Fundamental Vibrational Frequencies and Spectroscopic Constants of

Article pubs.acs.org/JPCA

Fundamental Vibrational Frequencies and Spectroscopic Constants of HOCS+, HSCO+, and Isotopologues via Quartic Force Fields Ryan C. Fortenberry,*,†,∥ Xinchuan Huang,‡ Joseph S. Francisco,§ T. Daniel Crawford,∥ and Timothy J. Lee*,† †

NASA Ames Research Center, Moffett Field, California 94035-1000, United States SETI, 189 Bernardo Avenue, Suite 100, Mountain View, California 94043, United States § Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States ∥ Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States ‡

ABSTRACT: Besides the ν1 O−H stretching mode at 3435 cm−1 for HOCS+, the fundamental vibrational frequencies for this cation and its HSCO+ isomer have not been determined experimentally. Because these systems are analogues to HOCO+, a detected interstellar molecule, and are believed to play an important role in reactions of OCS, which has also been detected in the interstellar medium, these cations are of importance to interstellar chemistry and reaction surface studies. This work provides the fundamental vibrational frequencies and spectroscopic constants computed with vibrational perturbation theory (VPT) at second order and the vibrational configuration interaction (VCI) method conjoined with the most accurate quartic force field (QFF) applied to date for these systems. Our computations match experiment to better than 2 cm−1 for the known O−H stretch. Additionally, there is strong agreement in the prediction of the fundamentals across methods and choices of QFFs. The consistency in the computations and the correspondence for the known mode should give accurate reference data for the rovibrational spectra of these cations and their singly substituted isotopologues for D, 18O, and 34S.

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rotational constants computed for HOCS+ and HSCO+ by Taylor and Scarlett12 assisted in the laboratory observation of the rotational lines for HOCS+ by Nakanga and Amano.13 In their analysis, Nakanga and Amano also determined the ν1 O− H stretch at 3435 cm−1. Further laboratory work14,15 refined the rotational spectrum of HOCS+, but the rotational lines for the HSCO+ isomer were not observed in the laboratory until 2007 by McCarthy and Thaddeus.10 Additional rovibrational reference data for any potential interstellar species including HOCS+ and HSCO+ would serve various rotational spectroscopists as well as larger projects such as the Atacama Large Millimeter Array (ALMA) and the future Square Kilometer Array (SKA). Additionally, the number of missions probing the infrared (IR) wavelengths of space in both the mid- and far-IR regimes is growing with the current usage of the Herschel Space Observatory, the Stratospheric Observatory for Infrared Astronomy (SOFIA) coming online, and the James Webb Space Telescope (JWST) set for launch later this decade. Unfortunately for IR measurements, only the aforementioned HOCS+ O−H stretch has been conclusively characterized experimentally.13 Nakanga and Amano13 were not able to observe the expected S−H stretch even though previous

INTRODUCTION Protonated carbon dioxide (HOCO+) and the thioformyl cation (HCS+) were both detected in the interstellar medium (ISM) and reported in the same paper by Thaddeus and coworkers1 over 30 years ago. Additionally, OCS was previously detected in the ISM a decade prior. 2,3 As a result, experimentalists and theorists began to study the sulfur analogues of HOCO+, protonated carbonyl sulfide in the HOCS+ and HSCO+ isomers, while the presence of these cations in the ISM was speculated.4,5 Like the HOCO radical, the related HOCS and HSCO radicals are believed to be formed as stable intermediates in the reaction of H + OCS or the respective diatomic reactions (OH + CS or SH + CO) even when deuterated.6,7 These or closely related reactions may be present on the surface of interstellar ice grains assisting in the creation of larger molecules like polycyclic aromatic hydrocarbons.8 Additionally, with OCS known to exist in the ISM, protons from various sources, including reactions involving the formaldehyde cation,9 are likely to form at least one isomer of protonated carbonyl sulfide in space or in simulated laboratory experiments. Various groups are working toward a radioastronomical detection of either isomer, as well as HSCS+, in regions of space similar to where HOCO+ has been observed.10,11 However, highly accurate reference data are necessary for these cation’s potential interstellar chemistry to be better understood. The © 2012 American Chemical Society

Received: July 24, 2012 Revised: September 4, 2012 Published: September 6, 2012 9582

dx.doi.org/10.1021/jp3073206 | J. Phys. Chem. A 2012, 116, 9582−9590

The Journal of Physical Chemistry A

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Table 1. Minimum Energy Structures (in Å and degrees) and Rotational Constants (in cm−1) for HOCS+ and HSCO+ with the CcCR QFF zero-point molecule +

HOCS

HSCO+

a

this work R(O−H) R(C−O) R(C−S) ∠H−O−C ∠O−C−S A0/e B0/e C0/e R(S−H) R(C−S) R(C−O) ∠H−S−C ∠S−C−O A0/e B0/e C0/e

0.986 16 1.237 18 1.500 04 117.922 174.397 25.941 13 0.191 93 0.190 35 1.367 38 1.659 24 1.122 75 90.201 176.115 9.314 33 0.190 05 0.186 05

Wheeler et al.a

equilibrium experimentb

25.633 0.190 0.189

26.107 92 0.191 82 0.190 23

9.281 0.188 0.185

0.188 025 6

this work

Wheeler et al.a

0.977 29 1.235 91 1.497 06 117.499 174.779 25.259 58 0.192 46 0.191 00 1.355 11 1.655 20 1.122 63 90.087 176.369 9.379 97 0.190 44 0.186 65

0.978 1.239 1.505 117.2 174.7 25.048 0.191 0.189 1.357 1.664 1.126 90.2 176.4 9.350 0.189 0.185

CCSD(T)/cc-pVQZ computation from ref 16. bHOCS+ data from ref 13 and HSCO+ Beff from ref 10.

