Dispersion energy constants C 6(A,B), dipole oscillator strength sums and refractivities for Li,N, O,H2, N2, O2, NH3, H2O,NO and N2O

Accurate values for the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C ₆(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H₂, N₂, O₂, NH₃, H₂O, NO, and N₂O. The calculations have been carried out by employing dipole oscillator strength distributions for these species that have been constructed (except in the case of H) by using discrete oscillator strength, photo-absorption, and high energy inelastic scattering data and by requiring the distributions to reproduce the Thomas-Reiche-Kuhn sum rule and, in the case of the molecules, available accurate refractivity and dispersion measurements for the relevant dilute gases. These oscillator strength distributions were also used to evaluate the refractivity R(λ), as a function of wavelength λ in the visible and ultra-violet region below the ultra-violet absorption thresholds, and the dipole oscillator strength sums S _-2l , l = 1, 2, …, 7, for each atom and molecule. The calculated values of R(λ) provide refractivities for wavelengths, especially in the ultra-violet region, for which accurate experimental data are often not available. The accurate results for C ₆(A, B) and for various dipole oscillator strength sums are used to make self-consistent tests of the adequacy of (1) the C ₆(A, A) bounds provided by Padé approximant methods and (2) various semi-empirical formulae for C ₆(A, B). Some problems that can arise in using other procedures to evaluate the S _-2l and C ₆(A, B) are discussed briefly.     

Static multipole polarizability of atoms and ions in the Thomas-Fermi model

A method based on the Thomas-Fermi model for the electrostatic potential is proposed to calculate the multipole polarizabilities α _K of atoms and ions. In the case of highly charged ions an equation having a simple analytical form is derived. The dipole α₁ and quadrupole α₂ polarizabilities of atoms and ions with more than half-filled electron shells are calculated. Translated from Trudy Fizicheskogo Instituta im. P. N. Lebedeva, Lebedev Physics Institute, Russian Academy of Sciences, Moscow, Vol. 195, pp. 179–194, 1989.     

Long range C,N and H atom-atom potential parameters from ab initio dispersion energies for different azabenzene dimers

After comparing theoretically the atom-atom model with the multipole expansion for the dispersion energy, we derive atom-atom potential parameters for C, N and H contacts by fitting the atom-atom dispersion energies to the dispersion interactions calculated by an ab initio method for the following (aza)-benzene molecules: benzene, pyridine, pyridazine, pyrimidine, pyrazine, s-triazine and s-tetrazine. The data base for the fit consists of 1200 randomly chosen configurations for each azabenzene dimer. The optimized parameters for the carbon and hydrogen contacts in particular are not unique ; reasonably good fits are obtained with different parameter sets. A very simple rule, which relates the atom-atom potentials to the isotropic molecular C₆ dispersion coefficients, already leads to good estimates for the parameters. From the empirical parameter sets available in the literature the William-Govers set yields results which are close to our ab initio dispersion energies.     

Spectra of direct excitation of phosphorescence in an isotopic mixed naphthalene crystal

Distributed polarizabilities of a series of n-alkanes C _n H_2n+2 (n = 2-7) in various conformations have been determined using Bader's topological theory of atoms in molecules. Using an appropriate localization scheme, a simple distributed model is constructed, where the methyl and methylene groups are characterized by their dipole polarizability tensors in local frames, and all charge flow polarizabilities between them are retained. A set of average polarizability parameters is proposed that takes into account the local environment of the methyl and methylene groups, and that not only reproduces the polarizability tensor for any member of the n-alkane series in an arbitrary conformation, but also is suitable for the calculation of induction energies.     

