1932

Abstract

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

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/content/journals/10.1146/annurev-physchem-090519-045916
2022-04-20
2024-03-28
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Literature Cited

  1. 1. 
    Baer R, Neuhauser D, Rabani E. 2013. Self-averaging stochastic Kohn-Sham density-functional theory. Phys. Rev. Lett. 111:10106402
    [Google Scholar]
  2. 2. 
    Neuhauser D, Gao Y, Arntsen C, Karshenas C, Rabani E, Baer R 2014. Breaking the theoretical scaling limit for predicting quasiparticle energies: the stochastic GW approach. Phys. Rev. Lett. 113:7076402
    [Google Scholar]
  3. 3. 
    Rabani E, Baer R, Neuhauser D. 2015. Time-dependent stochastic Bethe-Salpeter approach. Phys. Rev. B 91:23235302
    [Google Scholar]
  4. 4. 
    Willow SY, Kim KS, Hirata S 2012. Stochastic evaluation of second-order many-body perturbation energies. J. Chem. Phys. 137:20204122
    [Google Scholar]
  5. 5. 
    Booth GH, Grüneis A, Kresse G, Alavi A. 2013. Towards an exact description of electronic wavefunctions in real solids. Nature 493:7432365–70
    [Google Scholar]
  6. 6. 
    Gubernatis J, Kawashima N, Werner P. 2016. Quantum Monte Carlo Methods Cambridge, UK: Cambridge Univ. Press
  7. 7. 
    Wagner LK, Ceperley DM. 2016. Discovering correlated fermions using quantum Monte Carlo. Rep. Prog. Phys. 79:9094501
    [Google Scholar]
  8. 8. 
    Garniron Y, Scemama A, Loos PF, Caffarel M. 2017. Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory. J. Chem. Phys. 147:3034101
    [Google Scholar]
  9. 9. 
    Jeanmairet G, Sharma S, Alavi A. 2017. Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method. J. Chem. Phys. 146:4044107
    [Google Scholar]
  10. 10. 
    Becca F, Sorella S 2017. Quantum Monte Carlo Approaches for Correlated Systems Cambridge, UK: Cambridge Univ. Press, 1st ed..
  11. 11. 
    Deustua JE, Shen J, Piecuch P. 2017. Converging high-level coupled-cluster energetics by Monte Carlo sampling and moment expansions. Phys. Rev. Lett. 119:22223003
    [Google Scholar]
  12. 12. 
    Doran AE, Hirata S. 2019. Monte Carlo second- and third-order many-body Green's function methods with frequency-dependent, nondiagonal self-energy. J. Chem. Theory Comput. 15:116097–110
    [Google Scholar]
  13. 13. 
    Filip MA, Scott CJC, Thom AJW. 2019. Multireference stochastic coupled cluster. J. Chem. Theory Comput. 15:126625–35
    [Google Scholar]
  14. 14. 
    Lester WJ, Rothstein S, Tanaka S 2002. Recent Advances in Quantum Monte Carlo Methods II Singapore: World Sci.
  15. 15. 
    Hutchinson MF. 1990. A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. Commun. Stat. Simul. Comput. 19:2433–50
    [Google Scholar]
  16. 16. 
    Wang LW. 1994. Calculating the density of states and optical-absorption spectra of large quantum systems by the plane-wave moments method. Phys. Rev. B 49:151015458
    [Google Scholar]
  17. 17. 
    Wang LW, Zunger A. 1994. Dielectric constants of silicon quantum dots. Phys. Rev. Lett. 73:71039–42
    [Google Scholar]
  18. 18. 
    Sankey OF, Drabold DA, Gibson A. 1994. Projected random vectors and the recursion method in the electronic-structure problem. Phys. Rev. B 50:31376–81
    [Google Scholar]
  19. 19. 
    Iitaka T, Nomura S, Hirayama H, Zhao X, Aoyagi Y, Sugano T 1997. Calculating the linear response functions of noninteracting electrons with a time-dependent Schrödinger equation. Phys. Rev. E 56:11222–29
    [Google Scholar]
  20. 20. 
    Chen M, Baer R, Neuhauser D, Rabani E 2019. Overlapped embedded fragment stochastic density functional theory for covalently-bonded materials. J. Chem. Phys. 150:3034106
    [Google Scholar]
  21. 21. 
    Chen M, Baer R, Neuhauser D, Rabani E. 2019. Energy window stochastic density functional theory. J. Chem. Phys. 151:11114116
    [Google Scholar]
  22. 22. 
