Definitive thermochemistry and kinetics of the interconversions among conformers of n‐butane and n‐pentane

The focal‐point analysis (FPA) technique is used for the definitive characterization of conformational interconversion parameters, including activation energy barriers, activation free energies, and kinetic rate coefficients at 298 K, of two n‐alkanes, n‐butane, and n‐pentane, yielding the first complete analysis of their interconversion kinetics. The FPA implementation developed in this study is based on geometry optimizations and harmonic frequency computations carried out with density functional theory methods and single‐point energy computations up to the CCSD(T) level of electronic structure theory using atom‐centered Gaussian basis sets as large as cc‐pV5Z. The anharmonic vibrational computations are carried out, at the MP2/6‐31G* level of theory. Reflecting the convergence behavior of the Gibbs free‐energy terms and the interconversion parameters, well‐defined uncertainties, mostly neglected in previous theoretical studies, are provided. Finally, the effect of these uncertainties on the concentrations of the conformers of n‐butane and n‐pentane is examined via a global Monte–Carlo uncertainty analysis. © 2017 Wiley Periodicals, Inc.

[1]  T. Zwier,et al.  Infrared-induced conformational isomerization and vibrational relaxation dynamics in melatonin and 5-methoxy-N-acetyl tryptophan methyl amide. , 2004, The Journal of chemical physics.

[2]  M. Stojanović,et al.  The effect of steric repulsion on the torsional potential of n-butane: a theoretical study , 2015 .

[3]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[4]  Ludwik Adamowicz,et al.  Conformational Behavior of α-Alanine. Matrix-Isolation Infrared and Theoretical DFT and ab Initio Study , 1998 .

[5]  A. Császár,et al.  Hartree-Fock-limit energies and structures with a few dozen distributed Gaussians , 2007 .

[6]  T. Zwier,et al.  Direct Measurement of Energy Thresholds to Conformational Isomerization in Tryptamine , 2004, Science.

[7]  A. Becke,et al.  A density-functional model of the dispersion interaction. , 2005, The Journal of chemical physics.

[8]  S. Grimme.  Accurate calculation of the heats of formation for large main group compounds with spin-component scaled MP2 methods. , 2005, The journal of physical chemistry. A.

[9]  Mark A. Murcko,et al.  Rotational barriers. 2. Energies of alkane rotamers. An examination of gauche interactions , 1988 .

[10]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[11]  Mihály Kállay,et al.  Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree-Fock case. , 2008, The Journal of chemical physics.

[12]  Hans-Joachim Werner,et al.  Simplified CCSD(T)-F12 methods: theory and benchmarks. , 2009, The Journal of chemical physics.

[13]  Alexander D. MacKerell,et al.  An ab initio study on the torsional surface of alkanes and its effect on molecular simulations of alkanes and a DPPC bilayer. , 2005, The journal of physical chemistry. B.

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

[15]  Jan M. L. Martin,et al.  DSD-PBEP86: in search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections. , 2011, Physical chemistry chemical physics : PCCP.

[16]  A. Császár,et al.  Conformers of gaseous threonine , 2009 .

[17]  Nick C. Polfer,et al.  Reaction products in mass spectrometry elucidated with infrared spectroscopy. , 2007, Physical chemistry chemical physics : PCCP.

[18]  Jeremiah J. Wilke,et al.  Conformers of Gaseous Cysteine. , 2009, Journal of chemical theory and computation.

[19]  Henry F. Schaefer,et al.  In pursuit of the ab initio limit for conformational energy prototypes , 1998 .

[20]  A. Burin,et al.  Semiclassical Model for Vibrational Dynamics in Polyatomic Molecules: Investigation of Internal Vibrational Relaxation† , 2010 .

[21]  Marvin Douglas,et al.  Quantum electrodynamical corrections to the fine structure of helium , 1971 .

[22]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

[23]  T. Zwier.  Laser probes of conformational isomerization in flexible molecules and complexes. , 2006, The journal of physical chemistry. A.

[24]  W. D. Allen,et al.  Ab Initio Anharmonic Vibrational Analyses of Non-Rigid Molecules , 1993 .

