosted from the original 0.56% (without NH 4 SCN) to 11.01% with the optimized NH 4 SCN addition at n = 5, which is among the highest PCE values for the low‐ n ( n < 10) 2D perovskite‐based PVSCs. The improved performance is attributed to the vertically orientated highly crystalline 2D perovskite thin films as well as the balanced electron/hole transportation. The humidity stability of this oriented 2D perovskite thin film is also confirmed by the almost unchanged X‐ray diffraction patterns after 28 d exposed to the moisture in a humidity‐controlled cabinet ( H r = 55 ± 5%). The unsealed device retains 78.5% of its original PCE after 160 h storage in air atmosphere with humidity of 55 ± 5%. The results provide an effective approach toward a highly efficient and stable PVSC for future commercialization.

New exchange-correlation functionals that address the important issue of many-electron self-interaction are developed. This is carried out by considering the performance of the functional on systems with fractional numbers of electrons at the same time as more standard thermochemical tests. The inclusion of Coulomb-attenuated exchange in the functional is facilitated by use of the adiabatic connection coupled with a short-range and long-range splittings. The new functionals have a good performance on thermochemistry and a much improved description of the total energy versus number of electrons and henceforth a much smaller many-electron self-interaction error.

As the terminal step in photosystem II, and a potential half-reaction for artificial photosynthesis, water oxidation (2H(2)O --> O(2) + 4e(-) + 4H(+)) is key, but it imposes a significant mechanistic challenge with requirements for both 4e(-)/4H(+) loss and O-O bond formation. Significant progress in water oxidation catalysis has been achieved recently by use of single-site Ru metal complex catalysts such as [Ru(Mebimpy)(bpy)(OH(2))](2+) [Mebimpy = 2,6-bis(1-methylbenzimidazol-2-yl)pyridine; bpy = 2,2'-bipyridine]. When oxidized from to Ru(V) = O(3+), these complexes undergo O-O bond formation by O-atom attack on a H(2)O molecule, which is often the rate-limiting step. Microscopic details of O-O bond formation have been explored by quantum mechanical/molecular mechanical (QM/MM) simulations the results of which provide detailed insight into mechanism and a strategy for enhancing catalytic rates. It utilizes added bases as proton acceptors and concerted atom-proton transfer (APT) with O-atom transfer to the O atom of a water molecule in concert with proton transfer to the base (B). Base catalyzed APT reactivity in water oxidation is observed both in solution and on the surfaces of oxide electrodes derivatized by attached phosphonated metal complex catalysts. These results have important implications for catalytic, electrocatalytic, and photoelectrocatalytic water oxidation.

In plasmon-enhanced heterogeneous catalysis, illumination accelerates reaction rates by generating hot carriers and hot surfaces in the constituent nanostructured metals. In order to understand how photogenerated carriers enhance the nonthermal reaction rate, the effects of photothermal heating and thermal gradients in the catalyst bed must be confidently and quantitatively characterized. This is a challenging task considering the conflating effects of light absorption, heat transport, and reaction energetics. Here, we introduce a methodology to distinguish the thermal and nonthermal contributions from plasmon-enhanced catalysts, demonstrated by illuminated rhodium nanoparticles on oxide supports to catalyze the CO2 methanation reaction. By simultaneously measuring the total reaction rate and the temperature gradient of the catalyst bed, the effective thermal reaction rate may be extracted. The residual nonthermal rate of the plasmon-enhanced reaction is found to grow with a superlinear dependence on illumination intensity, and its apparent quantum efficiency reaches ∼46% on a Rh/TiO2 catalyst at a surface temperature of 350 °C. Heat and light are shown to work synergistically in these reactions: the higher the temperature, the higher the overall nonthermal efficiency in plasmon-enhanced catalysis.

The "small molecule universe" (SMU), the set of all synthetically feasible organic molecules of 500 Da molecular weight or less, is estimated to contain over 10(60) structures, making exhaustive searches for structures of interest impractical. Here, we describe the construction of a "representative universal library" spanning the SMU that samples the full extent of feasible small molecule chemistries. This library was generated using the newly developed Algorithm for Chemical Space Exploration with Stochastic Search (ACSESS). ACSESS makes two important contributions to chemical space exploration: it allows the systematic search of the unexplored regions of the small molecule universe, and it facilitates the mining of chemical libraries that do not yet exist, providing a near-infinite source of diverse novel compounds.

Vertically oriented highly crystalline 2D layered (BA) 2 (MA) n −1 Pb n I 3 n +1 (BA = CH 3 (CH 2 ) 3 NH 3 , MA = CH 3 NH 3 , n = 3, 4) perovskite thin‐films are fabricated with the aid of ammonium thiocyanate (NH 4 SCN) additive through one‐step spin‐coating process. The humidity‐stability of the film is certified by the almost unchanged X‐ray diffraction patterns after exposed to humid atmosphere ( H r = 55 ± 5%) for 40 d. The photovoltaic devices with the structure of indium tin oxide(ITO)/poly(3,4‐ethylenedioxythiophene):poly(styrene‐sulfonate)/(BA) 2 (MA) n −1 Pb n I 3 n +1 ( n = 3,4)/[6,6]‐phenyl‐C 61 ‐butyric acid methyl ester/Bathocuproine/Ag are fabricated. The devices based on (BA) 2 (MA) 2 Pb 3 I 10 perovskite ( n = 3) with the precursor composition of BAI:methylammonium iodide:PbI 2 :NH 4 SCN = 2:2:3:1 (by molar ratio) show an averaged power conversion efficiency (PCE) of 6.82%. In the case of (BA) 2 (MA) 3 Pb 4 I 13 ( n = 4), a higher PCE of 8.79% is achieved. Both of the unsealed devices perform unique stability with almost unchanged PCE during the period of storage in purified N 2 glove box. This work provides a simple and effective method to enhance the efficiency of the 2D perovskite solar cell.

MoS2 presents a promising catalyst for the hydrogen evolution reaction (HER) in water splitting, but its worse catalytic performance in neutral and alkaline media than in acidic environment may be problematic for practical application. This is because the other half reaction of water splitting, i.e., oxygen evolution reaction, often needs to be implemented in alkaline environment. Here we demonstrate a universal strategy that may be used to significantly improve the HER catalysis of MoS2 in all kinds of environments from acidic to alkaline, proton intercalation. Protons may be enabled to intercalate between monolayer MoS2 and underlying substrates or in the interlayer space of thicker MoS2 by two processes: electrochemically polarizing MoS2 at negative potentials (vs RHE) in acidic media or immersing MoS2 into certain acid solutions like TFSI. The improvement in catalytic performance is due to the activity enhancement of the active sites in MoS2 by the intercalated protons, which might be related with the effect of the intercalated protons on electrical conductance and the adsorption energy of hydrogen atoms. The enhancement in catalytic activity by the intercalated proton is very stable even in neutral and alkaline electrolytes.

