Fundamental Vibrational Frequencies and Spectroscopic Constants of

Article pubs.acs.org/JPCB

Fundamental Vibrational Frequencies and Spectroscopic Constants of cis- and trans-HOCS, HSCO, and Isotopologues via Quartic Force Fields Ryan C. Fortenberry,*,†,⊥ Xinchuan Huang,‡ Michael C. McCarthy,¶ T. Daniel Crawford,§ and Timothy J. Lee*,⊥ †

Department of Chemistry, Georgia Southern University, Statesboro, Georgia 30460, United States SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain View, California 94043, United States ¶ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, United States § Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States ⊥ NASA Ames Research Center, Moffett Field, California 94035-1000, United States ‡

S Supporting Information *

ABSTRACT: Highly accurate, coupled-cluster-based quartic force fields (QFFs) have been employed recently to provide spectroscopic reference for a myriad of molecules. Here, we are extending the same approach to provide vibrational and rotational spectroscopic reference data for the sulfur analogues of HOCO, HSCO, and HOCS, in both the cis and trans conformations as well as the D and 34S isotopologues of each system. The resulting energies corroborate previous computations showing that trans-HSCO is the lowest-energy isomer for this system. The vibrational frequencies are computed with both second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) methods. The VPT2 and VCI QFF frequencies largely agree with one another to better than 5.0 cm−1 (often better than 1.0 cm−1) and are also consistent with the type of behavior exhibited in previous studies. As such, the reference data provided here should assist in analysis of environments in which these sulfur systems may be found, including the interstellar medium, combustion flames, or laboratory simulations of either.

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3375.37413 cm−1, a difference of less than 1 cm−1.12 Additionally, experiment and VCI QFF computations both report the O−H stretch of NNOH+ to be 3330.9 cm−1.16 Furthermore, the B- and C-type rotational constants are also within 20 MHz or better of their corresponding experimental values for HOCO+ as well as cis- and trans-HOCO, HSCS+, NNOH+, and HNNO+.10,11,15,17,18 Hence, computational approaches that employ QFFs are now capable of generating spectroscopic reference data of sufficient accuracy to aid/guide laboratory and astronomical detection. Recently, this approach has been extended to systems where little or inadequate reference data has been available including HOCS+ and HSCO+, singly substituted sulfur analogues of HOCO+,19 as well as C3H+ and C3H− (refs 20 and 21). HOCS+ and HSCO+ have been postulated to exist in the ISM,22,23 but a positive detection has not been reported. Similarly, HOCS and HSCO are also viable candidates for

INTRODUCTION Sulfur-containing compounds are well-known to exist in interstellar environments1−5 as well as terrestrial combustion flames.6,7 However, detections of sulfur compounds in new flame environments or interstellar sulfur species can only be confirmed through spectroscopic analysis with adequate reference data. Quantum chemical computations have long been employed in the prediction of reference data for the detection of terrestrially unstable combustion intermediates or interstellar molecules, but recent advances have pushed the expected accuracy for these computed results into the spectroscopic (1 cm−1) domain for many vibrational fundamentals, while the accuracy may be in the few cm−1 range for vibrational modes that are either very anharmonic or possess a significant resonance. The HOCO cation8 is known to exist in the interstellar medium (ISM), and recent quantum chemical studies have provided a wealth of spectroscopic data on this molecule and its closely related radical and anion.9−15 Most notably, the ν1 O−H stretching frequency of HOCO+ has been computed through the use of coupled cluster theory, quartic force fields (QFFs), and vibrational configuration interaction (VCI) computations to be 3376.2 cm−1, while experiment places this value at © 2014 American Chemical Society

Special Issue: William C. Swope Festschrift Received: December 17, 2013 Revised: March 14, 2014 Published: March 17, 2014 6498

dx.doi.org/10.1021/jp412362h | J. Phys. Chem. B 2014, 118, 6498−6510

The Journal of Physical Chemistry B

Article

Table 1. Minimum-Energy Structures (in Å and degrees), Rotational Constants (in cm−1), and Dipole Momentsa for trans- and cis-HOCS with the CcCR QFF zero-point trans-HOCS

cis-HOCS

R(C−S) R(C−O) R(O−H) ∠O−C−S ∠H−O−C A0/e B0/e C0/e μ μA μB R(C−S) R(C−O) R(O−H) ∠O−C−S ∠H−O−C A0/e B0/e C0/e μ μA μB

equilibrium

standard

deuterated

HOC34S

this work

Rice et al.b

Lo et al.c

1.58381 1.32240 0.95831 131.877 108.799 5.10897 0.20059 0.19278

1.58352 1.32224 0.96113 131.863 108.637 4.85136 0.28865 0.18140

1.58377 1.32239 0.95828 131.877 108.800 5.09606 0.19567 0.18821

1.58799 1.30927 0.971 22 136.093 110.975 4.39285 0.20302 0.19380

1.58900 1.31144 0.986 26 136.034 110.303 3.37842 0.19731 0.18618

1.58796 1.30926 0.971 20 136.092 110.976 4.38164 0.19800 0.18920

1.57963 1.31625 0.96287 131.913 108.628 5.05810 0.20164 0.19390 2.27 D 2.18 D 0.63 D 1.58421 1.30488 0.971 32 135.896 112.4 4.33235 0.20425 0.19504 1.96 D 0.87 D 1.75 D

1.5861 1.3138 0.9664 132.1 110.0 − − − − − − 1.5900 1.2999 0.9774 136.9 110.276 − − − − − −

− − − − − − − − − − − 1.593 1.301 0.978 136.68 112.28 − − − − − −

a

Dipole moments are computed at the CCSD(T)/aug-cc-pV5Z level of theory. bB3LYP/6-311+G(2df,2p) data from ref 27. cB3LYP/aug-cc-pVTZ data from ref 28.

detection in space, and the related HOSO radical is believed to be present in combustion flames.7,24 The HOCS and HSCO potential energy surfaces are slightly more complicated than their corresponding cations. Like HOCO+, HOCS+ and HSCO+ both only exist as trans conformers with the heavy-atom bond angle approaching 180°.12,19,25 The radicals, however, exhibit both cis and trans minima on the potential energy surface, similar to HOCO (ref 26) and give rise to a total of four possible isomers. Previous QCISD(T)//UMP2/6-311+G(2df,2p) computations by Rice, Pai, and Chabalowski27 indicate that the trans-HSCO is the most stable isomer. The cis-HSCO conformer is 2.1 kcal/mol higher in energy with an energy barrier to conformational twisting at 4.0 kcal/mol higher than that for trans-HSCO. The HOCS conformers are nearly degenerate according to this study, with the trans conformer 0.6 kcal/mol lower in energy than the cis but with a 10.0 kcal/mol conformational barrier. Following from this, trans-HOCS is 15.2 kcal/mol higher in energy than the global minimum of trans-HSCO. The computational work by Rice, Pai, and Chabalowski was followed later by Lo et al.,28 who were able to assign Ar matrix reference frequencies to the C−O and C−S stretches as well as the H−S−C bend of trans-HSCO. They also report B3LYP/augcc-pVTZ harmonic vibrational frequencies for trans-HSCO, cis-HSCO, and cis-HOCS. However, complete, highly accurate data for these systems has yet to be calculated; one of the primary objectives of the present study is to provide this information for cis- and trans-HOCS and HSCO. This reference data for the sulfur analogues of HOCO should assist in their interstellar detection possibly from observatories such as the Stratospheric Observeratory For Infrared Astronomy (SOFIA), Atacama Large Millimeter Array (ALMA), or the upcoming James Webb Space Telescope (JWST). Additionally, spectral analysis of combustion flames or gas-phase laboratory studies should also benefit from

availability of this new data. Other conceivable isomers such as “T”-shaped structures or van der Waal’s complexes (like those known for HOCO29) are possible with the tetraatomic combinations of single hydrogen, sulfur, oxygen, and carbon atoms, but we are limiting ourselves to cis- and trans-HOCS and HSCO for the present study.

