1.Density Functional Theory
Hohenberg, Kohn and Sham, introducing DFT
[1] Hohenberg P, Kohn W. Inhomogeneous Electron Gas. Phys Rev, 1964, 136(3B):B864
[2] Kohn W, Sham LJ. Self-Consistent Equations Including Exchange and Correlation Effects. Phys Rev, 1965, 140(4A):A1133
[3] Kohn W. Nobel Lecture: Electronic structure of matter: wave functions and density functionals. Rev Mod Phys, 1999, 71(5):1253
Some review papers or books worth reading
[4] Jones RO, Gunnarsson O. The density functional formalism, its applications and prospects. Rev Mod Phys, 1989, 61(3):689
[5] Payne MC, Teter MP, Allan DC, Arias TA, Joannopoulos JD. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev Mod Phys, 1992, 64(4):1045
Description of Abinit code
[6] Gonze X, Beuken J-, Caracas R, et al. First-principles computation of material properties: the ABINIT software project. Computational Materials Science, 2002, 25(3):478-492
Description of VASP code.
[7] Kresse G, Furthm¨¹ller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science, 1996, 6(1):15-50
[8] Kresse G, Furthm¨¹ller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B, 1996, 54(16):11169
phonon and density-functional perturbation theory (DPFT)
[9] Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P. Phonons and related crystal properties from density-functional perturbation theory. Rev Mod Phys, 2001, 73(2):515.
[10] Electronic Structure : Basic Theory and Practical Methods, Richard M. Martin (published in Summer 2004), Cambridge University Press. ISBN: 0521782856). For details, see http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521782856
Exchange-correlation approximations and implementation
Local Density Approximation (LDA)
[11] CA: Ceperley D M, Alder B J. Ground State of the Electron Gas by a Stochastic Method. Phys Rev Lett, 1980, 45(7):566
[12] VMN: Vosko, S.H.;Wilk, L.;Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys, 1980, 58: 1200
[13] PZ: Perdew JP, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B, 1981, 23(10):5048
[14] PW92: Perdew J P, Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B, 1992, 45(23):13244
Generalized Gradient Approximation (GGA)
[15] PW91: Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J, Fiolhais C. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys Rev B, 1992, 46: 6671-6687
[16] PBE: Perdew J P, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. Phys Rev Lett, 1996, 77(18):3865
[17] PBE0: Adamo C, Barony V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J Chem Phys, 1998, 110: 6158-6170
[18] PPBE: Hammer B, Hansen L B, Norskov J K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Phys Rev B, 1999, 59: 7413-7421
[19] WC: Wu Z, Cohen R E, More accurate generalized gradient approximation for solids. Phys Rev B, 2006, 73: 235116
Projector-Augmented-plane-Wave method (PAW)
[20] Blöchl P E. Projector augmented-wave method. Phys Rev B, 1994, 50(24):17953
Sampling the Brillouin zone
The Monkhorst and Pack grids
[21] Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations. Phys Rev B, 1976, 13(12):5188
[22] Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations - a reply, Phys. Rev. B, 1977, 16: 1748-1749
tetrahedron
[23] Jepson O, Anderson OK. The electronic structure of h.c.p. Ytterbium. Solid State Communications, 1971, 9(20):1763-1767
[24] Blöchl P E, Jepsen O, Andersen O K. Improved tetrahedron method for Brillouin-zone integrations. Phys Rev B, 1994, 49(23):16223
Treatment of occupation numbers for metals
[25] Fu C, Ho K. First-principles calculation of the equilibrium ground-state properties of transition metals: Applications to Nb and Mo. Phys Rev B, 1983, 28(10):5480
