Soft X-Ray Spectra of Molecules

Abstract

The basic starting point for our discussion is to be the Spin-Polarized-Hartree-Fock method [1] (SPHF). In this model, the electronic wavefunction is assumed to be a single Slater determinant of one-particle wavefunctions. The Hamiltonian of the system is given to be

$$ {\rm H} = - \sum\limits_i {\nabla _i^2} - \sum\limits_{i,I} {\frac{{2{z_I}}}{{|{r_i} - {R_I}|}}} + \frac{1}{2}\sum\limits_{i,j} {\frac{2}{{|{r_i} - {r_j}|}}} + \frac{1}{2}\sum\limits_{I,J} {\frac{{2{Z_I}{Z_J}}}{{|{R_I} - {R_J}|}}} $$

(1)

In obtaining this Hamiltonian, one must make one of two approximations. Either one must separate out the nuclear motion by the Born-Oppenheimer approximation or one must assume the nuclei to be infinitely heavy [2]. The corrections to the theory due to the kinetic energy of the nuclei are beyond the scope of the pre-sent lecture. In equation (1), an atomic system of units is used. Here e = $\sqrt 2$, ħ = 1, m _e = 0.5 and the unit of energy is the Rydberg (1 Ry ≈ 13.6 eV), the unit of the length is the atomic unit (1 a.u. = 1 bohr radius ≈ 0.53 Å). The upper case letters refer to nuclear coordinates and properties, while the lower case letters refer to electronic coordinates and properties.

Work supported in part by the National Science Foundation under Grant GH-33634 and by the Aerospace Research Laboratory, Air Force Systems Command, USAF, Wright-Patterson AFB, Ohio, Contract No. F33615-72-C-1506.