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COMPUTATIONAL DETAILS The QFF procedure originially developed by Huang and Lee30 and implemented in the aforementioned studies is utilized here, as well. In short, the restricted open-shell31−33 coupled cluster singles doubles and perturbative triples,34 CCSD(T), level of theory is used to compute the reference geometry for each of the four HOCS/HSCO minima with a Dunning35,36 five-zeta basis set, cc-pV5Z. The sulfur atoms require the use of additional d functions in the basis. As such, we are using the cc-pV(5+d)Z basis set37 for sulfur, and it should be understood that any Dunning basis set reported in the rest of this work utilizes the additional d functions for the sulfur atom. The geometrical parameters are further corrected for core correlation effects by adding the differences between CCSD(T) geometries computed with the Martin−Taylor (MT) basis set38 with and without core electrons included in the computation. The MT basis for the sulfur atoms was first implemented in ref 19. From this reference geometry, a grid of 743 symmetry-unique points is created with displacements of 0.005 Å for the bond lengths and 0.005 radians for the bond angles and torsion. The six coordinates correspond to the H−X bond length, X−C bond length, C−Y bond length, H−X−C bond angle, X−C−Y bond angle, and the four-atom torsion, with X = O and Y = S for HOCS, while the converse is true for HSCO. At each point, CCSD(T)/aug-cc-pVXZ (for X = T, Q, 5; ref 39) energies are 6499



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Table 2. The CcCR Vibration−Rotation Interaction Constants, Quartic and Sextic Centrifugal Distortion Constants, and S Reduced Hamiltonian Terms for trans- and cis-HOCS, DOCS, and HOC34S vib−rot constants (MHz)

Watson S reduction

distortion constants

mode

αA

αB

αC

trans-HOCS

1 2 3 4 5 6

1024.1 3134.3 −2167.7 −3331.4 2685.5 −4394.8

1.8 18.1 10.0 28.9 8.2 −4.5

2.9 22.0 13.1 27.2 1.4 0.5

τ′aaaa τ′bbbb τ′cccc τ′aabb τ′aacc τ′bbcc

−135.820 −0.011 −0.008 0.603 0.472 −0.009

trans-DOCS

1 2 3 4 5 6

907.7 3681.2 −3319.5 −2917.2 −3138.2 2799.1

5.1 22.1 16.2 12.6 −12.3 10.4

5.7 22.9 20.7 13.3 0.2 −4.4


−99.099 −0.009 −0.007 0.413 0.346 −0.008

trans-HOC34S

1 2 3 4 5 6

1016.7 3112.1 −2145.5 −3411.1 2718.7 −4327.7

1.8 17.6 9.9 28.1 8.0 −4.5

2.8 21.3 12.7 26.6 1.5 0.3


−135.282 −0.011 −0.008 0.587 0.464 −0.009

cis-HOCS

1 2 3 4 5 6

−325.4 3026.7 −1164.1 −2356.6 1001.0 −3792.4

3.2 23.5 5.1 30.0 13.5 −1.9

2.1 27.4 11.1 28.4 2.7 2.8


−81.150 −0.012 −0.008 0.473 0.291 −0.010

cis-DOCS

1 2 3 4 5 6

492.6 1946.5 −1665.9 −677.4 −2296.4 847.9

2.0 22.0 13.9 18.8 13.3 −3.7

2.9 22.9 19.7 20.6 0.4 2.6


−33.090 −0.012 −0.008 0.249 0.260 −0.010

cis-HOC34S

1 2 3 4 5 6

−329.7 3007.0 −1147.4 −2417.3 1024.2 −3732.8

3.2 22.9 5.1 29.2 13.0 −2.0

2.1 26.5 10.9 27.7 2.7 2.5


−80.781 −0.012 −0.008 0.461 0.384 −0.010

(MHz)

(Hz) Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc 6500

2.364 0.003 0.001 −96.605 −0.127 −95.758 0.003 −0.044 0.002 −0.400 1.233 0.002 0.001 −43.426 −0.158 −53.112 0.002 0.002 0.002 −0.339 2.352 0.003 0.001 −94.022 −0.118 −93.584 0.003 −0.041 0.002 −0.367 1.085 0.004 0.001 −58.356 −0.032 −67.503 0.003 −0.084 0.002 −0.208 2396.720 0.004 0.001 −13.853 −0.046 −29.998 0.004 0.073 0.003 −0.124 1.078 0.003 0.001 −56.724 −0.029 −65.831 0.003 −0.080 0.002 −0.187

(MHz)

(Hz)

× 104

103 DJ DJK DK 103 d1 106 d2

2.426 −0.274 34.226 −0.208 −4.816

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

22.696 −0.181 −191.993 2.383 × 104 0.579 28.626 6.413

× 104

103 DJ DJK DK 103 d1 106 d2

1.984 −0.194 24.966 −0.257 −4.079

103HJ HJK HKJ HK 103 h1 106 h2 106 h3

1.591 −0.217 −96.956 1.243 × 104 0.387 18.932 4.246

× 104

103 DJ DJK DK 103 d1 106 d2

2.313 −0.267 34.086 −0.195 −4.417

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

2.114 −0.167 −187.265 2.372 × 104 0.529 25.729 5.635

× 104

103 DJ DJK DK 103 d1 106 d2

2.603 −0.221 20.506 −0.251 −7.189

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

2.363 −0.035 −125.777 1.097 × 104 0.633 44.415 8.712

103 DJ DJK DK 103 d1 106 d2

2.614 −0.132 8.402 −0.286 −12.148

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

2.518 −0.039 −43.753 2440.510 0.687 70.972 12.807

103 DJ DJK DK 103 d1 106 d2

2.480 −0.216 20.409 −0.234 −6.592

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

2.197 −0.029 −122.485 1.090 × 104 0.577 39.803 7.651

× 104



Article

Table 3. Quadratic, Cubic, and Quartic Force Constants (in mdyn/Ån·radm)a for trans-HOCS in the Defined Internal Coordinate Systemb for the CcCR QFF F11 F21 F22 F31 F32 F33 F41 F42 F43 F44 F51 F52 F53 F54 F55 F66 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333 F411 F421 F422

