Ajit J. Thakkar

Intermolecular forces via hybrid Hartree–Fock–SCF plus damped dispersion (HFD) energy calculations. An improved spherical model

Molecular interactions are partitioned in SCF and correlation energy parts. It is shown that for atomic systems, one can join high quality ’’a priori’’ SCF calculations with a semiempirical estimate of the correlation energy, made using the standard long range multipolar expansion and corrected assuming the 3Σ+u state of H2 as a model (scaling the ’’size’’ of the atomic charge distribution as the ionization potential to the negative 2/3 power) to obtain very good agreement with the available experimental information.

Ab initio dispersion coefficients for interactions involving rare‐gas atoms

Calculations of the dynamic dipole, quadrupole, and octopole polarizabilities of Ne, Ar, Kr, and Xe are carried out using both time‐dependent coupled Hartree–Fock and many‐body perturbation theory methods. Dispersion coefficients are calculated for interactions involving these species. The dynamic polarizabilities are combined with previously published dynamic polarizabilities of H, He, H2, N2, HF, and CO to obtain dispersion coefficients for the interactions involving one of these species and one of Ne, Ar, Kr, or Xe. The dipole–dipole dispersion coefficients agree quite well with the best available semiempirical estimates. The isotropic higher multipole coefficients are in reasonable agreement with previous semiempirical estimates where available, and the anisotropic ones are, in most cases, the first reliable ones to appear in the literature. Nonadditive three‐body dispersion coefficients for the Ne3, Ar3, Kr3, and Xe3 interactions are also calculated.

The generator coordinate method applied to variational perturbation theory. Multipole polarizabilities, spectral sums, and dispersion coefficients for helium

It is shown that a suitable variant of the generator coordinate method can be used for accurate variational perturbation theory calculations. The test problems chosen are calculations of the dipole, quadrupole, and octupole polarizabilities, spectral sums, two‐body dispersion coefficients, and nonadditive three‐body dispersion coefficients for the ground state of atomic helium. An accurate explicitly correlated wave function for the unperturbed problem is utilized along with explicitly correlated basis functions for the pseudospectra. The dipole results are in excellent agreement with previous high accuracy calculations. The quadrupole and octupole results are expected to be the most accurate ones currently available. Estimates of some hexadecapole properties are made.

Multipole moments, polarizabilities, and hyperpolarizabilities for N2 from fourth‐order many‐body perturbation theory calculations

All multipole moment, polarizability, and hyperpolarizability tensors up to the fourth rank are calculated for the ground 1Σ+g state of N2 at its equilibrium bond length. These properties are obtained from fourth‐order Mo/ller–Plesset perturbation theory energies of N2 in the presence of various configurations of point charges. Electron correlation was found to affect the longitudinal components the most. Some of the anisotropies of these tensors change by as much as 105% upon inclusion of electron correlation. The results are in good agreement with all previous reliable theoretical and experimental values. The calculated values of the quadrupole–quadrupole (C) and dipole–octopole polarizabilities, and the dipole–dipole–quadrupole (B) and dipole–dipole–dipole–dipole (γ) hyperpolarizabilities are the most accurate ones available. Our best vibrationless estimates of the isotropic averages of these quantities are C=40.371 e2 a40 E−1h, B=−149 e3 a40 E−2h, and γ=830e4 a40 E−3h.

A new generalized expansion for the potential energy curves of diatomic molecules

A new generalized expansion for the potential energy curves of diatomic molecules is proposed. It is given by where λ (p) = sgn(p) [1 − (Re/R)p], and contains both the Dunham and the Simons−Parr−Finlan (SPF) expansions as special cases corresponding to p = −1 and p = 1, respectively. In order to justify the new expansion, a perturbation theory is developed which yields the Born−Oppenheimer potential as a series identical in form to the new expansion. The perturbation is a purely kinetic−energy perturbation at Re. Prescriptions are given for obtaining both the expansion coefficients and the optimal value of p either from perturbation theory or from spectral data. In terms of spectral data p = −a1 −1. Applications of the new expansion to CO, HF, and 20 alkali halides indicate that it predicts dissociation energies in much closer agreement with experiment than the SPF expansion while maintaining the same quality of agreement with the RKR curve as the SPF expansion provides. A number of possible extensions ar...