Calculations of frequency-dependent properties by multiconfiguration time-dependent Hartree-Fock theory

Some theoretical and computational aspects of MC TDHF theory are analysed and two ways of solving the resulting equations are discussed. Numerical applications to the helium atom and the hydrogen molecule show that the frequency-dependent dipole polarizabilities can be obtained easily and with high accuracy in this approach. The polarizabilities at pure imaginary frequency are used to calculate the C ₆ coefficients for He-He, He-H₂ and H₂-H₂ interactions, also with high accuracy.     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

Atomic C 6 dispersion coefficients: a four-component relativistic Kohn–Sham study

We present C ₆ homo- and heteroatomic dispersion coefficients for all closed-shell atoms of the periodic table based on dipole–dipole polarizabilities at imaginary frequencies calculated using our recent extension of the complex polarization propagator approach to the four-component relativistic Kohn–Sham approach. Lack of proper reference data bars definite conclusions as to which density functional shows the overall best performance, and we therefore call for state-of-the-art wave function-based correlated calculations of dispersion coefficients. Scalar relativistic effects are significant already for elements as light as zinc, whereas spin–orbit effects must be taken into account only for very heavy elements.     

Theoretical studies on the nature and strength of an intermolecular non-covalent Te•••π interaction

ABSTRACT

DFT and MP2 calculations were used to determine the nature of non-covalent tellurium–π interactions in R₂Te???C₆H₆ (R = H, F, Cl, CH₃) and C₄H₄Te???C₆H₆ systems. The results showed that the strength of Te···π interaction follows the order F₂Te > Cl₂Te > tellurophene > H₂Te > Me₂Te. Also, the F₂X···π system complexes (X = Te or Se, π system = C₆F₆, C₆(CH₃)₆, Cr(C₆H₆)₂ and coronene) were studied for investigating the direction of charge flow in Te···π interaction. The obtained data expressed that the existence of electron withdrawing group on Te atom increases the strength of Te???π interaction while the fluorine atoms on benzene ring decrease it. The breakdown of ΔE_int in the R₂Te···C₆H₆ (R = H, F, Cl, CH₃) and C₄H₄Te···C₆H₆ systems using two dispersion corrected DFT methods showed that when the R group on divalent tellurium atom is an electron withdrawing substituent, the contribution of ΔE_elstat and ΔE_orb in total interaction energy increases and the value of ΔE_int is relatively large. The present data also showed that the intermolecular Te···π interactions are slightly stronger than corresponding Se···π interactions.     

Dispersion dipole between rare-gas atoms

Accurate calculations of the dispersion dipole coefficient D ₇ and its components are described for the systems HeH and HeHe, and used to check an approximate formula for D ₇ developed in a previous paper [1]. By means of a further approximation for a new atomic property, values of D ₇ are obtained for the rare-gas diatoms, based on semi-empirical Van der Waals C ₆ coefficients, Hartree-Fock expectation values and sum-rule values for the atoms. The dispersion contributions to the dipole are compared with the Hartree-Fock contributions [35], and at the conventional collision diameters are found to be of comparable magnitude but usually of opposite sign.     

On the convergence rate of a cusp-corrected damped multipole expansion for the second-order H-H+ induction energy

The improvement in the convergence rate of the damped multipole expansion for the second order H-H⁺ induction energy due to the inclusion into the first-order function of a term satisfying the electron-proton cusp condition is quantitatively investigated. Following a technique suggested by Schwartz, the multipole contributions to the energy are put in the form of series ordered by inverse powers of the quantum number l. It is shown that, for high values of l, the dependence of the leading terms is raised from l ^-4 to l ^-6 by the cusp correction.     

A comparative study of the static third-order polarizabilities of bowl/non-cage to cage structures: a structure-property correlation study

The average static third-order polarizabilities (γ) have been computed for the bowls and cages having the same number of carbon atoms. The bowls have higher (γ) than their corresponding cages. The dependence of (γ) on the average pyrimidalized angle (Θ_p) and maximal length L can be deduced. Near cages, having one open window (C₇₂ isomers), are capped with C₆ to generate five isolated pentagon rule (IPR) isomers of C₇₈ fullerenes following a circumscribing algorithm. The (γ) values for the C₇₈'s and C₇₂′s are correlated with (Θ_p) and L. The change in (γ) from C₇₂′s to C₇₈′s are correlated with a local parameter like the capped angle (α).     

