Reading list
Below is a running list of resources that are helpful in learning about the field. Please add references/papers/books/texts that you found helpful in your research.
We attempted to provide several references for each topic; the book chapters will be more useful at first, but we also included the original papers, which are good to go over once you are familiar with the basic principles. The readings are (generally) in order of what you should review. Within each topic, the references are also (generally) in order of least to most advanced, so start with the first few in each topic.
It is not necessary to go through every reference (in fact, it would be overwhelming to do so!); this is just a compiled list of resources we find are useful to get oriented in the literature. References with * are those that we recommend starting with in each sub-topic.
If you cannot find a copy of a text, ask around- there's likely a copy floating around somewhere!
A brief note on accessing journal articles off campus
Many journals require some kind of subscription to access journal articles (but soon not!).
For off-campus access, you can use the VPN (Virtual Private Network)
Or even easier, download the EZProxy browser add-on as bookmark
Introduction Books
Helpful Math References
Introduction to Linear Algebra, Gilbert Strang- Strang gives a charming intro to linear algebra with many practical examples.
Numerical Methods for Scientists and Engineers, R.W. Hamming- A useful reference for reminding yourself various mathematical techniques and their applications; as the name implies, more focused on numerical methods for implementation in codes
Mathematical Physics: Applied Mathematics for Scientists and Engineers, Bruce Kusse and Erik Westwig- Similar to above but with different emphasis on different topics; more mathematical in nature, larger emphasis on complex variables and analysis
Quantum Mechanics
Introduction to Quantum Mechanics. David J. Griffiths- This is the classic (ironic pun intended) text used in introductory quantum mechanics courses across undergraduate physics programs; it also has a good sense of humor and many example problems. No linear algebra knowledge needed.
Introduction to Quantum Theory and Atomic Structure (Oxford Chemistry Primers, 37) by P. A. Cox- A good quantum mechanics refresher that frames topics in a way especially useful for solid-state systems
Principles of Quantum Mechanics, R. Shankar- An upper undergrad/graduate-level textbook; considered one of the most modern textbooks in quantum mechanics
Modern Quantum Mechanics, J.J. Sakurai- similar to above, but perhaps a bit more advanced (and dense in prose)
Solid-state physics
*The Electron Structure and Chemistry of Solids (Oxford Science Publications), P.A. Cox- Similarly well-thought out text and more intuitive illustrations for introducing concepts from solid-state physics
*Introduction to Solid State Physics, C. Kittel- Useful to have for reference; basics in solid state
Solid State Physics, Ashcroft & Mermin- Useful reference book; graduate-level textbook; more mathematically intense compared to Kittel
Fundamental of Semiconductors: Physics & Materials Properties; Yu and Cardona- Graduate-level textbook; excellent prose and ability to summarize key theoretical concepts and pivotal papers for each topic
Density Functional Theory
DFT Exchange: Sharing Perspectives on the Workhorse of Quantum Chemistry and Materials Science: a great perspective article on what is DFT, where is DFT headed, why has DFT been so successful from some of the people who shaped it into what it is today.
*Kieron Burke, ABC’s of DFT: Available: https://dft.uci.edu/doc/g1.pdf -A good first read for the basics of the theory. From one of the early big names in DFT. Many more references from Burke at: https://dft.uci.edu/learnDFT.php
*Sholl and Steckel, Density Functional Theory: A Practical Introduction- link- Practical-Introduction -Also a good first read but includes a lot more practical information for actual calculations.
Richard Martin: Electronic Structure This book is more advanced, but detailed and comprehensive; a great reference for specific subject if you would like more information. It also has a thorough reference list, so it can be used to determine seminal papers about the different aspects of DFT.
Fiolhais, Nogueira, and Marques: A Primer in Density Functional Theory Available: link -A little more mathematically rigorous theory
Additional References:
These are a few additional references. If you do not understand some aspect and want to hear it explained in (possibly) a slightly different way, you can consult these:
*K. Capelle: A bird's-eye view of density-functional theory Available: http://arxiv.org/abs/cond-mat/0211443 -Another example of a high-level overview of the theory
*P. Blochl: Theory and Practice of Density-Functional Theory Available: http://arxiv.org/pdf/1108.1104v1.pdf -Another good general overview
*von Barth, U. Basic Density-Functional Theory; an Overview. Phys. Scr. T109, 9–39 (2004).
