Toshikatsu Koga

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.

Contracted Gaussian‐type basis functions revisited

The contracted Gaussian‐type function (CGTF) sets by Huzinaga and co‐workers are improved by an extensive optimization of exponents and contraction coefficients for the first‐row atoms Li to Ne. The largest improvements in the total energy are 1.043, 0.096, 0.122, 0.23, 0.24, and 0.36 mhartrees, respectively, for the (33/3), (43/4), (53/5), (64/5), (64/6), and (74/7) sets. The virial ratios are considerably improved by the present optimization. The change in exponents and contraction coefficients amounts to 19%. Splitting the valence part of the CGTFs and adding polarization functions, we have examined the effect of the polarization functions on the properties of N2 molecule in self‐consistent‐field (SCF) and configuration interaction (CI) calculations. Referring to the results of a very large basis set, we confirmed that both in the SCF and CI calculations, polarization functions added to the present CGTF sets almost work as pure polarization functions; no basis set superposition error was found both in ...

Contracted polarization functions for the atoms magnesium through argon

Abstract Contracted Gaussian-type function (GTF) sets are developed for polarization functions of the atoms from magnesium to argon. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are determined to minimize the difference from accurate atomic natural orbitals in polarization space. The present polarization functions yield greater than 99.5% of atomic correlation energies predicted by accurate natural orbitals of the same size. Molecular tests of the polarization functions are performed for the P 2 and Si 2 molecules at self-consistent field (SCF) and single and double excitation configuration interaction (SDCI) levels. The present polarization function sets are shown to be superior to both averaged atomic natural orbital (ANO) and Dunning et al.s correlation consistent sets.

Contracted Gaussian-type basis functions revisited II. Atoms Na through Ar

Abstract. We report five minimal-type contracted Gaussian-type function (CGTF) basis sets of the second-row atoms, Na – Ar, for molecular applications. Three of the present CGTF sets are revised versions of those given by Huzinaga and co-workers and the other two are newly developed for more accurate calculations. Practical utility and improved reliability of the present basis sets, augmented by polarization functions, are confirmed by test calculations on the P atom and P2 molecule both atu2009the self-consistent field (SCF) and configuration interaction (CI) levels.

Noninteger principal quantum numbers increase the efficiency of Slater-type basis sets: singly charged cations and anions

For the singly charged cations to and anions to in their ground state, Roothaan - Hartree - Fock calculations are carried out using a single-zeta (or minimal) basis set of extended Slater-type functions whose principal quantum numbers are allowed to be variationally optimum noninteger values. The resultant total energies are substantially lower than those obtained from the conventional single-zeta method which implicitly restricts the quantum numbers to be integer values. In the case of and ions, for example, the improvements amount to 11.4 and 11.0 Hartrees, respectively. The noninteger principal quantum numbers also improve the orbital energies. In particular, unphysical positive orbital energies predicted by the conventional single-zeta method for 56 atomic orbitals change to realistic negative values (with only three exceptions) by the use of noninteger principal quantum numbers without increasing the number of basis functions. Ionization potentials and electron affinities are improved as well within the single-zeta approximation.

Noninteger principal quantum numbers increase the efficiency of Slater-type basis sets: heavy atoms

Abstract For the atoms Cs (Z = 55) through Lr (Z = 103) in their ground state, Roothaan-Hartree-Fock calculations are performed using a single-zeta (or minimal) basis set of extended Slater-type functions whose principal quantum numbers are allowed to be variationally optimum noninteger values. The resultant total energies are superior to those obtained from the conventional single-zeta method which implicitly restricts the quantum numbers to be integer values. In the case of the Lr atom, the improvement amounts to 56.8 E h . The noninteger principal quantum numbers improve the orbital energies; unphysical positive d and f orbital energies predicted by the conventional single-zeta method change to realistic negative values by the use of noninteger principal quantum numbers.

Hyperbolic cosine functions applied to atomic Roothaan–Hartree–Fock wave functions

Abstract A hyperbolic cosine function coshxa0(βr) is incorporated into a Slater-type radial function rn−1expxa0(−αr) with noninteger principal quantum number n. The new radial basis functions rn−1expxa0(−αr)coshxa0(βr) are applied to Roothaan–Hartree–Fock calculations of atoms within the minimal-basis framework. The results of a systematic study on the neutral atoms from He (Z=2) to Lr (Z=103) in their ground state show that the total energy errors of the parent Slater-type functions, relative to the numerical Hartree–Fock values, are reduced to half or less by the addition of coshxa0(βr). Orbital energies are also improved. The present accuracy of the minimal-basis description of atoms supersedes the previous one achieved in the literature.

DOUBLE-ZETA SLATER-TYPE BASIS SETS WITH NONINTEGER PRINCIPAL QUANTUM NUMBERS AND COMMON EXPONENTS

Abstract A double-zeta basis set of extended Slater-type functions, whose principal quantum numbers are allowed to have noninteger values, is reported for the atoms He to Ar in their ground state. The total energies are lower than those from conventional and improved double-zeta basis sets, in which the principal quantum numbers are restricted to integer values. For the same atoms, we develop a new type of double-zeta basis set that combines the use of noninteger principal quantum numbers and the use of common exponents in Slater-type functions. The new double-zeta basis sets result in an improvement of the energy and a reduction of the computational time.