Polarization of two close metal spheres in an external homogeneous electric field

The dipole moment of each of two uncharged conducting spheres with radius R in an external electric field was calculated. The distance between the centers of the spheres is 2l. It was shown that, if R/l≲0.8, the influence of higher multipole moments is negligible.     

PNO-CI and PNO-CEPA studies of electron correlation effects

Dipole moments and static dipole polarizabilities are calculated for neon and the molecules HF, H₂O, NH₃, CH₄ and CO from SCF and correlated wavefunctions.

The construction of appropriate gaussian-type basis sets is discussed and the convergence of the correlation contributions to the polarizability is analysed. The effect of vibrational averaging is also investigated. The polarizabilities as obtained from the coupled electron pair approximation (CEPA) with the most extended basis sets differ from experimental values by less than 1·5 per cent in all cases. The calculated polarizability anisotropies appear to be correct to about 5–15 per cent. The correlation contributions to the polarizabilities are found to vary from 3 to 12 per cent.     

Simulation of molecular orientational dynamics in a model polar fluid

A molecular dynamics simulation of a Stockmayer fluid with μ* = 1·0, ρ* = 0·7 and T* = 1·13 (±0·03) is reported. In addition to evaluations of a number of static properties, orientational time correlation functions C_l (t) = <P(cos δθ(t))> were calculated for l = 1 through 4 ; P_l is a Legendre polynomial and δθ(t) is the angle of reorientation of the dipole in time t. These time correlation functions are characteristic of nearly free rotation and agree well with curves calculated from a perturbation theory for the memory functions that utilizes the simulated value of the mean square torque. The angular velocity autocorrelation function for this fluid was also simulated and compared with perturbation theory. Agreement is not good, primarily because of the presence of a pronounced long time tail in the simulated function. The relationship between these results and those of other simulations and theories is discussed.     

Dynamic multipole polarizabilities of Li and Na atoms interacting with Debye potentials

The effects of Debye potentials on the dynamic multipole polarizabilities of Li and Na atoms are investigated using the symplectic algorithm. Frequency-dependent multipole polarizabilities of Li(2s ²S) and Na(3s ²S) are reported in terms of scaled number density of the plasma electrons for arbitrary plasma temperature.     

Anatomy of molecular properties evaluated with explicitly correlated electronic wave functions

Static electric dipole and quadrupole moments were evaluated at the explicitly correlated second-order Møller–Plesset (MP2-F12) level for BH, CO, H₂O, and HF molecules. The electron correlation contributions to the multipole moments were further decomposed into the direct (unrelaxed) and indirect (orbital response) components; we found that both components are equally important for the conventional (MP2) contribution, whereas the F12 correction to these properties originates primarily from the orbital response effects. Finally, the direct contribution dominates in the perturbative Hartree–Fock basis set incompleteness (CABS singles) correction. Two basis set families were employed: the standard aug-cc-pVXZ series and the cc-pVXZ-F12 series designed specifically for the F12 methods. The aug-cc-pVXZ MP2-F12 multipole moments usually have smaller basis set errors than the cc-pVXZ-F12 counterparts, albeit their differences are small at the triple (X = T) and quadruple (X = Q) zeta level. With the MP2-F12 calculations, the basis set errors of dipole and quadrupole moments can be reduced to ～0.001 a.u., or roughly 0.1%, at the aug-cc-pVDZ and aug-cc-pVTZ levels, respectively.     

