Rayleigh-Schrodinger Perturbation ground state

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

Table 1 Convergence of the Rayleigh-Schrodinger perturbation expansion for the interaction of two ground-state helium atoms at R = 1.0 and 5.6 bohr. The variational interaction energies of the fully symmetric state are equal to -1.01904 hartree and -166.5301 hartree, respectively. The Coulomb energy for R = 5.6 bohr is equal to -77.4764 /ihartree. The B66 and B71 basis sets were used for distances 1.0 and 5.6 bohr, respectively. E(n) denotes the sum of perturbation corrections up to and including the nth-order and S(n) the percent error of E(n) with respect to the variational interaction energy. Energies are in hartree for R = 1 bohr, and in /ihartree for R = 5.6 bohr.

We start the presentation of our results with the Rayleigh-Schrodinger perturbation theory. The results presented in Table 1 show that for small interatomic distances the RS perturbation expansion converges to the energy of the mathematical ground state of the dimer. This state is a Pauli forbidden solution of the Schrodinger equation, completely symmetric un-... 

Table 4 Convergence of the symmetrized Rayleigh-Schrodinger perturbation expansion for the interaction of a ground-state helium atom with a hydrogen molecule at R = 6.5 bohr. The B83 basis set was used. (n) and 6(n) are defined as in Table 1. Energies are in /ihartree.

If the distance R12 between dipoles is small enough compared to the wavelength X, corresponding to transitions between the ground and excited states, within the second- and higher-order Rayleigh-Schrodinger perturbation theory as [92, 105, 106] there appear, as first shown by Fritz London [105, 106], the dispersion interaction [105, 106]... 

Some general remarks on the perturbation theory and the many-body approach are now in order. Let us review first the essence of the nondegenerate Rayleigh-Schrodinger perturbation theory. Consider the time-independent Schrodinger equation for the ground state ... 

In Rayleigh-Schrodinger perturbation theory, the expansion for the exact ground state energy of the perturbed system can also be written in the form... 

Let us now turn our attention to the Rayleigh-Schrodinger perturbation theory for the problem defined by eq. (4.132), (4.133) and (4.134). The expansion for the exact ground state energy given by Rayleigh-Schrodinger perturbation theory may be written... 

The adiabatic corrections to the ground state of H2, HD, and Di we shall calculate using second-order Rayleigh-Schrodinger many-body perturbation theory (RS-... 

As the ratio of the two perturbations is not known, the formalism of the double Rayleigh-Schrodinger (RS) perturbation theory can be used, which looks for the ground state of the total Hamiltonian... 

For the ground state a = 0) the denominators of Brillouin-Wigner perturbation theory are related to those of Rayleigh-Schrodinger pertm-bation theory by the identity... 

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