Higher acenes have drawn much attention as promising organic semiconductors with versatile electronic properties. However, the nature of their ground state and electronic excited states is still not fully clear. Their unusual chemical reactivity and instability are the main obstacles for experimental studies, and the potentially prominent diradical character, which might require a multireference description in such large systems, hinders theoretical investigations. Here, we provide a detailed answer with the particle-particle random-phase approximation calculation. The (1)Ag ground states of acenes up to decacene are on the closed-shell side of the diradical continuum, whereas the ground state of undecacene and dodecacene tilts more to the open-shell side with a growing polyradical character. The ground state of all acenes has covalent nature with respect to both short and long axes. The lowest triplet state (3)B2u is always above the singlet ground state even though the energy gap could be vanishingly small in the polyacene limit. The bright singlet excited state (1)B2u is a zwitterionic state to the short axis. The excited (1)Ag state gradually switches from a double-excitation state to another zwitterionic state to the short axis, but always keeps its covalent nature to the long axis. An energy crossing between the (1)B2u and excited (1)Ag states happens between hexacene and heptacene. Further energetic consideration suggests that higher acenes are likely to undergo singlet fission with a low photovoltaic efficiency; however, the efficiency might be improved if a singlet fission into multiple triplets could be achieved.

MoS2 holds great promise as a cost-effective alternative to Pt for catalyzing the hydrogen evolution reaction (HER) of water, but its reported catalytic efficiency is still worse than that of Pt, the best HER catalyst but too rare and expensive for mass production of hydrogen. We report a strategy to enable the catalytic activity of monolayer MoS2 films that are even better than that of Pt via engineering the interaction of the monolayer with supporting substrates. The monolayer films were grown with chemical vapor deposition processes and controlled to have an optimal density (7–10%) of sulfur vacancies. We find that the catalytic activity of MoS2 can be affected by substrates in two ways: forming an interfacial tunneling barrier with MoS2 and modifying the chemical nature of MoS2 via charge transfer (proximity doping). Following this understanding, we enable excellent catalytic activities at the monolayer MoS2 films by using substrates that can provide n-doping to MoS2 and form low interfacial tunneling barriers with MoS2, such as Ti. The catalytic performance may be further boosted to be even better than Pt by crumpling the films on Ti coated flexible polymer substrates, as the Tafel slope of the film is substantially decreased with the presence of crumpling-induced compressive strain. The monolayer MoS2 films show no degradation in catalytic performance after being continuously tested for over 2 months.

Unveiling the correlations among molecular structures, morphological characteristics, macroscopic properties and device performances is crucial for developing better photovoltaic materials and achieving higher efficiencies. To achieve this goal, a comprehensive study is performed based on four state-of-the-art non-fullerene acceptors (NFAs), which allows to systematically examine the above-mentioned correlations from different scales. It's found that extending conjugation of NFA shows positive effects on charge separation promotion and non-radiative loss reduction, while asymmetric terminals can maximize benefits from both terminals. Another molecular optimization is from alkyl chain tuning. The shortened alkyl side chain results in strengthened terminal packing and decreased π-π distance, which contribute high carrier mobility and finally the high charge collection efficiency. With the most-acquired benefits from molecular structure and macroscopic factors, PM6:BTP-S9-based organic photovoltaics (OPVs) exhibit the optimal efficiency of 17.56% (certified: 17.4%) with a high fill factor of 78.44%, representing the best among asymmetric acceptor based OPVs. This work provides insight into the structure-performance relationships, and paves the way toward high-performance OPVs via molecular design.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Generalized gradient approximations have been used to calculate the potential energy curves for six rare gas diatomic molecules. Several generalized gradient approximations are found to provide a good description of binding in these diatomic molecules and show a significant improvement over the local density approximation in the prediction of bond lengths and dissociation energies. It is shown here that the behavior of an exchange functional in the region of small density and large density gradient plays a very important role in the ability of the functional to describe this type of van der Waals attraction.

A direct optimization method is developed for the computation of the Kohn–Sham kinetic energy density functional Ts from a given electron density and the exchange–correlation potential vxc if this density is from a ground state. The method is based on the construction of a variational functional of the one-electron potential. This functional is derived from the conventional Levy constrained-search formulation and is shown to be closely related to the Lieb functional construction. The one-electron potential is expanded in terms of some fixed terms plus a linear expansion in a basis set. The determination of the Kohn–Sham kinetic energy for an input density is then turned into the maximization of this functional of potential. The analytic first and second derivatives of the variational functional with respect to the linear basis set expansion coefficients and also the nonlinear parameters in the basis set are derived. This enables very efficient iterative optimization of the potential and hence the calculation of Ts and vxc. The efficiency and accuracy of the method is shown in the numerical implementation for atomic and molecular calculations with Gaussian basis set expansions both for molecular orbitals and for one-electron potentials. Finally, this direct optimization method is extended to general density functionals and the analytic derivatives are also developed for use in optimization methods.

The conventional optimized effective potential method is based on a difficult-to-solve integral equation. In the new method, this potential is constructed as a sum of a fixed potential and a linear combination of basis functions. The energy derivatives with respect to the coefficients of the linear combination are obtained. This enables calculations by optimization methods. Accurate atomic and molecular calculations with Gaussian basis sets are presented for exact exchange functionals. This efficient and accurate method for the optimized effective potential should play an important role in the development and application of density functionals.

Fukui functions (softnesses) are calculated for three species - formaldehyde, the thiocyanate ion and carbon monoxide. The fukui function for a molecule has been defined as the derivative of electron density with respect to the change of number of electrons, keeping the positions of nuclei unchanged; this differentiation is performed by finite difference. Local softness and fukui function are proportional. The calculated results, expressed in terms of contour maps and condensed values of fukui functions, substantiate the previous argument that fukui functions serve as reactivity indices for chemical reactions. Particularly, it is confirmed that: (1) a nucleophilic reagent approaches the carbon atom in formaldehyde from the direction perpendicular to the molecular plane, while an electrophilic reagent approaches the oxygen atom in the molecular plane; (2) the sulphur end is softer than the nitrogen end in the thiocyanate ion; and (3) carbon monoxide behaves like a Lewis acid in bonding with transition metals.

Quantum interference in coherent transport through single molecular rings may provide a mechanism to control the current in molecular electronics. We investigate its applicability, using a single-particle Green function method combined with ab initio electronic structure calculations. We find that the quantum interference effect (QIE) is strongly dependent on the interaction between molecular π-states and contact σ-states. It is masked by σ tunneling in small molecular rings with Au leads, such as benzene, due to strong π−σ hybridization, while it is preserved in large rings, such as [18]annulene, which then could be used to realize quantum interference effect (QIE) transistors.

A formulation of the chemical potential (electronegativity) equalization principle is presented from the perspective of density-functional theory. The resulting equations provide a linear-response framework for describing the redistribution of electrons upon perturbation by an applied field. The method has two main advantages over existing electronegativity equalization and charge equilibration methods that allow extension to accurate molecular dynamics simulations. Firstly, the expansion of the energy is taken about the molecular ground state instead of the neutral atom ground states; hence, in the absence of an external field, the molecular charge distribution can be represented by static point charges and dipoles obtained from fitting to high-level ab initio calculations without modification. Secondly, in the presence of applied fields or interactions with other molecules, the density response can be modeled accurately using basis functions. Inclusion of basis functions with dipolar or higher order multipolar character allows molecules or chemical groups to have correct local anisotropic polarizabilities. A modified semiempirical form of the hardness matrix has been introduced that can be evaluated efficiently using Gaussians, and requires only one parameter per basis function. Applications at two basis-set levels demonstrate the method can accurately reproduce induced dipole moments and estimated chemical potentials obtained from density-functional calculations for a variety of molecules. Inclusion of basis functions beyond the conventional spherical-atom type is essential in some instances. The present formulation provides the foundation for a promising semi-empirical model for polarization and charge transfer in molecular simulations.

