Long-range Electrostatic Interaction And Short-range Pauli Repulsion In Ab Initio QM/MM Methods

Although chemical reactions in solution such as the enzyme catalysis have been extensively studied over a century, its complexity and importance still attract numerous interests both experimentally and theoretically in the scientific world. In the theoretical part, one of the central problems is how to improve the precision of the calculation, scientists then try to apply quantum mechanical method used in the electronic structure calculation of reaction in gas phase to condensed phase. However, for large systems containing protein and nucleic acid, the extremely heavy computational costs make it almost impossible to carry out the dynamical calculation even using the most efficient linear-scaling electronic structure computational methods. Fortunately, in most cases, the reaction center which needs to be accurately treated contains only a small number of atoms, and the rest of the system is unnecessary to be handled by the accurate methods, such as the traditional molecular mechanical methods. Among a variety of hybrid methods developed for these large systems, quantum mechanical/molecular mechanical (QM/MM) dynamics is one of the most popular method. With QM/MM, the whole system is divided into two parts. One is the active site of reaction or solute of solution which is calculated on quantum mechanical level and the rest as an environment is calculated by classical force fields.In the first chapter, the fundamental theory of hybrid quantum mechanical/molecular mechanical method is briefly introduced. For the ab-initio quantum mechanical method, the density functional theory (DFT) is emphasized for its excellent performance both in computing efficiency and accuracy. The basic idea of DFT, its framework and recent progress are briefly reviewed. For molecule mechanics part, the most popular force field and algorithms in classical molecular dynamic (MD) simulation are presented. And then a brief introduction of QM/MM MD method is presented.The electrostatic interaction plays a very important role in the simulation of biochemical reactions, it not only stabilizes the transition state, but also make the long time simulation stable. In classical molecular dynamic simulation the electrostatic interaction has been well studied, and even linear-scaling electrostatic interaction algorithm (the computing costs of the electrostatic energy calculation increase linearly with the size of the system) has been developed. Meanwhile, comparing with those in the classical molecular dynamic method, the electrostatic interaction calculation method in QM/MM method is far from being well established. In QM/MM method, the electronic structure of solute is deeply affected by the electrostatic environment. This interaction also stabilizes the big molecule. In fact, it also speeds up the rate of enzyme catalysis reactivity in some cases. So, it is critical that develop a scheme of the long-range electrostatic interaction calculation in QM/MM method for biochemical simulation.In second chapter our electrostatic interaction calculation method for QM/MM system with periodic boundary condition is introduced, including the theoretical background, main approximations, calculation details and test results. We introduce the Particle-Mesh Ewald algorithm, fast Fourier transformation and B-spline interpolation which are popular in classical molecular dynamics for our QM/MM electrostatic interaction calculation. To deal with the MQ image subsystems, our scheme introduces three approximations, which simplify the calculation significantly. In the end, we also try to deal with the non-neutral system and tested it with a methanol negative ion solution.In the traditional QM/MM method, the energy functional usually includes the energy of the quantum mechanics part, the energy of molecular mechanics part, and the electrostatic interaction energy between two parts, but omits the Pauli repulsion between QM and MM atoms near the boundary. Some methods consider the Pauli repulsion energy by adding the Van der Waals interaction. However Pauli repulsion is an electronic interaction. And it comes from the’Pauli exclusion principle--no two identical fermions can occupy the same quantum state simultaneously’. It affects the electronic and magnetic properties of the system strongly. Thus, Van der Waals-an atomic resolution interaction can neither represent the electronic resolution properties, nor can it repeat the energy of full quantum mechanics calculation.In the third chapter, the energy and dipole moment test results of several examples are presented, which demostrate the serious problems of the missing the Pauli repulsion in traditional QM/MM calculation. Moreover, we developed a semi-empirical method in which the Pauli repulsion is added into the self-consistent process of electronic structure calculation of QM part, is also introduced.In the last chapter, we tallied up the methods mentioned before, and proposed prospective directions of our methods and their probable applications in biochemistry.