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A coupled-cluster study of the HOSO and HSO2 radicals
Chemical Physics Letters 421 (2006) 562–565 www.elsevier.com/locate/cplett
A coupled-cluster study of the HOSO and HSO2 radicals Brian Napolion, John D. Watts
*
Computational Center for Molecular Structure and Interactions, Department of Chemistry, Jackson State University, 1400 J.R. Lynch Street, P.O. Box 17910 Jackson, MS 39217, United States Received 1 November 2005; in final form 25 January 2006 Available online 9 March 2006
Abstract CCSD(T) calculations with triple-zeta valence plus polarization basis sets have been performed on HOSO and HSO2 to determine structures, vibrational frequencies, and infrared intensities for the first time with coupled-cluster methods. It is found that the planarity of HOSO is very sensitive to basis set. The calculated frequencies and intensities offer further support for the identification of HOSO and HSO2 in rare gas matrices. Ó 2006 Elsevier B.V. All rights reserved.
1. Introduction Chemical species having the formula HSO2 have been of interest for some time as possible intermediates in the atmospheric and combustion chemistry of sulfur-containing compounds [1]. Limited experimental information is available on isomers of HSO2. McDowell et al. [2] obtained ESR data on what was thought to be the HSO2 isomer, i.e., a species with the hydrogen bonded to the sulfur. Frank et al. [3,4] have identified HSO2 and HOSO using mass spectrometry. Isoniemi et al. [5,6] have obtained infrared evidence for the formation of HSO2 and HOSO following UV irradiation of H2S and SO2 mixtures in rare gas matrices. Other isomers, namely HSOO and HOOS have apparently not been detected experimentally. A large number of theoretical studies have been performed with the goal of characterizing the various isomers of HSO2 [3–14]. The consensus of the calculations is that the most stable species is the cis conformer of HOSO. The next most stable species is HSO2, having Cs symmetry, while HSOO and HOOS are somewhat higher in energy. Less certain is whether planar cis-HOSO is a local minimum.
*
Corresponding author. Fax: +1 601 979 3674. E-mail address: [email protected] (J.D. Watts).
0009-2614/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.01.103
Binns and Marshall [9] performed geometry optimizations of planar cis-HOSO (constraining the dihedral angle s to be 0°) and planar trans-HOSO (s = 180°), and calculated harmonic vibrational frequencies at the HF/3-21G* and MP2/3-21G* levels. The HF/3-21G* a00 frequency of planar cis-HOSO is imaginary, while the MP2/3-21G* a00 frequency is real. For planar trans-HOSO both HF/321G* and MP2/3-21G* yield an imaginary a00 frequency. Subsequently, Morris and Jackson [10] found planar cisand trans-HOSO to be local minima at the MP2/DZP level. About the same time, Laakso et al. [11] found that planar cis-HOSO is a local minimum at the MP2/6-31G* level. In 1997, Frank et al. [3,4] found that both planar cis- and trans-HOSO are local minima at the MP2/6-31+G** level. Also in 1997, Qi et al. [12] performed MP2/6-311G** calculations on planar cis-HOSO and found it to be a local minimum at this level. In 2001, Isoniemi et al. [5] reported geometry optimizations and vibrational frequency calculations on HSO2 and cis- and trans-HOSO with MP2 and MP4 using the 6-311++G(2d,2p) basis set. Planar cisHOSO was found to be a local minimum in both sets of calculations. Planar trans-HOSO was found to be a transition state. The harmonic vibrational frequencies of both HSO2 and cis-HOSO matched the infrared bands observed following UV irradiation of H2S/SO2 mixtures in a Kr matrix. This work was later extended, including isotopic shifts and other rare gas matrices [6]. Very recently,
B. Napolion, J.D. Watts / Chemical Physics Letters 421 (2006) 562–565
Ballester and Varandas [13] have developed a double many-body expansion for the potential energy surface of HSO2. This work included full-valence complete active space (FVCAS) calculations with the aug-cc-pVDZ and aug-cc-PVTZ basis sets. Interestingly, this work found the cis-HOSO species to be planar with the aug-cc-pVDZ basis set, but slightly non-planar (s = 12.8°) with the augcc-pVTZ basis set. As part of a study of the SO2+HO2 reaction, Wang and Hou [14] performed a B3LYP/augcc-pV(T+d)Z geometry optimization of cis-HOSO, although the dihedral angle was not explicitly stated. Also, no comments were made about vibrational frequencies. This Letter reports the first coupled-cluster study of cisand trans-HOSO that includes geometry optimizations and harmonic vibrational frequency calculations. The aims of these calculations are to address whether planar cis-HOSO and trans-HOSO are local minima or not, to further characterize these species, and to compare CCSD(T) harmonic vibrational frequencies and infrared intensities with data obtained in rare gas matrices [5,6]. In addition, CCSD(T) frequencies and infrared intensities have been obtained for HSO2 species and compared with experimental data [5,6]. 