6.935946 0.807629 7.025641 −0.076098 0.122949 8.062883 0.409000 0.414463 0.061829 0.964270 0.050643 0.505577 0.158466 0.086800 0.775494 0.118246 −39.7112 −1.1685 −2.0977 −48.0171 −0.0400 0.1300 −1.4166 0.0413 0.5697 −56.9642 −0.8097 −0.9898 −0.6996

F431 F432 F433 F441 F442 F443 F444 F511 F521 F522 F531 F532 F533 F541 F542 F543 F544 F551 F552 F553 F554 F555 F661 F662 F663 F664 F665

−0.1098 −0.1620 0.0694 −1.0786 −1.0917 −0.1055 −1.4770 −0.1067 −0.0440 −1.1741 0.0012 −0.3228 −0.1467 −0.0902 0.1879 −0.0301 −0.0371 −0.1892 −0.6723 −0.2678 −0.1397 −0.8342 −0.0300 −0.2322 −0.0025 −0.0863 −0.0143

F1111 F2111 F2211 F2221 F2222 F3111 F3211 F3221 F3222 F3311 F3321 F3322 F3331 F3332 F3333 F4111 F4211 F4221 F4222 F4311 F4321 F4322 F4331 F4332 F4333 F4411 F4421 F4422 F4431

175.61 1.41 0.88 8.48 257.75 0.55 0.02 −0.16 6.66 −0.08 0.21 −3.12 0.03 0.49 351.43 2.63 2.09 1.78 −1.18 0.52 0.18 −0.45 −0.17 −0.21 −0.40 −0.62 1.87 2.04 0.14


0.72 −0.69 2.96 3.03 0.03 1.34 0.17 −0.06 −0.06 0.68 0.04 0.13 −0.52 −0.30 0.77 −1.92 −0.42 −0.10 −1.29 0.01 0.32 −0.23 0.11 −0.03 0.08 −0.54 −0.35 0.64 −0.45

F5531 F5532 F5533 F5541 F5542 F5543 F5544 F5551 F5552 F5553 F5554 F5555 F6611 F6621 F6622 F6631 F6632 F6633 F6641 F6642 F6643 F6644 F6651 F6652 F6653 F6654 F6655 F6666

0.20 0.38 −0.09 0.23 0.61 0.03 0.43 −0.30 −0.18 1.68 −0.08 −1.74 −0.15 0.09 0.04 0.07 −0.08 0.01 0.05 0.27 −0.07 0.12 −0.13 −0.04 0.21 −0.18 −0.29 −0.56

1 mdyn = 10−8 N; n and m are exponents corresponding to the number of units from the type of modes present in a given force constant. bAs listed sequentially in Table 1 with the torsion as coordinate 6. a

limiting behavior for the VCI calculations. This is a well-known requirement for variational calculations and has been discussed in detail recently in ref 48. All electronic structure computations utilized the MOLPRO 2010.1 quantum chemistry software package.51

computed and extrapolated to the complete basis set (CBS) limit via a three-point formula ⎛ ⎛ 1 ⎞−4 1 ⎞−6 E (l ) = A + B ⎜l + ⎟ + C ⎜l + ⎟ ⎝ ⎝ 2⎠ 2⎠

(1)

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defined in ref 40 and restated in ref 30, where l is the highest angular momentum and A, B, and C are energies computed with the three chosen basis sets. To this CBS energy, further corrections are made to the energy, one for core correlation with the MT basis set and additional correction for scalar relativity.41 These composite energies at each point produce the CcCR QFF defined in ref 10 after a least-squares fitting of these points to the fourth-order Taylor series approximation of the nuclear potential. The sum of squared residuals for each of the four isomers examined here is on the order of 10−17 au2, indicating a very precise fit. This fitting slightly shifts the reference geometry to the true CcCR equilibrium geometry in order to produce gradients that are essentially zero. The force constants are then transformed into Cartesian derivatives by the INTDER program42 for use in the SPECTRO program43 that employs perturbation theory at second-order to compute the anharmonic fundamental vibrational frequencies44,45 (VPT2) and spectroscopic constants.46 The force constants are also transformed into Morse-cosine coordinates47,48 for use in VCI computations with the MULTIMODE program.49,50 That is, by design, for the VPT2 calculations, the potential is represented in the normal coordinate system using the Watson Hamiltonian. However, the potential is transformed into a coordinate system that has proper

RESULTS AND DISCUSSION

The VPT2 computations of trans-HOCS and trans-HOC34S require the input of 2ν6 = ν4, 2ν5 = ν4, 2ν5 = ν3, ν5 + ν4 = ν3, and ν5 + ν4 = ν2 Fermi resonances treated as polyads52 in addition to a ν3/ν2 Coriolis resonance. The trans-DOCS requires the use of a 2ν6 = ν4 = ν3 Fermi resonance polyad and a ν6 + ν3 = ν2 type-2 Fermi resonance as well as 2ν6/2ν5 Darling−Dennison and ν6/ν5 Coriolis resonances. The 2ν5 = ν4 Fermi resonance and the 2ν6 = ν3, ν5 + ν4 = ν3 = ν2 Fermi resonances in a polyad as well as the same Darling−Dennison and Coriolis resonances as those of the trans conformer are necessary for proper VPT2 description of cis-HOCS. These resonances are the same for cis-HOC34S except that for Fermi resonances, only the type-2 ν5 + ν4 = ν2 is required. The cis-DOCS molecule exhibits 2ν5 = ν4 = ν3 and 2ν6 = ν4 = ν3 polyads, a ν6 + ν4 = ν2 Fermi resonance, 2ν6/2ν5 and 2ν4/2ν3 Darling−Dennison resonances, and a ν6/ν5 Coriolis resonance. The resonances required for trans-HSCO and H34SCO include the 2ν3 = ν2 and the 2ν6 = 2ν5 = ν4 = ν3 type-1 Fermi resonance and Fermi resonance polyads, a 2ν6/2ν5 Darling−Dennison resonance, and ν6/ν5 and ν5/ν4 Coriolis resonances. These are scaled down to the 2ν6 = 2ν5 = ν4 = ν3 Fermi resonance polyad, 2ν6/2ν5 and 2ν2/2ν1 Darling−Dennison 6501



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Table 4. Quadratic, Cubic, and Quartic Force Constants (in mdyn/Ån·radm)a for cis-HOCS in the Defined Internal Coordinate System for the CcCR QFF F11 F21 F22 F31 F32 F33 F41 F42 F43 F44 F51 F52 F53 F54 F55 F66 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333 F411 F421 F422 a

6.734476 0.717990 7.211892 −0.002602 0.374056 7.379534 0.447697 0.335460 −0.137453 0.979034 −0.032453 0.453748 0.143586 −0.078824 0.748280 0.106092 −38.5326 −1.0122 −1.7242 −49.1779 −0.1916 −0.1291 −2.7928 0.4666 1.6343 −54.8587 −0.9243 −1.1230 −0.8198