Electronic states with fractional spins arise in systems with large static correlation (strongly correlated systems). Such fractional-spin states are shown to be ensembles of degenerate ground states with normal spins. It is proven here that the energy of the exact functional for fractional-spin states is a constant, equal to the energy of the comprising degenerate pure-spin states. Dramatic deviations from this exact constancy condition exist with all approximate functionals, leading to large static correlation errors for strongly correlated systems, such as chemical bond dissociation and band structure of Mott insulators. This is demonstrated with numerical calculations for several molecular systems. Approximating the constancy behavior for fractional spins should be a major aim in functional constructions and should open the frontier for density functional theory to describe strongly correlated systems. The key results are also shown to apply in reduced density-matrix functional theory.

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified and extended to states with both fractional charge and fractional spin to give a much more stringent condition: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. Violation of this condition underlies the failure of all known approximate functionals to describe the gaps in strongly correlated systems. It is shown that explicitly discontinuous functionals of the density or orbitals that go beyond these currently used smooth approximations is the key for the application of density functional theory to strongly correlated systems.

A self-consistent method for calculating electron transport through a molecular device is developed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the framework of the nonequilibrium Green function approach. To avoid the substantial computational cost in finding the $I\text{\ensuremath{-}}V$ characteristic of large systems, we also develop an approximate but much more efficient non-self-consistent method. Here the change in effective potential in the device region caused by a bias is approximated by the main features of the voltage drop. As applications, the $I\text{\ensuremath{-}}V$ curves of a carbon chain and an aluminum chain sandwiched between two aluminum electrodes are calculated---two systems in which the voltage drops very differently. By comparing to the self-consistent results, we show that this non-self-consistent approach works well and can give quantitatively good results.

This book is a rigorous, unified account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. Containing a detailed discussion of the chemical potential and its derivatives, it provides an understanding of the concepts of electronegativity, hardness and softness, and chemical reactivity. Both the Hohenberg-Kohn-Sham and the Levy-Lieb derivations of the basic theorems are presented, and extensive references to the literature are included. Two introductory chapters and several appendices provide all the background material necessary beyond a knowledge of elementary quantum theory. The book is intended for physicists, chemists, and advanced students in chemistry.

We develop a self-interaction-free exchange-correlation functional which is very accurate for thermochemistry and kinetics. This is achieved by theoretical construction of the functional form and nonlinear fitting. We define a simple interpolation of the adiabatic connection that uses exact exchange, generalized gradient approximation (GGA) and meta-GGA functionals. The performance is optimized by fitting a small number of empirical parameters. Overall the new functional improves significantly upon hybrids and meta-GGAs while correctly describing one-electron systems. The mean absolute error on a large set of reaction barriers is reduced to 1.99kcal∕mol.

A linear-scaling method to carry out semiempirical quantum mechanical calculations for large systems has been developed based on the density matrix version of the divide-and-conquer approach. The method has been tested and demonstrated to be accurate and efficient. With this implementation, semiempirical quantum mechanical calculations are made possible for large molecules over 9000 atoms on a typical workstation. For biological macromolecules, solvent effects are included with a dielectric continuum model.

A novel nonempirical scaling correction method is developed to tackle the challenge of band gap prediction in density functional theory. For finite systems the scaling correction largely restores the straight-line behavior of electronic energy at fractional electron numbers. The scaling correction can be generally applied to a variety of mainstream density functional approximations, leading to significant improvement in the band gap prediction. In particular, the scaled version of a modified local density approximation predicts band gaps with an accuracy consistent for systems of all sizes, ranging from atoms and molecules to solids. The scaled modified local density approximation thus provides a useful tool to quantitatively characterize the size-dependent effect on the energy gaps of nanostructures.

The difficulty of approximate density functionals in describing the energetics of Diels-Alder reactions and dimerization of aluminum complexes is analyzed. Both of these reaction classes involve formation of cyclic or bicyclic products, which are found to be underbound by the majority of functionals considered. We present a consistent view of these results from the perspective of delocalization error. This error causes approximate functionals to give too low energy for delocalized densities or too high energy for localized densities, as in the cyclic and bicyclic reaction products. This interpretation allows us to understand better a wide range of errors in main-group thermochemistry obtained with popular density functionals. In general, functionals with minimal delocalization error should be used for theoretical studies of reactions where there is a loss of extended conjugation or formation of highly branched, cyclic, and cagelike molecules.

The conventional analysis of Perdew and Levy, and Sham and Schlüter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference. The present analysis further leads to several important results: (1) The lowest unoccupied molecular orbital (LUMO) in DFT has as much meaning in describing electron addition as the highest occupied molecular orbital (HOMO) in describing electron removal. (2) Every term in the total energy functional contributes to the energy gap because of the discontinuity of the derivative of the density (or density matrix) with respect to the number of electrons, \documentclass[12pt]{minimal}\begin{document}$((\partial \rho _{s}(\mathbf {r^{\prime }},\mathbf {r}))/\partial N )_{v_{s}}$\end{document}((∂ρs(r′,r))/∂N)vs, at integers. (3) Consistent with the Perdew-Levy-Sham-Schlüter conclusion that the exact Kohn-Sham energy gap differs from the fundamental bandgap by a finite correction due to the functional derivative discontinuity of the exchange-correlation energy, we show that the exchange-correlation functional cannot be an explicit and differentiable functional of the electron density, either local or nonlocal. The last result is further strengthened when we consider Mott insulators. There, the exact exchange-correlation functional needs to have an explicitly discontinuous (nondifferentiable) dependence on the density or the density matrix. (4) We obtain exact conditions on the derivatives of total energy with respect to the spin-up and spin-down number of electrons.

The long-standing problem of the large overestimation of polymer polarizabilities in density-functional theory is reexamined and largely solved using an exact exchange method. We have built an accurate optimized effective potential as the sum of a fixed potential and a linear combination of basis sets based on our direct optimization method. This effective potential properly develops a linear counteracting depolarization field, and it significantly improves recent results from approximate optimized potentials. The controversial case of hydrogen chains is now correctly described and the failure of the local density approach is attributed to the large self-interaction error in systems with a non-integer number of electrons.

Noncovalent interactions play a central role in many chemical and biological systems. In a previous study, Johnson et al developed a NonCovalent Interaction (NCI) index to characterize and visualize different types of weak interactions. To apply the NCI analysis to fluctuating environments as in solution phase, we here develop a new Averaged NonCovalent Interaction (i.e., aNCI) index along with a fluctuation index to characterize magnitude of interactions and fluctuations. We applied aNCI for various systems including solute-solvent and ligand-protein noncovalent interactions. For water and benzene molecules in aqueous solution, solvation structures and the specific hydrogen bond patterns were visualized clearly. For the Cl-+CH3Cl SN2 reaction in aqueous solution, charge reorganization influences over solvation structure along SN2 reaction were revealed. For ligand-protein systems, aNCI can recover several key fluctuating hydrogen bond patterns that have potential applications for drug design. Therefore, aNCI, as a complementary approach to the original NCI method, can extract and visualize noncovalent interactions from thermal noise in fluctuating environments.