2. Computational methods Geometry optimizations and harmonic vibrational frequency calculations have been performed on the HOSO and HSO2 isomers using the CCSD(T) method [15] and several basis sets. The CCSD(T) method includes singleand double-excitation clusters iteratively (the CCSD method [16]). Using CCSD amplitudes, a perturbative estimate of the effects of connected triple excitations is then made. The CCSD(T) method is complete through fourthorder terms, and it also includes the fifth-order singles–triples terms. In the absence of large multi-reference effects, the CCSD(T) method is a highly reliable method for structure, energetics, and other molecular properties [17–19]. Based on the CCSD wave functions, the species studied in this work do not have significant multi-reference character, so the CCSD(T) method should be suitable for this study. Since spin contamination was found to be very small at the SCF level, and even less at the correlated level, unrestricted Hartree–Fock (UHF) reference functions were used throughout this work. In all calculations, the core electrons were not correlated. All calculations were performed using the ACES II program [20], a product of the Quantum Theory Project, University of Florida. Authors: J.F. Stanton, J. Gauss, J.D. Watts, M. Nooijen, N. Oliphant, S.A. Perera, P.G. Szalay, W.J. Lauderdale, S.R. Gwaltney, S. Beck, A. Balkova´, D.E. Bernholdt, K.-K. Baeck, P. Rozyczko, H. Sekino, C. Huber, and R.J. Bartlett. Integral packages are VMOL (J. Almlo¨f and P.R. Taylor); VPROPS (P.R. Taylor) and ABACUS (T. Helgaker, H.J.Aa. Jensen, P. Jørgensen, J. Olsen, and P.R. Taylor). The basis sets used are the 6-31+G**, 6-311G**, and ccpVTZ basis sets. The first of these is a double-zeta valence
563
set, augmented with diffuse sp functions on O and S and a set of polarization functions (p on H, d on O and S) on each atom. The second is a triple-zeta valence basis set augmented with a set of polarization functions on all atoms. The cc-pVTZ basis set is a correlation-consistent polarized valence triple-zeta basis set. It contains 2p 1d polarization functions on H and 2d 1f polarization functions on O and S. The 6-31+G** and 6-311G** were used with Cartesian d functions, while for the cc-pVTZ basis set, real spherical harmonic d and f functions were used. 3. Results and discussion CCSD(T) geometry optimizations were performed on the ground state (2A00 ) of planar cis-HOSO and transHOSO. The harmonic vibrational frequencies were then calculated. The geometries, energies, and the out-of-plane harmonic vibrational frequencies (x6) are shown in Tables 1 and 2. From Tables 1 and 2, one can see that the basis set effects on the bond lengths of cis- and trans-HOSO follow the usual trend as the valence and polarization spaces are expanded. r(O–S) and r(S–O) decrease on going from 631+G* to 6-311G** and from 6-311G** to cc-pVTZ. The ˚ decrease in r(O–S) on going largest effect is the 0.02 A from 6-311G** to cc-pVTZ. r(H–O) decreases by less than ˚ on going from 6-31+G* to 6-311G**, but increases 0.01 A slightly on going to cc-pVTZ. The HOS angle is more sen-
Table 1 CCSD(T) geometry, energy, and the a00 harmonic vibrational frequency of cis-HOSO (s = 0°) 6-31+G*
6-311G**
cc-pVTZ
r(H–O) r(O–S) r(S–O) h(HOS) h(OSO) Energy x6 (a00 )
0.9741 0.9684 0.9694 1.6813 1.6718 1.6518 1.5036 1.4903 1.4838 107.82 106.35 105.85 108.10 108.28 107.98 548.290656 548.377342 548.548056 112i 158i 78 ˚ , the bond angles are in degrees, the energies are The bond lengths are in A in Hartrees, and the vibrational frequencies are in cm1.
Table 2 CCSD(T) geometry, energy, and the a00 harmonic vibrational frequency of trans-HOSO (s = 180°) 6-31+G*
6-311G**
r(H–O) r(O–S) r(S–O) h(HOS) h(OSO) Energy x6 (a00 )
cc-pVTZ
0.9723 0.9658 0.9671 1.6928 1.6809 1.6613 1.4940 1.4816 1.4748 108.65 106.50 106.86 105.12 105.74 105.23 548.285420 548.371485 548.543793 192i 224i 120i ˚ , the bond angles are in degrees, the energies are The bond lengths are in A in Hartrees, and the vibrational frequencies are in cm1.
