Comparative Study of Population Analysis Methods With Quasi Atomic-Orbitals

Abstract

Atom is not an observable of the molecular wavefunction, in quantum chemistry there are myriad ways of defining an atom in a molecule. Partitioning a molecule’s electrons between its atomic constituents (population analysis) remains a challenge. A popular approach is based on Mulliken’s overlap-based population analysis, which exploits the fact that molecular orbitals can be expressed as linear combinations of user-defined functions: atomic orbitals. In turn, this creates a dependency on the selection of the predetermined atomic orbitals that are used to expand the molecular orbitals. Chemically intuitive atomic orbitals like Minimal Atomic Orbitals (minAO) produces chemically intuitive atomic charges but a non-accurate wave function. Accurate wave functions can be obtained from large atomic basis sets like def2-QZVPd at the cost of chemically unintuitive atomic charges. With this problem in sight, Quasi-Atomic Orbitals (QAO) are constructed from the accurate wave function to resemble the minAO and maximally span the molecular orbital space. The key idea is Mulliken population analysis can be carried out for wave functions with the chemical intuitive power of minAO, without sacrificing the wave function’s accuracy by using QAO. To ensure that overlaps of QAO are divided between different atoms without bias. Zero-Bond Dipole (ZBD) orthogonalization is proposed as a novel way to orthogonalize QAO. Common population analysis from literature: Charge Model 5 (CM5), QH, Hu-Lu-Yang (ESP), Mulliken, NPA atomic charges will be compared to QAO (Mulliken with QAO) and ZBD-QAO (Mulliken after ZBD orthogonalization of QAO) and tested for mathematical accuracy and expected chemical trends.