Automated Selection of Active Orbital Spaces.

One of the key challenges of quantum-chemical multi-configuration methods is the necessity to manually select orbitals for the active space. This selection requires both expertise and experience and can therefore impose severe limitations on the applicability of this most general class of ab initio methods. A poor choice of the active orbital space may yield even qualitatively wrong results. This is obviously a severe problem, especially for wave function methods that are designed to be systematically improvable. Here, we show how the iterative nature of the density matrix renormalization group combined with its capability to include up to about 100 orbitals in the active space can be exploited for a systematic assessment and selection of active orbitals. These benefits allow us to implement an automated approach for active orbital space selection, which can turn multi-configuration models into black box approaches.

[1]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[2]  M. Reiher,et al.  Quantum-information analysis of electronic states of different molecular structures , 2010, 1008.4607.

[3]  Markus Reiher,et al.  Construction of environment states in quantum-chemical density-matrix renormalization group calculations. , 2006, The Journal of chemical physics.

[4]  M. Reiher,et al.  Determining factors for the accuracy of DMRG in chemistry. , 2014, Chimia.

[5]  Dimitri Van Neck,et al.  The density matrix renormalization group for ab initio quantum chemistry , 2014, The European Physical Journal D.

[6]  Laura Gagliardi,et al.  The restricted active space followed by second-order perturbation theory method: theory and application to the study of CuO2 and Cu2O2 systems. , 2008, The Journal of chemical physics.

[7]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[8]  J. Ivanic,et al.  Theoretical Study of the Low Lying Electronic States of oxoX(salen) (X = Mn, Mn-, Fe, and Cr-) Complexes , 2004 .

[9]  Toru Shiozaki,et al.  Quasi-diabatic States from Active Space Decomposition. , 2014, Journal of chemical theory and computation.

[10]  Sandeep Sharma,et al.  The density matrix renormalization group in quantum chemistry. , 2011, Annual review of physical chemistry.

[11]  P. Knowles,et al.  A second order multiconfiguration SCF procedure with optimum convergence , 1985 .

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

[13]  Franziska D. Hofmann,et al.  Computational Organometallic Chemistry with Force Fields , 2012 .

[14]  Björn O. Roos,et al.  Excitation energies in the nickel atom studied with the complete active space SCF method and second-order perturbation theory , 1992 .

[15]  M. Reiher,et al.  Entanglement Measures for Single- and Multireference Correlation Effects. , 2012, The journal of physical chemistry letters.

[16]  K. Pierloot,et al.  The CASPT2 method in inorganic electronic spectroscopy: from ionic transition metal to covalent actinide complexes* , 2003 .

[17]  Kirk A Peterson,et al.  Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn. , 2005, The Journal of chemical physics.

[18]  V. Van Speybroeck,et al.  Communication: DMRG-SCF study of the singlet, triplet, and quintet states of oxo-Mn(Salen). , 2014, The Journal of chemical physics.

[19]  K. Pierloot Transition metals compounds: Outstanding challenges for multiconfigurational methods , 2011 .

[20]  T. Yanai,et al.  High-performance ab initio density matrix renormalization group method: applicability to large-scale multireference problems for metal compounds. , 2009, The Journal of chemical physics.

[21]  Garnet Kin-Lic Chan,et al.  The ab-initio density matrix renormalization group in practice. , 2015, The Journal of chemical physics.

[22]  B. Roos The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[23]  S. Patai,et al.  The chemistry of peroxides , 2006 .

[24]  G. Chan,et al.  Chapter 7 The Density Matrix Renormalization Group in Quantum Chemistry , 2009 .

[25]  J. Sólyom,et al.  Optimizing the density-matrix renormalization group method using quantum information entropy , 2003 .

[26]  Gustavo E Scuseria,et al.  Exploring Copper Oxide Cores Using the Projected Hartree-Fock Method. , 2012, Journal of chemical theory and computation.

[27]  B. A. Hess,et al.  Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach , 2002, cond-mat/0204602.

[28]  C. Sherrill,et al.  The electronic structure of oxo-Mn(salen): single-reference and multireference approaches. , 2006, The Journal of chemical physics.

[29]  Peter Pulay,et al.  The unrestricted natural orbital–complete active space (UNO–CAS) method: An inexpensive alternative to the complete active space–self‐consistent‐field (CAS–SCF) method , 1989 .

