on the left by one of the basis AOs %y, and then integrating over the coordinates of the electron in o), one obtains Σ<xlx>Cl=E1E<xJx>C This is a matrix eigenvalue equation in which the E, and (Clu appear as eigenvalues and eigenvectors. The matrices <xl hel x and xl x> are called the Hamiltonian and overlap matrices, respectively. An explicit expression for the former is obtained by introducing the earlier definition of he <xlhlx>=<x-t/2m V-Ix>+<x Ze/r u> +2kCknCKx<xr)xn(r)errD|x(r)x:(r) An important thing to notice about the form of the matrix Hartree equations is that to compute the Hamiltonian matrix, one must know the LCAO coefficients CK, of the orbitals which the electrons occupy On the other hand these lcao coefficients are supposed to be found by solving the Hartree matrix eigenvalue equations. This paradox leads to the need to solve these equations iteratively in a so-called self-consistent field (SCF)technique. In the SCF process, one inputs an initial approximation to the ( CKy) coefficients This then allows one to form the hamiltonian matrix defined above The Hartree matrix equations Eu <xul x> Cu=E, Eu xl x>Cu are then solved for new(CKy,) coefficients and for the orbital energies(Ex). The new LCAO coefficients7 on the left by one of the basis AOs cn , and then integrating over the coordinates of the electron in fJ , one obtains Sm <cn | he | cm> CJ,m = eJ Sm <cn | cm> CJ,m . This is a matrix eigenvalue equation in which the eJ and {CJ,m} appear as eigenvalues and eigenvectors. The matrices <cn | he | cm> and <cn | cm> are called the Hamiltonian and overlap matrices, respectively. An explicit expression for the former is obtained by introducing the earlier definition of he : <cn | he | cm> = <cn | – h2 /2m Ñ 2 |cm> + <cn | -Ze2 /|r |cm > + SK CK,h CK,g <cn (r) ch (r’) |(e2 /|r-r’|) | cm (r) cg (r’)>. An important thing to notice about the form of the matrix Hartree equations is that to compute the Hamiltonian matrix, one must know the LCAO coefficients {CK,g} of the orbitals which the electrons occupy. On the other hand, these LCAO coefficients are supposed to be found by solving the Hartree matrix eigenvalue equations. This paradox leads to the need to solve these equations iteratively in a so-called self-consistent field (SCF) technique. In the SCF process, one inputs an initial approximation to the {CK,g} coefficients. This then allows one to form the Hamiltonian matrix defined above. The Hartree matrix equations Sm <cn | he | cm> CJ,m = eJ Sm <cn | cm> CJ,m are then solved for “new” {CK,g} coefficients and for the orbital energies {eK}. The new LCAO coefficients