A local contracted treatment of single and double excitations

Starting from localized bond or lone-pair Hartree-Fock molecular orbitals, one may define contracted doubly excited functions for each pair of bond molecular orbitals. These functions are obtained from local single- and double-configuration interaction (CISD) of moderate size. Then one may build a contracted CISD matrix for the whole molecule, spanned by the Hartree-Fock determinant and these contracted doubly excited functions, the number of which is indeed moderate, as scaling at most as the square of the number of bonds. The calculation of the off-diagonal elements of this matrix is straightforward. Its diagonalization provides an upper bound to the lowest CISD eigenvalue. The well-known size-consistency error may be overcome through self-consistent dressings such as coupled-electron pair approximations, and cutoff criteria will lead to linear scaling. Numerical tests on a series of covalent and ionic systems show that the results are very close to that of coupled-cluster calculations. Possible improvements of this already efficient algorithm are suggested.