Extremely localized molecular orbitals (ELMO): a non-orthogonal Hartree-Fock method

A new optimization method for extremely localized molecular orbitals (ELMO) is derived in a non-orthogonal formalism. The method is based on a quasi Newton-Raphson algorithm in which an approximate diagonal-blocked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric updating 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, matrix 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 and thus reduces the number of iterations to converge. The delocalization effects are included by a Jacobi correction (JC) which allows the accurate calculation of the total energy with a limited number of operations. This extension, referred to as ELMO(JC), is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less than 2 kcal/mol for a reduced total cost compared to standard HF methods. The small number of variables, even for a very large system, and the limited number of operations potentially makes ELMO a method of choice to study large systems. Received: 30 December 1996 / Accepted: 5 June 1997