On the vibrational spectra of HSO and SOH

Spectrochimica Acta Part A 72 (2009) 720–725

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On the vibrational spectra of HSO and SOH Pablo A. Denis ∗ Computational Nanotechnology, DETEMA, Facultad de Química, UDELAR, CC 1157, 11800 Montevideo, Uruguay

a r t i c l e

i n f o

Article history: Received 21 September 2008 Received in revised form 31 October 2008 Accepted 10 November 2008 Keywords: Reduced sulfur compounds Coupled cluster theory Anharmonic force fields Vibrational spectra Vibration–rotation corrections Correlation consistent basis set Rotational constants

a b s t r a c t The harmonic and fundamental vibrational frequencies, rotational constants, vibration–rotation corrections and Zero point energies of HSO and SOH and their deuterated isomers (DSO and SOD) have been determined employing the CCSD(T) methodology in conjunction with the aug-cc-pV(X+d)Z and cc-pwCVQZ basis sets. The calculated fundamental frequencies of SOH are 830, 1150 and 3577 cm−1 , for the SO , bend and OH , respectively. In the case of HSO the computed fundamentals are 1002, 1077 and 2335 cm−1 , for the SO , bend and SH , respectively. The values are discussed in terms of the experimental determinations available. The rotational constants reported for HSO are in reasonable agreement with experiment; the computed values are 301,271, 20,557 and 19,192 MHz. In the case of SOH, for the first time, we report the rotational constants including vibration–rotation corrections, they are: 654,236, 16,621, 16,178 MHz. The force fields calculated allowed as to estimate accurate ZPEs, the suggested values are 6.48 and 8.19 kcal/mol for HSO and SOH, respectively. Finally, we recommend the following structural parameters for HSO rSO = 1.4924 Å, rSH = 1.3649 Å and ∠HSO = 104.76◦ ; whereas for SOH we recommend rSO = 1.6302 Å, rOH = 0.9629 Å and ∠SOH = 107.97◦ . © 2008 Elsevier B.V. All rights reserved.

1. Introduction The HSO radical is one of the key intermediates in the atmospheric oxidation of SH2 to sulfuric acid. It has been proposed that HSO can participate in catalytic cycles that cause stratospheric ozone depletion [1]. For these reasons, HSO and its isomer SOH have been the subject of several experimental [2–20] and theoretical investigations [21–39]. In a previous work [29] we have focused our attention on, perhaps, the most controversial property of HSO, its enthalpy of formation. For a detailed description of this problem we refer the readers to reference [29]. The present investigation is devoted to improve the spectroscopic characterization of HSO and SOH, to guide in their experimental identification, and characterization. For example, the fundamental vibrational frequencies are needed to accurately estimate the Zero point energy corrections, which are necessary to predict the enthalpies of formation. The HSO radical has been detected in several experiments [1–20]; however, the spectroscopic characterization of HSO is far from being complete. To the best of our knowledge, only one fundamental vibrational frequency of HSO has been observed, the SO stretching mode. Schurath et al. [3] recommended that SO = 1013 ± 5 cm−1 . The SH stretch was not manifested in the spectra and was assumed to come close to that of the SH group

∗ Tel.: +598 29290705; fax: +598 29241906. E-mail address: [email protected]. 1386-1425/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2008.11.002

frequency, 2570 cm−1 , whereas the bending mode was calculated to be bend = 1063 cm−1 . Some years later, Hirota and coworkers [4–6] performed three spectroscopic investigations of HSO and DSO. They determined the rotational constants [4–5] and the structural parameters [6]. Employing these results, and other spectroscopic parameters such as the force constants of SH (2 ) and SH (2 + ) they determined that SO = 1026 cm−1 , SH = 2271 cm−1 , and bend = 1164 cm−1 . Among the several theoretical investigations performed about HSO and SOH, Wang and Wilson [32] determined the fundamental vibrational frequencies of these isomers employing density functional theory and correlation consistent basis sets up to aug-cc-pV(5+d)Z. The evidence presented above confirms our previous statement, much work is necessary to complete the spectroscopic characterization of HSO and also its isomer SOH, for which none experimental information is available. To perform a detailed spectroscopic investigation, the rotational constants, vibration–rotation corrections, harmonic and fundamental vibrational frequencies, dipole moments and Zero point energies of the HSO and SOH isomers must be determined. To reach that end, because HSO and SOH are strongly correlated systems [22–23,29] we have used CCSD(T) to compute for the for the first time at this level, a cubic force field and the semidiagonal part of the quartic, which is enough to obtain fundamental vibrational frequencies. This work continues the efforts made by other investigators and us, devoted to gain a better understanding of sulfur containing molecules [40–62], which may help to reduce the presence of sulfuric acid in the atmosphere. It is important to note that sulfuric acid is one of the components of the polar stratospheric clouds which

