Analytical formulas for the coefficients occurring in some two-center integrals

Guseinov, I. I.; Mursalov, T. M.; Imamov, É. M.

doi:10.1007/bf00747875

J Struct Chem

1976

DOI: 10.1007/bf00747875

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Analytical formulas for the coefficients occurring in some two-center integrals

I. I. Guseinov¹,

T. M. Mursalov²,

É. M. Imamov³

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2004

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“…Hence, calculation of the energy 1 ( ) N V + r is reduced to analytical calculation of concentric potential function (6) for which a general analytical formula can be derived in the basis of the real Slater functions using the procedure described in [8].…”

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Calculation of the Potential Energy of Electron-Atom Interaction in the Basis of the Slater Functions

2004

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Theoretical investigation of the electrostatic electron-atom interaction is an urgent problem in connection with the quantum-mechanical study of electron scattering by atoms, photoluminescence and photoionization of atoms, etc. [1,2]. Therefore, simpler analytical formulas suitable for computer calculations of the potential energy of electrostatic electronatom interaction are required. In the present work, such formulas are derived by the Hartree-Fock-Rutan (HFR) method in the basis of the Slater functions most suitable from the physical viewpoint.According to quantum mechanics concepts, the potential energy of electrostatic electron interaction with an Nelectron atom is given by the formulaHere 1 N + r is the radius-vector of the electron approaching the atom counted from the origin of coordinates, U is the deterministic atomic wave function determined by the HFR method, d τ denotes integration over the spatial coordinates and summation over the spin coordinates of all N atomic electrons, int H is the operator of energy of interaction between electron No. (N + 1) and the atom expressed in atomic units:where Z is the serial number of the atom, 1 N r + and 1 N r µ + are distances from electron No. (N + 1) to the nucleus and the µth electron, respectively. Substituting Eq. (2) into Eq. (1), taking advantage of the theorem about calculation of the matrix elements of scalar operators symmetric about permutations of identical particles among deterministic wave functions [3], and summing over the electron spins, we obtain 1

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Calculation of the Potential Energy of Electron-Atom Interaction in the Basis of the Slater Functions

2004

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Analytical formulas for the coefficients occurring in some two-center integrals

Cited by 1 publication

References 1 publication

Calculation of the Potential Energy of Electron-Atom Interaction in the Basis of the Slater Functions

Calculation of the Potential Energy of Electron-Atom Interaction in the Basis of the Slater Functions

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