Hiroshi Tatewaki

Chemically reliable uncontracted Gaussian-type basis sets for atoms H to Lr

Abstract Highly accurate Gaussian-type function basis sets are developed for 103 atoms from H (atomic number Z =1) to Lr ( Z =103). Choosing the last atoms of the seven periods and referring to the numerical Hartree–Fock total energies, the sizes of the present sets are so determined that the total energy errors are less than 1 millihartree. The average total energy error over the 103 atoms is only 0.79 millihartrees and the maximum error is 1.47 millihartrees for the Zn atom, indicating that the new sets are well-balanced throughout the atoms in the periodic table. The basis sets are tested for the GdF molecule.

Numerical Hartree–Fock energies of low‐lying excited states of neutral atoms with Z≤18

Numerical Hartree–Fock calculations have been performed for low‐lying excited states of the neutral atoms from He to Ar. Total energies, orbital energies, and the mean values of r of the outermost orbitals of each symmetry are tabulated as an aid to calibration of algebraic basis sets.

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 ...

The ground state of the Fe2 molecule

The Fe2 molecule is a typical transition metal dimer which has a rather large dissociation energy and a small bond distance compared with the inter‐nuclear distance in the crystalline metal. We have investigated the Fe2 molecule with multireference self‐consistent‐field (MCSCF) and multireference configuration interaction (CI) calculations. The dissociation energy (De), the equilibrium nuclear distance (Re), and the zero‐point frequency (ωe) were calculated (with observed in parentheses) as 1.57 (1.30±0.22) eV, 2.06 (1.87 to 2.02) A, and 260.9 (299.6) cm−1, respectively. Thus the agreement between experiment and calculation is very satisfactory, and is a marked improvement on previous theoretical studies. The contribution of the d electrons to the bonding is important and a proper description of correlation effects among the d electrons is indispensable.

Numerical Hartree-Fock energies of singly charged cations and anions with N~54

Numerical Hartree–Fock (NHF) calculations have been performed for the singly charged cations Li+–Cs+ and anions H−–I− in their ground states. For the cations, the NHF values in the literature are found to be insufficiently accurate, while for the anions our NHF study covers the whole series H−–I− (except Sc− and Pd−) for the first time. Atomic ionization potentials and electron affinities are computed and compared with experiment.

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.

ALL-ELECTRON DIRAC-FOCK-ROOTHAAN CALCULATIONS ON THE ELECTRONIC STRUCTURE OF THE GDF MOLECULE

The electronic structure of the GdF molecule is investigated using all-electron Dirac–Fock–Roothaan calculations. It is found that, in the ground state, the Gd atom transfers a 5d electron to the 2p spinors of the F atom, so that the molecule is ionic, having the configuration of Gd+F−. However, the molecule is not purely ionic, since the electrostatic field produced by Gd+ and F− causes the spinor energies of Fu20092s and one of the Gd 5p to be almost energetically degenerate so that these spinors strongly mix with each other and form covalent bonds. The electrostatic field also causes a large energy lowering for one of the 4f spinors, giving further stability to GdF. The 4f electrons of Gd should be regarded as valence electrons. The lower excited states and positively and negatively ionized states are found to be roughly described by Gd atomlike excitations, ionization, and electron attachments.

Four-component relativistic calculations on the complexes between a water molecule and trivalent lanthanoid and actinoid ions

Abstract Complexes between a water molecule and trivalent lanthanoid and actinoid ions were investigated by all-electron four-component relativistic calculations using the Dirac–Hartree–Fock (DHF) method. DHF-based relativistic second-order M o ller–Plesset perturbation (RMP2) calculations were also performed to incorporate electron correlation for the closed-shell systems. Non-relativistic calculations using the HF and MP2 methods were carried out in parallel to compare with the DHF and RMP2 results. Metal–oxygen distances and stabilization energies were evaluated, and a separability between relativity and correlation was found. Mulliken population analysis and spinor projection were used to analyze the wave functions, and a nature of coordinate bond was revealed.

Modification of nonrelativistic Gaussian basis sets for relativistic calculations

A simple method is proposed in which basis sets of Gaussian-type functions (GTFs), suitable for relativistic Dirac–Fock–Roothaan (DFR) calculations, are derived from their nonrelativistic analogs. The relativistic basis set is obtained through augmenting the nonrelativistic one by several GTFs determined from relativistic calculations for hydrogen-like atoms. The usefulness and reliability of the method is illustrated by DFR calculations of the ground-state energies of lanthanide and actinide atoms.

Even-tempered Roothaan-Hartree-Fock wave functions for the third- and fourth-row atoms

SummaryRoothaan-Hartree-Fock wave functions composed of 12s8p6d, 12s10p6d, and 12s10p8d even-tempered (ET) Slater-type functions (STFs), respectively, are reported for the atoms K-Zn, Ga-Kr, and Rb-Xe in their ground state. Despite the limited variational freedom in the Et method, the resultant atomic energies are found to compare well with fully-optimized wave functions of similar sizes. In particular, the present ET results reproduce almost completely the fully-optimized Sekiya-Tatewaki energies with the same basis set size for the atoms K-Zn. All the present energies are also lower than the Clementi-Roetti ones with slightly smaller but fully-optimized basis sets. A generalized even-tempered scheme is suggested and shown to give good results for Xe.