HCO+ Vibrational Frequencies and Spectroscopic Constants from

Article pubs.acs.org/JPCA

The 1 3A′ HCN and 1 3A′ HCO+ Vibrational Frequencies and Spectroscopic Constants from Quartic Force Fields Ryan C. Fortenberry,*,† Xinchuan Huang,‡ T. Daniel Crawford,§ and Timothy J. Lee*,† †

NASA Ames Research Center, Moffett Field, California 94035-1000, United States SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain View, California 94043, United States § Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States ‡

ABSTRACT: Building on previous studies involving coupled cluster quartic force fields for the description of spectroscopic constants and vibrational frequencies of astronomically relevant molecules, this work applies the same techniques to the elucidation of such properties for the bent 1 3A′ state of HCN and the isoelectronic 1 3A′ HCO+. Core correlation is treated both by explicit means and as a correction. Each approach gives closely comparable spectroscopic constants and vibrational frequencies once more, indicating that the composite method is a viable and less costly alternative. We are providing fundamental vibrational frequencies for these systems where agreement with experiment in previous studies has been within 4 cm−1 or better. Frequencies for the first overtones and combination bands as well as various spectroscopic constants are also reported.

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INTRODUCTION Neither the rotational nor vibrational spectra of the first triplet states (13A′) of the isoelectronic pair HCN and HCO+ have been measured experimentally or computed theoretically. Spectroscopic constants as well as vibrational frequencies for the fundamentals and some overtones and combination bands for the linear X̃ 1Σ+ states of HCN and HCO+ have been characterized experimentally1−7 and have been predicted or reproduced accurately with theoretical quartic force fields (QFFs).8−11 Because these two species have been detected in the interstellar medium (ISM),12−15 examination of these systems’ rotational spectroscopy has also grown in recent years examining how these and related small systems behave in higher energy regimes even into the THz range.16−20 Data from theoretical computations21−23 indicates that the first excited state for these systems are triplet (1 3A′) states that lie more than 4 eV above the ground state. The photochemistry of regions in which these interstellar molecules are known to exist such as the Orion Molecular Cloud14 or the atmospheres of Jupiter24 or Titan25,26 are chemically active enough21,26,27 for the 1 3A′ states of both HCN and HCO+ to be observed rotationally or potentially even vibrationally. Hence, experimental work in the laboratory on 1 3A′ HCN and HCO+ and potential subsequent interstellar observation, especially through the newest generation of space telescopes like the Stratospheric Observatory for Infrared Astronomy (SOFIA), the HIFI instrument on the Herschel Space Observatory, or even the upcoming James Webb Space Telescope (JWST), is growing and will benefit from accurate theoretical computations of the spectroscopic constants and vibrational frequencies for the triplet forms of both of these common systems. Quartic force fields have recently been applied to the computation of the © 2012 American Chemical Society

fundamental vibrational frequencies and spectroscopic constants for various systems of astrochemical importance with accuracies often reported to 1 cm−1 or better for fundamental vibrational frequencies and 0.001 cm−1 for the B- and C-type rotational constants.28−34 Hence, we will apply these same methods to the 1 3A′ states of HCN and HCO+ to accurately elucidate the rovibrational nature of these molecules.

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COMPUTATIONAL DETAILS The reference geometries are optimized at the coupled cluster singles, doubles, and perturbative triples [CCSD(T)] level of theory35 with a restricted open-shell reference wave function.36−38 The aug-cc-pV5Z basis set39−41 geometrical parameters are further modified for effects from core-correlation by utilizing the Martin−Taylor (MT) core-correlating basis set.42 From this reference geometry, the energies of 129 symmetry-unique points of each Cs system are computed to give the QFF. Using the simple-internal coordinates, the two bond lengths are displaced by 0.005 Å while the bond angle is displaced by 0.005 radians per step (up to four steps). The composite energy of each point is defined from a CCSD(T)/aug-cc-pVXZ (where X = T, Q, 5) complete basis limit extrapolated43 energy with corrections for core-correlation from the MT basis set and scalar relativistic (ccpVTZ-DK) corrections.44 This full energy gives the CcCR QFF whereas removal of the core-correlation terms gives the CR QFF. Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: September 17, 2012 Revised: November 1, 2012 Published: November 2, 2012 9324

dx.doi.org/10.1021/jp309243s | J. Phys. Chem. A 2013, 117, 9324−9330

The Journal of Physical Chemistry A

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employing the MULTIMODE program52,53 are also undertaken for comparison of the vibrational frequencies between VPT and VCI.

