Towards the intrinsic error of the correlation consistent Composite Approach (ccCA)

The correlation consistent Composite Approach (ccCA) has been made more robust by (a) modifying the basis set used in computing B3LYP equilibrium geometries and harmonic vibrational frequencies so that the correlation consistent basis sets are used throughout ccCA; (b) separately extrapolating the MP2 and Hartree–Fock complete basis set limit energies; (c) uniformly treating unrestricted open shell wave functions; (d) utilizing newly recommended enthalpies of formation for C, B, Al, and Si atoms; and (e) using theoretically derived vibrational scale factors. This modified ccCA formulation has been used to compute the 454 energetic properties (enthalpies of formation, dissociation energies, ionization potentials, electron affinities, and proton affinities) in the G3/05 test set. This new formulation, which does not contain any optimized parameters, has a small systematic statistical bias (mean signed deviation of −0.20 kcal mol−1), and has a mean absolute deviation of 1.01 kcal mol−1 with the incorporation of modification d) or 0.99 kcal mol−1 without. This is compared to a G4(MP2) MAD of 1.04 kcal mol−1 and a G3(MP2) MAD of 1.39 kcal mol−1. These modifications result in minimal change with respect to the computational requirements of the current ccCA methodology. The ccCA model chemistry is the first MP2-based model chemistry to achieve an accuracy of ± 1.00 kcal mol−1 for the G3/05 training set without any optimized parameters, and it is the only MP2-based model chemistry uniformly applicable to systems comprised of elements from H to Kr.

[1]  D. Dixon,et al.  Heats of Formation of Simple Perfluorinated Carbon Compounds , 1999 .

[2]  P. Taylor,et al.  Basis set convergence of post-CCSD contributions to molecular atomization energies. , 2007, The Journal of chemical physics.

[3]  W. D. Allen,et al.  Complete basis set limit studies of conventional and R12 correlation methods: The silicon dicarbide (SiC2) barrier to linearity , 2003 .

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

[5]  K. Morokuma,et al.  Ab initio molecular orbital study of potential energy surface for the NH+NO2 reaction , 1994 .

[6]  D. Dixon,et al.  Molecular Structure, Vibrational Frequencies, and Energetics of the HCO, HOCO, and HCO2 Anions , 2003 .

[7]  T. Crawford,et al.  Sources of error in electronic structure calculations on small chemical systems. , 2006, The Journal of chemical physics.

[8]  Per Jensen,et al.  Computational molecular spectroscopy , 2000, Nature Reviews Methods Primers.

[9]  Nathan J. DeYonker,et al.  Quantitative computational thermochemistry of transition metal species. , 2007, The journal of physical chemistry. A.

[10]  Cristina Puzzarini,et al.  Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements , 2005 .

[11]  Nathan J. DeYonker,et al.  Performance of the correlation consistent composite approach for transition states: a comparison to G3B theory. , 2007, The Journal of chemical physics.

[12]  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.

[13]  Trygve Helgaker,et al.  Highly accurate calculations of molecular electronic structure , 1999 .

[14]  David J. Frurip,et al.  Theoretical Methods for Computing Enthalpies of Formation of Gaseous Compounds , 2007 .

[15]  Krishnan Raghavachari,et al.  GAUSSIAN-3 THEORY USING DENSITY FUNCTIONAL GEOMETRIES AND ZERO-POINT ENERGIES , 1999 .

[16]  Matthew L. Leininger,et al.  The standard enthalpy of formation of CH2 , 2003 .

[17]  Robert J. Harrison,et al.  Parallel Douglas-Kroll Energy and Gradients in NWChem. Estimating Scalar Relativistic Effects Using Douglas-Kroll Contracted Basis Sets. , 2001 .

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

[19]  Melita L. Morton,et al.  IUPAC Critical Evaluation of Thermochemical Properties of Selected Radicals. Part I , 2005 .

[20]  Leo Radom,et al.  Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors , 1996 .

[21]  John A. Montgomery,et al.  A complete basis set model chemistry. V. Extensions to six or more heavy atoms , 1996 .

[22]  W. D. Allen,et al.  Definitive ab initio studies of model SN2 reactions CH(3)X+F- (X=F, Cl, CN, OH, SH, NH(2), PH(2)). , 2003, Chemistry.

