Study And Application Of Molecular Integral Algorithms Based On Simbolic Caculation

It is imperative to develop a credible general theoretical model and computationalutilities to study the structures and functions of biological macromolecules in theoreticalbiology. Based on the convincing and well-explained theory, quantum mechanicalcalculation has been widely applied in chemistry with remarkable precision, yet itsapplication in simulating biological macromolecules is still limited by today’scomputing power due to the huge computational cost. In order to improve the efficiencyof quantum chemistry calculation, we studied the molecular integral algorithms whichare essential in a quantum chemistry code in this thesis.We explore quantum mechanism calculation with new ideas inspired by symboliccalculation method and proposed improvements on molecular integral algorithm in thisthesis. Our work mainly includes following parts:We study the nature of various algorithms of molecular integral and the form oftheir expressions, and verified the mathematical equivalence of them. The operationsequence and the calculation path is different due to the different process oftwo-electron repulsion integrals in each algorithm, while the mathematical expressionform of the result is identical after transformation. The question of the design of optimalmolecular integral algorithm can be answered by asking how to optimize the expressionequivalent to each algorithm.1) Analyzing advantages and shortages of PRISM algorithm, exploring room forimprovements. PRISM algorithm inherits the advantages of the third generationalgorithms by using the recursion formula to calculate the high angular momentum ofthe two-electron repulsion integrals, which avoids redundant computation by sharing theintermediate variable between the same type of molecular integrals and solves thecontraction problem by comparing all possible calculation paths and finding the optimalone for each type of molecular integral previously. But how Gill counted the number offloating point of PRISM-Path is not theoretically complete, and his implementation ofalgorithm is limited by tradition numerical computation method. Prism-path onlyrestricted in few options than any others. 2) Testing various possible optimizing method of two-electron repulsion integralexpression based on symbolic calculation, including Simplify, Horner, Optimize,MD-Cache method, exploring the effect of HRR, finally proposed the best scheme ofmethod combination. Moreover, we compare the efficiency of the SymQM algorithmand the PRISM algorithm.3) Exploring the implementation of quantum mechanism calculation softwarepackage SymQM. We use the layered-design method to control the complexity of thewhole software, and combining dynamic and static programming languages to buildSymQM package, make it efficient, flexible and extensible.This thesis mainly focus on implementation an efficient quantum chemistrycalculation package SymQM, by using symbolic calculation to optimize, compile thearithmetic expressions of molecular integral. The SymQM package has successfullypassed the test and is functional.