A third QFF is defined from CCSD(T)/aug-cc-pCVXZ (where X = T, Q, 5) complete basis limit extrapolated energies where core correlation is treated explicitly. This QFF is also corrected for scalar relativistic effects thta give the “R” term added to the core corrected CBS energies (the “cC” term) in the new cCR QFF. Similar QFFs to the CcCR have been shown in the past28−30 to treat core correlation just as well as explicit correlation in the QFF, and this work should corroborate those results. The MOLPRO 2010.1 quantum chemistry package45 is used in all electronic structure computations. A least-squares fit of the points for each QFF, where the sum of residuals squared is on the order of 10−17 au2, returns the equilibrium geometry for the system of interest. The INTDER program46 computes the Cartesian derivatives necessary for the second-order vibrational perturbation theory (VPT)47−49 to be executed in the SPECTRO program.50 The vibrational frequencies and spectroscopic constants are then returned. Finally, after a conversion of the force constants into Morse-cosine coordinates,51 vibrational configuration interaction (VCI) computations

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RESULTS AND DISCUSSION Geometries. Unlike the linear singlet ground state for each of these isoelectronic systems, the 1 3A′ states bend (Figures 1 and 2) to around what would be expected in an sp2 hybridized system, roughly 120°. The linear (core)3σ24σ25σ21π42π0 orbital occupation is excited into (core)3σ24σ25σ21π32π1 for the triplet state. The excitation removes an electron from a π bonding orbital along the axis of the molecule and excites it into a π antibonding orbital giving a bent structure with a (core) 3a′24a′25a′21a″26a′17a′1 configuration. This has been known for HCN where adiabatic computations put the excitation energy at 4.44 eV (EOM-CCSD/aug-cc-pVTZ from ref 22) and 4.69 eV (CASPT2/ANO-L from ref 23). Our CCSD(T)/aug-cc-pV5Z computations adiabatically predict the 1 3A′ state of HCN to lie 4.84 eV above the X̃ 1Σ+ state, somewhat above the previous computations. The CCSD(T)/aug-cc-pV5Z adiabatic 13A′ ← X̃ 1 + Σ transition energy for HCO+ is higher still at 5.86 eV. The excited state nature of these systems may lead to questions of reliability for the coupled cluster computations, but the T1 and D1 diagnostics can gauge how well a single-reference method performs.54−57 The aug-cc-pV5Z T1 diagnostic for 1 3A′ HCN is 0.028 and 0.029 for 1 3A′ HCO+. These values are higher than those for the ground state singlets,58 but computations involving ozone, for example, have similar T1 diagnostics (0.025−0.030 depending on the basis) and produce fundamental vibrational frequencies that are within 2 cm−1 of experiment.59 Hence, our T1 diagnostics are well-within the acceptable reliability range for the CCSD(T) method. The D1 diagnostic for 1 3A′ HCN is 0.072 and 0.071 for 1 3A′ HCO+ (aug-cc-pV5Z). The T1/D1 ratio for 1 3A′ HCN is 0.387 and 0.424 for 1 3A′ HCO+. The D1 diagnostics are higher than those found for many systems but lower than for others such as X̃ 2Σ+ CN for which CCSD(T) performs very well.57,60,61 Both of these 3A′ potential surfaces possess two minima. The lowest energy points correspond to 1 3A′ HCN and HCO+, the

Figure 1. cCR equilibrium geometry of 1 3A′ HCN.

Figure 2. cCR equilibrium geometry of 1 3A′ HCO+.

