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Research is presented demonstrating use of the Fukui function and maximum hardness principle as tools for describing chemical reactivity in a theoretical way.

A study of a family of substituted acetylenes indicates that the removal of electrons from these molecules causes the electron density along the C-C bond to increase, provided that the Fukui function is negative. Substantial evidence is provided to show that the molecular Fukui function is sometimes negative due to orbital relaxation.

The clarification of the derivative of the Hirshfeld atoms in molecules from information theory is presented. The importance for chemistry of the concept of atoms in molecules (AIM) is stressed, and it is argued that this concept, while highly, useful, constitutes a noumenon in the sense of Kant.

Strong ionic binding of the cationic probe rhodamine 6G (R6G) to the anionic surface of silica particles in water provides a convenient labeling procedure to study the particle growth kinetics and surface modification by time-resolved fluorescence anisotropy (TRFA). The results rule out the presence of local R6G wobbling when bound ionically to colloidal silica and support the rigid sphere model to describe the TRFA decays for R6G-Ludox.

A study of the analytical representations of the energy, W(R) = W(S), and the generation of the analytical series, W(S) =sigma(S)summation(sub n) b(sub n) P(sub n)[S(sub n)], where P(sub n)(S) are the orthogonal polynomials with weight function sigma(S) over the range (-1, +1), for S for a diatomic molecule is presented. The results show that for neutral diatomic, the Jacobi polynomials, P(sup 1.6)(sub n) (S) with weight function (1+s)(1-S)(sup 6), is appropriate when the potential for large R is of special interest.

Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way that clarifies the enormous freedom one has within the information-theoretic ansatz. [ABSTRACT FROM AUTHOR]

Research into the impact of changing the external potential on chemical reactivity is presented. It has been possible to define four new indices, including the stabilization energy for the equilibrium nuclear geometry.

Issues concerning the use of the Fukui reaction to rationalize the rule of W. Grochala, A.C. Albrecht and R. Hoffmann that, for many inorganic and organic molecules, the bond lengths in the cation, first triplet excited state, neutral state and anion roughly satisfy R+ = R- - Rgs - Res = 0 are discussed.

In an attempt to master the overwhelming amount of data on the properties of substances and their reactions, chemists scrutinize them for underlying common patterns. In modern times quantum mechanics (QM) has played a leading role in the understanding of chemical reactivity. In the late 1960s, Woodward and Hoffmann (WH) proposed one of the most successful and elegant approaches to interpret the outcome of an important type of reaction: they could predict the allowed or forbidden character of pericyclic reactions through inspection of the phase and symmetry of the orbitals of the reactants obtained by simple extended Hückel theory. Today much more powerful computational techniques, such as density functional theory (DFT), are available that yield highly accurate results even for large systems. By focusing on the electron density, ρ(r), a fundamental carrier of information compared with the much more complicated wave function in conventional QM, DFT became the computational workhorse for systems of ever increasing complexity. However, the need for the interpretation of computational (and obviously experimental) results remains, and “conceptual DFT” has provided the answer to this challenge within the context of DFT. This branch of DFT has given precision to chemical concepts such as electronegativity, hardness, and softness and has embedded them in a perturbational approach to chemical reactivity. Previously, researchers have successfully applied conceptual DFT to generalized acid–base and, more recently, to radical and redox reactions. In this Account, we present a conceptual DFT ansatz for pericyclic reactions, a stringent test for this density-only approach, because the density has trivial symmetry and no phase. [ABSTRACT FROM AUTHOR]

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popuiar scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface ofthe electron density is closely linked to the form of the kinetic energy, so it is somewhat surpnsing that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Ftamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltoman should be sufllaent Ilar qualitative descriptions of molecular electronic sttucture across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms. [ABSTRACT FROM AUTHOR]

We introduce the general mathematical framework of variational Hirshfeld partitioning, wherein the best possible approximation to a molecule's electron density is obtained by minimizing the f -divergence between the molecular density and a non-negative linear combination of (normalized) basis functions. This framework subsumes several existing methods that variationally optimize their pro-atoms, like (Gaussian) iterative stockholder analysis (ISA and GISA) and minimal basis iterative stockholder partitioning (MBIS), and provides a solid foundation for developing mathematically rigorous partitioning schemes. In this paper, we delve into the mathematical underpinnings of Hirshfeld-inspired partitioning schemes and show that among all the valid f -divergence measures only the extended Kullback-Leibler is a suitable choice. This led us to develop a novel partitioning scheme, called additive variational Hirshfeld (AVH), which constructs the pro-molecular density as a convex linear combination of the densities from selected states of isolated atoms and atomic ions. The AVH method is size-consistent with a unique solution and provides a straightforward approach for adding constraints for fragment properties. It also results in an intuitively appealing valence-bond-like decomposition of the molecular density as a weighted average of the densities of the atomic states in the molecule; that is, the AVH atomic density is a minimal deformation of the corresponding isolated atomic reference state's density. Compared to other variational Hirshfeld variants, our numerical results show that AVH yields chemically interpretable and sensible atomic charges that are not excessively large and demonstrate computational robustness.

