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The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting “Hirshfeld-I charges” correlate well with electrostatic potential derived atomic charges. [ABSTRACT FROM AUTHOR]

Classical dynamics can be described with Newton’s equation of motion or, totally equivalently, using the Hamilton-Jacobi equation. Here, the possibility of using the Hamilton-Jacobi equation to describe chemical reaction dynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the Hamilton-Jacobi equation; here we solve Hamilton-Jacobi equations on a Cartesian grid using Sethian’s fast marching method [J. A. Sethian, Proc. Natl. Acad. Sci. USA 93, 1591 (1996)]. Using this method, we can—starting from an arbitrary initial conformation—find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the H+H2→H2+H reaction. Least-time paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the Hamilton-Jacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Molecular solubility is among the key properties that determine the clinical performance of a drug candidate because poor molecular solubility often indicates inadequate bioavailability. Using the CombiSolv-Exp database, we test several models (Gaussian process regression, decision trees, k-nearest neighbors) for hydration free energies by integrating Δ -learning and a universal quantum-chemistry continuum solvation model, SMD. The optimal model is Gaussian process regression with MAE of 0.63 kcal/mol. The reported models improve the accuracy of SMD, but have negligible additional computational cost. [ABSTRACT FROM AUTHOR]

The numerical ill‐conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater‐type functions is overcome by using the (extended) Kullback–Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non‐negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non‐negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non‐negative basis functions. We present a fixed‐point iteration method for optimizing the Kullback–Leibler divergence and compare it to conventional gradient‐based optimization methods. These algorithms are released through the free and open‐source BFit package, which also includes a L2‐norm squared optimization routine applicable to any square‐integrable scalar function. [ABSTRACT FROM AUTHOR]

The topology of the molecular electron density of benzene dithiol gold cluster complex Au4−S−C6H4−S′−Au′4 changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization. Quantum theory of atoms in molecules (QTAIM) topology of benzene dithiol gold cluster at the zero‐order regular approximation unrestricted level of theory is reported. Considering a gold cluster complex as a case study, the sensitivity of molecular topology to various physical phenomena is demonstrated. Specifically, new bond paths between hydrogen and gold atoms appeared upon the inclusion of relativistic effects. [ABSTRACT FROM AUTHOR]

Ground state eigenvectors of the reduced Bardeen–Cooper–Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree–Fock is the starting point for weakly correlated electrons. [ABSTRACT FROM AUTHOR]

Review: 46 refs. [ABSTRACT FROM AUTHOR]

The finite field method was used to calculate the static first and second hyperpolarizabilities (β and γ) for organic molecules. The dependence of β and γ on the applied electric field strength was investigated and used to determine the optimal field strength for each individual molecule. For γ, we designed a protocol that uses the maximum atomic distance within the molecule along the direction of the applied field to estimate optimal field strengths. However, β is nearly independent of the descriptors we considered, and largely depends on the composition (e.g., the presence of certain functional groups) of the molecule. [ABSTRACT FROM AUTHOR]

Fanpy is a free and open‐source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to convert the mathematical formulation of a new wavefunction ansätze to a working implementation. Fanpy is designed based on our recently introduced Flexible Ansatz for N‐electron Configuration Interaction (FANCI) framework, where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin‐orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system's Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly explore new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for various operating systems. In addition, it adheres to principles of modern software development, including comprehensive documentation, extensive testing, quality assurance, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library. [ABSTRACT FROM AUTHOR]

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Using the energy components associated with density-functional theory (DFT) calculations and various descriptors from the density-functional reactivity theory (conceptual DFT), we explore which chemical effects are most important for determining the ordering the conformers of the twenty natural amino acids in terms of their relative energetic stability. Electrostatic and steric (alternatively, electrostatic and exchange–correlation) interactions are found to be most descriptive of conformer stability. We also introduce an approach for determining how well one or more descriptors order the conformers, without requiring a linear (or any other) correlation between the descriptors. This ordering/ranking paradigm is likely to be useful in many other contexts also. [ABSTRACT FROM AUTHOR]

