Theoretical prediction of FKrOH

Chemical Physics Letters 537 (2012) 6–10

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Theoretical prediction of FKrOH Brent R. Wilson, Katheryn Shi, Angela K. Wilson ⇑ Center for Advanced Scientific Computing and Modeling (CASCaM), Department of Chemistry, University of North Texas, Denton, TX 76203-5070, United States

a r t i c l e

i n f o

Article history: Received 2 February 2011 In final form 2 April 2012 Available online 11 April 2012

a b s t r a c t Since the discovery that rare gases may form metastable compounds with electronegative atoms, much research has been devoted to the determination of novel bound species. In this work, our laboratory has used B3LYP as a survey method to identify possible new potential rare gas molecules. The ab initio methods, MP2 and CCSD(T), in combination with aug-cc-pVnZ (n = D, T and Q) basis sets have been used to confirm the results of the B3LYP calculations. Our calculations predict that FKrOH should exist and we report optimized geometries, vibrational frequencies and relative energies as evidence of our prediction. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction The rare gas elements have long been considered inert and unable to form molecules with other atoms, but this notion was refuted by the synthesis of Xe+[PtF6] by Bartlett in 1962 [1]. Subsequently, many compounds containing rare gas elements have been theoretically predicted and/or experimentally synthesized. Many of these newly discovered molecules are of the form HRgX, where Rg is a rare gas and X is an electronegative fragment [2]. These compounds, rare gas hydrides, often contain either xenon or krypton and are made primarily by matrix isolation [3]. An experimentally prepared neutral compound containing argon, HArF, was synthesized by photolyzing hydrogen fluoride in a solid argon matrix [4]. Rare gas cations containing argon, neon, or helium (ArX+, NeX+ and HeXn+, respectively, where X = Li–Ne and n = 1,2), have also been theoretically predicted at the MP4(SDTQ) and MP2 levels using the 6-311G(2df, 2pd) and 6-31G(d,p) basis sets, respectively [MP4(SDTQ)/6-311G(2df, 2pd) and MP2/6-31G(d,p)] [5,6]. In addition to rare gas hydrides, other rare gas compounds containing silicon have been theoretically predicted, including an argon compound, FArSiF3, which was predicted to be a stable molecule by the MP2 and CCSD(T) methods [7–9] in conjunction with the correlation consistent basis sets (cc-pVnZ and aug-ccpVnZ where n = D, T, Q and 5) as well as the 6-311++G(2d,2p) basis sets. Two low-energy isomers of F3SiXe+ have also been experimentally detected [10] via the selected-ion flow tube method [11,12]. A prior study conducted in our laboratory also predicted the first krypton–germanium compound, FKrGeF3 [9]. Previous research conducted by our laboratory predicted the existence of novel rare gas compounds HKrCl [13], FKrAF3 (A = C, Si, and Ge) [9], XRgCCX and XRgCCRgX (Rg = Kr, Ar; X = F, Cl) [14]. ⇑ Corresponding author. E-mail address: [email protected] (A.K. Wilson). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.04.003

DFT is often used due to its relatively lower computational cost compared to ab initio post-HF methods, however DFT’s utility in the prediction of novel rare gas compounds is uncertain. For example, in a study which compared DFT optimal geometries, dissociation energies, and frequencies to those computed by the ab initio methods, MP2 and CCSD(T), both B3LYP and B1LYP predicted minimum energy structures for the molecules HHeI, HNeCl, HNeBr, and HNeI that could not be reproduced with MP2 or CCSD(T) [8]. This prior work, therefore, recommended that no DFT functional be used independently to predict new rare gas molecules; instead, high-level ab initio methods should be used to verify results calculated using the DFT method. In this study, we combine the use of the B3LYP functional, MP2, and CCSD(T) to identify and characterize possible new rare gas compounds. Forty-seven potential molecules have been considered; two of these molecules were further studied through vibrational analysis, relative energetics calculations, and dissociation channel calculations. The results of these calculations suggested the likely stability of only one compound, FKrOH. 2. Methodology We employed the hybrid density functional, B3LYP [15,16], due to its widespread use, and utility in prior rare gas studies [9,14], and the ab initio methods, MP2 [17] and CCSD(T) [18,19] to compute the optimal geometries, vibrational frequencies, and relative energies of HKrOF and FKrOH. These methods were used in combination with the augmented correlation consistent basis sets, augcc-pVnZ (where n = D, T and Q) [19–21]. The correlation consistent basis sets are useful, as they were designed to recover increasing amounts of correlation energy with increasing basis set size. The augmented basis sets include diffuse functions in order to better account for long range interactions. B3LYP was used as a survey method due to its greater computational efficiency compared to

