• Abstract and Figures
• Public Full-text

Available online at www.sciencedirect.com Chemical Physics 346 (2008) 56–68 www.elsevier.com/locate/chemphys Accurate ab initio computation of thermochemical data for C3Hx ðx ¼ 0; ...; 4Þ species Jorge Aguilera-Iparraguirre a, A. Daniel Boese b, Wim Klopper a,b,*, Branko Ruscic c a Lehrstuhl fu¨r Theoretische Chemie, Institut fu¨r Physikalische Chemie, Universita¨t Karlsruhe (TH), D-76128 Karlsruhe, Germany b Institut fu¨r Nanotechnologie, Forschungszentrum Karlsruhe, P.O. Box 3640, D-76021 Karlsruhe, Germany c Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL 60439, USA Received 15 November 2007; accepted 30 January 2008 Available online 7 February 2008 Dedicated to Professor Dr. Peter Botschwina on the occasion of his 60th birthday. Abstract We have computed the atomization energies of nineteen C3Hx molecules and radicals using explicitly-correlated coupled-cluster the- ory including corrections for core–core and core–valence correlation, scalar and spin–orbit relativistic effects, and anharmonic vibra- tional zero-point energies. Equilibrium geometries were obtained at the coupled-cluster level [CCSD(T) model] in a correlation- consistent polarized core–valence quadruple-zeta basis set, using a spin-restricted Hartree–Fock reference wave function, and including all electrons in the correlation treatment. Applied to a set of selected CHx and C2Hx systems, our approach yields highly accurate atom- ization energies with a mean absolute deviation of 1.4 kJ/mol and a maximum deviation of 4.2 kJ/mol (for dicarbon) from the Active Thermochemical Tables (ATcT) values. The explicitly-correlated coupled-cluster approach provides energies near the basis-set limit of the CCSD(T) model, which is the coupled-cluster model with single and double excitations (CCSD) augmented with a perturbative correction for triple excitations (T). To obtain even more accurate atomization energies than those presented here, it would be required to include full triple excitations (CCSDT) and corrections for excitations beyond triples, as for instance done in the CCSDT(Q) model, which includes a perturbative correction for quadruple excitations (Q). Ó 2008 Elsevier B.V. All rights reserved. Keywords: Thermochemistry; Hydrocarbons; Radicals; Carbenes; Coupled-cluster theory 1. Introduction [10] may lead to naphthalene, and so on. Since many C3H3 and C3Hx isomers are involved in the formation of PAHs C3Hx species with x ¼ 0; ...; 4 play an important role in and soot, the modeling of their formation under pyrolysis the formation and growth of polycyclic aromatic hydrocar- conditions requires the accurate knowledge of thermo- bons (PAHs), in particular of small PAHs such as benzene chemical data and rate constants of hundreds of species and naphthalene during combustion or pyrolysis [1–8]. The and elementary reactions [11,12]. self reaction of the propargyl radical (2-propynyl, Furthermore, C3Hx species have been observed in inter- CH2CCH), for example, is thought to be the dominant stellar space [13]. Examples are tricarbon (C3), [14] linear reaction leading to the formation of benzene [4,7]. Reac- [15] and cyclic C3H, [16] propadienylidene and cyclopro- tions of phenyl radicals with propyne [9] or vinyl acetylene penylidene [17,18]. Ab initio quantum chemical calculations can provide very accurate structural, spectroscopic and energetic data * Corresponding author. Address: Lehrstuhl fur Theoretische Chemie, ¨ of small polyatomic molecules, radicals and carbenes of rel- Institut fu¨r Physikalische Chemie, Universita¨t Karlsruhe (TH), D-76128 Karlsruhe, Germany. Fax: +49 721 6083319. evance to interstellar cloud chemistry and combustion pro- E-mail address: [email protected] (W. Klopper). cesses. Particularly successful have been calculations 0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.01.057 J. Aguilera-Iparraguirre et al. / Chemical Physics 346 (2008) 56–68 57 employing the coupled-cluster method that includes single extended to single-reference open-shell cases with unre- and double excitations (CCSD, cf. Refs. [19,20]) as well stricted Hartree–Fock (UHF) and restricted open-shell as a perturbative treatment of triple excitations [CCSD(T), Hartree–Fock (ROHF) reference determinants [46,47]. cf. Refs. [21–25]]. Examples of such successes can be found Recent illustrative applications of explicitly-correlated in Refs. [26–30]. coupled-cluster theory are reported in Refs. [48–54]. In all The present article is concerned with the highly accurate of these works, the explicitly-correlated coupled-cluster calculation of the equilibrium structures and ground-state approach was used with two-electron basis functions that energies of the C3Hx species with x ¼ 0; ...; 4. In the pres- are linear in the interelectronic distance. In conjunction with ent work, the same set of molecules and radicals as studied very large one-electron basis sets, such a linear r12 approach by Vereecken and co-workers [31] at