Table 1. CCSD(T)/aug-cc-pVTZ Geometries (in Å and deg), Dipole Moments (in D), and Relative Energies, ΔETZ/5Za (in kcal/mol) for 1 3A′ HCN ⇌ 1 3A′ HCN and 1 3A′ HCO+ ⇌ 1 3A′ HOC+1 1 3A′ HCN

1 3A′ HNC

1 3A′ c-HCN(TS)

R(C−H) R(C−N) ∠H−C−N μ ΔETZ ΔE5Z R(C−H) R(N−C) ∠H−N−C μ ΔETZ ΔE5Z R(C−H) R(C−N) ∠H−C−N ΔETZ ΔE5Z

1 3A′ HCO+

1.104 1.297 120.9 1.72 0.0 0.0 1.036 1.273 111.7 1.05 10.9 10.4 1.271 1.312 57.4 49.2 48.9

1 3A′ HOC+

1 3A′ c-HCO+(TS)

R(C−H) R(C−O) ∠H−C−O μb ΔETZ ΔE5Z R(C−H) R(O−C) ∠H−O−C μb ΔETZ ΔE5Z R(C−H) R(C−O) ∠H−C−O ΔETZ ΔE5Z

1.109 1.274 118.1 2.52 0.0 0.0 0.998 1.236 115.1 1.81 2.5 1.6 1.317 1.256 57.5 44.2 43.6

a ΔETZ are the CCSD(T)/aug-cc-pVTZ energies at the geometries optimized with this same level relative to HCN/HCO+ on the 1 3A′ triplet surface. ΔE5Z are the relative CCSD(T)/aug-cc-pV5Z energies at the CCSD(T)/aug-cc-pVTZ geometries. bThe dipole moments for the cations utilize the center-of-mass as the origin.

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Table 2. Minimum Energy Structures (in Å and deg), Rotational Constants (in GHz), and Dipole Moments (in D) for 1 3A′ HCN and 1 3A′ HCO+ with the cCR QFF equilibrium molecule 1 3A′ HCN

R(C−H) R(C−N) ∠H−C−N Ae/0 Be/0 Ce/0 μb R(C−H) R(C−O) ∠H−C−O Ae/0 Be/0 Ce/0 μb

1 3A′ HCO+

zero-point (this work)

this work

Li et al.a

standard

deuterated

1.10118 1.28739 120.587 668.4273 40.91867 38.55841 1.72 1.10648 1.26394 117.705 620.9625 40.24594 37.79633 2.51

1.100 1.298 121.7

1.11584 1.29171 120.542 678.6587 40.82843 38.30231

1.11257 1.29116 120.540 400.4413 35.87790 32.72706

1.12090 1.26765 117.560 626.5590 40.19985 37.56728

1.11780 1.26777 117.575 367.9407 35.43172 32.12384

a

CASPT2/ANO-L computations from Li and co-workers (ref 23). bThe dipole moments are computed via CCSD(T)/aug-cc-pV5Z with the centerof-mass at the origin.

Table 3. 1 3A′HCN and HCO+ cCR QFF Quadratic, Cubic, and Quartic Force Constants [in mdyn/(Ån·radm)] for in the Simple-Internal Coordinate System HCO+

HCN F11 F21 F22 F31 F32 F33 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333

9.383 969 0.440 869 4.740 874 −0.084 727 0.155 463 0.623 891 −59.4030 −2.7668 1.4309 −30.0142 0.7824 −0.3971 0.0382 −0.6098 −0.1528 −0.4985

F1111 F2111 F2211 F2221 F2222 F3111 F3211 F3221 F3222 F3311 F3321 F3322 F3331 F3332 F3333

F11 F21 F22 F31 F32 F33 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333

298.35 14.55 −7.81 1.14 146.75 −3.88 1.26 −0.60 −0.95 1.06 −0.04 −0.50 0.16 0.55 −0.86

9.263 581 0.313 625 4.797 050 −0.260 761 0.163 840 0.619 112 −59.0150 −3.6971 1.1243 −29.0260 2.4609 −0.8226 0.1283 −0.0901 −0.4480 −0.4966