P.A. Denis / Spectrochimica Acta Part A 72 (2009) 720–725

are one causes of the large decrease in ozone during the austral spring over the Antarctica.

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Table 1 Harmonic and fundamental vibrational frequencies determined for HSO and DSO at the CCSD(T)/aug-cc-pV(T+d)Z level of theorya . HSO

2. Theoretical methods The UCCSD(T) methodology was employed [63–66], in conjunction with the aug-cc-pV(T+d)Z and cc-pwCVQZ [67–68] basis sets. The theoretical harmonic vibrational frequencies were determined at the frozen core CCSD(T)/aug-cc-pV(T+d)Z level of theory and fundamentals were calculated as implemented in ACESII [69–71]. Briefly, the full cubic force field together with the semidiagonal part of the quartic force field is calculated and the fundamental vibrational frequencies are obtained employing second order perturbation theory starting from the harmonic-oscillator rigid rotator approximation. The rotational constants were calculated combining the equilibrium rotational constants determined at the full CCSD(T)/cc-pwCVQZ level of theory and the vibration–rotation corrections obtained at the frozen-core CCSD(T)/aug-cc-pV(T+d)Z level of theory. The 1 s electrons of sulfur were not correlated in the full CCSD(T) calculations. It has been demonstrated by Coriani et al. [73] that for molecules composed by second row atoms a well balanced error cancellation between the one-electron and N-electron descriptions can be achieved at the full CCSD(T)/cc-pCVQZ level. Therefore, because we cannot perform CCSDTQ optimizations for HSO and SOH, we decided to use the error cancellation approach described in reference [73], to determine the structure of HSO and SOH. All the calculations were performed with ACESII (MainzAustin-Budapest version) [69–70].

Fundamentals

Harmonics

Anh. Contrib.

Intensities ZPE

This work Schurath [3] Ohashi [6] Wang–Wilson [32]b Wang–Wilson [32]c This work Wang–Wilson [32]b Wang–Wilson [32]c This work Wang–Wilson [32]b Wang–Wilson [32]c This work