Improved Roothaan–Hartree–Fock wave functions for atoms and ions with N≤54

Improved Roothaan–Hartree–Fock wave functions are reported for the ground states of all the neutral atoms from He to Xe, singly charged cations from Li+ to Cs+, and stable singly charged anions from H− to I−. Our neutral atom wave functions are an improvement over those of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)], Bunge et al. [Phys. Rev. A 46, 3691 (1992)] and Koga et al. [Phys. Rev. A 47, 4510 (1993)]. The ion wave functions are an improvement over those of Clementi and Roetti, and Koga et al. [J. Phys. B 26, 2529 (1993)]. In all cases, the current wave functions predict energies within 1.3×10−5 hartrees of the numerical Hartree–Fock limit.

The electron—electron cusp condition for the spherical average of the intracule matrix

Abstract The Kato electron—electron cusp condition is used to derive a corresponding cusp condition for the spherical average of the intracule matrix. The numerical utility of this condition is illustrated by considering the Hart and Herzberg 20-parameter Hylleraas-type wavefunctions for the helium-like ions. It is shown that these functions do not satisty the cusp condition. The analytic utility of the latter is illustrated by considering the asymptotic behaviour of the total X-ray scattering intensity.

Polarizabilities and hyperpolarizabilities of carbon dioxide

The dipole (α), quadrupole (C), and dipole–octopole (E) polarizabilities, the dipole–dipole–quadrupole (B) and second dipole (γ) hyperpolarizabilities, and the quadrupole (θ) and hexadecapole (Φ) moments are calculated for the ground state of CO2 at its equilibrium geometry. The values are obtained from fourth‐order many‐body perturbation theory energies of CO2 in the presence of various configurations of point charges. Electron correlation affects the longitudinal components more than the transverse ones; hence, electron correlation effects are greater for the anisotropies than for the isotropic averages of these properties. Our best vibrationless estimates for the isotropic values are ᾱ≂17.63 e2a20E−1h, C≂77.8 e2a40E−1h, B≂−2.1×102 e3a40E−2h, γ≂1.20×103 e4a40E−3h, and θzz≂−3.24 ea20. The quadrupole moment, mean dipole polarizability and hyperpolarizability are in satisfactory agreement with experiment. On the other hand, the polarizability anisotropy Δα≂14.3 e2a20E−1h agrees with experimental estimat...

Analytical Hartree–Fock wave functions subject to cusp and asymptotic constraints: He to Xe, Li+ to Cs+, H− to I−

Analytical, variational approximations to Hartree-Fock wave functions are constructed for the ground states of all the neutral atoms from He to Xe, the cations from Li{sup +} to Cs{sup +}, and the stable anions from H{sup {minus}} to I{sup {minus}}. The wave functions are constrained so that each atomic orbital agrees well with the electron-nuclear cusp condition and has good long-range behavior. Painstaking optimization of the exponents and principal quantum numbers of the Slater-type basis functions allows one to reach this goal while obtaining total energies that, at worst, are a few microHartrees above the numerical Hartree-Fock limit values. The wave functions are freely available by anonymous ftp from okapi-chem.unb,ca or upon request to the authors.

Higher dispersion coefficients: Accurate values for hydrogen atoms and simple estimates for other systems

The dispersion coefficients Cn (n≤30) and Z(l,λ,L) (l+λ+L≤13) which appear in the multipole expansions of the pair and nonadditive three‐body interaction energies, respectively, are calculated to an accuracy of no less than 15 decimal digits for interactions among ground state hydrogen atoms. The pseudostate technique used is as simple and accurate as the momentum‐space method recently advocated for this problem. The oscillator and hydrogenic models are used to obtain simple formulas for the estimation of higher dispersion coefficients from two or three of the leading coefficients. These formulas should prove useful in models of intermolecular potentials.