    Li W, Chen M, Rabani E, Baer R, Neuhauser D. 2019. Stochastic embedding DFT: theory and application to p-nitroaniline in water. J. Chem. Phys. 151:17174115
    [Google Scholar]
  23. 23. 
    Chen M, Baer R, Neuhauser D, Rabani E 2021. Stochastic density functional theory: real- and energy-space fragmentation for noise reduction. J. Chem. Phys. 154:20204108
    [Google Scholar]
  24. 24. 
    Fabian MD, Shpiro B, Rabani E, Neuhauser D, Baer R. 2019. Stochastic density functional theory. WIREs Comput. Mol. Sci. 9:6e1412
    [Google Scholar]
  25. 25. 
    Shpiro B, Fabian MD, Rabani E, Baer R. 2021. Forces from stochastic density functional theory under nonorthogonal atom-centered basis sets. arXiv:2108.06770 [physics.chem-ph]
  26. 26. 
    Neuhauser D, Rabani E, Cytter Y, Baer R. 2016. Stochastic optimally tuned range-separated hybrid density functional theory. J. Phys. Chem. A 120:193071–78
    [Google Scholar]
  27. 27. 
    Lee AJ, Chen M, Li W, Neuhauser D, Baer R, Rabani E. 2020. Dopant levels in large nanocrystals using stochastic optimally tuned range-separated hybrid density functional theory. Phys. Rev. B 102:3035112
    [Google Scholar]
  28. 28. 
    Cytter Y, Rabani E, Neuhauser D, Baer R 2018. Stochastic density functional theory at finite temperatures. Phys. Rev. B 97:115207
    [Google Scholar]
  29. 29. 
    Cytter Y, Rabani E, Neuhauser D, Preising M, Redmer R, Baer R 2019. Transition to metallization in warm dense helium-hydrogen mixtures using stochastic density functional theory within the Kubo-Greenwood formalism. Phys. Rev. B 100:19195101
    [Google Scholar]
  30. 30. 
    White AJ, Collins LA. 2020. Fast and universal Kohn-Sham density functional theory algorithm for warm dense matter to hot dense plasma. Phys. Rev. Lett. 125:5055002
    [Google Scholar]
  31. 31. 
    Arnon E, Rabani E, Neuhauser D, Baer R 2017. Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory. J. Chem. Phys. 146:22224111
    [Google Scholar]
  32. 32. 
    Arnon E, Rabani E, Neuhauser D, Baer R 2020. Efficient Langevin dynamics for “noisy” forces. J. Chem. Phys. 152:16161103
    [Google Scholar]
  33. 33. 
    Ge Q, Gao Y, Baer R, Rabani E, Neuhauser D 2013. A guided stochastic energy-domain formulation of the second order Møller Plesset perturbation theory. J. Phys. Chem. Lett. 5:1185–89
    [Google Scholar]
  34. 34. 
    Neuhauser D, Rabani E, Baer R 2013. Expeditious stochastic approach for MP2 energies in large electronic systems. J. Chem. Theory Comput. 9:124–27
    [Google Scholar]
  35. 35. 
    Neuhauser D, Rabani E, Baer R 2013. Expeditious stochastic calculation of random-phase approximation energies for thousands of electrons in three dimensions. J. Phys. Chem. Lett. 4:71172–76
    [Google Scholar]
  36. 36. 
    Takeshita TY, de Jong WA, Neuhauser D, Baer R, Rabani E. 2017. Stochastic formulation of the resolution of identity: application to second order Møller–Plesset perturbation theory. J. Chem. Theory Comput. 13:104605–10
    [Google Scholar]
  37. 37. 
    Neuhauser D, Baer R, Zgid D. 2017. Stochastic self-consistent second-order Green's function method for correlation energies of large electronic systems. J. Chem. Theory Comput. 13:5396–403
    [Google Scholar]
  38. 38. 
    Schäfer T, Ramberger B, Kresse G. 2018. Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling. J. Chem. Phys. 148:6064103
    [Google Scholar]
  39. 39. 
    Takeshita TY, Dou W, Smith DGA, de Jong WA, Baer R et al. 2019. Stochastic resolution of identity second-order Matsubara Green's function theory. J. Chem. Phys. 151:4044114
    [Google Scholar]
  40. 40. 
    Vlček V, Rabani E, Neuhauser D, Baer R 2017. Stochastic GW calculations for molecules. J. Chem. Theory Comput. 13:104997–5003
    [Google Scholar]
  41. 41. 
