Basis Sets in Computational Chemistry

✍ Scribed by Eva Perlt

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 260
• Series: Lecture Notes in Chemistry, 107
• Edition: 1
• Category: Library

✦ Synopsis

This book addresses the construction and application of the major types of basis sets for computational chemistry calculations. In addition to a general introduction, it includes mathematical basics and a discussion of errors arising from incomplete or inappropriate basis sets. The different chapters introduce local orbitals and orbital localization as well as Slater-type orbitals and review basis sets for special applications, such as those for correlated methods, solid-state calculations, heavy atoms and time-dependent adaptable Gaussian bases for quantum dynamics simulations. This detailed review of the purpose of basis sets, their design, applications, possible problems and available solutions provides graduate students and beginning researchers with information not easily obtained from the available textbooks and offers valuable supporting material for any quantum chemistry or computational chemistry course at the graduate and/or undergraduate level. This book is also useful as a guide for researchers who are new to computational chemistry but are willing to extend their research tools by applying such methods. 

✦ Table of Contents

Preface
Contents
1 An Introduction and Overview of Basis Sets for Molecular and Solid-State Calculations
1.1 Introduction
1.2 Nomenclature for Basis Sets
1.3 The GTO Versus STO Discussion
1.4 Gaussian-Type Orbitals
1.5 Slater-Type Orbitals
1.6 Basis Sets With Local Support, Finite Difference, and Spline Approaches
1.7 Conclusion and Outlook
References
3 Local Orbitals in Quantum Chemistry
3.1 Introduction
3.2 Localization Formalism
3.2.1 A Posteriori Techniques
3.2.2 A Priori Localization
3.3 A Simple Application: The Hückel Hamiltonian
3.3.1 A Posteriori Approach
3.3.2 A Priori Local Orbitals
3.4 Selected Applications of Localized Orbitals
3.4.1 Small Linear Molecules: C2H2, C2F2
3.4.2 Bond Dissociation of C2HF
3.4.3 Benzene and Trans-Stilbene
3.4.4 Coordination Complexes
3.4.5 Large Systems: Polycyclic Aromatic Hydrocarbons
3.5 Conclusion
References
4 An Introduction to Discretization Error Analysis for Computational Chemists
4.1 Introduction
4.2 Basic Concepts in Discretization Error Analysis
4.2.1 Variational Approximations
4.2.2 A Priori Error Analysis
4.2.3 A Posteriori Error Estimators and Post-Processing
4.2.4 Asymptotic Expansions and Extrapolation
4.3 Periodic Gross-Pitaevskii and Kohn-Sham Models
4.3.1 Plane-Wave Discretization of the Gross-Pitaevskii Model
4.3.2 A Priori Error Analysis
4.3.3 A Posteriori Error Analysis and Post-Processing
4.3.4 Error Balancing
4.4 Error Cancellation Phenomenon
4.5 Conclusion
References
5 Basis Sets for Correlated Methods
5.1 Introduction
5.2 The Structure of Gaussian Basis Sets
5.2.1 Gaussian Exponents
5.2.2 Contraction Schemes
5.3 The Correlation Problem
5.3.1 Choice of Correlated Method
5.3.2 Partitioning of the Orbital Space
5.3.3 The ``Zeta'' (ζ) Classification and the Complete Basis Set Limit
5.3.4 Diffuse Functions
5.4 Correlated Basis Sets
5.4.1 Pople-Style Basis Sets
5.4.2 Atomic Natural Orbitals
5.4.3 Segmented Basis Sets Based on Atomic Natural Orbitals
5.4.4 Correlation Consistent Basis Sets
5.4.5 n-tuple-Zeta Augmented Polarized Basis Sets
5.4.6 Oliveira and Jorge's nZP
5.4.7 Polarization Consistent Basis Sets
5.5 Conclusion
References
6 Gaussian Basis Sets for Solid State Calculations
6.1 Introduction
6.2 Basis Set Types
6.3 Gaussian Basis Sets
6.3.1 Angular Part
6.3.2 Exponents: Even Tempered Basis Sets
6.4 Choice of Basis Sets
6.4.1 Exponents: Choice From Databases
6.4.2 Exponents: General Recommendations
6.4.3 Test of a Basis Set
6.5 Guidelines to Generate a New Basis Sets
6.5.1 Generating An All-Electron Basis Set
6.5.2 Generating a Basis Set to be Used With an Effective Core Potential
6.5.3 Improve An Existing Basis Set: Re-optimise Exponents
6.5.4 A Basis Set for the Free Atom
6.5.5 A Simple Basis Set From Scratch: Even Tempered Basis Sets for Solids
6.6 Conclusion
References
7 Basis Sets for Heavy Atoms
7.1 Motivation
7.2 The Atomic Basis Sets
7.2.1 Relativistic Effects
7.2.2 Basis Sets for Heavy Atoms
7.3 Applications of Basis Sets for Heavy Atoms
7.3.1 Structure and Reactivity of Cisplatin
7.3.2 NMR Spectroscopy for Pt(II) Complexes
7.4 Concluding Remarks
References
8 Adaptable Gaussian Bases for Quantum Dynamics of the Nuclei
8.1 Introduction
8.2 Evolution of a Gaussian Wavepacket
8.3 Time-Independent Gaussian Bases Adapted to PES
8.3.1 Optimized Distributed Gaussian Bases
8.3.2 Quasi-random Distributed Gaussians
8.3.3 Calculation of the Energy Levels for Triatomic Molecules
8.4 Time-Dependent Gaussian Bases Adapted to the Wavefunction Dynamics
8.4.1 The Formalism
8.4.2 Implementation and Model Problems
8.5 Time-Sliced Dynamics With Stationary Gaussian Bases
8.6 Summary and Outlook
References
Index