S–O stretch

HSO bend

S–H stretch

1002.3 1013 ± 5 1026 1009

1076.8 1064 1164 1080

2335.1 2570 2271 2287

1028

1095

2302

1020.9 1020

1096.7 1096

2459.4 2420

1033

1108

2439

−18.6 −11

−19.9 −16

−124.3 −133

−5

−13

−137

17.3

48.6

11.1

HSO 6.54 6.48

Harmonic Anharmonic DSO

Fundamentals Harmonics Anh. Contrib. Intensities

This work This work This work This work

ZPE

Harmonic Anharmonic

S–O stretch

DSO bend

S–D stretch

1041 1059 18 2.5

772 784 12 25.6

1704 1768 63 26.6

3. Results and discussion 3.1. Vibrational spectra of HSO and SOH The calculated intensities, fundamental and harmonic vibrational frequencies of HSO are presented in Table 1, along with the values observed or calculated by Schurath et al. [3], those calculated by Ohashi et al. [6] and those calculated by Wang and Wilson [32] at the DFT level. The comparison between experiment and theory can be made only for the S–O stretching mode, because it is the only one that has been observed. The value measured by Schurath et al. [3] for the fundamental SO stretch is 1013 ± 5 cm−1 . This value is in excellent agreement with the determined by us 1002.3 cm−1 , at the CCSD(T)/aug-cc-pV(T+d)Z level of theory. The empirical value suggested by Ohashi et al. [6] is 1026 cm−1 , 24 cm−1 larger than our estimation. The anharmonic correction for the SO stretch is relatively small, 18.7 cm−1 . The remaining vibrational modes have not been directly observed but they have been inferred. In the case of the bending mode the empirical values suggested [3,6] present important differences. Schurath et al. [3] recommended bend = 1063 cm−1 , whereas Ohashi et al. [6] calculated a much higher value, bend = 1164 cm−1 . In this case theory is a great help to decide which value is the correct one. Our coupled cluster results suggested that the bending mode is located at 1076.8 cm−1 , only 13 cm−1 larger than the value determined by Schurath et al. [3] and almost a 100 cm−1 larger that that reported in reference [6]. Finally, we have the SH stretching mode, which is without doubts the most problematic one, because no signal has been detected. This a bit contradictory, on one hand it is well known that SH stretching modes are difficult to study, however, on the other hand, the results presented in Table 1 show that, it is by far the mode intense vibrational mode, almost 5 times more intense than the SO stretch. As expressed in the introduction, in the experimental investigation by Schurath et al. [3] the SH stretch was not manifested in the spectra and was assumed to come close to that of the SH group at 2570 cm−1 ; whereas Ohashi et al. [6] employed the force constants

Fundamentals

CCSD(T) Experiment

HSO 5.16 5.12 HSOH

cc-pV(T+d)Z [53–57]

S–H stretch

O–H stretch

2537 2538

3640 3625.6

a Fundamentals and harmonics are reported in cm−1 , intensities in km/mol and ZPEs in kcal/mol. b Determined at the B3LYP/aug-cc-pV(5+d)Z level of theory. c Determined at the B3W91/aug-cc-pV(5+d)Z level of theory.

of SH (2 ) and SH (2 + ) to determine SH = 2271 cm−1 . The fundamental SH stretch determined by us is 2335 cm−1 , 64 cm−1 larger than the value suggested by Ohashi et al. [6]. Considering the drastic assumptions made in the latter work, we recommend our value for the SH stretch. In short, our results indicated that the for SO stretching and the bending modes there is an excellent agreement between the values reported by Schurath et al. [3] and those calculated by us. However, for the SH stretching we propose our value 2335 cm−1 . The results obtained for SOH are presented in Table 2. To the best of our knowledge there is no experimental information about its vibrational spectra. This is somewhat surprising if we take in consideration that it is only 4.6 kcal/mol less stable than HSO [29] and also that the isomerization barrier is very high [23,28]. The values recommended for the SO , bend and OH are 830.2, 1150.2 and 3577.3 cm−1 , respectively. The SO stretch in SOH is about 200 cm−1 smaller than that observed for HSO, reasonable if we consider that the S–O distance in SOH is 1.6302 Å, 0.15 Å larger that in HSO (see Section 3.3). The SO stretch in SOH can be compared with that determined for HSOH in an Argon matrix, 762.5 cm−1 [53–57]. The SO stretch in HSOH is smaller than that determined for SOH because the SO bond length is longer in the former, namely 1.6614 Å at the

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P.A. Denis / Spectrochimica Acta Part A 72 (2009) 720–725

Table 2 Harmonic and fundamental vibrational frequencies determined for SOH and SOD at the CCSD(T)/aug-cc-pV(T+d)Z level of theorya . SOH

Fundamentals

Harmonics

Anh. Contrib.

Intensities ZPE

This work Wang–Wilson [32]b Wang–Wilson [32]c This work Wang–Wilson [32]b Wang–Wilson [32]c This work Wang–Wilson [32]b Wang–Wilson [32]c This work

