DFT and ab initio composite methods: Investigation of oxygen fluoride species

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Highlights

  • Enthalpies of formation and structures of oxygen fluorides have been determined.

  • Ab initio composite methods ccCA, G3, and G3B3 and DFT (M06 and M06-2X) were used.

  • ccCA results in the best, overall performance, with MAD for ΔH°f, 298′s of <1.0 kcal mol−1.

Abstract

The capability of ccCA, G3, and G3B3 for the prediction of the enthalpies of formation of oxygen fluoride species was evaluated. In addition to these composite methods, the performance of M06 and M06-2X in conjunction with the correlation consistent basis sets (aug-cc-pVnZ), where n = D, T, Q, was also examined for predicting the structures and enthalpies of formation of oxygen fluoride species. A set of various oxygen fluorides were considered, including FOx radicals, FOxH, and FOxF, where x = 1–3. The effects of basis set size and spin contamination were also considered.

Introduction

The oxygen fluorides have attracted interest because they can be employed as propellants in the rocket industry and can be used as strong fluorinating and oxidizing agents. In addition, oxygen fluorides play a role as intermediates in atmospheric chemistry and are believed to make a minor contribution to the destruction of ozone [1], [2], [3], [4], [5], [6]. The source of fluorine in the atmosphere originates from the decomposition of chlorofluorocarbons (CFCs) and their radical fragments, but most of the atmospheric fluorine is in the form of hydrogen fluoride (HF). Hydrogen fluoride is formed from the fast reaction of a fluorine atom with methane and water vapor [5], [7]. Although the role of fluorine in ozone depletion is minor, the percentage of fluorine in the atmosphere has been reported to be increasing with time [8], [9], [10]. Thus, accurate thermochemical properties are required for modeling fluorine compounds in the study of atmospheric reactions. Due to the unstable nature of oxygen fluorides, experimental measurements of the energetic properties have been limited. Computational approaches can aid in understanding such systems.

Investigating the structural properties of the oxygen fluorides has been a challenge to the computational chemical community, particularly for FOO and FOOF. The F-O bond in oxygen fluorides is a covalent bond between two highly electronegative atoms where both atoms contain lone pair electrons. Therefore, the F-O bond exhibits strong electron lone pair – lone pair repulsion and can become very long in molecules such as FOO and FOOF (∼0.2 Å longer than the F-O bond in FOF) [11], [12], requiring consideration of high-level electron correlation methods. In FOO and FOOF, the O-O bond length is similar to that in the O2 molecule but ∼0.2 Å shorter than the O-O bond length in HOOH [11]. The unusual geometry of FOO and FOOF presented a computational difficulty for electronic structure methods, which led to numerous investigations of oxygen fluorides using a variety of methods to study their structures and energetic properties [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]. Many methods have been unsuccessful in predicting the right structure for oxygen fluorides, such as FOO, FOOO, and FOOF, with respect to the experimental geometries, as will be seen in the following sections.

As a full literature review of these efforts is outside the scope of this paper, a number of significant and recent investigations are highlighted. The FOO structure and enthalpy of formation (ΔH°f, 298) have been computed by Francisco et al. [16] using Møller-Plesset perturbation theory (MP2, MP3, and MP4), complete active space self-consistent field (CASSCF), and quadratic configuration interaction [QCISD(T)] in conjunction with Pople’s basis sets. The study found that all MPn methods underestimated the FO bond length by >0.2 Å. QCISD(T)/6-31G(d) yielded the best FO bond length that is only shorter by 0.002 Å from the experimental length (expt. re (F-O) = 1.649 ± 0.013 Å [31], where re indicates an equilibrium structure), whereas the best CASSCF description of the F-O bond length is 0.8 Å shorter than experiment. Francisco’s study reported an enthalpy of formation at 0 K for FOO of 8.9 ± 3 kcal mol−1 by using isodesmic and isogyric reaction schemes using QCISD(T)/6-311G(d,p) results [16]. Ventura and Kieninger’s [26] study on FOO concluded that B3LYP/6-311++G(3df, 3pd) is a reliable method to describe structures and predict reaction enthalpies for molecules involving F-O bonds. Studies by Denis [30], [32], [33] found that the inclusion of the full treatment of the triple excitation [CCSDT instead of CCSD(T)] overcame the spin contamination problem presented in UCCSD(T), hence CCSDT predicted an accurate structure and energetics of the FOO molecule. Karton et al. [20] reported the ΔH°f, 298 of FOO of 5.87 ± 0.16 kcal mol−1 in excellent agreement with experiment (6.1 ± 0.5 kcal mol−1) using the high-level computationally demanding W4 method [34]. A recent theoretical study by Feller et al. [15] obtained a correct structure of FOO using R/UCCSD(T)/aug-cc-pVTZ level of theory and with a calculated value of ΔH°f, 298 of 6.4 ± 0.7 kcal mol−1 using a composite approach that is based on coupled cluster theory with up to quadruple excitations. The difference in the uncertainties estimated by Karton’s (5.87 ± 0.16 kcal mol−1 [20]) and Feller (6.4 ± 0.7 kcal mol−1 [15]) imputes to their different approaches. While W4 estimates uncertainties based on the performance of a set of 25 small molecules [20], Feller’s approach uses molecule-by-molecule criteria to calculate the estimated uncertainties [15].

