Exploring Do-It-Yourself Approaches in Computational Quantum Chemistry: The Pedagogical Benefits of the Classical Boys Algorithm

Abstract

The ever-increasing impact of molecular quantum calculations over chemical sciences implies a strong and urgent need for the elaboration of proper teaching strategies in university curricula. In such perspective, this paper proposes an extensive project for a student-driven, cooperative, from-scratch implementation of a general Hartree-Fock self-consistent-field code. The project is primarily (but not exclusively) intended for a one-semester laboratory course in graduate physical-chemistry curricula: students are divided into working groups devoted to the implementation of specific subroutines, which are then gradually assembled in the final code. The resulting program is not limited to the overused, trivial case of two-electron diatomic systems, but can treat arbitrary closed-shell molecules with first- and second-row atoms at the STO-3G basis-set level and includes very useful features such as geometry optimization, population analysis, and calculation of dipole moments. The heart of the program is the by now historical algorithm devised by S. F. Boys for evaluating generic molecular integrals through repeated differentiation of fundamental integrals involving only s-type Gaussian orbitals. Though highly inefficient and completely outdated from a computational point of view, this method is reasonably fast for small- and even medium-size molecules (for instance, fixed-geometry calculations on methane and benzene take about 1 s and 6 min, respectively, on a modest home computer). More importantly, unlike newer advanced algorithms, it can be easily understood and implemented by students: thus, it becomes particularly appealing for a didactics based on reflexivity and active knowledge building, rather than on a comfortable but often premature and uncritical use of ready-made professional software packages.