This R&D project seeks the development of quantum-mechanical code applicable to large molecules. A factor limiting application of quantum-mechanical methods to biological molecular systems is that these methods typically scale as some power of the number of atoms. This project was conceived as the implementation of the divide-and-conquer approach that had been proposed by Yang for large-scale calculations via the density functional approach, and application of this code to macromolecular problems. In the second year of the project Yang and coworkers discovered how the divide-and-conquer approach could be applied to, inherently much faster, semi-empirical calculations. This has been further elaborated during the past year. Linearly scaling semiempirical quantum mechanical method for biological macromolecules: A linearly scaling method to carry out semiempirical quantum mechanical calculations for large systems has been developed. This method is based on the density-matrix version of the divide-and-conquer approach which the Yang group has pioneered. The method has been tested and has been demonstrated to be both accurate and efficient. With this implementation, it has become possible to perform semiempirical quantum mechanical calculations for large molecules, e.g. over 9000 atoms, on a typical workstation. For biological macromolecules, solvent effects are included with a dielectric continuum model. (Yang & Lee, A density-matrix divide-and-conquer approach for electronic structure calculations of large molecules, 1995; Lee, York & Yang, Linear-Scaling Semiempirical Quantum Calculations for Macromolecules, 1996; York, Lee & Yang, Parametrization and efficient implementation of a solvent model for linear-scaling semiempirical quantum mechanical calculations of biological macromolecules,1996). This was the first demonstration that the divide-and-conquer approach can go far beyond the conventional method and is capable of treating very large systems. Linearly scaling density functional approach: We have made steady progress in developing overall linearly scaling algorithms for density-functional calculations of large systems (Perez-Jorda and Yang: An algorithm for 3D numerical integration that scales linearly with the size of the molecule, 1995; A simple O(N log N) algorithm for the rapid evaluation of particle-particle interactions, 1995; A concise redefinition of the solid spherical harmonics and its use in the fast multipole methods, 1996; Linear scaling for first-principles electronic structure calculations, 1996). Application: Aqueous polarization effects on biological macromolecules. We report the application of a linearly scaling quantum-mechanical method to the study of aqueous polarization effects in biological macromolecules. The polarization contribution to the solvation free energy is observed to be in the range of 5-15% for proteins and 1-3% for DNA. Results suggest that polarization of proteins and DNA in the process of solvation can be well approximated by a linear-response model. The development presented here extends the realm of quantum chemical techniques to applications of macromolecular systems in solution. (York, Lee & Yang: Quantum mechanical study of aqueous polarization effects on biological macromolecules, 1996)