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either MP2 or CCSD(T). We examined molecules which were similar to previously discovered rare gas compounds in order to increase the likelihood of identifying a new metastable compound. Those species for which B3LYP did not predict an energy minimum were not studied further. We studied the compounds for which DFT did predict a bound structure with MP2 and CCSD(T). In this work we report the optimized geometries, vibrational frequencies and relative energies of the species which were predicted to be metastable. The B3LYP and MP2 calculations were performed with GAUSSIAN 03 [22]. The CCSD(T) computations were performed with MOLPRO 2006 [23].

3. Results and discussion Forty-seven compounds were considered as potential bound structures. A list of these possible molecules is provided in Table 1. Of the 47 structures examined, B3LYP calculations predicted a bound structure for nine different species. In comparison to the results which we obtained using the MP2 and CCSD(T) methods, the B3LYP method tended to overpredict the stability of these potential compounds. Seven of the species which B3LYP predicted to exist as energy minimum structures were not predicted to exist as bound structures by our subsequent MP2 and CCSD(T) calculations. The only novel species for which minimum energy geometries could be found with both MP2 and CCSD(T) across the full series of augcc-pVnZ (where n = D, T and Q) basis sets are HKrOF and FKrOH. As HKrOH was predicted to be stable relative to its constituent, isolated atoms by previous theoretical studies [24,25], and in a separate study [26] HXeOF was found to be lower in energy than its isolated atoms, our consideration of the stability of HKrOF and FKrOH has precedent. The optimized geometries for HKrOF and FKrOH are listed in Table 2. At the B3LYP level of theory there is a decrease in the predicted bond lengths for each species with respect to increasing f-level (i.e., from aug-cc-pVDZ to aug-cc-pVTZ), as well as a slight increase in bond angle (Kr–O–F or Kr–O–H). For FKrOH this behavior also occurred for MP2 and CCSD(T). For HKrOF, convergence in the H–Kr bond length is essentially reached with the aug-cc-pVTZ basis set, even for MP2 and CCSD(T), while the other bond lengths decrease with respect to increasing basis set size. In HKrOF and FKrOH, the H–Kr–O and F–Kr–O bond angles, respectively, are linear. The MP2 and CCSD(T) bond angles (Kr–O–F) changed very little (<1°) with respect to basis set size, as shown in the table. The calculated geometric values of our compounds are similar to previously predicted metastable rare gas species. In comparison to HKrOH [24], where the0 Kr–O bond length was calculated (MP2/ aug-cc-pVTZ) as 0 2.101 Å A in comparison to our MP2/aug-cc-pVTZ 0 values of 2.120 Å A (HKrOF) and 1.963 Å A (FKrOH). 0 HKrOH was also calculated to have an H–Kr bond length of 1.545 Å A where in HKrOF 0 this bond length is shorter at 1.497 Å A. To confirm that our optimized geometries were minima on the potential energy surface, we computed harmonic vibrational frequencies using each method and basis set combination for both HKrOF and FKrOH (see Table 3). For each of the molecules, the highest energy mode is a stretch of the bond which contains hydrogen. For HKrOF, the H–Kr stretching mode is the highest energy mode [1598 cm1 by CCSD(T)/aug-ccpVQZ)] and for FKrOH the O–H stretching mode is the highest in energy [3769 cm1 by CCSD(T)/aug-cc-pVQZ)]. Another similarity between the two molecules is that both HKrOF and FKrOH are predicted to have a bending mode (involving F–O–Kr and F–Kr– O, respectively) at approximately 200 cm1. The other four vibrational modes of HKrOF do not have analogues in FKrOH. As an initial step towards evaluating the possible stability of HKrOF and FKrOH, the relative energies of these compounds as well as their fragments and constitutional isomers (see Table 4)