S–O stretch

SOH bend

O–H stretch

830.2 830 853 843.8 841 865 −13.6 −11 −12 69.3

1150.2 1132 1139 1184.9 1169 1175 −34.7 −37 −36 47.7

3577.3 3552 3573 3766.0 3750 3770 −188.7 −198 −197 95.8

SOH 8.28 8.19

Harmonic Anharmonic SOD

Fundamentals Harmonics Anh. Contrib. Intensities

This work This work This work This work

ZPE

Harmonic Anharmonic

S–O stretch

SOD bend

O–D stretch

829 841 12 49.4

848 868 20 43.4

2643 2743 100 54.1

SOD 6.36 6.31

a Fundamentals and harmonics are reported in cm−1 , intensities in km/mol and ZPEs in kcal/mol. b Determined at the B3LYP/aug-cc-pV(5+d)Z level of theory. c Determined at the B3W91/aug-cc-pV(5+d)Z level of theory.

full CCSD(T)/cc-pwCVQZ level [53–57,62]. It important to discuss the expected error of the procedure employed to estimate the fundamental vibrational frequencies. In a recent work [62] we have calculated the fundamental vibrational frequencies of HSOH at the CCSD(T)/cc-pV(T+d)Z level of theory. The fundamental vibrational frequencies of HSOH have been determined experimentally, although only the SH and OH modes were detected in the gas phase, the rest were observed in Ar matrix. The experimental values are 2538 and 3625.6 cm−1 , for the SH and OH , respectively [53–57]. These values are in excellent agreement with our determinations SH = 2537 cm−1 and OH = 3640 cm−1 , the SH stretch is only 1 cm−1 smaller than the experimental result and the OH stretch is 15 cm−1 larger, reasonable considering the strong anharmonic characteristics of the latter vibrational mode. For the remaining fundamental vibrational frequencies the agreement was excellent but the comparison can be done only in semi-quantitative terms because they were observed in Ar matrix and thus, a shift from the gas phase is expected. Therefore, for the purpose of the present work we can consider the vibrational frequencies of HSO have an uncertainty of ±10 cm−1 ; however, for SOH it is larger, ±20 cm−1 , because of the presence of the OH stretching mode. Finally, it is interesting to compare the fundamental vibrational frequencies obtained in this work with those reported at the DFT level by Wang and Wilson [32]. In the case of HSO, there is a very good agreement between the SO and bend computed at the B3LYP/aug-cc-pV(5+d)Z and the CCSD(T) levels; the performance of B3PW91 is also good for these two modes, but the deviation from the CCSD(T) results is larger. However, for the SH stretch the B3PW91 is closer to the CCSD(T)/aug-cc-pV(T+d)Z results. For SOH, the results obtained at the DFT level are in good agreement with the CCSD(T) ones; the B3PW91 method is closer for the OH and bend modes and B3LYP gives a better agreement for the SO . In Table 1 we have also included the anharmonic corrections necessary to compute the fundamental vibrational frequencies of HSO