torsional modes for the HOCO radicals and cis anion23,28 are probably lacking, and VPT does a better job describing these modes. However, the large (>10 cm−1) discrepancies in the prediction of the fundamental vibrational frequencies for the torsional mode between VPT and VCI for these systems are not present for the HOCO+ cation26 restoring confidence in this approach to predict accurately the frequencies for the torsional mode. Hence, in this work, we are building on our previous experience computing fundamental vibrational frequencies and spectroscopic constants of the related various HOCO species, as well as examination of molecules with second-row atoms,30 to provide highly accurate computations of the fundamental vibrational frequencies and spectroscopic constants of HOCS+ and HSCO+. The spectroscopic constants computed in this study are quite useful to interpret even purely rotational spectra. Additionally, we also report these data for the systems with single isotopic substitution for the D, 18O, and 34S isotopologues in both cation isomers.

computations appear to indicate HSCO+ is the more stable isomer.12,16 Saebø and co-workers17 were able to provide theoretical fundamental vibrational frequencies for HOCS+ and HSCO+, as well as the deuterated forms, by empirically adjusting the harmonic ab initio values for known anharmonic corrections. However, the conjoined experimental search was not able to examine any of the fundamental frequencies because the setup used would not allow for analysis beyond 2500 cm−1, very close to where the S−H fundamental mode is computed to be.17 Later, Wheeler and co-workers16 provided theoretical predictions for the fundamental vibrational frequencies and some spectroscopic constants of both cation isomers using high level coupled cluster computations. CCSD(T)/cc-pVTZ cubic and partial quartic force fields combined with a vibrational perturbation theory (VPT) analysis at second order were utilized to predict fundamental vibrational frequencies for HOCS+ and HSCO+. They were able to reproduce the HOCS+ O−H stretch to within 1 cm−1 of the experimental result of 3435 cm−1. Even though the relative energies of the stationary points were carefully executed by Wheeler and co-workers16 with corrections for various considerations beyond standard ab initio computations, the large numbers of computations necessary to calculate a force field did not allow for such extensive work at each of the force field points. It is noteworthy that the O−H stretch is in such good agreement with experiment, but the predicted frequencies of the other modes may not be as accurate. Recent work by Huang and co-workers18−20 has shown the need to include various terms in the computation of full quartic force fields (QFFs) that allow for a more complete description of the energy at each point. Recently, we have implemented this approach utilizing VPT and vibrational configuration interaction (VCI) schemes to predict fundamental vibrational frequencies of the trans-HOCO radical to within 4 cm−1 of experiment21,22 for the O−H and CO stretches23 as well as the HOCS+\HSCO+ analogous HOCO+ O−H stretch to within 1 cm−1 of experiment24,25 and the CO stretch to, again, within 4 cm−1.26,27 We also examined the closed-shell cisHOCO− anion and the cis-HOCO radical.28 It has been noted by Mladenović29 that the previous VCI computations of the

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COMPUTATIONAL DETAILS To obtain highly accurate ground state geometries, HOCS+ and HSCO+ are optimized with coupled cluster theory at the singles, doubles, and perturbative triples [CCSD(T)] level31 with the cc-pV5Z basis set32,33 for the H, O, and C atoms and the cc-pV(5+d)Z basis set for sulfur.34 The bond lengths and bond angles are further corrected for core-correlation effects through CCSD(T) computations involving the Martin−Taylor (MT) basis sets specifically designed to treat these effects.35 All of these closed-shell computations make use of spin-restricted Hartree−Fock reference wave functions.36,37 The QFFs38−41 are computed by displacements for the simple internal coordinates of 0.005 Å for bond lengths and 0.005 radians for bond angles from the reference geometry. However, the near-linearity of the O−C−S bond angle necessitates the use of LINX/LINY coordinates available in the INTDER program42 for the O−C−S bond angle coupled to the dihedral angle. This is discussed previously in ref 26. A total of 743 symmetry-unique points in both cation Cs isomers define the QFFs for the present molecules. At each of these, 9583



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origin, HOCS+ has a 2.217 D dipole moment whereas that of HSCO+ is 1.975 D. The spectroscopic constants for HOCS+ and HSCO+ are given in Table 2. All of this data for the other isotopologues of both cation isomers is listed in Table 3. The force constants for HOCS+ and HSCO+ are given in Tables 4 and 5, respectively, where the coordinate number for the force constant corresponds to the simple internal coordinate. They follow sequentially from the geometrical parameters in Table 1 with the addition of the torsion labeled as coordinate 6. The computed zero-point rotational constants for HOCS+ in Table 1 are in very good agreement with experiment13 for the B0 and C0 constants with discrepancies on the order of 0.0001 cm−1 or less. This is consistent with similar systems in our recent work.23,26,28 Also, the values computed for the HOCS+ A0 constant vary from experiment by about 0.06 cm−1, which is about the same as what has been computed in the previous studies. Hence, our HOCS+ zero-point geometry given here should be an accurate representation of this system. Only the Beff has been experimentally reported for HSCO+ by McCarthy and Thaddeus,10 and it falls nearly exactly in between our B0 and C0 values. In fact, the averaging B0 and C0 gives 0.188 05 cm−1, which varies from the experimental Beff (0.188 025 6 cm−1) by less than 0.000 03 cm−1. Hence, our HSCO+ geometry, which is computed in the same fashion as the other cation isomer, should be an accurate representation of that molecule, as well. Additionally, Deff has been reported for HOCS+ (ref 14) and HSCO+ (ref 10). The CcCR computed DJ value, given in Table 2, agrees with Deff to better than 50 Hz for HOCS+. This agreement is not as good for HSCO+, but the computed value and that from experiment are of the same order of magnitude. McCarthy and Thaddeus10 also report Deff for the deuterated and 34S isotopologues of HSCO+. The comparison of these values to their theoretically computed counterparts is given in Table 3. The comparison of the experimental Deff to the computed DJ for H34SCO+ performs similarly to the main isotopologue. Comparison between Deff and DJ for DSCO+ differs by an order of magnitude, but this results from the definition of Deff where deuteration increases the structural asymmetry terms that are included therein but not in DJ. However, the Beff values for these two isotopologues also fall nicely between the computed B0 and C0 constants like HSCO+. The average of B0 and C0 for DSCO+ (0.183 82 cm−1) varies from the experimental Beff by 0.000 04 cm−1, and the variance for the average in these two rotational constants from the experimental Beff for H34SCO+ (0.183 65 cm−1) is the same. Hence, our isotopologue geometries should give the same type of performance compared to experiment as the main isotopologues. HOCS+. Table 6 gives the harmonic, VPT, and VCI computed fundamental vibrational frequencies for both the CcCR and CR QFFs for HOCS+ and its isotopologues. The VPT HOCS+ computations require the inclusion of the Fermi resonance polyads, 2ν4 = ν2 = ν3 + ν4 and 2ν5 = 2ν6 = ν4, and the type-1 Fermi resonance 2ν5 = ν3. A ν6 and ν5 Coriolis and Darling−Dennison resonance are also present. All of the VCI computations reported for HOCS+ and its isotopologues are 5mode representation (5MR) functions of the anharmonic VCI wave function (analogous to CISDTQP in electronic structure theory) making use of 21 604 a′ and 14 146 a′ basis functions. Most of the frequencies actually converge to better than 1 cm−1 in basis space closer to 11 000 a′ and 7000 a″ functions, but a few of the modes need larger bases to converge. For

