Finite-field method calculations. IV. Higher-order moments,dipole moment gradients,polarisability gradients and field-induced shifts in molecular properties: Application to N2, CO,CN−, HCN and HNC

In this paper, theoretical methods developed in III are applied in calculating polarisabilities, polarisability gradients and field-induced shifts, by the finite-field method. Values of dipole moment gradients and higher-order moments, calculated from the unperturbed wavefunctions, are also reported. Results for N₂, CO, CN^?, HCN and HNC have been obtained at the SCF level; some CI results for the N₂ polarisability components and moments and for the dipole moment gradients of HCN are also given. The calculated polarisability gradients and dipole moment gradients have been used to estimate the Raman scattering intensities and depolarisation ratios and the IR absorption intensities. Model calculations of field-induced shifts in bond length, vibrational levels, spectroscopic constants, force constants and dipole moment gradient are reported for N₂ and CO.The discrepancy between the SCF and experimental bond dipole moment gradients for HCN, previously noted in the literature, has been re-examined and resolved by our CI results.     

Anisotropic optical polarisabilities of the complexes LCr(CO)5 (L = PMe3, NMe3 or NH3): A study of π-back-bonding

Dipole moments and electric birefringences are reported for the complexes LCr(CO)₅ where L is PMe₃, NMe₃ or NH₃. Comparison of the molecular optical polarisability anisotropies of PMe₃Cr(CO)₅ and NMe₃Cr(CO)₅ shows a large enhancement of polarisability specifically in the L-Cr-(trans)CO direction for the phosphorus compound; the polarisabilities perpendicular to the symmetry axis are closely similar for the two complexes. The results are interpreted as direct evidence for a highly deformable π-component in PCr bonding. This work presents a new experimental approach to the study of π-back-bonding.     

A new method of determination of radii of ions with arbitrary effective charges

An equation for calculation of the radii of ions with an arbitrary effective charge has been derived. The ionic radii of halogens, chalcogens, and other atoms with different charges have been calculated. Under the assumption of pure ionic bond character, these values have been used for calculating the R ₁₂ distances for a large group of different molecules—halogens, interhalides, oxygen, chalcogens, and nitrogen and their compounds—by the previously derived equation for the a priori determination of internuclear distances. The error of calculation of the internuclear distance for halogens and interhalides is no more than 0.07 Å (3–4%). The internuclear distance in dihalogen cations Hal ₂ ⁺ and binary ionic molecules of p elements and their oxides and sulfides have been calculated. It has been demonstrated that the coordination (environment) of atoms should be taken into account and that there is a possibility of estimating the bond multiplicity and the character of bonding electron pairs in a molecule.     

Bethe logarithm and Lamb shift for the hydrogen molecular ion

A variational method is used to evaluate Bethe logarithm for the ground electronic state of the hydrogen molecular ion. The trial function employed in the calculations analytically represents the singular behavior of the exact solution of the variational problem for high virtual photon energies. This ensures that the accuracy of six significant figures can be obtained with basis sets not exceeding 70 functions. For the equilibrium internuclear separation of 2.0 bohr, the calculated value of the Bethe logarithm, equal to 2.31936, lies outside the bounds 2.35 and 2.56, representing the best previous estimation of this quantity. The accurate values of the Bethe logarithm for internuclear separations ranging from 0.6 to 6.0 bohr are tabulated and used to calculate the radiative corrections to the rovibrational energy levels of H₂⁺, HD⁺, and D₂⁺. The influence of these corrections on the transition and dissociation energies is also examined.     

Elastic scattering of electrons by H2 in the born approximation

This paper presents accurate computation of the differential cross sections for the elastic and vibrational excitation of ground state H₂ by fast electrons. The electronic matrix elements are evaluated at 20 internuclear separations and proper averaging over vibrational wavefunctions is carried out. The comparison to experiment yields excellent agreement. Different computational procedures appropriate for low and moderate values of momentum transfer are compared.     

Theoretical electronic structure including spin–orbit effects of the alkali dimer cation

A theoretical study of the electronic structure of has been performed, including or not spin–orbit coupling. Potential energy curves for all the molecular states dissociating up to the limit Cs⁺ + Cs (8s ²S_1/2), i.e 26 states in the representation and 38 states in the representation Ω_g,u, are displayed. Equilibrium distances, transition energies and depths for the wells predicted at short and large range of internuclear separation R are reported. The existence of some of the long-range wells are confirmed by a long range model. Extensive tables of energy values versus internuclear distances are available at the following address: http://lasim.univ-lyon1.fr/allouche/cs2plus.htm.     