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B. Napolion, J.D. Watts / Chemical Physics Letters 421 (2006) 562–565
sitive to basis set than is the OSO angle. The HOS angles from 6-31+G* and 6-311G** differ by about 1.5°. To compare CCSD(T) and the simplest correlation method, i.e., MP2, we compare our CCSD(T)/6-311G** results for planar cis-HOSO with the MP2/6-311G** results ˚ , r(O–S) = 1.663 A ˚ , r(S– of Qi et al. [12]: r(H–O) = 0.965 A ˚ O) = 1.458 A, h(HOS) = 107.8° and h(OSO) = 107.2°. There is broad agreement, but some variation. The CCSD(T)/6-311G** bond lengths are slightly larger than the MP2 values. In particular, the CCSD(T) r(S–O) is ˚ larger than the MP2 value. One can also about 0.03 A compare the CCSD(T) results with the MP4 geometry of Isoniemi et al. [5]. Our CCSD(T)/6-311G** geometry for planar cis-HOSO is quite close to the MP4 geometry: ˚ , r(O–S) = 1.669 A ˚ , r(S–O) = 1.4852 A ˚, r(H–O) = 0.9698 A h(HOS) = 105.89° and h(OSO) = 108.85°. The out-of-plane bending frequencies in Table 1 are very interesting for several reasons. With the 6-31+G* and 6311G** basis sets, the CCSD(T) values of x6 are imaginary, implying that planar cis-HOSO is not a local minimum. That is, CCSD(T)/6-31+G* and CCSD(T)/6-311G** calculations indicate that cis-HOSO has a non-planar geometry with no symmetry elements. These results are in opposition to what is found in MP2 calculations with these basis sets, which yield real values of x6. They are also contrary to what is found in MP2 and MP4 calculations with the 6-311++G(2d,2p) basis set [5]. CCSD(T)/cc-pVTZ calculations, give a real x6, although the value is quite small. Evidently, there are subtle basis set and correlation effects in cis-HOSO beyond the previously noted tendency of uncorrelated calculations to indicate a non-planar geometry [9–12]. During the revision of the manuscript, we performed CCSD(T) calculations on planar cis-HOSO with the 6-311++G(2d,2p) and 6-311++G(3df,3pd) basis sets. The values obtained for x6 are 96i and 37i cm1, respectively. For a definitive answer on the planarity question, we anticipate that a basis set of at least cc-pVQZ quality is needed. The behavior of the out-of-plane bending frequency of planar trans-HOSO (Table 2) is more uniform than for planar cis-HOSO. With all basis sets, CCSD(T) calculations yield an imaginary x6. This is in accord with MP2 calculations [9–12]. Thus, there is general agreement that planar trans-HOSO is not a local minimum. From the energies in Tables 1 and 2, we can calculate the CCSD(T) relative energies of planar cis- and trans-HOSO. For the 6-31+G*, 6-311G**, and cc-pVTZ basis sets, the energies of trans-HOSO relative to cis-HOSO are 3.29, 3.68, and 2.68 kcal mol1, respectively. Having found that planar cis-HOSO is not a local minimum at the CCSD(T)/6-31+G* and 6-31G** levels, we next reoptimized the geometry allowing the H atom to move out of the plane of the molecule. The results are shown in Table 3. There are minor changes in the bond lengths. The changes in the bond angles are larger, but they are also small. The dihedral angle is apparently quite sensitive to basis set. The energy lowering on
Table 3 CCSD(T) geometries and energies of C1 cis-HOSO r(H–O) r(O–S) r(S–O) h(HOS) h(OSO) s Energy
6-31+G**
6-311G**
0.9736 1.6803 1.5031 108.50 108.56 26.80 548.290719
0.9675 1.6691 1.4894 107.87 109.16 39.77 548.377600
˚ , the bond angles are in degrees and the energies The bond lengths are in A are in Hartrees.
going to the non-planar C1 structures is very small (<0.2 kcal mol1). The CCSD(T) harmonic vibrational frequencies and infrared intensities of cis-HOSO are presented in Table 4, along with the Kr matrix data [6]. The 6-31+G** and 6311G** results are quite close. There are some quite significant changes in frequencies (>30 cm1) on going to the more complete cc-pVTZ basis set, and the results with this basis set are expected to be the most reliable. The calculated frequencies are harmonic frequencies of an isolated species, while the observed frequencies are anharmonic frequencies of a species in a Kr matrix. The observed frequencies are slightly smaller than the corresponding CCSD(T)/cc-pVTZ harmonic frequencies, namely 6%, 3%, 4%, and 1% for modes 1–4. Deviations of these magnitudes and this direction between calculated harmonic frequencies and observed frequencies are reasonable for an advanced correlated method with an extended basis set. By contrast, the MP2 and MP4 frequencies for modes 2 and 4 [5,6] are smaller than the observed values. Regarding the infrared intensities in Table 4, with the exception of the cc-pVTZ result for mode 6, CCSD(T) calculations predict mode 4 to be the most intense, while those of modes 1 and 2 are 40–60% smaller. The largest observed intensities are for modes 1 and 4, which are very close, while the intensity of mode 2 is about 20% smaller. MP2 calculations predict mode 2 to be the most intense band [5,6]. The CCSD(T) harmonic frequencies and intensities of HSO2 and the observed data were reported in Table 5. Table 4 CCSD(T) harmonic vibrational frequencies (cm1) and relative infrared intensities of cis-HOSO
x1 x2 x3 x4 x5 x6
6-31+G**
6-311G**
cc-pVTZ
Experiment
3780 (0.45) 1150 (0.58) 1074 (0.07) 738 (1.00) 376 (0.21) 138 (0.70)
3805 (0.43) 1152 (0.50) 1069 (0.11) 737 (1.00) 388 (0.27) 171 (0.71)
3761 (0.55) 1196 (0.56) 1098 (0.08) 783 (1.00) 379 (0.16) 78 (2.74)
3525 (0.99) 1164 (0.81) 1050a 773 (1.00)
For the first two basis sets, the geometries are the C1 geometries given in Table 3. The cc-pVTZ geometry is given in Table 1. Experimental data were the Kr matrix data from [6]. The scale factors for the calculated infrared intensities are 187.6, 162.8, and 168.4 km mol1 for the 6-31+G**, 6-311G**, and cc-pVTZ basis sets, respectively. a Tentative assignment from [5]; not included in [6].
