Analytic Gradients for Complete Active Space Pair-Density Functional Theory.

Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present analytical gradients for multiconfiguration pair-density functional theory (MC-PDFT) when used with a state-specific complete active space self-consistent field reference wave function. Our approach constructs a Lagrangian that is variational in all wave function parameters. We find that MC-PDFT locates equilibrium geometries for several small- to medium-sized organic molecules that are similar to those located by complete active space second-order perturbation theory but that are obtained with decreased computational cost.

[1]  Hans Lischka,et al.  A general multireference configuration interaction gradient program , 1992 .

[2]  H. Hellmann,et al.  Einführung in die Quantenchemie , 2015 .

[3]  Donald G Truhlar,et al.  Multiconfiguration Pair-Density Functional Theory Spectral Calculations Are Stable to Adding Diffuse Basis Functions. , 2015, The journal of physical chemistry letters.

[4]  Kimihiko Hirao,et al.  Multireference Møller-Plesset method , 1992 .

[5]  Roland Lindh,et al.  A direct implementation of the second-order derivatives of multiconfigurational SCF energies and an analysis of the preconditioning in the associated response equation , 1999 .

[6]  Xiao He,et al.  MN15-L: A New Local Exchange-Correlation Functional for Kohn-Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids. , 2016, Journal of chemical theory and computation.

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

[8]  G. Scuseria,et al.  Analytic energy gradient for the projected Hartree-Fock method. , 2014, The Journal of chemical physics.

[9]  Kwang S. Kim,et al.  Theory and applications of computational chemistry : the first forty years , 2005 .

[10]  H. Lischka,et al.  Multiconfiguration self-consistent field and multireference configuration interaction methods and applications. , 2012, Chemical reviews.

[11]  H. Nakatsuji.  Common nature of the electron cloud of a system undergoing change in nuclear configuration , 1974 .

[12]  Donald G Truhlar,et al.  Multireference Model Chemistries for Thermochemical Kinetics. , 2008, Journal of chemical theory and computation.

[13]  R. Feynman.  Forces in Molecules , 1939 .

[14]  M. Karplus,et al.  Analysis of Charge Distributions: Hydrogen Fluoride , 1964 .

[15]  Burke,et al.  Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[16]  J. Park,et al.  Analytical Derivative Coupling for Multistate CASPT2 Theory. , 2017, Journal of chemical theory and computation.

[17]  M. Ratner.  Molecular electronic-structure theory , 2000 .

[18]  Mark S. Gordon,et al.  Parallel coupled perturbed CASSCF equations and analytic CASSCF second derivatives , 2006, J. Comput. Chem..

[19]  Francesco A. Evangelista,et al.  Analytic gradients for Mukherjee's multireference coupled-cluster method using two-configurational self-consistent-field orbitals. , 2010, The Journal of chemical physics.

[20]  Rebecca K. Carlson,et al.  Multiconfiguration Pair-Density Functional Theory. , 2014, Journal of chemical theory and computation.

[21]  Trygve Helgaker,et al.  Molecular Hessians for large‐scale MCSCF wave functions , 1986 .

[22]  Felipe Zapata,et al.  Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table , 2016, J. Comput. Chem..

[23]  Trygve Helgaker,et al.  Analytical Calculation of Geometrical Derivatives in Molecular Electronic Structure Theory , 1988 .

[24]  K. Morokuma,et al.  Multireference Ab Initio Density Matrix Renormalization Group (DMRG)-CASSCF and DMRG-CASPT2 Study on the Photochromic Ring Opening of Spiropyran. , 2013, Journal of chemical theory and computation.

[25]  M. Page,et al.  Multireference CI Gradients and MCSCF Second Derivatives. , 1984 .

[26]  San-Fabián,et al.  Density-functional formalism and the two-body problem. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[27]  Rebecca K. Carlson,et al.  On-Top Pair Density as a Measure of Left-Right Correlation in Bond Breaking. , 2017, The journal of physical chemistry. A.

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

[29]  Kimihiko Hirao,et al.  State-specific multireference Møller—Plesset perturbation treatment for singlet and triplet excited states, ionized states and electron attached states of H2O , 1993 .

[30]  Trygve Helgaker,et al.  Configuration-interaction energy derivatives in a fully variational formulation , 1989 .

[31]  Donald G Truhlar,et al.  Efficient algorithm for multiconfiguration pair-density functional theory with application to the heterolytic dissociation energy of ferrocene. , 2017, The Journal of chemical physics.

[32]  H. Schaefer,et al.  The analytic configuration interaction gradient method: Application to the cyclic and open isomers of the S3 molecule , 1986 .

[33]  Roland Lindh,et al.  Analytical gradients of a state average MCSCF state and a state average diagnostic , 2001 .

[34]  Isaiah Shavitt,et al.  New implementation of the graphical unitary group approach for multireference direct configuration interaction calculations , 2009 .

[35]  A. Becke,et al.  Extension of the local-spin-density exchange-correlation approximation to multiplet states , 1995 .

[36]  V. Barone,et al.  Correction to Semi-Experimental Equilibrium Structure Determinations by Employing B3LYP/SNSD Anharmonic Force Fields: Validation and Application to Semirigid Organic Molecules. , 2015, The journal of physical chemistry. A.

[37]  R. Lindh,et al.  Using on-top pair density for construction of correlation functionals for multideterminant wave functions , 2004 .

[38]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[39]  Donald G Truhlar,et al.  Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems. , 2017, Accounts of chemical research.

[40]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[41]  Uğur Bozkaya,et al.  Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation. , 2016, The Journal of chemical physics.

[42]  Keiji Morokuma,et al.  Energy gradient in a multi-configurational SCF formalism and its application to geometry optimization of trimethylene diradicals , 1979 .

[43]  Kimihiko Hirao,et al.  Multireference Møller—Plesset perturbation theory for high-spin open-shell systems , 1992 .

[44]  H. Schaefer,et al.  Analytic energy second derivatives for general MCSCF wave functions , 1984 .

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

[46]  William H. Press,et al.  Numerical Recipes in Fortran 77 , 1992 .

[47]  Rebecca K. Carlson,et al.  Separated-pair approximation and separated-pair pair-density functional theory , 2015, Chemical science.

[48]  Ilaria Ciofini,et al.  Multiconfiguration Pair-Density Functional Theory Predicts Spin-State Ordering in Iron Complexes with the Same Accuracy as Complete Active Space Second-Order Perturbation Theory at a Significantly Reduced Computational Cost. , 2017, The journal of physical chemistry letters.

[49]  Donald G Truhlar,et al.  Multiconfiguration Pair-Density Functional Theory Is as Accurate as CASPT2 for Electronic Excitation. , 2016, The journal of physical chemistry letters.

[50]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.