Elsevier

Chemical Physics Letters

Volume 558, 12 February 2013, Pages 109-113
Chemical Physics Letters

G3X-K theory: A composite theoretical method for thermochemical kinetics

https://doi.org/10.1016/j.cplett.2012.12.045Get rights and content

Abstract

A composite theoretical method for accurate thermochemical kinetics, G3X-K, is described. This method is accurate to around 0.5 kcal mol−1 for barrier heights and 0.8 kcal mol−1 for enthalpies of formation. G3X-K is a modification of G3SX theory using the M06-2X density functional for structures and zero-point energies and parameterized for a test set of 223 heats of formation and 23 barrier heights. A reduced perturbation-order variant, G3X(MP3)-K, is also developed, providing around 0.7 kcal mol−1 accuracy for barrier heights and 0.9 kcal mol−1 accuracy for enthalpies, at reduced computational cost. Some opportunities to further improve Gn composite methods are identified and briefly discussed.

Highlights

► A composite theoretical method specifically for thermochemical kinetics. ► Better than 0.5 kcal mol−1 accuracy for barrier heights. ► Around 0.8 kcal mol−1 accuracy for enthalpies of formation. ► Cost-effective reduced perturbation order variant available.

Introduction

Composite electronic structure theory methods have gained widespread use for the efficient calculation of chemical reaction energies. At one end, methods from the Gn [1], [2], [3], [4] and CBS [5], [6] classes can provide thermochemical properties with mean unsigned errors (MUEs) at around ‘chemical accuracy’ of 1 kcal mol−1 (∼4 kJ mol−1) for even moderately large compounds (tens of heavy atoms). At the other end, methods such as those in the Wn [7], [8] and HEAT [9], [10] classes, based on extrapolating coupled cluster energies to the complete basis set limit, can provide ‘benchmark accuracy’ of 1 kJ mol−1 (∼0.25 kcal mol−1) but at such an increased cost that they can only be routinely applied to molecules with less than say 6 heavy atoms. The ‘chemically accurate’ methods in particular have been widely used to calculate barrier heights for theoretical kinetic modeling, although relatively little attention has been paid to developing [11] (or even benchmarking [12]) composite theoretical methods for thermochemical kinetics. In contrast, the last decade has seen a number of exchange–correlation functionals developed with kinetics applications in mind [13], [14], [15].

Zheng et al. [12] have recently developed a representative set of barrier heights, DBH24/08, and used it to benchmark a wide selection of wavefunction theory, density functional theory (DFT) and composite (or multilevel) methods. Of the composite methods examined, G3SX and G3SX(MP3) [16] were the best-performed, both achieving a MUE of 0.57 kcal mol−1. The accuracy of these methods is comparable to CCSD(T) theory with a correlation consistent polarized valence triple-zeta basis set, calculations that are well over an order of magnitude more computationally expensive. The G3SX and G3SX(MP3) methods also offered a slight improvement over the more-expensive G4 theory (MUE of 0.58 kcal mol−1) and significantly outperformed the popular CBS-QB3 method (MUE of 1.62 kcal mol−1). It is thus apparent that G3SX theory offers an excellent balance between cost and accuracy for barrier heights of moderately sized systems, and for this reason it has been used extensively in our recent work [17], [18], [19], [20], [21], [22], [23], [24]. The results of Zheng et al. come with a caveat, however; they are for optimized geometries obtained with QCISD theory and a triple-zeta quality Gaussian basis set (MG3). The original G3SX method [16] uses B3LYP/6-31G(2df,p) optimized structures, and it is well-known that the B3LYP functional performs poorly for the non-bonded interactions necessary to accurately describe the energy, and to a lesser extent structure [25], of transition states. Here we show that B3LYP structures seriously degrade the performance of G3SX theory for the DBH24/08 barrier heights. To rectify this we have implemented a modification of G3SX theory that uses the M06-2X density functional [26] (which does perform well for barrier heights) in place of B3LYP. The resultant method, referred to as G3X-K theory, provides a MUE of less than 0.5 kcal mol−1 for the DBH24/08 barrier heights and around 0.8 kcal mol−1 for G3/99 test set [27] atomization enthalpies of formation. A cost-effective reduced perturbation order variant, G3X(MP3)-K, is also described. Finally, the implications of this work for the development of future composite methods are discussed.

