CamCASP/Programming/2

CamCASP => Programming => The DF-INTEGRAL module

Outline

This module consists of modules to calculate integrals needed for density-fitting, the density-fitting module, and modules to calculate integrals *using* primitive integrals in the auxiliary basis set and the density-fitting solution.

Through module df_int_operations and a lot of procedure overloading, a number of logical and computational operations are hidden from the higher-level energy subroutines. For example, to calculate the generalized OOOOAAAB-type 4-index Coulomb integral needed for the first-order exchange repulsion, subroutine calculate_e1exchS2 makes a call to open_gen_2eint('OOOO','AAAB',...) which does the following:

• DF: Performs the density-fitting for monomer A and dimer density-fitting. The integrals needed for the density-fitting will be automatically calculated.
• Integrals: The generalized integrals need various overlap, nuclear and 2-index Coulomb integrals. These will be identified and calculated.
• Assembly: All the components will be assembled into the required integrals.

These modules also need to decide on what needs re-calculation when molecules rotate. If the molecular basis alters, then everything needs to be re-calculated, but if all that happens is a rotation, then some molecular quantities need not be calculated again. In particular, the density-fitting solution remains invariant with respect to rotations. But rotations mix symmetry components of a shell. For example, (px,py,pz) would be mixed into (py,pz,-px) under a rotation by 90 degrees about the z-axis. This means that you cannot directly combine the density-fitting solution with primitive integrals calculated with the molecule in another orientation.