Theory
Let be a zero-order CASCI wavefunction, defined as a linear combination of Slater determinants
obtained diagonalizing the true Hamiltonian inside the CASCI space
where is the projector inside the CASCI space. It is possible to define perturber wavefunctions in NEVPT as zero-order wavefunctions of the outer space (external to CAS) where electrons are removed from the inactive part (core and virtual orbitals) and added to the valence part (active orbitals). At second order of perturbation . Decomposing the zero-order CASCI wavefunction as an antisymmetrized product of the inactive part and a valence part
then the perturber wavefunctions can be written as
The pattern of inactive orbitals involved in the procedure can be grouped as a collective index, so to represent the various perturber wavefunctions as, with an enumerator index for the different wavefunctions. The number of these functions is relative to the degree of contraction of the resulting perturbative space.
Supposing indexes and referring to core orbitals, and referring to active orbitals and and referring to virtual orbitals, the possible excitation schemes are:
- two electrons from core orbitals to virtual orbitals (the active space is not enriched nor depleted of electrons, therefore )
- one electron from a core orbital to a virtual orbital, and one electron from a core orbital to an active orbital (the active space is enriched with one electron, therefore )
- one electron from a core orbital to a virtual orbital, and one electron from an active orbital to a virtual orbital (the active space is depleted with one electron, therefore )
- two electrons from core orbitals to active orbitals (active space enriched with two electrons, )
- two electrons from active orbitals to virtual orbitals (active space depleted with two electrons, )
These cases always represent situations where interclass electronic excitations happen. Other three excitation schemes involve a single interclass excitation plus an intraclass excitation internal to the active space:
- one electron from a core orbital to a virtual orbital, and an internal active-active excitation
- one electron from a core orbital to an active orbital, and an internal active-active excitation
- one electron from an active orbital to a virtual orbital, and an internal active-active excitation
Read more about this topic: N-electron Valence State Perturbation Theory
Famous quotes containing the word theory:
“[Anarchism] is the philosophy of the sovereignty of the individual. It is the theory of social harmony. It is the great, surging, living truth that is reconstructing the world, and that will usher in the Dawn.”
—Emma Goldman (1869–1940)
“We have our little theory on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.”
—Thomas Carlyle (1795–1881)
“It is not enough for theory to describe and analyse, it must itself be an event in the universe it describes. In order to do this theory must partake of and become the acceleration of this logic. It must tear itself from all referents and take pride only in the future. Theory must operate on time at the cost of a deliberate distortion of present reality.”
—Jean Baudrillard (b. 1929)