CCSD(T) single point energies are computed with the aug-ccpVTZ, aug-cc-pVQZ, and aug-cc-pV5Z basis sets.43 The sulfur atoms use aug-cc-pV(X+d)Z where mention of bases for this atom will be folded into the discussion as aug-cc-pVXZ from here on. These energies are then extrapolated to the oneparticle complete basis set (CBS) limit with Martin’s threepoint formula.44 Additional corrections used in the energies at each point in the QFF include the core-correlation effects mentioned above and corrections for scalar relativity45 with the cc-pVTZ-DK basis set. Usage of all three terms gives the CcCR QFF whereas removal of the core-correlation terms gives the CR (for CBS and Relativity) QFF. All electronic structure computations utilize the MOLPRO 2010.1 program.46 A tight least-squares fit of these composite energies must have the sum of the residuals squared on the order of at most 10−16 au2 to achieve high accuracy; the QFFs computed in this study are of this order or better. The potential is defined from the subsequent force constants, Fij..., and displacments, Δi: 1 1 V = ∑ FijΔi Δj + ∑ FikjΔi Δj Δk 2 ij 6 ijk +

1 24

∑ FikjlΔiΔjΔk Δl ijkl

(1)

The fitting of the QFF also provides the equilibrium geometry on which the subsequent VPT and VCI computations are based. Cartesian transformations of the derivatives computed by the INTDER program42 for the full QFF are fed into the SPECTRO program,47 which predicts the spectroscopic constants and fundamental vibrational frequencies via VPT at second order48−50 similar to the work by Wheeler and coworkers16 but also for other isotopologues. Going a step beyond, we employ VCI in the MULTIMODE program51,52 after the force constants are transformed into Morse−Cosine coordinates40 to give variational predictions of the fundamental frequencies, as well.

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RESULTS AND DISCUSSION The geometrical parameters and rotational constants for HOCS+ and HSCO+ are given in Table 1, and visual depictions of each cation in its trans form are shown in Figures 1 and 2.

Figure 1. CcCR equilibrium geometry of HOCS+.

Figure 2. CcCR equilibrium geometry of HSCO+.

Like the HOCO+ cation analogue,26 only the trans isomers of HOCS+ and HSCO+ exist as minima on the potential curve with respect to the torsional angle. This gives a smooth energy decrease from any cis arrangement to the trans precluding the existence of any cis isomers. Using the center-of-mass as the 9584



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Table 2. CcCR Vibration−Rotation Interaction Constants, Quartic and Sextic Centrifugal Distortion Constants, and S Reduced Hamiltonian Terms for HOCS+ and HSCO+ vib−rot constants (MHz) HOCS+

HSCO+

a

Watson S reduction

distortion constants

mode

αA

αB

αC

1 2 3 4 5 6

37392.4 7666.0 −93575.9 1560.1 13526.5 −7433.0

4.2 39.9 −2.0 14.2 −8.6 −15.8

6.1 39.5 1.8 14.3 −14.2 −8.7

τ′aaaa τbbbb ′ τ′cccc τ′aabb τ′aacc τ′bbcc

−2623.020 −0.004 −0.004 −0.915 0.163 −0.004

1 2 3 4 5 6

8396.4 168.2 −6187.9 −44.0 3517.8 −1914.3

−2.3 29.2 −5.0 27.4 −6.9 −18.7

0.6 28.0 2.1 27.9 −12.6 −10.3

τaaaa ′ τ′bbbb τ′cccc τ′aabb τ′aacc τ′bbcc

−63.171 −0.006 −0.006 −0.554 0.008 −0.006

(MHz)

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

(MHz)

2.787 × 106 0.000 0.000 489.528 2.806 −1766.464 0.000 −0.023 0.000 0.329 827.696 0.000 0.000 5.930 0.444 −185.646 −0.001 −0.027 −0.001 0.396

Deffa DJ DJK DK d1 d2

1.064 1.016 0.268 655.486 −7.084 −8.299

Deffb DJ DJK DK d1 d2

3.1 × 1.481 0.137 15.654 −3.014 −3.829

× 10−3 × 10−3

× 10−6 × 10−7

10−3 × 10−3

× 10−5 × 10−6

(Hz) HJ HJK HKJ HK h1 h2 h3

0.000 0.216 −1277.289 2.788 × 106 0.000 0.000 0.000

HJ HJK HKJ HK h1 h2 h3

0.000 0.361 −180.366 −647.690 0.000 0.000 0.000

Experimental Deff for HOCS+ from ref 14. bExperimental Deff for HSCO+ from ref 10.

