Performance of the VBSCF method for pericyclic and π bond shift reactions

The performance of the valence bond self‐consistent field (VBSCF) method was investigated in this paper by predicting the activation barriers and reaction energies in pericyclic and π bond shift reactions for hydrocarbons. The benchmarking set includes 3 electrocyclic reactions, 3 sigmatropic shifts, 3 cycloadditions, 2 cycloreversions, and 7 π bond shift reactions, where the first 11 reactions are taken from Houk's standard set (J. Phys. Chem. A 2003, 107, 11445). Computational results reveal that the VB(CI) method, which performs VBSCF calculations first with full covalent structures and then includes all mono‐ and di‐ionic structures to compute the total energy without further orbital optimization, matches the accuracy of the complete active space SCF (CASSCF) method very well. The mean absolute error values (the deviations from the CASSCF data) are 0.01 kcal/mol for the reaction energy, and 0.26 and 0.32 kcal/mol for the activation energy with the 6‐31G and 6‐31G(d) basis sets, respectively. © 2018 Wiley Periodicals, Inc.

[1]  Y. Mo,et al.  Energy decomposition analysis of intermolecular interactions using a block-localized wave function approach , 2000 .

[2]  Luis Lain,et al.  Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions. , 2013, The Journal of chemical physics.

[3]  W. Goddard,et al.  Generalized valence bond description of bonding in low-lying states of molecules , 1973 .

[4]  Sonia Coriani,et al.  From pentalene to dicyclopenta[b,g]naphthalene, or the change towards delocalized structures. , 2006, Chemphyschem : a European journal of chemical physics and physical chemistry.

[5]  A. Faessler,et al.  Quasi-elastic electroproduction of charged $ \rho$ -mesons on nucleons , 2010 .

[6]  Wei Wu,et al.  XMVB : A program for ab initio nonorthogonal valence bond computations , 2005, J. Comput. Chem..

[7]  Linus Pauling,et al.  THE NATURE OF THE CHEMICAL BOND. APPLICATION OF RESULTS OBTAINED FROM THE QUANTUM MECHANICS AND FROM A THEORY OF PARAMAGNETIC SUSCEPTIBILITY TO THE STRUCTURE OF MOLECULES , 1931 .

[8]  Sason Shaik,et al.  Classical valence bond approach by modern methods. , 2011, Chemical reviews.

[9]  Andrew G. Leach,et al.  A Standard Set of Pericyclic Reactions of Hydrocarbons for the Benchmarking of Computational Methods: The Performance of ab Initio, Density Functional, CASSCF, CASPT2, and CBS-QB3 Methods for the Prediction of Activation Barriers, Reaction Energetics, and Transition State Geometries , 2003 .

[10]  Sason Shaik,et al.  Breathing-orbital valence bond method – a modern valence bond method that includes dynamic correlation , 2002 .

[11]  Wei Wu,et al.  Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. IV. The automatic implementation of the Hessian based VBSCF method. , 2014, The Journal of chemical physics.

[12]  David L. Cooper,et al.  Core‐valence separation in the spin‐coupled wave function: A fully variational treatment based on a second‐order constrained optimization procedure , 1992 .

[13]  Linus Pauling,et al.  THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND , 1931 .

[14]  F. D. Greene.  Resonance in organic chemistry , 1956 .

[15]  Patrick W. Fowler,et al.  Localisation and reversal of paratropic ring currents in molecules with formal anti-aromatic electron countsPresented at the ESF Exploratory Workshop: New Perspectives on Aromaticity, Exeter, UK, July 5?9, 2003. , 2004 .

[16]  Wei Wu,et al.  Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. II. An efficient algorithm for matrix elements and analytical energy gradients in VBSCF method. , 2013, The Journal of chemical physics.

[17]  Donald G. Truhlar,et al.  Small Representative Benchmarks for Thermochemical Calculations , 2003 .

[18]  P. Hiberty,et al.  Chapter 7 – BOVB - A valence bond method incorporating static and dynamic correlation effects , 2002 .

[19]  Sason Shaik,et al.  When does electronic delocalization become a driving force of chemical bonding , 1988 .

[20]  Jessica Schulze,et al.  The Nature Of The Chemical Bond , 2016 .

[21]  William A. Goddard,et al.  IMPROVED QUANTUM THEORY OF MANY-ELECTRON SYSTEMS. II. THE BASIC METHOD. , 1967 .

[22]  Jonas Boström,et al.  Ab Initio Density Fitting: Accuracy Assessment of Auxiliary Basis Sets from Cholesky Decompositions. , 2009, Journal of chemical theory and computation.

[23]  Sason Shaik,et al.  Valence bond perturbation theory. A valence bond method that incorporates perturbation theory. , 2009, The journal of physical chemistry. A.

[24]  Sason Shaik,et al.  The charge-shift bonding concept. Electron-pair bonds with very large ionic-covalent resonance energies , 1992 .

[25]  Wei Wu,et al.  A comparative study on seniority-based MO and VB calculations of the singlet and triplet energy gaps of open-shell molecules , 2017 .

[26]  John C. Slater,et al.  Molecular Energy Levels and Valence Bonds , 1931 .

