Electron interaction energy

Consequently, we introduce the second approximation which is to use an approximate electrostatic potential in Eq.(4-21) to determine inter-fragment electronic interaction energies. Thus, the electronic integrals in Eq. (4-21) are expressed as a multipole expansion on molecule J, whose formalisms are not detailed here. If we only use the monopole term, i.e., partial atomic charges, the interaction Hamiltonian is simply given as follows ... 

T p represents the electronic kinetic energy functional Vec[p the electron-electron interaction energy functional... 

The physical picture that emerges out of the exercise above is that the electron-electron interaction energy... 

Fermi s Golden Rule Nuclear Factors and Electronic Interaction Energies. 58... 

The exchange-correlation (xc) energy functional defined above is shown to consist of two contributions a difference between the interacting and noninteracting kinetic energy functionals and the nonclassical part of the electron-electron interaction energy functional. Using Eq. (44) we rewrite Eq. (14) as... 

Let us start from the energy expression (34). We write it as a sum of a one-electron energy and an electron interaction energy E2. 

The electron interaction energy E2 can be further decomposed into the following contributions ... 

Exchange Energy. An attractive (negative) component of the electron-electron interaction energy. Arises due to an overestimation of the repulsive (positive) component or Coulomb energy. 

This data clearly shows that corrections to the SCF model (see the above table) represent significant fractions of the inter-electron interaction energies (e.g., 1.234 eV compared to 5.95- 1.234 = 4.72 eV for the two 2s electrons of Be), and that the interelectron interaction energies, in turn, constitute significant fractions of the total energy of each orbital (e.g., 5.95 -1.234 eV = 4.72 eV out of-15.4 eV for a 2s orbital of Be). 

Methods of density functional theory (DFT) originate from the Xa method originally proposed by Slater [78] on the base of statistical description of atomic electron structure within the Thomas-Fermi theory [79]. From the point of view of Eq. (3), fundamental idea of the DFT based methods consist first of all in approximate treatment of the electron-electron interaction energy which is represented as ... 

Van Vleck (80) illustrated how Eq. (73) can be identified in the energy expression of the two interacting electrons in a non-relativistic field-free framework. For such a system the contribution to the electron-electron interaction energy Ey comprises the Coulomb energy Jy and the exchange energy Ky,... 

In forming intermolecular H-bonds the intensity alteration depends upon the -electron interaction energy share, With large energy. shares of the -electron interaction the integral band intensity remains either almost equal to that of a free group (a-oxyderivative of... 

For the details and derivation of the physical interpretation we refer the reader to the original literature14,15. Since the Coulomb self-energy component of the KS electron-interaction energy functional and its derivative, the Hartree potential, are known functionals of the density, we provide in Section HA the expressions governing the interpretation of the KS exchange-correlation energy... 

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