Molecule‐specific determination of atomic polarizabilities with the polarizable atomic multipole model

Recently, many polarizable force fields have been devised to describe induction effects between molecules. In popular polarizable models based on induced dipole moments, atomic polarizabilities are the essential parameters and should be derived carefully. Here, we present a parameterization scheme for atomic polarizabilities using a minimization target function containing both molecular and atomic information. The main idea is to adopt reference data only from quantum chemical calculations, to perform atomic polarizability parameterizations even when relevant experimental data are scarce as in the case of electronically excited molecules. Specifically, our scheme assigns the atomic polarizabilities of any given molecule in such a way that its molecular polarizability tensor is well reproduced. We show that our scheme successfully works for various molecules in mimicking dipole responses not only in ground states but also in valence excited states. The electrostatic potential around a molecule with an externally perturbing nearby charge also exhibits a near‐quantitative agreement with the reference data from quantum chemical calculations. The limitation of the model with isotropic atoms is also discussed to examine the scope of its applicability. © 2012 Wiley Periodicals, Inc.     

Calculations of dynamic dipole polarizabilities of Li and Na atoms in debye plasma using the model potential technique

The effects of Debye plasma on the frequency‐dependent polarizabilities of Li and Na atoms are investigated using symplectic algorithm within the framework of the pseudostate summation technique. Dynamic dipole polarizabilities of Li (2s ²S) and Na(3s ²S) as functions of scaled number density of the plasma electrons for arbitrary plasma temperature are presented. Screening effects on the resonance frequencies are also presented. In free‐atomic cases, our calculated results are comparable with the reported theoretical and experimental predictions. © 2012 Wiley Periodicals, Inc.     

Theory of intermolecular interactions: The long range terms in the dipole–dipole,monopoles–dipole,and monopoles–bond polarizabilities approximations

The problem of evaluating the long range terms (electrostatic, polarization, dispersion) of the interaction energy between molecules at intermediate distances (i.e. distances of the order of magnitude of the molecular dimensions) is considered. Instead of being approximated by its dipole part, the exact interaction Hamiltonian is treated as proposed by Longuet-Higgins [11], i.e. the matrix elements are interpreted as electrostatic interactions between state and transition charge distributions. These charge distributions are approximated in a systematic way by sets of point charges (localized on the atoms) or sets of dipoles (localized on the bonds). The various contributions to the energy may then be expressed in terms of atomic net charges and bond polarizabilities. More refined approximations of the charge distributions could be used and correspondingly improved formulae could be derived: as an example, a formula for the σ-π dispersion energy is derived, where the σ charge distributions are approximated by bond transition dipoles (leading to σ bond polarizabilities in the final formula) while the π charge distributions are approximated by atomic charges.     

Hirshfeld‐based intrinsic polarizability density representations as a tool to analyze molecular polarizability

In this work, a general scheme to visualize polarizability density distributions is proposed and implemented in a Hirshfeld‐based partitioning scheme. This allows us to obtain easy‐to‐interpret pictorial representations of both total and intrinsic polarizabilities where each point of the density is formed by the contribution of any atom or group of atoms in the molecule. In addition, the procedure used here permits the possibility of removing the size dependence of the electric‐dipole polarizability. Such a development opens new horizons in exploring new applications for the analysis of the molecular polarizability tensor. For instance, this visualization shows which atoms or regions are more polarizable distinguishing, moreover, the fine structure of atoms affected by the vicinity, and might extend the dipole polarizability as a tool for aromaticity studies in polycyclic aromatic hydrocarbons. Additionally, this approach can serve us to assess the methods performance in describing the interaction of electric fields with a molecule and local electron correlation effects in intrinsic polarizabilities. © 2015 Wiley Periodicals, Inc.     