Section snippets

Method description

The G3X-K and G3X(MP3)-K methods represent relatively minor modifications of the G3SX and G3SX(MP3) methods, which are described in detail in Ref. [16]. There are, indeed, three essential differences between the original and the ‘kinetics’ versions of these methods:

  • (i)

    The use of M06-2X/6-31G(2df,p) optimized structures and scaled zero point energies.

  • (ii)

    The use of coupled cluster theory energies in place of quadratic configuration interaction theory [28].

  • (iii)

    Determination of new scaling factors that

Results and discussion

Barrier heights in the DBH24/08 database have been calculated using the G3X-K and G3X(MP3)-K methods, with MUEs reported in Table 2. Included in this table are MUEs obtained using the original G3SX method as well as the results of Zheng et al. using QCISD/MG3 optimized structures, which we denote G3SX//QCI. As discussed above, it is apparent from the work of Zheng et al. that G3SX theory is capable of providing an accurate description of barrier heights, with an MUE of only 0.57 kcal mol−1 for

Acknowledgments

This work was supported by the Australian Research Council through Discovery Project DP110103889. Computational resources provided in part by the Victorian Partnership for Advanced Computing.

References (43)

  • Y. Zhao et al.

    Theor. Chem. Acc.

    (2008)
  • L.A. Curtiss et al.

    J. Chem. Phys.

    (2002)
  • L.A. Curtiss et al.

    Chem. Phys. Lett.

    (2010)
  • L.A. Curtiss et al.

    J. Chem. Phys.

    (1991)
  • L.A. Curtiss et al.

    J. Chem. Phys.

    (1999)
  • L.A. Curtiss et al.

    J. Chem. Phys.

    (2007)
  • B. Chan et al.

    J. Chem. Theory Comput.

    (2010)
  • J.W. Ochterski et al.

    J. Chem. Phys.

    (1996)
  • J.A. Montgomery et al.

    J. Chem. Phys.

    (1999)
  • J.M.L. Martin et al.

    J. Chem. Phys.

    (1999)
  • A.D. Boese et al.

    J. Chem. Phys.

    (2004)
  • A. Tajti et al.

    J. Chem. Phys.

    (2004)
  • Y.J. Bomble et al.

    J. Chem. Phys.

    (2006)
  • B. Chan et al.

    J. Chem. Theory Comput.

    (2011)
  • J. Zheng et al.

    J. Chem. Theory Comput.

    (2009)
  • A.D. Boese et al.

    J. Chem. Phys.

    (2004)
  • Y. Zhao et al.

    J. Phys. Chem. A

    (2004)
  • Y. Zhao et al.

    J. Chem. Theory Comput.

    (2006)
  • L.A. Curtiss et al.

    J. Chem. Phys.

    (2001)
  • G. da Silva et al.

    Environ. Sci. Technol.

    (2010)
  • G. da Silva et al.

    J. Phys. Chem. A

    (2010)
  • Cited by (46)

    • Kinetics, mechanism, and application of sodium persulfate activated by sodium hydroxide for removing 1,2-dichloroethane from groundwater

      2023, Environmental Research
      Citation Excerpt :

      The mass spectra of the peaks corresponding to dichloromethane, trichloromethane, and tetrachloromethane are presented in Fig. S5; these peak intensities did not accumulate over time, and therefore, these intermediates were likely transformed into CO2, H2O, and/or Cl− (Duan et al., 2016). On the basis of density functional theory (DFT) (Da, 2013; Frisch et al., 2010; Zhao and Truhlar, 2008), the B3LYP functional was combined with the 6-31þG(d) basis set in the Gaussian 09 program to calculate the reaction potential energy surface of the reactants, intermediates (IM), and transient states (TS) involved in 1,2-DCA degradation (Fig. 4). According to the computed reaction potential energy surface, the degradation of 1,2-DCA can be divided into three stages: (I) the formation of VC, (II) the oxidation of VC to generate formic acid and formaldehyde, and (III) mineralization.