0.1309 0.4830 −0.2538 −1.0757 −1.1247 0.0650 −1.7666 0.0275 0.0042 −0.9472 0.0213 −0.4416 −0.1999 −0.0343 −0.0459 −0.0203 −0.1354 −0.2322 −0.6466 −0.2385 0.0380 −0.8959 0.0051 −0.2528 0.0382 −0.0454 −0.0562


171.38 1.35 −0.64 7.10 264.81 −0.62 −1.09 2.29 15.43 −1.11 −2.63 −10.88 0.06 5.88 329.23 1.15 −0.19 3.56 4.24 0.81 −13.31 −1.54 1.11 −1.00 −3.01 −1.22 1.07 −7.50 0.97


−1.06 −2.27 1.64 7.94 −1.43 0.85 −0.60 0.31 0.60 4.61 −0.41 0.32 0.94 −0.46 0.97 −2.09 0.47 0.63 −0.02 −0.08 0.28 −0.58 0.35 1.24 −1.05 1.09 0.03 1.91 0.61


−1.35 1.21 −0.42 −0.64 −1.29 −0.84 −0.08 0.88 1.21 0.53 0.22 −0.17 −0.19 0.54 −0.65 −0.45 0.01 0.00 −0.63 0.73 −0.58 −0.11 0.08 0.70 −0.31 0.06 0.26 −0.28

1 mdyn = 10−8 N; n and m are exponents corresponding to the number of units from the type of modes present in a given force constant.

resonances, and ν6/ν5 Coriolis resonance for trans-DSCO. The cis-HSCO conformer and its 34S isotopologue exhibit 2ν3 = ν2 and ν5 + ν4 = ν3 Fermi resonances; 2ν6 = 2ν5 = 2ν4 = ν3 Fermi resonance polyads; 2ν5/2ν4, 2ν6/2ν4, and 2ν6/2ν5 Darling− Dennison resonances; and ν6/ν5 and ν5/ν4 Coriolis resonances. The cis-DSCO isotopologue makes use of a 2ν6 = 2ν5 = ν5 + ν4 = ν3 Fermi resonance polyad, 2ν2/2ν1 and 2ν6/2ν5 Darling− Dennison resonances, and ν6/ν4 and ν6/ν5 Coriolis resonances. The VCI computations reported here are all at the 5 moderepresentation (5MR) level. Many of the molecules make use of bases in the VCI comptuations composed of 31 primitive vibrational basis functions contracted down to 16 vibrational basis functions with 21 Hermite−Gauss (HEG) quadrature points for ν6, 31 primitives contracted to 15 functions with 20 HEG points for ν5−ν2, and 31 primitives contracted down to 13 functions with 18 HEG points for ν1. The trans-HSCO and H34SCO molecules utilize a different basis scheme. For these systems, 26 primitives contracted down to 15 harmonic vibrational functions with 22 HEG points make the basis for ν5, ν3, and ν2; 26 primitives contracted down to 16 functions with 22 HEG points produce the ν6 basis; 21 primitives contracted to 11 functions with 16 HEG points give the ν4 basis; and 26 primitives are contracted to 13 bases with 20 HEG points for ν1. Computations on cis-HSCO use 31 primitives contracted down to 14 functions with 20 HEG points for all modes except ν1, which is contracted down to 11 functions with 16 HEG points. The cis-H34SCO basis also differs from the standard set. The 25 primitives are contracted down to 11 functions with 16 HEG points for all modes except ν2, which has 21 primitives contracted

down to 11 basis functions but also with 16 HEG points. Smaller bases and mode-representation levels were used in the computation to determine convergence for each of the modes. Convergence is defined here as a difference of less than 1.0 cm−1 between bases differing by at least 1000 a′ basis functions. The sizes of the basis sets used here are consistent with those employed previously in related systems to produce high-accuracy results, even for the smaller, but converged basis used in cis-H34SCO.10,11,19 Congruous with the results reported by Rice, Pai, and Chabalowski,27 the CcCR energies computed here indicate that trans-HSCO is the lowest of the four isomers in energy, with cis-HSCO as the next most stable. Our computations put the HSCO conformational energy difference at 2.3 kcal/mol, very close to the 2.1 kcal/mol value computed previously.27 The transHOCS isomer is 12.8 kcal/mol above the trans-HSCO isomer and 0.6 kcal/mol lower than cis-HOCS. Hence, the energy separation between cis- and trans-HOCS is identical to that from the previous QCISD(T)//UMP2/6-311+G(2df,2p) computations.27 The agreement with previous work indicates that our computations are well-behaved, but the additional energy terms and fitting step present in determining the CcCR energies should make our values even more accurate. HOCS. The geometrical parameters for the HOCS conformers as well as the deuterated and 34S isotopologues are given in Table 1. The equilibrium aug-cc-pV5Z dipole moments for the most abundant isotopologues are also given in Table 1, with the largest dipole moment of the four isomers examined here belonging to trans-HOCS at 2.27 D. Comparison between 6502



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Table 5. Harmonic and Anharmonic CcCR QFF Fundamental Vibrational Frequencies (in cm−1) for trans- and cis-HOCS from VPT2 and VCI Computations CcCR

previous theory

description

mode

harmonic

VPT2

VCI

Rice et al.a

trans-HOCS

a′ O−H stretch a′ C−O stretch a′ H−O−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode a′ O−D stretch a′ C−O stretch a′ C−S stretch a′ D−O−C bend a′ O−C−S bend a″ torsional mode

trans-HOC34S

a′ O−H stretch a′ C−O stretch a′ H−O−C bend a′ C−34S stretch a′ O−C−34S bend a″ torsional mode

cis-HOCS

a′ O−H stretch a′ C−O stretch a′ H−O−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode

cis-DOCS

a′ O−D stretch a′ C−O stretch a′ D−O−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode

cis-HOC34S

a′ O−H stretch a′ C−O stretch a′ H−O−C bend a′ C−34S stretch a′ O−C−34S bend a″ torsional mode

3796.1 1442.1 1245.0 918.3 445.1 526.0 4186.3 2763.4 1407.8 1051.7 826.2 432.2 396.4 3438.9 3796.1 1440.1 1244.9 910.5 442.3 525.7 4179.8 3627.4 1420.6 1270.9 903.7 442.6 576.0 4120.6 2637.3 1416.2 1017.2 874.6 409.2 473.6 3414.1 3627.4 1418.7 1270.7 896.2 439.8 575.8 4114.3

3599.2 1402.5 1200.8 904.7 441.5 488.3 4124.3 2659.4 1371.7 1024.2 810.2 429.4 375.6 3402.2 3599.2 1400.4 1200.7 897.4 438.7 488.1 4117.9 3392.2 1380.4 1250.9 887.1 432.6 553.6 4058.1 2514.5 1374.7 1004.0 848.9 400.6 457.2 3371.6 3392.2 1379.3 1250.5 880.1 429.9 553.3 4051.7