B. Napolion, J.D. Watts / Chemical Physics Letters 421 (2006) 562–565 Table 5 CCSD(T) harmonic vibrational frequencies (cm1) and relative infrared intensities of HSO2 x1 x2 x3 x4 x5 x6
(a 0 ) (a 0 ) (a 0 ) (a 0 ) (a00 ) (a00 )
6-31+G**
6-311G**
cc-pVTZ
Experiment
2398 (0.14) 1011 (0.09) 794 (0.01) 431 (0.06) 1267 (1.00) 1044 (0.08)
2322 (0.44) 1028 (0.19) 818 (0.04) 441 (0.13) 1273 (1.00) 1041 (0.06)
2324 1073 810 453 1296 995
2142 (0.14) 1074 (0.24) 797 (0.04) 465 (0.21) 1281 (1.00) 958
Experimental data were the Kr matrix data from [6]. The scale factors for the calculated infrared intensities are 456.6 and 218.4 km mol1 for the 631+G** and 6-311G** basis sets, respectively.
The harmonic frequencies obtained with the cc-pVTZ basis set are in the best agreement with the observed frequencies. The observed Kr matrix frequencies for modes 1, 3, 5, and 6 are, respectively, 8%, 2%, 1%, and 4% smaller than the CCSD(T)/cc-pVTZ harmonic frequencies. The calculated frequencies of modes 2 and 4 are slightly smaller (1 and 12 cm1) than the observed values. Larger basis set calculations may give harmonic frequencies above the observed values for these modes. The CCSD(T)/cc-pVTZ frequencies account better for the observed frequencies than do the MP2 and MP4 results [5,6]. In particular for x5, and x6, MP2 and MP4 give somewhat higher values (1412 and 1377 cm1 (x5) and 1078 and 1041 cm1 (x6)). Concerning the relative infrared intensities, there is agreement on which is the most intense band, and fair agreement for the others. 4. Conclusion We report a CCSD(T) study of HOSO and HSO2, including geometry optimizations and vibrational frequency and infrared intensity calculations. We have found that the issue of the planarity of cis-HOSO is very sensitive to basis set and remains an open question. However, the energy difference between planar and non-planar structures is very small. The CCSD(T) frequencies and infrared intensities provide further support for the observation of cisHOSO and HSO2 in rare gas matrices [5,6]. Acknowledgments This study was supported by the National Science Foundation (NSF300423-190200-21000), the National Institutes of Health (S06 GM08047), and the Louis Stokes MAMP program. Computer facilities were provided by the Army
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High Performance Computing Research Center. The content of this Letter does not necessarily reflect the position or policy of the United States government, and no official endorsement should be inferred. Basis sets in ACES II were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 1.0, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory, which is part of the Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, and funded by the US Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute for the US Department of Energy under contract DE-AC06-76RLO 1830. Contact David Feller, Karen Schuchardt, or Don Jones for further information. References [1] G.S. Tyndall, A.R. Ravishankara, Int. J. Chem. Kinet. 23 (1991) 483. [2] C.A. McDowell, F.G. Herring, J.C. Tait, J. Chem. Phys. 63 (1975) 3278. [3] A.J. Frank, M. Sadı´lek, J.G. Ferrier, F. Turecˇek, J. Am. Chem. Soc. 118 (1996) 11321. [4] A.J. Frank, M. Sadı´lek, J.G. Ferrier, F. Turecˇek, J. Am. Chem. Soc. 119 (1997) 12343. [5] E. Isoniemi, L. Khriachtchev, J. Lundell, M. Ra¨sa¨nen, J. Mol. Struct. 563–564 (2001) 261. [6] E. Isoniemi, L. Khriachtchev, J. Lundell, M. Ra¨sa¨nen, Phys. Chem. Chem. Phys. 4 (2002) 1549. [7] R.J. Boyd, A. Gupta, R.F. Longler, S.P. Lowrie, J.A. Pincock, Can. J. Chem. 58 (1980) 331. [8] A. Hinchliffe, J. Mol. Struct. 71 (1981) 349. [9] D. Binns, P. Marshall, J. Chem. Phys. 95 (1991) 4940. [10] V.R. Morris, W.M. Jackson, Chem. Phys. Lett. 223 (1994) 445. [11] D. Laakso, C.E. Smith, A. Goumri, J.R. Rocha, P. Marshall, Chem. Phys. Lett. 227 (1994) 377. [12] J.-X. Qi, W.-Q. Deng, K.-L. Han, G.-Z. He, J. Chem. Soc., Faraday Trans. 93 (1997) 25. [13] M.Y. Ballester, A.J.C. Varandas, Phys. Chem. Chem. Phys. 7 (2005) 2305. [14] B. Wang, H. Hou, Chem. Phys. Lett. 410 (2005) 235. [15] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479. [16] G.D. Purvis III, R.J. Bartlett, J. Chem. Phys. 76 (1982) 1910. [17] J.M.L. Martin, J. Chem. Phys. 100 (1994) 8186. [18] T.J. Lee, G.E. Scuseria, in: S.R. Langhoff (Ed.), Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, Kluwer Academic, Dordrecht, 1994, p. 47. [19] R.J. Bartlett, in: D.R. Yarkony (Ed.), Modern Electronic Structure Theory, Part 1, World Scientific, Singapore, 1995, p. 1047. [20] J.F. Stanton, J. Gauss, J.D. Watts, W.J. Lauderdale, R.J. Bartlett, Int. J. Quantum Chem. Symp. 26 (1992) 879.
