SMMP - Stochastic Methods for Molecular Properties

Possible titles:

  1. Stochastic Methods for Molecular Properties (SMMP)

  2. Stochastic Methods for Chiroptical Properties (SMCP or ChiroStoch)

  3. Deterministic methods need large Hilbert spaces for effective expansions of the many-electron wave function
    This is however largely redundant (Ivanic 2001)

  4. Stochastic algorithms are highly parallelizable in the number of walkers.
    I will develop my skills in parallel programming techniques by developing this project.

Research questions:

  • Understanding chiroptical properties for large chemical systems

Objectives of the project:

  • The calculation of molecular properties with high accuracy and for systems of relevant size

    1. High accuracy means coupled cluster (CC) wave functions
    2. Systems for which CC is an option are limited by its polynomial scaling
    3. It is possible to reduce the scaling, e.g. by means of local approaches to the electron correlation problem,
      but this has been proven to not be as effective for molecular properties as for energies
  • Devise the appropriate stochastic approach to the solution of response equations

    1. We want the stochastic approach because it's (supposedly) embarassingly parallel.
      This can enable the study of the response properties for larger systems and provide benchmark
      results for lower level calculations.
    2. Low scaling (or better parallelization options) + (perhaps?) controllable error of stochastic methods
      are the key advantages. Find relevant literature on both!
      (Booth 2014), (Coccia 2012)
  • The creation of the appropriate software toolbox with good scalability.

    1. The toolbox will be freely available under the appropriate open source license (GPL most likely!)

General background on quantum chemistry:

State of the art:

Problems to address:

  • The fermion sign problem. How do FCIQMC and CCMC avoid it?
    The sign problem is NP-hard (Troyer 2005) thus not solvable in polynomial time

TODO:

  • Size of the systems investigated by stochastic methods in Fock space?
  • Properties by stochastic methods? VMC/DMC/FCIQMC?
  • Local correlation approaches for molecular properties?
  • L. Guidoni might have published some FCIQMC calculations on large molecular systems.

References

  1. Joseph Ivanic, Klaus Ruedenberg. Identification of deadwood in configuration spaces through general direct configuration interaction. Theor Chem Acc 106, 339–351 Springer Science \(\mathplus\) Business Media, 2001. Link

  2. George H. Booth, Simon D. Smart, Ali Alavi. Linear-scaling and parallelisable algorithms for stochastic quantum chemistry. Molecular Physics 112, 1855–1869 Informa UK Limited, 2014. Link

  3. Emanuele Coccia, Olga Chernomor, Matteo Barborini, Sandro Sorella, Leonardo Guidoni. Molecular Electrical Properties from Quantum Monte Carlo Calculations: Application to Ethyne. J. Chem. Theory Comput. 8, 1952–1962 American Chemical Society (ACS), 2012. Link

  4. C. David Sherrill. Frontiers in electronic structure theory. The Journal of Chemical Physics 132, 110902 AIP Publishing, 2010. Link

  5. Timothy J. Lee, Gustavo E. Scuseria. Achieving Chemical Accuracy with Coupled-Cluster Theory. 47–108 In Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy. Springer Science \(\mathplus\) Business Media, 1995. Link

  6. Trygve Helgaker, Torgeir A. Ruden, Poul Jørgensen, Jeppe Olsen, Wim Klopper. Apriori calculation of molecular properties to chemical accuracy. Journal of Physical Organic Chemistry 17, 913–933 Wiley-Blackwell, 2004. Link

  7. Attila Tajti, Pe'ter G. Szalay, Attila G. Csa'sza'r, Miha'ly Ka'llay, Jürgen Gauss, Edward F. Valeev, Bradley A. Flowers, Juana Va'zquez, John F. Stanton. HEAT: High accuracy extrapolated ab initio thermochemistry. The Journal of Chemical Physics 121, 11599 AIP Publishing, 2004. Link

  8. Trygve Helgaker, Poul Jørgensen, Jeppe Olsen. Molecular Electronic-Structure Theory. Wiley-Blackwell, 2000. Link

  9. W. A. Goddard. Theoretical Chemistry Comes Alive: Full Partner with Experiment. Science 227, 917–923 American Association for the Advancement of Science (AAAS), 1985. Link

  10. Matúš Dubecký, Lubos Mitas, Petr Jurečka. Noncovalent Interactions by Quantum Monte Carlo. Chemical Reviews American Chemical Society (ACS), 2016. Link

  11. Julien Toulouse, Roland Assaraf, Cyrus J. Umrigar. Introduction to the Variational and Diffusion Monte Carlo Methods. 285–314 In Advances in Quantum Chemistry. Elsevier BV, 2016. Link

  12. Brian M. Austin, Dmitry Yu. Zubarev, William A. Lester. Quantum Monte Carlo and Related Approaches. Chemical Reviews 112, 263–288 American Chemical Society (ACS), 2012. Link

  13. R J Needs, M D Towler, N D Drummond, P López Ríos. Continuum variational and diffusion quantum Monte Carlo calculations. Journal of Physics: Condensed Matter 22, 023201 IOP Publishing, 2009. Link

  14. Roland Assaraf, Michel Caffarel, Anatole Khelif. The fermion Monte Carlo revisited. Journal of Physics A: Mathematical and Theoretical 40, 1181–1214 IOP Publishing, 2007. Link

  15. M. D. Towler. The quantum Monte Carlo method. physica status solidi (b) 243, 2573–2598 Wiley-Blackwell, 2006. Link

  16. W. M. C. Foulkes, L. Mitas, R. J. Needs, G. Rajagopal. Quantum Monte Carlo simulations of solids. Reviews of Modern Physics 73, 33–83 American Physical Society (APS), 2001. Link

  17. G. C. Wick. Properties of Bethe-Salpeter Wave Functions. Phys. Rev. 96, 1124–1134 American Physical Society (APS), 1954. Link

  18. Alex J. W. Thom. Stochastic Coupled Cluster Theory. Phys. Rev. Lett. 105 American Physical Society (APS), 2010.