3600.9 1402.7 1201.1 905.5 441.9 482.3 4125.5 2659.7 1372.0 1023.9 810.0 429.4 362.8 3405.2 3600.8 1400.6 1201.0 898.1 439.1 482.2 4109.4 3391.2 1381.1 1249.8 887.1 432.4 533.9 4047.2 2514.9 1375.1 1002.0 870.4c 399.7 435.6 3366.1 3391.1 1379.2 1249.3 880.0 429.7 533.7 4040.9

3798 1500 1292 1018 457 611

trans-DOCS

ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE

molecule

3627 1507 1271 975 455 645

Lo et al.b

3516.8 1417.6 1243.7 886.7 436.5 587.3

a c

Harmonic MP2/6-311G+(2df,2p) fundamental frequencies from ref 27. bHarmonic B3LYP/aug-cc-pVTZ cis-HOCS frequencies are from ref 28. A lower-frequency state at 823.6 cm−1 also corresponds to this mode. See in-text discussion.

distinguished from the normal isotopologue with modern, highresolution experimental and observational techniques. The D and 34S isotopologues are chosen here because these are the most likely to be found in space or in laboratory experiments after lines of the normal species are detected. The other spectroscopic constants for each conformer and isotopologue of HOCS are given in Table 2. The quartic and sextic distortion constants, for example, are included in this table. The force constants for both trans- and cis-HOCS are given in Tables 3 and 4. The Morse-cosine transformed coordinates tables are given in the Supporting Information. Comparisons of previously computed MP2 and B3LYP harmonic vibrational frequencies27,28 to those computed in this

previous theory and the CcCR HOCS equilibrium geometries is reasonable for the differences in the methods employed here and by Rice, Pai, and Chabalowski27 as well as Lo et al.28 The Rα vibrationally averaged zero-point geometries and rotational constants for the standard isotopologue shift from their corresponding equilibrium values and should produce more physically meaningful values, as has been observed in previous studies.10,11,15−19,25 Deuteration reduces the A0 and C0 rotational constants across the set. B0 actually increases in magnitude upon deuteration of trans-HOCS but decreases for cis-DOCS. Substitution with 34S reduces the rotational constants for each species but only by about 2% or so. Even though these shifts are relatively slight, rotational lines of the 34S isotopologue can frequently be 6503



Article

Table 6. CcCR trans- and cis-HSCO Minimum-Energy Structures (in Å and degrees), Dipole Momentsa, and Rotational Constants (in cm−1) zero-point trans-HSCO

cis-HSCO

R(C−O) R(C−S) R(S−H) ∠S−C−O ∠H−S−C A0/e B0/e C0/e μ μA μB R(C−O) R(C−S) R(S−H) ∠S−C−O ∠H−S−C A0/e B0/e C0/e μ μA μB

equilibrium

standard

deuterated

H34SCO

this work

Rice et al.b

Lo et al.c

1.17057 1.80918 1.33619 127.799 92.928 3.53330 0.19648 0.18592

1.16995 1.80783 1.33879 127.875 92.878 2.79198 0.19152 0.17902

1.17057 1.80903 1.33620 127.799 92.931 3.51843 0.19187 0.18174

1.17339 1.78543 1.34723 130.389 96.609 3.39502 0.19987 0.18852

1.17291 1.78494 1.34944 130.325 96.440 2.48623 0.19845 0.18354

1.17339 1.78538 1.34724 130.392 96.613 3.39463 0.19498 0.18416

1.17000 1.79159 1.33567 127.993 93.3 3.54263 0.19860 0.18806 1.92 D 1.73 D 0.83 D 1.17303 1.77003 1.346377 130.289 97.6 3.37691 0.20218 0.19076 1.55 D 1.39 D 0.69 D

1.1688 1.8058 1.3407 128.5 93.015 − − − − − − 1.1725 1.7792 1.3531 131.1 96.349 − − − − − −

1.169 1.812 1.343 128.25 93.42 − − − − − − 1.172 1.787 1.356 130.81 97.42 − − − − − −

a

Dipole moments are computed at the CCSD(T)/aug-cc-pV5Z level of theory. bB3LYP/6-311+G(2df,2p) data from ref 27. cB3LYP/aug-cc-pVTZ data from ref 28.

VPT2 ν6 frequency as 553.6 cm−1 and VCI as 533.9 cm−1, a VPT2 − VCI difference of 19.7 cm−1. Even though this difference is substantially larger than differences for any of the other fundamental frequencies of this isomer, this difference is consistent with that from the aforementioned cis-HOCO analogue.11 Both cis-HOCO and cis-HOCS possess O−C−O and O−C−S bond angles, respectively, that are substantially less than 180°. If the bond angle is much closer to 180°, as it is with various closed-shell tetra-atomic Cs molecules previously examined, quasi-linear coordinates are necessary to define the heavy-atom bending displacements, and this may be a factor in minimizing the VPT2 − VCI difference.12,19,21 It is believed that the VPT2 torsional frequency is more accurate than the VCI value when the two exhibit such a large disagreement,13 but a definitive confirmation of this observation has not been firmly established. Despite this, the ν1 O−H stretches of cis-HOCS and HOC34S differ by only 1.0 and 1.1 cm−1, respectively. Previous work has shown exceptional accuracy for the prediction of this mode with the VCI method. Conversely, the ν4 C−S stretch of cis-DOCS is computed to be 848.9 cm−1 with VPT2 but 870.4 cm−1 with VCI. This behavior is not present in the other conformer or isotopologues of HOCS, but the VPT2 − VCI difference for ν4 of HOCS+ is 12.9 cm−1.19 The discrepancy is caused by a significant mixing of states between ν4, ν3, 2ν5, and 2ν6. The mixing is especially strong between ν4 and 2ν5, with the ν4 coefficient to the 2ν5 frequency (904.7 cm−1) from the Fermi resonance polyad treatment within VPT2 being 0.22. In the VCI computations, there is a lower-frequency mode (823.6 cm−1) and a higher-frequency mode (870.4 cm−1) that are both composed of this fundamental in the VCI expansion. The higher-frequency mode has a much larger coefficient of 0.82 for the ν4 C−S stretch than the lower-frequency mode coefficient of 0.51.