and SOH. The values determined at the B3LYP and B3PW91 levels by Wang and Wilson [32] are in good agreement with the CCSD(T) ones. Overall, the comparison between the DFT and CCSD(T) results suggest that the agreement is good and that it may be possible to compute at the DFT level the fundamental vibrational frequencies of larger sulfur containing molecules, for which CCSD(T) cannot be used because of the tremendous computational cost of the latter methodology. Further computations are necessary to confirm this statement. 3.2. Rotational constants and structural parameters of HSO and SOH In Table 3 and we present the rotational constants (RC) determined for HSO and DSO, whereas in Table 4 we report those calculated for SOH and SOD. In the case of HSO the RC have been determined experimentally by Endo et al. [5]. The agreement between the latter and the Ao , Bo , and Co calculated by us at the full-CCSD(T)/cc-pwCVQZ level using the vibration–rotation corrections determined at the CCSD(T)/aug-cc-pV(T+d)Z level of theory is acceptable for Bo , and Co . Indeed, the deviation is only 0.3% in both cases. However, for Ao the deviation is twice larger 0.6%. For DSO, the differences between the RC0 determined at the full-CCSD(T)/ccpwCVQZ level of theory and those observed by Endo et al. [5] are similar to those observed for HSO. Indeed, the deviation observed for Ao is 0.5%, almost twice larger than that computed for Bo and Co . In the case of SOH and SOD we report for the first time the rotational constants including vibration–rotation corrections, for SOH they are: 654,236, 16,621, 16,178 MHz and for SOD the are: 355,543, 15,620 and 14,925 MHz. To gauge the accuracy of our RC we have compared those calculated for HSOH with experiment. The RC0 determined at the full-CCSD(T)/cc-pWCVQZ level of theory are 202,198, 15,285 and 14,846 MHz, in excellent agreement with the experimental constants 202,069, 15,282 and 14,840 MHz [53–57]. In the case of HSOH, the differences between experiment and theory are one order of magnitude smaller than those determined for HSO, 0.06%, 0.02% and 0.04% for Ao , Bo and Co , respectively. Since HSO is a strongly correlated system we consider that the origin of the larger differences is the lack of complete quadruple excitations in our systems. 3.3. Structural parameters and dipole moment The estimation of the structural parameters for molecules containing second row atoms is not an easy task [43,62,72–74]. We have observed that the bond distances determined at the relativisticfull-CCSD(T)/CBS level of theory [43,62] are systematically shorter than the experimental results. Indeed, at the latter level of theory, in the case of SO2 , the SO bond distance is 0.0024 Å shorter than the experimental value. Thus, to achieve a better agreement between experiment and theory, higher excitations must increase the bond distances. These problems can be solved in part, if CCSDT geometry optimizations are performed, since CCSDT gives longer bond distances than CCSD(T) in nearly all of the sulfur containing molecules that we have investigated previously [43]. This has been recently corroborated by Feller [72], who found that quadruples excitations may be extremely important to accurately estimate the bond distances in sulfur containing molecules. In the case of S2 , the quadruple excitations increase the bond distance 0.003 Å [72]. Since, we cannot perform CCSDTQ/aug-cc-pV(T+d)Z geometry optimizations for HSO and SOH, it is necessary to find a basis set which in conjunction with the CCSD(T) method can give accurate structural parameters; such an approach was proposed by Coriani et al. [73]. They studied a set of molecules composed by second row atoms and concluded that, a well balanced error cancella-

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Table 3 Rotational constants determined for HSO and DSO (MHz). HSO

CCSD(T)-fc CCSD(T)-full

CCSD(T)-fc CCSD(T)-full Experiment

CCSD(T)-fc

Ae

Be

Ce

300,678 303,278

20,270 20,626

18,989 19,312

Ao

Bo

Co

298,671 301,271 299,484.63

20,202 20,558 20,504.56

18,869 19,192 19,133.93

Ae − Ao

Be − Bo

Ce − Co

2,007

68

120

Ae

Be

Ce

158,647 160,149

19,618 19,946

17,459 17,737

aug-cc-pV(T+d)Z cc-pwCVQZ

aug-cc-pV(T+d)Z cc-pwCVQZa Endo [5]

aug-cc-pV(T+d)Z

DSO

CCSD(T)-fc CCSD(T)-full

CCSD(T)-fc CCSD(T)-full Experiment

CCSD(T)-fc

aug-cc-pV(T+d)Z cc-pwCVQZ

aug-cc-pV(T+d)Z cc-pwCVQZa Endo et al. [5] Ohashi et al. [6]

Ao

Bo

Co

158,036 159,538 158,726.938(71) 158,750(18)

19,554 19,882 19,836.533(89) 19,836.2(28)

17,340 17,618 17,570.206(87) 17,573.6(26)

aug-cc-pV(T+d)Z

Ae − Ao

Be − Bo

Ce − Co

611

64

119

HSOH

CCSD(T)-fc CCSD(T)-full Experiment

CCSD(T)-fc a b

cc-pV(T+d)Z cc-pwCVQZb [53–57]

cc-pV(T+d)Z

Ao

Bo

Co

200,630 202,198 202,069

15,110 15,285 15,282

14,682 14,846 14,840

Ae − Ao

Be − Bo

Ce − Co

1,425

121

138

The vibration–rotation corrections were determined at the CCSD(T)/aug-cc-pV(T+d)Z level of theory. The vibration–rotation corrections were determined at the CCSD(T)/cc-pV(T+d)Z level of theory.

