Development of Standard Atomic Wave Functions for Helium through Lawrencium

Clementi和Roetti在1974年发表了从氦到氙原子的roothan - hartree - fock （RHF）波函数。麦克林和麦克林在1981年发表了铯到铀的原子波函数。元素周期表中镎之后的原子的波函数还没有被报道过。已发表的氦-铀的波函数在原子分子物理和化学学界一直被视为标准的参考波函数。然而，这些波函数经常被指出存在不小的误差和精度不足。在本项目中，我们首先考察了将要使用的基函数的数量，充分优化了基函数中的变分参数，并开发了改进的氦-氙原子RHF波函数。由此产生的总能量基本上再现了哈特里-福克极限值。然而，当对新波函数的性质进行检验时，我们发现在尖端和远程渐近行为中存在一些不准确之处。因此，我们通过施加一些正确的Hartree-Fock性质作为约束，重构了改进的原子波函数。我们最终的RHF波函数可以真正地被称为近hartree - fock波函数。对于从铯到劳伦斯的原子，我们从分配每个原子合适的基电子构型和项开始。对所需的基函数数进行了仔细的检查，对变分参数进行了充分的优化，并对从铯到劳伦斯的所有较重的原子开发了改进的波函数。本课题开发的一套原子RHF波函数将为原子和分子的物理化学研究提供新的标准参考。

Roothaan-Hartree-Fock (RHF) wave functions for the atoms from helium to xenon were published by Clementi and Roetti in 1974. Atomic wave functions for cesium through uranium were published by McLean and McLean in 1981. Wave functions for the atoms after neptunium in the periodic table have not been reported yet. The published wave functions for helium to uranium have been long regarded as the standard reference wave functions in the society of atomic and molecular physics and chemistry. However, the presence of nontrivial errors and insufficient accuracies has been often pointed out for these wave functions.In this project, we have first examined the number of basis functions to be employed, optimized the variational parameters in the basis functions sufficiently, and developed improved atomic RHF wave functions for helium through xenon. The resultant total energies essentially reproduce the Hartree-Fock-limit values. When the properties of the new wave functions have been examined, however, we have detected some inaccuracies in the cusp and long-range asymptotic behaviors. Therefore, we have reconstructed improved atomic wave functions by imposing some correct Hartree-Fock properties as constraints. Our final RHF wave functions can be truly called near-Hartree-Fock wave functions. For the atoms from cesium to lawrencium, we have started from the assignment of the proper ground electronic configuration and term for each atom. Required number of basis functions has been carefully checked, the variational parameters have been sufficiently optimized, and improved wave functions have been developed for all the heavier atoms from cesium to lawrencium. A set of atomic RHF wave functions developed in this project will be a new standard reference in physics and chemistry of atoms and molecules.