The Field-Adapted ADMA Approach: Introducing Point Charges

Abstract

New developments of the adjustable density matrix assembler (ADMA) approach to macromolecular quantum chemistry are described, based on the original fuzzy density matrix fragmentation scheme combined with an approach of using point charges to approximate the effects of additional, distant parts of a given macromolecule in the quantum chemical calculation of each fragment. The ADMA approach divides a macromolecule (the target molecule) into fuzzy fragments, for which conventional quantum chemical calculations are performed using moderate-sized “parent molecules” which contain both the fragment and all the local interactions of the fuzzy fragment with its surroundings within a preselected distance. For any such distance criterion, that is, for any size limit for the parent molecules, the computational time scales linearly with the size of the macromolecule. As demonstrated in earlier papers, in the original, linear-scaling ADMA approach, the accuracy is fully controlled by this distance, and with a large enough distance criterion nearly exact results are obtained when compared with the conventional Hartree−Fock method. In the new field-adapted ADMA method the same accuracy can be achieved using a smaller distance criterion for the parent molecules if in each parent molecule calculation point charges are also used to represent distant parts of the macromolecule. This allows one to use smaller parent molecules and faster overall calculations resulting in the same overall accuracy that can be achieved only with larger parent molecules in the original ADMA method. Specifically, in the quantum chemical calculations determining the fragment density matrices, each parent molecule is placed within a point-charge field representing the rest of the macromolecule. Consequently, not only the short-range interactions within the actual parent molecule, but also the approximate effects of longer-range electrostatic interactions present in the rest of the macromolecule, are included in the new fragment density matrices. With a number of test calculations of small oligopeptides and proteins, it is shown that the inclusion of partial charges is an efficient tool to obtain results of a uniform accuracy for all these test cases, and that this approach can be used to reduce the need to include longer-range interactions by explicit quantum chemical calculation for much larger parent molecules for the fragments. With a large increase in accuracy and the decrease in computational demand, the field-adapted ADMA approach is now able to describe efficiently very large biomolecular systems at the ab initio quality level.