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6.1 Example of first-order perturbation theory – ground-state energy of the quartic oscillator 6.2 Example of first- and second-order perturbation theory – quantum pendulum 6.3 Potential energy as a perturbation
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.
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 ...
The second-order perturbation approach was employed by Pearson in 1975 to predict instabilities and distortions in molecular systems; [11] he called it "second-order JTE" (SOJTE). The first explanation of PJT origin of puckering distortion as due to the vibronic coupling to the excited state, was given for the N 3 H 3 2+ radical by Borden ...
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]
In quantum chemistry, n-electron valence state perturbation theory (NEVPT) is a perturbative treatment applicable to multireference CASCI-type wavefunctions.It can be considered as a generalization of the well-known second-order Møller–Plesset perturbation theory to multireference complete active space cases.
Second-order arithmetic, an axiomatization allowing quantification of sets of numbers; Second-order differential equation, a differential equation in which the highest derivative is the second; Second-order logic, an extension of predicate logic; Second-order perturbation, in perturbation theory
The Rashba effect can be understood as a second order perturbation theory in which a spin-up hole, for example, jumps from a |,; state to a |,, +,; with amplitude then uses the spin–orbit coupling to flip spin and go back down to the |, +,; with amplitude . Note that overall the hole hopped one site and flipped spin.