Accurate parametrized variational calculations of the molecular electronic polarizability by NDDO‐based methods

The variational method for the calculation of the electronic polarizability of molecules within the NDDO‐based semiempirical MO methods MNDO, AM1, and PM3 was parametrized to improve its accuracy. A training set of 156 compounds was used to fit 34 parameters simultaneously for 12 elements using a simplex optimization. The resulting parameters were tested for a test set of 83 molecules and the calculated polarizabilities compared with the experimental data. For AM1, the RMS deviation between experimental and calculated polarizabilities was reduced from 2.99 (using the original variational treatment) to 0.70 ų for the test set and from 2.81 to 0.40 ų for the training set. MNDO and PM3 gave similar improvements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 17–31, 1999     

Quantum chemical investigation of linear hydrogen bonding in ONCCN···HX (X = F,Cl, Br) dimers

Linear hydrogen bonding formed between the nitrogen end of cyanogen‐N‐oxide (ONCCN) and hydrogen halides HX (X = F, Cl, Br) has been observed in their ground Σ states. The order of agreement of energetic stabilities between the correlated functionals used in this calculation is: B3LYP < PBE0 < PBE < PW91 in conjunction with the 6–311++G(3df,3pd) basis set. Analysis of various parameters describing the existence of H‐bonds in these dimers follows the conventional trend: ONCCN···HF > ONCCN···HCl > ONCCN···HBr in the series, except H‐bond lengths and static dipole polarizabilities which are in reverse order. The atomic charges obtained from the Mulliken and natural population analysis is used to assess the charge transfer effects that accompany the dimer formation. It is found from the investigation that the dimers having highest binding energy are accompanied by the highest transfer of charge. The ¹⁴N nuclear quadrupole coupling constants of the monomer ON¹CCN² are found to be decreased upon complection and in the series it increases from F through Br. We observed enhancements in the values of the dimer dipole moment and intrinsic dipole polarizabilities compared with the sum of the monomer values by intermolecular electrical interaction. Investigation reveals vibrational spectral shifts of HX and CN stretching modes similar to the conventional red‐shifted H‐bonded dimers; for the former case, the infrared band intensity increases significantly. Finally, the new vibrational modes originated from the intermolecular interaction are outlined. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Comparative study of unscreened and screened molecular static linear polarizability in the Hartree–Fock,hybrid‐density functional,and density functional models

The sum‐over‐states (SOS) polarizabilities are calculated within approximate mean‐field electron theories such as the Hartree–Fock approximation and density functional models using the eigenvalues and orbitals obtained from the self‐consistent solution of the single‐particle equations. The SOS polarizabilities are then compared with those calculated using the finite‐field (FF) method. Three widely used mean‐field models are as follows: (1) the Hartree–Fock (HF) method, (2) the three parameter hybrid generalized gradient approximation (GGA) (B3LYP), and (3) the parameter‐free generalized gradient approximation due to Perdew–Burke–Ernzerhof (PBE). The comparison is carried out for polarizabilities of 142 molecules calculated using the 6‐311++G(d,p) basis set at the geometries optimized at the B3LYP/6‐311G** level. The results show that the SOS method almost always overestimates the FF polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF method. A few exceptions to these trends are found. The mean absolute errors (MAE) in the screened (FF) and unscreened (SOS) polarizability are 0.78, 1.87, and 3.44 ų for the HF, B3LYP, and PBE‐GGA methods, respectively. Finally, a simple scheme is devised to obtain FF quality polarizability from the SOS polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A density functional theory-based chemical potential equalisation approach to molecular polarizability

The electron density changes in molecular systems in the presence of external electric fields are modeled for simplicity in terms of the induced charges and dipole moments at the individual atomic sites. A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few illustrative numerical calculations are shown to predict the molecular polarizabilities in good agreement with available results. The usefulness of the approach to the calculation of intermolecular interaction needed for computer simulation is highlighted.     