[27]  Philippe C. Hiberty,et al.  Compact valence bond functions with breathing orbitals: Application to the bond dissociation energies of F2 and FH , 1994 .

[28]  F. London,et al.  Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik , 1927 .

[29]  E. Condon.  The Theory of Groups and Quantum Mechanics , 1932 .

[30]  William A. Goddard,et al.  The symmetric group and the spin generalized scf method , 2009 .

[31]  Wei Wu,et al.  Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions. , 2013, The Journal of chemical physics.

[32]  David L. Cooper,et al.  Optimized spin-coupled virtual orbitals , 1996 .

[33]  J. H. van Lenthe,et al.  The valence‐bond self‐consistent field method (VB–SCF): Theory and test calculations , 1983 .

[34]  Gilbert N. Lewis,et al.  The Atom and the Molecule , 1916, Resonance.

[35]  David L. Cooper,et al.  Spin-coupled valence bond theory , 1988 .

[36]  John C. Slater,et al.  The Theory of Complex Spectra , 1929 .

[37]  F. Matthias Bickelhaupt,et al.  A chemist's guide to valence bond theory , 2009, J. Comput. Chem..

[38]  Huaiyu Zhang,et al.  Nonorthogonal orbital based n-body reduced density matrices and their applications to valence bond theory. III. Second-order perturbation theory using valence bond self-consistent field function as reference. , 2014, The Journal of chemical physics.

[39]  Sason Shaik,et al.  Valence Bond Diagrams and Chemical Reactivity. , 1999, Angewandte Chemie.

[40]  Laimutis Bytautas,et al.  Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy. , 2011, The Journal of chemical physics.

[41]  Y. Mo,et al.  Theoretical analysis of electronic delocalization , 1998 .

[42]  Wei Wu,et al.  Seniority Number in Valence Bond Theory. , 2015, Journal of chemical theory and computation.

[43]  Wei Wu,et al.  The application of cholesky decomposition in valence bond calculation , 2016, J. Comput. Chem..

[44]  Yirong Mo,et al.  XMVB 2.0: A new version of Xiamen valence bond program , 2015 .

[45]  Sason Shaik,et al.  A qualitative valence-bond approach to organic reactivity , 1982 .

[46]  a Sason Shaik,et al.  A Kekulé-Crossing Model for the “Anomalous” Behavior of the b2u Modes of Aromatic Hydrocarbons in the Lowest Excited 1B2u State , 1996 .

[47]  B. H. Chirgwin,et al.  The electronic structure of conjugated systems. VI , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[48]  Peifeng Su,et al.  VBEFP: a valence bond approach that incorporates effective fragment potential method. , 2012, The journal of physical chemistry. A.

[49]  I Røeggen,et al.  Cholesky decomposition of the two-electron integral matrix in electronic structure calculations. , 2008, The Journal of chemical physics.

[50]  Yirong Mo,et al.  Bond-Distorted Orbitals and Effects of Hybridization and Resonance on C−C Bond Lengths , 1996 .

[51]  David L. Cooper,et al.  Expansion of the spin-coupled wavefunction in Slater determinants , 1993 .

[52]  Sason Shaik,et al.  VBPCM: A Valence Bond Method that Incorporates a Polarizable Continuum Model , 2004 .

[53]  Paul von Ragué Schleyer,et al.  The Long Elusive Acepentalene—Experimental and Theoretical Evidence for its Existence , 1996 .

[54]  J. H. van Lenthe,et al.  The valence-bond scf (VB SCF) method.: Synopsis of theory and test calculation of oh potential energy curve , 1980 .

[55]  Donald G. Truhlar,et al.  Assessing the performance of ab initio classical valence bond methods for hydrogen transfer reactions , 2017 .

[56]  Sason Shaik,et al.  Valence bond configuration interaction: A practical ab initio valence bond method that incorporates dynamic correlation , 2002 .

[57]  Martin Schütz,et al.  Molpro: a general‐purpose quantum chemistry program package , 2012 .

[58]  M. Nascimento,et al.  The nature of the chemical bond , 2008 .

[59]  Philippe C. Hiberty,et al.  Compact and accurate valence bond functions with different orbitals for different configurations: application to the two-configuration description of F2 , 1992 .

[60]  Sason Shaik,et al.  What happens to molecules as they react? A valence bond approach to reactivity , 1981 .

[61]  Wei Wu,et al.  A practical valence bond method: A configuration interaction method approach with perturbation theoretic facility , 2004, J. Comput. Chem..

[62]  William A. Goddard,et al.  The Description of Chemical Bonding From AB Initio Calculations , 1978 .

[63]  David L. Cooper,et al.  STUDY OF THE ELECTRONIC STATES OF THE BENZENE MOLECULE USING SPIN-COUPLED VALENCE BOND THEORY , 1994 .

[64]  Benoît Champagne,et al.  Size dependences of the diradical character and the second hyperpolarizabilities in dicyclopenta-fused acenes: relationships with their aromaticity/antiaromaticity. , 2011, Physical chemistry chemical physics : PCCP.

[65]  Peifeng Su,et al.  Ab initio nonorthogonal valence bond methods , 2013 .