[30]  Shawn T. Brown,et al.  Advances in methods and algorithms in a modern quantum chemistry program package. , 2006, Physical chemistry chemical physics : PCCP.

[31]  M. Reiher,et al.  DMRG control using an automated Richardson-type error protocol , 2010 .

[32]  Markus Reiher,et al.  New electron correlation theories for transition metal chemistry. , 2011, Physical chemistry chemical physics : PCCP.

[33]  Wataru Mizukami,et al.  Density matrix renormalization group for ab initio calculations and associated dynamic correlation methods: A review of theory and applications , 2015 .

[34]  M. Reiher,et al.  Decomposition of density matrix renormalization group states into a Slater determinant basis. , 2007, The Journal of chemical physics.

[35]  F. Neese,et al.  Interplay of Correlation and Relativistic Effects in Correlated Calculations on Transition-Metal Complexes: The (Cu2O2)(2+) Core Revisited. , 2011, Journal of chemical theory and computation.

[36]  Scott R. Wilson,et al.  Enantioselective Epoxidation of Unfunctionalized Olefins Catalyzed by (salen)Manganese Complexes , 1990 .

[37]  Garnet Kin-Lic Chan,et al.  Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory. , 2010, The Journal of chemical physics.

[38]  Debashree Ghosh,et al.  An Introduction to the Density Matrix Renormalization Group Ansatz in Quantum Chemistry , 2007, 0711.1398.

[39]  S. White,et al.  Measuring orbital interaction using quantum information theory , 2005, cond-mat/0508524.

[40]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[41]  Roland Lindh,et al.  Accurate ab initio density fitting for multiconfigurational self-consistent field methods. , 2008, The Journal of chemical physics.

[42]  Jeppe Olsen,et al.  Second‐order Mo/ller–Plesset perturbation theory as a configuration and orbital generator in multiconfiguration self‐consistent field calculations , 1988 .

[43]  Michael W. Schmidt,et al.  Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model , 1982 .

[44]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

[45]  Toru Shiozaki,et al.  Communication: Active-space decomposition for molecular dimers. , 2013, The Journal of chemical physics.

[46]  Matthias Troyer,et al.  An efficient matrix product operator representation of the quantum chemical Hamiltonian. , 2015, The Journal of chemical physics.

[47]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[48]  Valera Veryazov,et al.  How to Select Active Space for Multiconfigurational Quantum Chemistry , 2011 .

[49]  F. Verstraete,et al.  Tensor product methods and entanglement optimization for ab initio quantum chemistry , 2014, 1412.5829.

[50]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[51]  B. Roos,et al.  A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach , 1980 .

[52]  A. Thom,et al.  Choosing RASSCF orbital active spaces for multiple electronic states , 2014 .

[53]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[54]  Markus Reiher,et al.  The Density Matrix Renormalization Group Algorithm in Quantum Chemistry , 2010 .

[55]  P. Knowles,et al.  An efficient second-order MC SCF method for long configuration expansions , 1985 .

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

[57]  Peter Pulay,et al.  Selection of active spaces for multiconfigurational wavefunctions. , 2015, The Journal of chemical physics.

[58]  J. Sólyom,et al.  Applications of Quantum Information in the Density-Matrix Renormalization Group , 2008 .

[59]  T. Katsuki,et al.  Catalytic asymmetric epoxidation of unfunctionalized olefins , 1990 .

[60]  Cristina Puzzarini,et al.  Theoretical models on the Cu2O2 torture track: mechanistic implications for oxytyrosinase and small-molecule analogues. , 2006, The journal of physical chemistry. A.

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

[62]  Hans W. Horn,et al.  ELECTRONIC STRUCTURE CALCULATIONS ON WORKSTATION COMPUTERS: THE PROGRAM SYSTEM TURBOMOLE , 1989 .

[63]  Giovanni Li Manni,et al.  The generalized active space concept in multiconfigurational self-consistent field methods. , 2011, The Journal of chemical physics.

[64]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[65]  Yuki Kurashige,et al.  Multireference electron correlation methods with density matrix renormalisation group reference functions , 2014 .

[66]  Markus Reiher,et al.  Density matrix renormalization group with efficient dynamical electron correlation through range separation. , 2015, The Journal of chemical physics.