A coupled-cluster study of the HOSO and HSO2 radicals Brian Napolion, John D. Watts
*
Computational Center for Molecular Structure and Interactions, Department of Chemistry, Jackson State University, 1400 J.R. Lynch Street, P.O. Box 17910 Jackson, MS 39217, United States Received 1 November 2005; in final form 25 January 2006 Available online 9 March 2006
Abstract CCSD(T) calculations with triple-zeta valence plus polarization basis sets have been performed on HOSO and HSO2 to determine structures, vibrational frequencies, and infrared intensities for the first time with coupled-cluster methods. It is found that the planarity of HOSO is very sensitive to basis set. The calculated frequencies and intensities offer further support for the identification of HOSO and HSO2 in rare gas matrices. Ó 2006 Elsevier B.V. All rights reserved.
1. Introduction Chemical species having the formula HSO2 have been of interest for some time as possible intermediates in the atmospheric and combustion chemistry of sulfur-containing compounds [1]. Limited experimental information is available on isomers of HSO2. McDowell et al. [2] obtained ESR data on what was thought to be the HSO2 isomer, i.e., a species with the hydrogen bonded to the sulfur. Frank et al. [3,4] have identified HSO2 and HOSO using mass spectrometry. Isoniemi et al. [5,6] have obtained infrared evidence for the formation of HSO2 and HOSO following UV irradiation of H2S and SO2 mixtures in rare gas matrices. Other isomers, namely HSOO and HOOS have apparently not been detected experimentally. A large number of theoretical studies have been performed with the goal of characterizing the various isomers of HSO2 [3–14]. The consensus of the calculations is that the most stable species is the cis conformer of HOSO. The next most stable species is HSO2, having Cs symmetry, while HSOO and HOOS are somewhat higher in energy. Less certain is whether planar cis-HOSO is a local minimum.
*
Corresponding author. Fax: +1 601 979 3674. E-mail address: [email protected] (J.D. Watts).
0009-2614/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.01.103
Binns and Marshall [9] performed geometry optimizations of planar cis-HOSO (constraining the dihedral angle s to be 0°) and planar trans-HOSO (s = 180°), and calculated harmonic vibrational frequencies at the HF/3-21G* and MP2/3-21G* levels. The HF/3-21G* a00 frequency of planar cis-HOSO is imaginary, while the MP2/3-21G* a00 frequency is real. For planar trans-HOSO both HF/321G* and MP2/3-21G* yield an imaginary a00 frequency. Subsequently, Morris and Jackson [10] found planar cisand trans-HOSO to be local minima at the MP2/DZP level. About the same time, Laakso et al. [11] found that planar cis-HOSO is a local minimum at the MP2/6-31G* level. In 1997, Frank et al. [3,4] found that both planar cis- and trans-HOSO are local minima at the MP2/6-31+G** level. Also in 1997, Qi et al. [12] performed MP2/6-311G** calculations on planar cis-HOSO and found it to be a local minimum at this level. In 2001, Isoniemi et al. [5] reported geometry optimizations and vibrational frequency calculations on HSO2 and cis- and trans-HOSO with MP2 and MP4 using the 6-311++G(2d,2p) basis set. Planar cisHOSO was found to be a local minimum in both sets of calculations. Planar trans-HOSO was found to be a transition state. The harmonic vibrational frequencies of both HSO2 and cis-HOSO matched the infrared bands observed following UV irradiation of H2S/SO2 mixtures in a Kr matrix. This work was later extended, including isotopic shifts and other rare gas matrices [6]. Very recently,
B. Napolion, J.D. Watts / Chemical Physics Letters 421 (2006) 562–565
Ballester and Varandas [13] have developed a double many-body expansion for the potential energy surface of HSO2. This work included full-valence complete active space (FVCAS) calculations with the aug-cc-pVDZ and aug-cc-PVTZ basis sets. Interestingly, this work found the cis-HOSO species to be planar with the aug-cc-pVDZ basis set, but slightly non-planar (s = 12.8°) with the augcc-pVTZ basis set. As part of a study of the SO2+HO2 reaction, Wang and Hou [14] performed a B3LYP/augcc-pV(T+d)Z geometry optimization of cis-HOSO, although the dihedral angle was not explicitly stated. Also, no comments were made about vibrational frequencies. This Letter reports the first coupled-cluster study of cisand trans-HOSO that includes geometry optimizations and harmonic vibrational frequency calculations. The aims of these calculations are to address whether planar cis-HOSO and trans-HOSO are local minima or not, to further characterize these species, and to compare CCSD(T) harmonic vibrational frequencies and infrared intensities with data obtained in rare gas matrices [5,6]. In addition, CCSD(T) frequencies and infrared intensities have been obtained for HSO2 species and compared with experimental data [5,6]. 