Eiichi Ishiguro

On the Polarizability of the Hydrogen Molecule

The polarizability of the hydrogen molecule is calculated theoretically The energy of the molecule, under an external electrostatic field, is calculated by the variation method, using 11+10 terms and 11+9 terms James-Coolidge type wave functions, for the polarizability parallel to and perpendicular to the molecular axis respectively. By expanding the energy in powers of the field strength, the polarizability is determined. By using a Morse function for the adiabatic potential of the molecule, the 0-0 and 0-1 matrix elements of the polarizability between vibrational states are calculated, with the result: α00=7.89, γ00=2.78, α01=1.39, γ01=0.90 for ordinary hydrogen H2, and α00=7.75, γ00=2.68, α01=1.13, γ01=0.71 for heavy hydrogen D2 (in units of 10-25 cm3), where α is the mean polarizability and γ the anisotropy.

Spin Orbit Coupling Constants in Simple Diatomic Molecules

Spin orbit coupling constant is calculated for various diatomic molecules. SCF MO theory is adopted. Two-center integrals are neglected except the overlap integral. One-center integrals are estimated from atomic ζ n , l . The agreement with experiment is excellent. Correlation between the electro-negativity difference and the coupling constant is pointed out. As an application of the theory, electronic structures of the ground state and the lower excited states of the O 2 + molecule are discussed.

Tables of Integrals Useful for the Calculations of Molecular Energies. III

Coulomb, exchange, ionic integrals and one-electron integrals which involve 2 s and 2 p orbitals have been calculated for homopolar diatomic molecules. Slater type orbitals have been used, with equal values for the exponent δ. Two-center integrals are tabulated as functions of α=δ R ( R : internuclear distance). This work completes the project of tabulation of molecular integrals of which Parts I and II were published in Proc. Phys.-Math. Soe. Japan 20 (1938), 22 (1940), Extra Nos.

The Electronic Structure of the Ground State of the HeH^+ Molecule

The total electronic energy of HeH + is calculated with the wave functions in which the “in-out correlation” is included by using two different 1 s Slater type atomic orbitals of He. The conclusion is that the effect of the in-out correlation of electrons in the vicinity of the He nucleus is considerable in HeH + , though it is somewhat smaller than that in the He atom. Among the four wave functions employed here, the simplest one can give the qualitative explanation of the electronic structure of this system. The results computed with the simplest wave function are E ( R e )=-2.935026999a.u., R e =1.4666a.u. ω e =3.1×10 3 cm -1 and D e =1.62 eV. The best values of E ( R e ) and R e , calculated by use of the most flexible wave function, amount to -2.93819775 a.u. and 1.4648 a.u., respectively.

Note on the Exchange Polarization and In-Out Effect

To investigate the correlation of electrons in the same shell due to the exchange correlation with the other unpaired electron, and so-called in-out effect, several approximate methods (Hartree-Fock, unrestricted Hartree-Fock, projected unrestricted Hartree-Fock, split shell and spin degenerate state configuration interaction) are developed. As the simplest example, the ground state 2 S and first excited state 2 P of the Li atom are considered. Slater type 1s, 2s, and 2p orbitals are adopted and the wave functions and total energies are determined by the variational method. The electron spin density at the nucleus (ψ 2 (0)) is given for the respective cases. Discussions on the results are given.