study with the CcCR QFF (given in Table 5) show similar levels of correlation as the relative energies and geometrical parameters. The MP2/6-311G+(2df,2p) computations by Rice, Pai, and Chabalowski27 yield harmonic O−H stretching frequencies within 2.0 cm−1 of the present CcCR values. However, the anharmonic corrections from VPT2 or VCI are necessary to produce reference data for direct comparsion to experiment. Contrary to the cations,19 none of the modes for any of the conformers or isotopologues of HOCS display positive anharmonicities. This is consistent with the analogous cis- and trans-HOCO radicals.10,11 The ν5 O−C−S bend has the smallest anharmonicity for trans-HOCS, 4.2 cm−1, with VCI. This mode also has the smallest anharmonicity for cis-HOCS at 10.2 cm−1. The ν1 O−H stretch is the most anharmonic mode in terms of both magnitude and percent shift relative to the harmonic frequency. The anharmonicity decreases upon deuteration but is nearly unaffected by 34S substitution. The agreement between VPT2 and VCI is exceptionally consistent for trans-HOCS and its isotopologues. The fundamental frequencies produced by both methods vary by no more than 1.7 cm−1 for ν1−ν5. The ν6 torsional mode has a larger frequency discprepancy between VPT2 and VCI. VPT2 predicts ν6 to be 488.3 cm−1, while the VCI value is 482.3 cm−1, a difference of 6.0 cm−1. A similar VPT2 − VCI difference of 6.3 cm−1 has been previously reported for CcCR trans-HOCO.10 Other CcCR QFF computations have reported dicrepancies between VPT2 and VCI computations of tetra-atomic Cs molecules to be 26.3 cm−1 for the torsion of the cis-HOCO radical and 14.5 cm−1 for the anion.11,15 Hence, a 6.0 cm−1 difference is relatively small. The difference between VPT2 and VCI for the torsional mode of cis-HOCS and its isotopologues is much greater than that found for the trans conformer. Table 5 shows the cis-HOCS 6504



Article

Table 7. CcCR QFF trans- and cis-HSCO, DSCO, and H34SCO Vibration−Rotation Interaction Constants, Quartic and Sextic Centrifugal Distortion Constants, and S Reduced Hamiltonian Terms vib−rot constants (MHz)

Watson S reduction

distortion constants

mode

αA

αB

αC

trans-HSCO

1 2 3 4 5 6

941.0 559.3 −182.3 −579.3 421.5 −601.1

−0.3 7.0 7.0 70.8 26.7 15.8

2.0 7.5 15.8 67.0 14.6 21.3


−36.244 −0.021 −0.015 0.183 0.202 −0.017

trans-DSCO

1 2 3 4 5 6

770.8 267.9 −547.3 −854.1 −264.5 1266.4

1.4 7.5 7.6 61.4 11.9 22.2

3.9 7.4 14.8 63.2 17.4 6.1


−13.809 −0.018 −0.013 −0.012 0.077 −0.015

trans-H34SCO

1 2 3 4 5 6

940.9 560.1 −178.3 −623.1 413.4 −566.3

−0.4 6.7 6.9 67.8 26.2 16.3

1.8 7.2 15.3 64.4 14.6 21.3


−35.824 −0.019 −0.015 0.180 0.199 −0.017

cis-HSCO

1 2 3 4 5 6

133.5 574.9 −600.0 −138.5 662.8 −1718.3

−4.9 13.9 21.2 85.0 24.4 −1.0

−4.2 13.8 27.8 77.0 14.5 5.4


−34.662 −0.019 −0.014 0.209 0.189 −0.016

cis-DSCO

1 2 3 4 5 6

511.1 308.3 −468.3 −179.3 −977.0 724.0

−3.2 13.2 14.4 81.0 1.2 16.8

−0.3 12.7 20.1 73.2 5.9 8.3


−10.470 −0.020 −0.013 0.029 0.102 −0.015

cis-H34SCO

1 2 3 4 5 6

130.1 576.1 −599.7 −219.7 664.2 −1651.2

−4.9 13.5 21.0 81.8 23.7 −0.6

−4.2 13.4 27.2 74.2 14.3 5.5


−34.683 −0.018 −0.013 0.203 0.184 −0.015

(MHz)

6505

(Hz) Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc Φaaa Φbbb Φccc Φaab Φabb Φaac Φbbc Φacc Φbcc Φabc

2316.437 −0.002 −0.005 −24.996 −0.579 −23.132 −0.005 −0.177 −0.007 −0.956 376.713 −0.003 −0.004 0.731 −0.415 −8.482 −0.005 −0.118 −0.006 −0.611 2278.893 −0.002 −0.005 −14.588 −0.545 −22.434 −0.005 −0.170 −0.006 −0.898 2493.306 0.001 −0.003 −19.608 −0.426 −20.313 −0.002 −0.181 −0.004 −0.864 295.552 0.001 −0.002 1.805 −0.267 −7.523 −0.001 −0.066 −0.003 −0.454 2497.583 0.000 −0.003 −19.006 −0.405 −19.690 −0.002 −0.176 −0.004 −0.817

(MHz)

(Hz)

103 DJ DJK DK 103 d1 106 d2

4.486 −0.105 9.162 −0.344 −11.876

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

−3.555 −0.805 −36.495 2353.741 0.687 29.082 11.445

103 DJ DJK DK 103 d1 106 d2

3.889 −0.024 3.472 −0.232 −17.145

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

−3.440 −0.559 −6.602 383.878 0.402 20.385 13.171

103 DJ DJK DK 103 d1 106 d2

4.313 −0.103 9.055 −0.324 −10.960

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

−3.373 −0.759 −35.483 2315.139 0.632 26.819 10.165

103 DJ DJK DK 103 d1 106 d2

4.122 −0.108 8.769 −0.349 −11.575

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

−1.287 −0.670 −38.573 2532.550 0.893 54.856 12.380

103 DJ DJK DK 103 d1 106 d2

4.038 −0.041 2.655 −0.420 −23.237

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

−7.108 −0.385 −4.922 300.859 0.853 89.864 21.960

103 DJ DJK DK 103 d1 106 d2

3.932 −0.105 8.772 −0.324 −10.533

103 HJ HJK HKJ HK 103 h1 106 h2 106 h3

−1.397 −0.639 −37.412 2535.635 0.805 48.553 10.774



Article

Table 8. Quadratic, Cubic, and Quartic Force Constants (in mdyn/Ån·radm) for CcCR trans-HSCO in the Defined Internal Coordinate Systema F11 F21 F22 F31 F32 F33 F41 F42 F43 F44 F51 F52 F53 F54 F55 F66 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333 F411 F421 F422 a

14.717820 1.450541 1.935618 −0.052979 0.003466 4.305096 0.313525 0.254736 0.024961 0.842398 0.030436 0.278485 0.008741 0.197842 0.882231 0.107886 −103.6747 −4.1988 −0.1547 −15.6966 0.0361 0.0814 −0.2846 0.0220 0.1036 −22.7420 −0.3386 −0.5525 −1.0805


−0.0660 −0.0354 −0.0542 −1.0685 −0.6404 −0.0909 −0.7429 0.1498 −0.0658 −1.0235 −0.0071 −0.1754 0.0535 −0.2257 0.0702 −0.0732 −0.1208 0.0464 −1.1034 −0.2721 0.1196 −0.8867 0.0456 −0.2540 −0.0150 −0.0686 0.0715


602.74 6.40 2.73 −0.98 67.59 0.27 −0.11 −0.79 0.84 −0.50 0.79 −1.07 0.11 −0.55 102.74 0.82 0.21 1.65 −0.02 −0.11 0.71 0.25 −0.23 −0.01 −0.44 −1.05 2.48 −3.29 0.25


−0.29 −0.87 0.93 2.05 0.05 0.49 −0.04 −0.56 1.49 1.02 −0.02 0.54 0.52 0.24 −0.71 −0.38 0.56 −0.93 −1.80 0.18 0.91 0.14 0.04 0.47 0.12 0.35 −1.70 1.18 −1.65


−0.16 −0.08 −0.56 −0.49 0.28 0.27 −0.00 1.19 −0.98 0.47 −0.17 −0.83 −0.87 0.96 −0.34 −0.30 −0.26 0.04 −0.98 −0.42 −0.23 0.09 0.82 −1.04 −0.53 −0.32 −0.72 −0.21

As listed in Table 6 with the torsion as coordinate 6.