The astronomical number of accessible discrete chemical structures makes rational molecular design extremely challenging. We formulate the design of molecules with specific tailored properties as performing a continuous optimization in the space of electron-nuclear attraction potentials. The optimization is facilitated by using a linear combination of atomic potentials (LCAP), a general framework that creates a continuous property landscape from an otherwise unlinked set of discrete molecular-property values. A demonstration of this approach is given for the optimization of molecular electronic polarizability and hyperpolarizability. We show that the optimal structures can be determined without enumerating and separately evaluating the characteristics of the combinatorial number of possible structures, a process that would be much slower. The LCAP approach may be used with quantum or classical Hamiltonians, suggesting possible applications to drug design and new materials discovery.

A recently developed approach for the direct calculation of electron density is implemented for polyatomic molecules: benzene and a tetrapeptide with four glycine residues. The method uses the density as the basic variable, divides a system into subsystems, and determines the density for each subsystem. It is found that the method is capable of describing the electronic structure with accuracy comparable to the Kohn-Sham method. This substantiates the hope for ab initio calculations of large systems beyond the reach of conventional methods.

A new derivation of the Weizsacker-type gradient corrections to Thomas-Fermi (TF) kinetic energy functional is presented. The development is based on the first-order reduced density matrix as obtained from the one-body Green's function in the mean-path approximation devised for the purpose, using the Feynman path-integral approach; the mean-path approximation turns out to be essentially equivalent to the eikonal approximation used in quantum collision theory for high-energy collisions. This derivation agrees with the conventional gradient expansion truncated at second order, in that it gives the kinetic energy functional of the TF-(1/9)W model, that is, the sum of the original TF kinetic energy and (1/9) of the Weizsacker gradient correction. However, in the present derivation, TF-(1/9)W results from a reduced density matrix of closed form; the original TF local relation between particle, density, and one-body potential is preserved; and the kinetic energy density contains a Laplacian of particle density with a factor half of that from the gradient expansion. Most significantly, the TF-(1/9)W kinetic energy functional is the consequence of representing both the diagonal and off-diagonal elements of the density matrix correctly to zero order through the mean-path approximation to the one-body Green's function, whereas in the conventional TF approximation, the zero order of the gradient expansion, off-diagonal elements are not correct to the same order. Other results of the present approach include a nonlocal exchange energy functional of density, a one-body effective potential that contains a contribution from the kinetic energy functional derivative, and the construction of closed-form density matrices that give various kinetic energy functionals of TF-\ensuremath{\lambda}W form (justifying various existing empirical \ensuremath{\lambda} values). Also presented are the results of numerical calculation for rare-gas atoms of TFD-\ensuremath{\lambda}W models (TFD denotes Thomas-Fermi-Dirac) with \ensuremath{\lambda}=(1/3), 0.186, (1/6), and (1/9). .AE

Structural and energetic changes are two important characteristic properties of a chemical reaction process. In the condensed phase, studying these two properties is very challenging because of the great computational cost associated with the quantum mechanical calculations and phase space sampling. Although the combined quantum mechanics/molecular mechanics (QM/MM) approach significantly reduces the amount of the quantum mechanical calculations and facilitates the simulation of solution-phase and enzyme-catalyzed reactions, the required quantum mechanical calculations remain quite expensive and extensive sampling can be achieved routinely only with semiempirical quantum mechanical methods. QM/MM simulations with ab initio QM methods, therefore, are often restricted to narrow regions of the potential energy surface such as the reactant, product and transition state, or the minimum-energy path. Such ab initio QM/MM calculations have previously been performed with the QM/MM-free energy (QM/MM-FE) method of Zhang et al. (J. Chem. Phys. 2000, 112, 3483−3492) to generate the free-energy profile along the reaction coordinate using free-energy perturbation calculations at fixed structures of the QM subsystems. Results obtained with the QM/MM-FE method depend on the determination of the minimum-energy reaction path, which is based on local conformations of the protein/solvent environment and can be difficult to obtain in practice. To overcome the difficulties associated with the QM/MM-FE method and to further enhance the sampling of the MM environment conformations, we develop here a new method to determine the QM/MM minimum free-energy path (QM/MM-MFEP) for chemical-reaction processes in solution and in enzymes. Within the QM/MM framework, we express the free energy of the system as a function of the QM conformation, thus leading to a simplified potential of mean force (PMF) description for the thermodynamics of the system. The free-energy difference between two QM conformations is evaluated by the QM/MM free-energy perturbation method. The free-energy gradients with respect to the QM degrees of freedom are calculated from molecular dynamics simulations at given QM conformations. With the free energy and free-energy gradients in hand, we further implement chain-of-conformation optimization algorithms in the search for the reaction path on the free-energy surface without specifying a reaction coordinate. This method thus efficiently provides a unique minimum free-energy path for solution and enzyme reactions, with structural and energetic properties being determined simultaneously. To further incorporate the dynamic contributions of the QM subsystem into the simulations, we develop the reaction path potential of Lu, et al. (J. Chem. Phys. 2004, 121, 89−100) for the minimum free-energy path. The combination of the methods developed here presents a comprehensive and accurate treatment for the simulation of reaction processes in solution and in enzymes with ab initio QM/MM methods. The method has been demonstrated on the first step of the reaction of the enzyme triosephosphate isomerase with good agreement with previous studies.

The collocation method for obtaining the bound solutions of the Schrödinger equation is investigated. The technique does not require the evaluation of integrals and is very simple to implement. It is closely connected with other pointwise representations used recently, but has the advantage of requiring less effort to construct the algebraic eigenvalue equations. The method is tested on two Morse oscillator problems and found to give results which are as accurate as the conventional variational approach. In conjunction with a distributed Gaussian basis the collocation method is shown to be capable of describing highly excited states.

In this paper, we introduce a trajectory-based nonadiabatic dynamics algorithm which aims to correct the well-known overcoherence problem in Tully's popular fewest-switches surface hopping algorithm. Our simultaneous-trajectory surface hopping algorithm propagates a separate classical trajectory on each energetically accessible adiabatic surface. The divergence of these trajectories generates decoherence, which collapses the particle wavefunction onto a single adiabatic state. Decoherence is implemented without the need for any parameters, either empirical or adjustable. We apply our algorithm to several model problems and find a significant improvement over the traditional algorithm.

