氫分子和水分子基態能量的Ab Initio計算

Abstract

以Ab initio方法來計算氫分子和水分子的基態能量。我們計算能量的理論基礎是密度泛函理論(DFT)和局部密度近似法(LDA)，我們首先以原子軌道為基底函數，並對他們做正交歸一化，接著再求每一項能量密度泛函的值，最後運用Lagrange multipliers對總密度能量泛函做最小化，再以最速下降法求得基態總能

Computation of the ground-state energies of H2 and H2O is concerned. Based on the density functional theory (DFT) the ground state energy of a many-electron system can be expressed by electronic density and is the minimum value of a density functional. So the computation can be done by finding a minimum value of a total energy density functional. Firstly, we use linear combination of atomic orbitals (LCAO) to construct the molecular orbital and calculate each term of the density functional, for example, kinetic energy, electron-electron Coulomb energy, electron-core Coulomb energy, and exchange-correlation energy. Next, we take an initial guess and minimize the total density energy functional by using Largrange multipliers method. Finally by steepest descent method, the ground state total energy is obtained. In some special care is needed for the computation of Coulomb potential to avoid the singular points.