F1111 F2111 F2211 F2221 F2222 F3111 F3211 F3221 F3222 F3311 F3321 F3322 F3331 F3332 F3333

306.41 30.96 −11.64 2.56 144.28 −13.60 3.98 −0.60 −0.32 −0.94 0.94 −0.30 0.28 0.87 −0.60

include core-correlation effects and the CASPT2/ANO-L geometry from Li and co-workers.23 Mainly, we are predicting a 0.011 Å shorter C−N bond and a 120.587° bond angle instead of 121.7°. Additionally in Table 2, the other geometrical parameters and the rotational constants (in GHz) are given for both molecules and their deuterated forms. The vibrationally averaged Rα C−H bond lengths are shortened slightly upon deuteration, and the rotational constants are understandably reduced. The force constants for each of the triplet systems are listed in Table 3. The “1” coordinate corresponds to the C−N bond, the “2” coordinate is the C−H bond, and “3” is the lone bond angle. The spectroscopic constants of all four systems of interest are computed from VPT with SPECTRO and are given in Table 4. Vibrational Frequencies. Table 5 lists the harmonic and anharmonic vibrational frequencies of 1 3A′ HCN and DCN as well as 1 3A′ HCO+ and DCO+. Besides the fundamental vibrational frequencies, the first overtones and combination bands are also reported here. For the VPT computations, no resonances of any kind are present in HCN. HCO+ exhibits a 2ν2 = ν1 type-1

systems studied here, whereas a second minimum results from isomerization to 1 3A′ HNC and HOC+. As shown in Table 1, CCSD(T)/aug-cc-pVTZ computations place 1 3A′ HCN 10.9 kcal/mol below the 1 3A′ HNC isomer. However, the barrier to isomerization is 49.2 kcal/mol, similar to what has been reported for X̃ 1A′ HCN ⇌ X̃ 1A′ HNC.62 CCSD(T)/ aug-cc-pV5Z single point energies computed at the optimized CCSD(T)/aug-cc-pVTZ geometries lower these relative energies slightly, but not by nearly enough to lead to a different conclusion. Hence, these two isomers exist as distinct systems on their 1 3A′ potential surface. 1 3A′ HOC+ is only 2.5 kcal/mol higher than 1 3A′ HCO + for the triple-ζ basis set and 1.6 kcal/mol higher for the quintuple-ζ basis set. Even so, the barrier still remains high (at more than 43 kcal/mol) for this potential surface. As with 1 3A′ HCN and HNC, 1 3A′ HCO+ and HOC+ are also distinct minima. For this study, we are limiting ourselves to discussion of the two lower energy isomers on each potential surface. The equilibrium geometries of 1 3A′ HCN, given in Table 2, differ between our CCSD(T)/aug-cc-pV5Z results modified to 9326



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Table 4. 1 3A′ HCN and HCO+ cCR Vibration−Rotation Interaction Constants, Quartic and Sextic Centrifugal Distortion Constants, and S Reduced Hamiltonian Terms vib-rot constants (MHz) HCN

αA

αB

αC

1 2 3

35816.4 −2839.4 −53418.8

−101.8 398.9 −116.6

8.4 365.2 138.5

(MHz)

(Hz)

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

−2305.037 −0.638 −0.438 −4.848 5.867 −0.515

DCN

1 2 3

15932.8 −2161.8 −25490.1

−9.6 353.4 −138.6

71.0 316.7 95.8

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

−904.339 −0.622 −0.328 1.796 4.798 −0.430

HCO+

1 2 3

32362.8 −5416.8 −38138.0

−118.0 423.3 −207.3

−4.2 394.8 62.1

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

−1730.121 −0.698 −0.469 −4.302 6.852 −0.560

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

−680.461 −0.699 −0.359 1.683 5.174 −0.481

DCO+

1 2 3

14804.1 −2675.3 −18832.8

−57.0 383.4 −205.4

Watson S reduction

distortion constants

mode

36.9 344.8 48.7

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

Fermi resonance, and both DCN and DCO+ exhibit a 2ν3 = ν2 type-1 Fermi resonance and a ν3 + ν2 = ν1 type-2 Fermi resonance. For VCI, the maximum number of mode couplings that can be included in the computation is 3. Hence, all computations are 3MR which is analogous to a full-CI description in electronic structure computations. Three of the systems examined here exhibit convergence in the basis space to within 0.5 cm−1 at 680 a′ basis functions, but DCN requires fully 969 functions to achieve convergence for the energy levels reported here. HCN and DCN. For HCN, the cCR fundamental vibrational frequencies given in Table 5 differ by no more than 2.1 cm−1 from their CcCR counterparts. This is true whether one is considering VPT or VCI. The overtones and combination bands are not as consistent. The cCR VPT 2ν3 is computed to be 1949.6 cm−1, 6.1 cm−1 below the CcCR 2ν3 at 1956.0 cm−1. However, most other frequencies vary between the QFFs by 3 cm−1 or less. The neglect of core correlation in the CR QFF