[23]  Nathan J DeYonker,et al.  The correlation-consistent composite approach: application to the G3/99 test set. , 2006, The Journal of chemical physics.

[24]  D. Dixon,et al.  Coupled Cluster Theory Determination of the Heats of Formation of Combustion-Related Compounds: CO, HCO, CO2, HCO2, HOCO, HC(O)OH, and HC(O)OOH , 2003 .

[25]  Hess,et al.  Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations. , 1985, Physical review. A, General physics.

[26]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[27]  D R Yarkony,et al.  Modern electronic structure theory , 1995 .

[28]  H. Stoll,et al.  Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements , 2003 .

[29]  Krishnan Raghavachari,et al.  Gaussian‐1 theory of molecular energies for second‐row compounds , 1990 .

[30]  Branko Ruscic,et al.  Simultaneous Adjustment of Experimentally Based Enthalpies of Formation of CF3X , 1998 .

[31]  Rudolf Kippenhahn,et al.  Methods in Computational Physics , 1967 .

[32]  L. Radom,et al.  G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry , 2003 .

[33]  V. Barone.  Accurate Vibrational Spectra of Large Molecules by Density Functional Computations beyond the Harmonic Approximation: The Case of Azabenzenes , 2004 .

[34]  Nathan J DeYonker,et al.  The correlation consistent composite approach (ccCA): an alternative to the Gaussian-n methods. , 2006, The Journal of chemical physics.

[35]  Angela K. Wilson,et al.  Harmonic Vibrational Frequencies: Scaling Factors for HF, B3LYP, and MP2 Methods in Combination with Correlation Consistent Basis Sets , 2004 .

[36]  Nathan J. DeYonker,et al.  Accurate enthalpies of formation of alkali and alkaline earth metal oxides and hydroxides: assessment of the correlation consistent composite approach (ccCA). , 2006, The journal of physical chemistry. A.

[37]  D. Dixon,et al.  Heats of formation and ionization energies of NHx, x=0–3 , 2001 .

[38]  J. Stanton,et al.  Ab initio determination of the heat of formation of ketenyl (HCCO) and ethynyl (CCH) radicals , 2005 .

[39]  Michael J. Frisch,et al.  Theoretical thermochemistry. 1. Heats of formation of neutral AHn molecules (A = Li to Cl) , 1985 .

[40]  Kirk A. Peterson,et al.  Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction , 1994 .

[41]  D. Dixon,et al.  Theoretical study of the heats of formation of small silicon-containing compounds , 1999 .

[42]  Mihaly Kallay,et al.  W3 theory: robust computational thermochemistry in the kJ/mol accuracy range. , 2003, Journal of Chemical Physics.

[43]  L. Curtiss,et al.  Gaussian-4 theory. , 2007, The Journal of chemical physics.

[44]  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.

[45]  L. Curtiss,et al.  EVALUATION OF BOND ENERGIES TO CHEMICAL ACCURACY BY QUANTUM CHEMICAL TECHNIQUES , 1995 .

[46]  L. Curtiss,et al.  Assessment of Gaussian-3 and density functional theories for a larger experimental test set , 2000 .

[47]  Jan M.L. Martin,et al.  Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities , 2001 .

[48]  Vincenzo Barone,et al.  Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation. , 2004, The Journal of chemical physics.

[49]  B. Ruscic,et al.  W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions. , 2006, The Journal of chemical physics.

[50]  L. Radom,et al.  Heats of formation of alkali and alkaline earth oxides and hydroxides: some dramatic failures of the G2 method , 1999 .

[51]  Juana Vázquez,et al.  High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification. , 2006, The Journal of chemical physics.

[52]  Krishnan Raghavachari,et al.  Accurate thermochemistry for larger molecules : gaussian-2 theory with bond separation energies. , 1997 .

[53]  Nathan J. DeYonker,et al.  Computation of gas-phase enthalpies of formation with chemical accuracy: The curious case of 3-nitroaniline , 2006 .

[54]  B. Ruscic,et al.  Benchmark atomization energy of ethane: Importance of accurate zero-point vibrational energies and diagonal Born–Oppenheimer corrections for a ‘simple’ organic molecule , 2007 .