Abstract Regulation of the crystallization of perovskite films and avoiding the oxidation of Sn 2+ during the deposition process are very important for achieving Sn/Pb binary perovskite solar cells (PVSCs) with high power conversion efficiency (PCE) and producibility. In this work, a high‐quality HC(NH 2 ) 2 Pb 0.7 Sn 0.3 I 3 (FAPb 0.7 Sn 0.3 I 3 ) film deposited from the two‐step solution process by introducing methylammonium thiocyanate (MASCN) as a bifunctional additive into the precursor solution containing PbI 2 and SnI 2 is reported. MASCN can not only tune the morphology of the perovskite film but also stabilize the precursor solution via retarding the oxidation of Sn 2+ through a strong coordination between SCN − and Sn 2+ . The Sn/Pb binary inverted PVSCs based on FAPb 0.7 Sn 0.3 I 3 present a high fill factor of 0.79 and the best PCE of 16.26% in the case of 0.25 MASCN addition. The device fabrication producibility is also greatly improved due to the stabilized precursor solution with the aid of MASCN. The PCE of the device is almost independent of the storage time of the precursor solution within 124 d in the N 2 ‐filled glove box. These results indicate that the precursor engineering with multifunctionality additive is an effective approach toward highly efficient and producible PVSCs for future commercialization.

Abstract The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC–DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.

Direct molecular dynamics (MD) simulation with ab initio quantum mechanical and molecular mechanical (QM/MM) methods is very powerful for studying the mechanism of chemical reactions in a complex environment but also very time-consuming. The computational cost of QM/MM calculations during MD simulations can be reduced significantly using semiempirical QM/MM methods with lower accuracy. To achieve higher accuracy at the ab initio QM/MM level, a correction on the existing semiempirical QM/MM model is an attractive idea. Recently, we reported a neural network (NN) method as QM/MM-NN to predict the potential energy difference between semiempirical and ab initio QM/MM approaches. The high-level results can be obtained using neural network based on semiempirical QM/MM MD simulations, but the lack of direct MD samplings at the ab initio QM/MM level is still a deficiency that limits the applications of QM/MM-NN. In the present paper, we developed a dynamic scheme of QM/MM-NN for direct MD simulations on the NN-predicted potential energy surface to approximate ab initio QM/MM MD. Since some configurations excluded from the database for NN training were encountered during simulations, which may cause some difficulties on MD samplings, an adaptive procedure inspired by the selection scheme reported by Behler [ Behler Int. J. Quantum Chem. 2015 , 115 , 1032 ; Behler Angew. Chem., Int. Ed. 2017 , 56 , 12828 ] was employed with some adaptions to update NN and carry out MD iteratively. We further applied the adaptive QM/MM-NN MD method to the free energy calculation and transition path optimization on chemical reactions in water. The results at the ab initio QM/MM level can be well reproduced using this method after 2-4 iteration cycles. The saving in computational cost is about 2 orders of magnitude. It demonstrates that the QM/MM-NN with direct MD simulations has great potentials not only for the calculation of thermodynamic properties but also for the characterization of reaction dynamics, which provides a useful tool to study chemical or biochemical systems in solution or enzymes.

Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S(2) operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.

A cross ELF-NCI analysis is tested over prototypical organic reactions. The synergetic use of ELF and NCI enables the understanding of reaction mechanisms since each method can respectively identify regions of strong and weak electron pairing. Chemically intuitive results are recovered and enriched by the identification of new features. Non covalent interactions are found to foresee the evolution of the reaction from the initial steps. Within NCI, no topological catastrophe is observed as changes are continuous to such an extent that future reaction steps can be predicted from the evolution of the initial NCI critical points. Indeed, strong convergences through the reaction paths between ELF and NCI critical points enable to identify key interactions at the origin of the bond formation. VMD scripts enabling the automatic generation of movies depicting the cross NCI/ELF analysis along a reaction path (or following a Born-Oppenheimer molecular dynamics trajectory) are provided as S.I.

Molecular dynamics simulation with multiscale quantum mechanics/molecular mechanics (QM/MM) methods is a very powerful tool for understanding the mechanism of chemical and biological processes in solution or enzymes. However, its computational cost can be too high for many biochemical systems because of the large number of ab initio QM calculations. Semiempirical QM/MM simulations have much higher efficiency. Its accuracy can be improved with a correction to reach the ab initio QM/MM level. The computational cost on the ab initio calculation for the correction determines the efficiency. In this paper we developed a neural network method for QM/MM calculation as an extension of the neural-network representation reported by Behler and Parrinello. With this approach, the potential energy of any configuration along the reaction path for a given QM/MM system can be predicted at the ab initio QM/MM level based on the semiempirical QM/MM simulations. We further applied this method to three reactions in water to calculate the free energy changes. The free-energy profile obtained from the semiempirical QM/MM simulation is corrected to the ab initio QM/MM level with the potential energies predicted with the constructed neural network. The results are in excellent accordance with the reference data that are obtained from the ab initio QM/MM molecular dynamics simulation or corrected with direct ab initio QM/MM potential energies. Compared with the correction using direct ab initio QM/MM potential energies, our method shows a speed-up of 1 or 2 orders of magnitude. It demonstrates that the neural network method combined with the semiempirical QM/MM calculation can be an efficient and reliable strategy for chemical reaction simulations.

Small bandgap 2D perovskites were synthesized with desired orientation and the corresponding solar cells presented high efficiency and good stability.

Flexible electronics are developing rapidly due to promising applications in displays, sensors, and energy conversion fields. For biodegradable, lightweight, and flexible thin film electronics to be explored, O-(2,3-Dihydroxypropyl) cellulose (DHPC) was synthesized by homogeneous etherification of cellulose in 7 wt % NaOH/12 wt % urea aqueous solution without extra catalyst. DHPC exhibited a high level of transparency, outstanding ductility, and good adhesiveness but poor mechanical properties. Thus, stiff tunicate cellulose nanocrystals (TCNCs) were introduced to construct tough nanocomposite papers. The reinforcement of nanocomposite papers was well predicted by a percolating model, indicating the formation of the network of TCNCs. On the basis of the excellent interfacial compatibility between TCNCs and DHPC, supported by atomic force microscope mapping, the nanocomposite papers exhibited smooth surface, high transparency, as well as satisfactory mechanical properties, which were suitable for the construction of flexible polymer solar cells. Tin-doped indium oxide could be directly coated on the adhesive transparent paper without any glue as electrode, and the power conversion efficiency of the resulting flexible inverted polymer solar cells was 4.98%, suggesting its potential application as biodegradable and wearable electronics or optoelectronics. This work is important for developing clean energy by using sustainable materials derived from renewable resources.

Abstract The simultaneous achievement of a low energy loss and high external quantum efficiency (EQE) response is the prerequisite for high power conversion efficiencies of organic solar cells (OSCs). Herein, this issue is examined through the design of two novel near‐infrared (NIR) nonfullerene acceptors (X‐PCIC and X1‐PCIC) with an absorption extending to 900 nm, which is realized by using benzobis(thiazole) unit as the core. This study reveals that benzobis(thiazole) unit with the quinoid‐resonance effect and electron‐withdrawing property is a good building block in extending absorption and maintaining suitable energy levels. Single crystal cultivation proves the function of S···N noncovalent interaction in locking molecular geometry. Besides, through adopting two different terminals (fluorinated terminal for X‐PCIC and thiophene‐fused terminal for X1‐PCIC), it is found that an increase in the J‐aggregation strength has a significant positive effect on the EQE response of the devices through the formation of more suitable domain sizes and crystallinity in the films, while the energy loss remains low (≈0.53 eV) and unaffected. Thus, a high efficiency of 11.50% is presented for OSC based on the X‐PCIC with stronger J‐aggregation strength, better than that (10.17%) based on the X1‐PCIC with weaker J‐aggregation strength. This work clearly demonstrates the application of benzobis(thiazole) unit in efficient small molecule acceptors and the importance of J‐aggregation modulation for the simultaneous achievement of low energy loss and high EQE response.

