Correlated molecular and multicenter multipole moments in ground and excited states from multiple reference double-excitation configuration interaction calculations

Correlated molecular mulitpole moments and compact correlated cumulative atomic multipole moment (CCAMM) representation of molecular charge distribution in ground as well as in excited states have been derived directly from multiple reference double-excitation configuration interaction (MRD-CI) wave functions for BH and H₂CO molecules using several extended basis sets with multiple polarization functions. This approach extends previously introduced uncorrelated and correlated CAMMs, and allows obtaining inexpensive modeling of electrostatic effects involving molecules in excited electronic states. © 1992 by John Wiley & Sons, Inc.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

Partial atomic multipoles for internally consistent microelectrostatic calculations

An extension of the extant microelectrostatic methodologies, based on the concept of distributed generalized polarizability matrix derived from the Coupled Perturbed Hartree–Fock (CPHF) equations, is proposed for self‐consistent calculation of charge carrier and charge‐transfer (CT) state electrostatic energies in molecular solids, including the doped, defected and disordered ones. The CPHF equations are solved only once and the generalized molecular polarizability they yield enables low cost iterations that mutually adjust the molecular electronic distributions and the local electric field in which the molecules are immersed. The approach offers a precise picture of molecular charge densities, accounting for atomic partial multipoles up to order 2, which allows one to reproduce the recently reported large charge‐quadrupole contributions to CT state energies in low‐symmetry local environments. It is particularly well suited for repetitive calculations for large clusters (up to 300,000 atoms), and may potentially be useful for describing electrostatic solvent effects. © 2017 Wiley Periodicals, Inc.     

Electrostatic interactions in host-guest complexes 2

In this article the quantum chemically calculated charge density distribution of 18-crown-6 and the K⁺ …18-crown-6 complex are compared with the charge density distribution of smaller molecules and corresponding complexes which can be considered as fragments of the 18-crown-6 molecule. An analysis of the charge density distribution in terms of atomic charge distribution according to the stockholder recipe gives accurate rules for the transferability of the charge density distribution. This gives us the possibility to construct the charge density distribution of large molecules out of accurate large basis set results on small molecules.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Building molecular charge distributions from fragments: Application to HIV-1 protease inhibitors

Interaction energies are a function of the molecular charge distribution. In previous work, we found that the set of atomic partial charges giving the best agreement with experimental vacuum dipole moments were from density functional theory calculations using an extended basis set. Extension of such computations to larger molecules requires an atomic partial charge calculation beyond present computational resources. A solution to this problem is the calculation of atomic partial charges for segments of the molecule and reassociation of such fragments to yield partial charges for the entire molecule. Various partitions and reassociation methods for five molecules relevant to HIV-1 protease inhibitors are examined. A useful method of reassociation is introduced in which atomic partial charges for a large molecule are computed by fitting to the combined electrostatic potential calculated from the fragment partial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. © 1997 by John Wiley & Sons, Inc.     

The ellipsoidal Gaussian basis in molecular orbital theory

The ellipsoidal Gaussian basis function used in a minimal valence atomic orbital representation is compared with the double-zeta spherical Gaussian basis orbital representation for some seventeen molecules made up of first row atoms and hydrogen. Except for acetylene the double-zeta basis gives consistently better total electronic energies and generally better property values than the optimized ellipsoidal single zeta basis. Difference molecular density contour maps comparing the two basis sets, as well as other one-electron property values, indicate that the ellipsoidal basis exaggerates the transfer of charge from the atomic regions to the interatomic and lone pair regions of molecules. Apparently, the forced complete elliptization of the valence atomic orbital in the single-zeta representation does not allow the basis set sufficient flexibility to simultaneously represent both the basically spherical atomic part of these orbitals and the non-spherical molecular bond formation. Other properties and aspects of the ellipsoidal Gaussian basis are also discussed.     

Local electric dipole moments: A generalized approach

We present an approach for calculating local electric dipole moments for fragments of molecular or supramolecular systems. This is important for understanding chemical gating and solvent effects in nanoelectronics, atomic force microscopy, and intensities in infrared spectroscopy. Owing to the nonzero partial charge of most fragments, “naively” defined local dipole moments are origin‐dependent. Inspired by previous work based on Bader's atoms‐in‐molecules (AIM) partitioning, we derive a definition of fragment dipole moments which achieves origin‐independence by relying on internal reference points. Instead of bond critical points (BCPs) as in existing approaches, we use as few reference points as possible, which are located between the fragment and the remainder(s) of the system and may be chosen based on chemical intuition. This allows our approach to be used with AIM implementations that circumvent the calculation of critical points for reasons of computational efficiency, for cases where no BCPs are found due to large interfragment distances, and with local partitioning schemes other than AIM which do not provide BCPs. It is applicable to both covalently and noncovalently bound systems. © 2016 Wiley Periodicals, Inc.     

