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For the first-order perturbation, we need solve the perturbed Hamiltonian restricted to the degenerate subspace D, | = | + | , simultaneously for all the degenerate eigenstates, where are first-order corrections to the degenerate energy levels, and "small" is a vector of () orthogonal to D.
The pseudo Jahn–Teller effect (PJTE), occasionally also known as second-order JTE, is a direct extension of the Jahn–Teller effect (JTE) where spontaneous symmetry breaking in polyatomic systems (molecules and solids) occurs even when the relevant electronic states are not degenerate. The PJTE can occur under the influence of sufficiently ...
The standard exposition of perturbation theory is given in terms of the order to which the perturbation is carried out: first-order perturbation theory or second-order perturbation theory, and whether the perturbed states are degenerate, which requires singular perturbation. In the singular case extra care must be taken, and the theory is ...
In this, the Schrieffer–Wolff transformation is an operator version of second-order perturbation theory. The Schrieffer–Wolff transformation is often used to project out the high energy excitations of a given quantum many-body Hamiltonian in order to obtain an effective low energy model. [1]
It involves expanding the eigenvalues and eigenkets of the Hamiltonian H in a perturbation series. The degenerate eigenstates with a given energy eigenvalue form a vector subspace, but not every basis of eigenstates of this space is a good starting point for perturbation theory, because typically there would not be any eigenstates of the ...
Even systems that in the undistorted symmetric configuration present electronic states which are near in energy but not precisely degenerate, can show a similar tendency to distort. The distortions of these systems can be treated within the related theory of the pseudo Jahn–Teller effect (in the literature often referred to as "second-order ...
Such degenerate states are often the case of atomic and molecular valence states. To counter the restrictions, there was an attempt to implement second-order perturbation theory in conjunction with complete active space self-consistent field (CASSCF) wave functions. [3]
Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry.It improves on the Hartree–Fock method by adding electron correlation effects by means of Rayleigh–Schrödinger perturbation theory (RS-PT), usually to second (MP2), third (MP3) or fourth (MP4) order.