A solution-processed CuOx film has been successfully integrated as the hole-transporting layer (HTL) for inverted planar heterojunction perovskite solar cells (PVSCs). The CuOx layer is fabricated by simply spin-coating a copper acetylacetonate (Cu(acac)2) chloroform solution onto ITO glass with high transparency in the visible range. The compact and pinhole-free perovskite film with large grain domains is grown on the CuOx film. The inverted PVSCs with the structure of ITO/CuOx/MAPbI3/PC61BM/ZnO/Al are fabricated and show a best PCE of 17.43% under standard AM 1.5G simulated solar irradiation with a VOC of 1.03 V, a JSC of 22.42 mA cm−2, and a fill factor of 0.76, which is significantly higher and more stable than that fabricated from the often used hole-transporting material PEDOT:PSS (11.98%) under the same experimental conditions. The enhanced performance is attributed to the efficient hole extraction through the CuOx layer as well as the high-quality CH3NH3PbI3 films grown on the CuOx. Our results indicate that low-cost and solution-processed CuOx film is a promising HTL for high performance PVSCs with better stability.

Thin-film organic near-infrared (NIR) photodiodes can be essential building blocks in the rapidly emerging fields including the internet of things and wearable electronics. However, the demonstration of NIR organic photodiodes with not only high responsivity but also low dark current density that is comparable to that of inorganic photodiodes, for example, below 1 nA cm–2 for silicon photodiodes, remains a challenge. In this work, we have demonstrated non-fullerene acceptor-based NIR photodiodes with an ultralow dark current density of 0.2 nA cm–2 at −2 V by innovating on charge transport layers to mitigate the reverse charge injection and interfacial defect-induced current generation. The same device also shows a high external quantum efficiency approaching 70% at 850 nm and a specific detectivity of over 1013 Jones at wavelengths up to 940 nm. Furthermore, the versatility of our approach for mitigating dark current is demonstrated using a NIR photodetector utilizing different non-fullerene systems. Finally, the practical application of NIR organic photodiodes is demonstrated with an image sensor integrated on a silicon CMOS readout. This work provides new insight into the device stack design of low-dark current NIR organic photodiodes for weak light detection.

Locality in physical space is critical in understanding chemical reactivity in the analysis of various phenomena and processes in chemistry, biology, and materials science, as exemplified in the concepts of reactive functional groups and active sites. Frontier molecular orbitals (FMOs) pinpoint the locality of chemical bonds that are chemically reactive because of the associated orbital energies and thus have achieved great success in describing chemical reactivity, mainly for small systems. For large systems, however, the delocalization nature of canonical molecular orbitals makes it difficult for FMOs to highlight the locality of the chemical reactivity. To obtain localized molecular orbitals that also reflect the frontier nature of the chemical processes, we develop the concept of frontier molecular orbitalets (FMOLs) for describing the reactivity of large systems. The concept of orbitalets was developed recently in the localized orbital scaling correction method, which aims for eliminating the delocalization error in common density functional approximations. Orbitalets are localized in both physical and energy spaces and thus contain both orbital locality and energy information. The FMOLs are thus the orbitalets with energies highest among occupied orbitalets and lowest among unoccupied ones. The applications of FMOLs to hexadeca-1,3,5,7,9,11,13,15-octaene in its equilibrium geometry, inter- and intra-molecular charge-transfer systems, and two transition states of a bifurcating reaction demonstrate that FMOLs can connect quantum mechanical treatments of chemical systems and chemical reactivities by locating the reactive region of large chemical systems. Therefore, FMOLs extend the role of FMOs for small systems and describe the chemical reactivity of large systems with energy and locality insight, with potentially broad applications.

The GW approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy. We present a comprehensive benchmark study of different GW methodologies (starting point optimized, partial and full eigenvalue-self-consistent, Hedin shift, and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three GW schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot GW calculations based on an optimized hybrid functional starting point, and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean absolute errors <0.2 eV the best results.

Protein structure and dynamics are the keys to a wide range of problems in biology. In principle, both can be fully understood by using quantum mechanics as the ultimate tool to unveil the molecular interactions involved. Indeed, quantum mechanics of atoms and molecules have come to play a central role in chemistry and physics. In practice, however, direct application of quantum mechanics to protein systems has been prohibited by the large molecular size of proteins. As a consequence, there is no general quantum mechanical treatment that not only exceeds the accuracy of state-of-the-art empirical models for proteins but also maintains the efficiency needed for extensive sampling in the conformational space, a requirement mandated by the complexity of protein systems. Here we show that, given recent developments in methods, a general quantum mechanical-based treatment can be constructed. We report a molecular dynamics simulation of a protein, crambin, in solution for 350 ps in which we combine a semiempirical quantum-mechanical description of the entire protein with a description of the surrounding solvent, and solvent-protein interactions based on a molecular mechanics force field. Comparison with a recent very high-resolution crystal structure of crambin (Jelsch et al., Proc Natl Acad Sci USA 2000;102:2246-2251) shows that geometrical detail is better reproduced in this simulation than when several alternate molecular mechanics force fields are used to describe the entire system of protein and solvent, even though the structure is no less flexible. Individual atomic charges deviate in both directions from "canonical" values, and some charge transfer is found between the N and C-termini. The capability of simulating protein dynamics on and beyond the few hundred ps timescale with a demonstrably accurate quantum mechanical model will bring new opportunities to extend our understanding of a range of basic processes in biology such as molecular recognition and enzyme catalysis.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTToward the Accurate Modeling of DNA: The Importance of Long-Range ElectrostaticsDarrin M. York, Weitao Yang, Hsing Lee, Tom Darden, and Lee G. PedersenCite this: J. Am. Chem. Soc. 1995, 117, 17, 5001–5002Publication Date (Print):May 1, 1995Publication History Published online1 May 2002Published inissue 1 May 1995https://doi.org/10.1021/ja00122a034RIGHTS & PERMISSIONSArticle Views298Altmetric-Citations127LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (300 KB) Get e-Alerts Get e-Alerts

We develop here a new method to fit the molecular electrostatic potentials obtained in quantum mechanical calculations to a set of classical electrostatic multipoles, usually point charges located at atomic positions. We define an object function of fitting as an integration of the difference of electrostatic potentials in the entire 3-dimensional physical space. The object function is thus rotationally invariant with respect to the molecular orientation and varies smoothly with respect to molecular geometric fluctuations. Compared with commonly employed methods such as the Merz-Singh-Kollman and CHELPG schemes, this new method, while possessing comparable accuracy, shows greatly improved numerical stability with respect to the molecular positions and geometries. The method can be used in the fitting of electrostatic potentials for the molecular mechanics force fields and also can be applied to the calculation of electrostatic polarizabilites of molecular or atomic systems.