[55]  Jan M. L. Martin,et al.  Heats of formation of beryllium, boron, aluminum, and silicon re-examined by means of W4 theory. , 2007, The journal of physical chemistry. A.

[56]  B. Ruscic,et al.  Photoionization studies of (BH3)n (n=1,2) , 1988 .

[57]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[58]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited , 2001 .

[59]  Angela K. Wilson,et al.  Effects of Basis Set Choice upon the Atomization Energy of the Second-Row Compounds SO2, CCl, and ClO2 for B3LYP and B3PW91 , 2003 .

[60]  D. Dixon,et al.  Theoretical prediction of the heats of formation of C2H5O* radicals derived from ethanol and of the kinetics of beta-C-C scission in the ethoxy radical. , 2007, The journal of physical chemistry. A.

[61]  Vincenzo Barone,et al.  Anharmonic vibrational properties by a fully automated second-order perturbative approach. , 2005, The Journal of chemical physics.

[62]  David Feller,et al.  The use of systematic sequences of wave functions for estimating the complete basis set, full configuration interaction limit in water , 1993 .

[63]  L. Curtiss,et al.  Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation , 1997 .

[64]  Kaizar Amin,et al.  Introduction to Active Thermochemical Tables: Several “Key” Enthalpies of Formation Revisited† , 2004 .

[65]  W. A. Jong,et al.  Performance of coupled cluster theory in thermochemical calculations of small halogenated compounds , 2003 .

[66]  David A Dixon,et al.  Accurate thermochemical properties for energetic materials applications. II. Heats of formation of imidazolium-, 1,2,4-triazolium-, and tetrazolium-based energetic salts from isodesmic and lattice energy calculations. , 2007, The journal of physical chemistry. B.

[67]  D. Bakowies.  Extrapolation of electron correlation energies to finite and complete basis set targets. , 2007, The Journal of chemical physics.

[68]  Angela K. Wilson,et al.  Benchmark calculations with correlated molecular wave functions. X. Comparison with , 1997 .

[69]  Juana Vázquez,et al.  HEAT: High accuracy extrapolated ab initio thermochemistry. , 2004, The Journal of chemical physics.

[70]  Theresa L Windus,et al.  Thermodynamic properties of the C5, C6, and C8 n-alkanes from ab initio electronic structure theory. , 2005, The journal of physical chemistry. A.

[71]  David Feller,et al.  Probing the limits of accuracy in electronic structure calculations: is theory capable of results uniformly better than "chemical accuracy"? , 2007, The Journal of chemical physics.

[72]  L. Curtiss,et al.  Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies. , 2005, The Journal of chemical physics.

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

[74]  P. Taylor,et al.  The anharmonic force field of ethylene, C2H4, by means of accurate ab initio calculations , 1995 .

[75]  G. A. Petersson,et al.  A Journey from Generalized Valence Bond Theory to the Full CI Complete Basis Set Limit , 2000 .

[76]  C. Schwartz,et al.  Importance of Angular Correlations between Atomic Electrons , 1962 .

[77]  Vincenzo Barone,et al.  Vibrational computations beyond the harmonic approximation: Performances of the B3LYP density functional for semirigid molecules , 2005, J. Comput. Chem..

[78]  D. Dixon,et al.  Accurate thermochemical properties for energetic materials applications. I. Heats of formation of nitrogen-containing heterocycles and energetic precursor molecules from electronic structure theory. , 2006, The journal of physical chemistry. A.

[79]  Trygve Helgaker,et al.  Basis-set convergence of the energy in molecular Hartree–Fock calculations , 1999 .

[80]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[81]  D. Dixon,et al.  Heats of formation of diphosphene, phosphinophosphinidene, diphosphine, and their methyl derivatives, and mechanism of the borane-assisted hydrogen release. , 2007, The journal of physical chemistry. A.

[82]  Nathan J. DeYonker,et al.  Application of the Correlation Consistent Composite Approach (ccCA) to Third-Row (Ga-Kr) Molecules. , 2008, Journal of chemical theory and computation.

[83]  Branko Ruscic,et al.  Active Thermochemical Tables: accurate enthalpy of formation of hydroperoxyl radical, HO2. , 2006, The journal of physical chemistry. A.

