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.     

Calculated polarizabilities for some aliphatic and aromatic hydrocarbons

Ground-state molecular polarizabilities of some aliphatic and aromatic hydrocarbons have been calculated using the method of Marchese and Jaffé. The polarizability components for the typical normal alkane n-heptane are found to be very nearly independent of conformation; those for biphenyl show a significant dependence but the average polarizability is approximately constant. The polarizabilities of the n-alkanes in general are seriously underestimated, but relatively good agreement with experiment is obtained for benzene and biphenyl.     

A fast empirical method for the calculation of molecular polarizability

Summary A simple empirical method for the calculation of static molecular polarizability is described. The method is based on Slater's rules for the calculation of effective atomic nuclear shielding constants. The calculated molecular polarizabilities of a series of organic molecules correlated well (r=0.98) with experimental measurements. Accurate calculated polarizabilities can be obtained rapidly by this method and may prove useful in deriving relationships between chemical structure and properties.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

Anomalous density and refractive index variation of a nematic liquid crystal

This paper reports the results of the measurement of refractive indices and densities of p-ethoxyphenyl trans-4-butyl cyclohexane carboxylate at different temperatures. The molecular polarizabilities have been calculated from refractive indices using Vuks' formula and orientational order parameters are determined from the polarizability values. The order parameter values have been compared with those obtained from Maier-Saupe theory. The compound shows anomalous behaviour regarding variation of density, ordinary refractive index and order parameter values with temperature. This is consistent with our previous X-ray study of this compound. The possible reason for this peculiar behaviour has been discussed.     

On the Determination of Partial Molar Volumes,Partial Molar Refractions,Mean Electronic Polarizabilities and Effective Molecular Radii from Dilute Multi-component Data alone using Response Surface Models

A quaternary system consisting of three solutes, namely ethanol, diethylene glycol (DEG) and triethylene glycol (TEG) in benzene at 298.15 K and 1.0125 × 10⁵ Pa was studied. An experimental design in the range of concentration 0.006 < x _solute−i < 0.023 was explored, optimizing the metric distance among the solutes to avoid clustering. On-line simultaneous experimental measurements using a densitometer and a refractometer were utilized to measure bulk solution density and bulk refractive index, respectively. Response surface models describing the total molar volume and total molar refraction were employed to determine the partial molar volumes and the partial molar refractions of each solute from the dilute multi-component data alone. Neither densities nor refractive indices of any of the pure components were used and no binary information was required for the analysis. Definitions for the mean electronic polarizability and the effective molecular radius of a solute based on the partial molar refraction were introduced. Subsequently, the mean electronic polarizabilities and the effective molecular radii for each solute in multi-component solutions, as well as the solvent were determined. The results obtained for the partial molar volumes, partial molar refractions, electronic polarizabilities and the effective molecular radii were in good agreement with those obtained from independent binary experiments as well as those from literature binary data.     

Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields

New derivations are given of equations relating molecular electric multipole moments and polarizabilities of general order to the electrostatic energy. The unabridged moment convention is shown to yield relatively simple relations between derivatives of the energy with respect to field gradients and the multipole moments and polarizabilities. Care is taken to distinguish various forms of these derivatives, and one form leads to a proof of a general symmetry of polarizability tensors with respect to permutations of rank indices. The condition of internal equilibrium is shown to be fundamental to the existence of this symmetry. The transformation of multipole moment and polarizability tensors under translation of the coordinate origin is expressed in relatively simple general form. The traceless multipole and polarizability tensors of Buckingham and McLean and Yoshimine are obtained as linear combinations of the unabridged tensors and their traces.     

Effective molecular polarizabilities and crystal refractive indices estimated from x-ray diffraction data

Although it was proposed some time ago that (hyper)polarizabilities might be estimated from the results of x-ray charge density refinements, early results were unconvincing. In this work we show that the one particle density obtained from the usual multipole refinement model does not contain sufficient information to determine these response properties and instead pursue the "constrained wave function" approach of fitting to x-ray structure factors. Simplified sum-over-states expressions are derived for determining the dipole polarizability from these wave functions, and these clearly show that the earlier work ignored important two-electron expectation values for the dipole polarizability, and two- and three-electron terms for Beta, etc. Correction factors for the simplified sum-over-states polarizability tensors from the constrained wave function are obtained by calibration against coupled Hartree-Fock ab initio results to yield in-crystal effective polarizability tensors. Results obtained for benzene, urea, and 2-methyl-4-nitroaniline demonstrate that the effective molecular polarizabilities clearly include the effects of intermolecular interactions and electron correlation, especially for urea where the effects on the polarizability are known to be quite large. We also carefully consider the way in which the linear bulk susceptibility, chi((1)), and refractive indices are determined from the x-ray fitted polarizabilities, employing three models based on a rigorous treatment of the local field. Incorrect results are obtained for the sort of molecules that are of interest in nonlinear optical applications if the molecules are approximated by single point dipoles. In contrast, the use of Lorentz-factor tensors averaged over several sites yields excellent results, with refractive indices obtained using this model in remarkably good agreement with optical measurements extrapolated to zero frequency.     

