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! \cite{Booth2014}, \cite{Coccia2012}
  • 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:

  • "Frontiers in electronic structure theory" (Sherrill 2010)
  • Quantum chemistry as an effective complement to experiment \cite{Lee1995}, \cite{Helgaker2004}, \cite{Tajti2004}, \cite{Helgaker2000}, (Goddard 1985)

State of the art:

  • QMC:

    • Recent reviews on QMC approaches: \cite{Dubeck_2016}, \cite{Toulouse2016}, \cite{Austin2012}, \cite{Needs2009}, \cite{Assaraf2007}, \cite{Towler2006} and (Foulkes 2001)
    • DMC (Wick rotation of the Schrodinger equation (Wick 1954) and isomorphism with a classical diffusion problem)
    • Self-Healing QMC
    • Auxiliary Field QMC
    • Fermion QMC
    • FCIQMC
    • Stochastic Coupled Cluster: Thom introduces the FCIQMC-like stochastic algorithm for solving the CC equations \cite{Thom2010} The methods leverages the stochastic sampling strategies of the FCI wave function in a discrete Fock space first proposed by Alavi _et al.(Booth 2009)
    • Linked Coupled Cluster Monte Carlo: the stochastic algorithm for the solution of the CC equations in the linked (term-by-term size-extensive) form (Franklin 2016)
    • Initiator approximation: the same group proposes the initiator approximation for the CCMC algorithm (Spencer 2016)
    • Stochastic Møller-Plesset (Thom 2007)
    • Local approaches to QMC \cite{Manten2003}, \cite{Williamson2001}
  • Properties by QMC

    • Dynamic polarizabilities \cite{Caffarel1993}, \cite{Mella2001}
    • Large systems \cite{Filippi2012}, \cite{Valsson2010}
    • Forces: correlated sampling \cite{Filippi2000} and space warp coordinate transformation \cite{Umrigar2009} Work by Assaraf and Caffarel on improved estimators \cite{Assaraf2000} and \cite{Assaraf2003}
    • Static electric properties (dipole and quadrupole moments, static polarizabilities): polarizabilities by finite differences for ethyne \cite{Coccia2012} polarizability of the hydrogen atom by modified sampling \cite{Li2007}
  • Chiroptical properties:

    • Eliel "Stereochemistry of organic compounds" (find appropriate ref)
    • Barron's book \cite{Barron2004} Rosenfeld's formulation \cite{Rosenfeld1929}
    • OR and ECD review by Pecul and Ruud (Pecul 2005)
    • Berova's book (Comprehensive Chiropt...)
    • Daniel's reviews \cite{Crawford2005}, \cite{Crawford2007a}, (Crawford 2012)
    • Octant rule \cite{Snatzke1979} and its failure \cite{Rinderspacher2004}
    • Chiroptical properties by DFT \cite{Cheeseman2000}, \cite{Furche2000}, \cite{Grimme2001} \cite{Stephens2001} \cite{Stephens2002} \cite{Grimme2002} \cite{Autschbach2002} \cite{Autschbach2002b} (Autschbach 2003)
    • Chiroptical properties by CC \cite{Tam2004} \cite{Crawford2005} \cite{Ruud2002} \cite{Ruud2003}
    • Computational studies available on a variety of molecules \cite{Tam2006} \cite{Kowalczyk2006} \cite{Crawford2005} \cite{Tam2007} \cite{Crawford2007a} \cite{Crawford2007b} \cite{Wiberg2008}\cite{Crawford2008} \cite{Crawford2009} \cite{Pedersen2009} \cite{Pedersen2009b} \cite{Lambert2012} \cite{Rinderspacher2004} \cite{Wilson2005} \cite{Furche2000} \cite{Pulm1997} \cite{Kondru1998} \cite{Grimme1998} \cite{Polavarapu1999} \cite{Ribe2000} \cite{Polavarapu2002} \cite{Diedrich2003} \cite{Polavarapu2003} \cite{Norman2004} (Diedrich 2004) \cite{Stephens2005} \cite{Wiberg2005a} \cite{Wiberg2005b} \cite{Wiberg2006} \cite{Autschbach2009} \cite{Pritchard2010} \cite{Mach2011} \cite{Mach2014}
    • Ultrasensitive Cavity Ring-Down Polarimetry (CRDP) \cite{Wilson2005} \cite{Mller2002} \cite{Mller_2000}
    • Local approaches to the correlation problem in response theory \cite{Russ2004} \cite{Russ2008}
  • Response theory:

    • Most recent review on wave function-based response theory (Helgaker 2012)
    • Foundational work \cite{Olsen1985}, \cite{Christiansen1998}, \cite{Pawowski2015}, (Coriani 2016)
    • CC response theory
    • Local approaches to CC (really a lot of literature...)
    • Local approaches to CC response theory \cite{Friedrich2015}, \cite{McAlexander2012}, (McAlexander 2016)

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 F