Table 9. Quadratic, Cubic, and Quartic Force Constants (in mdyn/Ån·radm) for CcCR cis-HSCO in the Defined Internal Coordinate System (as for trans-HSCO) F11 F21 F22 F31 F32 F33 F41 F42 F43 F44 F51 F52 F53 F54 F55 F66 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333 F411 F421 F422

14.527371 1.318284 2.097911 0.026626 0.116517 4.017294 0.259063 0.365600 −0.072880 0.827768 0.016677 0.202805 −0.045668 −0.183086 0.686337 0.105196 −102.2435 −4.0990 0.5345 −16.7651 −0.1284 −0.1522 −0.7244 0.1473 0.3680 −21.7630 −0.1846 −0.6377 −1.7210


0.1084 0.3474 −0.1210 −1.0502 −0.6866 −0.0637 −0.7351 −0.1810 0.0516 −0.4132 0.1613 −0.1335 −0.0270 0.2388 0.1269 −0.0136 −0.3685 0.2481 −1.1123 −0.2516 −0.3061 −0.4679 0.0328 −0.2894 0.0312 −0.0469 0.0202

F1111 F2111 F2211 F2221 F2222 F3111 F3211 F3221 F3222 F3311 F3321 F3322 F3331 F3332 F3333 F4111 F4211 F4221 F4222 F4311 F4321 F4322 F4331 F4332 F4333 F4411 F4421 F4422 F4431 6506

592.76 9.34 −1.10 0.03 72.75 −0.56 1.56 0.55 3.50 −0.01 −0.86 −1.61 0.36 0.30 98.99 1.28 0.04 3.42 2.97 −0.66 −1.20 −1.16 0.45 0.75 −0.56 0.27 2.29 −1.93 0.71


1.01 −0.46 0.90 4.09 0.00 1.66 −0.33 0.31 −1.53 0.07 −0.25 0.23 1.14 0.06 −0.20 0.06 0.46 −0.05 0.95 0.25 −0.38 −0.39 0.34 0.99 −0.37 0.50 −1.93 1.83 0.21


−0.34 0.98 −0.49 1.42 0.39 −0.26 1.42 0.91 1.04 0.16 1.10 0.75 0.44 −0.53 1.99 −1.62 1.08 0.32 −0.42 0.45 0.38 2.39 1.25 0.97 −0.74 −0.92 0.03 1.35



Article

Table 10. trans- and cis-HSCO Harmonic and VPT2/VCI Anharmonic CcCR QFF Fundamental Vibrational Frequencies (in cm−1) CcCR molecule trans-HSCO

previous a

theoryb

description

mode

harmonic

VPT2

VCI

theory

a′ S−H stretch a′ C−O stretch a′ H−S−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode

ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE ω/ν1 ω/ν2 ω/ν3 ω/ν4 ω/ν5 ω/ν6 ZPE

2734.6 1866.4 957.5 580.7 379.4 387.5 3453.1 1964.2 1864.4 731.5 559.8 372.3 314.9 2903.6 2732.2 1866.3 956.4 578.1 375.4 387.5 3448.0 2641.7 1854.6 889.7 527.9 393.0 403.9 3355.4 1897.3 1854.1 716.8 512.9 360.7 337.2 2839.5 2639.4 1854.6 888.6 522.8 391.2 403.2 3349.9

2623.7 1843.5 925.4 529.7 363.5 363.5 3405.8 1907.0 1840.2 708.3d 518.3 358.7 299.3 2873.1 2621.5 1846.4 933.2 527.4 359.6 363.5 3401.9 2527.8 1837.3 873.5 479.6 394.5 463.4 3340.0 1840.5 1834.4 703.4 469.3 360.0 380.2 2830.0 2525.6 1837.2 871.7 475.5 392.5 462.6 3334.6

2623.6 1845.3 920.8 535.2 361.2 348.9 3399.5 1907.2 1840.4 714.5d 517.5 356.7 288.6 2867.2 2620.9 1843.8 919.7 533.7 357.3 349.1 3394.7 2526.8 1836.7 871.1 480.5 393.0 435.8 3330.5 1844.1 1829.3 702.4 469.0 359.6 361.3 2823.8 2525.2 1837.1 870.0 477.0 391.1 436.2 3325.4

2754 1851 966 632 395 404

2696.3 1881.3 947.8 552.7 369.1 392.0

2662 1844 910 566 401 420

2506.3 1864.0 872.4 479.9 386.4 412.9

trans-DSCO

a′ S−D stretch a′ C−O stretch a′ C−S stretch a′ D−S−C bend a′ O−C−S bend a″ torsional mode

trans-H34SCO

a′ 34S−H stretch a′ C−O stretch a′ H−34S−C bend a′ C−34S stretch a′ O−C−34S bend a″ torsional mode

cis-HSCO

a′ S−H stretch a′ C−O stretch a′ H−S−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode

cis-DSCO

a′ S−D stretch a′ C−O stretch a′ D−S−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode

cis-H34SCO

a′ 34S−H stretch a′ C−O stretch a′ H−34S−C bend a′ C−34S stretch a′ O−C−34S bend a″ torsional mode

exp.c 1823.3 931.6 553.3

a Harmonic MP2/6-311G+(2df,2p) fundamental frequencies from ref 27. bHarmonic B3LYP/aug-cc-pVTZ trans - and cis -HSCO fundamentals are from ref 28. cExperimental Ar matrix data for trans -HSCO are from ref 28. dSubstantial mixing is present for these states and the 2ν5 state. See intext discussion.

