An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory.

A fully atomic orbital (AO)-based reformulation of second-order Møller-Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear. Our formulation avoids any transformation between the AO and the molecular orbital (MO) basis and employs pseudodensity matrices similar to the AO-MP2 energy expressions within the Laplace scheme for energies. The explicit computation of perturbed one-particle density matrices emerging in the new AO-based gradient expression is avoided by reformulating the Z-vector method of Handy and Schaefer [J. Chem. Phys. 81, 5031 (1984)] within a density matrix-based scheme.

[1]  Jon Baker,et al.  An efficient atomic orbital based second-order Møller-Plesset gradient program. , 2004, The Journal of chemical physics.

[2]  D. Cremer,et al.  Analytical evaluation of energy gradients in quadratic configuration interaction theory , 1988 .

[3]  Philippe Y. Ayala,et al.  Atomic orbital Laplace-transformed second-order Møller–Plesset theory for periodic systems , 2001 .

[4]  Yihan Shao,et al.  Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller-Plesset Perturbation Theory. , 2007, Journal of chemical theory and computation.

[5]  J. Gauss,et al.  Analytic first and second derivatives for the CCSDT-n (n = 1-3) models : a first step towards the efficient calculation of ccsdt properties , 2000 .

[6]  R. Bartlett,et al.  Third‐order MBPT gradients , 1985 .

[7]  R. Mcweeny.  Some Recent Advances in Density Matrix Theory , 1960 .

[8]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[9]  Michael J. Frisch,et al.  A direct MP2 gradient method , 1990 .

[10]  Graham D. Fletcher,et al.  A parallel second-order Møller-Plesset gradient , 1997 .

[11]  Michael J. Frisch,et al.  Semi-direct algorithms for the MP2 energy and gradient , 1990 .

[12]  Julia E. Rice,et al.  The elimination of singularities in derivative calculations , 1985 .

[13]  Julia E. Rice,et al.  Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application , 1987 .

[14]  Gustavo E. Scuseria,et al.  Analytic evaluation of energy gradients for the singles and doubles coupled cluster method including perturbative triple excitations: Theory and applications to FOOF and Cr2 , 1991 .

[15]  Christian Ochsenfeld,et al.  Rigorous integral screening for electron correlation methods. , 2005, The Journal of chemical physics.

[16]  Alistair P. Rendell,et al.  Analytic gradients for coupled-cluster energies that include noniterative connected triple excitations: Application to cis- and trans-HONO , 1991 .

[17]  Ida M. B. Nielsen,et al.  A new direct MP2 gradient algorithm with implementation on a massively parallel computer , 1996 .

[18]  Jörg Kussmann,et al.  A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels. , 2007, The Journal of chemical physics.

[19]  Jan Almlöf,et al.  Laplace transform techniques in Mo/ller–Plesset perturbation theory , 1992 .

[20]  P. C. Hariharan,et al.  The influence of polarization functions on molecular orbital hydrogenation energies , 1973 .

[21]  Péter R. Surján,et al.  The MP2 energy as a functional of the Hartree–Fock density matrix , 2005 .

[22]  Henry F. Schaefer,et al.  On the evaluation of analytic energy derivatives for correlated wave functions , 1984 .

[23]  T. C. Fung,et al.  Computation of the matrix exponential and its derivatives by scaling and squaring , 2004 .

[24]  Jörg Kussmann,et al.  Ab initio NMR spectra for molecular systems with a thousand and more atoms: a linear-scaling method. , 2004, Angewandte Chemie.

[25]  J. Gauss,et al.  Analytical differentiation of the energy contribution due to triple excitations in quadratic configuration interaction theory , 1989 .

[26]  Reinhart Ahlrichs,et al.  Semidirect MP2 gradient evaluation on workstation computers: The MPGRAD program , 1993, J. Comput. Chem..

[27]  Mark S. Gordon,et al.  Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements , 1982 .

[28]  Peter Pulay,et al.  Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules , 1969 .

[29]  J. Pople,et al.  Derivative studies in configuration–interaction theory , 1980 .

[30]  N. Handy,et al.  The analytic evaluation of second-order møller-plesset (MP2) dipole moment derivatives , 1987 .

[31]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[32]  J. Grotendorst,et al.  Modern methods and algorithms of quantum chemistry : winterschool 21. - 25. February 2000 Forschungszentrum Jülich : proceedings / org. by John von Neumann Institute for Computing , 2000 .

[33]  Martin Head-Gordon,et al.  Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method. , 2004, The Journal of chemical physics.

[34]  Johannes Grotendorst,et al.  Modern methods and algorithms of quantum chemistry , 2000 .

[35]  Mark S. Gordon,et al.  A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions , 2003 .

[36]  Y. Yamaguchi,et al.  A New Dimension to Quantum Chemistry: Analytic Derivative Methods in AB Initio Molecular Electronic Structure Theory , 1994 .

[37]  C. Loan,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix , 1978 .

[38]  Michael J. Frisch,et al.  Direct analytic SCF second derivatives and electric field properties , 1990 .

[39]  J. Gauss,et al.  Analytical differentiation of the energy contribution due to triple excitations in fourth-order Møller-Plesset perturbation theory , 1988 .

[40]  Jörg Kussmann,et al.  Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory. , 2007, The Journal of chemical physics.

[41]  Kimihiko Hirao,et al.  An approximate second-order Møller–Plesset perturbation approach for large molecular calculations , 2006 .

[42]  Jan Almlöf,et al.  Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach , 1991 .

[43]  Guntram Rauhut,et al.  Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory , 1998 .

[44]  Christian Ochsenfeld,et al.  Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals. , 2005, The Journal of chemical physics.

[45]  Marco Häser,et al.  Møller-Plesset (MP2) perturbation theory for large molecules , 1993 .

[46]  J. Kussmann,et al.  Linear‐Scaling Methods in Quantum Chemistry , 2007 .

[47]  K. P. Lawley,et al.  Ab initio methods in quantum chemistry , 1987 .

[48]  Bernard R. Brooks,et al.  Analytic gradients from correlated wave functions via the two‐particle density matrix and the unitary group approach , 1980 .

[49]  Frederick R Manby,et al.  Analytical energy gradients for local second-order Møller-Plesset perturbation theory using density fitting approximations. , 2004, The Journal of chemical physics.

[50]  Christian Ochsenfeld,et al.  A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme , 1997 .

[51]  Peter Pulay,et al.  Analytical Derivative Methods in Quantum Chemistry , 2007 .

[52]  Masato Kobayashi,et al.  Implementation of Surjan's density matrix formulae for calculating second-order Møller-Plesset energy , 2006 .

[53]  Trygve Helgaker,et al.  A numerically stable procedure for calculating Møller-Plesset energy derivatives, derived using the theory of Lagrangians , 1989 .