Table 4 Rotational constants determined for SOH and SOD (MHz). SOH Ae CCSD(T)-fc CCSD(T)-full

aug-cc-pV(T+d)Z cc-pwCVQZ

646,118 652,140 Ao

CCSD(T)-fc CCSD(T)-full

aug-cc-pV(T+d)Z cc-pwCVQZa

CCSD(T)-fc

aug-cc-pV(T+d)Z

Be 16,442 16,693 Bo

Ce 16,034 16,277 Co

648,204 654,226

16,370 16,621

15,935 16,178

Ae − Ao

Be − Bo

Ce − Co

−2,086

72

99

SOD Ae CCSD(T)-fc CCSD(T)-full

aug-cc-pV(T+d)Z cc-pwCVQZ

CCSD(T)-fc CCSD(T)-full

aug-cc-pV(T+d)Z cc-pwCVQZa

CCSD(T)-fc

aug-cc-pV(T+d)Z

Be

351,151 354, 499 Ao

a

15,450 15,682 Bo

Ce 14,799 15,017 Co

352,195 355,543

15,388 15,620

14,707 14,925

Ae − Ao

Be − Bo

Ce − Co

−1,044

62

92

The vibration–rotation corrections were determined at the CCSD(T)/aug-cc-pV(T+d)Z level of theory.

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P.A. Denis / Spectrochimica Acta Part A 72 (2009) 720–725

Table 5 Structural parameters determined for the HSO and SOH radicalsa . HSO

CCSD(T)

CCSD(T) MRCI B3LYP B3PW91 CCSD(T) Recommended a b

aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z cc-pwCVTZ fc cc-pwCVTZ fu cc-pVTZ DK cc-pVTZ SR ∞(T,D) ∞(Q,T) ∞(Q,T)+Core ∞(Q,T)+Core+SR cc-pwCVQZ fu cc-pVQZ aug-cc-pV(5+d)Z aug-cc-pV(5+d)Z cc-pV(Q+d)Z

SOH

Reference

re H-S

re O-S

∠H-S-O

re H-O

re O-S

∠H-S-O

1.3777 1.3684 1.3665 1.3669 1.3653 1.3717 1.3715 0.0002 1.3645 1.3651 1.3635 1.3637 1.3649 1.361 1.374 1.374 1.3687 1.3649

1.5389 1.5060 1.4986 1.4990 1.4963 1.5163 1.5161 0.0002 1.4922 1.4932 1.4905 1.4907 1.4924 1.506 1.500 1.494 1.4977 1.4924

103.79 104.43 104.50 104.86 104.82 104.31 104.32 0.010 104.70 104.55 104.51 104.52 104.76 104.95 104.54 104.71 104.69 104.76

0.9720 0.9667 0.9645 0.9645 0.9636 0.9651 0.9651 0.0 0.9645 0.9629 0.9620 0.9620 0.9629 0.963 0.966 0.965 0.9636 0.9629

1.6771 1.6429 1.6355 1.6375 1.6346 1.6489 1.6482 0.0007 1.6285 1.6301 1.6282 1.6289b 1.6302 1.645 1.637 1.628 1.6350 1.6302

107.23 107.85 108.06 107.32 107.39 106.84 106.87 0.03 108.11 108.31 108.14 108.84 107.97 106.37 109.29 108.89 107.83 107.97

[29] [29] [29] [29] [29] [29] [29] [29] [29] [29] [29] [29] This work [23] [32] [32] [31] This work

Distances in Å and angles in degrees. In Ref. [5] the value is 1.6389 but it is wrong. The correct value is 1.6282 + 0.0007 = 1.6289.

