## Abstract

The key concept of Slater-type orbitals (STOs) underpinning quantum chemical calculations of polyatomic systems has been elucidated via a discourse on mathematical challenges of solving immanent multicenter integrals in density functional theory (DFT). Two types of orbitals viz. Gaussian-type orbitals (GTOs) and STOs are being discussed about their importance in atomic orbital-based calculations and compared their advantages and disadvantages in solving chemistry-related problems of molecules. The third type of orbitals obtained through plane-wave basis sets are excluded in this discussion, as they are mostly used to solve condensed-phase problems. The rudiments of STOs have been discussed without radical analysis of programmatic implementations of mathematical algorithms. The discussions are mainly focused on the DFT calculations, and the concepts of various Slater atomic basis sets are being introduced. In the final part of the article, a few specific examples are considered related to the application of DFT-STOs to different chemical problems. We place emphasis on benchmark studies of simple molecular structures, excitation energy calculations, excitation energy spectrum of UO22+ as well as resonance Raman spectrum analysis.

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@inbook{Majumdar2021, title = {Chapter: Slater-Type Orbitals}, author = {Devashis Majumdar, Pabitra Narayan Samanta, Szczepan Roszak, and Jerzy Leszczynski}, editor = {Eva Perlt}, doi = {https://doi.org/10.1007/978-3-030-67262-1_2}, issn = {2192-6603}, year = {2021}, date = {2021-05-07}, volume = {107}, pages = {17-40}, publisher = {Springer, Cham.}, chapter = {2}, series = {Lecture Notes in Chemistry}, abstract = {The key concept of Slater-type orbitals (STOs) underpinning quantum chemical calculations of polyatomic systems has been elucidated via a discourse on mathematical challenges of solving immanent multicenter integrals in density functional theory (DFT). Two types of orbitals viz. Gaussian-type orbitals (GTOs) and STOs are being discussed about their importance in atomic orbital-based calculations and compared their advantages and disadvantages in solving chemistry-related problems of molecules. The third type of orbitals obtained through plane-wave basis sets are excluded in this discussion, as they are mostly used to solve condensed-phase problems. The rudiments of STOs have been discussed without radical analysis of programmatic implementations of mathematical algorithms. The discussions are mainly focused on the DFT calculations, and the concepts of various Slater atomic basis sets are being introduced. In the final part of the article, a few specific examples are considered related to the application of DFT-STOs to different chemical problems. We place emphasis on benchmark studies of simple molecular structures, excitation energy calculations, excitation energy spectrum of UO22+ as well as resonance Raman spectrum analysis.}, type = {Book: Basis Sets in Computational Chemistry}, keywords = {Benchmark studies, Excitation energy calculations, Resonance Raman spectrum analysis, Slater-type orbitals}, pubstate = {published}, tppubtype = {inbook} }