Table 3. Zero-Point Energy Structuresa (in Å and degrees), Rotational Constants (in cm−1), and S Reduced Watson Hamiltonian Terms (in MHz) for for the isotopologues of HOCS+ and HSCO+ with the CcCR QFF

a b

DOCS+

H18OCS+

HOC34S+

R(O−H) R(C−O) R(C−S) ∠H−O−C ∠O−C−S A0 B0 C0

0.984 067 1.237 520 1.499 800 117.805 174.506 14.191 46 cm−1 0.182 07 cm−1 0.179 56 cm−1

0.986 08 1.237 13 1.499 98 117.922 174.398 25.616 02 cm−1 0.180 84 cm−1 0.179 43 cm−1

0.986 15 1.237 16 1.500 02 117.922 174.397 25.941 10 cm−1 0.187 25 cm−1 0.185 75 cm−1

DJ DJK DK d1 d2

9.026 × 10−4 0.091 265.628 −1.617 × 10−5 −2.147 × 10−4

9.048 × 10−4 0.258 628.245 −5.676 × 10−6 −6.677 × 10−7

9.696 × 10−4 0.256 655.508 −6.585 × 10−6 −7.538 × 10−7

R(S−H) R(C−S) R(C−O) ∠H−S−C ∠S−C−O A0 B0 C0 Beffb Deffb DJ DJK DK d1 d2

DSCO+

HSC18O+

H34SCO+

1.363 98 1.659 44 1.122 67 90.179 176.202 4.836 77 cm−1 0.187 44 cm−1 0.180 20 cm−1 0.183 783 7 cm−1 1.20 × 10−2 1.387 × 10−3 0.132 3.951 −5.318 × 10−5 −1.302 × 10−5

1.367 34 1.659 14 1.122 89 90.200 176.114 9.313 87 cm−1 0.178 43 cm−1 0.174 91 cm−1

1.367 37 1.659 19 1.122 73 90.201 176.114 9.294 51 cm−1 0.185 56 cm−1 0.181 74 cm−1 0.183 61 cm−1 2.9 × 10−3 1.419 × 10−3 0.130 15.698 −2.830 × 10−5 −3.490 × 10−6

1.288 × 10−3 0.122 15.715 −2.465 × 10−5 −3.013 × 10−6

All equilibrium structures for the isotopologues are the same as the variables reported in Table 1 due to the Born−Oppenheimer Approximation. HSCO+ experimental isotopologue data from ref 10.

where VPT and VCI differ greatly, VPT could be more trustworthy.29 However, the discrepancy between VPT and VCI for the particular mode in discussion,29 the torsional mode as observed in the HOCO radicals and cis anion,23,28 is not present in HOCS+ like it is not in HOCO+, either.26 In fact, the CR QFF computes the torsional fundamental vibrational frequency to be 488.4 cm−1 for VPT and 489.1 cm−1 for VCI, a mere 0.7 cm−1 difference. The experimental 3435 cm−1 O−H stretch reported by Nakanga and Amano13 falls between the CcCR and CR computed frequencies for this mode. The experimental value is much closer to the CcCR 3436.4 cm−1 value than the CR 3428.7 cm−1. It is unclear which QFF is systematically more accurate because only one gas phase fundamental vibrational

consistency, all VCI computations reported here use the larger number of basis functions. Additionally, 5MR computations differ from their smaller 4MR counterparts by less than 1 cm−1, indicating convergence in this regime where higher order mode representation (i.e., 6MR) computations are, thus, unnecessary. The first thing worth note from Table 6 is the excellent agreement between VPT and VCI within a given QFF in nearly every case. For a large number of the modes listed, VPT and VCI agree to within 1 cm−1 of each other. Rarely are the deviations between VPT and VCI greater than 5 cm−1. The exception for HOCS+ is the C−S stretching frequency which differs, for example, between the computational methods for the CR QFF by 14.8 cm−1 (858.6 cm−1 for VPT and 843.8 cm−1 for VCI). Recent work has shown that in some cases 9585



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Table 4. Quadratic, Cubic, and Quartic Force Constants (in mdyn/Ån·radm)a for HOCS+ in the Simple-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

10.132 462 0.621 441 11.042 808 −0.163 917 0.202 600 7.351 485 −0.025 859 0.693 551 0.173 973 0.571 773 0.024 014 0.126 844 0.017 908 0.039 839 0.544 780 0.589 084 −58.5378 −1.1432 −2.2276 −74.5552 0.1441 0.2916 −1.6933 −0.0632 0.3319 −51.8650 0.0022 0.0217 −0.6780

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

−0.0161 −0.5115 −0.1941 −0.1459 −0.0540 −0.3692 −1.0538 −0.0541 −0.1395 −0.2161 −0.0566 −0.0771 −0.0240 −0.0719 0.1092 −0.0389 −0.1266 −1.0920 −0.7915 0.0532 0.0050 −0.1983 −0.9855 −0.8912 0.0254 −0.0246 −0.0744

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

262.52 1.85 1.58 5.98 410.71 0.24 −0.17 −0.66 4.76 −0.21 0.41 −1.20 −0.02 −0.60 321.84 −0.04 −0.36 −0.05 −0.39 −0.00 −0.08 0.27 −0.12 0.29 −0.97 0.04 0.08 0.67 −0.00


0.47 0.28 0.20 −0.28 0.91 −0.35 0.05 −0.07 0.29 −0.10 0.03 0.15 0.16 0.00 −0.06 −0.10 −0.07 −0.14 −0.05 0.06 0.21 −0.01 0.16 −0.02 0.12 −0.15 0.53 1.48 1.32

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

0.10 −0.09 0.19 0.03 −0.03 −0.12 0.46 0.37 0.26 0.07 −0.07 3.84 0.48 1.45 0.87 0.02 −0.06 −0.03 −0.00 −0.01 −0.00 0.06 0.10 0.13 −0.00 −0.02 1.31 3.59

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.