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of unbalanced, and thus unsuitable, basis sets. A modified functional incorporating a regularizing smoothness measure of the OEP is introduced. This provides a condition on balanced basis sets for the potential, as well as a method to determine the most appropriate OEP potential and energy from calculations performed with any finite basis set.

Here we describe the design, single-molecule transport measurements, and theoretical modeling of a ferrocene-based organometallic molecular wire, whose bias-dependent conductance shows a clear Lorentzian form with magnitude exceeding 70% of the conductance quantum ${G}_{0}$. We attribute this unprecedented level of single-molecule conductance to a manifestation of the low-lying molecular resonance and extended orbital network long predicted for a conjugated organic system. A similar-in-length, all-organic conjugated phenylethynyl oligomer molecular framework shows much lower conductance.

The performance of the optimized effective potential procedure for exact exchange in calculating static electric-field response properties of push-pull pi-conjugated systems has been studied, with an emphasis on NO2-(CH=CH)n-NH2 chains. Good agreement with Hartree-Fock dipole moments and (hyper)polarizabilities is obtained; particularly noteworthy is the chain length dependence for beta/n. Thus, the problem that conventional density-functional theory functionals dramatically overestimate these properties is largely solved, although there remains a significant correlation contribution that cannot be accounted for with current correlation functionals.

The concept of nonorthogonal localized molecular orbital (NOLMO) is investigated in this paper. Given a set of the commonly used canonical molecular orbitals, a direct minimization algorithm is proposed to obtain both the orthogonal localized molecular orbitals (OLMO) and NOLMO by using the Boys criterion and conjugate gradient minimization. To avoid the multiple-minimum problem, the absolute energy minimization principle of Yang is employed to obtain initial guesses. Contrary to the early conclusion drawn by Lipscomb and co-workers who claimed that OLMOs and the corresponding NOLMOs are more or less the same, we found that NOLMOs are about 10%–30% more localized than OLMOs. More importantly, the so-called “delocalization tail” that plagues OLMOs is not present in NOLMOs, showing that NOLMOs are more compact and less oscillatory and capable of providing greater transferability in describing the electronic structure of molecules. We also found that main lobes of NOLMOs are slightly larger in size than those of OLMOs because of the normalization requirement. These features establish NOLMOs to be valuable as building blocks in electronic structure theory and for the understanding of chemical bonding. They show the promise for the utilization of NOLMOs—the most localized possible—in the linear scaling approaches of the electronic structure theory for molecules and solids.

Using benzene sandwiched between two Au leads as a model system, we investigate from first principles the change in molecular conductance caused by different atomic structures around the metal-molecule contact. Our motivation is the variable situations that may arise in break junction experiments; our approach is a combined density functional theory and Green function technique. We focus on effects caused by (1) the presence of an additional Au atom at the contact and (2) possible changes in the molecule-lead separation. The effects of contact atomic relaxation and two different lead orientations are fully considered. We find that the presence of an additional Au atom at each of the two contacts will increase the equilibrium conductance by up to two orders of magnitude regardless of either the lead orientation or different group-VI anchoring atoms. This is due to a resonance peak near the Fermi energy from the lowest energy unoccupied molecular orbital. In the nonequilibrium properties, the resonance peak manifests itself in a negative differential conductance. We find that the dependence of the equilibrium conductance on the molecule-lead separation can be quite subtle: either very weak or very strong depending on the separation regime.

Two absolute energy minimum principles are developed for first-principle linear-scaling electronic structure calculations. One is with a normalization constraint and the other without any constraint. The density matrix is represented by a set of nonorthogonal localized orbitals and an auxiliary matrix which at the minimum becomes a generalized inverse of the overlap matrix of the localized orbitals. The number of localized orbitals is allowed to exceed the number of occupied orbitals. Comparison with other variational principles is made and numerical tests presented.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTMolecular softness as the average of atomic softnesses: companion principle to the geometric mean principle for electronegativity equalizationWeitao Yang, Chengteh Lee, and Swapan K. GhoshCite this: J. Phys. Chem. 1985, 89, 25, 5412–5414Publication Date (Print):December 1, 1985Publication History Published online1 May 2002Published inissue 1 December 1985https://doi.org/10.1021/j100271a019Request reuse permissionsArticle Views234Altmetric-Citations112LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (327 KB) Get e-Alerts

To accurately determine the reaction path and its energetics for enzymatic and solution-phase reactions, we present a sequential sampling and optimization approach that greatly enhances the efficiency of the ab initio quantum mechanics/molecular mechanics minimum free-energy path (QM/MM-MFEP) method. In the QM/MM-MFEP method, the thermodynamics of a complex reaction system is described by the potential of mean force (PMF) surface of the quantum mechanical (QM) subsystem with a small number of degrees of freedom, somewhat like describing a reaction process in the gas phase. The main computational cost of the QM/MM-MFEP method comes from the statistical sampling of conformations of the molecular mechanical (MM) subsystem required for the calculation of the QM PMF and its gradient. In our new sequential sampling and optimization approach, we aim to reduce the amount of MM sampling while still retaining the accuracy of the results by first carrying out MM phase-space sampling and then optimizing the QM subsystem in the fixed-size ensemble of MM conformations. The resulting QM optimized structures are then used to obtain more accurate sampling of the MM subsystem. This process of sequential MM sampling and QM optimization is iterated until convergence. The use of a fixed-size, finite MM conformational ensemble enables the precise evaluation of the QM potential of mean force and its gradient within the ensemble, thus circumventing the challenges associated with statistical averaging and significantly speeding up the convergence of the optimization process. To further improve the accuracy of the QM/MM-MFEP method, the reaction path potential method developed by Lu and Yang [Z. Lu and W. Yang, J. Chem. Phys. 121, 89 (2004)] is employed to describe the QM/MM electrostatic interactions in an approximate yet accurate way with a computational cost that is comparable to classical MM simulations. The new method was successfully applied to two example reaction processes, the classical SN2 reaction of Cl−+CH3Cl in solution and the second proton transfer step of the reaction catalyzed by the enzyme 4-oxalocrotonate tautomerase. The activation free energies calculated with this new sequential sampling and optimization approach to the QM/MM-MFEP method agree well with results from other simulation approaches such as the umbrella sampling technique with direct QM/MM dynamics sampling, demonstrating the accuracy of the iterative QM/MM-MFEP method.

The effect of the exchange-correlation potential in ab initio electron transport calculations is investigated by constructing optimized effective potentials (OEP) using different energy functionals or the electron density from second-order perturbation theory. We calculate electron transmission through two atomic chain systems, one with charge transfer and one without. Dramatic effects are caused by two factors: changes in the energy gap and the self-interaction error. The error in conductance caused by the former is about one order of magnitude while that caused by the latter ranges from several times to two orders of magnitude, depending on the coupling strength and charge transfer. The implications for accurate quantum transport calculations are discussed.

A single-molecule spintronic switch and spin valve using two cobaltocene moieties is proposed. Spin-dependent transport through a lead−molecule−lead junction has been calculated using first-principles density functional and nonequilibrium Green function methods. We find that the antiparallel (singlet) configuration of the cobaltocene spins blocks electron transport near the Fermi energy, while the spin parallel (triplet) configuration enables much higher current. The energy difierence between the antiparallel and parallel states depends on the insulating spacer separating the two cobaltocenes, allowing switching through the application of a moderate magnetic field.

