Symmetry-adapted basis sets. Automatic generation for problems in chemistry and physics (Q2910630)

Two of the authors \textit{J.S. Avery} and \textit{J.E. Avery} have introduced the generalized Sturmian method applied to atoms in their book, Generalized Sturmians and atomic spectra. (2006; Zbl 1113.81005). If interelectron repulsion is entirely neglected, the energy reduces to NEWLINE\[NEWLINEE_0= -(1/2)(\mathbb{Z}\mathbb{R}_\nu)^2= -(\mathbb{Z}^2/2)(n^{-2}+ (n^{-2}+ (n'')^{-2}+\cdots),NEWLINE\]NEWLINE where \(\mathbb{Z}\) is the nuclear charge, and \(n,n',n'',\dots\): the principal quntum numbers of the atomic spin-orbitals. When a large-\(\mathbb{Z}\) approximation is introduced, the energy of an atomic state is given by NEWLINE\[NEWLINEE_\kappa\approx-(1/2)(\mathbb{Z}\mathbb{R}_\nu-|\lambda_\kappa|)^2,NEWLINE\]NEWLINE where \(\lambda_\kappa\) is a root of the energy-independent interelectron repulsion matrix \(T_{\nu',\nu}'\). The eigenfunctions of the equation NEWLINE\[NEWLINE\sum_\nu [T_{\nu',\nu}'- \lambda_\kappa \delta_{\nu',\nu}]\, C_{\nu,\kappa}= 0NEWLINE\]NEWLINE were the Russell-Saunders states. These states could be used as symmetry-adapted basis functions for more refined calculations.NEWLINENEWLINE In the present book, the authors are joined by the Lektor \textit{Sten Rettrup}, who is the author of the Lecture notes on quantum chemistry. (2003). Chapter 5 sketches the extension of the generalized Sturmian method to molecules. In this chapter they try to show how Sturmian basis functions can be used in \(N\)-electron molecules. To do this, they need to evaluate many-center interelectron repulsion integrals. They propose a new method for evaluating these integrals making use of the Fock projection, which maps Coulomb Sturmians onto sets of 4-dimensional hyperspherical harmonics. These evaluations are also given in Appendix D, beginning with the generalized Slater-Condon rules (in Appendix B and in Appendix E), written in precise form.