The structure and the ΔH°f, 298 of FOOF have been studied extensively with a broad variety of quantum chemical methods. The computational challenge in the FOOF structure arises from the anomeric delocalization effect that exists in FOOF between the oxygen lone pair and the antibonding orbital of the F-O bond [29]. Although CCSD(T)/aug-cc-pVTZ [15] and B3LYP/6-311++G(2d) [18] can provide a qualitatively correct geometry for FOOF, very few methods used in previous work reproduced the experimental FOOF structure. In fact, a local density functional (LDF) paired with numerical and Gaussian basis sets [35] and the local SVWN functional paired with 6-311++G(2d) [18] were two methods that predicted the closest re of the F-O bond compared to experiment, with LDF being superior. LDF predicted F-O and O-O bond lengths that are 0.01 Å and 0.001 Å off from experimental geometries (rs(F-O) = 1.575 ± 0.003 Å and rs(O-O) = 1.217 ± 0.003 Å [11]), respectively. LDF predicted this good description for FOOF likely due to the high and evenly distributed electron density in FOOF, as justified in Ref. [34]. MP2, MP3, and MP4 with different size and type of basis sets, on the other hand, predicted incorrect geometries for FOOF with respect to experiment, however MP6 at the complete basis set (CBS) limit predicted an accurate geometry [29]. Not only is the structure of FOOF problematic but its ΔH°f, 298 has also been difficult to predict. The calculated ΔH°f, 298 of FOOF using even high-level ab initio methods has a large deviation from the experimental value reported in the NIST-JANAF thermochemical table (4.6 ± 0.5 kcal mol−1) [36], [37]. The ΔH°f, 298’s reported by Karton et al. [20] is 7.84 ± 0.18 kcal mol−1 and 8.21 ± 0.18 kcal mol−1 using W4 energies at the CCSD(T)/cc-pVQZ and experimental geometries, respectively. The most recent value of the ΔH°f, 298 of FOOF is 6.4 ± 0.7 kcal mol−1 and was calculated using a coupled cluster-base composite approach [15]. These are only a few examples of this large deviation from experiment.

Predicting the conformational structure of FOOO has also been challenging. Frecer et al. [38] investigated the FOOO that formed by F + O3 reaction and found that FO(O)2 is the most stable structure with F-O being a weak bond (3.671 Å). However, FOOO was observed later as a stabilized intermediate in dilute mixtures of F2 and O3 in solid argon by FT-IR spectroscopy [39]. Based on the reported frequencies of FOOO, it is characterized as a FO-O2 complex, and it cannot be a weak van der Waals complex [39], which differs from Frecer’s stable structure [38], mentioned above. Quantum chemical studies by Li et al. [40] and Peiró-García et al. [41] of the F + O3 reaction mechanisms using MP2/6-31G(d) and QCISD/6-311+G(d,p), respectively, also could not predict the FOOO ground state complex observed experimentally in the argon matrix [39]. A geometry optimization and frequency calculations of FOOO were performed by Roohi et al. [25] at the CCSD/aug-cc-pVDZ, CCSD/6-311+G(d), and QCISD/aug-cc-pVDZ levels of theory. Roohi’s study [25] showed that the planar FOOO with dihedral angle of 0.0° is the most stable structure, with its calculated frequencies agreeing well with the reported experimental frequencies [39]. No ΔH°f, 298 for FOOO has been previously reported, to our knowledge. The structure of the corresponding hydride FOOOH has only been studied previously by MINDO [42] and by MP2/6-3lG(d) [43]. As MP2 theory has encountered difficulty for calculating the FO and the OO bond lengths, an additional investigation of the FOOOH structure has to be done.

While methods such as CCSDT and QCISD are computationally demanding, ab initio composite methods have been developed to circumvent the computational demands of such methods. One such approach, the correlation consistent Composite Approach (ccCA) [44], [45], [46], is a method that has been demonstrated to be practical and reliable for the prediction of thermochemical properties, such as enthalpies of formation, ionization potentials, and electron affinities. The targeted accuracy of ccCA for main group molecules is to yield a mean absolute deviation of approximate chemical accuracy, 1 kcal mol−1 at reduced computational cost. This is in contrast to coupled cluster-based composite methods, which generally strive for a chemical accuracy of ±0.24 kcal mol−1, such as the W4 composite method [20], [34] and the approach used by Feller et al. [15]. Because the performance of ccCA for a variety of halogen oxides and their related hydrides has not been examined in detail, it is of our interest to consider the utility of ccCA in describing oxygen fluorides, such as FOO, FOOF, and FOOO.