Table 1 List of molecules considered in this study. Molecule HArN HKrN HKrS HKrSe HKrAr HKrNe ArCAr FArKr FKrAr HArKr HArO HKrO HKrKr FKrN ArCCCAr ArCCAr HeCCHe KrCCCKr KrCCKr ClKrCCKrCl FArCCArF FKrCCKrCCKrCCKrF FKrSiSiKrF ClArSiSiArCl ClArCCArCl BrKrGeGeKrBr ClArCCCArCl ClArCCArCCArCl ClNeCCCNeCl FNeCCCNeF FNeCCNeCCNeF FNeCCNeF FNeCNeCCCNeCNeF ClNeCCNeCCNeCl ClArCArCCCArCArCl ClArCCArCl ClKrPPKrCl ClNeCCNeCl ClNeCNeCCCNeCNeCl FKrCCKrCCCKrCCKrF FKrKrCCCKrKrF FKrSiCKrF HeCCCHe KrCKr Kr(CO)6 HKrOF FKrOH

Type Ia

Type IIb

Type IIIc

Type IVd

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

a A converged geometry was not found for at least one (but not all) of the aug-ccpVnZ (n = D, T and Q) series. b Convergent geometry found with B3LYP/aug-cc-pVnZ, but with the presence of imaginary frequencies (indicating a non-minimum energy geometry). c Minimum energy geometry found with B3LYP/aug-cc-pVnZ calculations, but not with MP2 and CCSD(T) calculations. d Minimum energy geometry found with B3LYP, MP2 and CCSD(T)/aug-cc-pVnZ calculations.

were computed. Using CCSD(T)/aug-cc-pVQZ, Kr + FOH is the most energetically favored species and FKrOH was the next lowest in energy. Fragments of FKrOH followed, with the energies of [F + KrOH] and [F + Kr + OH] being of similar energy to each other and 0.355 and 0.377 eV higher in energy, respectively than FKrOH (and more than 2.1 eV higher than Kr + FOH). Two fragments of HKrOF, [H + KrOF] and [HKr + OF] produce the next lowest relative energies at 4.556 and 4.569 eV, respectively. The compound, HKrOF, was predicted as being 4.944 eV higher in energy than Kr + FOH (and 3.141 eV higher in energy than its constitutional isomer, FKrOH). The importance of the bond between oxygen and either hydrogen or fluorine in both the HKrOF and FKrOH may be seen in the relative energies of [FKrO + H] and [HKrO + F] which are 6.893 and 8.257 higher in energy than Kr + FOH. The isolated atoms are predicted to have the highest relative energy of all species studied, 8.966 eV higher than Kr + FOH.

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Table 2 Optimized bond lengths (Å) and bond angles (degrees) for HKrOF and FKrOH at various theory/basis set combinations. HKrOF

B3LYP aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ MP2 aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ CCSD(T) aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ

FKrOH

r(H–Kr)

r(Kr–O)

r(O–F)

a(Kr–O–F)

r(F–Kr)

r(Kr–O)

r(O–H)

a(Kr–O–H)

