Zope Rajendra R, Dunlap Brett I
Department of Chemistry, George Washington University, Washington, D.C., 20052.
Code 6189, Theoretical Chemistry Section, U.S. Naval Research Laboratory, Washington, D.C. 20375.
J Chem Theory Comput. 2005 Nov;1(6):1193-200. doi: 10.1021/ct050166w.
Recently, we formulated a fully analytical and variational implementation of a subset of density functional theory using Gaussian basis sets to express orbital and the one-body effective potential. The implementation, called the Slater-Roothaan (SR) method, is an extension of Slater's Xα method, which allows arbitrary scaling of the exchange potential around each type of atom in a heteroatomic system. The scaling parameter is Slater's exchange parameter, α, which can be determined for each type of atom by choosing various criteria depending on the nature of problem undertaken. Here, we determine these scaling parameters for atoms H through Cl by constraining some physical quantity obtained from the self-consistent solution of the SR method to be equal to its exact value. Thus, the sets of α values that reproduce the exact atomic energies have been determined for four different combinations of basis sets. A similar set of α values that is independent of a basis set is obtained from numerical calculations. These sets of α parameters are subsequently used in the SR method to compute atomization energies of the G2 set of molecules. The mean absolute error in atomization energies is about 17 kcal/mol and is smaller than that of the Hartree-Fock theory (78 kcal/mol) and the local density approximation (40 kcal/mol) but larger than that of a typical generalized gradient approximation (∼8 kcal/mol). A second set of α values is determined by matching the highest occupied eigenvalue of the SR method to the negative of the first ionization potential. Finally, the possibility of obtaining α values from the exact atomization energy of homonuclear diatomic molecules is explored. We find that the molecular α values show much larger deviation than what is observed for the atomic α values. The α values obtained for atoms in combination with an analytic SR method allow elemental properties to be extrapolated to heterogeneous molecules. In general, the sets of different α values might be useful for calculations of different properties using the analytic and variational SR method.
最近，我们使用高斯基组来表示轨道和一体有效势，制定了密度泛函理论一个子集的完全解析变分实现方法。这种实现方法称为斯莱特 - 罗特汉（SR）方法，它是斯莱特Xα方法的扩展，该方法允许在异原子系统中围绕每种类型的原子对交换势进行任意缩放。缩放参数是斯莱特交换参数α，可根据所处理问题的性质通过选择各种标准来为每种类型的原子确定该参数。在此，我们通过将从SR方法的自洽解中获得的某些物理量约束为等于其精确值，来确定从氢原子到氯原子的这些缩放参数。因此，对于基组的四种不同组合，已经确定了能重现精确原子能量的α值集。从数值计算中获得了一组与基组无关的类似α值。随后，这些α参数集被用于SR方法中，以计算G2分子集的原子化能。原子化能的平均绝对误差约为17千卡/摩尔，小于哈特里 - 福克理论（78千卡/摩尔）和局域密度近似（40千卡/摩尔），但大于典型的广义梯度近似（约8千卡/摩尔）。通过将SR方法的最高占据本征值与第一电离势的负值匹配，确定了第二组α值。最后，探讨了从同核双原子分子的精确原子化能中获得α值的可能性。我们发现分子α值的偏差比原子α值的偏差大得多。结合解析SR方法获得的原子α值可用于将元素性质外推到异质分子。一般来说，不同的α值集可能有助于使用解析变分SR方法进行不同性质的计算。