    • Quantum mechanical thermochemical predictions 100 years after the Schrödinger equation

      2022, Annual Reports in Computational Chemistry
      Citation Excerpt :

      Over the past 30-odd years, a wide range of composite ab initio methods has been developed. Popular examples include the Gaussian-n (Gn) methods (6–10) and variants thereof (11–18), complete basis set (CBS) model chemistries (19–25), focal-point analysis (FPA) (26–30), Weizmann-n (Wn) (31–36), WnX (37–39), multi-coefficient correlation methods (MCCMs) (40–45), high-accuracy extrapolated ab initio thermochemistry (HEAT) (46–50), correlation consistent composite approach (ccCA) (51–60), Feller–Peterson–Dixon (FPD) (61–67), ab initio thermochemistry using optimal-balance models with isodesmic corrections (ATOMIC) (68–70), interference-corrected explicitly correlated second-order perturbation theory (INT-MP2-F12) (71), and the so-called cheap composite scheme (ChS) (72,73) procedures. Today, composite ab initio methods are among the most accurate means for examining chemical processes at the atomic level.

    • Low-temperature oxidation of monobromobenzene: Bromine transformation and yields of phenolic species

      2021, Chemosphere
      Citation Excerpt :

      Boese and Martin (2004) explained that such satisfactory kinetic performance is accompanied with a matching accurate description of equilibrium properties (i.e., enthalpies of reactions and geometries of molecules). Likewise(Khan et al., 2020) have recently illustrated that thermo-kinetic parameters by the BMK method are in accord with analogous values computed with the G3X–K (da Silva, 2013) method for a halogenated system (thermal decomposition of perfluorinated sulfonic acids). It was also shown that the BMK method outperforms the commonly applied meta-hybrid M06–2X (Zhao and Truhlar, 2008).

    • Kinetics of C<inf>5</inf>H<inf>4</inf> isomer + H reactions and incorporation of C<inf>5</inf>H<inf>x</inf> (x = 3 – 5) chemistry into a detailed chemical kinetic model

      2021, Combustion and Flame
      Citation Excerpt :

      Quantum chemistry computations were employed in Gaussian 16 [28]. The geometries, frequencies, and energies of all reactants, products, intermediates, and transition states were calculated and optimized using the G3X-K composite theoretical method [29] which is specifically designed for thermochemical kinetics and is capable of predicting barrier heights and enthalpies of formation with ~0.5 kcal mol−1 accuracy. In this method, M06–2X/6–31G(2df,p) optimized structures are used in a series of single-point energy calculations starting from HF and terminates at the CCSD(T) theory with incrementally decreasing size basis sets.

    • Decomposition kinetics of perfluorinated sulfonic acids

      2020, Chemosphere
      Citation Excerpt :

      For the model compounds (PFMS, PFES), the geometries of reactants, products, intermediates, and transition states were fully optimized by employing the following DFT methods; BMK, M06-2X, and M06, in conjunction with the 6-31G(2df,p), 6-31++G(2df,p), and 6-311++G(2df,p) basis sets (Supplementary Information). The equilibrium structures thus obtained were subsequently re-optimized at the M06-2X/6-31G(2df,p) level of theory and utilized in high-level composite G3X-K energy calculations (da Silva, 2013). Electronic energies of PFMS were also calculated according to the G4 composite method.

    • From theoretical reaction dynamics to chemical modeling of combustion

      2017, Proceedings of the Combustion Institute
      Citation Excerpt :

      Nevertheless, we believe that it will provide an important piece toward improving the accuracy of predictions for larger molecules. Meanwhile, the M06-2X method provides improved (relative to B3LYP) treatments of torsional potentials and low-barrier TSs, for example, and has been used in a recently proposed composite scheme [131]. The last 10 years has seen spectacular progress in the accuracy of high level ab initio thermochemistry predictions, with a number of schemes, such as the W4 [132], HEAT [133], focal point [134], and Peterson–Feller–Dixon [135] methods, now yielding 2σ uncertainties of about 0.2 kcal/mol.

    View all citing articles on Scopus
    View full text