Brief Review of Elementary Quantum Chemistry

In the field of materials science and engineering, ab initio or first principles calculation typically implies finding the approximate solution of the time-indepen-dent, nonrelativistic Schrodinger equation 

PerovsHtes and Related Mixed Oxides Cancels and AppUcaUonSf Fii Edition. 

Edited by Pascal Granger, Vasile L Parvulesci Serge l liaguine, and Wilfrid PrelHer. 

Hamiltonian of the target system is related to the total energy  

In the above equation, A and B run over the M nuclei while i and J are assigned for the N electrons in the system. The first two terms describe the kinetic energy of the electrons and the nuclei, respectively. The symbol represents the Laplacian operators in Cartesian coordinates and Ma is the mass of nucleus A in multiples of the mass of an electron. The last three terms describe the potential part contributed by attractive electrostatic interactions between the nuclei and the electrons, the repulsive potential due to the electron-electron interactions, and the repukive potential due to the nucleus-nucleus interactions, respectively. The distance between particles p and q is denoted by rpq (and in a similar case Rpq)- the wave function of the fill state of the 

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