In this brief report, we show that the three different chemical hardness definitions developed in the framework of the temperature-dependent density functional theory—namely, the electronic, the thermodynamic, and the Helmholtz hardnesses—imply both the hard and soft acids and bases (HSAB) principle and the maximum hardness (MH) principle. These hardnesses are identified as the second derivative of a thermodynamic state function and avoid the somewhat arbitrary approach, based on the parabolic interpolation of the energy versus electron number, that is normally used to justify these principles. This not only leads to a more mathematically sound justification of the HSAB and MH principles in the low-temperature limit but also establishes that the HSAB and the MH principles hold at any temperature of chemical relevance. [ABSTRACT FROM AUTHOR]

Alternatives to the Ornstein-Zernike direct correlation function (DCF) are proposed, parameterized to reproduce the homogeneous electron liquid, and applied to atomic and molecular systems. This generalizes the work of Amovilli and March [ Phys. Rev. B 76, 195104 (2007)], where the ordinary Ornstein-Zernike DCF was used. Unlike the Ornstein-Zernike DCF, one of the alternative DCFs explored in this present work produces normalized exchange-correlation holes. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Pin1 is an enzyme that specificallycatalyzes the cis–transisomerization of prolineamide bonds in peptides that contain aphosphorylated threonine or serine residue in the position precedingproline. In the cell, the isomerization reaction is associated withcellular signaling and has been related to diseases such as Alzheimerand cancer. The catalytic mechanism by which Pin1 accelerates theisomerization reaction, however, is still unknown. In this study,we use molecular dynamics simulation in combination with the QM/MMmethodology to disclose the influence of the residues Ser-154 andCys-113 in the enzyme and the phosphorylated threonine residue inthe peptide on the reaction mechanism. To account for the correctelectrostatic interaction between the three residues and the reactivecenter, we derive atomic charges that account for the varying electrostaticfield in the catalytic cavity. Different methods based on reproducingthe molecular electrostatic potential or an atoms in molecules approachwere investigated. Finally, the reaction mechanism is analyzed withthe mean reaction force and the influence of the three residues isdisclosed. Our results show that Pin1 specifically catalyzes the isomerizationof the transconformer in a jump-rope type of motion,as suggested by us and confirmed experimentally by others. This isaccomplished by anchoring the threonine phosphate residue on one endof the peptide through electrostatic interactions with the basic triadof the enzyme and at the other end through specific enzyme–peptidehydrogen bonds. Cys-113 reduces the structural contribution to theactivation free energy through the stabilization of the cisconformer, and Ser-154 in combination with Gln-131 assist in theisomerization reaction of the transisomer. [ABSTRACT FROM AUTHOR]

pH-responsive molecular tweezers have been proposed as an approach for targeting drug-delivery to tumors, which tend to have a lower pH than normal cells. We performed a computational study of a pH-responsive molecular tweezer using ab initio quantum chemistry in the gas-phase and molecular dynamics (MD) simulations in solution. The binding free energy in solution was calculated using steered MD. We observe, in atomistic detail, the pH-induced conformational switch of the tweezer and the resulting release of the drug molecule. Even when the tweezer opens, the drug molecule remains near a hydrophobic arm of the molecular tweezer. Drug release cannot occur, it seems, unless the tweezer is in a hydrophobic environment with low pH. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We present an efficient approach to the electron correlation problem that is well suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for one-dimensional Hubbard rings with different numbers of sites, and for the nonrelativistic quantum-chemical Hamiltonian exploring the symmetric dissociation of the H50 hydrogen chain. [ABSTRACT FROM AUTHOR]

The orbital dependence of closed-shell wavefunction energies is investigated by performing doubly-occupied configuration interaction (DOCI) calculations, representing the most general class of these wavefunctions. Different local minima are examined for planar hydrogen clusters containing two, four, and six electrons applying (spin) symmetry-broken restricted, unrestricted, and generalised orbitals with real and complex coefficients. Contrary to Hartree–Fock (HF), restricted DOCI is found to properly break bonds and thus unrestricted orbitals, while providing a quantitative improvement of the energy, are not needed to enforce a qualitatively correct bond dissociation. For the beryllium atom and the BH diatomic, the lowest possible HF energy requests symmetry-broken generalised orbitals, whereas accurate results for DOCI can be obtained within a restricted formalism. Complex orbital coefficients are shown to increase the accuracy of HF and DOCI results in certain cases. The computationally inexpensive AP1roG geminal wavefunction is proven to agree very well with all DOCI results of this study. [ABSTRACT FROM AUTHOR]