2. Computational methods Geometry optimizations and harmonic vibrational frequency calculations have been performed on the HOSO and HSO2 isomers using the CCSD(T) method [15] and several basis sets. The CCSD(T) method includes singleand double-excitation clusters iteratively (the CCSD method [16]). Using CCSD amplitudes, a perturbative estimate of the effects of connected triple excitations is then made. The CCSD(T) method is complete through fourthorder terms, and it also includes the fifth-order singles–triples terms. In the absence of large multi-reference effects, the CCSD(T) method is a highly reliable method for structure, energetics, and other molecular properties [17–19]. Based on the CCSD wave functions, the species studied in this work do not have significant multi-reference character, so the CCSD(T) method should be suitable for this study. Since spin contamination was found to be very small at the SCF level, and even less at the correlated level, unrestricted Hartree–Fock (UHF) reference functions were used throughout this work. In all calculations, the core electrons were not correlated. All calculations were performed using the ACES II program [20], a product of the Quantum Theory Project, University of Florida. Authors: J.F. Stanton, J. Gauss, J.D. Watts, M. Nooijen, N. Oliphant, S.A. Perera, P.G. Szalay, W.J. Lauderdale, S.R. Gwaltney, S. Beck, A. Balkova´, D.E. Bernholdt, K.-K. Baeck, P. Rozyczko, H. Sekino, C. Huber, and R.J. Bartlett. Integral packages are VMOL (J. Almlo¨f and P.R. Taylor); VPROPS (P.R. Taylor) and ABACUS (T. Helgaker, H.J.Aa. Jensen, P. Jørgensen, J. Olsen, and P.R. Taylor). The basis sets used are the 6-31+G**, 6-311G**, and ccpVTZ basis sets. The first of these is a double-zeta valence
563
set, augmented with diffuse sp functions on O and S and a set of polarization functions (p on H, d on O and S) on each atom. The second is a triple-zeta valence basis set augmented with a set of polarization functions on all atoms. The cc-pVTZ basis set is a correlation-consistent polarized valence triple-zeta basis set. It contains 2p 1d polarization functions on H and 2d 1f polarization functions on O and S. The 6-31+G** and 6-311G** were used with Cartesian d functions, while for the cc-pVTZ basis set, real spherical harmonic d and f functions were used. 3. Results and discussion CCSD(T) geometry optimizations were performed on the ground state (2A00 ) of planar cis-HOSO and transHOSO. The harmonic vibrational frequencies were then calculated. The geometries, energies, and the out-of-plane harmonic vibrational frequencies (x6) are shown in Tables 1 and 2. From Tables 1 and 2, one can see that the basis set effects on the bond lengths of cis- and trans-HOSO follow the usual trend as the valence and polarization spaces are expanded. r(O–S) and r(S–O) decrease on going from 631+G* to 6-311G** and from 6-311G** to cc-pVTZ. The ˚ decrease in r(O–S) on going largest effect is the 0.02 A from 6-311G** to cc-pVTZ. r(H–O) decreases by less than ˚ on going from 6-31+G* to 6-311G**, but increases 0.01 A slightly on going to cc-pVTZ. The HOS angle is more sen-
Table 1 CCSD(T) geometry, energy, and the a00 harmonic vibrational frequency of cis-HOSO (s = 0°) 6-31+G*
6-311G**
cc-pVTZ
r(H–O) r(O–S) r(S–O) h(HOS) h(OSO) Energy x6 (a00 )
0.9741 0.9684 0.9694 1.6813 1.6718 1.6518 1.5036 1.4903 1.4838 107.82 106.35 105.85 108.10 108.28 107.98 548.290656 548.377342 548.548056 112i 158i 78 ˚ , the bond angles are in degrees, the energies are The bond lengths are in A in Hartrees, and the vibrational frequencies are in cm1.
Table 2 CCSD(T) geometry, energy, and the a00 harmonic vibrational frequency of trans-HOSO (s = 180°) 6-31+G*
6-311G**
r(H–O) r(O–S) r(S–O) h(HOS) h(OSO) Energy x6 (a00 )
cc-pVTZ
0.9723 0.9658 0.9671 1.6928 1.6809 1.6613 1.4940 1.4816 1.4748 108.65 106.50 106.86 105.12 105.74 105.23 548.285420 548.371485 548.543793 192i 224i 120i ˚ , the bond angles are in degrees, the energies are The bond lengths are in A in Hartrees, and the vibrational frequencies are in cm1.
