Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory

Based on the orbital invariant formulation of Mo/ller–Plesset (MP) perturbation theory, analytical energy gradients have been formulated and implemented for local second order MP (LMP2) calculations. The geometry-dependent truncation terms of the LMP2 energy have to be taken into account. This leads to a set of coupled-perturbed localization (CPL) equations which must be solved together with the coupled-perturbed Hartree–Fock (CPHF) equations. In analogy to the conventional non-local theory, the repeated solution of these equations for each degree of freedom can be avoided by using the z-vector method of Handy and Schaefer. Explicit equations are presented for the Pipek–Mezey localization. Test calculations on smaller organic molecules demonstrate that the local approximations introduce only minor changes of computed equilibrium structures.

[1]  Svein Saebo,et al.  Avoiding the integral storage bottleneck in LCAO calculations of electron correlation , 1989 .

[2]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

[3]  Roland Lindh,et al.  The reduced multiplication scheme of the Rys-Gauss quadrature for 1st order integral derivatives , 1993 .

[4]  Peter Pulay,et al.  Local configuration interaction: An efficient approach for larger molecules , 1985 .

[5]  Peter Pulay,et al.  An efficient reformulation of the closed‐shell self‐consistent electron pair theory , 1984 .

[6]  Richard A. Friesner,et al.  Pseudospectral localized Mo/ller–Plesset methods: Theory and calculation of conformational energies , 1995 .

[7]  T. Martínez,et al.  LOCAL WEAK PAIRS SPECTRAL AND PSEUDOSPECTRAL SINGLES AND DOUBLES CONFIGURATION INTERACTION , 1996 .

[8]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[9]  Hans-Joachim Werner,et al.  Local treatment of electron correlation in coupled cluster theory , 1996 .

[10]  Peter Pulay,et al.  Orbital-invariant formulation and second-order gradient evaluation in Møller-Plesset perturbation theory , 1986 .

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

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

[13]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[14]  Jürgen Gauss,et al.  An unconventional scf method for calculations on large molecules , 1986 .

[15]  P. Pulay,et al.  Modeling localized electron pair correlation energies , 1995 .

[16]  Andrew Komornicki,et al.  Molecular gradients and hessians implemented in density functional theory , 1993 .

[17]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

[18]  Peter Pulay,et al.  Efficient elimination of basis set superposition errors by the local correlation method: Accurate ab initio studies of the water dimer , 1993 .

[19]  Peter Pulay,et al.  Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method , 1987 .

[20]  E. Carter,et al.  Removal of the bottleneck in local correlation methods , 1997 .

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

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

[23]  Paul G. Mezey,et al.  A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions , 1989 .

[24]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[25]  Peter Pulay,et al.  The local correlation treatment. II. Implementation and tests , 1988 .

[26]  Peter Pulay,et al.  Comparison of the boys and Pipek–Mezey localizations in the local correlation approach and automatic virtual basis selection , 1993, J. Comput. Chem..

[27]  Michael J. Frisch,et al.  MP2 energy evaluation by direct methods , 1988 .

[28]  R. Bartlett,et al.  The full CCSDT model for molecular electronic structure , 1987 .

[29]  J. Cizek.  On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[30]  Peter Pulay,et al.  Ab initio geometry optimization for large molecules , 1997, J. Comput. Chem..

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

[32]  F. Weigend,et al.  RI-MP2: first derivatives and global consistency , 1997 .

[33]  Curtis L. Janssen,et al.  An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations , 1988 .

[34]  Nicholas C. Handy.  Density Functional Theory , 1996 .

[35]  J. Almlöf,et al.  Principles for a direct SCF approach to LICAO–MOab‐initio calculations , 1982 .

[36]  Ian M. Mills,et al.  Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations. I , 1968 .

[37]  Benny G. Johnson,et al.  The performance of a family of density functional methods , 1993 .

[38]  Henry F. Schaefer,et al.  Analytic second derivative techniques for self-consistent-field wave functions. A new approach to the solution of the coupled perturbed hartree-fock equations , 1983 .

[39]  Richard A. Friesner,et al.  Pseudospectral localized generalized Mo/ller–Plesset methods with a generalized valence bond reference wave function: Theory and calculation of conformational energies , 1997 .

[40]  Henry F. Schaefer,et al.  Accelerating the convergence of the coupled-cluster approach: The use of the DIIS method , 1986 .

[41]  Richard A. Friesner,et al.  Accurate ab Initio Quantum Chemical Determination of the Relative Energetics of Peptide Conformations and Assessment of Empirical Force Fields , 1997 .

[42]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[43]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[44]  Josef Paldus,et al.  Correlation problems in atomic and molecular systems III. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methodst†‡§ , 1971 .

[45]  R. Bartlett.  Coupled-cluster approach to molecular structure and spectra: a step toward predictive quantum chemistry , 1989 .

[46]  R. Bartlett.  Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules , 1981 .

[47]  E. Hylleraas.  Über den Grundterm der Zweielektronenprobleme von H−, He, Li+, Be++ usw. , 1930 .