Analysis of the effect of changing the a0 parameter of the Becke3-LYP hybrid functional on the transition state geometries and energy barriers in a series of prototypical reactions

A series of eleven gas-phase chemical reactions have been examined to assess the dependence of transition state geometries and energy barriers, as well as energy differences between reactants and products, on the a0 B3LYP functional parameter. Throughout the study we have changed the a0 parameter from 0.1 to 0.9 and for the ac and ax parameters we have followed the relationships ax = 1 − a0 and ac = ax. By comparing with the QCISD transition state geometries and energy barriers, our systematic study allows us to identify the influence of the a0 parameter in the reactions studied. In general, B3LYP calculations with the original parameters underestimate energy barriers, this trend being corrected when the a0 parameter increases. Our study also shows that the fraction of Hartree–Fock exchange needed to predict accurate barrier heights differs from the optimal fraction needed to predict thermochemical properties and geometries.

[1]  T. Ziegler,et al.  Combined Density Functional Theory and Intrinsic Reaction Coordinate Study on the Conrotatory Ring-Opening of Cyclobutene , 1995 .

[2]  Joseph S. Francisco.  A computational study of the reaction of the FO radical with H2 , 1994 .

[3]  W. L. Jorgensen,et al.  Substituent effects and transition structures for Diels-Alder reactions of butadiene and cyclopentadiene with cyanoalkenes , 1989 .

[4]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[5]  J. Standard,et al.  Density functional calculations exploring the methylene-water interaction in the gas phase and in solution☆ , 1998 .

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

[7]  T. Ziegler,et al.  Nonlocal density functional theory as a practical tool in calculations on transition states and activation energies. Applications to elementary reaction steps in organic chemistry , 1992 .

[8]  Dimas Suárez,et al.  Theoretical study of the gas‐phase addition of HF and HCl to ethylene: Analysis of the catalytic action of dimeric halides , 1995, J. Comput. Chem..

[9]  D. Wales,et al.  Gradient line reaction path of HF addition to ethylene , 1994 .

[10]  D. L. Cooper,et al.  Modern valence-bond description of chemical reaction mechanisms: the 1,3-dipolar addition of diazomethane to ethene. , 2001, The Journal of organic chemistry.

[11]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

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

[13]  Vincenzo Barone,et al.  Proton transfer in the ground and lowest excited states of malonaldehyde: A comparative density functional and post‐Hartree–Fock study , 1996 .

[14]  Miquel Solà,et al.  Parametrization of the Becke3‐LYP hybrid functional for a series of small molecules using quantum molecular similarity techniques , 2001, J. Comput. Chem..

[15]  Robert G. Bell,et al.  AB INITIO AND DENSITY FUNCTIONAL THEORY STUDIES OF PROTON TRANSFER REACTIONS IN MULTIPLE HYDROGEN BOND SYSTEMS , 1995 .

[16]  Christopher E. Dateo,et al.  A global ab initio potential for HCN/HNC, exact vibrational energies, and comparison to experiment , 1992 .

[17]  A. Becke.  A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[18]  Paul von Ragué Schleyer,et al.  Theoretical investigation of the relative stabilities of XSSX and X2SS isomers (X = F, Cl, H, and CH3) , 1995, J. Comput. Chem..

[19]  Craig,et al.  Gas-phase ionic reactions: dynamics and mechanism of nucleophilic displacements , 1998, Science.

[20]  Martin Head-Gordon,et al.  Quadratic configuration interaction. A general technique for determining electron correlation energies , 1987 .

[21]  Vincenzo Barone,et al.  Diels–Alder reactions: An assessment of quantum chemical procedures , 1997 .

[22]  Wang,et al.  Generalized gradient approximation for the exchange-correlation hole of a many-electron system. , 1996, Physical review. B, Condensed matter.

[23]  Vincenzo Barone,et al.  THEORETICAL-STUDY OF DIRECT AND WATER-ASSISTED ISOMERIZATION OF FORMALDEHYDE RADICAL-CATION - A COMPARISON BETWEEN DENSITY-FUNCTIONAL AND POST-HARTREE-FOCK APPROACHES , 1994 .

[24]  R. Wyatt,et al.  Highly vibrationally excited HCN/HNC: Eigenvalues, wave functions, and stimulated emission pumping spectra , 1993 .