Fermi-Dirac function
[26] Mermin N D. Thermal Properties of the Inhomogeneous Electron Gas. Phys Rev, 1965, 137(5A):A1441
Gaussian-Hermite smearing
[27] Methfessel M, Paxton AT. High-precision sampling for Brillouin-zone integration in metals. Phys Rev B, 1989, 40(6):3616
The free energy for different smearing schemes
[28] de Gironcoli S. Lattice dynamics of metals from density-functional perturbation theory. Phys Rev B, 1995, 51(10):6773
[29] An extensive presentation of different treatments, and the "cold smearing" technique N. Marzari, PhD dissertation, U. of Cambridge (1996), Available at http://nnn.mit.edu/ph
[30] Marzari N, Vanderbilt D, De Vita A, Payne M C. Thermal Contraction and Disordering of the Al(110) Surface. Phys Rev Lett, 1999, 82(16):3296
Computation of forces
[31] Accelerating the convergence of force calculations in electronic-structure computations. Chan CT, Bohnen K P, Ho K M. Accelerating the convergence of force calculations in electronic-structure computations. Phys Rev B, 1993, 47(8):477
Norm-conserving Pseudo-Potentials (NC-PP)
[32] Hamann D R, Schluter M, Chiang C. Norm-Conserving Pseudopotentials. Phys Rev Lett, 1979, 43:1494-1497
[33] Rappe A M, Rabe K M, Kaxiras E, Joannopoulos J D. Optimized pseudopotentials. Phys Rev B, 1990, 41: 1227-1230
[34] Lin J S, Qteish A, Payne M C, Heine V. Optimized and transferable nonlocal separable ab initio pseudopotentials. Phys. Rev. B, 1993, 47: 4174-4180
[35] fhi98PP codes: Hammann and Troullier-Martins pseudopotential, http://www.fhi- berlin.mpg.de/th/fhi98md/fhi98PP
[36] Fuchs M, Scheffler M. Comput Phys Commun, Comput. Phys Commun, 1999, 119:67-98
[37] Jose-Luis Martins' code: Troullier-Martins, Hamann-Schluter-Chiang, and Kerker pseudopotential£¬http://bohr.inesc-mn.pt/~jlm/pseudo.htm
Ultra-Soft Pseudo-Potentials (US-PP)
[38] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B, 1990, 41(11):7892
[39] David Vanderbilt's code: http://www.physics.rutgers.edu/~dhv/uspp/index.htm
[40] Laasonen K, Pasquarello A, Car R, Lee C, Vanderbilt D. Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials. Phys. Rev. B, 1993, 47:10142-10153
Real-space mesh techniques
[41] Thomas L Beck. Real-space mesh techniques in density-functional theory. Rev Mod Phys, 2000, 72,4:1041
Car Parrinello Molecular Dynamics (CPMD)
[42] Car R and Parrinello M. Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Lett., 1985 55:2471
2.Molecular Dynamics
[43] Alder B J, Wainwright T E. Molecular motions. Scient Am, 1959. 201(4):113
[44] Allen M P, Tildesley D J. Computer Simulation of Liquids. 1989: Oxford University Press, USA.
[45] Allen M P, Tildesley D J. Computer Simulation in Chemical Physics. 1993: Springer
[46] Campbell G H, et al. Atomic structure of the (310) twin in niobium: Experimental determination and comparison with theoretical predictions. Phys Rev Lett, 1993, 70(4): 449-452
[47] Daw M S, Foiles S M, Baskes M I. Embedded atom method--a review of theory and applications. Materials Science Reports, 1993, 9(7):251-310
[48] Finnis M W. The theory of metal-ceramic interfaces. J Phys: Condensed Matter, 1996. 8: 5811-5836
[49] Finnis, M W, Kruse C, Sch?nberger U. Ab initio calculations of metal/ceramic interfaces: what have we learned, what can we learn? Nanostructured Materials, 1995, 6(1-4):145-155
[50] Foiles S M, Adams J B. Thermodynamic properties of fcc transition metals as calculated with the embedded-atom method. Phys Rev B, 1989, 40(9):5909-5915
[51] Gilmer G H, Grabow M H, Bakker A F. Modeling of epitaxial growth. Materials science & engineering. B, Solid-state materials for advanced technology, 1990, 6(2-3): 101-112