theoretical work, but the systematic difference in the frequencies for the other modes is sizable where the QFFs used in this study are more complete and descriptive of the energies at each point. There exists an additional consistency between the fundamental vibrational frequencies computed in this study and those computed by Wheeler and co-workers.16 This is the positive anharmonicities in the ν5 O−C−S bend and the ν6 torsional mode. The VCI CcCR positive anharmonicity for ν5 is 22.9 cm−1 and 17.9 cm−1 for ν6. Wheeler and co-workers report a 20 cm−1 positive anharmonicity for both modes, a similar result. Additionally, it follows that the previously computed harmonic frequencies differ from the ones reported here by the same amount as the anharmonic frequencies. The positive anharmonicity is probably a result of the pseudolinear nature of the O−C−S bond angle. Positive anharmonicities are present in the HOCO+ system,26 and it is not surprising that this isovalent and structurally similar system has them, as well. Positive anharmonicities for the O−C−S bend and torsional modes are also present in all of the HOCS+ isotopologues, as well. HOCS+ Isotopologues. Although the isotopologues would not be nearly as common in the ISM as HOCS+, their rovibrational data definitely assist in laboratory studies where further understanding may be gained. The VCI results given in Table 6 are also 5MR big basis computations as discussed above, but the number and type of VPT Fermi resonance polyads increases as a result of the changes in mass for DOCS+. Here, the requisite type-1 Fermi resonance includes 2ν3 = ν2

frequency is known experimentally, but core-correlation appears to be much more important for the presence of the larger sulfur atom in HOCS+ than for the HOCO systems. The need for core-correlation corrections in the QFF is further evidenced in that the CR fundamental values (regardless of choice between the VPT or VCI method) are systematically lower than their CcCR counterparts. Inclusion of corecorrelation in trans-HOCO needed to be further balanced by inclusion of higher-order electron correlation effects, which were not well modeled in that study.23 However, these affects do not appear to be as important for HOCS+ where the electronic description of this system is already balanced. Additionally, the agreement between VPT and VCI is slightly better on average for the CcCR QFF than it is for the CR QFF. For instance, the difference between VPT and VCI for the C−S stretch is 12.6 cm−1 for the CcCR QFF whereas it is 14.8 cm−1 for the CR QFF. The O−H stretch computed by Wheeler and co-workers16 is coincident with the experimental result and differs from our CcCR value by about 1 cm−1. However, the other fundamental frequencies differ from the CcCR VCI values by an average of 13 cm−1 where our ν3 to ν6 modes are lower in energy. The average difference between the CR VCI frequencies and those computed by Wheeler and co-workers16 is 16 cm−1. Hence, our quartic force field and the additional terms included in the QFF alter the computation of the fundamental vibrational frequencies. It cannot be conclusively stated which set of results are more accurate because similar accuracies for the one known frequency are present between this and the previous 9586



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Table 5. Quadratic, Cubic, and Quartic Force Constants (in mdyn/Ån·radm)a for HSCO+ in the Simple-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

19.601 146 0.736 081 4.744 957 −0.091 674 0.086 075 3.906 930 0.010 104 0.161 587 0.088 904 0.893 554 0.028 412 0.001 143 −0.002 348 0.140 711 0.448 685 0.513 410 −141.0282 −1.0694 −1.5950 −28.5933 0.0370 0.1851 −0.3216 −0.0450 0.0608 −20.6339 −0.1491 0.0508 −0.3975

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

0.0213 −0.3381 −0.0423 −0.3466 0.0642 −0.6617 −0.7504 −0.0479 −0.0386 0.0277 −0.0148 −0.0566 −0.0019 −0.1299 −0.0221 −0.0948 −0.0601 −0.6805 −0.5645 0.0401 −0.1205 −0.1103 −0.6388 −0.8034 0.0071 −0.0376 −0.0485


829.14 −3.02 4.98 0.94 131.46 0.74 −0.22 −0.12 0.52 0.34 0.35 0.22 0.12 −0.08 94.82 0.05 −0.16 0.28 0.68 0.09 −1.12 −0.36 0.06 0.73 −1.15 0.77 0.28 −1.55 −0.04


0.72 0.16 1.45 −0.29 0.85 0.87 0.81 0.35 0.68 −0.02 −0.41 −0.25 0.24 0.28 0.15 −0.79 −0.23 −0.56 −0.01 0.25 0.71 −0.21 0.55 −0.17 −0.51 0.49 −0.44 1.23 0.80

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

−0.22 −0.22 −0.14 0.43 0.07 −0.67 0.66 0.67 −0.40 −0.24 0.14 2.39 0.11 0.42 1.09 −0.21 −1.04 0.73 −0.27 −0.09 0.54 −0.29 0.33 0.06 −0.19 −0.26 0.87 3.03

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.

shifts down by 43.8 cm−1. These results indicate a notable coupling of modes. The 18O isotopologue requires input into VPT for the same resonances as the standard HOCS+ cation but without the inclusion of the 2ν4 = ν2 type-1 Fermi resonance. Agreement within a given QFF between VPT and VCI is about the same as the previously discussed isotopologues with differences on the order of 5 cm−1 for the C−O stretch and 10 cm−1 for the C−S stretch. The other four modes of H18OCS+ have agreement between VPT and VCI to 1 cm−1 or better. Additionally, all of the CR fundamental vibrational frequencies are less than their CcCR counterparts. The 34S isotopologue of HOCS+ requires the same resonances as the main isotopologue. There is better agreement (to 1 cm−1) between VPT and VCI for the C−O stretch with the CcCR QFF for HOC34S+ compared to HOCS+. The C−S stretch varies from VPT to VCI by 11.0 cm−1 for the CcCR QFF. The other modes are, again, more consistent between the vibrational methods. The CR fundamental vibrational frequencies are as little as 4.6 cm−1 lower than their CcCR counterparts for the H−O−C bend and as much as 14.6 cm−1 for the C−O stretch. The fundamental vibrational frequencies of H18OCS+ are somewhat affected by the larger atomic mass as compared to the frequencies given for HOCS+, but the HOC34S+ isotopologue is not as heavily influenced by the heavier atom as the others. HSCO+ and Its Isotopologues. The fundamental vibrational frequencies for the HSCO+ isomer and its isotopologues are given in Table 7. The VCI results are, again, 5MR/big basis computations, and VPT for HSCO+ only requires 2ν6 = ν3 = ν4