The corresponding VCI coupling magnitudes between the ν4 C−S stretch and 2ν5 are much smaller for the normal and 34S isotopologues. As such, the 870.4 cm−1 frequency mode provides a better description of the fundamental, and because of the very strong mixing, we expect the VCI result to be more accurate than its VPT2 counterpart. The other states of cis-HOCS and its isotopologues all exhibit VPT2 and VCI frequencies that are in very good agreement with each other, indicating that each are reliable reference values. HSCO. The geometrical parameters, rotational constants, and equilibrium CCSD(T)/aug-cc-pV5Z dipole moments for the HSCO conformers are reported in Table 6. The equilibrium structures compare well with previous theory, and the zero-point

corrections are similar to those produced for the HOCS isomers and isotopologues. The other spectroscopic constants for the HSCO family of molecules are shown in Table 7, while the force constants utilized in the CcCR QFFs for both conformers of HSCO are given in Tables 8 and 9. The Morse-cosine transformed coordinates tables for both conformers of HSCO are also given in the Supporting Information. The harmonic and VPT2/VCI CcCR QFF anharmonic vibrational frequencies are listed in Table 10. Comparison between the harmonic vibrational frequencies computed here for the standard isotopologues of trans- and cis-HSCO and those frequencies computed previously27,28 gives the same qualitative pattern. However, the MP2/6-311G+(2df,2p) harmonic 6507



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frequencies27 are not as consistent with the CcCR values for the HSCO conformers as they were for the HOCS conformers. Regardless, the two sets do not show significant deviations. The degree of anharmonicity for the CcCR QFF is similar between the trans-HOCS and trans-HSCO molecules, but a positive anharmonicity is predicted for cis-HSCO and its isotopologues. Positive anharmonicities have been found for quasi-linear molecules12,19,21 but not when employing this methodology for tetra-atomics with the heavy-atom bond angle as far from 180° as the 130.389° ∠S−C−O in cis-HSCO. Regardless, the comparison between experimental rotational constants and the previously computed vibrationally averaged rotational constants for those molecules with positive anharmonicities has been quite good, indicating that such results are reliable. Hence, similar behavior should be present here. The ν1 hydrogen stretching frequency is much lower in HSCO than it is in HOCS because this motion now involves the much heavier sulfur atom instead of an oxygen. Deuteration decreases the ν1 frequency to levels close to ν2, especially for cis-DSCO. 34S substitution for trans-HSCO minimally changes the fundamental frequencies, with the largest change coming from a 3.9 cm−1 shift for the VCI ν5 O−C−S bending mode, which is 361.2 cm−1 in the standard isotopologue and 349.1 cm−1 with the heavier sulfur isotope. This shift in the 34S isotopologues is also exhibited in the VPT2 computations. The agreement between anharmonic methods is also quite good for both trans- and cis-HSCO and their isotopologues. The VPT2 − VCI difference is typically less than 5.0 cm−1 and often less than 1.0 cm−1. The standard exception for the ν6 torsional mode is once more present for HSCO. The VPT2 − VCI difference for this mode is larger for trans-HSCO (14.6 cm−1) than it is for trans-HOCS (6.0 cm−1) discussed before. The 28.6 cm−1 VPT2 − VCI difference for cis-HSCO is coincidentally exactly the same VPT2 − VCI difference as the ν6 frequency of cis-HOCS. The VPT2 − VCI torsional difference is lessened upon isotopic substitution in the cis-HSCO family, but it is still on the order of 20 cm−1 with the substitution of D or 25 cm−1 with 34S. Lo et al.28 also reported condensed-phase Ar matrix ν2, ν3, and ν4 frequencies for trans-HSCO, and these are also listed in Table 10. The VCI ν2 C−O stretching frequency is 1845.3 cm−1, with the condensed-phase frequency 22.0 cm−1 lower at 1823.3 cm−1. A similar difference of 14.2 cm−1 is also present for this same CcCR VCI frequency of trans-HOCO as compared to Ne matrix data.10 The ν4 C−S stretch is a lower-energy frequency of 535.2 cm−1 for the gas-phase computations compared to the Ar matrix value of 553.3 cm−1, similar in behavior to the same mode of cis-HOCO as compared to CO matrix data.11 The ν3 H−S−C bend is 10.8 cm−1 less than its condensed-phase counterpart. It is interesting to note that the ν3 discrepancy between VPT2 and VCI increases from 4.6 to 13.5 cm−1 when 32S is substituted by 34 S. The polyad resonances involved here include ν3 = ν4, ν3 = 2ν5, and ν3 = 2ν6. This enlarged difference is attributed to the deficiency of VPT2 theory to fully couple these modes as they are in VCI. In contrast, the 34S substitution reduces the ν3 (VCI) fundamental by 1.0 cm−1, which is consistent with the 2.6 cm−1 reduction in ω3. The VCI ν3 are probably more reliable for both trans-HSCO and trans-H34SCO. It should be further noted that the trans-DSCO ν3 frequency (the C−S stretch) and 2ν5 (O−C−S bend) are strongly coupled together, and it is difficult to make definitive assignments as to the two components of the resonances present in both the VCI and VPT2 computations. The two states in question produced are 708.3 and 717.9 cm−1 (VPT2) or 703.6 and 714.5 cm−1

(VCI). The dominant eigenfunction of the VPT2 resonance polyad corresponds to the 708.3 cm−1 with a coefficient of 0.76, but the 717.9 cm−1 frequency’s coefficient is 0.62. For the VCI expansion, the 714.5 cm−1 frequency is composed of the ν3 mode with a 0.76 CI coefficient, where the 2ν5 mode contributes sizeably with a 0.62 coefficient. The VCI 703.6 cm−1 frequency is composed of the 2ν5 mode with a 0.73 coefficient and the ν3 mode with a 0.63 coefficient. As such, we are choosing the larger coefficients to label the ν3 frequency as 708.3 cm−1 for VPT2 and 714.5 cm−1 for VCI. This attribution is done in the same way as it is for cis-DOCS.

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CONCLUSIONS Because it is well-established that the HOCO radical forms during the reaction of HO + CO in atmospheric conditions,10,26 the data produced in this work can assist in elucidating the possible formation of the single sulfur analogues whether such reactions take place in terrestrial flames or the depths of space. The vibrational frequencies and spectroscopic constants of transand cis-HOCS/HSCO as well as the D and 34S isotopologues are produced in full to assist future studies. The agreement between the VPT2 and VCI computations are such that the computed results for the HOCS and HSCO radicals should be in line with the accuracies produced for similar systems where comparison to experimental reference data is possible. The torsional mode is again more difficult to describe using VCI computations for all species examined, especially for the cis conformers. Regardless, the vibrational frequencies calculated here should guide experimental studies of combustion or simulated interstellar environments, and molecular structures, electric dipoles, and rotational constants reported herein should serve as an invaluable aid in dedicated searches for the rotational spectra of these species in the radio band.

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ASSOCIATED CONTENT

S Supporting Information *

The QFFs transformed into a Morse-cosine coordinate system are provided. This coordinate system provides correct limiting behavior, which is necessary for use in the VCI calculations. A discussion is given in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (R.C.F.). *E-mail: [email protected] (T.J.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the following sources of funding: RCF, the NASA Postdoctoral Program administered by Oak Ridge Associated Universities, as well as Georgia Southern University for start-up funds; M.C.M., NASA Award NNX13AE59G; T.D.C., NSF Award CHE-1058420; X.H., NASA/SETI Institute Cooperative Agreement NNX12AG96A; T.J.L., NASA Grant 10-APRA10-0167; R.C.F. and T.D.C., NSF Multi-User Chemistry Research Instrumentation and Facility (CRIF:MU) Award CHE-0741927; and R.C.F., X.H., and T.J.L., NASA’s Laboratory Astrophysics ‘Carbon in the Galaxy’ Consortium Grant (NNH10ZDA001N). 6508



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