Density functionals provide another option, as, overall, functionals have a lower formal computational scaling than post-HF methods such as CCSD(T) and CCSDT, though DFT predictions such as for enthalpies of formation, in general, do not reach the accuracies achievable by composite methods, such as ccCA. Thus, they are system dependent methods and are worth considering for each system. For example, the Minnesota density functionals M06 [47] and M06-2X [47] were used by Meyer and Kass [48], in conjunction with the correlation consistent basis sets [49], [50], [51] to assess their performance for predicting the ΔH°f, 298’s of a set of chlorine oxides and related hydrides (ClOx and ClOxH, where x = 1–4) with respect to the ΔH°f, 298’s of W4 method [34]. The capability of G3 [52] and G3B3 [53] for calculating ΔH°f, 298’s of chlorine oxides were also investigated in the same study [48]. The main findings from the Meyer and Kass study are that M06 ΔH°f, 298’s were found to differ by an average of 1.3 kcal mol−1 from the W4 ΔH°f, 298’s, while M06-2X resulted in larger error (6.2 kcal mol−1). G3 and G3B3 ΔH°f, 298’s yielded an average error of 4.6 kcal mol−1 and 6.5 kcal mol−1, respectively. The author attributed the large errors of G3 and G3B3 ΔH°f, 298’s to their poor predicted geometries. Although M06 and M06-2X functionals were examined for the prediction of the ΔH°f, 298’s of chlorine oxides, the capability of M06 and M06-2X to predict structures and ΔH°f, 298’s has not been assessed for other halogen oxides. Thus, it is of interest to evaluate these functionals for oxygen fluoride species, as well as examine the performance of G3 and G3B3 methods for these systems. G3 and G3B3 are used here, largely, as they were included in the Mayer and Kass study [48]. Though G4 is a more modern method, beginning with an MP4 reference energy is a costly start, and as shown in previous studies, G4 predicts very similar energies as G3 [54], [55].

In the present study, the reliability of ccCA, G3, and G3B3 for the prediction of the ΔH°f, 298’s of oxygen fluoride species was evaluated. In addition to these composite methods, the performance of M06 and M06-2X was also examined for predicting the structures and enthalpies of formation of oxygen fluoride species. A set of various oxygen fluorides were considered in this study, including FO, FOO, FOOO, and the related hydrides (FOH, FOOH, and FOOOH) and difluorides (FOF, FOOF, and FOOOF), where the ΔH°f, 298’s of FOOO and FOOOH have not been reported previously. The effects of basis set size and spin contamination were also considered. For comparison, the ΔH°f, 298’s of chlorine oxides and related hydrides have been provided, whereas full theoretical investigations for chlorine oxides and related hydrides can be found in the Meyer and Kass study and references therein [48].

Section snippets

Computational methodology

All calculations were performed using the Gaussian 09 software package [56]. The hybrid-meta-generalized gradient approximation (HMGGA) Minnesota functionals (M06 [47] and M06-2X [47]) in conjunction with the augmented correlation consistent polarized valence basis sets (aug-cc-pVnZ), where n = D, T, Q [49], [50], [51], were used to optimize the structures of all molecules under investigation. The tight-d correlation consistent basis set of Dunning et al. [57], aug-cc-pV(n + d)Z, where n = D, T, Q,

Structures

The structural parameters obtained by M06 and M06-2X for all of the species are listed in Table 1. The optimized structures at the B3LYP/aug-cc-pVTZ, MP2(full)/6-31G(d), and B3LYP/6-31G(d) levels, which are used for geometry optimizations in ccCA, G3, and G3B3, respectively, were also considered (shown in Table 1). Experimental structural parameters of FO [22], FOO [31], FOF [12], FOOF [11], and FOH [17], have been reported and were utilized as reference data to determine the performance of the

Conclusion

The capability of ccCA, G3, and G3B3 for the prediction of the enthalpies of formation of oxygen fluoride species was evaluated. In addition, the performance of M06 and M06-2X in conjunction with the correlation consistent basis sets (aug-cc-pVnZ), where n = D, T, Q, was also examined for predicting the structures and enthalpies of formation of oxygen fluoride species. An important finding from this study is that though M06 and M06-2X are useful functionals for many main group species (including

Acknowledgments

This material is based on work supported by the National Science Foundation under grant CHE-1362479. Computational resources were provided by Texas’ Academic Computing Services at the University of North Texas for the use of the UNT Research Clusters. Z. H. A. A. would like to acknowledge financial support from the University of Dammam, Saudi Arabia.

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