Wepresent a quantum mechanics/molecular mechanics (QM/MM) methodto evaluate the partial charges of amino acid residues for use inMM potentials based on their protein environment. For each residueof interest, the nearby residues are included in the QM system whilethe rest of the protein is treated at the MM level of theory. Aftera short structural optimization, the partial charges of the centralresidue are fit to the electrostatic potential using the restrainedelectrostatic potential (RESP) method. The resulting charges and electrostaticpotential account for the individual environment of the residue, althoughthey lack the transferable nature of library partial charges. To evaluatethe quality of the QM/MM RESP charges, thermodynamic integration isused to measure the pKashift of the asparticacid residues in three different proteins, turkey egg lysozyme, beta-cryptogein,and Thioredoxin. Compared to the AMBER ff99SB library values, theQM/MM RESP charges show better agreement between the calculated andexperimental pKavalues for almost allof the residues considered. [ABSTRACT FROM AUTHOR]

The mechanism of a simple SN2 reaction, viz;OH–+ CH3F = CH3OH + F–has been studied within the framework of reactionforce and reactionelectronic flux. We have computationally investigated three differenttypes of reaction mechanisms with two different types of transitionstates, leading to two different products. The electronic transfercontribution of the reaction electronic flux was found to play a crucialrole in this reaction. Natural bond order analysis and dual descriptorprovide additional support for elucidating the mechanism of this reaction. [ABSTRACT FROM AUTHOR]

Using the recently solved crystal structure of the human adenosine A2Areceptor, we applied MM/PBSA to compare the binding modes of caffeine with those of the high-affinity selective antagonist ZM241385. MD simulations were performed in the environment of the lipid membrane bilayer. Four low-energy binding modes of caffeine-A2Awere found, all of which had similar energies. Assuming an equal contribution of each binding mode of caffeine, the computed binding free energy difference between caffeine and ZM241385 is −2.4 kcal/mol, which compares favorably with the experimental value, −3.6 kcal/mol. The configurational entropy contribution of −0.9 kcal/mol from multiple binding modes of caffeine helps explain how a small molecule like caffeine can compete with a significantly larger molecule, ZM241385, which can form many more interactions with the receptor. We also performed residue-wise energy decomposition and found that Phe168, Leu249, and Ile274 contribute most significantly to the binding modes of caffeine and ZM241385. [ABSTRACT FROM AUTHOR]

Abstract: Information theoretic atomic properties within the quantum theory of atoms in molecules (QTAIM) are discussed. The fate of the dimensions of the electron density inserted into the logarithm of Shannon’s entropy is examined. It is shown that referencing the atomic missing information function to the corresponding uniform electron gas captures most of the size-dependence and converts the non-transferable atomic missing information into a transferable property. A striking trend relates an atom’s contribution to the overall Coulombic correlation energy and that atom’s Shannon’s entropy. The information theoretic atomic properties obtained from MP2, DFT, or Hartree–Fock (H–F) are almost perfectly correlated. [Copyright &y& Elsevier]

Exploiting the locality of the chemical potential of an excited state when it is evaluated using the ground state Density Functional Theory (DFT), a new local descriptor for excited states has been proposed (J. Chem. Theory Comput. 2009,5,2274). This index is based on the assumption that the relaxation of the electronic density toward that of the ground state drives the chemical reactivity of excited states. The sign of the descriptor characterizes the electrophilic or nucleophilic behavior of atomic regions. Through an exact excited state DFT formalism provided by Gross, Oliveira, and Kohn, a mathematical argument is given for this descriptor only for the first excited state. It is afterward used to rationalize the occurrence and the regioselectivity of some DNA lesions based on the [2 + 2] cydoaddition between two adjacent bases. [ABSTRACT FROM AUTHOR]

Abstract: In this communication, a very simple method is proposed to calculate the potential energy profile of a reaction step for a system in its first electronic excited state. It is based on an extension of the Grochala–Albrecht–Hoffmann rule. Theoretical arguments supporting this extension are given. The proposed method is validated on two examples that are interesting from a biological point of view: photocycloadditions [2+2] involved in the formation of pyrimidic dimers under DNA exposition to UV radiation. [Copyright &y& Elsevier]