and the necessary Fermi resonance polyad is 2ν5 = 2ν6 = ν3 = ν4 = ν2 + ν1. The same Coriolis resonance is necessary for the deuterated cation, but in addition to a ν6 and ν5 Darling− Dennison resonance, there is also one present for ν4 and ν3. Also, the ordering of the modes changes from HOCS+ with the inclusion of the deuterium isotope. The D−O−C bend frequency decreases such that it is less than the C−S stretch. The VPT and VCI agreement within a given QFF for the DOCS+ cation, also given in Table 6, is about the same as that for HOCS+, and most of the modes have correspondence between VPT and VCI for a given QFF to better than 1 cm−1. The CR QFF values are, again, all lower in energy than the CcCR fundamentals except for the ν3 C−S stretch at 811.2 cm−1 from CR VCI. Comparison of the fundamental vibrational frequencies with the theoretically computed and empirically altered frequencies provided by Saebø and co-workers17 shows a strong correlation to our modes that involve the sulfur atom, but poor correlation to the other three modes. The difference between CcCR VCI and Saebø and co-workers’ ν2 C−O stretch is more than 150 cm−1 (1865.2 cm−1 compared with 1713 cm−1, respectively), which indicates that we are predicting this frequency to be less anharmonic than previously computed. The ν1 stretching frequency decreases upon deuteration whereas the C−O stretch is largely unaffected by the change in mass for the hydrogen atom. All of the other frequencies exhibit a much larger decrease than this mode. However, even the CcCR VCI C−S stretch on the other side of the molecule decreases by 57.2 cm−1 after deuteration, and the O−C−S bend 9587



Article

Table 6. Harmonic and Anharmonic CcCR and CR QFF Fundamental Vibrational Frequencies (in cm−1) for HOCS+ and Its Isotopologues from VPT and VCI Computations as Well as Previous Theory and Experimental Results CcCR molecule HOCS

+

DOCS+

H18OCS+

HOC34S+

CR

previous

description

mode

harmonic

VPT

VCI

harmonic

VPT

VCI

theorya

expb

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 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−H stretch a′ C−O stretch a′ H−O−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 ω\ν1 ω\ν2 ω\ν3 ω\ν4 ω\ν5 ω\ν6 ω\ν1 ω\ν2 ω\ν3 ω\ν4 ω\ν5 ω\ν6 ω\ν1 ω\ν2 ω\ν3 ω\ν4 ω\ν5 ω\ν6

3624.9 1910.5 1073.0 909.5 431.9 473.3 2641.4 1898.6 827.5 915.2 402.4 467.5 3613.1 1893.6 1065.0 881.9 429.5 470.0 3624.9 1907.7 1072.9 898.1 431.1 472.4

3436.7 1868.4 1030.4 871.1 454.4 494.6 2539.0 1864.9 814.2 906.2 411.3 477.3 3425.9 1849.0 1022.7 851.0 451.9 491.1 3436.7 1864.8 1030.3 863.4 453.6 493.7

3436.4 1865.9 1028.9 858.5 454.8 495.2 2539.4 1865.2 801.3 900.6 411.0 477.4 3425.6 1846.7 1021.7 842.1 452.2 491.8 3436.4 1863.8 1028.8 852.4 454.0 494.4

3619.0 1902.0 1075.7 904.9 429.2 470.4 2637.0 1890.1 828.0 911.8 400.2 464.5 3607.2 1885.1 1067.7 877.4 426.8 467.2 3619.0 1899.1 1075.7 893.5 428.4 469.5

3429.2 1858.1 1025.3 858.6 444.4 488.4 2533.2 1857.1 812.2 894.8 403.8 471.6 3418.4 1838.2 1018.5 840.7 442.0 485.0 3429.2 1854.4 1025.2 852.1 443.7 487.6

3428.7 1853.8 1024.2 843.8 445.0 489.1 2532.9 1856.7 811.2 890.1 403.7 471.7 3417.9 1833.1 1018.1 829.7 442.5 485.7 3428.7 1849.2 1024.2 838.9 444.3 488.3

3435 1845 1042 870 465 507 2558 1713 808 926 404 473

3435

a

HOCS+ data are CCSD(T)/cc-pVTZ QFF VPT theoretical results from ref 16, and DOCS+ are empircally corrected QCISD/6-311G++(2df,2pd) frequencies from ref 17. bGas phase result from Nakanga and Amano.13

3 cm−1. The rearrangement of the sulfur atom and the oxygen atom in HSCO+ gives better correlation between the two studies for this ν3 H−S−C bend. For HOCS+, ν3 differs between our computations and Wheeler and co-workers’ by 18 cm −1 for CR VCI. Furthermore, complete basis set extrapolation, the inclusion of scalar relativistic effects, and the use of a full quartic force field affect the computation of the fundamental vibrational frequencies fairly significantly for all modes except for the ν3 H−S−C bend. Our computations agree with Saebø and co-workers17 that the S−H stretch should fall very close to 2496 cm−1, which may explain whey they were not able to observe this frequency. The S−H stretch is 937.5 cm−1 lower than the O−H stretch in the other cation isomer for CcCR VCI. The frequencies of the other modes differ with the atomic rearrangement, and the HSCO+ torsional frequency is even 14.9 cm−1 less than its HOCS+ analogue. Positive anharmonicities are, again, present for the ν5 O−C−S bend and the ν6 torsional mode, as well. For CcCR VCI, these are much less at 5.8 and 6.0 cm−1, respectively, in the HSCO+ system than in the other isomer. The positive anharmonicity is of this same order for the 18O and 34S isotopologues, but it is only 1.2 and 1.4 cm−1, respectively, for DSCO+. Deuterating HSCO+ results in a shift in the ordering, again, for the fundamental frequencies, but it is the D−S stretch lowered from 2498.9 to 1814.6 cm−1 within VCI for the CcCR QFF that is affected here making the C−O stretch the most energetic in this system. All of the frequencies for the fundamentals are lowered upon deuteration of this cation save for the C−O stretch, which increases from 2213.6 to 2216.1 cm−1 for CcCR VCI. The ν3 D−S−C bend, for example,

