Stark effect,polarizabilities and the electric dipole moment of heteronuclear diatomic molecules in 1Σ states

The theory of second-order Stark effect in ¹Σ states of heteronuclear diatomic molecules is thoroughly reviewed. The rigorous treatment given demonstrates that by introducing rotational, vibrational and electronic branch polarizabilities, the intrinsic character of the second-order Stark effect in diatomic molecules can be shown to be related more closely to polarizabilities than to dipole moments. The well-known expression for the Stark shift in ¹Σ levels which is dominated by the square of the dipole moment is only a crude, though sufficient approximation whenever large dipole moments are involved. For small dipole moments, however, this approximation is likely to fail, leading to an erroneous determination of such dipole moments. In the limiting case of negligible influence of the molecular rotation on the vibronic matrix elements, the arithmetic mean of the electronic branch polarizabilities turns out to be equal to the well-known static electronic polarizabilities α_∥ and α_⊥. The results are applied to the interpretation of the Stark splitting in the A¹Σ⁺, υ′ = 5, J′ = 1 level of ⁷LiH, recently determined by Stark quantum-beat spectroscopy.     

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.     

Calculation of molecular polarizabilities: the indo method applied to some aromatic hydrocarbons1

Molecular polarizabilities calculated by the all valence electron INDO method are reported for benzene, naphthalene, anthracene, phenanthrene, biphenyl and p-terphenyl. For these molecules INDO is better than other semi-empirical methods at predicting the polarizability anisotropy.     

Perturbation theories and wave functions for calculation of electronic polarizabilities application to DNA bases

Three different forms of perturbation theories, variational perturbation, finite perturbation and second-order, are evaluated regarding their value for calculation of electronic polarizabilities of small and intermediate size molecules. It is concluded that with the practical constraint of a small basis set the variational perturbation method is the most promising alternative for calculation of polarizabilities. For several small molecules, our calculated polarizabilities indicate that both IEHT and ab initio wave functions give values in close agreement with each other. Variational perturbation calculations of polarizabilities with IEHT wave functions also include the DNA bases.     

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     

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.     

Spherical tensor theory of long-range intermolecular forces

General expressions are given for the electrostatic, induction and dispersion energies of a pair of interacting, molecules in terms of spherical tensor components of the molecular multipole moments and polarizabilities. The orientation dependence is given in terms of the scalar expansion functions S_l1l2l^k1k2.     

How important are temperature effects for cluster polarizabilities?

State-of-the-art first-principle all-electron density functional theory calculations on small sodium clusters are performed to study the temperature dependency of their polarizabilities. For this purpose Born-Oppenheimer molecular dynamics simulations with more than 100,000 time steps (>200 ps) are recorded employing gradient corrected functionals in combination with a double-zeta valence polarization basis set. For each cluster 18 trajectories between 50 and 900 K are collected. The cluster polarizabilities are then calculated along these trajectories employing a triple-zeta valence polarization basis set augmented with field-induced polarization functions. The analysis of these calculations shows that the temperature dependency of the sodium cluster polarizabilities varies strongly with cluster size. For several clusters characteristic changes in the polarizability per atom as a function of temperature are observed. It is shown that the inclusion of finite temperature effects resolves the long-standing mismatch between calculated and measured sodium cluster polarizabilities.     

Transferability in the natural linear-scaled coupled-cluster effective Hamiltonian approach: Applications to dynamic polarizabilities and dispersion coefficients

A natural linear-scaled coupled-cluster (CC) method has been developed to calculate the response properties of large molecules, for example, dynamic polarizabilities and dispersion coefficients. The method is based on the transferability of the CC effective Hamiltonian from the equation-of-motion (EOM)-CC methods, subject to its representation in terms of highly transferable natural localized molecular orbitals. This transferability allows the interactions among regions in a molecule to be classified according to their important inter-region excitations and de-excitations. Dynamic polarizabilities determined in this way provide insight into calculating the excited states of large molecules using localized orbital concepts. Dispersion coefficients for the interactions within large molecules can be similarly determined. These could be useful in constructing corrective long-range potentials. Applications to alkanes, tryptophan, and polyglycine are presented. For those cases which are possible, conventional results can be reproduced. Dynamic polarizabilities of tryptophan indicate that the first excited state is localized to the indole group, while the second is localized to the carboxyl group.     