1.557 1.545 1.545

2.199 2.187 2.185

1.447 1.444 1.443

99.376 99.523 99.733

1.974 1.958 1.955

1.978 1.961 1.956

0.973 0.969 0.968

103.157 103.280 103.429

1.515 1.497 1.500

2.148 2.120 2.112

1.454 1.437 1.433

97.527 97.940 97.877

1.959 1.929 1.920

2.010 1.963 1.951

0.979 0.973 0.971

100.668 101.299 101.419

1.573 1.541 1.542

2.196 2.165 2.157

1.484 1.462 1.456

96.629 96.898 96.879

2.000 1.954 1.942

2.038 1.973 1.960

0.977 0.970 0.967

100.177 101.365 101.594

Table 3 Frequencies (cm1) for HKrOF and FKrOH at various theory/basis set combinations. B3LYP HKrOF F–O–Kr bend Kr–O stretch H out of plane bend O–Kr–H bend O–F stretch Kr–H stretch MP2 F–O–Kr bend Kr–O stretch H out of plane bend O–Kr–H bend O–F stretch Kr–H stretch CCSD(T) F–O–Kr bend Kr–O stretch H out of plane bend O–Kr–H bend O–F stretch Kr–H stretch

aug-cc-pVDZ

aug-cc-pVTZ

aug-cc-pVQZ

157.1 388.9 603.5 662.7 913.7 1792.2

159.1 388.3 618.7 670.6 928.9 1835.4

157.2 388.7 620.4 671.3 924.2 1832.2

178 .0 435.5 678.3 726.1 961.3 1873.8

175.4 446.8 697.5 746.9 997.9 1923.9

179.3 449.9 696.6 745.5 995.6 1907.2

163.8 402.2 604.1 643.5 797.3 1359.0

169.3 415 640 684.1 860.4 1585.1

173.5 419.2 644.6 687.1 865.6 1598.75

Table 4 CCSD(T)/aug-cc-pVQZ energies (eV) relative to Kr + FOH in ascending order. Species

Relative energy

Kr + FOH FKrOH F + KrOH F + Kr + OH H + KrOF HKr + OF HKrOF FKrO + H HKrO + F H + Kr + O + F

0.000 1.803 2.158 2.180 4.556 4.569 4.944 6.893 8.257 8.966

The synthesis of either HKrOF or FKrOH is unlikely if these species exist with a minimal barrier to dissociation. We determined the relative energetics for these new species, their transition states and dissociation products (two-body dissocation from HKrOF to Kr + HFO and from FKrOH to HF + KrO) across the B3LYP, MP2, and CCSD(T) levels of theory with the aug-cc-pVTZ basis set (Table 5; Figures 1 and 2). The CCSD(T) energies were calculated at the optimized MP2/aug-cc-pVTZ geometries. For HKrOF, each of the levels of theory predicted a 1.2 eV barrier to dissociation (to [Kr + HFO]), while for FKrOH dissociation (to [HF + KrO]); the barrier was nearly twice as large – greater than 2.1 eV. Each of these barriers to dissociation is quite high and suggests a kinetic

B3LYP FKrOH F–Kr–O in plane bend F–Kr–O out of plane bend F–Kr–O symmetric stretch F–Kr–O asymmetric stretch O–H wag O–H stretch MP2 F–Kr–O in plane bend F–Kr–O out of plane bend F–Kr–O symmetric stretch F–Kr–O asymmetric stretch O–H wag O–H stretch CCSD(T) F–Kr–O in plane bend F–Kr–O out of plane bend F–Kr–O symmetric stretch F–Kr–O asymmetric stretch O–H wag O–H stretch

aug-cc-pVDZ

aug-cc-pVTZ

aug-cc-pVQZ

204.9 210.9 433.2 540.2 1077.7 3744.6

216.7 220.4 441.2 544.9 1087.3 3757.6

215.1 216.7 439.2 540.7 1087.8 3763.7

206.8 210.7 401.2 569.1 1053.2 3682.1

220.4 225.3 429.2 576.6 1065.8 3718.1

224.5 229.8 441.5 586.3 1075.7 3734.1

188.8 189.8 309.8 516.3 1056.5 3709.1

211.3 213.2 381.2 542.9 1083.1 3751.1

217.5 219.3 400.2 553.2 1094.0 3769.8

Table 5 Relative energies (eV) of the transition states and dissociation products (Kr + HFO and HF + KrO, respectively) of HKrOF and FKrOH using the bound molecule’s energy as a reference (all calculations used the aug-cc-pVTZ basis set). HKrOF