On the many-body contributions to the interaction polarisability and hyperpolarisability of Hen

The many-body contributions to the interaction polarisability and hyperpolarisability of He _{n (n}=3,4, 5), for various configurations and distances have been determined and analysed. Several cases have been found where the three-body terms contribute more than 20% to or of He _n . The remarkable dependence of the above interaction properties on the internuclear distances and the shape of the cluster has been demonstrated. The interaction hyperpolarisabilities are shown to be uniquely sensitive probes of the electronic structure changes induced by variation of the cluster configuration. The results were computed by employing a computational procedure which relies on anab initio wave function, McWeeny's et al. coupled Hartree-Fock perturbation theory and an efficient algorithm for the determination of hyperpolarisabilities starting from a non-orthogonal basis set. The function counterpoise method has been used to reduce the basis set superposition error.     

Anisotropy of local relaxation properties of macromolecules. Spin-lattice relaxation of 13C nuclei,the nuclear overhauser effect and the estimation of parameters of an equivalent ellipsoid for kinetic segments of polymer chains

The expressions for the functions of spectral density at different orientations of the components of the internuclear vector with respect to the chain backbone, the frequency dependences of the spin-lattice relaxation time of ¹³C nuclei (T_1C) and the values of the nuclear Overhauser effect (NOE) were obtained for the tetrahedral lattice model of a polymer chain with three-unit kinetic elements. It was shown that peculiar features of the behavior of T_1C and NOE reflect the characteristic properties of the spectra of relaxation (correlation) times for “longitudinal” and “transverse” components of the internuclear vector. It was established that in the range of relatively short times of the relaxation spectrum the dynamics of an anisotropic kinetic segment of the chain may be described with the aid of a simple model of an elongated ellipsoid of rotation with an axial ratio of about 10. It is shown that the equivalent-ellipsoid model leads to significant differences from a more specific model of chain dynamics when a broad frequency range is considered.     

Dynamic polarizabilities and raman intensities of CO,N2, HCl and Cl2

We have performed first-order (identical to coupled Hartree-Fock) and second-order polarization propagator calculations of the dynamic dipole polarizability tensor for the CO, N₂, HCl and Cl₂ molecules. The derivatives of the polarizability tensor with respect to the internuclear distance at the equilibrium internuclear separation are compared with related data obtained from non-resonance Raman spectra. In most cases the correlation contributions beyond the coupled Hartree-Fock approximation have a more pronounced effect on the derivatives of the polarizability tensor than on the polarizability tensor itself. At both levels of approximation we found that derivatives of the dynamic polarizability tensor with respect to the internuclear separation increase with 10–15% for variation of the frequency from 0 (static polarizability) to about 28500 cm^?1. The depolarization ratio calculated from the polarizability derivatives shows no variation with frequency in the same frequency range.     

Velocity dependence of the total cross section for helium-argon,neon-krypton and neon-xenon scattering

Velocity dependences of the total collision cross sections for scattering of helium by argon, neon by krypton and neon by xenon were measured using a time of flight method of velocity selection. For neon scattering glory oscillations were observed from which values of ?r_m (the product of the well depth and the internuclear separation at the minimum) were determined for various Lennard-Jones potentials. Comparison is made with the results from diffusion experiments and differential scattering measurements.     

Determination of molecular constants of scandium triiodide monomer and dimer from electron diffraction data

The molecular intensity function of a ScI₃+SC₂I₆ mixture is solved using gas-phase electron diffractometry and taking into account the theoretical values of l(Sc-I). The symmetry of geometrical configuration, the internuclear distances, and vibration frequencies of the scandium triiodide monomer and dimer are determined. Translated fromZhurnal Struktumoi Khimii, Vol. 38, No. 3, pp. 489–494, May–June, 1997.     

Ab initio investigations of structure and stability of the LiBeF3 molecule

Ab initio calculations of the potential energy surface of LiBeF₃ have been performed using the basis set of Roos and Siegbahn. The extremum and saddle points were made more precise with Huzinaga-Dunning basis sets in double-and triple-zeta contractions The “bidentate” structure (symmetry group C_2v) is found to have the lowest energy and is much more advantageous than the others, and the LiBeF₃ molecule turns out to be rigid with respect to migration of the cation around the anion. The calculated internuclear distances and the energy of complex formation are in agreement with experimental values within 0.03 Å and 2 kcal/mole. The results are compared with similar ab initio data for LiBeH₃ and LiNO₃.     

