Abstract
Quantum Monte Carlo (QMC) comprises a set of techniques that use random numbers to address quantum mechanical problems. They are some of the most accurate techniques that can address large systems. This chapter gives the basics of QMC techniques on first principles models of materials.
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References
Bajdich M, Mitas L, Drobný G, Wagner LK, Schmidt KE (2006) Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations. Phys Rev Lett 96(13):130201. http://link.aps.org/doi/10.1103/PhysRevLett.96.130201
Bennett MC, Melton CA, Annaberdiyev A, Wang G, Shulenburger L, Mitas L (2017) A new generation of effective core potentials for correlated calculations. J Chem Phys 147(22):224106. http://aip.scitation.org/doi/abs/10.1063/1.4995643
Bijl A (1940) The lowest wave function of the symmetrical many particles system. Physica 7(9):869–886. https://doi.org/10.1016/0031-8914(40)90166-5, http://www.sciencedirect.com/science/article/pii/0031891440901665
Burkatzki M, Filippi C, Dolg M (2007) Energy-consistent pseudopotentials for quantum Monte Carlo calculations. J Chem Phys 126(23):234105–234105–8. https://doi.org/10.1063/1.2741534, http://jcp.aip.org/resource/1/jcpsa6/v126/i23/p234105_s1
Burkatzki M, Filippi C, Dolg M (2008) Energy-consistent small-core pseudopotentials for 3D-transition metals adapted to quantum Monte Carlo calculations. J Chem Phys 129(16):164115–164115–7. https://doi.org/10.1063/1.2987872, http://jcp.aip.org/resource/1/jcpsa6/v129/i16/p164115_s1?isAuthorized=no
Casula M (2006) Beyond the locality approximation in the standard diffusion Monte Carlo method. Phys Rev B 74(16). http://link.aps.org/doi/10.1103/PhysRevB.74.161102
Casula M, Moroni S, Sorella S, Filippi C (2010) Size-consistent variational approaches to nonlocal pseudopotentials: standard and lattice regularized diffusion Monte Carlo methods revisited. J Chem Phys 132(15):154113. http://scitation.aip.org/content/aip/journal/jcp/132/15/10.1063/1.3380831
Changlani HJ, Kinder JM, Umrigar CJ, Chan GKL (2009) Approximating strongly correlated wave functions with correlator product states. Phys Rev B 80(24):245116. http://link.aps.org/doi/10.1103/PhysRevB.80.245116
Changlani HJ, Zheng H, Wagner LK (2015) Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions. J Chem Phys 143(10):102814. http://scitation.aip.org/content/aip/journal/jcp/143/10/10.1063/1.4927664
Chiesa S, Ceperley D, Martin R, Holzmann M (2006) Finite-size error in many-body simulations with long-range interactions. Phys Rev Lett 97(7). http://link.aps.org/doi/10.1103/PhysRevLett.97.076404
Dingle RB (1949) LI. The zero-point energy of a system of particles. Lond Edinb Dublin Philos Mag J Sci 40(304):573–578. https://doi.org/10.1080/14786444908521743
Doblhoff-Dier K, Meyer J, Hoggan PE, Kroes GJ, Wagner LK (2016) Diffusion Monte Carlo for accurate dissociation energies of 3D transition metal containing molecules. J Chem Theory Comput 12(6):2583–2597. http://pubs.acs.org/doi/abs/10.1021/acs.jctc.6b00160
Drummond N, Needs R, Sorouri A, Foulkes W (2008) Finite-size errors in continuum quantum Monte Carlo calculations. Phys Rev B 78(12). http://link.aps.org/doi/10.1103/PhysRevB.78.125106
Feynman RP, Cohen M (1956) Energy spectrum of the excitations in liquid helium. Phys Rev 102(5):1189–1204. http://link.aps.org/doi/10.1103/PhysRev.102.1189
Filippi C, Assaraf R, Moroni S (2016) Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo. J Chem Phys 144(19):194105. http://scitation.aip.org/content/aip/journal/jcp/144/19/10.1063/1.4948778
Holzmann M, Ceperley DM, Pierleoni C, Esler K (2003) Backflow correlations for the electron gas and metallic hydrogen. Phys Rev E 68(4):046707. http://link.aps.org/doi/10.1103/PhysRevE.68.046707
Jastrow R (1955) Many-body problem with strong forces. Phys Rev 98(5):1479–1484. https://link.aps.org/doi/10.1103/PhysRev.98.1479
