Implementation of analytical first derivatives for evaluation of the many‐body nonadiabatic wave function with explicitly correlated Gaussian functions

The many-body wavefunction of the unbound He-Ps system has been studied by the exact diagonalization of a explicitly correlated gaussians basis optimized by a stochastic variational method. The nucleus-positron distance has been varied by constraining the parameters of the nucleus-positron correlated gaussian term. The constraining technique allows to describe He and Ps interacting at different distances. The calculated wavefunction can be approximated as composed by weakly perturbed He and Ps atoms. The electron forming the Ps tends to be farther from the nucleus than the positron due to the strong electron-electron Pauli repulsion with the electrons of He. The described technique gives accurate energy and wave functions for Ps interacting with atoms that can be used to calculate the interaction potential of Ps with molecular matter.

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An effective method for generating nonadiabatic many‐body wave function using explicitly correlated Gaussian‐type functions

The Journal of Chemical Physics ◽

10.1063/1.461538 ◽

1991 ◽

Vol 95 (9) ◽

pp. 6681-6698 ◽

Cited By ~ 53

Author(s):

Pawel M. Kozlowski ◽

Ludwik Adamowicz

Keyword(s):

Wave Function ◽

Body Wave ◽

Many Body ◽

Gaussian Type ◽

Explicitly Correlated

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Correlation energy in triplet electronic states. Application of the many-body Rayleigh-Schrödinger perturbation theory in the restricted Roothaan-Hartree-Fock formalism

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19811324 ◽

1981 ◽

Vol 46 (6) ◽

pp. 1324-1331 ◽

Cited By ~ 3

Author(s):

Petr Čársky ◽

Ivan Hubač

Keyword(s):

Wave Function ◽

Perturbation Theory ◽

Correlation Energy ◽

Electronic States ◽

Many Body ◽

Third Order ◽

Explicit Formulas ◽

Hartree Fock ◽

The Many ◽

Schrödinger Perturbation

Explicit formulas over orbitals are given for the correlation energy in triplet electronic states of atoms and molecules. The formulas were obtained by means of the diagrammatic many-body Rayleigh-Schrodinger perturbation theory through third order assuming a single determinant restricted Roothaan-Hartree-Fock wave function. A numerical example is presented for the NH molecule.

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Wave equation for dissipative systems derived from a quantized many-body problem

Canadian Journal of Physics ◽

10.1139/p80-140 ◽

1980 ◽

Vol 58 (7) ◽

pp. 1019-1025 ◽

Cited By ~ 4

Author(s):

M. Razavy

Keyword(s):

Wave Function ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Body Problem ◽

Body Wave ◽

Time Dependent ◽

Dissipative Systems ◽

Many Body ◽

Dependent Part ◽

The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

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Gaussian Wave Functions and the Many-Body Problem

Canadian Journal of Physics ◽

10.1139/p72-048 ◽

1972 ◽

Vol 50 (4) ◽

pp. 305-311 ◽

Cited By ~ 14

Author(s):

R. L. Hall

Keyword(s):

Bound States ◽

Wave Functions ◽

Permutation Symmetry ◽

Many Body ◽

Single Product ◽

Gaussian Functions ◽

Energy Expectation ◽

The Many ◽

Body Energy ◽

Exact Energy

A system of identical nonrelativistic particles is considered. It is shown that the wave functions for relative motion, which have the correct permutation symmetry, must satisfy two functional equations. In the case of bosons these equations are solved for those bound states where the wave function is also in a single-product form. The only solutions are Gaussian functions. Consequently these are the only functions which can reduce the N-body energy expectation to an integral over a single variable. Furthermore, we show that our reduced two-body Hamiltonian which in general gives energy lower bounds yields the exact energy of the entire system only for the Hooke's law interaction. Neither possibility is allowed by fermions.

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