In the present article, we report a comparative study between the Hirshfeld and Mulliken population analysis schemes (abbreviated as HPA and MPA, respectively). Trends of atomic charges derived from these two population analysis schemes are compared with those expected from other commonly used chemical concepts like electronegativity, inductive effects, and resonance effects. Although previous studies on intramolecular reactivity sequences demonstrated that HPA generates reliable and non-negative (and thus physically more realistic) condensed Fukui function (FF) values, the present study reveals problems with the HPA charge partitioning technique. Specifically, HPA fails to reproduce reliable intermolecular and intramolecular charge trends in several systems. Reasons for the success and failure of HPA are discussed and a method for improving the Hirshfeld charge partitioning is proposed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

We introduce a method to compute atomic properties according to the “quantum theory of atoms in molecules.” An integration grid in real space is partitioned into subsets, ωi. The subset, ωi, is composed of all grid points contained in the atomic basin, Ωi, so that integration over Ωi is reduced to simple quadrature over the points in ωi. The partition is constructed from deMon2k's atomic center grids by following the steepest ascent path of the density starting from each point in the grid. We also introduce a technique that exploits the cellular nature of the grid to make the algorithm faster. The performance of the method is tested by computing properties of atoms and nonnuclear attractors (energies, charges, dipole, and quadrupole moments) for a set of representative molecules. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009 [ABSTRACT FROM AUTHOR]

Abstract: An improved version of our method for computing QTAIM [J.I. Rodríguez, A.M. Köster, P.W. Ayers, A. Santos-Valle, A. Vela, G. Merino, J. Comput. Chem. (2009), in press, doi:10.1002/jcc.21134] is presented. Vectorization and parallelization of the previous algorithm, together with molecular symmetry, make the present algorithm as much as two orders of magnitude faster than our original method. The present method scales linearly with both system size and the number of processors. The performance of the method is demonstrated by computing the QTAIM atomic properties of a series of carbon nanotubes. Our results show that the CPU time for a QTAIM property calculation is comparable to that of a SCF-single point calculation. The accuracy of the original method is also improved. [Copyright &y& Elsevier]

Abstract: We derive a correction term to the Fermi–Dirac energy for the system of noninteracting electrons confined to a cube with sides of infinite potential. This correction term is compared to one derived by Pauncz [R. Pauncz, Acta Physica Academiae Scientarium Hungaricae 1 (1952) 277]. Both models are compared to the exact quantum mechanical result with systems of 1 to 5000 electrons being considered. Agreement is seen to increase with particle number. [Copyright &y& Elsevier]

Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, Nα and Nβ, has a derivative discontinuity on a line segment where the number of electrons, Nα + Nβ, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, Nα - Nβ, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare-we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested-but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals. [ABSTRACT FROM AUTHOR]

The drive to develop maximal atom‐efficient catalysts coupled to the continuous striving for more sustainable reactions has led to an ever‐increasing interest in single‐atom catalysis. Based on a periodic conceptual density functional theory (cDFT) approach, fundamental insights into the reactivity and adsorption of single late transition metal atoms supported on a fully hydroxylated amorphous silica surface have been acquired. In particular, this investigation revealed that the influence of van der Waals dispersion forces is especially significant for a silver (98 %) or gold (78 %) atom, whereas the oxophilicity of the Group 8–10 transition metals plays a major role in the interaction strength of these atoms on the irreducible SiO2 support. The adsorption energies for the less‐electronegative row 4 elements (Fe, Co, Ni) ranged from −1.40 to −1.92 eV, whereas for the heavier row 5 and 6 metals, with the exception of Pd, these values are between −2.20 and −2.92 eV. The deviating behavior of Pd can be attributed to a fully filled d‐shell and, hence, the absence of the hybridization effects. Through a systematic analysis of cDFT descriptors determined by using three different theoretical schemes, the Fermi weighted density of states approach was identified as the most suitable for describing the reactivity of the studied systems. The main advantage of this scheme is the fact that it is not influenced by fictitious Coulomb interactions between successive, charged reciprocal cells. Moreover, the contribution of the energy levels to the reactivity is simultaneously scaled based on their position relative to the Fermi level. Finally, the obtained Fermi weighted density of states reactivity trends show a good agreement with the chemical characteristics of the investigated metal atoms as well as the experimental data. [ABSTRACT FROM AUTHOR]

IOData is a free and open‐source Python library for parsing, storing, and converting various file formats commonly used by quantum chemistry, molecular dynamics, and plane‐wave density‐functional‐theory software programs. In addition, IOData supports a flexible framework for generating input files for various software packages. While designed and released for stand‐alone use, its original purpose was to facilitate the interoperability of various modules in the HORTON and ChemTools software packages with external (third‐party) molecular quantum chemistry and solid‐state density‐functional‐theory packages. IOData is designed to be easy to use, maintain, and extend; this is why we wrote IOData in Python and adopted many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. This article is the official release note of the IOData library. [ABSTRACT FROM AUTHOR]

