A Tour of the Foundations of
Computational Chemistry and Material Science
Lecture 1: ab initio Methods



Multi-Channel Transistion Determination: Introduction

MCTD approximation for excited states is the movement of excited particles in the 'frozen field' of other MCHF/MCDF ground state orbitals the tex2html_wrap_inline348 field. The multi-channel MCTD excited state function can be written as,

equation13

where, tex2html_wrap_inline350 and tex2html_wrap_inline352 and tex2html_wrap_inline354 is the configuration state function (CSF) corresponding to transistions (channels) to excited orbitals, discrete and continuous ones too. tex2html_wrap_inline356 is the CSF corresponding to transistions among valence orbitals tex2html_wrap_inline358. The coefficients tex2html_wrap_inline360 are equal to the coefficients of the corresponding parent ground state configuration. The equation for the coefficients tex2html_wrap_inline362 where tex2html_wrap_inline364 is,

equation23

One can derive the MCTD orbital equations, in the same way the MCDF/MCHF equations are derived, from the variational principle by taking variations only with respect to the excited orbitals tex2html_wrap_inline366. The MCTD orbital equations could then be deduced from the MCDF/MCHF equations by the following replacements: (which can be easily seen from the MCDF equations)

eqnarray34

and,

equation43


equation58

Note, the configuration averaged angular coefficients, which are the sums of the coefficients in the MCDF case. Reduced to only one term because there is only one excited state configuration with the given excited orbital tex2html_wrap_inline366 .




Author: Dr. Warren Perger and Ken Flurchick