Engel and R.M. Dreizler: Density Functional Theory: An Advanced Course Available: http://www.springerlink.com/content/978-3-642-14089-1/contents/ -This is a great reference if you would like more mathematical rigor
R.O. Jones and O. Gunnerson: The density functional formalism, its applications and prospects Available: http://rmp.aps.org/abstract/RMP/v61/i3/p689_1
Additional Resources:
Many formal tutorials and courses have been done for DFT. Some examples are:
Practical DFT, a course from Prof. Tom Arias of Cornell- some parts of the video lecture series are missing, but it offers some nice insight into how DFT is implemented in various electronic structure codes.
Original papers
These are the original papers that established the DFT we know today. They are not intended to be introductory texts, but cool to read the writing of the founders of DFT.
Density functional theory
*Inhomogeneous electron gas, Hohenberg and W. Kohn, Phys. Rev. 136, B864–B871 (1964)
*W. Kohn and L. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133–A1138 (1965).
Basis sets
Momentum-space formalism for the total energy of solids. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C 12, 4409 (1979).
Pseudopotentials
Norm-conserving pseudopotentials: R. Hamann, M. Schlüter, and C. Chiang, Phys. Rev. Lett. 43, 1494–1497 (1979).
Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. David Vanderbilt, Phys. Rev. B 41 (Rapid Communications), 7892 (1990).
Ab initio molecular dynamics
Unified Approach for Molecular Dynamics and Density-Functional Theory. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471(1985).
Overview papers
The pseudopotential panacea. Cohen, Physics Today 32, 40 (1979).
Density functional theory. Schlüter and L. J. Sham, Phys. Today, February 1982, p. 36.
Pseudopotentials and Total Energy Calculations. L. Cohen, Physica Scripta T1, 5 (1982).
The pseudopotential-density-functional method applied to semiconducting crystals, P.J.H. Denteneer, Ph.D. thesis, Eindhoven University of Technology (1987). [link]
Overview papers re. codes
Iterative minimization techniques for ab-initio total-energy calculations: molecular dynamics and conjugate-gradients
M.C.Payne, M.P.Teter, D.C.Allan, T.A.Arias, J.D.Joannopoulos Rev.Mod.Phys. 64, 1045-1097 (1992) [doi]
This rather detailed review paper gives a good starting point to understand the basic concepts of DFT calculations.
Density-functional theory calculations for poly-atomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics
Bockstedte, A. Kley, J. Neugebauer, M. Scheffler Comput. Phys. Commun. 107, 187-222 (1997) [doi]
This article is dedicated to the fhi98md code. It explains how a pseudopotential-planewave code generally works.
Related to codes
*Abinit tutorial: http://www.abinit.org/ABINIT/Infos/Tutorial/welcome.html. Abinit makes great tutorials that break down the practical aspects of running calculations.
Quantum ESPRESSO: Advanced capabilities for materials modelling with Quantum ESPRESSO P. Giannozzi et al. Journal of Physics: Condensed Matter. 29, 465901 (2017) [doi] https://www.quantum-espresso.org/
Quantum ESPRESSO (QE) has tutorials released with the source code and typically have a published paper to accompany each capability
VASP:
References related to the code:
G. Kresse and J. Hafner, Phys. Rev. B 47 , 558 (1993); ibid. 49 , 14 251 (1994).
G. Kresse and J. Furthmüller, Comput. Mat. Sci. 6 , 15 (1996).
G. Kresse and J. Furthmüller, Phys. Rev. B 54 , 11 169 (1996).
Ultrasoft pseudopotentials should be referenced as
G. Kresse and J. Hafner, J. Phys.: Condens. Matt. 6, 8245 (1994).
If the PAW-version is used, an additional reference should be made to
G. Kresse and D. Joubert, Phys. Rev. 59 , 1758 (1999).
Pseudopotentials
Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Fuchs, M. Scheffler, Comput. Phys. Commun. 119, 67-98 (1999). [doi]
Learn how pseudopotentials can be generated.
SG ONCV Norm-conserving pseudopotentials: http://www.quantum-simulation.org/potentials/sg15_oncv/
Pseudo Dojo: http://www.pseudo-dojo.org/
Opium, a code to help generate pseudopotentials: http://opium.sourceforge.net/
QE libary (and can also generate some pseudopotentials: https://www.quantum-espresso.org/pseudopotentials/
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