[52] Goringe C M, et al. The GaAs (001)-(2 x 4) Surface: Structure, Chemistry, and Adsorbates. J Phys Chem B, 1997, 101:1498-1509
[53] Harrison J A, et al. Effect of atomic-scale surface roughness on friction-A molecular dynamics study of diamond surfaces. Wear, 1993, 168(1): p. 127-133
[54] Heermann, D W, Burkitt A N. Parallel Algorithms in Computational Science, volume 24 of Information Sciences. 1991, Springer, Berlin
[55] Holzman L M, et al. Properties of the liquid-vapor interface of fee metals calculated using the embedded atom method. J Mater Res, 1991, 6(2):299
[56] Jhan R E J, Bristowe P D. A molecular dynamics study of grain boundary migration without the participation of secondary grain boundary dislocations. Scripta metallurgica, 1990, 24(7):1313-1318
[57] Kubin, L.P., V. Pontikis, and H.O. Kirchner, Computer simulation in materials science. 1996: Kluwer Academic Publishers Boston
[58] Liu C L, Plimpton S J. Molecular-statics and molecular-dynamics study of diffusion along [001] tilt grain boundaries in Ag. Phys Rev B, 1995, 51(7):4523-4529
[59] Lutsko J F, et al. Molecular-dynamics method for the simulation of bulk-solid interfaces at high temperatures. Phys Rev B, 1988, 38(16):11572-11581
[60] Parrinello M, Rahman A. Polymorphic transitions in single crystals: a new molecular dynamics approach. J. Appl. Phys, 1981, 52:7182-7190
[61] Sinnott S B, et al. Surface patterning by atomically-controlled chemical forces: molecular dynamics simulations. Surf Sci, 1994, 316(1-2):1055-1060
[62] Smith R W, Srolovitz D J. Void formation during film growth: A molecular dynamics simulation study. J Appl Phys, 1996, 79(3):1448
[63] Stoneham A M, Harding J H. Computer simulation of interfaces: What do we need to know? Acta Materialia, 1998, 46(7):2255-2261
[64] Tildesley D J, Pinches M R S. Molecular dynamics simulations of the melting of CF4 adsorbed on graphite. Surf Sci, 1996, 367(2):177-195
[65] Verlet L. Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev, 1967. 159(1):98-103
3.Monte Carlo Method
General theorey
[66] Gould H, Tobochnik J. An Introduction to Computer Simulation Methods (Addison- Wesley£¬ Reading, 1988). Part 2, chaps 10-12, 14, 15
[67] Hermann D W. Computer Simulation Methods (Springer-Verlag, Berlin, 1990), 2nd ed., chap 4
[68] Binder K, Hermann D W. Monte Carlo Simulation in Statistical Physics, An Introduction (Springer-Verlag,Berlin, 1988)
[69] Lewis E E, Miller W F. Computational Methods of Neutron Transport (American Nuclear Society, La Grange Park, IL, 1993), chap 7
[70] Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H, Teller E. Equation of State Calculations by Fast Computing Machines. J Chem Phys, 1953, 21:1087
[71] Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by Simulated Annealing. Science, 1983, 220: 671
Classical statistical mechanics
[72] Nightingale M P. in Quantum Monte Carlo Methods in Physics and Chemistry, Kluwer Academic, Dordrecht, 1999, Vol. 525 of NATO Advanced-Study Institute, p. 1
The Metropolis algorithm
[73] Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H, Teller E. Equation of State Calculations by Fast Computing Machines. J Chem Phys, 1953, 21:1087
KMC
[74] Mae K. Molecular dynamics aided Kinetic Monte Carlo simulations of thin film growth of Ag on Mo(110) with structural evolution. Surf Sci, 2001, 482: 860-865
[75] Adams J B, Wang Z Y, Li Y. Modeling Cu thin film growth. Thin Solid Films, 2000, 365: 201£210
[76] Gilmer G H, Huang H C, Christopher R. Thin film deposition: Fundamentals and modeling. Comp Mat Sci, 1998, 12: 354£380
