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Slater-Type Orbitals

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Basis Sets in Computational Chemistry

Part of the book series: Lecture Notes in Chemistry ((LNC,volume 107))

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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Abbreviations

ADF:

Amsterdam density functional code

a 0 :

Bohr radius

ALDA:

Adiabatic local density approximation

CCSD:

Coupled cluster singles and doubles

CCSD(T):

CCSD including triple excitations

CGTO:

Contracted GTO

CT:

Charge transfer

DFT:

Density functional theory

EOM:

Equation of motion

F :

Fock matrix operator

GTO:

Gaussian-type orbital

h :

One-electron operator

HOMO:

Highest occupied molecular orbital

J :

Coulomb operator

K :

Exchange operator

LDA:

Local density approximation

LCAO:

Linear combination of atomic orbital

LUMO:

Lowest unoccupied molecular orbital

M-L:

Metal–ligand

MO:

Molecular orbital

NL:

Nonlocal

PA:

Polyacetylene

RI:

Raman intensity

SCF:

Self-consistent field

SERS:

Surface-enhanced Raman spectroscopy

SOC:

Spin–orbit coupling

STO:

Slater-type orbital

TDDFT:

Time-dependent density functional theory

VK:

Vignale–Kohn

VWN:

Vosko–Wilk–Nausair

XC:

Exchange–correlation

ZORA:

Zeroth-order regular approximation

\(\zeta\) :

Slater exponent

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Acknowledgements

This work has been supported by NSF-CREST (Award No. 154774) and EPSCOR R-II (Award No. OIA - 1632899). One of the authors (S.R.) acknowledges the financial support by a statutory activity subsidy from Polish Ministry of Science and Technology of Higher Education for the Faculty of Chemistry of Wroclaw University of Technology.

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Authors and Affiliations

  1. Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS, 39217, USA

    Devashis Majumdar, Pabitra Narayan Samanta & Jerzy Leszczynski

  2. Advanced Materials Engineering and Modelling Group, Faculty of Chemistry, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland

    Szczepan Roszak

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  1. Devashis Majumdar
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  2. Pabitra Narayan Samanta
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  3. Szczepan Roszak
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  4. Jerzy Leszczynski
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Correspondence to Devashis Majumdar , Szczepan Roszak or Jerzy Leszczynski .

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  1. Department of Chemistry, University of California, Irvine, CA, USA

    Eva Perlt

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Majumdar, D., Samanta, P.N., Roszak, S., Leszczynski, J. (2021). Slater-Type Orbitals. In: Perlt, E. (eds) Basis Sets in Computational Chemistry. Lecture Notes in Chemistry, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-030-67262-1_2

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