Computational Chemistry 4.8 - Excited Determinants
Short lecture on excited Slater determinants for N-electron wavefunctions.
A ground state Slater determinant contains all N electrons of a molecular system in the N spin orbitals with the lowest possible energy (i.e. it follows the aufbau principle). An excited Slater determinant contains at least one electron which does not occupy the lowest energy spin-orbital available to it. In a system with K atomic orbital basis functions, the are 2K total spin orbitals (K alpha [spin up] and K beta [spin down]). This means that any Slater determinant has N occupied and 2K-N virtual (unoccupied) spin orbitals, meaning that even for a modest number of basis functions there are an enormous (exponential) number of possible excited state determinants due to this combinatoric explosion. One excited electron is a singly excited determinant; doubly for two; triply for three, etc.
Notes Slide: https://i.imgur.com/4GVKSuD.png
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