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sitive to basis set than is the OSO angle. The HOS angles from 6-31+G* and 6-311G** differ by about 1.5°. To compare CCSD(T) and the simplest correlation method, i.e., MP2, we compare our CCSD(T)/6-311G** results for planar cis-HOSO with the MP2/6-311G** results ˚ , r(O–S) = 1.663 A ˚ , r(S– of Qi et al. [12]: r(H–O) = 0.965 A ˚ O) = 1.458 A, h(HOS) = 107.8° and h(OSO) = 107.2°. There is broad agreement, but some variation. The CCSD(T)/6-311G** bond lengths are slightly larger than the MP2 values. In particular, the CCSD(T) r(S–O) is ˚ larger than the MP2 value. One can also about 0.03 A compare the CCSD(T) results with the MP4 geometry of Isoniemi et al. [5]. Our CCSD(T)/6-311G** geometry for planar cis-HOSO is quite close to the MP4 geometry: ˚ , r(O–S) = 1.669 A ˚ , r(S–O) = 1.4852 A ˚, r(H–O) = 0.9698 A h(HOS) = 105.89° and h(OSO) = 108.85°. The out-of-plane bending frequencies in Table 1 are very interesting for several reasons. With the 6-31+G* and 6311G** basis sets, the CCSD(T) values of x6 are imaginary, implying that planar cis-HOSO is not a local minimum. That is, CCSD(T)/6-31+G* and CCSD(T)/6-311G** calculations indicate that cis-HOSO has a non-planar geometry with no symmetry elements. These results are in opposition to what is found in MP2 calculations with these basis sets, which yield real values of x6. They are also contrary to what is found in MP2 and MP4 calculations with the 6-311++G(2d,2p) basis set [5]. CCSD(T)/cc-pVTZ calculations, give a real x6, although the value is quite small. Evidently, there are subtle basis set and correlation effects in cis-HOSO beyond the previously noted tendency of uncorrelated calculations to indicate a non-planar geometry [9–12]. During the revision of the manuscript, we performed CCSD(T) calculations on planar cis-HOSO with the 6-311++G(2d,2p) and 6-311++G(3df,3pd) basis sets. The values obtained for x6 are 96i and 37i cm1, respectively. For a definitive answer on the planarity question, we anticipate that a basis set of at least cc-pVQZ quality is needed. The behavior of the out-of-plane bending frequency of planar trans-HOSO (Table 2) is more uniform than for planar cis-HOSO. With all basis sets, CCSD(T) calculations yield an imaginary x6. This is in accord with MP2 calculations [9–12]. Thus, there is general agreement that planar trans-HOSO is not a local minimum. From the energies in Tables 1 and 2, we can calculate the CCSD(T) relative energies of planar cis- and trans-HOSO. For the 6-31+G*, 6-311G**, and cc-pVTZ basis sets, the energies of trans-HOSO relative to cis-HOSO are 3.29, 3.68, and 2.68 kcal mol1, respectively. Having found that planar cis-HOSO is not a local minimum at the CCSD(T)/6-31+G* and 6-31G** levels, we next reoptimized the geometry allowing the H atom to move out of the plane of the molecule. The results are shown in Table 3. There are minor changes in the bond lengths. The changes in the bond angles are larger, but they are also small. The dihedral angle is apparently quite sensitive to basis set. The energy lowering on
Table 3 CCSD(T) geometries and energies of C1 cis-HOSO r(H–O) r(O–S) r(S–O) h(HOS) h(OSO) s Energy
6-31+G**
6-311G**
0.9736 1.6803 1.5031 108.50 108.56 26.80 548.290719
0.9675 1.6691 1.4894 107.87 109.16 39.77 548.377600
˚ , the bond angles are in degrees and the energies The bond lengths are in A are in Hartrees.
going to the non-planar C1 structures is very small (<0.2 kcal mol1). The CCSD(T) harmonic vibrational frequencies and infrared intensities of cis-HOSO are presented in Table 4, along with the Kr matrix data [6]. The 6-31+G** and 6311G** results are quite close. There are some quite significant changes in frequencies (>30 cm1) on going to the more complete cc-pVTZ basis set, and the results with this basis set are expected to be the most reliable. The calculated frequencies are harmonic frequencies of an isolated species, while the observed frequencies are anharmonic frequencies of a species in a Kr matrix. The observed frequencies are slightly smaller than the corresponding CCSD(T)/cc-pVTZ harmonic frequencies, namely 6%, 3%, 4%, and 1% for modes 1–4. Deviations of these magnitudes and this direction between calculated harmonic frequencies and observed frequencies are reasonable for an advanced correlated method with an extended basis set. By contrast, the MP2 and MP4 frequencies for modes 2 and 4 [5,6] are smaller than the observed values. Regarding the infrared intensities in Table 4, with the exception of the cc-pVTZ result for mode 6, CCSD(T) calculations predict mode 4 to be the most intense, while those of modes 1 and 2 are 40–60% smaller. The largest observed intensities are for modes 1 and 4, which are very close, while the intensity of mode 2 is about 20% smaller. MP2 calculations predict mode 2 to be the most intense band [5,6]. The CCSD(T) harmonic frequencies and intensities of HSO2 and the observed data were reported in Table 5. Table 4 CCSD(T) harmonic vibrational frequencies (cm1) and relative infrared intensities of cis-HOSO
x1 x2 x3 x4 x5 x6
6-31+G**
6-311G**
cc-pVTZ
Experiment
3780 (0.45) 1150 (0.58) 1074 (0.07) 738 (1.00) 376 (0.21) 138 (0.70)
3805 (0.43) 1152 (0.50) 1069 (0.11) 737 (1.00) 388 (0.27) 171 (0.71)
3761 (0.55) 1196 (0.56) 1098 (0.08) 783 (1.00) 379 (0.16) 78 (2.74)
3525 (0.99) 1164 (0.81) 1050a 773 (1.00)
For the first two basis sets, the geometries are the C1 geometries given in Table 3. The cc-pVTZ geometry is given in Table 1. Experimental data were the Kr matrix data from [6]. The scale factors for the calculated infrared intensities are 187.6, 162.8, and 168.4 km mol1 for the 6-31+G**, 6-311G**, and cc-pVTZ basis sets, respectively. a Tentative assignment from [5]; not included in [6].