Microwave and far-infra-red dielectric absorption inn-alkanes

Summary The power absorption coefficient (α) forn-hexane (C₆),n-heptane (C₇),n-dodecane (C₁₂) andn-tetradecane (C₁₄), benzene and cyclohexane has been studied at 20 °C, in the wave number range 20 to 300 cm⁻¹ within an accuracy of 2%. The power absorption measurements onn-alkanes (C₅−C₁₄ except for C₈, C₁₁ and C₁₃) are discussed in conjunction with the dielectric loss in the frequency range (9⋎140) GHz. The results indicate that, unlike other nonpolar liquids,n-alkanes show a broad dielectric dispersion in the microwave frequency range followed by a second dispersion in the far infra-red. The results are interpreted in terms of a dipole moment of 0.09 D in alkanes. A possible explanation for the origin of the dipole moment is discussed. A reference is also made to measurements of the dielectric loss and the Stark effect on the lower-series alkanes in the gas phase.

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Riassunto Si è studiato il coefficiente di assorbimento di potenza (α) pern-esano (C₆),n-eptano (C₇),n-dodecano (C₁₂) en-tetradecano (C₁₄), nel benzene e nel cicloensano a 20 °C nell’intervallo di numeri d’onda da 20 a 300 cm⁻¹ con un’accuratezza del 2%. Le misurazioni dell’assorbimento di potenza neglin-alcani (C₅−C₁₄, eccetto che per C₈, C₁₁ e C₁₃) sono discusse insieme alla perdita dielettrica nell’intervallo di frequenza (9⋎140) GHz. I risultati indicano che, diversamente da altri liquidi non polari, glin-alcani mostrano un’ampia dispersione dielettrica nell’intervallo di frequenza delle microonde, seguíta da una seconda dispersione nel lontano infrarosso. I risultati sono interpretati in termini di un momento dipolare di 0.09 D negli alcani. Si discute una possibile spiegazione dell’origine del momento dipolare. Si fa anche un accenno alle misurazioni della perdita dielettrica e dell’effetto di Stark sugli alcani della serie inferiore in fase gassosa.

     

Dust acoustic wave oscillations in C60 molecule

In this letter, dispersion properties of low-frequency electrostatic waves in a C₆₀ molecule are investigated. It is assumed that C₆₀ molecule is charged due to the field emission, and hence the C₆₀ molecule can be regarded as charged dust spheres surrounded by degenerate electrons and ions. We obtain the dispersion relation for the low-frequency electrostatic oscillations in the C₆₀ molecule by using the quantum hydrodynamic model in conjunction with the Poisson equation.     

Variational calculations of the static polarizability of H2 and of the dipole-dipole contribution to the dispersion energy between two hydrogen molecules

The convergence of variation-perturbation calculations using non-linear variation parameters has been examined for the static polarizability of H₂ and for the coefficient (C₆) of the R ^-6 term in the multipole expansion of the H₂-H₂ dispersion energy. Using a correlated ground state wavefunction, and one excited state for each of the parallel and perpendicular components of the polarizability, a single variational parameter for each state gave 96 per cent of the exact value of α_⊥ and 91 per cent of the exact value of α_‖. A second variational parameter for the parallel component gave 94 per cent of α_‖. The same procedure gave the spherical average and anisotropy of C₆ to an accuracy of about 90 per cent. By extending the calculations into the region where overlap of the orbitals of the two molecules becomes significant, it is shown for the end-on configuration that the C₆ R ^-6 term underestimates the dispersion energy near the van der Waals' minimum by roughly 10 per cent.     

A new method for deriving atomic charges and dipoles for n, -alkanes: investigation of transferability and geometry dependence

Atomic charge models are known to be unsatisfactory for representing the ab initio electrostatic potential (ESP) of n, -alkanes. A new method for deriving atomic charges and dipoles is proposed and applied to n-alkanes ranging from C₄ to C₁₀. Electrostatic parameters found by this method reproduce accurately the ab initio ESP. The issues of transferability and conformational dependence are also addressed by introducing charges and dipoles taken from a truncated distributed multipole analysis, in the same spirit as the restrained electrostatic potential method. A transferable model is proposed for larger alkanes (>C₁₀). We also estimate the error made when using a set of Boltzmann-weighted electrostatic parameters for all conformers. The reduced number of electrostatic sites considered in our model makes it suitable for computer simulation of liquid n-alkanes.