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


  • 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.


  1. Joseph Ivanic, Klaus Ruedenberg. Identification of deadwood in configuration spaces through general direct configuration interaction. Theor Chem Acc 106, 339–351 (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 (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 (2012). Link

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

  5. Timothy J. Lee, Gustavo E. Scuseria. Achieving Chemical Accuracy with Coupled-Cluster Theory. 47–108 (1995). Link

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

  7. Attila Tajti, Peter G. Szalay, Attila G. Csaśzaŕ, Mihaĺy Kaĺlay, Jürgen Gauss, Edward F. Valeev, Bradley A. Flowers, Juana Vaźquez, John F. Stanton. HEAT: High accuracy extrapolated ab initio thermochemistry. The Journal of Chemical Physics 121, 11599 (2004). Link

  8. Trygve Helgaker, Poul J, Jeppe Olsen. Molecular Electronic-Structure Theory. (2000). Link

  9. W. A. Goddard. Theoretical Chemistry Comes Alive: Full Partner with Experiment. Science 227, 917–923 (1985). Link

  10. MatúDubecký, Lubos Mitas, Petr Jure. Noncovalent Interactions by Quantum Monte Carlo. Chemical Reviews (2016). Link

  11. Julien Toulouse, Roland Assaraf, Cyrus J. Umrigar. Introduction to the Variational and Diffusion Monte Carlo Methods. 285–314 (2016). Link

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

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

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

  15. M. D. Towler. The quantum Monte Carlo method. physica status solidi (b) 243, 2573–2598 (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 (2001). Link

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

  18. Alex J. W. Thom. Stochastic Coupled Cluster Theory. Phys. Rev. Lett. 105 (2010). Link

  19. George H. Booth, Alex J. W. Thom, Ali Alavi. Fermion Monte Carlo without fixed nodes: A game of life death, and annihilation in Slater determinant space. The Journal of Chemical Physics 131, 054106 (2009). Link

  20. R. S. T. Franklin, J. S. Spencer, A. Zoccante, A. J. W. Thom. Linked coupled cluster Monte Carlo. The Journal of Chemical Physics 144, 044111 (2016). Link

  21. James S. Spencer, Alex J. W. Thom. Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas. The Journal of Chemical Physics 144, 084108 (2016). Link

  22. Alex J. W. Thom, Ali Alavi. Stochastic Perturbation Theory: A Low-Scaling Approach to Correlated Electronic Energies. Phys. Rev. Lett. 99 (2007). Link

  23. Sebastian Manten, Arne Lüchow. Linear scaling for the local energy in quantum Monte Carlo. The Journal of Chemical Physics 119, 1307 (2003). Link

  24. A. J. Williamson, Randolph Q. Hood, J. C. Grossman. Linear-Scaling Quantum Monte Carlo Calculations. Phys. Rev. Lett. 87 (2001). Link

  25. Michel Caffarel, Michel Rérat, Claude Pouchan. Evaluating dynamic multipole polarizabilities and van der Waals dispersion coefficients of two-electron systems with a quantum Monte Carlo calculation: A comparison with some ab initio calculations. Phys. Rev. A 47, 3704–3717 (1993). Link

  26. Massimo Mella, Dario Bressanini, Gabriele Morosi. Variational Monte Carlo calculation of dynamic multipole polarizabilities and van der Waals coefficients of the PsH system. Phys. Rev. A 63 (2001). Link

  27. Claudia Filippi, Francesco Buda, Leonardo Guidoni, Adalgisa Sinicropi. Bathochromic Shift in Green Fluorescent Protein: A Puzzle for QM/MM Approaches. J. Chem. Theory Comput. 8, 112–124 (2012). Link

  28. Omar Valsson, Claudia Filippi. Photoisomerization of Model Retinal Chromophores: Insight from Quantum Monte Carlo and Multiconfigurational Perturbation Theory. J. Chem. Theory Comput. 6, 1275–1292 (2010). Link

  29. Claudia Filippi, C. J. Umrigar. Correlated sampling in quantum Monte Carlo: A route to forces. Phys. Rev. B 61, R16291–R16294 (2000). Link

  30. C. J. Umrigar. Two aspects of quantum monte carlo: Determination of accurate wavefunctions and determination of potential energy surfaces of molecules. Int. J. Quantum Chem. 36, 217–230 (2009). Link