B. Napolion, J.D. Watts / Chemical Physics Letters 421 (2006) 562–565 Table 5 CCSD(T) harmonic vibrational frequencies (cm1) and relative infrared intensities of HSO2 x1 x2 x3 x4 x5 x6
(a 0 ) (a 0 ) (a 0 ) (a 0 ) (a00 ) (a00 )
6-31+G**
6-311G**
cc-pVTZ
Experiment
2398 (0.14) 1011 (0.09) 794 (0.01) 431 (0.06) 1267 (1.00) 1044 (0.08)
2322 (0.44) 1028 (0.19) 818 (0.04) 441 (0.13) 1273 (1.00) 1041 (0.06)
2324 1073 810 453 1296 995
2142 (0.14) 1074 (0.24) 797 (0.04) 465 (0.21) 1281 (1.00) 958
Experimental data were the Kr matrix data from [6]. The scale factors for the calculated infrared intensities are 456.6 and 218.4 km mol1 for the 631+G** and 6-311G** basis sets, respectively.
The harmonic frequencies obtained with the cc-pVTZ basis set are in the best agreement with the observed frequencies. The observed Kr matrix frequencies for modes 1, 3, 5, and 6 are, respectively, 8%, 2%, 1%, and 4% smaller than the CCSD(T)/cc-pVTZ harmonic frequencies. The calculated frequencies of modes 2 and 4 are slightly smaller (1 and 12 cm1) than the observed values. Larger basis set calculations may give harmonic frequencies above the observed values for these modes. The CCSD(T)/cc-pVTZ frequencies account better for the observed frequencies than do the MP2 and MP4 results [5,6]. In particular for x5, and x6, MP2 and MP4 give somewhat higher values (1412 and 1377 cm1 (x5) and 1078 and 1041 cm1 (x6)). Concerning the relative infrared intensities, there is agreement on which is the most intense band, and fair agreement for the others. 4. Conclusion We report a CCSD(T) study of HOSO and HSO2, including geometry optimizations and vibrational frequency and infrared intensity calculations. We have found that the issue of the planarity of cis-HOSO is very sensitive to basis set and remains an open question. However, the energy difference between planar and non-planar structures is very small. The CCSD(T) frequencies and infrared intensities provide further support for the observation of cisHOSO and HSO2 in rare gas matrices [5,6]. Acknowledgments This study was supported by the National Science Foundation (NSF300423-190200-21000), the National Institutes of Health (S06 GM08047), and the Louis Stokes MAMP program. Computer facilities were provided by the Army
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High Performance Computing Research Center. The content of this Letter does not necessarily reflect the position or policy of the United States government, and no official endorsement should be inferred. Basis sets in ACES II were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 1.0, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory, which is part of the Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, and funded by the US Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute for the US Department of Energy under contract DE-AC06-76RLO 1830. Contact David Feller, Karen Schuchardt, or Don Jones for further information. References [1] G.S. Tyndall, A.R. Ravishankara, Int. J. Chem. Kinet. 23 (1991) 483. [2] C.A. McDowell, F.G. Herring, J.C. Tait, J. Chem. Phys. 63 (1975) 3278. [3] A.J. Frank, M. Sadı´lek, J.G. Ferrier, F. Turecˇek, J. Am. Chem. Soc. 118 (1996) 11321. [4] A.J. Frank, M. Sadı´lek, J.G. Ferrier, F. Turecˇek, J. Am. Chem. Soc. 119 (1997) 12343. [5] E. Isoniemi, L. Khriachtchev, J. Lundell, M. Ra¨sa¨nen, J. Mol. Struct. 563–564 (2001) 261. [6] E. Isoniemi, L. Khriachtchev, J. Lundell, M. Ra¨sa¨nen, Phys. Chem. Chem. Phys. 4 (2002) 1549. [7] R.J. Boyd, A. Gupta, R.F. Longler, S.P. Lowrie, J.A. Pincock, Can. J. Chem. 58 (1980) 331. [8] A. Hinchliffe, J. Mol. Struct. 71 (1981) 349. [9] D. Binns, P. Marshall, J. Chem. Phys. 95 (1991) 4940. [10] V.R. Morris, W.M. Jackson, Chem. Phys. Lett. 223 (1994) 445. [11] D. Laakso, C.E. Smith, A. Goumri, J.R. Rocha, P. Marshall, Chem. Phys. Lett. 227 (1994) 377. [12] J.-X. Qi, W.-Q. Deng, K.-L. Han, G.-Z. He, J. Chem. Soc., Faraday Trans. 93 (1997) 25. [13] M.Y. Ballester, A.J.C. Varandas, Phys. Chem. Chem. Phys. 7 (2005) 2305. [14] B. Wang, H. Hou, Chem. Phys. Lett. 410 (2005) 235. [15] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479. [16] G.D. Purvis III, R.J. Bartlett, J. Chem. Phys. 76 (1982) 1910. [17] J.M.L. Martin, J. Chem. Phys. 100 (1994) 8186. [18] T.J. Lee, G.E. Scuseria, in: S.R. Langhoff (Ed.), Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, Kluwer Academic, Dordrecht, 1994, p. 47. [19] R.J. Bartlett, in: D.R. Yarkony (Ed.), Modern Electronic Structure Theory, Part 1, World Scientific, Singapore, 1995, p. 1047. [20] J.F. Stanton, J. Gauss, J.D. Watts, W.J. Lauderdale, R.J. Bartlett, Int. J. Quantum Chem. Symp. 26 (1992) 879.