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

Hydrogen cyanide (HCN) and formaldehyde (H 2 CO) are key precursors to biomolecules such as nucleobases and amino acids in planetary atmospheres. However, many reactions which produce and destroy these species in atmospheres containing CO 2 and H 2 O are still missing from the literature. We use a quantum chemistry approach to find these missing reactions and calculate their rate coefficients using canonical variational transition state theory and Rice-Ramsperger-Kassel-Marcus/master equation theory at the BHandHLYP/aug-cc-pVDZ level of theory. We calculate the rate coefficients for 126 total reactions and validate our calculations by comparing with experimental data in the 39% of available cases. Our calculated rate coefficients are most frequently within a factor of 2 of experimental values and generally always within an order of magnitude of these values. We discover 45 previously unknown reactions and identify 6 from this list that are most likely to dominate H 2 CO and HCN production and destruction in planetary atmospheres. We highlight 1 O + CH 3 → H 2 CO + H as a new key source and H 2 CO + 1 O → HCO + OH as a new key sink, for H 2 CO in upper planetary atmospheres. In this effort, we develop an oxygen extension to our consistent reduced atmospheric hybrid chemical network (CRAHCN-O), building off our previously developed network for HCN production in N 2 -, CH 4 -, and H 2 -dominated atmospheres (CRAHCN). This extension can be used to simulate both HCN and H 2 CO production in atmospheres dominated by any of CO 2 , N 2 , H 2 O, CH 4 , and H 2 .

Thirty years ago, Parr and Yang postulated that favorable chemical processes are associated with large changes in the electronic chemical potential or, equivalently, the electronegativity. They called this the "|Δμ| big is good" rule and noted that if the rule could be justified, then it "would constitute a validation of frontier theory from first principles." We provide a simple and insightful justification for the "|Δμ| big is good" rule, with special emphasis on electron-transfer reactions. Furthermore, we show that it implies Pearson's hard/soft acid/base principle mathematically and confirm this result with numerical examples. This supports Parr's intuition that many other reactivity precepts arise as corollaries to the more fundamental "|Δμ| big is good" rule. In all of this, it is essential to consider the intensive nature of the chemical potential.

The temperature-dependence of the Helmholtz free energy with respect to the number of electrons is analyzed within the framework of the Grand Canonical Ensemble. At the zero-temperature limit, the Helmholtz free energy behaves as a Heaviside function of the number of electrons; however, as the temperature increases, the profile smoothens and exhibits a minimum value at noninteger positive values of the fractional electronic charge. We show that the exact average electronic energy as a function of the number of electrons does not display this feature at any temperature, since this behavior is solely due to the electronic entropy. Our mathematical analysis thus indicates that the widely used parabolic interpolation model should not be viewed as an approximation for the average electronic energy, but for the dependence of the Helmholtz free energy upon the number of electrons, and this analysis is corroborated by numerical results. Finally, an electrophilicity index is defined for the Helmholtz free energy showing that, for a given chemical species, there exists a temperature value for which this quantity is equivalent to the electrophilicity index defined within the parabolic interpolation of the electronic energy as a function of the number of electrons. Our formulation suggests that the convexity property of the energy versus the number of electrons together with the entropic contribution does not allow for an analogous nucleophilicity index to be defined.

When one defines the energy of a molecule with a noninteger number of electrons by interpolation of the energy values for integer-charged states, the interpolated electron density, Fukui function, and higher-order derivatives of the density are generally not normalized correctly. The necessary and sufficient condition for consistent energy interpolation models is that the corresponding interpolated electron density is correctly normalized to the number of electrons. A necessary, but not sufficient, condition for correct normalization is that the energy interpolant be a linear function of the reference energies. Consistent with this general rule, polynomial interpolation models and, in particular, the quadratic E vs N model popularized by Parr and Pearson, do give normalized densities and density derivatives. Interestingly, an interpolation model based on the square root of the electron number also satisfies the normalization constraints. We also derive consistent least-norm interpolation models. In contrast to these models, the popular rational and exponential forms for E vs N do not give normalized electron densities and density derivatives.