    Vlček V, Li W, Baer R, Rabani E, Neuhauser D. 2018. Swift GW beyond 10,000 electrons using sparse stochastic compression. Phys. Rev. B 98:7075107
    [Google Scholar]
  42. 42. 
    Vlček V, Rabani E, Neuhauser D 2018. Quasiparticle spectra from molecules to bulk. Phys. Rev. Mater. 2:3030801
    [Google Scholar]
  43. 43. 
    Vlček V, Baer R, Rabani E, Neuhauser D. 2018. Simple eigenvalue-self-consistent . J. Chem. Phys. 149:17174107
    [Google Scholar]
  44. 44. 
    Vlček V. 2019. Stochastic vertex corrections: linear scaling methods for accurate quasiparticle energies. J. Chem. Theory Comput. 15:116254–66
    [Google Scholar]
  45. 45. 
    Dou W, Takeshita TY, Chen M, Baer R, Neuhauser D, Rabani E 2019. Stochastic resolution of identity for real-time second-order Green's function: ionization potential and quasi-particle spectrum. J. Chem. Theory Comput. 15:126703–11
    [Google Scholar]
  46. 46. 
    Vlček V, Rabani E, Baer R, Neuhauser D. 2019. Nonmonotonic band gap evolution in bent phosphorene nanosheets. Phys. Rev. Mater. 3:6064601
    [Google Scholar]
  47. 47. 
    Brooks J, Weng G, Taylor S, Vlček V 2020. Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene. J. Phys. Condens. Matter 32:23234001
    [Google Scholar]
  48. 48. 
    Dou W, Chen M, Takeshita TY, Baer R, Neuhauser D, Rabani E 2020. Range-separated stochastic resolution of identity: formulation and application to second-order Green's function theory. J. Chem. Phys. 153:7074113
    [Google Scholar]
  49. 49. 
    Gao Y, Neuhauser D, Baer R, Rabani E. 2015. Sublinear scaling for time-dependent stochastic density functional theory. J. Chem. Phys. 142:3034106
    [Google Scholar]
  50. 50. 
    Zhang X, Lu G, Baer R, Rabani E, Neuhauser D 2020. Linear-response time-dependent density functional theory with stochastic range-separated hybrids. J. Chem. Theory Comput. 16:21064–72
    [Google Scholar]
  51. 51. 
    Baer R, Rabani E. 2012. Expeditious stochastic calculation of multiexciton generation rates in semiconductor nanocrystals. Nano Lett 12:42123–28
    [Google Scholar]
  52. 52. 
    Eshet H, Baer R, Neuhauser D, Rabani E 2014. Multiexciton generation in seeded nanorods. J. Phys. Chem. Lett. 5:152580–85
    [Google Scholar]
  53. 53. 
    Philbin JP, Rabani E. 2020. Auger recombination lifetime scaling for type I and quasi-type II core/shell quantum dots. J. Phys. Chem. Lett. 11:135132–38
    [Google Scholar]
  54. 54. 
    Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21:61087–92
    [Google Scholar]
  55. 55. 
    Giannozzi P, Baroni S 2009. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21:39395502
    [Google Scholar]
  56. 56. 
    Drabold DA, Sankey OF. 1993. Maximum entropy approach for linear scaling in the electronic structure problem. Phys. Rev. Lett. 70:233631–34
    [Google Scholar]
  57. 57. 
    Silver RN, Röder H. 1997. Calculation of densities of states and spectral functions by Chebyshev recursion and maximum entropy. Phys. Rev. E 56:44822–29
    [Google Scholar]
  58. 58. 
    Neuhauser D, Baer R, Rabani E. 2014. Embedded fragment stochastic density functional theory. J. Chem. Phys. 141:4041102
    [Google Scholar]
  59. 59. 
    Nguyen M, Li W, Li Y, Baer R, Rabani E, Neuhauser D. 2021. Tempering stochastic density functional theory. J. Chem. Phys. 155:20204105
    [Google Scholar]
  60. 60. 
    Stefanucci G, van Leeuwen R. 2013. Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction Cambridge, UK: Cambridge Univ. Press
  61. 61. 
    Feyereisen M, Fitzgerald G, Komornicki A 1993. Use of approximate integrals in ab initio theory. An application in MP2 energy calculations. Chem. Phys. Lett. 208:5–6359–63
    [Google Scholar]
  62. 62. 
    Weigend F, Häser M, Patzelt H, Ahlrichs R. 1998. RI-MP2: optimized auxiliary basis sets and demonstration of efficiency. Chem. Phys. Lett. 294:1–3143–52
    [Google Scholar]
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