Basis Sets Of Gaussian-type Functions Research Articles

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions.

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence.

Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar.

Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order.

The Dirac equation in the algebraic approximation. VI. Molecular self-consistent field studies using basis sets of Gaussian-type functions

The matrix Dirac-Hartree-Fock equations are presented for molecular systems of arbitrary symmetry. The advantages of using basis sets of Gaussian-type functions in relativistic self-consistent field calculations are described. Prototype calculations for the ground state of the HCl molecule at three geometries close to the experimentally determined equilibrium geometry are presented and discussed. Relativistic energies are compared with basis set truncation effects and non-relativistic electron correlation energies and their geometry dependence is analysed. The accuracy with which the non-relativistic limit can be approached by multiplying the speed of light c by a scalar p and allowing lambda =pc to become large is investigated. Dipole moments are calculated.

Second-order correlation energy of the argon atom using basis sets of Gaussian-type functions

The second-order correlation energy of the ground state of the argon atoms is calculated using basis sets of Gaussian-type functions. It is demonstrated that accurate second-order correlation energies can be obtained by employing systematic sequences of even-tempered basis sets of Gaussian-type functions. The pair correlation energies are compared with those obtained by Jankowski et al. (1979) using basis sets of exponential-type functions.

The orbital amplitude difference function for systematic sequences of even-tempered basis sets of gaussian-type functions

The orbital amplitude difference function is shown to provide a useful method for displaying basis set deficiencies, particularly in calculations using systematic sequences of even-tempered basis functions. An application to the beryllium atom is presented.

The well-tempered GTF basis sets and their applications in the SCF calculations on N2, CO, Na2, and P2

We have started to prepare a new family of high-quality Gaussian-type function basis sets capable of producing near Hartree–Fock atomic and molecular wave functions. A conspicuous feature of the family of basis sets is that many of the exponent parameters are shared among s-, p-, d-, and f-basis functions. In the present paper we report the first phase of the work covering atoms from Li to Ar, together with near Hartree–Fock calculations on N2, CO, Na2, and P2 as the applications. A modified form of Raffenetti's contraction scheme is used.

The effect of p, d, and f Gaussian polarization functions on the computed one-electron properties of AHn oxygen and sulfur hydrides

A series of LCAO-MO-SCF calculations, using various basis sets of Gaussian-type functions, has been made in order to study the effects of p, d, and f polarization functions on calculated one-electron properties for a 10-electron isoelectronic series of oxygen hydrides and for an 18-electron series of sulfur hydrides. Conclusions from these results suggest that several one-electron properties have a predictable, although not monotonic convergence pattern. Except for calculated field gradients, f GPF's have only a small effect on the calculated values.

Calibration constant forFe57Mössbauer isomer shifts derived fromab initioself-consistent-field calculations on octahedral FeF6and Fe(CN)6clusters

Ab initio self-consistent-field molecular-orbital calculations were performed on octahedral Fe${\mathrm{F}}_{6}$ and Fe${(\mathrm{CN})}_{6}$ clusters using extensive basis sets of Gaussian-type functions. Two distances relevant for ferrous and ferric compounds are considered. In this paper, we report the part of our results that is relevant for a determination of the isomer-shift calibration constant for Fe. Good overall consistency with available $^{57}\mathrm{Fe}$ M\ossbauer data is found resulting in a value of ${\ensuremath{\alpha}}_{\mathrm{HF}}=(\ensuremath{-}0.30\ifmmode\pm\else\textpm\fi{}0.03){a}_{0}^{3}$mm ${\mathrm{sec}}^{\ensuremath{-}1}$ for the calibration constant to be used in conjunction with densities on the nucleus calculated in the spin- and symmetry-restricted Hartree-Fock approximation. This value is compared with previous estimates, a number of which can be corrected on the basis of the present work and are then shown to agree with our results. Recent attempts to obtain quantitative relativistic corrections by solving the Fock-Dirac equations for Fe and its ions are discussed. A value for the calibration constant appropriate to densities calculated by this method of ${\ensuremath{\alpha}}_{\mathrm{FD}}=(\ensuremath{-}0.22\ifmmode\pm\else\textpm\fi{}0.02){a}_{0}^{3}$mm ${\mathrm{sec}}^{\ensuremath{-}1}$ is tentatively derived.

Gaussian-Orbital Basis Sets for the First-Row Transition-Metal Atoms

Contracted Gaussian-type function basis sets have been produced for the first-row transition-metal atoms Sc through Cu for use in molecular SCF calculations. The basis functions consist of 15 s-type, eight p-type, and five d-type Gaussian primitives contracted to a four s-type, two p-type, and one d-type basis set and are exponent and coefficient optimized after contraction. It is shown that this basis set is of single-zeta quality for the core functions and of double-zeta quality for the valence-electron functions. Relaxation of the degree of contraction results in a significant lowering of the total energy.

Near-Molecular Hartree—Fock Wavefunction for CH3−

Ab initio LCAO—MO—SCF calculations have been performed on CH3− with a C–H bond length of 1.95 Bohr atomic units, using Gaussian-type functions (GTF) as the basis set. By successive increases in the size (N) of the basis set of GTF (N = 12, 20, 28, 36, 40) it was possible to approach the estimated molecular Hartree—Fock limit within 0.06 Hartree atomic units. The best calculated total energy was −39.4798 hartrees. The Hartree—Fock limit has been estimated to be −39.535 hartrees for the equilibrium C–H distance, and as high as −39.501 hartrees for the above C–H separation. The variation of the geometry of CH3− indicated that the molecule is pyramidal in its ground state, with the HCH angle approximately equal to 115°. The inversion-barrier height is estimated to be 1.22 kcal/mole. The charge distribution, as deduced from Mulliken's population analysis, was such that there was approximately 1.099 negative charge on the carbon atom and 0.033 positive charge on each of the three hydrogen atoms. Due to its symmetry, the planar molecule possessed zero dipole moment but it assumed finite values in pyramidal conformations. The total electron density as well as the near-Hartree—Fock molecular-orbital densities are presented in the form of contour maps. Within the framework of a single Slater determinantal wavefunction, estimation for the energy values of some of the low-lying electronic excited states of CH3− have been made.