[25]  Mikhail N. Glukhovtsev,et al.  High-Level Computational Study of the Stereoelectronic Effects of Substituents on Alkene Epoxidations with Peroxyformic Acid , 1998 .

[26]  Jordi Mestres,et al.  Use of ab Initio Quantum Molecular Similarities as an Interpretative Tool for the Study of Chemical Reactions , 1994 .

[27]  Jan M.L. Martin,et al.  Benchmark ab Initio Energy Profiles for the Gas-Phase SN2 Reactions Y- + CH3X → CH3Y + X- (X,Y = F,Cl,Br). Validation of Hybrid DFT Methods , 2000 .

[28]  S. Sakai.  Theoretical Analysis of Concerted and Stepwise Mechanisms of Diels−Alder Reaction between Butadiene and Ethylene , 2000 .

[29]  Miquel Solà,et al.  An assessment of density functional theory on evaluating activation barriers for small organic gas-phase rearrangement reactions , 1996 .

[30]  P. Politzer,et al.  Variation of parameters in Becke‐3 hybrid exchange‐correlation functional , 2000 .

[31]  R. Gandolfi,et al.  Ab Initio Study of the Regiochemistry of 1,3-Dipolar Cycloadditions. Reactions of Diazomethane and Formonitrile Oxide with Ethene, Propene, Acrylonitrile, and Methyl Vinyl Ether. , 1998, The Journal of organic chemistry.

[32]  Xavier Fradera,et al.  New Insights in Chemical Reactivity by Means of Electron Pairing Analysis , 2001 .

[33]  Martin J. Field,et al.  MC−SCF study of the Diels-Alder reaction between ethylene and butadiene , 1988 .

[34]  Brian J. Smith,et al.  Unimolecular rearrangements connecting hydroxyethylidene (CH3-C-OH), acetaldehyde (CH3-CH:O), and vinyl alcohol (CH2:CH-OH). , 1991, Journal of the American Chemical Society.

[35]  Kenneth M. Merz,et al.  Density functional transition states of organic and organometallic reactions , 1994 .

[36]  J. Bertrán,et al.  Ab initio study of substituent effect on the addition of hydrogen fluoride to fluoroethylenes , 1989 .

[37]  Vincenzo Barone,et al.  Study of prototypical Diels-Alder reactions by a hybrid density functional/Hartree-Fock approach , 1996 .

[38]  Vincenzo Barone,et al.  Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models , 1998 .

[39]  K. Yoshizawa,et al.  Thermal Addition of Disilacyclobutenes and Acetylene: A Theoretical Study on Diels−Alder Type Reactions , 1999 .

[40]  B. Jursic,et al.  Theoretical investigation of the conrotatory ring opening of cyclobutene and 1, 2‐dihydro‐1, 2‐diazacyclobutadienes with ab initio and density functional Gaussian‐type‐orbital approach , 1995 .

[41]  J. I. Brauman,et al.  Phase-Shifting Acceleration of Ions in an Ion Cyclotron Resonance Spectrometer: Kinetic Energy Distribution and Reaction Dynamics , 1997 .

[42]  Donald G. Truhlar,et al.  How Well Can Hybrid Density Functional Methods Predict Transition State Geometries and Barrier Heights , 2001 .

[43]  Kuangsen Sung.  A theoretical study on catalyzed ethen-1,1-diol-acetic acid tautomerizations , 1999 .

[44]  James S. Harris,et al.  Adiabatic-connection approach to Kohn-Sham theory , 1984 .

[45]  Roland H. Hertwig,et al.  On the parameterization of the local correlation functional. What is Becke-3-LYP? , 1997 .

[46]  J. Seinfeld,et al.  Prediction of bond dissociation energies and transition state barriers by a modified complete basis set model chemistry , 1997 .

[47]  Carlo Adamo,et al.  Predicting proton transfer barriers with density functional methods , 1999 .

[48]  V. R. Jensen,et al.  An investigation of the quantum chemical description of the ethylenic double bond in reactions: II. Insertion of ethylene into a titanium–carbon bond , 1998 .

[49]  Michael T. Bowers,et al.  The nonstatistical dissociation dynamics of chloride(bromomethane) Cl-(CH3Br): evidence for vibrational excitation in the products of gas-phase SN2 reactions , 1991 .

[50]  John-David R. Rocha,et al.  Computational studies of the potential energy surface for O(1D)+H2S: Characterization of pathways involving H2SO, HOSH, and H2OS , 1994 .