Computation of overlap integrals over Slater-type orbitals using auxiliary functions

Analytical expressions through the binomial coefficients and recursive relations are derived for the expansion coefficients of overlap integrals in terms of a product of well-known auxiliary functions A_k and B_k. These formulas are especially useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the computer results is satisfactory for the values of quantum numbers up to 50 and for the arbitrary values of screening constants of atomic orbitals and internuclear distances. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 199–204, 1998     

The effect of orientation of the lateral methyl substituent on the mesophase behaviour of 4-alkoxyphenylazo aryl benzoates

Two homologous series of 4-alkoxyphenylazo 4?-(2?- (and 3?-) methyl-) 4?-substituted benzoates (IIn_a–f and IIIn_a–f, six series each) were prepared and investigated. Within each series, the length of the terminal alkoxy group varies among 6, 8, 10 and 12 carbons, while the other terminal substituent, X, is a polar group that alternatively changes between the electron-donating CH₃O, CH₃, and the electron-withdrawing Br, NO₂ and CN groups, in addition to the un-substituted analogue, X = H, aiming to investigate the effect of the different orientations of the methyl groups substituted on the central benzene ring, on the mesophase behaviour. The mesomorphic properties were discussed in terms of steric and polarisability effects. The mesophase stability was correlated with the polarisability anisotropy of bonds to the terminal substituent X. Comparative studies were made between the prepared isomers with each other and with the previously investigated laterally neat analogues 4-(4?-alkoxyphenylazo) phenyl 4?-substituted benzoates (In_a–f).     

Effect of exchange of terminal substituents on the mesophase behaviour of some azo/ester compounds

Six homologous series of 4-(4′-alkoxy phenylazo) phenyl 4″-substituted benzoates (In_a-f) were prepared in which, within each homologous series, the length of the terminal alkoxy chain varies between 6, 8, 10, and 12 carbons, while the other terminal substituent, X, is a polar group that alternatively changed from CH₃O, CH₃, H, Br, NO₂ and CN. Compounds prepared were characterised by spectroscopic methods, and their mesophase behaviour investigated by differential scanning calorimetry (DSC) and polarised optical microscopy (POM). The results were discussed in terms of mesomeric and polarisability effects. In each group of compounds, bearing the same alkoxy substituent, the nematic-to-isotropic transition temperatures (T_C) were successfully correlated with the polarisability anisotropy of bonds to the substituent X. A comparative study was made between the investigated compounds and their previously prepared isomers, namely, 4-(4′-substituted phenylazo) phenyl 4″-alkoxybenzoates (IIn_a-f) in which the two terminal (alkoxy- and X) groups are exchanged.     

On the use of “effective harmonic potentials” and “effective normal coordinates” in computing the vibrational energy levels of polyatomic molecules

The purpose of this paper is to discuss the possibility of improving the physical significance of the internuclear potential function derived from the energy levels observed in rotation—vibration spectra. In performing the perturbation calculation, it might be efficient to use normal coordinates and zeroth-order harmonic hamiltonians which depend upon the range of vibrational energies or upon the values of the vibrational quantum numbers. A limited application of this method is made in the case of CO₂, in order to overcome the difficulties linked to the large value of the coefficient k₁₃₃ in the cubic anharmonic potential.     

Studies of chemical hardness and Fukui function using the exact solution of the density functional theory

Neal's procedure has been applied to determine the electron density ρ(x) for the H₂ molecule. The chemical hardness has been calculated employing the ab initio and density functional theory methods and the values are found to be reasonably good. The principle of maximum hardness (PMH) was tested. Fukui functions and the distribution of electron density around the internuclear distance were studied employing the electron density of the H₂ molecule. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 4–10, 2001     

A new intensity equation for electron diffraction analysis: A barrier to pseudorotation in PF5 from diffraction data

Using the cumulant expansion for the statistical average of the exponent

the molecular intensity of scattered electrons is expressed in terms of the equilibrium internuclear distances and moments of the displacements of internuclear distances

. The new intensity equation is suitable for practical analysis of diffraction data for any molecular system including those where anharmonicity factors are thought to be particularly important. The trigonal bipyramidal PF₅ molecule was chosen as a test system mainly with the aim of determining the barrier to pseudorotation which is thus estimated to be 3.41 kcal mol^?1, in excellent agreement with the recently available spectroscopy and ab initio values.     

Origin of the variation with vibrational and rotational state of the fine-structure constants in O2, SO and S2

Calculations of the spin—orbit part λ_SO of the fine-structure parameter λ have been performed at several internuclear distances for the molecules O₂, SO and S₂ in their ground (X ³Σ^?) states. Only the interaction with the lowest ¹Σ⁺ state was considered and two-centre integrals were neglected. λ_SO is found to make the dominant contribution to λ. The variation of the matrix elements in λ_SO with internuclear distance has been derived and when combined with expressions for the variation of the energy denominator in λ_SO enables the coefficients for the vibrational and rotational dependence of λ to be estimated. Excellent agreement with experiment is found.