Kolodrubetz MH, Spencer JS, Clark BK, Foulkes WM (2013) The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem. J Chem Phys 138(2):024110. http://aip.scitation.org/doi/abs/10.1063/1.4773819
Kwon Y, Ceperley DM, Martin RM (1993) Effects of three-body and backflow correlations in the two-dimensional electron gas. Phys Rev B 48(16):12037. http://link.aps.org.libproxy.mit.edu/doi/10.1103/PhysRevB.48.12037
López RÃos P, Ma A, Drummond ND, Towler MD, Needs RJ (2006) Inhomogeneous backflow transformations in quantum Monte Carlo calculations. Phys Rev E 74(6):066701. http://link.aps.org/doi/10.1103/PhysRevE.74.066701
Melton CA, Zhu M, Guo S, Ambrosetti A, Pederiva F, Mitas L (2016) Spin-orbit interactions in electronic structure quantum Monte Carlo methods. Phys Rev A 93(4):042502. http://link.aps.org/doi/10.1103/PhysRevA.93.042502
Neuscamman E (2012) Size consistency error in the antisymmetric geminal power wave function can be completely removed. Phys Rev Lett 109(20):203001. http://link.aps.org/doi/10.1103/PhysRevLett.109.203001
Saritas K, Mueller T, Wagner L, Grossman JC (2017) Investigation of a quantum Monte Carlo protocol to achieve high accuracy and high-throughput materials formation energies. J Chem Theory Comput 13(5):1943–1951. https://doi.org/10.1021/acs.jctc.6b01179
Suzuki M (1976) Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Commun Math Phys 51(2):183–190. https://link.springer.com/article/10.1007/BF01609348
Taddei M, Ruggeri M, Moroni S, Holzmann M (2015) Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids. Phys Rev B 91(11):115106. https://link.aps.org/doi/10.1103/PhysRevB.91.115106
Toulouse J, Umrigar CJ (2008) Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules. J Chem Phys 128(17):174101. http://scitation.aip.org.proxy2.library.illinois.edu/content/aip/journal/jcp/128/17/10.1063/1.2908237
Trail JR, Needs RJ (2013) Pseudopotentials for correlated electron systems. J Chem Phys 139(1):014101. http://aip.scitation.org/doi/10.1063/1.4811651
Trotter HF (1959) On the product of semi-groups of operators. Proc Am Math Soc 10(4):545–551. http://www.jstor.org/stable/2033649
Umrigar CJ (2015) Observations on variational and projector Monte Carlo methods. J Chem Phys 143(16):164105. http://scitation.aip.org.proxy2.library.illinois.edu/content/aip/journal/jcp/143/16/10.1063/1.4933112
Umrigar CJ, Nightingale MP, Runge KJ (1993) A diffusion Monte Carlo algorithm with very small time-step errors. J Chem Phys 99(4):2865–2890. https://doi.org/10.1063/1.465195, http://jcp.aip.org/resource/1/jcpsa6/v99/i4/p2865_s1?isAuthorized=no
Umrigar CJ, Toulouse J, Filippi C, Sorella S, Hennig RG (2007) Alleviation of the Fermion-Sign problem by optimization of many-body wave functions. Phys Rev Lett 98(11):110201. http://link.aps.org/doi/10.1103/PhysRevLett.98.110201
Wagner L, Mitas L (2003) A quantum Monte Carlo study of electron correlation in transition metal oxygen molecules. Chem Phys Lett 370(3–4):412–417. https://doi.org/10.1016/S0009-2614(03)00128-3, http://www.sciencedirect.com/science/article/pii/S0009261403001283
Williams KT, Wagner LK (2016) Using local operator fluctuations to identify wave function improvements. Phys Rev E 94(1):013303. http://link.aps.org/doi/10.1103/PhysRevE.94.013303
Wouters S, Verstichel B, Van Neck D, Chan GKL (2014) Projector quantum Monte Carlo with matrix product states. Phys Rev B 90(4):045104. https://link.aps.org/doi/10.1103/PhysRevB.90.045104
Acknowledgements
This work was supported in part by the Simons collaboration on the many-electron problem. Thanks to Kittithat Kronchon and Kiel Williams for careful reading of the manuscript.
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Wagner, L.K. (2018). Correlations and Effective Interactions from First Principles Using Quantum Monte Carlo. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_10-1
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DOI: https://doi.org/10.1007/978-3-319-42913-7_10-1
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