Halgren T A, Lipscomb W N
Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138.
Proc Natl Acad Sci U S A. 1972 Mar;69(3):652-6. doi: 10.1073/pnas.69.3.652.
Unparameterized and parameterized versions are outlined of a new method for approximating self-consistent field wavefunctions from first principles at the minimum basis set level for complex molecules containing hydrogen and first-row atoms. The Hartree-Fock self-consistent field equations for closed-shell molecules are solved, retaining all one-electron integrals, and approximating the two-electron Coulomb integrals, hybrid integrals, and exchange integrals of the form (i(A)j(A)[unk]i(A)j(A)) and (i(A)j(B)[unk]i(A)j(B)) for centers A and B. A symmetrically orthogonalized basis set is used and rotational invariance is achieved by transformation to local axes that are unique for atoms in anisotropic environments. Parameterization based upon first-principle self-consistent field wavefunctions for a large number of molecules yields F-matrix elements to 0.007 atomic units (au), density matrix elements to 0.007 electrons, orbital populations and atomic charges to 0.01-0.02 electrons, orbital energies to 0.01 au, and total energies to 0.02 au (all standard deviations), in computational times only a few times larger than those required for complete neglect of differential overlap calculations.
本文概述了一种新方法的无参数化和参数化版本，该方法用于在包含氢和第一行原子的复杂分子的最小基组水平上，从第一原理近似自洽场波函数。求解了闭壳层分子的Hartree-Fock自洽场方程，保留了所有单电子积分，并近似了中心A和B的双电子库仑积分、混合积分以及形式为(i(A)j(A)[unk]i(A)j(A))和(i(A)j(B)[unk]i(A)j(B))的交换积分。使用了对称正交化基组，并通过转换为各向异性环境中原子特有的局部轴来实现旋转不变性。基于大量分子的第一原理自洽场波函数进行参数化，得到的F矩阵元精确到0.007原子单位（au），密度矩阵元精确到0.007电子，轨道布居和原子电荷精确到0.01 - 0.02电子，轨道能量精确到0.01 au，总能量精确到0.02 au（均为标准偏差），计算时间仅比完全忽略微分重叠计算所需的时间大几倍。
