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.

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

Publisher Summary This chapter focuses on the recent developments in the experimental and theoretical determination of the polarizabilities of simple atoms and molecules. Polarizability values (related to the “quadratic Stark effect”) are accurately known for the noble gas atoms and for hydrogen, in theory, but the remainder of the periodic table has proven much more difficult to deal with, both theoretically and experimentally. The static electric dipole polarizability of the ground-state hydrogen atom is almost exactly 4.5a30, where a0 is the Bohr radius. Across rows of the periodic table, polarizabilities range from hundreds (of a30 units) for the alkali metal atoms generally monotonically down to a few for noble gas atoms. Excited atoms have much larger polarizabilities; recent polarizability measurements for atoms in Rydberg orbits have yielded values on the order of 1010a30. Further research on molecular polarizabilities can help in the determination of polarizability anisotropies whether through state selection or with beams of different temperatures. Supersonic molecular beams are found to have low internal energies, and the internal energy can be controlled somewhat in “seeded” beams.

Atomic and Molecular Polarizabilities-A Review of Recent Advances

The effect of neutral nonresonant collisions on the shape, shift, and intensity of atomic spectral-line profiles is reviewed. A general treatment for the study of an atomic spectral line is developed by establishing reasonable assumptions about the relevant collision processes and by finding an expression for the Fourier transform of the line profile. The authors look at parallel developments of other methods of calculation, consider special limits of practical interest, and illustrate numerical evaluations of complete line profiles. Interatomic potentials for use in line-profile calculations are described, and the problems imposed by nonadditivity and nonadiabaticity are also noted. The observation of line profiles by both conventional and tunable-laser techniques is surveyed. Representative experimental measurements of the widths and shifts of collision-broadened spectral line cores are tabulated, and the phenomena of satellites, oscillations, and power-law behavior of line wings are compared with theoretical expectations. The use of experimental results for the determination of excited atom-atom interactions, the prediction of collision broadening in stellar atmospheres, and the effect of foreign gases on laboratory standard wavelengths are also discussed.

The effect of neutral nonresonant collisions on atomic spectral lines

A general method is proposed for quantum‐mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure. This consists of the calculation of self‐consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations. The general theory of such methods is presented together with a preliminary discussion of numerical error.

Self‐Consistent Perturbation Theory. I. Finite Perturbation Methods

The perturbation equations of the self-consistent density matrix perturbation theory are derived for open-shell configurations in the restricted Hartree-Fock approximation. It is assumed that the b...

Self-consistent perturbation theory: Open-shell states in perturbation-dependent non-orthogonal basis sets This work was partly supported by the Institute of Low Temperatures and Structure Research of the Polish Academy of Sciences under contract No. MR-I.9.4.3/2.

Electric dipole, quadrupole, and octupole polarizabilities and shielding factors are calculated for a large number of two- to twenty-electron $S$-state atoms and ions. The calculations are carried out within the framework of an uncoupled Hartree-Fock approximation, subject to the proviso that the exchange part of the Fock potential be expressable as a multiplicative function. All zeroth-order functions used are of the anayltical Hartree-Fock type. The resulting numerical values are found to be strongly sensitive to the quality of the Hartree-Fock function used in the calculation, in agreement with Sternheimer's previous conclusion. This point proves to be of special importance in the case of the negative ions. In addition, it is shown that the variational method pioneered by Das and Bersohn, if carried out under proper orthogonality conditions, is equivalent to the present uncoupled Hartree-Fock approximation. Finally, it is noted that the variational method used in this work is less accurate than the Sternheimer numerical method; however, use of the variational method allows some simplification in the computational procedure.

Multipole Polarizabilities and Shielding Factors from Hartree-Fock Wave Functions

Electric Dipole Hyperpolarizabilities for S-State Atoms and Ions

Fully coupled Hartree-Fock calculations of the refractive index, dynamic polarizability, and Verdet coefficients of He, Be, Ne, and the corresponding 2-, 4-, and 10-electron isoelectronic series are presented. The time-dependent Hartree-Fock perturbation equations are derived and solved using a variational method, in which the zero-order and the perturbed wave functions are represented by analytical functions containing adjustable parameters which are optimized according to the variational technique. The numerical results for both the refractive index and the Verdet coefficients are fitted to polynomials in even powers of $\frac{1}{\ensuremath{\lambda}}$, where $\ensuremath{\lambda}$ is the wavelength. In this work it is found that the computed refractive indices differ from the corresponding experimental values due to Cuthbertson and Cuthbertson by a very nearly constant amount. That is, if the computed dynamic polarizabilities are adjusted so as to equal the experimental polarizability $\ensuremath{\alpha}$ at zero frequency, then the experimental and theoretical curves of refractive index versus frequency are nearly identical. This adjustment in $\ensuremath{\alpha}$ is around 5% (for He) and 10% (for Ne) of the experimental static polarizabilities. Finally, the calculated transition frequencies are around 2% too large for He, 17% too large for Ne, and 9% too small for Be.

R. P. Hurst

Papers

Multipole Polarizabilities and Shielding Factors from Hartree-Fock Wave Functions

Electric Dipole Hyperpolarizabilities for S-State Atoms and Ions

Fully coupled hartree--fock calculations of the refractive index, dynamic polarizability, and verdet coefficients of helium, beryllium, and neon.

Uniform-Electric-Field Quadrupole Polarizabilities and Shielding Factors for S -State Atoms and Ions