Molecular orbital theory eigenvalue equation

HF theory is one of the most important methods in quantum chemistry. Used by itself, it produces good qualitative descriptions of molecular systems. Additionally, many quantitative descriptions of molecules build upon the HF result, first requiring a solution of the HF equations. The basic problem in HF theory is to solve the Roothaan equations, which can be written as the matrix eigenvalue problem, FC = SCe, where F is the Fock matrix and S is the overlap matrix. We solve for C, the orbital coefficients, and the eigenvalues, e. For closed-shell molecules, the electron density of the system, D, is related to C by... 

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