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.     

Anomalous density and refractive index variation of a nematic liquid crystal

Abstract

This paper reports the results of the measurement of refractive indices and densities of p-ethoxyphenyl trans-4-butyl cyclohexane carboxylate at different temperatures. The molecular polarizabilities have been calculated from refractive indices using Vuks' formula and orientational order parameters are determined from the polarizability values. The order parameter values have been compared with those obtained from Maier-Saupe theory. The compound shows anomalous behaviour regarding variation of density, ordinary refractive index and order parameter values with temperature. This is consistent with our previous X-ray study of this compound. The possible reason for this peculiar behaviour has been discussed.     

Effective molecular polarizabilities in some aromatic hydrocarbon crystals

Two equivalent methods of calculating effective molecular polarizabilities from crystal electric susceptibilities are compared. For monoclinic crystals containing two molecules per unit cell, there is no unique solution. The range of solutions is examined for naphthalene, anthracene, biphenyl, p-terphenyl and phenanthrene, treated as polarizable points. For all these molecules the largest polarizability component is unacceptable, owing to the point molecule approximation. When the interactions between molecules are calculated as averages between aromatic rings, more realistic polarizabilities result, showing variations consistent with the molecular geometry. Comparable results are obtained for benzene (orthorhombic). It is concluded that reliable polarizabilities should become available by developments of such an approach.     

A new form of electric-field-dependent basis functions for the calculation of electric polarizabilities and dipole moments

An ab-initio molecular orbital theory of electrical polarization is presented in which the molecular orbitals are written as linear combinations of atomic functions which depend explicitly on the strength of a uniform external electric field. The wavefunctions in the presence of such a field are determined using self-consistent field perturbation theory. It is shown that the use of field-dependent atomic functions provides an efficient technique for the calculation of electric polarizability tensors. Polarizability tensors and electric-dipole moments calculated using both a minimal and a split-valence-shell basis set are compared with experimental results. Both polarizability-tensor components and dipole moments are seriously underestimated at the minimal bases-set level. The split-valence basis approach yields substantially better results; the calculated values at this level are in reasonable agreement with the corresponding experimental values. The experimental ordering of isotropic polarizabilities for a set of small molecules is duplicated quite closely by both the minimal and the split-valence-shell calculations.     

On the dipole and higher polarizabilities of Ne(1S)

The dipole polarizability and the higher-order polarizabilities of Ne(¹S) are calculated in the LCAO SCF approximation. The higher polarizabilities are found to be strongly basis-set dependent. Our final values for α, C, B and γ are 2.37, 2.04, -13.6 and 78 (in atomic units).     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

The inclusion of electron correlation in intermolecular potentials: applications to the formamide dimer and liquid formamide

A test of the quality of the electrostatic properties and polarizabilities used in the nonempirical molecular orbital (NEMO) potential is carried out for formamide by calculating the molecular dipole moment and polarizability at the second-order M?ller–Plesset (MP2) level of theory. The molecular dipole moment is 11% lower at the MP2 level than at the Hartree–Fock (HF) level, whereas the isotropic part of the polarizability is increased by 36% by adding electron correlation and using a considerably larger basis set. The atomic charges, dipole moments and polarizabilities obtained at the HF level are rescaled to get the correct molecular properties at the MP2 level. The potential minimum for the cyclic dimer of formamide is −17.50 kcal/mol with the MP2-scaled properties and is significantly lower than other potentials give. Two intermolecular potentials are constructed and used in subsequent molecular dynamics simulations: one with the regular NEMO potential and the other with the rescaled MP2 properties. A damping of the electrostatic field at short intermolecular distances is included in the present NEMO model. The average energies for liquid formamide are lower for the MP2-scaled model and are in good agreement with experimental results. The lowering of the simulation energy for the MP2-scaled potential indicates the strong dispersive interactions in liquid formamide. Received: 20 March 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

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     

Ab initio dynamic polarizabilities of polymers. I. Hydrogen chain models

Ab initio dynamic polarizabilities per unit cell of infinite stereoregular molecular hydrogen chains are calculated at the coupled Hartree-Fock level of approximation by using the random-phase approximation and the STO -3G and double-zeta atomic basis sets. Comparison with molecular calculations on increasingly large oligomeric chains emphasizes the nice extrapolation property of the polymeric technique that provides asymptotic values very close to the largest oligomeric values. The poles of the polarization propagator associated with the electric dipole polarizability correspond to the singlet excitation energies. Comparisons are performed with other techniques that provide the band gap. © 1996 John Wiley & Sons, Inc.