skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Monte Carlo MP2-F12 for Noncovalent Interactions: The C60 Dimer

Journal Article · · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States); Quantum Simulation Technologies, Inc., Cambridge, MA (United States)
  2. Univ. of Illinois at Urbana-Champaign, IL (United States); Helium Development, LLC., Port Orchard, WA (United States)
  3. Univ. of Illinois at Urbana-Champaign, IL (United States)

A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green’s functions in real space and imaginary time. Furthermore, these integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol–1 for the C60 dimer at the center distance of 9.748 Å.

Research Organization:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division
Grant/Contract Number:
SC0006028
OSTI ID:
1818888
Journal Information:
Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Vol. 125, Issue 33; ISSN 1089-5639
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (85)

Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy journal January 2014
Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams journal January 2014
Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in Three Dimensions journal March 2013
Quantum Monte Carlo Study of the Water Dimer Binding Energy and Halogen−π Interactions journal August 2019
Symmetry-adapted perturbation theory of intermolecular forces: Symmetry-adapted perturbation theory journal August 2011
Quantum Monte Carlo simulations of solids journal January 2001
Projector Monte Carlo method based on Slater determinants: a new sampling method for singlet state calculations journal September 2011
Stochastic evaluation of fourth-order many-body perturbation energies journal April 2021
Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs journal January 2006
Structure of the Benzene Dimer—Governed by Dynamics journal April 2013
High accuracy benchmark calculations on the benzene dimer potential energy surface journal October 2007
Brueckner-Goldstone quantum Monte Carlo for correlation energies and quasiparticle energy bands of one-dimensional solids journal November 2014
Projector Monte Carlo method based on configuration state functions. Test applications to the H4 system and dissociation of LiH journal October 2008
Semistochastic Projector Monte Carlo Method journal December 2012
Communication: Benzene dimer—The free energy landscape journal November 2013
Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions journal November 2017
Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems journal December 2012
A Guided Stochastic Energy-Domain Formulation of the Second Order Møller–Plesset Perturbation Theory journal December 2013
Accurate ab Initio Binding Energies of the Benzene Dimer journal April 2006
Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory journal July 2017
Initiation of explicitly correlated Slater-type geminal theory journal November 2004
Estimates of the Ab Initio Limit for π−π Interactions:  The Benzene Dimer journal September 2002
Evidence for van der Waals adhesion in gecko setae journal August 2002
Stochastic evaluation of second-order Dyson self-energies journal April 2013
Multireference Stochastic Coupled Cluster journal October 2019
Explicit correlation factors journal September 2017
Large scale parallelization in stochastic coupled cluster journal November 2018
Interaction Energy of Large Molecules from Restrained Denominator MP2-F12 journal October 2014
Stochastic evaluation of second-order many-body perturbation energies journal November 2012
New implementation of second-order Møller-Plesset perturbation theory with an analytic Slater-type geminal journal January 2007
Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling journal September 2020
Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates journal September 2020
Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models journal June 2012
Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes journal November 1994
Potential Energy Surface of the Benzene Dimer: Ab Initio Theoretical Study journal April 1994
Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers journal September 2013
Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations journal July 2015
Evaluating two-electron-repulsion integrals over arbitrary orbitals using zero variance Monte Carlo: Application to full configuration interaction calculations with Slater-type orbitals journal August 2019
Molecular Handshake: Recognition through Weak Noncovalent Interactions journal July 2006
Benchmark Theoretical Study of the π–π Binding Energy in the Benzene Dimer journal May 2014
On the Importance and Origin of Aromatic Interactions in Chemistry and Biodisciplines journal June 2012
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space journal January 2009
Calculation of intermolecular interactions in the benzene dimer using coupled-cluster and local electron correlation methods journal January 2006
Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy journal October 2019
Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states journal April 2013
A Survey of the Role of Noncovalent Sulfur Interactions in Drug Design journal March 2015
Quantum Monte Carlo for Ab Initio calculations of energy-relevant materials journal August 2013
Introduction to the Variational and Diffusion Monte Carlo Methods book January 2016
Quantum Monte Carlo Methods Describe Noncovalent Interactions with Subchemical Accuracy journal September 2013
Metropolis Evaluation of the Hartree–Fock Exchange Energy journal September 2014
Monte Carlo MP2 on Many Graphical Processing Units journal September 2016
Perturbation expansion theory corrected from basis set superposition error II. Charge transfer, pair correlationand dispersion terms journal September 2006
Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures journal January 2004
Noncovalent Interactions by Quantum Monte Carlo journal April 2016
M ONTE C ARLO M ETHODS IN E LECTRONIC S TRUCTURES FOR L ARGE S YSTEMS journal October 2000
Fast and accurate quantum Monte Carlo for molecular crystals journal February 2018
Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems journal October 2017
Quantum Monte Carlo benchmarking of large noncovalent complexes in the L7 benchmark set journal November 2020
Accurate Intermolecular Potential for the C 60 Dimer: The Performance of Different Levels of Quantum Theory journal December 2016
A quantum chemistry study of benzene dimer journal August 1996
Monte Carlo explicitly correlated second-order many-body perturbation theory journal October 2016
The Nature of Stacking Interactions between Organic Molecules Elucidated by Analysis of Crystal Structures. journal January 1994
Potential Energy Surface for the Benzene Dimer and Perturbational Analysis of π−π Interactions journal August 2006
Nature and magnitude of aromatic base stacking in DNA and RNA: Quantum chemistry, molecular mechanics and experiment journal June 2013
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo journal January 2010
Applications of quantum Monte Carlo methods in condensed systems journal January 2011
Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method journal January 2017
Basis set effects on the calculated bonding energies of neutral benzene dimers: importance of diffuse polarization functions journal April 1996
Ground State of the Electron Gas by a Stochastic Method journal August 1980
Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions journal December 2017
On the T-shaped structures of the benzene dimer journal April 2007
Linear-scaling and parallelisable algorithms for stochastic quantum chemistry journal January 2014
Stochastic many-body perturbation theory for electron correlation energies journal December 2019
Quantum Monte Carlo and Related Approaches journal December 2011
Water on BN doped benzene: A hard test for exchange-correlation functionals and the impact of exact exchange on weak binding journal November 2014
The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors journal October 1970
Modeling Polymorphic Molecular Crystals with Electronic Structure Theory journal March 2016
Modeling Adsorption and Reactions of Organic Molecules at Metal Surfaces journal June 2014
Projector Monte Carlo method based on Slater determinants: Test application to singlet excited states of H2O and LiF journal January 2010
Ab Initio Molecular Crystal Structures, Spectra, and Phase Diagrams journal April 2014
Meldola Lecture. The role of aromatic interactions in molecular recognition journal January 1994
Assembly and encapsulation with self-complementary molecules journal January 1996
Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum journal October 2019
Monte Carlo explicitly correlated many-body Green’s function theory journal November 2018
Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory journal September 2017