EXTREMELY LOCALIZED MOLECULAR-ORBITALS (ELMO) - A NONORTHOGONAL HARTREE-FOCK METHOD

A new optimization method fur extremely localized molecular orbitals ( ELMO) is derived in a nonorthogonal formalism. The method is based on a quasi Newton-Raphson algorithm ill which an approximate diagonal-blo cked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric upda ting procedure to account for the intrinsically small coupling between the orbitals. The updated orbitals are obtained with approximately n( 2) operations. No n(3) processes such as matrix diagonalization, matri x multiplication or orbital orthogonalization are employed. The use of localized orbitals allows for the creation of high-quality initial '' guess'' orbitals from optimized molecular orbitals of small systems an d thus reduces the number of iterations to converge. The delocalizatio n effects are included by a Jacobi correction (JC) which allows the ac curate calculation of the total energy with a limited number of operat ions. This extension, referred to as ELMO(JC). is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less th an 2 kcal/mol for a I-educed total cost compared to standard HF method s. The small number of variables, even for a very large system, and th e limited number of operations potentially makes ELMO a method of choi ce to study large systems.