tion between the one-electron and N-electron descriptions can be achieved at the CCSD(T,full)/cc-pCVQZ level. Indeed, the mean absolute error at this level of theory is 0.0013 Å for bond distances and 0.3◦ for bond angles; our results for HSOH and SO2 [62] confirmed that a good compromise between computational cost and accuracy is reached at the full-CCSD(T)/cc-pwCVQZ level. This conclusion is similar to the obtained in reference [73] although they used the cc-pCVQZ basis set. The structural parameters determined in this work and some of the previously reported by us [29] and other investigators [23,31] are reported in Table 5. In our most recent work [29], after extrapolation to the CBS limit, including core-valence and scalar relativistic corrections we have suggested rSO = 1.4907 Å, rSH = 1.3637 Å and ∠HSO = 104.5◦ for SOH and rSO = 1.6289 Å, rOH = 0.9620 Å and ∠SOH = 108.3◦ for SOH. The values determined for HSO cannot be directly compared with those determined by Ohashi et al. [6] because they reported r0 distances, 1.494(5) and 1.389(5) for the SO and SH bond distances and 106.6◦ for the HSO angle. As explained above, the values proposed are those obtained at the full CCSD(T)/cc-pwCVQZ level of theory. For HSO they are rSO = 1.4924 Å, rSH = 1.3649 Å and ∠HSO = 104.76◦ , whereas those obtained for SOH are rSO = 1.6302 Å, rOH = 0.9629 Å and ∠SOH = 107.97◦ . As expected, the bond distances proposed in this work are slightly longer than those suggested in reference [29]. This is because of the underestimation of the bond distances at relativistic-full-CCSD(T)/CBS level of theory explained in the previous paragraph. We expect that the higher order corrections to the bond distances of HSO and SOH would be similar to the difference between the values obtained in this work and those reported in our previous work [29]. The experimental dipole moment along the a axis of this near-prolate asymmetric top is a = 2.20 ± 0.08 Debye in excellent agreement with our determination 2.21 Debye. The dipole moment along the b direction is 0.68 Debye. For SOH a = 0.72 Debye and b = 1.46 Debye. 3.4. Implications for the thermochemistry of HSO and SOH The spectroscopic constants determined in this work for HSO and SOH allow us to estimate zero-point energies corrected by anharmonic effects. The recommended ZPEs for HSO and SOH are 6.48 and 8.19 kcal/mol, respectively. These values can be compared with those employed by us in our very accurate estimation of the

enthalpies of formation of these two isomers [29], which are 6.50 and 8.24 kcal/mol for HSO and SOH, respectively. Thus, these corrections marginally change the enthalpies of formation of HSO and o (HSO) = −5.25 ± 0.5 kcal/mol and SOH. The new values are Hf,298 o Hf,298 (SOH) = −1.62 ± 0.5 kcal/mol.

4. Conclusions The vibrational spectra of HSO and SOH has been investigated employing the CCSD(T) methodology and the correlation consistent basis sets. The main conclusions of the present investigation are: 1. The vibrational spectra of HSO must be reinvestigated. For the first time an anharmonic force field has been computed at the CCSD(T) level. The fundamental vibrational frequencies suggested are 1002, 1077 and 2335 cm−1 , for the SO , bend and SH , respectively. The infrared intensities obtained are: 11, 17 and 49 km/mol for the SO , bend and SH , respectively. 2. The rotational constants determined for HSO are 301,271, 20,558 and 19,192 MHz. These values are in reasonable agreement with experiment. An important contribution from complete quadruples excitations is expected if the structure of HSO is optimized at the CCSDTQ level of theory. 3. For the first time we report the fundamental vibrational frequencies and intensities of SOH at the CCSD(T) level, which may guide to experimentalists in its identification. The calculated fundamental frequencies of SOH are 830, 1150 and 3577 cm−1 , for the SO , bend and OH , respectively. The infrared intensities are 69, 48, and 96 km/mol SO , bend and OH , respectively. In addition to this, the rotational constants including vibration–rotation corrections are reported, they are: 654,236, 16,621, 16,178 MHz. 4. The force field calculated allowed us to estimate accurate ZPEs for HSO and SOH; the recommended values are 6.48 and 8.19 kcal/mol, respectively. 5. The recommended structural parameters for HSO are: rSO = 1.4924 Å, rSH = 1.3649 Å and ∠HSO = 104.76◦ ; and for SOH we propose rSO = 1.6302 Å, rOH = 0.9629 Å and ∠SOH = 107.97◦ . Acknowledgements The author thanks PEDECIBA (UNESCO PNUD) and CSIC for financial support.

P.A. Denis / Spectrochimica Acta Part A 72 (2009) 720–725

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