Fermi resonance polyads, and ν6 coupled to ν5 in both Darling−Dennison and Coriolis resonances. DSCO+ further requires 2ν5 to be included in the resonance polyad, as well as ν4 and ν3 in both a Darling−Dennison and Coriolis resonance. The HSC18O+ VPT computations require only the 2ν6 = ν4 type-1 Fermi resonance and the ν6\ν5 Darling−Dennison and Coriolis resonances whereas H34SCO+ VPT resonance input is the same as that for HSCO+. The first thing to note from Table 7 is the exceptional agreement between VPT and VCI within a given QFF. Nearly all of the frequencies are within 1 cm−1 for VPT and VCI, and no differences are greater than 4.1 cm−1. This minor outlier corresponds to the CcCR C−S stretch of the HSC18O+ isotopologue. Regarding the differences between the CR and CcCR QFFs, the C−O stretch is consistently 8 cm−1 less for the CR QFF for all isotopologues, and the C−S stretch is about 4 cm−1 less for the CR QFF than its CcCR counterpart. Hence, core-correlation is necessary for these modes to some small degree but is not a substantial consideration for the other four modes indicating that higher-order correlation effects are also small for HSCO+. All of the other modes differ between QFFs by 1 cm−1 or less. Quite this level of consistency between vibrational methods and QFFs has not been observed in previous studies of the related systems,23,26,28 but it strengthens our prediction for the fundamental frequencies of this cation. Previously computed vibrational frequencies for HSCO+ by Wheeler and co-workers16 typically differ by about 20 cm−1 from our computed values. The exceptions to this roughly 20 cm−1 motif are the CcCR C−O stretch, which at 2213.6 cm−1 is 30 cm−1 higher than Wheeler and co-workers’ 2184 cm−1, and the H−S−C bend, which differs between computations by only 9588



Article

Table 7. CcCR and CR QFF Harmonic and Anharmonic Fundamental Vibrational Frequencies (in cm−1) for HSCO+ and Its Isotopologues from VPT and VCI Computations as Well as Previous Theoretical Results CcCR molecule HSCO

+

DSCO+

HSC18O+

H34SCO+

CR

previous

description

mode

harmonic

VPT

VCI

harmonic

VPT

VCI

theorya

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 a′ C−O stretch a′ S−D stretch a′ D−S−C bend a′ C−S stretch a′ O−C−S bend a″ torsional mode 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 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 ω\ν1 ω\ν2 ω\ν3 ω\ν4 ω\ν5 ω\ν6 ω\ν1 ω\ν2 ω\ν3 ω\ν4 ω\ν5 ω\ν6 ω\ν1 ω\ν2 ω\ν3 ω\ν4 ω\ν5 ω\ν6

2605.6 2246.3 986.9 712.9 395.3 464.3 2248.1 1869.2 781.2 695.0 368.7 463.3 2605.5 2199.2 986.6 697.6 390.7 459.1 2603.3 2246.2 985.2 703.7 394.9 463.7

2499.1 2213.5 970.5 697.0 401.5 470.6 2215.9 1814.8 772.2 680.1 369.7 465.0 2499.0 2167.6 969.8 678.1 396.7 463.5 2497.0 2213.3 968.8 688.4 401.1 470.1

2498.9 2213.6 970.5 697.1 401.1 470.3 2216.1 1814.6 774.8 680.0 369.5 464.7 2498.7 2168.5 970.1 682.2 396.6 465.1 2496.8 2213.4 968.8 688.5 400.8 469.8

2600.0 2237.7 984.3 708.6 392.9 461.5 2239.5 1865.1 778.5 691.3 366.6 460.5 2599.9 2190.8 984.0 693.5 388.4 456.3 2597.7 2237.6 982.6 699.5 392.5 460.9

2496.1 2205.8 970.0 692.9 401.3 468.6 2208.4 1811.9 771.3 676.4 369.4 462.9 2495.9 2160.1 969.8 678.1 396.7 463.5 2494.0 2205.6 968.3 684.4 400.9 468.1

2495.8 2205.8 969.9 693.0 400.8 468.2 2208.5 1811.7 773.5 676.4 368.9 462.6 2495.5 2160.1 969.6 678.3 396.2 463.1 2493.6 2205.6 968.2 684.5 400.4 467.7

2475 2184 967 676 422 486 2050 1824 760 692 369 459

a

Again, the HSCO+ data are CCSD(T)/cc-pVTZ QFF VPT theoretical results from ref 16 and DSCO+ are empircally corrected QCISD/6-311G+ +(2df,2pd) frequencies from ref 17.

is reduced by 195.7 cm−1 from 970.5 to 774.8 cm−1. The O− C−S bend is nearly coincident with the prediction made by Saebø and co-workers17 like with the CR QFF for HOCS+, but again, the other modes vary substantially between the two sets of computations. The computations for the HSC 18 O + and H 34 SCO + fundamentals are very consistent within methods and QFFs. It is hoped that the consistency observed gives a strong correlation as to what experiment would observe for these frequencies. Except for the C−O stretch, inclusion of 18O in the system changes the frequencies from HSCO+ by 6 cm−1 or less. The C−O stretch is decreased from 2213.6 to 2168.5 cm−1 for CcCR VPT. Inclusion of 34S in the system has even less effect when compared to the standard HSCO+ cation. Aside from the C−S stretch which is reduced by 8.6 cm−1 from 697.1 to 688.5 cm−1, the other five modes are decreased by no more than 1.9 cm−1 with the inclusion of the heavier atom.

been more robust and taken advantage of advances in theory development and computational hardware. Our computations reproduce the rotational constants to within 1% of their experimental values for the HOCS+ system13 and within 0.000 03 cm−1 for Beff as compared with the average of B0 and C0 for the HSCO+ isomer.10 We also closely match (∼1 cm−1) previous theory16 for the prediction of the experimentally known O−H stretching frequency13 at 3435 cm−1 but also differ from previous theory in the computation of the other fundamental vibrational frequencies for HOCS+ as well as HSCO+. Our use of a complete quartic force field defined by energies accounting for complete basis set extrapolation, scalar relativistic effects, and (for the CcCR QFF) core-correlation effects should provide the more accurate results for the other, currently unknown modes of this cation. Additionally, we are providing the same data for the isotopologues involving single substitution of D, 18O, and 34S for HOCS+ and also HSCO+ to give similarly accurate reference data for future studies involving those systems. For all systems, the O−C−S bend and torsional mode are positively anharmonic. This is consistent with HOCO+ (ref 26) and previous studies of HOCS+ and HSCO+ (refs 16 and 17). VPT and VCI give very similar results even though they solve the Watson Hamiltonian equations in different ways.49,52 Including the core-correlation effects in the CcCR QFF increases the HOCS+ frequencies for each mode. This is dramatically reduced in the HSCO+ system where only the C− O and C−S stretches are greatly affected by core-correlation. These internal consistencies and the correlation with experiment for the HOCS+ O−H stretch give a strong indication of