the level of density- yields benchmark results near the limit of a complete basis functional theory will be investigated at the CCSD(T) level. set, as demonstrated for example in Refs. [53,54]. Since a Corrections for core–core and core–valence correlation few years, however, several research groups have started to effects, anharmonic zero-point vibrational energies and rel- develop explicitly-correlated coupled-cluster approaches ativistic effects (both scalar and spin–orbit effects) will be with Slater-type geminals (STGs), first proposed by Ten- taken into account in an attempt to compute the atomiza- no in 2004 [55–58]. The main advantage of using STGs in tion energies of the species studied with chemical accuracy, place of the linear r12 terms is that in the STG approach that is, accurate to within 1 kcal/mol, respectively 4 kJ/ much smaller one-electron basis sets may be used than in mol. Here, accuracy refers to a 95% confidence limit. This the linear r12 approach. Because only linear r12 coupled-clus- means that atomization energies must be calculated with a ter approaches have been implemented for open-shell sys- mean absolute deviation of 1–2 kJ/mol from experimental tems, only these approaches could be used in the present data (vide infra). Such accuracy can only be achieved by work, using very large basis sets. We expect that the results performing the CCSD(T) calculations in very large and presented in the present article may serve as benchmark data nearly complete one-electron basis sets, followed by for future calculations using STGs and smaller basis sets. basis-set extrapolation, [32–34] or by expanding the cou- The present paper is organized as follows: The computa- pled-cluster wavefunction in a many-electron basis that tional details of all of our calculations are described in Sec- contains terms that depend explicitly on the interelectronic tion 2. The results for the C3Hx species are presented in distances in the system [35–37]. Section 3. This section also contains computed thermo- Very recently, Wheeler and co-workers published very chemical data for the CHx and C2Hx systems in compari- accurate calculations of the enthalpies of formation of son with the Active Thermochemical Tables (vide infra) the following four key intermediates in soot formation: to highlight the accuracy of the ab initio calculations (Sec- propargyl, 1-propynyl, cycloprop-1-enyl, and cycloprop- tion 3.1). Conclusions are given in Section 4. 2-enyl [8]. These authors used the CCSD(T) method in con- junction with basis-set extrapolation techniques, that is, in 2. Computational details the framework of the focal-point analysis [38,39] and also added corrections for core–core and core–valence correla- 2.1. Basis sets tion effects, anharmonic zero-point vibrational energies and relativistic effects. They even added diagonal Born– The standard CCSD(T) coupled-cluster calculations Oppenheimer corrections and correlation effects from triple were performed in correlation-consistent polarized core– excitations beyond the CCSD(T) level as obtained at the valence basis sets of triple-(cc-pCVTZ0) and quadruple-zeta full CCSDT model, and from quadruple excitations as (cc-pCVQZ0) quality [59,60]. We have attached a prime to described at the CCSDT(Q) level [40]. these sets to indicate that cc-pCVTZ0 refers to the basis cc- The purpose of the present work is to provide highly pCVTZ for C, but only cc-pVDZ for H. Similarly, the cc- accurate thermochemical data (i.e., atomization energies) pCVQZ0 refers to the basis cc-pCVQZ for C, but only cc- for the above four key intermediates as well as for a number pVTZ for H. of other C3Hx species from explicitly-correlated coupled- The effect of using the ‘‘primed” basis sets in place of the cluster calculations, that is, without resorting to basis-set full basis sets, that is, the effect of using basis sets with a extrapolation techniques, [32–34] and to obtain the equilib- smaller cardinal number for H than for C, has been inves- 2 3 rium geometries at a CCSD(T) coupled-cluster level at the tigated in detail for the molecules CH ( P state), CH2 ( B1 1 limits of what is technically feasible today (i.e., CCSD(T) state) and CH4 ( A1). Concerning the equilibrium geome- calculations correlating all electrons in a correlation-consis- tries of these molecules, we find that in the cc-pCVQZ0 tent polarized core–valence quadruple-zeta basis). basis, the C–H bond lengths are 0.1 pm longer than in Explicitly-correlated coupled electron-pair approxima- the full cc-pCVQZ basis (in CH2, the H–C–H angle is tion and coupled-cluster methods were developed in the reduced by 0.06° in the full cc-pCVQZ basis). Moreover, early 1990s for closed-shell atoms and molecules [41–45]. we can compare our cc-pCVQZ0 geometry of singlet prop- The general theory of the explicitly-correlated coupled- adienylidene with the equilibrium geometry obtained by cluster theory is described in detail in Ref.

Load more

  13

Copy Link