[77] Battailr C C, Srolovitz D J. A Kinetic Monte Carlo method for the atomic-scale simulation of chemical vapor deposition:Application to diamond. J Appl Phys, 1996, 82: 6293£6300
[78] Wang L G, Clancy P. Kinetic Monte Carlo simulation of the growth of polycrystalline Cu film. Surf Sci, 2001, 473: 25£38
[79] Bruschi P, Cagnoni P, Nannini A. Temperature-dependent Monte Carlo simulation of thin metal film growth and percolation. Phys Rev B, 1997, 55: 7955£7963
[80] Landau D P, Pal S, Shim S Y. Monte Carlo simulations of film growth. Comp Phys Comm, 1999, 121-122:341£346
[81] Numinen L, Kuroen A, Kaski K. Kinetic Monte Carlo simulation of nucleation on patterned substrates. Phys Rev B, 2000, 63: 035407-1£7
[82] Bruschi P, Nannini A, Pitto M. Three-dimensional Monte Carlo simulations of electron-migration in polycrystalline thin films. Comp Mat Sci, 2000, 17: 299£304
[83] Bruschi P, Nannini A, Pieri F. Monte Carlo simulation of polycrystalline thin film deposition. Phys Rev B, 2000, 63: 0345406-1£8
[84] Pomeroy M, Joachim J, Colin C, et al. Kinetic Monte Carlo molecular dynamics investigations of hyper-thermal copper deposition on Cu(111). Phys Rev B, 2002, 66: 235412-1£8
[85] Wadley H N G, Zhou X, Johnson R A, et al. Mechanisms, models and methods of vapor deposition. Prog Mat Sci, 2001, 46: 329£377
[86] Zhang P F, Zheng X P, He D Y. Kinetic Monte Carlo simulation of Cu thin film growth. Vaccum, 2004, 72: 405£410
The quantum Monte Carlo (QMC) technique
[87] Foulkes W M C, Mitas L, Needs R J, Rajagopal G. Quantum Monte Carlo simulations of solids Rev. Mod. Phys. 2001, 73(1): 33
[88] Alf¨¨ D, Gillan M J. Linear-scaling quantum Monte Carlo technique with non-orthogonal localized orbitals. J Phys: Condens. Matter, 2004, 16: L305¨CL311
auxiliary-field QMC
[89] Senatore G, March N H, Recent progress in the field of electron correlation. Rev. Mod. Phys. 1994, 66: 445
[90] Baer R, Head-Gordon M, Neuhauser D. Shifted-contour auxiliary field Monte Carlo for ab initio electronic structure: Straddling the sign problem. J Chem Phys, 1998, 109: 6219
[91] Baer R, Neuhauser D, Molecular electronic structure using auxiliary field Monte Carlo, plane waves and pseudopotentials. J Chem Phys, 2000, 112: 1679
path-integral QMC
[92] Ceperley D M. Path integrals in the theory of condensed helium. Rev. Mod. Phys. 1995a, 67: 279
[93] Ceperley, D. M. in Strongly Interacting Fermions and High-Tc Superconductivity, Proceedings of the Les Houches Summer School, Session LVI, edited by B. Doucot and J. Zinn-Justin (Elsevier, Amsterdam), 1995b, p427
variational quantum Monte Carlo
[94] McMillan W L. Ground State of Liquid He4. Phys Rev, 1965, 138: A442
[95] Ceperley D M, Chester G V, Kalos M H. Monte Carlo Simulation of a Many-Fermion System. Phys. Rev. B, 1977, 16: 3081
diffusion quantum Monte Carlo
[96] Baroni S, Moroni S. Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations. Phys Rev Lett, 1999, 82: 4745
[97] Reynolds P J, Ceperley D M, Alder B J, Lester W A, Jr. Fixed-node Quantum Monte Carlo for Molecules. J Chem Phys, 1982, 77:5593
[98] Anderson J B. A random-walk simulation of the Schrödinger equation: H+3. J Chem Phys, 1975, 63: 1499
localized-orbital methods
[99] Stoneham A M. Theory of Defects in Solids. Oxford: Oxford University Press, 1975, section 7.5
O(N)
[100] CASINO code: http://www.tcm.phy.cam.ac.uk/~mdt26/casino.html
[101] Needs R J, Towler M D, Drummond N D, Kent P R C. 2004 CASINO Version 1.7 User Manual (Cambridge: University of Cambridge)
[102] Williamson A J, Hood R Q, Grossman J C. Phys. Rev. Lett. 2001, 87: 246406
Statistical foundations
[103] Feller W. An Introduction to Probability Theory and its Applications, 1968, 3rd ed. (Wiley, New York), Vol. 1