[84]  L. Curtiss,et al.  Gaussian‐1 theory: A general procedure for prediction of molecular energies , 1989 .

[85]  Jan M. L. Martin.  Ab initio total atomization energies of small molecules — towards the basis set limit , 1996 .

[86]  Kaizar Amin,et al.  A Grid Service-Based Active Thermochemical Table Framework , 2002, GRID.

[87]  Nathan J. DeYonker,et al.  Computational s-block thermochemistry with the correlation consistent composite approach. , 2007, The journal of physical chemistry. A.

[88]  G. A. Petersson,et al.  A complete basis set model chemistry. VI. Use of density functional geometries and frequencies , 1999 .

[89]  Trygve Helgaker,et al.  Basis-set convergence in correlated calculations on Ne, N2, and H2O , 1998 .

[90]  K. Peterson,et al.  An examination of intrinsic errors in electronic structure methods using the Environmental Molecular Sciences Laboratory computational results database and the Gaussian-2 set , 1998 .

[91]  T. Dunning,et al.  The HSO−SOH Isomers Revisited: The Effect of Tight d Functions† , 2004 .

[92]  C. W. Bauschlicher,et al.  A modification of the Gaussian‐2 approach using density functional theory , 1995 .

[93]  L. Curtiss,et al.  Gaussian-3 (G3) theory for molecules containing first and second-row atoms , 1998 .

[94]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

[95]  Kirk A. Peterson,et al.  Approximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules , 2000 .

[96]  L. Curtiss,et al.  Gaussian-3X (G3X) theory : use of improved geometries, zero-point energies, and Hartree-Fock basis sets. , 2001 .

[97]  W. Klopper.  Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques , 2001 .

[98]  D. Dixon,et al.  Heats of formation of boron hydride anions and dianions and their ammonium salts [BnHmy-][NH4+]y with y=1-2. , 2007, Inorganic chemistry.

[99]  L. Curtiss,et al.  Gaussian-4 theory using reduced order perturbation theory. , 2007, The Journal of chemical physics.

[100]  Werner Kutzelnigg,et al.  Rates of convergence of the partial‐wave expansions of atomic correlation energies , 1992 .

[101]  Amir Karton,et al.  Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267] , 2005, physics/0509216.

[102]  D. Dixon,et al.  Predicting the heats of formation of model hydrocarbons up to benzene , 2000 .

[103]  L. Curtiss,et al.  Heats of formation of alkali metal and alkaline earth metal oxides and hydroxides: Surprisingly demanding targets for high-level ab initio procedures , 2003 .

[104]  D. Dixon,et al.  Reliable predictions of the thermochemistry of boron-nitrogen hydrogen storage compounds: BxNxHy, x = 2, 3. , 2007, The journal of physical chemistry. A.

[105]  Vincenzo Barone,et al.  Vibrational spectra of large molecules by density functional computations beyond the harmonic approximation: the case of pyrrole and furan , 2004 .

[106]  Timothy J. Lee,et al.  The atomization energy and proton affinity of NH3. An ab initio calibration study , 1996 .

[107]  L. Radom,et al.  An evaluation of harmonic vibrational frequency scale factors. , 2007, The journal of physical chemistry. A.

[108]  Jan M. L. Martin,et al.  TOWARDS STANDARD METHODS FOR BENCHMARK QUALITY AB INITIO THERMOCHEMISTRY :W1 AND W2 THEORY , 1999, physics/9904038.

[109]  Nathan J. DeYonker,et al.  Systematically convergent correlation consistent basis sets for molecular core-valence correlation effects: the third-row atoms gallium through krypton. , 2007, The journal of physical chemistry. A.

[110]  V. Barone,et al.  Performances of different density functionals in the computation of vibrational spectra beyond the harmonic approximation , 2004 .

[111]  David Feller,et al.  Application of systematic sequences of wave functions to the water dimer , 1992 .

[112]  Wesley D. Allen,et al.  The heat of formation of NCO , 1993 .

[113]  Nathan J. DeYonker,et al.  Hartree-Fock complete basis set limit properties for transition metal diatomics. , 2008, The Journal of chemical physics.