Rayleigh light scattering from hydrogen‐bonded dimers of small astrophysical molecules

High level ab initio calculations of the Rayleigh scattering activities of the hydrogen‐bonded dimers of formic acid (HCOOH), nitrosyl hydride (HNO), and hydrogen cyanide (HCN) molecules have been performed. All these molecules have already been detected in interstellar space and are of great importance from the astrochemical point of view. The geometries of the homo‐ and hetero‐dimers have been optimized using Hartree–Fock and second‐order Møller‐Plesset perturbation theory. Dipole moment, mean dipole polarizability, and polarizability anisotropy have been calculated utilizing Pople‐type 6‐311++G(d,p) and Dunning's aug‐cc‐pVDZ basis sets for all the complexes. The polarizabilities are then used to calculate and analyze the Rayleigh scattering parameters. The results for the dimers, HCN···HCN, HCOOH···HCOOH, HNO···HNO, HCN···HCOOH, HCN···HNO, and HNO···HCOOH are compared with those of the isolated molecules, HCN, HCOOH, and HNO to see the effect of hydrogen bond formation on the molecular interaction with radiation. © 2011 Wiley Periodicals, Inc.     

Partitioning of higher multipole polarizabilities: numerical evaluation of transferability

In this work, the partitioning of higher multipole polarizabilities, such as dipole-quadrupole, quadrupole-dipole, and quadrupole-quadrupole polarizabilities, into atomic contributions is studied. Partitioning of higher multipole polarizabilities is necessary in the study of accurate interaction energies where dispersion interactions are of importance. The fractional occupation Hirhsfeld-I (FOHI) method is used to calculate the atomic polarizabilities and is briefly explained together with the methodology for partitioning of the polarizabilities. The atomic multipole polarizabilities are calculated for different sets of molecules, linear alkanes, water clusters, and small organic molecules with different functional groups. It is found that the atomic and group contributions of the dipole and quadrupole polarizabilities are transferable as a function of the functional groups.     

Contracted basis sets for electrical property calculations derived from Second-order Møller–Plesset theory atomic natural orbitals

 Using established methods based on correlated atomic natural orbitals (ANOs), sets of contracted polarization functions are derived for use in calculations of atomic and molecular electrical properties (especially electric moments, dipole polarizabilities and related property hypersurfaces). Through test calculations on Ne, Ar, NH₃ and CO₂, these polarization functions are shown to reproduce the accuracy of larger basis sets, to incorporate dynamical electron correlation effects and are economical to use in conjunction with sophisticated electron-correlation treatments. We also show how triple-zeta polarized ANO and double-zeta polarized ANO basis sets are constructed from these contracted polarization functions for use in the calculation of reliable zero-point vibrational averages of electrical properties. Received: 20 December 1999 / Accepted: 15 February 2000 / Published online: 12 May 2000     

A DFT Quantum‐Chemical Study of Ion‐Pair Formation for the Catalyst Cp2ZrMe2 /MAO

A process of ion‐pair formation in the system Cp₂ZrMe₂/methylaluminoxane (MAO) has been studied by means of density functional theory quantum‐chemical calculations for MAOs with different structures and reactive sites. An interaction of Cp₂ZrMe₂ with a MAO of the composition (AlMeO)₆ results in the formation of a stable molecular complex of the type Al₅Me₆O₅Al(Me)O–Zr(Me)Cp₂ with an equilibrium distance r(Zr–O) of 2.15 Å. The interaction of Cp₂ZrMe₂ with “true” MAO of the composition (Al₈Me₁₂O₆) proceeds with a tri‐coordinated aluminum atom in the active site (OAlMe₂) and yields the strongly polarized molecular complex or the μ‐Me‐bridged contact ion pair ( d ) [Cp₂(Me)Zr(μMe)Al≡MAO] with the distances r(Zr–μMe) = 2.38 Å and r(Al–μMe) = 2.28 Å. The following interaction of the μ‐Me contact ion pair ( d ) with AlMe₃ results in a formation of the trimethylaluminum (TMA)‐separated ion pair ( e ) [Cp₂Zr(μMe)₂AlMe₂]⁺–[MeMAO]^– with r[Zr–(MeMAO)] equal to 4.58 Å. The calculated composition and structure of ion pairs ( d ) and ( e ) are consistent with the ¹³C NMR data for the species detected in the Cp₂ZrMe₂/MAO system. An interaction of the TMA‐separated ion pair ( e ) with ethylene results in the substitution of AlMe₃ by C₂H₄ in a cationic part of the ion pair ( e ), and the following ethylene insertion into the Zr–Me bond. This reaction leads to formation of ion pair ( f ) of the composition [Cp₂ZrCH₂CH₂CH₃]⁺–[Me‐MAO]^– named as the propyl‐separated ion pair. Ion pair ( f ) exhibits distance r[Zr–(MeMAO)] = 3.88 Å and strong C_γ‐agostic interaction of the propyl group with the Zr atom. We suppose this propyl‐separated ion pair ( f ) to be an active center for olefin polymerization.     

Excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state of diphenylpolyenes

This paper discusses the excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state (S₁) of diphenylpolyenes by using the time‐dependent density functional theory. Two hybrid exchange‐correlation (xc) potentials Becke‐3 Lee‐Yang‐Parr (B3LYP) and Perdew‐Burke‐Ernzerhof (PBE1PBE) were employed. Our calculations indicate that the magnitude of the excess polarizability will decrease while the molecule evolves from the unrelaxed S₁ state to the relaxed S₁ state. This decreasing trend is found to be independent of substituents, though substituents can change the value of the excess polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Polarizability of negatively charged helium‐like ions interacting with Coulomb and screened Coulomb potentials

The dipole and quadrupole polarizabilities (both static and dynamic) of negatively charged helium‐like ions are investigated. The mass dependence of the polarizability is studied by changing the mass of the positively charged particle from one unit of electron mass to infinitely heavy. The calculations are carried out in the framework of the pseudostate summation method using exponential correlated wave functions having pseudorandomly generated nonlinear variational parameters. The dipole and quadrupole polarizabilities in terms of frequency and nuclear mass are reported for the first time. The effect of screened Coulomb potentials on the polarizabilities of D^–, T^–, ¹H^–,Pi^–, Mu^–, and Ps^– are also presented.     

Study of the molecular configuration and the dipole moment in fluorinated liquid crystals

We have investigated the relationship between the molecular configuration and dipole moment of some fluorinated liquid crystals (LCs). The geometries of the molecules were preliminarily optimized at empirical AM1 and then were further optimized at B3LYP/6‐31G(d) level. The dipole moment has been calculated. It is strongly influenced by the position and number of fluorine substituents in the benzene ring of the molecule. The polarizability, mean polarizabilities, and anisotropic polarizability of the phenylbicyclohexane (PBC) fluorine substituents are also given and discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the generation of MCs+ ions in SIMS with Cs+ primary beams

The formation of MCs⁺ secondary ions in SIMS operated with Cs⁺ ion beams is discussed on the basis of a well-confirmed quadratic dependence of MCs⁺ yields on the atomic polarizabilities of elements M contained in semiconductor samples. This behavior is understood by the generation of a dipole induced in M by the positive charge of a neighboring Cs⁺ projectile and the mutual induction of a dipole in Cs⁺, both dipoles depending on the atomic polarizability of M. An evaluation of the dipole–dipole interaction energy indicates that MCs⁺ ions generated at the target are emitted according to the direct emission model (DEM). This mechanism is in contrast with an association model where constituents of MCs⁺ are assumed to combine after their independent sputter emission.     

An atomic charge study of highly ionic diatomic molecular systems

Four atomic charge formalisms are compared using highly ionic diatomic molecules, such as LiF, NaF, KF, LiCl, NaCl, KCl, BF, AlF, GaF, BeO, and MgO. All calculations were done at the QCISD/6‐311G(2df) level. The only formalism consistent with the characteristics of all these systems is Quantum theory of atoms in molecules (QTAIM). Absolute Mulliken charge values are small. ChelpG charges are not reliable for systems in which the atoms are largely anisotropic. Generalized atomic polar tensor values are contaminated with charge fluxes and atomic dipole fluxes and fail when these contributions are important and do not cancel each other. Finally, the charge–charge flux–dipole flux model was applied to dipole moment derivatives with QTAIM. This analysis shows that charge flux and atomic dipole flux contributions during bond stretching are almost null, except for oxides. There are also evidences that the lone electron pair at Group 13 elements in fluorides becomes less localized as the bond is stretched. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010