Ab Initio Modeling of Materials

The basis of ab initio modeling of materials is the time-independent Schrodinger equation in which the state of a molecular system is described with a wavefunction  

Hatree-Fock Approximation and Single Electron Hamiltonian 

Under the Hartree-Fock (i.e., HF) approximation, the function of in variables for the solutions of the electronic Hamiltonian is reduced to n functions, which are referenced as molecular orbitals (MOs), each dependent on only three variables. Each MO describes the probability distribution of a single electron moving in the average field of all other electrons. Because of the requirements of the Pauli principle or antisymmetry with respect to the interchange of any two electrons, and indistinguishability of electrons, the HF theory is to approximate the many-electron wavefunction by an antisymmetrized product of one-electron wavefunctions and to determine these wavefunctions by a variational condition applied to the expected value of the Hamiltonian in the resulting one-electron equations, 

Local Density Approximation Local density approximation (LDA) is the first practical approximation based on the assumption that the exchange-correlation energy of a single electron at the position r is equal to the exchange-correlation energy, Exc [ ( )], of an electron in a homogeneous electron gas of a density n(r) equal 

The most important feature of the ab initio quantum chemistry computation is the capability of describing the breaking and 

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