The bonding and antibonding character of individual molecular orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as dynamical orbital forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn–Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, dynamical orbital forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations. [ABSTRACT FROM AUTHOR]

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases. [ABSTRACT FROM AUTHOR]

Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations. [ABSTRACT FROM AUTHOR]

Using the ratio of two fluctuations in the temperature-dependent density functional theory, the local counterpart of a global response function and the linear (non-local) counterpart of a local response function can be constructed. Here, we analyze the local chemical potential, local hardness, Fukui kernel and dual descriptor kernel and test their performance for describing and interpreting reactivity features for a diverse set of organic chemical reactions, including acid–base reactions, aliphatic nucleophilic substitutions, aromatic electrophilic substitutions and Markovnikov additions. Despite important differences in size and functionalization between some substrates belonging to a given chemical reaction type, temperature-dependent chemical reactivity descriptors were able to reproduce experimental or computational trends in all cases. We identify relevant chemical interactions belonging to a particular family of reactions and the molecular moieties responsible for such interactions. In general, our results are consistent with traditional chemical interpretations. However, in some cases the information contained in the temperature-dependent chemical reactivity descriptors allows one to gain new insights about the organic chemistry reactions considered here. [ABSTRACT FROM AUTHOR]

We analyze the problem of selecting the model that best describes a given dataset. We focus on the case where the best model is the one with the smallest error, respect to the reference data. To select the best model, we consider two components: (a) an error measure to compare individual data points, and (b) a function that combines the individual errors for all the points. We show that working with the most general definition of consistency, it is impossible to extend individual error measures in a way that provides a unanimous consensus about which is the best model. We also prove that, in the best case, modifying the notion of consistency leads to expressions that are too ill-behaved to be of any practical utility. These results show that selecting the model that best describes a dataset depends heavily on the way one measures the individual errors, even if these measures are consistent. [ABSTRACT FROM AUTHOR]

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability. [ABSTRACT FROM AUTHOR]

Despite the importance of non-singlet molecules in chemistry, most variational second order density matrix calculations have focused on singlet states. Ensuring that a second order density matrix is derivable from a proper N-electron spin state is a difficult problem because the second order density matrix only describes one- and two-particle interactions. In pursuit of a consistent description of spin in second order density matrix theory, we propose and evaluate two main approaches: we consider constraints derived from a pure spin state and from an ensemble of spin states. This paper makes a comparative assessment of the different approaches by applying them to potential energy surfaces for different spin states of the oxygen and carbon dimer. We observe two major shortcomings of the applied spin constraints: they are not size consistent and they do not reproduce the degeneracy of the different states in a spin multiplet. First of all, the spin constraints are less strong when applied to a dissociated molecule than when they are applied to the dissociation products separately. Although they impose correct spin expectation values on the dissociated molecule, the dissociation products do not have correct spin expectation values. Secondly, both under 'pure spin state conditions' and under 'ensemble spin state' conditions is the energy a convex function of the spin projection. Potential energy surfaces for different spin projections of the same spin state may give a completely different picture of the molecule's bonding. The maximal spin projection always gives the most strongly constrained energy, but is also significantly more expensive to compute than a spin-averaged ensemble. In the dissociation limit, both the problem of nondegeneracy of equivalent spin projections, size-inconsistency and unphysical dissociation can be corrected by means of subspace energy constraints. [ABSTRACT FROM AUTHOR]

The eigenvectors of the electronic stress tensor can be used to identify where new bond paths form in a chemical reaction. In cases where the eigenvectors of the stress tensor are not available, the gradient-expansion-approximation suggests using the eigenvalues of the second derivative tensor of the electron density instead; this approximation can be made quantitatively accurate by scaling and shifting the second-derivative tensor, but it has a weaker physical basis and less predictive power for chemical reactivity than the stress tensor. These tools provide an extension of the quantum theory of atoms and molecules from the characterization of molecular electronic structure to the prediction of chemical reactivity. [ABSTRACT FROM AUTHOR]