B3LYP MP2 CCSD(T)a a

FKrOH

Transition state

Product

Transition state

Product

1.284 1.213 1.199

2.320 2.322 2.551

2.146 2.669 2.551

0.117 0.010 0.260

Calculated using the MP2/aug-cc-pVTZ optimized geometries.

stability to this two-body dissociation pathway. The dissociation of HKrOF or FKrOH to Kr + HOF should also be considered. Though the calculations for this particular two-body dissociation pathway are not included, we may make some inferences as to the barriers to dissociation of HKrOF and FKrOH to Kr + FOH by examining HKrOH and HKrF. Previously, HKrOH was calculated as being 5.525 eV higher in energy than Kr + H2O with a 1.505 eV barrier to dissociation [24], while HKrF was calculated to be 4.874 eV higher in energy that Kr + HF while existing with a 1.392 eV barrier to dissociation [27]. Considering HKrOH and HKrF’s analogous dissociation channels, HKrOF was calculated as having a similar energy difference (4.944 eV) and FKrOH is much closer in energy to Kr + FOH (1.803 eV). This dissociation channel however, was not the lowest energy pathway in the case of HKrOH or HKrF. For both

B.R. Wilson et al. / Chemical Physics Letters 537 (2012) 6–10

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Figure 1. Plot of reaction coordinate (steps of 0.1 amu1/2 Bohr) versus energy (eV) for the dissociation of HKrOF to Kr + HFO (calculated using MP2/aug-cc-pVTZ).

Figure 2. Plot of reaction coordinate (steps of 0.1 amu1/2 Bohr) versus energy (eV) for the dissociation of FKrOH to HF + KrO (calculated using MP2/aug-cc-pVTZ).

of these molecules, three-body dissociation was the much more favorable dissociation pathway [24,27]. The study of the three-body dissociation (to [H + Kr + OF] and [F + Kr + OH]) requires a sophisticated multireference treatment [24], though we do not calculate the barriers to the three-body dissociation of HKrOF and FKrOH, we may infer as to the possible stability of HKrOF and FKrOH based upon their energetic relative to similar compounds. For HKrOF’s stability to dissociation, the calculated barrier height to HKrOH’s dissociation is informative. Previously, HKrOH was calculated as having a barrier to three-body dissociation of 0.15 eV, despite the fact that HKrOH was predicted to be only 0.95 eV higher in energy than [H + Kr + OH] [24]. The fact that HKrOF is much higher in energy (by 2.771 eV) than its threebody dissociation products in comparison to the difference between HKrOH and its three-body dissociation products does not

bode well for HKrOF’s prospects to exist as a stable molecule. The compound, FKrOH, however, is lower (by 0.377 eV) than its three-body dissociation products, and as such, may exist as a stable molecule. In comparison, HXeOBr was calculated to be 0.84 eV lower in energy than its three-body dissociation products [H + Xe + OF] with a 1.43 eV three-body dissociation barrier [26], and was subsequently synthesized via matrix isolation [28].

4. Conclusion Theoretical calculations have been used to investigate the possible existence of novel rare gas compounds. This investigation involved geometry optimization, harmonic frequency, relative energy and barrier height calculations. While the theoretical

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prediction of FKrOH is not entirely confirmed, there is evidence to support its possible synthesis. FKrOH is much lower in energy than its isolated atoms, is lower in energy than the products which would be formed by its three-body dissociation and should likely have a considerable barrier to two-body dissociation. Acknowledgements The authors thank the National Science Foundation (CHE0809762). As well support from the United States Department of Education for the Center for Advanced Scientific Computing and Modeling (CASCaM) is acknowledged. Computing resources were provided via a National Science Foundation CRIF award (CHE0741936) and via Academic Computing Services at the University of North Texas. K.S. was supported by a summer research fellowship from the Texas Academy of Mathematics and Science. References [1] [2] [3] [4]

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