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g., obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method, but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Scheffler scheme for dispersion interactions.

We present a linearized coupled cluster (LCC) correction based on a reference state of the antisymmetric product of 1-reference orbital geminals (AP1roG). In our LCC ansatz, the cluster operator is restricted to double or to single and double excitations, as in standard single-reference CC theory. The performance of the AP1roG-LCC models is tested for the dissociation of diatomic molecules in their lowest-lying singlet state (C2, F2, and BN), the symmetric dissociation of the H50 hydrogen chain, and spectroscopic constants of the uranyl cation (UO2 2+). Our study indicates that an LCC correction based on an AP1roG reference function is more robust and reliable than corrections based on perturbation theory, yielding spectroscopic constants that are in very good agreement with theoretical reference data.

We introduce new nonvariational orbital optimization schemes for the antisymmetric product of one-reference orbital geminal (AP1roG) wave function (also known as pair-coupled cluster doubles) that are extensions to our recently proposed projected seniority-two (PS2-AP1roG) orbital optimization method [ J. Chem. Phys. 2014 , 140 , 214114 )]. These approaches represent less stringent approximations to the PS2-AP1roG ansatz and prove to be more robust approximations to the variational orbital optimization scheme than PS2-AP1roG. The performance of the proposed orbital optimization techniques is illustrated for a number of well-known multireference problems: the insertion of Be into H2, the automerization process of cyclobutadiene, the stability of the monocyclic form of pyridyne, and the aromatic stability of benzene.

A system in a spatially (quasi-)degenerate ground state responds in a qualitatively different way to a change in the external potential. Consequently, the usual method for computing the Fukui function, namely, taking the difference between the electron densities of the N- and N ± 1 electron systems, cannot be applied directly. It is shown how the Fukui matrix, and thus also the Fukui function, depends on the nature of the perturbation. One thus needs to use degenerate perturbation theory for the given perturbing potential to generate the density matrix whose change with respect to a change in the number of electrons equals the Fukui matrix. Accounting for the degeneracy in the case of nitrous oxide reveals that an average over the degenerate states differs significantly from using the proper density matrix. We further show the differences in Fukui functions depending on whether a Dirac delta perturbation is used or an interaction with a true point charge (leading to the Fukui potential).

A system in a spatially degenerate ground state responds in a qualitatively different way to positive and negative point charges. This means that the molecular electrostatic potential is ill-defined for degenerate ground states due to the ill-defined nature of the electron density. It also means that it is impossible, in practice, to define fixed atomic charges for molecular mechanics simulations of molecules with (quasi-)degenerate ground states. Atomic-polarizability-based models and electronegativity-equalization-type models for molecular polarization also fail to capture this effect. We demonstrate the ambiguity in the electrostatic potential using several molecules of different degree of degeneracy, quasi-degeneracy, and symmetry.

We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

Nonlocal exchange-correlation energy functionals are constructed using the accurate model exchange-correlation hole for the uniform electron gas developed by Gori-Giorgi and Perdew. The exchange-correlation hole is constrained to be symmetric and normalized, so the resulting functionals can be viewed as symmetrized versions of the weighted density approximation; we call them two-point weighted density approximations. Even without optimization of parameters or functional forms, the exchange-correlation energies for small molecules are competitive with those of the best generalized gradient approximation functionals. Two-point weighted density approximations seem to be an interesting new direction for functional development. A more general version of the conditions that define the energy for fractional electron number and fractional spin are presented. These "generalized flat-planes" conditions are closely linked to the normalization of the spin-resolved exchange-correlation hole at noninteger electron number. This and many other properties of the exact exchange-correlation functional can be imposed straightforwardly and directly in symmetrized weighted density approximation.

A procedure for determining force constants that is independent of the internal redundant coordinate choice is presented. The procedure is based on solving each bond and angle term separately, using the Wilson B matrix. The method only requires a single ab initio frequency calculation at the minimum energy structure and is made available in the software "parafreq". The methodology is validated with a set of small molecules, by showing it can reproduce ab initio frequencies better than other methods such as taking the diagonal terms of the Hessian in internal coordinates or by using standard AMBER force fields. Finally, the utility of the method is demonstrated by parametrizing the dizinc scaffold of bis-dipicolylamine (BDPA) bound to phosphotyrosine, which is then functionalized into promising antitumor drug proteomimetics.