■

CONCLUSIONS The HOCS+ and HSCO+ systems are expected to exist in the ISM8,10 because the HOCO+ analogue1 has been detected along with OCS.2 Various reactions have been studied that give rise to either of these sulfur-containing cationic isomers or the corresponding radicals.6,7,9 To study these systems in the laboratory or to help inform studies of interstellar molecules with the newest generation of observing tools, the fundamental vibrational frequencies and more spectroscopic constants must be provided. Only the O−H stretch in HOCS+ has been conclusively determined at 3435 cm−1.13 Previous theoretical work16,17 has provided the fundamental vibrational frequencies for these systems, but the work done in the present study has 9589



Article

(23) Fortenberry, R. C.; Huang, X.; Francisco, J. S.; Crawford, T. D.; Lee, T. J. J. Chem. Phys. 2011, 135, 134301. (24) Amano, T.; Tanaka, K. J. Chem. Phys. 1985, 82, 1045−1046. (25) Amano, T.; Tanaka, K. J. Chem. Phys. 1985, 83, 3721−3728. (26) Fortenberry, R. C.; Huang, X.; Francisco, J. S.; Crawford, T. D.; Lee, T. J. J. Chem. Phys. 2012, 136, 234309. (27) Douberly, G. E.; Ricks, A. M.; Ticknor, B. W.; Duncan, M. A. J. Phys. Chem. A 2008, 112, 950−959. (28) Fortenberry, R. C.; Huang, X.; Francisco, J. S.; Crawford, T. D.; Lee, T. J. J. Chem. Phys. 2011, 135, 214303. (29) Mladenović, M. J. Chem. Phys. 2012, 137, 014306. (30) Fortenberry, R. C.; Crawford, T. D. J. Chem. Phys. 2011, 134, 154304. (31) Raghavachari, K.; Trucks., G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479−483. (32) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007−1023. (33) Peterson, K. A.; Dunning, T. H. J. Chem. Phys. 1995, 102, 2032− 2041. (34) Dunning, T. H.; Peterson, K. A.; Wilson, A. K. J. Chem. Phys. 2001, 114, 9244. (35) Martin, J. M. L.; Taylor, P. R. Chem. Phys. Lett. 1994, 225, 473. (36) Scheiner, A. C.; Scuseria, G. E.; Rice, J. E.; Lee, T. J.; Schaefer, H. F., III. J. Chem. Phys. 1987, 87, 5361−5373. (37) Scuseria, G. E. J. Chem. Phys. 1991, 94, 442−447. (38) Rendell, A. P.; Lee, T. J.; Taylor, P. R. J. Chem. Phys. 1990, 92, 7050−7058. (39) Martin, J. M. L.; Lee, T. J. Chem. Phys. Lett. 1992, 200, 502. (40) Dateo, C. E.; Lee, T. J.; Schwenke, D. W. J. Chem. Phys. 1994, 101, 5853−5859. (41) Lee, T. J.; Martin, J. M. L.; Taylor, P. R. J. Chem. Phys. 1995, 102, 254−261. (42) INTDER 2005 is a general program written by W. D. Allen and co-workers, which performs vibrational analysis and higher-order nonlinear transformations, 2005. (43) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796−6806. (44) Martin, J. M. L.; Lee, T. J. Chem. Phys. Lett. 1996, 258, 136. (45) Douglas, M.; Kroll, N. Ann. Phys. 1974, 82, 89. (46) Werner, H.-J.; et al. MOLPRO, version 2010.1, a package of ab initio programs, 2010, see http://www.molpro.net. (47) Gaw, J. F.; Willets, A.; Green, W. H.; Handy, N. C. SPECTROprogram, version 3.0, 1996. (48) Mills, I. M. . In Molecular Spectroscopy - Modern Research; Rao, K. N., Mathews, C. W., Eds.; Academic Press: New York, 1972. (49) Watson, J. K. G. . In Vibrational Spectra and Structure; During, J. R., Ed.; Elsevier: Amsterdam, 1977. (50) Papousek, D.; Aliev, M. R. Molecular Vibration-Rotation Spectra; Elsevier: Amsterdam, 1982. (51) Carter, S.; Bowman, J. M.; Handy, N. C. Theor. Chem. Acc. 1998, 100, 191−198. (52) Bowman, J. M.; Carter, S.; Huang, X. Int. Rev. Phys. Chem 2003, 22, 533−549.

where these fundamentals may be observed in a laboratory or interstellar spectrum.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Part of this work was funded by the U.S. National Science Foundation to support the work by R.C.F. and T.D.C. through a Multi-User Chemistry Research Instrumentation and Facility (CRIF:MU) award CHE-0741927 and through award CHE1058420. R.C.F. was also funded, in part, through the NASA Postdoctoral Program administered by Oak Ridge Associated Universities through a contract with NASA. The work undertaken by T.J.L. was made possible through NASA Grant 10-APRA10-0096 and NASA Grant 10-APRA10-0167. X.H. also acknowledges funding from the NASA/SETI Institute Cooperative Agreements NNX09AI49A and NNX12AG96A. We also thank the reviewers for their insights which strengthened this paper, especially with regards to Deff. The CheMVP program (courtesy of Dr. Andrew Simmonett of the University of Georgia) was utilized in the creation of the figures.

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REFERENCES

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Fundamental Vibrational Frequencies and Spectroscopic Constants of

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