Determination of average molecular polarizabilities of polycyclic aromatic hydrocarbons directly from retention indices

Summary A significant correlation has been found between the retention indices of polycyclic aromatic hydrocarbons on non-polar stationary phases and the average molecular polarizabilities of the molecules separated on these phases. Equations have been derived for the determination of the average molecular polarizabilities, directly from the retention indices.     

Second-order properties of bonds

By defining a localized hamiltonian for a saturated molecule its second order molecular properties may be regarded as a sum of bond contributions. Static and dynamic polarizabilities are calculated for the CH bond in methane and the latter one used to calculate the van der Waals interaction between two CH₄ molecules.     

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.     

Electronic structure and hyperpolarizability of some conjugated molecules in excited states

For the examples of aromatic and antiaromatic five-membered heterocycles, the static electronic polarizabilities and hyperpolarizabilities are determined in the ground and first singlet- and triplet-excited electronic states. The theoretical calculations are carried out in the SOS formalism and the correlation effects are taken into account using all mono- and biexcited configuration in the PPP approximation. It is shown that the singlet excitation of the molecules for the antiaromatic case is connected to an significant decrease of both polarizabilities and hyperpolarizabilities. Their values are discussed in terms of the index of average bond-order alternation for the ground and excited states and the localization of the electronic transitions in the molecules. © 1993 John Wiley & Sons, 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.     

Conformational characteristics of polyethylene glycol macromolecules in aqueous solutions according to refractometry data

The aqueous solutions of polyethylene glycols with molecular masses of 600, 1000, 1500, 3000, 6000, and 20000 were studied by refractometry. The conformational polarizabilities, mean-square distances between the ends of the macromolecular chain, segment lengths, and the number of Kuhn segments in a macromolecule were determined using the Lorentz-Lorentz equation. The polarizability of a hydrated macro-molecule was represented as the sum of polarizabilities of the nonhydrated macromolecule with retained conformation and polarizabilities of the water molecules involved in hydration of macromolecules. The size of macromolecules stabilized starting from a certain concentration. It was concluded that the initial concentration of stabilization shifts toward low concentrations as the molecular mass of polyethylene glycol increases. The dependence of the mean-square distance between the ends of the macromolecular chain on the number of Kuhn segments was expressed as the exponential function with index 0.3.     

Structure-retention studies on the inclusion complex formation of some polycyclic aromatic hydrocarbons with β-cyclodextrin

Summary The retention behaviour of a group of polycyclic aromatic hydrocarbons having nearly equal ionization potentials but different molecular polarizability values was investigated using reversed-phase HPLC. Methanol-water binary systems containing -cyclodextrin were applied as the mobile phase. The relationships between the capacity factors, molecular polarizabilities and the shape parameter of solute molecules are discussed.     

Intermolecular forces for D2, N2, O2, F2 and CO2

The intermolecular potentials for D₂, N₂, O₂, F₂ and CO₂ are determined on the basis of the second virial coeffincients, the polarizabilities parallel and perpendicular to the molecular axes, and the electric quadrupole moment. The repulsive parts of the potentials are taken from the corresponding Kihara core-potentials. Effects of the octopolar induction are taken into consideration in a unique way. The potential depends on relative orientations of the two molecules as well as the distance r between the molecular centers. This dependence is shown in graphs. A measure of the anisotropy of the potential depth is 0.72 for CO₂ 0.36 for D₂, and smaller than 0.27 for N₂ O₂ and F₂. The remarkable anisotropy for CO₂ and D₂ is due to strong electrostatic quadrupole interactions.     

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.