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Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4997997· OSTI ID:1410666
 [1];  [1]
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.
Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1410666
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 147; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (80)

An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis journal April 2007
New parallel algorithm for MP2 energy gradient calculations journal January 2007
Semidirect MP2 gradient evaluation on workstation computers: The MPGRAD program journal August 1993
Analytical gradients of the second-order Møller-Plesset energy using Cholesky decompositions journal October 2013
Derivative studies in hartree-fock and møller-plesset theories journal March 1979
Accelerating GPU Kernels for Dense Linear Algebra book January 2011
A numerically stable procedure for calculating M�ller-Plesset energy derivatives, derived using the theory of Lagrangians journal January 1989
A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions
  • Aikens, Christine M.; Webb, Simon P.; Bell, Rob L.
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 110, Issue 4 https://doi.org/10.1007/s00214-003-0453-3
journal November 2003
RI-MP2: first derivatives and global consistency journal October 1997
The elimination of singularities in derivative calculations journal October 1985
On the efficient evaluation of analytic energy gradients journal December 1985
Theory and application of MBPT(3) gradients: The density approach journal October 1987
Theory and implementation of the MBPT density matrix. An application to one-electron properties journal June 1988
A direct MP2 gradient method journal February 1990
Semi-direct algorithms for the MP2 energy and gradient journal February 1990
Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach journal June 1991
Gradient theory applied to restricted (open-shell) Møller—Plesset theory journal November 1992
Kohn—Sham density-functional theory within a finite basis set journal November 1992
A new direct MP2 gradient algorithm with implementation on a massively parallel computer journal June 1996
The analytic evaluation of second-order møller-plesset (MP2) dipole moment derivatives journal May 1987
Fragment molecular orbital-based molecular dynamics (FMO-MD) method with MP2 gradient journal February 2011
Partial geometry optimization with FMO-MP2 gradient: Application to TrpCage journal May 2012
Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction Energies journal June 2015
Benchmark ab Initio Conformational Energies for the Proteinogenic Amino Acids through Explicitly Correlated Methods. Assessment of Density Functional Methods journal December 2015
Building a More Predictive Protein Force Field: A Systematic and Reproducible Route to AMBER-FB15 journal April 2017
Generating Efficient Quantum Chemistry Codes for Novel Architectures journal November 2012
Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller−Plesset Perturbation Theory journal March 2007
Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation journal January 2008
Quartic-Scaling Analytical Gradient of Quasidegenerate Scaled Opposite Spin Second-Order Perturbation Corrections to Single Excitation Configuration Interaction journal April 2009
Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation journal March 2009
Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics journal August 2009
Parallel Unrestricted MP2 Analytic Gradients Using the Distributed Data Interface journal April 2004
Assessment of the MP2 Method, along with Several Basis Sets, for the Computation of Interaction Energies of Biologically Relevant Hydrogen Bonded and Dispersion Bound Complexes journal August 2007
Analytic Energy Gradient in Combined Second-Order Møller–Plesset Perturbation Theory and Polarizable Force Field Calculation journal October 2011
Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) Time journal July 2013
High-Level Ab Initio Electronic Structure Calculations of Water Clusters (H 2 O) 16 and (H 2 O) 17 : A New Global Minimum for (H 2 O) 16 journal October 2010
Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory journal October 2013
Distributed memory parallel implementation of energies and gradients for second-order Møller–Plesset perturbation theory with the resolution-of-the-identity approximation journal January 2006
Advances in methods and algorithms in a modern quantum chemistry program package journal January 2006
Coulombic potential energy integrals and approximations journal May 1973
An efficient atomic orbital based second-order Møller–Plesset gradient program journal June 2004
Analytical energy gradients for local second-order Møller–Plesset perturbation theory using density fitting approximations journal July 2004
Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method journal November 2004
An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory journal April 2008
Analytic derivatives for the Cholesky representation of the two-electron integrals journal July 2008
Minimax approximation for the decomposition of energy denominators in Laplace-transformed Møller–Plesset perturbation theories journal July 2008
Møller–Plesset perturbation theory gradient in the generalized hybrid orbital quantum mechanical and molecular mechanical method journal February 2010
Analytic energy gradient for second-order Møller-Plesset perturbation theory based on the fragment molecular orbital method journal July 2011
Analytic energy gradients in combined second order Møller-Plesset perturbation theory and conductorlike polarizable continuum model calculation journal October 2011
On the evaluation of analytic energy derivatives for correlated wave functions journal December 1984
Analytic energy gradients for general coupled‐cluster methods and fourth‐order many‐body perturbation theory journal November 1986
Mo/ller–Plesset energy derivatives journal August 1988
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Laplace transform techniques in Mo/ller–Plesset perturbation theory journal January 1992
Restricted open‐shell Hartree–Fock‐based many‐body perturbation theory: Theory and application of energy and gradient calculations journal November 1992
The performance of a family of density functional methods journal April 1993
Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method journal May 2012
Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme journal September 2012
Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory journal April 1998
Tensor hypercontraction. II. Least-squares renormalization journal December 2012
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions journal December 2012
Analytical energy gradients in second-order Mo/ller–Plesset perturbation theory for extended systems journal September 1998
An effective energy gradient expression for divide-and-conquer second-order Møller–Plesset perturbation theory journal January 2013
Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2 journal March 2013
Analytic energy gradients for the orbital-optimized second-order Møller–Plesset perturbation theory journal May 2013
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction journal May 2014
Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory journal September 2014
Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach journal September 2015
Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity journal May 2016
Geometry optimization made simple with translation and rotation coordinates journal June 2016
Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction journal January 2017
Low rank factorization of the Coulomb integrals for periodic coupled cluster theory journal March 2017
Analytical nuclear gradients for the MP2-R12 method journal October 2007
Analytic gradients for the combined sr -DFT/ lr -MP2 method: application to weakly bound systems journal December 2010
On the orbital contribution to analytical derivatives of perturbation theory energies journal June 1995
A parallel second-order MØller-Plesset gradient journal June 1997
An improved semidirect MP2 gradient method journal February 1999
Approximation of 1/x by exponential sums in [1, ∞) journal October 2005
Note on an Approximation Treatment for Many-Electron Systems journal October 1934
Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range N -Body Potentials in Many-Body Quantum Problems journal September 2013

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