[25]  A. Császár,et al.  Conformers of gaseous proline. , 2003, Chemistry.

[26]  Timothy S Zwier,et al.  Conformational Dynamics in a Dipeptide After Single-Mode Vibrational Excitation , 2002, Science.

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

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

[29]  V. Barone,et al.  General Perturbative Approach for Spectroscopy, Thermodynamics, and Kinetics: Methodological Background and Benchmark Studies. , 2012, Journal of chemical theory and computation.

[30]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple zeta correlation consistent basis sets for boron through neon , 1996 .

[31]  Troy Van Voorhis,et al.  Nonlocal van der Waals density functional: the simpler the better. , 2010, The Journal of chemical physics.

[32]  K. Gubbins,et al.  A remarkable shape-catalytic effect of confinement on the rotational isomerization of small hydrocarbons. , 2008, The Journal of chemical physics.

[33]  Krishnan Raghavachari,et al.  Rotational potential surface for alkanes: Basis set and electron correlation effects on the conformations of n‐butane , 1984 .

[34]  S. Grimme.  Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies , 2003 .

[35]  J. Noga,et al.  Proton Affinity and Enthalpy of Formation of Formaldehyde , 2009 .

[36]  M. G. Evans,et al.  Some applications of the transition state method to the calculation of reaction velocities, especially in solution , 1935 .

[37]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[38]  A. Becke,et al.  A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections. , 2006, The Journal of chemical physics.

[39]  Markus Reiher,et al.  Exact decoupling of the Dirac Hamiltonian. I. General theory. , 2004, The Journal of chemical physics.

[40]  Jan M. L. Martin.  What can we learn about dispersion from the conformer surface of n-pentane? , 2013, The journal of physical chemistry. A.

[41]  J. L. Mackey,et al.  Origin of stability in branched alkanes. , 2010, Chemistry.

[42]  K. Burke,et al.  Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] , 1997 .

[43]  Simple algebraic solutions to the kinetic problems of triangle, quadrangle and pentangle reactions , 2015, Journal of Mathematical Chemistry.

[44]  V. Barone,et al.  Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems , 2015, International journal of quantum chemistry.

[45]  Kazuo Ito.  On the Heats of Formation and Potential Barriers for the Internal Rotation in Hydrocarbon Molecules , 1953 .

[46]  T. Zwier,et al.  Experimental determination of conformational isomerization energy thresholds in serotonin. , 2008, The journal of physical chemistry. A.

[47]  K. Rao,et al.  Molecular Spectroscopy: Modern Research , 1972 .

[48]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[49]  Manoj K. Kesharwani,et al.  The S66x8 benchmark for noncovalent interactions revisited: explicitly correlated ab initio methods and density functional theory. , 2016, Physical chemistry chemical physics : PCCP.

[50]  Hess,et al.  Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. , 1986, Physical review. A, General physics.

[51]  Mihály Kállay,et al.  Enthalpy Differences of the n-Pentane Conformers. , 2016, Journal of chemical theory and computation.

[52]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[53]  M. Hafezi,et al.  Study of the torsional potential energies of 2-methylpropane, n-butane, and 2-methylbutane with high-level ab initio calculations , 2007 .

[54]  Russell D. Johnson,et al.  NIST Computational Chemistry Comparison and Benchmark Database , 2005 .

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

[56]  Mihály Kállay,et al.  The origin of systematic error in the standard enthalpies of formation of hydrocarbons computed via atomization schemes. , 2006, Chemphyschem : a European journal of chemical physics and physical chemistry.

[57]  Mark S. Gordon,et al.  The conformational potential energy surface of glycine : a theoretical study , 1991 .

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

[59]  A. Császár,et al.  Accurate ab initio determination of spectroscopic and thermochemical properties of mono- and dichlorocarbenes. , 2005, Physical chemistry chemical physics : PCCP.

[60]  Jim Pfaendtner,et al.  The 1-D hindered rotor approximation , 2007 .

[61]  A Koide,et al.  A new expansion for dispersion forces and its application , 1976 .

[62]  W. D. Allen,et al.  The effect of 1s correlation on De, re, and ωe of first‐row diatomics , 1996 .