In the course of a reaction it is the shape of the Fukui potential that guides a distant reagent toward the site where an electrophile/nucleophile is willing to accept/donate charge. In this paper we explore the mathematical characteristics of the Fukui potential and demonstrate its relationship to the hardness and the ability of an atom in a molecule to change its charge. The Fukui potential not only determines the active site for electron transfer, but it also approximates the distribution of hardness of a molecule: it is the Coulomb contribution to the frontier local hardness. The Fukui potential at the position of the nuclei is equal to the variation of the chemical potential with the nuclear charge and therefore measures the sensitivity of the system to changes in atom type. In the specific case of atoms and slightly charged ions, the Fukui potential at the nucleus measures the hardness. The strong correlation between the hardness and the Fukui potential at the nucleus suggests that the Fukui potential at the nucleus is an alternative definition for the chemical hardness.

A set of linear free energy models are presented for determining the pK(a) values of amines, alcohols, and carboxylic acids. Models are determined from a series of pK(a) predictors, taken both from traditional natural atomic orbital analysis (NAO) and from a novel approach introduced here of using a reference molecule: an ammonium ion for amines and a hydrogen sulfide molecule for alcohols and carboxylic acids. Using these reference molecules, we calculate the barrier to proton transfer and show that a number of properties associated with the transition state are correlated with the pK(a). By considering 38 predictors, we obtain a four-variable model for amines and a three-variable model for oxygen-containing compounds. The model for amines is based on 145 compounds and has a root mean squared error (RMSE) of 0.45 and R(2) = 0.98. The oxygen set has 48 molecules: RMSE = 0.26, and R(2) = 0.993. Similar, linear, and multilinear models are constructed after separating the sets into chemically similar categories: alcohols, carboxylic acids, and primary, secondary, tertiary, and aromatic amines. This separation gives simpler models with relatively low RMSE values, where the most important predictor of the pK(a) is the difference in energy between transferring the proton from the reference molecular base to the conjugate acid from the data set.

We investigate the effect of systematically applying molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) to docked poses in an attempt to improve the correspondence between theoretical prediction and experimental observation. The proposed scheme involves running a short time scale MD simulation on a docked ligand pose (and any known structurally important crystal structure waters in the active site), followed by QM/MM minimization. Both of these steps are relatively fast for moderately sized ligands; longer time scale MD involving the protein is not found to improve the results. The final binding energy is given in terms of the QM/MM total energy, a van der Waals correction, and a term to account for desolvation effects. This methodology is first tested with a trypsin inhibitor, for which we establish the importance of running MD before reoptimizing with QM/MM. The method is then applied to cytochrome c peroxidase using a set of binders and decoys. In this example, the proposed methodology affords much better discrimination between binders and decoys than the traditional docking approach used. For both systems presented, application of this protocol results in a significantly better energetic ranking and a smaller root mean squared deviation from known crystallographic ligand poses. This work highlights the importance of including polarization effects through QM/MM and of sampling with MD to refine a set of initial docked poses.

Two new algorithms are presented for determining the minimum energy reaction path (MEP) on the reduced potential energy surface (RPES) starting with only the reactant. These approaches are based on concepts from the fast marching method (FMM), which expands points outward as a wavefront on a multidimensional grid from the reactant until the product is reached. The MEP is then traced backward to the reactant. Since the number of possible grid points that must be considered grows exponentially with increasing dimensionality of the RPES, interpolation is important for maintaining manageable computational costs. In this work, we use Shepard interpolation, which we have modified to resolve problems in overfitting. In contrast to FMM, which accurately locates the MEP, the new algorithms focus on locating the single rate-limiting transition state and provide only a rough estimate of the MEP. They do this by mapping out the RPES on a coarse grid and then refining a least action path on a finer grid. This is done so that the majority of the interpolation is done on the finer grid, which minimizes the amount of extrapolation inherent in an outward searching algorithm. The first method scans the entire PES before iteratively locating the transition state (TS) for the MEP on the lower bound estimate of the fine PES. The second method explores the coarse grid in a similar manner to FMM and then iteratively locates the rate-limiting TS in the same manner as the first method. Both methods are shown to be capable of rapidly obtaining (in less than 30 constrained optimization cycles) an approximation to the MEP and the rate limiting TS for three example systems: the 4-well potential, the molecule N-hydroxymethyl-methylnitrosaminee (HMMN), and a cluster model of DNA-uracil glycosylase.