On the Low-Lying Electronically Excited States of Azobenzene Dimers: Transition Density Matrix Analysis

Azobenzene-containing molecules may associate with each other in systems such as self-assembled monolayers or micelles. The interaction between azobenzene units leads to a formation of exciton states in these molecular assemblies. Apart from local excitations of monomers, the electronic transitions to the exciton states may involve charge transfer excitations. Here, we perform quantum chemical calculations and apply transition density matrix analysis to quantify local and charge transfer contributions to the lowest electronic transitions in azobenzene dimers of various arrangements. We find that the transitions to the lowest exciton states of the considered dimers are dominated by local excitations, but charge transfer contributions become sizable for some of the lowest ππ* electronic transitions in stacked and slip-stacked dimers at short intermolecular distances. In addition, we assess different ways to partition the transition density matrix between fragments. In particular, we find that the inclusion of the atomic orbital overlap has a pronounced effect on quantifying charge transfer contributions if a large basis set is used.     

Coupled atomic charge selectivity for optimal ligand-charge distributions at protein binding sites

Charge optimization as a tool for both analyzing and enhancing binding electrostatics has become an attractive approach over the past few years. An interesting feature of this method for molecular design is that it provides not only the optimal charge magnitudes, but also the selectivity of a particular atomic center for its optimal charge. The current approach to compute the charge selectivity at a given atomic center of a ligand in a particular binding process is based on the binding-energy cost incurred upon the perturbation of the optimal charge distribution by a unit charge at the given atomic center, while keeping the other atomic partial charges at their optimal values. A limitation of this method is that it does not take into account the possible concerted changes in the other atomic charges that may incur a lower energetic cost than perturbing a single charge. Here, we describe a novel approach for characterizing charge selectivity in a concerted manner, taking into account the coupling between the ligand charge centers in the binding process. We apply this novel charge selectivity measure to the celecoxib molecule, a nonsteroidal anti-inflammatory agent binding to cyclooxygenase 2 (COX2), which has been recently shown to also exhibit cross-reactivity toward carbonic anhydrase II (CAII), to which it binds with nanomolar affinity. The uncoupled and coupled charge selectivity profiles over the atomic centers of the celecoxib ligand, binding independently to COX2 and CAII, are analyzed comparatively and rationalized with respect to available experimental data. Very different charge selectivity profiles are obtained for the uncoupled versus coupled selectivity calculations.     

On topological charge stabilization in heterocyclic compounds

According to Gimarc's principle of topological chargestabilization, heteroatomic molecules are topologically stabilized when more electronegative atoms are placed in those positions where atom-atom connectivity and the electron-filling level provide the highest electron charge in the reference hydrocarbon frame. Recently, we showed that the relative atomic moments of energy (the frequencies of atomic self-returning walks) in such uniform molecular skeletons are equal to the respective squared principal eigenvector coefficients. We show here that for conjugated heteroryclic molecules these partial atomic charges follow closely the patterns mirrored by topological charge stabilization and, by producing a nonuniform charge distribution in alternant molecules, enable the broader application of this principle to such molecules.Texas A&M university, Galveston, Texas. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1011–1022,August, 1995. Original article submitted May 19, 1995.Dedicated to N. S. Zefirov for his important contributions to mathematical chemistry, as well as for his friendly help to those who need it.     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

New Investigation of Potential Acting on an Electron in a Molecule to Draw Molecular Faces

A new approach to calculate the potential acting on an electron in a molecule(PAEM) has been established for drawing the molecular face(MF) of a macromolecule, according to the classic point charge model and the atom-bond electronegativity equalization method(ABEEMσπ) for one electron in a molecule. We introduced a dynamic charge distribution from the view of a local electron movement in a molecule based on the new approach, and as further direct evidence, we calculated some physical quantities using the original ab initio method and the new method to verify the accuracy of the method, such as the boundary distance(BD), molecular face surface area(MFSA) and molecular reactivities indicated by the MFs for a variety of organic molecules. All the results by the new method are in agreement with the results by ab initio method.