This is a book for all chemists who don't want to become theoretical chemists, but who want to understand user articles and presentations with theoretical concepts included and who want to use theoretical chemistry for there own projects. It gives an overview about: Hartree Fock Theory, Post-Hartree-Fock-Methods, Density-Functional-Theory, Solid-State-Physics, Force-Field Methods and Molecular Dynamics.
Everything the chemist of the 21th century should know about Theoretical Chemistry, to be able to read articles with a satisfying yield of new informations, to be able to effectively talk to and work with theoretical chemists and to plan own calculations.
The author offers an overview about Post-Hartree-Fock-Methods (Coupled Cluster (incl. Example for Application of Perturbation-Theory), Full CI, explicitly correlated methods) Density-Functional-Theory (Basic Equations, reason of lower computational cost, important Types of Functionals (LSD-Functionals, GGA-Functionals, Hybrid-Functionals)), Important points in searching the right method), Force-Field-methods (Basic Theory, Basic Equations, practical tips as tool in quantum-chemical Calculations), theoretical Solid-State Physics (differences to quantum chemical equations, special behavior of solid-state-systems, atomic groups with single-particle-behavior – like phonons, polarons, ...), the role of special techniques (Perturbation Theory, Group Theory) and shows connections of those techniques to molecular dynamics.
For that he shows all necessary mathematics and derivations, when they are needed but just as deep as necessary. Not with the target to make the reader a theoretician. In front of the derivative part he commits his pictorial imagination of Hilbert-space, basis set, and quantum-chemical-calculations.
Table of Contents
0. Preface
0.1. Short Description, target audience, required Preknowledge
0.2. Introduction to the used Pathways of Argumentation and examples for the need of understanding more about Theoretical Chemistry
1. Overview about Theoretical-Methods
2. Basis set
2.1. Introduction
2.2. Pictorial-Imagination of Hilbert-Space
2.3. Orthogonality and relative behavior between different Solutions of the Schrödinger-Equation
2.4. First look at real Basis-Functions and appearing Integrals
2.5. The Schrödinger-Equation for the Hydrogen-Atom with a Gaussian-Ansatz
2.6. Ground-Principles of modern Basis-Set
2.6.1. Contracted-Gaussians
2.6.2. Basic Terms of modern Basis-Set
3. Post-Hartree-Fock-Methods
3.1. The Hartree-Product
3.2. Introduction to Slater-Determinants and Properties of Functionals
3.2.1. Construction of Slater-Determinants from Spin-Orbitals
3.2.2. Functionals
3.3. Hartree-Fock-Theory
3.3.1. Introduction, deepening of our Comprehension of Hilbert-Space and Eigenvalue-Equations
3.3.2. Derivation of the Hartree-Fock-Equations
3.3.3. The Hartree-Fock-Equations
3.4. Application of the Hartree-Fock-Theory
3.4.1. Roothaan-Hall-Equations
3.4.2. Open-Shell-Calculations, Configuration-Interaction, Full-CI and Correlation-Energy
3.4.3. Coupled-Cluster-Theory and Introduction to Application of Perturbation-Theory
5. Fundamental Principles of Density-Functional-Theory and Variations of DFT-Methods
6. Other Theories
6.1. Semi-Empirical-Methods
6.2. Quantum-Theory and Basis-Set in Solid-State-Physics (and esoteric☺)
6.3. How to find the best theoretical method, Necessary for my desired Answer and how to chose the Optimal Functional for a DFT-Calculation with my System-Properties?
7. The most important Conclusion from modern Theoretical-Chemistry
8. Important Calculation-Types
8.1. Interaction-Energy, Potential-Energy-Surfaces and Counterpoise-Correction
8.2. Geometrical Optimizations vs. Varying Coefficients for Energy-Minims in other Calculations, Definition of the different Variations
8.3. Density-Calculations and other possible Calculations following the Geometry-Optimization
8.4. Spectra-Calculation; Pre-Calculations and Simplification using Group-Theory of Symmetry-Operators and Symmetry-Elements, Symmetry-Adapted-Methods
9. Molecular Dynamics/Monte-Carlo-Simulations and Future-Perspectives of Theoretical Chemistry
10. Literature
11. Acknowledgements
Objectives and Topics
The work aims to provide graduate students and practical chemists with an accessible understanding of theoretical chemistry methods, enabling them to evaluate computational results and interpret scientific literature. It bridges the gap between complex quantum mechanical theory and its practical application in chemical research.
- Overview of Post-Hartree-Fock, Density Functional Theory (DFT), and Force-Field methods.
- Development of a pictorial understanding of Hilbert-space and basis sets.
- Introduction to the mathematical foundations needed to understand modern computational cost.
- Practical guidance on selecting the appropriate theoretical method for specific chemical problems.
Excerpt from the book
0.2. Introduction to the used Pathways of Argumentation and examples for the need of understanding more about Theoretical Chemistry
Today in the most scientific articles and presentations theoretical calculations are included and experience shows that especially after finishing master studies there's an information-deficit about theoretical chemistry among a huge part of practical working chemists.
