Pseudospectral double excitation configuration interaction

Recently, we have presented’ a pseudospectral formulation of the full configuration interaction (FCI) problem. The method was accurate to a mhartree after corrections, but the size of the numerical grids required made it impossible to realize any computational advantage for systems feasible with today’s hardware. In this paper, we present the first application of the pseudospectral method to truncated configuration interaction, the double-excitation configuration interaction (DCI) method. Since the scaling of the conventional DC1 method is not combinatorial like full CI, it is easier to realize the pseudospectral advantage. The method we present here has several striking characteristics. First, the method will be faster than conventional DC1 approaches for sufficiently large cases, as the scaling is decreased from 0( n6) to O(n5), where n is the number of molecular orbitals. This scaling advantage will be realizable for cases of rather modest dimension, where we consider modest to mean the calculation would take < 10 min of cpu time on a CRAY YMP or equivalent using conventional methods. Second, it provides a framework within which LLdirect,“2 in the sense of “direct selfconsistent field ( SCF) ,“3 correlated techniques can be realized. By “direct,” we mean that neither the Hamiltonian matrix nor the two-electron integrals are stored on disk. This approach will become necessary as correlation treatments are applied to large systems, and the pseudospectral method is well-suited to it because of the ability to organize the required data (which will be combined to form the two-electron integrals) by blocks of gridpoints. Finally, it allows one to take advantage of locality without introducing the approximations suggested by Pulay and Saebo.4 This can be done by using “cutoffs” where the requisite summations are restricted to a subset of the physical space grid. Note that the approximations of Pulay and Saebo may be used along with “cutoffs” to gain even greater advantage. At this point, we have only coded the equations for the molecular orbital basis, and therefore we provide numerical evidence supporting only the first of these claims. A forthcoming paper will address the last two issues. SELF-CONSISTENT ELECTRON PAIR THEORY FOR DOUBLES Cl