[63]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[64]  Michel Waroquier,et al.  Ab Initio Calculation of Entropy and Heat Capacity of Gas-Phase n-Alkanes Using Internal Rotations , 2003 .

[65]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[66]  Richard L. Jaffe,et al.  Quantum Chemistry Study of Conformational Energies and Rotational Energy Barriers in n-Alkanes , 1996 .

[67]  George C Schatz,et al.  Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics. , 2008, The journal of physical chemistry. A.

[68]  Roman M. Balabin.  Enthalpy difference between conformations of normal alkanes: Raman spectroscopy study of n-pentane and n-butane. , 2009, The journal of physical chemistry. A.

[69]  B. Braams,et al.  Uncertainty estimates for theoretical atomic and molecular data , 2016, 1603.05923.

[70]  A. Császár,et al.  Benchmarking Experimental and Computational Thermochemical Data: A Case Study of the Butane Conformers. , 2012, Journal of chemical theory and computation.

[71]  Justin T. Fermann,et al.  The torsional conformations of butane: Definitive energetics from ab initio methods , 1997 .

[72]  Fujio Mizukami,et al.  Quantum algebraic–combinatoric study of the conformational properties of $$n$$ ‐alkanes. I , 1999 .

[73]  A. Becke,et al.  Exchange-hole dipole moment and the dispersion interaction revisited. , 2007, The Journal of chemical physics.

[74]  Mihály Kállay,et al.  Approximate treatment of higher excitations in coupled-cluster theory. , 2005, The Journal of chemical physics.

[75]  Jan M. L. Martin,et al.  Spin‐component‐scaled double hybrids: An extensive search for the best fifth‐rung functionals blending DFT and perturbation theory , 2013, J. Comput. Chem..

[76]  G. Ercolani.  Numerical Evaluation of Energy Levels and Wave Functions for Hindered Internal Rotation , 2000 .

[77]  Roland Tóbiás,et al.  First-order chemical reaction networks I: theoretical considerations , 2016, Journal of Mathematical Chemistry.

[78]  J. Laane,et al.  Structures and Conformations of Non-Rigid Molecules , 1993 .

[79]  H. Quiney,et al.  Anatomy of relativistic energy corrections in light molecular systems , 2001 .

[80]  Andrew C Simmonett,et al.  Anchoring the Absolute Proton Affinity Scale. , 2008, Journal of chemical theory and computation.

[81]  Henry F. Schaefer,et al.  Molecular structures of the two most stable conformers of free glycine , 2007, J. Comput. Chem..

[82]  H. Eyring.  The Activated Complex in Chemical Reactions , 1935 .

[83]  G. Scuseria,et al.  Gaussian 03, Revision E.01. , 2007 .

[84]  J. Durig,et al.  Enthalpy Difference between Conformers of n-Butane and the Potential Function Governing Conformational Interchange , 1995 .

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

[86]  Similarity analysis of the conformational potential energy surface of n-pentane , 2011 .

[87]  W. D. Allen,et al.  Lowest-Lying Conformers of Alanine: Pushing Theory to Ascertain Precise Energetics and Semiexperimental Re Structures. , 2010, Journal of chemical theory and computation.

[88]  E. Tavasoli,et al.  Conformational behavior and potential energy profile of gaseous histidine , 2010 .

[89]  Markus Reiher,et al.  Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order. , 2004, The Journal of chemical physics.

[90]  Mihály Kállay,et al.  Coupled-cluster methods including noniterative corrections for quadruple excitations. , 2005, The Journal of chemical physics.

[91]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[92]  W. Heiden,et al.  Relative electronic and free energies of octane's unique conformations , 2017 .

[93]  Stefan Grimme,et al.  Accurate description of van der Waals complexes by density functional theory including empirical corrections , 2004, J. Comput. Chem..

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

[95]  a Mark A. Murcko,et al.  Carbon−Carbon Rotational Barriers in Butane, 1-Butene, and 1,3-Butadiene , 1996 .

[96]  Mihály Kállay,et al.  Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory. , 2006, The Journal of chemical physics.

[97]  M. Sambridge,et al.  Monte Carlo analysis of inverse problems , 2002 .