  31. Roland Assaraf, Michel Caffarel. Computing forces with quantum Monte Carlo. The Journal of Chemical Physics 113, 4028 (2000). Link

  32. Roland Assaraf, Michel Caffarel. Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces. The Journal of Chemical Physics 119, 10536 (2003). Link

  33. Yu Li, Jan Vrbik, Stuart M. Rothstein. Towards a field-free quantum Monte Carlo approach to polarizabilities of excited states: Application to the n=2 hydrogen atom. Chemical Physics Letters 445, 345–349 (2007). Link

  34. Laurence D. Barron. Molecular Light Scattering and Optical Activity. (2004). Link

  35. L. Rosenfeld. Quantenmechanische Theorie der natürlichen optischen Aktivität von Flüssigkeiten und Gasen. Zeitschrift für Physik 52, 161–174 (1929). Link

  36. Magdalena Pecul, Kenneth Ruud. The Ab Initio Calculation of Optical Rotation and Electronic Circular Dichroism. 185–212 (2005). Link

  37. . Comprehensive Chiroptical Spectroscopy. (2011). Link

  38. T. Daniel. Crawford. Ab initio calculation of molecular chiroptical properties. Theor Chem Acc 115, 227–245 (2005). Link

  39. T. Daniel Crawford, Mary C. Tam, Micah L. Abrams. The Current State of Ab Initio Calculations of Optical Rotation and Electronic Circular Dichroism Spectra. J. Phys. Chem. A 111, 12057–12068 (2007). Link

  40. T. Daniel Crawford. High-Accuracy Quantum Chemistry and Chiroptical Properties. 675–697 (2012). Link

  41. G�nther Snatzke. Circular Dichroism and Absolute Conformation: Application of Qualitative MO Theory to Chiroptical Phenomena. Angewandte Chemie International Edition in English 18, 363–377 (1979). Link

  42. B. Christopher Rinderspacher, Peter R. Schreiner. Structure-Property Relationships of Prototypical Chiral Compounds:  Case Studies . J. Phys. Chem. A 108, 2867–2870 (2004). Link

  43. James R. Cheeseman, Michael J. Frisch, Frank J. Devlin, Philip J. Stephens. Hartree-Fock and Density Functional Theory ab Initio Calculation of Optical Rotation Using GIAOs:  Basis Set Dependence. J. Phys. Chem. A 104, 1039–1046 (2000). Link

  44. Filipp Furche, Reinhart Ahlrichs, Claudia Wachsmann, Edwin Weber, Adam Sobanski, Fritz Vögtle, Stefan Grimme. Circular Dichroism of Helicenes Investigated by Time-Dependent Density Functional Theory. J. Am. Chem. Soc. 122, 1717–1724 (2000). Link

  45. Stefan Grimme. Calculation of frequency dependent optical rotation using density functional response theory. Chemical Physics Letters 339, 380–388 (2001). Link

  46. P. J. Stephens, F. J. Devlin, J. R. Cheeseman, M. J. Frisch. Calculation of Optical Rotation Using Density Functional Theory. J. Phys. Chem. A 105, 5356–5371 (2001). Link

  47. P. J. Stephens, F. J. Devlin, J. R. Cheeseman, M. J. Frisch, C. Rosini. Determination of Absolute Configuration Using Optical Rotation Calculated Using Density Functional Theory. Org. Lett. 4, 4595–4598 (2002). Link

  48. Stefan Grimme, Filipp Furche, Reinhart Ahlrichs. An improved method for density functional calculations of the frequency-dependent optical rotation. Chemical Physics Letters 361, 321–328 (2002). Link

  49. Jochen Autschbach, Tom Ziegler, Stan J. A. van Gisbergen, Evert Jan Baerends. Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules. The Journal of Chemical Physics 116, 6930 (2002). Link

  50. Jochen Autschbach, Serguei Patchkovskii, Tom Ziegler, Stan J. A. van Gisbergen, Evert Jan Baerends. Chiroptical properties from time-dependent density functional theory. II. Optical rotations of small to medium sized organic molecules. The Journal of Chemical Physics 117, 581 (2002). Link

  51. Jochen Autschbach, Francisco E. Jorge, Tom Ziegler. Density Functional Calculation