[51]  B. Jursic.  Can hybrid DFT methods correctly compute the potential energy surface formic acid dimerization and proton transfer in the formic acid dimer? A comparison of hybrid DFT computed values with experimental and G1, G2, and G2MP2 generated data , 1997 .

[52]  H. Schaefer,et al.  Reaction path Hamiltonian: Tunneling effects in the unimolecular isomerization HNC→HCN , 1980 .

[53]  Henry Chermette,et al.  A density functional especially designed for hydrogen-only systems , 1997 .

[54]  J. Andzelm,et al.  Theoretical study of chemical reactions using density functional methods with nonlocal corrections , 1993 .

[55]  Manabu Igarashi,et al.  A direct ab-initio dynamics study on a gas phase SN2 reaction F−+CH3Cl → CH3F+Cl−: dynamics of near-collinear collision , 1999 .

[56]  Olivier Kahn,et al.  Competing spin interactions and degenerate frustration for discrete molecular species , 1997 .

[57]  K. Houk,et al.  Secondary Kinetic Isotope Effects of Diastereotopic Protons in Pericyclic Reactions: A New Mechanistic Probe , 1995 .

[58]  C. Sosa,et al.  Density functional description of transition structures using nonlocal corrections. Silylene insertion reactions into the hydrogen molecule , 1993 .

[59]  B. Jursic.  Density functional theory and ab initio study of CH 3NC and HNC isomerization , 1996 .

[60]  T. Ziegler.  Approximate Density Functional Theory as a Practical Tool in Molecular Energetics and Dynamics , 1991 .

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

[62]  Sreedhara V. Rao.  Mechanism of some 1:2 hydrogen transfer reactions through bond variation indices , 2000 .

[63]  J. Baker,et al.  A study of some organic reactions using density functional theory , 1995 .

[64]  István Kolossváry,et al.  Simple tests for density functional methods , 1997 .

[65]  Steve Scheiner,et al.  Critical Assessment of Density Functional Methods for Study of Proton Transfer Processes (FHF) , 1995 .

[66]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[67]  Donald G. Truhlar,et al.  Adiabatic connection for kinetics , 2000 .

[68]  Tom Ziegler.  The 1994 Alcan Award Lecture Density functional theory as a practical tool in studies of organometallic energetics and kinetics. Beating the heavy metal blues with DFT , 1995 .

[69]  T. Ziegler,et al.  The application of density functional theory to the optimization of transition state structures. I. Organic migration reactions , 1990 .

[70]  Mark S. Gordon,et al.  Algorithms and accuracy requirements for computing reaction paths by the method of steepest descent , 1988 .

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

[72]  G. Frenking,et al.  Theoretical Studies of Some Transition-Metal-Mediated Reactions of Industrial and Synthetic Importance. , 2000, Chemical reviews.

[73]  Jan Lundell,et al.  Density Functional Study of Hydrogen-Bonded Systems: The Water−Carbon Monoxide Complex , 1997 .

[74]  Axel D. Becke,et al.  Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing , 1996 .

[75]  E. Jemmis,et al.  AN AB INITIO MO STUDY OF PERFLUORO-EFFECT IN THERMAL CYCLIZATION OF BUTA-1,3-DIENE TO CYCLOBUTENE , 1996 .

[76]  B. A. Gilbert,et al.  Evaluation and comparison of transition states with the HCTH98 and FT97 functionals , 2000 .

[77]  H. Bock,et al.  Photoelectron spectra and molecular properties. 59. Ionization energies of disulfur dihalides and isomerization surfaces XSSX .dblarw. SSX2 , 1977 .

[78]  San-Yan Chu,et al.  Cycloadditions of 16-Electron 1,3-Dipoles with Ethylene. A Density Functional and CCSD(T) Study. , 1999, The Journal of organic chemistry.

[79]  J. Mestres,et al.  Exploring the possibility of a bimolecular reaction channel for the F2SS/FSSF rearrangement process , 1998 .

[80]  N. Russo,et al.  Density-Functional Approach to Hardness Evaluation and Its Use in the Study of the Maximum Hardness Principle , 1998 .

[81]  B. Jursic.  Ab initio and density function theory computational studies of the CH4 + H → CH3 + H2 reaction , 1998 .

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

[83]  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 .

[84]  Joseph L. Durant,et al.  Evaluation of transition state properties by density functional theory , 1996 .