Variational second order density matrix theory under 'two-positivity' constraints tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F3- by applying subspace energy constraints on mono- and diatomic subspaces of the molecular basis space. Monoatomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting second order density matrix method does not exactly correspond to a system of noninteracting units. [ABSTRACT FROM AUTHOR]

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges. [ABSTRACT FROM AUTHOR]

A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to single-index atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made consistent with well-known partitions of the electron density over atom in the molecule basins, either with sharp or with fuzzy boundaries. The method is applied to a test set of about 50 molecules, representative for various types of chemical binding. A close correlation is observed between the trace of the bond matrices and the shared electron density index. [ABSTRACT FROM AUTHOR]

A variational optimization of the second-order density matrix under the P-, Q-, and G-conditions was carried out for a set of diatomic 14-electron molecules, including N2, O22+, NO+, CO, and CN-. The dissociation of these molecules is studied by analyzing several chemical properties (dipole moments, population analysis, and bond indices) up to the dissociation limit (10 and 20 Å). Serious chemical flaws are observed for the heteronuclear diatomics in the dissociation limit. A careful examination of the chemical properties reveals that the origin of the dissociation problem lies in the flawed description of fractionally occupied species under the P-, Q-, and G-conditions. A novel constraint is introduced that imposes the correct dissociation and enforces size consistency. The effect of this constraint is illustrated with calculations on NO+, CO, CN-, N2, and O22+. [ABSTRACT FROM AUTHOR]

A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P,Q,G) or even three-index (T1,T2) conditions [H. Van Aggelen et al., Phys. Chem. Chem. Phys. 11, 5558 (2009)]. Heteronuclear molecules tend to dissociate into fractionally charged atoms. In this paper we introduce a general class of N-representability conditions, called subsystem constraints, and show that they cure the dissociation problem at little additional computational cost. As a numerical example the singlet potential energy surface of Be B+ is studied. The extension to polyatomic molecules, where more subsystem choices can be identified, is also discussed. [ABSTRACT FROM AUTHOR]

Relationships between third-order reactivity indicators in the closed system [N, v(r)], open system [μ, v(r)], and density [ρ(r)] pictures are derived. Our method of derivation unifies and extends known results. Among the relationships is a link between the third-order response of the energy to changes in the density and the quadratic response of the density to changes in external potential. This provides a link between hyperpolarizability and the system’s sensitivity to changes in electron density. The dual descriptor is a unifying feature of many of the formulas we derive. [ABSTRACT FROM AUTHOR]

The number of the potential energy calculations required by the quadratic string method (QSM), and the fast marching method (FMM) is significantly reduced by using Shepard interpolation, with a moving least squares to fit the higher-order derivatives of the potential. The derivatives of the potential are fitted up to fifth order. With an error estimate for the interpolated values, this moving least squares enhanced Shepard interpolation scheme drastically reduces the number of potential energy calculations in FMM, often by up 80%. Fitting up through the highest order tested here (fifth order) gave the best results for all grid spacings. For QSM, using enhanced Shepard interpolation gave slightly better results than using the usual second order approximate, damped Broyden-Fletcher-Goldfarb-Shanno updated Hessian to approximate the surface. To test these methods we examined two analytic potentials, the rotational dihedral potential of alanine dipeptide and the SN2 reaction of methyl chloride with fluoride. [ABSTRACT FROM AUTHOR]

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory. [ABSTRACT FROM AUTHOR]

The chemical reactivity concepts of density functional theory are studied through a unified view in the temperature‐dependent approach provided by the grand canonical ensemble. This procedure leads to a more general perspective that enriches our understanding of the behavior of the average energy and its derivatives with respect to the average number of electrons, provides alternative definitions for those quantities that are "ill defined" at zero temperature, and allows one to determine the relationships among reactivity concepts at any temperature. In particular, it has been found that at high temperatures the parabolic model for reactivity indicators may be justified through the electronic entropy term in the Helmholtz free energy, and that at nonzero temperatures there is an electronic heat capacity contribution to the average energy. In summary, the unified view of the temperature‐dependent approach is an important complement to the zero‐temperature formulation that clarifies fundamental issues therein. This work presents a unified view of the chemical reactivity concepts of density functional theory within the grand canonical ensemble to obtain the corresponding temperature‐dependent expressions, to establish the general relationships among them, and to show how to obtain well‐behaved quantities, when they are "ill defined" at zero temperature. This unified view is an important complement to the zero‐temperature formulation. [ABSTRACT FROM AUTHOR]