Discrete and continuum contributions to multipole polarizabilities and shielding factors of hydrogen

Discrete and continuum contributions to the multipole polarizabilities and shielding factors of atomic hydrogen are computed. The discrete series show logarithmic convergence which can be accelerated by the u-transform. The continuum contributions increase with increasing multipole order and are already dominant in the quadrupole polarizability and shielding factor. The shielding factors have greater continuum contributions than the polarizabilities.     

Distributed polarizability analysis for para-nitroaniline and meta-nitroaniline: functional group and charge-transfer contributions

Topological partitioning of electronic properties is used to investigate the polarizability of para-nitroaniline and meta-nitroaniline. The distributed polarizabilities for atoms are combined into total local or generalized distributed contributions for the amino, ring, and nitro functional groups; generalized distributed group contributions have not been calculated before. The local group contributions are transferable between the two molecules only when charge transfer is suppressed, but the generalized distributed contributions prove surprisingly similar in the two molecules, apparently because they treat charge-transfer contributions explicitly.     

The calculation of molar polarizabilities by the CNDO/2 method: Correlation with the hydrophobic parameter,log P

Results of molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO /2) method on 50 small molecules are reported. The summation of calculated atomic polarizabilities are equated with molecular polarizabilities, and these are compared with experimentally determined values. It is found that there is very good agreement between calculated and experimental molecular polarizability. This provides a reliable method for the determination of molecular polarizabilities for compounds for which experimental values are not known. The relationship between log P and polarizability is discussed and analyzed in terms of contributions from electronic components to the partitioning energy.     

Multipole moments for embedding potentials: Exploring different atomic allocation algorithms

Polarizable quantum mechanical (QM)/molecular mechanics (MM)‐embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins and RNA/DNA, and of molecules in solution. Our aim is to develop a computational methodology for distributed multipole moments and their associated multipole polarizabilities which is accurate, computationally efficient, and with smooth convergence with respect to multipole order. As the first step toward this goal, we herein investigate different ways of obtaining distributed atom‐centered multipole moments that are used in the construction of the electrostatic part of the embedding potential. Our objective is methods that not only are accurate and computationally efficient, but which can be consistently extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well‐known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we show that the classical embedding potential can be systematically improved, also when using basis sets with diffuse functions, and that very accurate embedding potentials suitable for QM/MM embedding calculations can be acquired. © 2016 Wiley Periodicals, Inc.     

Accuracy of distributed multipoles and polarizabilities: comparison between the LoProp and MpProp models

Localized multipole moments up to the fifth moment as well as localized dipole polarizabilities are calculated with the MpProp and the newly developed LoProp methods for a total of 20 molecules, predominantly derived from amino acids. A comparison of electrostatic potentials calculated from the multipole expansion obtained by the two methods with ab initio results shows that both methods reproduce the electrostatic interaction with an elementary charge with a mean absolute error of approximately 1.5 kJ/mol at contact distance and less than 0.1 kJ/mol at distances 2 A further out when terms up to the octupole moments are included. The polarizabilities are tested with homogenous electric fields and are found to have similar accuracy. The MpProp method gives better multipole moments unless diffuse basis sets are used, whereas LoProp gives better polarizabilities.     

Supplement to spherical tensor theory of long-range interactions between two molecules

We simplify a recently obtained approximate formula for the third-order interaction energy between two molecules expressed in terms of irreducible spherical polarizabilities and multipole moments of interacting systems. Similarly, we can simplify analogous higher-order expressions. Then we briefly examine the magnitudes of the various third-order contributions in comparison with the second-order categories of long-range interactions for some specific systems.     

Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis

We apply time-dependent density-functional quadratic response theory to investigate the static and dynamic second-order polarizabilities (first hyperpolarizability) beta. A new implementation using Slater-type basis functions, numerical integration, and density fitting techniques is reported. The second order coupled perturbed Kohn-Sham equations are solved and the second-order perturbed charge density is obtained. It is useful to highlight atomic and bond contributions to understand the relation between molecular structure and properties. Four moderately sized molecules (para-nitroaniline and derivatives thereof) are investigated to assess the accuracy of the time-dependent density-functional theory computations and to investigate the distribution of the second-order charge density as well as the "beta density." Our results highlight the contributions from atoms and bonds on different functional groups to the total value of beta with Mulliken-type and natural bond orbital (NBO) analyses, and demonstrate in some cases how contributions from a particular bond may be identified easily by visual inspection of the beta density. In addition, the position of side group substitution on carbon-carbon bonds significantly affects the hyperpolarizability. A contribution analysis as performed here might be helpful for the design of new materials with desired properties.     

Linear-scaling formation of Kohn-Sham Hamiltonian: application to the calculation of excitation energies and polarizabilities of large molecular systems

We present calculations of excitation energies and polarizabilities in large molecular systems at the local-density and generalized-gradient approximation levels of density-functional theory (DFT). Our results are obtained using a linear-scaling DFT implementation in the program system DALTON for the formation of the Kohn-Sham Hamiltonian. For the Coulomb contribution, we introduce a modification of the fast multipole method to calculations over Gaussian charge distributions. It affords a simpler implementation than the original continuous fast multipole method by partitioning the electrostatic Coulomb interactions into "classical" and "nonclassical" terms which are explicitly evaluated by linear-scaling multipole techniques and a modified two-electron integral code, respectively. As an illustration of the code, we have studied the singlet and triplet excitation energies as well as the static and dynamic polarizabilities of polyethylenes, polyenes, polyynes, and graphite sheets with an emphasis on the trends observed with system size.     