The following remarks want to help finding entrance to theoretical chemistry. The main task is to mediate the extent of available methods and to explain what these methods can do on which accuracy and what not. Without any insight in the underlying theory of the used methods of theoretical chemistry there's danger to take informations from a calculation which can’t be taken from that calculation, because desired properties are neglected in the underlying theory.
An example: You have the results of a force-field-calculation, which is relatively fast available, for a complex of two organic compounds with π-systems, donor-acceptor-positions for hydrogen-bridges to nitrogen- or oxygen-atoms on both compounds and from the received geometrical data you conclude on which positions in your complex you have π-π-interactions and hydrogen-bonds stabilizing your system. You have chosen a theoretical method cause your real system can’t be directly observed because your system works on a surface like color from a printer on a paper. Your color-complex-system works in an organic solution but not on the paper. Your problem is now that your forcefield-calculation isn’t capable to directly describe hydrogen bonds or π-π-interactions, because it uses classical mechanics and don’t calculates electrons with quantum-mechanical behavior. It only can simulate the development basing on parameters from other calculations. For very big Systems like biological systems, these methods are often the only possibility, for smaller systems they can’t be used to state something or answer a new question, because it’s just saying that something is possible, that it is maybe possible you have already known before.
Summary of Chapters
0. Preface: Introduces the author's motivation and outlines the target audience, emphasizing the need for accessible theoretical chemistry knowledge for experimentalists.
1. Overview about Theoretical-Methods: Provides a high-level comparison of fast force-field methods versus more complex quantum-mechanical approaches for chemical modeling.
2. Basis set: Develops a conceptual understanding of Hilbert space and the role of Gaussian-type functions in modern electronic structure calculations.
3. Post-Hartree-Fock-Methods: Explains the limitations of the Hartree-product and the necessity of Slater-determinants and advanced methods like Coupled-Cluster for electron correlation.
5. Fundamental Principles of Density-Functional-Theory and Variations of DFT-Methods: Details the Kohn-Sham approach and explains why DFT provides a computationally efficient alternative to traditional ab-initio methods.
6. Other Theories: Discusses semi-empirical methods and specific considerations for applying theoretical models to solid-state physics.
7. The most important Conclusion from modern Theoretical-Chemistry: Highlights the critical importance of polarized basis sets in accurately capturing complex molecular interactions.
8. Important Calculation-Types: Reviews practical application types, including potential energy surfaces, geometry optimization, and the importance of Counterpoise Correction.
9. Molecular Dynamics/Monte-Carlo-Simulations and Future-Perspectives of Theoretical Chemistry: Briefly addresses the role of advanced simulation techniques and future trends in computational chemistry.
10. Literature: Lists the academic sources used to build the theoretical arguments presented throughout the book.
11. Acknowledgements: Credits the author's mentors, colleagues, and friends for their support during the development of this work.
Keywords
Theoretical Chemistry, Hilbert-Space, Basis-Set, Hartree-Fock, Post-Hartree-Fock, Density-Functional-Theory, Force-Field, Quantum Mechanics, Slater-Determinant, Coupled-Cluster, Perturbation Theory, Geometry Optimization, Electron Correlation, Molecular Orbitals, Computational Cost
Frequently Asked Questions
What is the core purpose of this book?
The book serves as a guide for graduate students and experimental chemists to understand and evaluate theoretical chemistry methods and terminology commonly found in modern chemical research.
What are the primary fields discussed in the work?
The work covers Force-Field methods, Hartree-Fock theory, Post-Hartree-Fock methods, Density Functional Theory (DFT), and elements of solid-state physics.
What is the main objective or research question of this book?
The primary goal is to provide a "pictorial imagination" of quantum-chemical concepts, enabling non-specialists to judge the computational feasibility and reliability of theoretical methods for their specific research needs.
Which scientific methods are primarily analyzed?
The book analyzes methods ranging from fast classical mechanics (Force-Field) to high-level quantum mechanical calculations, including Coupled-Cluster and F12 explicitly correlated methods.
What does the main part of the book treat?
The main part systematically builds the reader's knowledge from basis set concepts and the Schrödinger-equation to the derivation of Hartree-Fock equations and the application of more advanced Post-Hartree-Fock techniques.
Which keywords characterize this work?
Key terms include Theoretical Chemistry, Hilbert-Space, Basis-Set, Hartree-Fock, Density-Functional-Theory, and Electron Correlation.
How does the author handle the complex mathematics involved?
The author attempts to present mathematical details only when necessary and at a level understandable to a graduate chemist, often using pictorial representations and analogies to aid conceptual understanding.
Does the book contain specific examples of research applications?
Yes, the book includes examples from the author's own academic work, such as calculations involving perfluorocarbons and the interaction energy in specific molecular complexes, to demonstrate real-world applicability.
- Quote paper
- Tobias Grömke (Author), 2016, Theoretical Chemistry for Chemists, Munich, GRIN Verlag, https://www.grin.com/document/373462
