This week we submitted a paper related to our ongoing work regarding the use of Coulomb Sturmian basis functions in electronic structure theory. Given the recent progress, which has been made with regards to the evaluation of molecular integrals based on these exponential-type functions, molecular calculations based on Coulomb Sturmians are within reach. This is a very promising prospect due to the abilities of the Coulomb Sturmians to represent the features of the wave function both at the nucleus as well as at large distances.
Our work takes a first look at the convergence of Coulomb Sturmian discretisations in electronic structure theory, expanding on ideas suggested in my PhD thesis. We suggest a simple construction scheme for Coulomb Sturmian basis sets and discuss its properties. A key aspect is to connect the basis set parameters to physical features of the wave function or other chemically intuitive quantities such as the exponents obtained by Clementi and Raimondi, i.e. the effective nuclear charge. The abstract of the paper reads
The first discussion of basis sets consisting of exponentially decaying Coulomb Sturmian functions for modelling electronic structures is presented. The proposed basis set construction selects Coulomb Sturmian functions using separate upper limits to their principle, angular momentum and magnetic quantum numbers. Their common Coulomb Sturmian exponent is taken as a fourth parameter. The convergence properties of such basis sets are investigated for second and third row atoms at the Hartree-Fock level. Thereby important relations between the values of the basis set parameters and the physical properties of the electronic structure are recognised. For example, an unusually large limit for the angular momentum quantum number in unrestricted Hartree-Fock calculations can be linked to the breaking of spherical symmetry in such cases. Furthermore, a connection between the optimal, i.e. minimum-energy, Coulomb Sturmian exponent and the average Slater exponents values obtained by Clementi and Raimondi (E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686 (1963)) is made. These features of Coulomb Sturmian basis sets emphasise their ability to correctly reproduce the physical features of Hartree-Fock wave functions.
Michael F. Herbst, James E. Avery and Andreas Dreuw.
Quantum chemistry with Coulomb Sturmians: Construction and convergence of Coulomb Sturmian basis sets at Hartree-Fock level.
Published in Physical Review A, 99, 012512 (2019).
[DOI 10.1103/PhysRevA.99.012512] [pdf] [arXiv:1811.05777] [further details]