Molecular polarizabilities and induced dipole moments in molecular mechanics

Molecular polarizabilities may be divided into either atomic contributions or bond contributions. The common way to estimate molecular polarizabilities is to assign atomic or bond parameters for each atom or bond type to fit experimental or quantum mechanical results. In this study we have taken a different approach. A general formula based on MM3 force constants and bond lengths was used to compute bond polarizabilities and molecular polarizabilities. New parameters for polarizabilities are not required. A fair agreement between experimental and computed molecular polarizabilities was obtained, with a RMS deviation of 0.82 ų (11.7%) and signed average error of 0.01 ų for a broad selection of 57 molecules studied. Two methods, the many‐body interaction and the pair‐interaction approaches, have been used to study induced dipole moments using the bond polarizabilities estimated from the new formula. The pair‐interaction approximation, which involves much less computation than the many‐body interaction approach, gives a satisfactory representation of induced dipole interaction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 813–825, 2000     

Charge distributions and multipole moments in molecules

The consideration of multipole moments is suggested as a new criterion for the validity of assignments of atomic charges in molecules. The total quadrupole and octupole moments generated by our definition of atomic charges are compared with the exact moments of the underlying wavefunction for various basis sets in selected diatomics. The analysis includes also total overlap and total dipole moment partitioning as well as 1σ MO overlap partitioning. All considerations together allow us to assess the validity of our charge definition as compared to Mulliken's and Löwdin's and the quality of the basis set.     

Local properties of quantum chemical systems: the LoProp approach

A new method is presented, which makes it possible to partition molecular properties like multipole moments and polarizabilities, into atomic and interatomic contributions. The method requires a subdivision of the atomic basis set into occupied and virtual basis functions for each atom in the molecular system. The localization procedure is organized into a series of orthogonalizations of the original basis set, which will have as a final result a localized orthonormal basis set. The new localization procedure is demonstrated to be stable with various basis sets, and to provide physically meaningful localized properties. Transferability of the methyl properties for the alkane series and of the carbon and hydrogen properties for the benzene, naphtalene, and anthracene series is demonstrated.     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

Linear-scaling calculation of static and dynamic polarizabilities in Hartree-Fock and density functional theory for periodic systems

We present a linear-scaling method for analytically calculating static and dynamic polarizabilities with Hartree-Fock and density functional theory, using Gaussian orbitals and periodic boundary conditions. Our approach uses the direct space fast multipole method to evaluate the long-range Coulomb contributions. For exact exchange, we use efficient screening techniques developed for energy calculations. We then demonstrate the capabilities of our approach with benchmark calculations on one-, two-, and three-dimensional systems.     

A Hirshfeld partitioning of polarizabilities of water clusters

A new Hirshfeld partitioning of cluster polarizability into intrinsic polarizabilities and charge delocalization contributions is presented. For water clusters, density-functional theory calculations demonstrate that the total polarizability of a water molecule in a cluster depends upon the number and type of hydrogen bonds the molecule makes with its neighbors. The intrinsic contribution to the molecular polarizability is transferable between water molecules displaying the same H-bond scheme in clusters of different sizes, and geometries, while the charge delocalization contribution also depends on the cluster size. These results could be used to improve the existing force fields.     

Multipole polarizabilities and shielding factors of the hydrogen atom from the hydrodynamic analogy to quantum mechanics. III

Variational iterative solutions for multipole polarizabilities of the H atom have been carried out. The resulting numerical values of the Cauchy coefficients are in harmony with our recent work. The large frequency expansion of the multipole polarizabilities of the H atom is also calculated. The first term in such expansions, the multipole oscillator strength sum rule, is in harmony with earlier work.     

The elusive atomic rationale for DNA base pair stability

A systematic analysis of the electrostatic interaction between 27 natural DNA base pairs was carried out, based on ab initio correlated wave functions and the topology of the electron density. Using high rank multipole moments we show that the atomic partitioning of the interaction energy contains many substantial contributions between distant atoms. Profiles of cumulative energy versus internuclear distance show large fluctuations and provide an electrostatic fingerprint of the partitioning of interaction energy in a complex. A quantified comparison between each pair of energy profiles, one for each base pair, makes clear that there is no correlation between the total base pair interaction energy and the shape of the profile. In other words, base pairs with similar interaction energy are not stable for the same reasons in terms of atomic partitioning. In summary, simple rules to rationalize the pattern of energetic stability of naturally occurring base pairs in terms of subsets of atoms are elusive. Our work cautions against inappropriate use of Jorgensen's secondary interaction hypothesis.     

An analysis of dynamic linear response properties at RPA level

A separation of the dynamic linear response is developed, which distinguishes between the one- and two-electron contributions to the molecular response, by partitioning the RPA equation. The derivation of the partitioning is given in both an RPA , equation of motion, type approach and using the alternative, but equivalent, density matrix method. Three physically distinct contributions are obtained, called the direct, interaction, and back contributions. The direct term is composed entirely of one-electron effects, while the interaction and back terms account for the electron-interaction contributions to the response. Results for the dynamic dipole polarizability suggest that while the one-electron contribution is dominant in the zero-frequency limit, the two-electron contribution becomes increasingly important as the frequency of the perturbation increases. This implies that approximation of the linear response by only one-electron contributions is acceptable for the static case, but is less relevant for the dynamic case. The ramifications of this observation, for the scaling of sum-over-states-type calculations of large molecular systems, is briefly discussed, as is the application of our partitioning method to the higher polarizabilities. © 1995 John Wiley & Sons, Inc.