The morphology of multiple-shell fullerenes is investigated by ab initio calculations using Yang's O(N) method. It is found that for large single-shell fullerenes with ${\mathit{I}}_{\mathit{h}}$ symmetry, the spherical morphology has lower energy than that of polyhedrons. The formation energy per atom follows a simple scaling law. Including an estimate of intershell van de Waals interactions leads to the conclusion that spherical multiple-shell fullerenes are likely the most stable structure of large carbon clusters. These results are in good agreement with recent experiments.

Various approximate density functionals for the kinetic energy density of atoms and molecules are analyzed. These include the results of a gradient expansion to first and second orders and a form recently derived from a new Green's function approximation [W. Yang, preceding paper, Phys. Rev. A 34, 4575 (1986)]. All the approximate functionals studied diverge to minus infinity at a nucleus, due to the ${\ensuremath{\nabla}}^{2}$\ensuremath{\rho} term that is in them, while the exact functional is positive and finite everywhere. Away from nuclei, however, the Hartree-Fock results are well reproduced, including the atomic shell structure. New functionals are proposed to correct the divergent behavior, and accurate total kinetic energy values are obtained from a new formula for kinetic energy density ${t}_{\mathrm{MP}(\mathrm{r})={C}_{k}\mathrm{\ensuremath{\rho}}{(\mathrm{r})}^{5/3}}$ +(1/72)\ensuremath{\Vert}\ensuremath{\nabla}\ensuremath{\rho}(r)${\ensuremath{\Vert}}^{2}$/\ensuremath{\rho}(r)+( 1/12)${\ensuremath{\nabla}}^{2}$\ensuremath{\rho}(r), with a divergence correction.

The conventional Ewald expression for the electrostatic energy and forces is recast in a form that can be evaluated to high accuracy in order N log(N) steps using fast Fourier transforms. The fast Fourier Poisson method does not rely on interpolation approaches or Taylor/multipole expansions, and can be easily integrated with conventional molecular dynamics algorithms.

Studies of the nonlinear electronic response of donor/acceptor substituted nanotubes suggest a behavior that is both surprising and qualitatively distinct from that in conventional conjugated organic species. We find that the carbon nanotubes serve as both electronic bridges and acceptors, leading to a donor-nanotube paradigm for the effective design of large first hyperpolarizabilities. We also find that tuning the donor orientation, relative to the nanotube, can significantly enhance the first hyperpolarizability.

Based on a multiobjective optimization framework, we develop a new quadratic string method for finding the minimum-energy path. In the method, each point on the minimum-energy path is minimized by integration in the descent direction perpendicular to path. Each local integration is done on a quadratic surface approximated by a damped Broyden-Fletcher-Goldfarb-Shanno updated Hessian, allowing the algorithm to take many steps between energy and gradient calls. The integration is performed with an adaptive step-size solver, which is restricted in length to the trust radius of the approximate Hessian. The full algorithm is shown to be capable of practical superlinear convergence, in contrast to the linear convergence of other methods. The method also eliminates the need for predetermining such parameters as step size and spring constants, and is applicable to reactions with multiple barriers. The effectiveness of this method is demonstrated for the Müller-Brown potential, a seven-atom Lennard-Jones cluster, and the enolation of acetaldehyde to vinyl alcohol.

We have developed a second-order perturbation theory (PT) energy functional within density-functional theory (DFT). Based on PT with the Kohn-Sham (KS) determinant as a reference, this new ab initio exchange-correlation functional includes an exact exchange (EXX) energy in the first order and a correlation energy including all single and double excitations from the KS reference in the second order. The explicit dependence of the exchange and correlation energy on the KS orbitals in the functional fits well into our direct minimization approach for the optimized effective potential, which is a very efficient method to perform fully self-consistent calculations for any orbital-dependent functionals. To investigate the quality of the correlation functional, we have applied the method to selected atoms and molecules. For two-electron atoms and small molecules described with small basis sets, this new method provides excellent results, improving both second-order Moller-Plesset expression and any conventional DFT results significantly. For larger systems, however, it performs poorly, converging to very low unphysical total energies. The failure of PT based energy functionals is analyzed, and its origin is traced back to near degeneracy problems due to the orbital- and eigenvalue-dependent algebraic structure of the correlation functional. The failure emerges in the self-consistent approach but not in perturbative post-EXX calculations, emphasizing the crucial importance of self-consistency in testing new orbital-dependent energy functionals.

Nonlinear optical chromophores containing (porphyrinato)Zn(II), proquinoid, and (terpyridyl)metal(II) building blocks were optimized in a library containing approximately 10(6) structures using the linear combination of atomic potentials (LCAP) methodology. We report here the library design and molecular property optimizations. Two basic structural types of large beta(0) chromophores were examined: linear and T-shaped motifs. These T-shaped geometries suggest a promising NLO chromophoric architecture for experimental investigation and further support the value of performing LCAP searches in large chemical spaces.

In this paper, we show that a remarkably simple correction can be made to the equation of motion which governs the evolution of the electronic wavefunction over some prescribed nuclear trajectory in the fewest-switches surface hopping algorithm. This corrected electronic equation of motion can then be used in conjunction with traditional or modified surface hopping methods to calculate nonadiabatic effects in large systems. Although the correction adds no computational cost to the algorithm, it leads to a dramatic improvement in scattering probabilities for all model problems studied thus far. We show that this correction can be applied to one of Tully's original one-dimensional model problems or to a more sophisticated two-dimensional example and yields substantially greater accuracy than the traditional approach.

Molecular nanojunctions may support efficient thermoelectric conversion through enhanced thermopower. Recently, this quantity has been measured for several conjugated molecular nanojunctions with gold electrodes. Considering the wide variety of possible metal/molecule systems—almost none of which have been studied—it seems highly desirable to be able to calculate the thermopower of junctions with reasonable accuracy and high efficiency. To address this task, we demonstrate an effective approach based on the single particle green function (SPGF) method combined with density functional theory (DFT) using B3LYP and PBE0 energy functionals. Systematic good agreement between theory and experiment is obtained; indeed, much better agreement is found here than for comparable calculations of the conductance.

We have investigated the conductance of individual optically switchable dithienylethene molecules in both their conducting closed configuration and nonconducting open configuration, using the technique of repeatedly formed break-junctions. We employed pyridine groups to link the molecules to gold electrodes in order to achieve relatively well-defined molecular contacts and stable conductance. For the closed form of each molecule, we observed a peak in the conductance histogram constructed without any data selection, allowing us to determine the conductance of the fully stretched molecules. For two different dithienylethene derivatives, these closed-configuration conductances were (3.3 ± 0.5) × 10(-5)G(0) and (1.5 ± 0.5) × 10(-6)G(0), where G(0) is the conductance quantum. For the open configuration of the molecules, the existence of electrical conduction via the molecule was evident in traces of conductance versus junction displacement, but the conductance of the fully stretched molecules was less than the noise floor of our measurement. We can set a lower limit of 30 for the on/off ratio for the simplest dithienylethene derivative we have investigated. Density functional theory calculations predict an on/off ratio consistent with this result.