1.968 0.683 0.113 7514.976 55.221 −2.126 0.244 34.184 0.198 85.814 4.871 1.302 0.174 −604.357 40.867 −8104.797 0.422 26.960 0.305 27.536 1.195 1.211 0.271 6929.577 48.126 −1.763 0.733 30.756 0.523 74.460 2.984 2.032 0.310 48.256 32.991 −6672.074 0.969 25.735 0.620 25.879

(MHz) × 106

(Hz)

DJ DJK DK d1 d2

0.132 −0.514 576.641 −0.012 −0.001

HJ HJK HKJ HK h1 h2 h3

0.267 0.500 −1.379 × 104 1.982 × 106 0.129 0.065 0.013

× 105

DJ DJK DK d1 d2

0.115 −1.876 227.845 −0.018 −0.001


0.516 35.170 −8.753 × 104 4.956 × 106 0.259 0.111 0.023

× 106

DJ DJK DK d1 d2

0.143 −0.917 433.304 −0.014 −0.001


0.576 39.015 −1.073 × 104 1.206 × 106 0.220 0.083 0.015

DJ DJK DK d1 d2

0.128 −1.967 171.954 −0.021 −0.002


0.891 26.291 −6650.024 3.050 × 105 0.404 0.140 0.027

× 104

× 104

× 105

is more noticeable. The two fundamental stretching modes are about 8 cm−1 less than either of the core correlated QFFs. The bending mode, on the other hand, varies by less than 3.2 cm−1. The overtones for the bond stretches are comparably less energetic when the CR QFF is used, but interestingly, the cCR and CR 2ν3 transitions have more similar frequencies than between either and the CcCR QFF. The VPT cCR 2ν3 frequency is 1949.6 cm−1 whereas its CR counterpart is 1949.4 cm−1. Besides this one case, however, the CR QFF predicts frequencies much lower than the core correlating QFFs, especially for the combination bands where ν1 + ν2 with VCI differs from the cCR QFF by 16.4 cm−1 and from the CcCR QFF by 14.9 cm−1. For 1 3A′ HCN, VPT and VCI are quite consistent regardless of the choice in QFF. Such behavior has been observed with similar closed-shell molecules.33,34 For instance, the difference between VPT and VCI for the ν2 C−N stretch at 2758.1 cm−1 (cCR VCI) varies by no more than 0.1 cm−1 within any of the 9327



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Table 5. Harmonic and Anharmonic cCR, CcCR, and CR QFF Fundamental Vibrational Frequencies (in cm−1) for the 1 3A′ States of HCN, HCO+, and Deuterated Forms with VPT and VCI cCR molecule

description

HCN

a′ C−H stretch a′ C−N stretch a′ H−C−N bend

DCN

HCO+

DCO+

a′ C−D stretch a′ C−N stretch a′ D−C−N bend

a′ C−H stretch a′ C−O stretch a′ H−C−O bend

a′ C−D stretch a′ C−O stretch a′ D−C−O bend

mode ν1 ν2 ν3 2ν1 2ν2 2ν3 ν1 + ν1 + ν2 + ν1 ν2 ν3 2ν1 2ν2 2ν3 ν1 + ν1 + ν2 + ν1 ν2 ν3 2ν1 2ν2 2ν3 ν1 + ν1 + ν2 + ν1 ν2 ν3 2ν1 2ν2 2ν3 ν1 + ν1 + ν2 +

ν2 ν3 ν3

ν2 ν3 ν3

ν2 ν3 ν3

ν2 ν3 ν3

CcCR

CR

harmonic

VPT

VCI

harmonic

VPT

VCI

harmonic

VPT

VCI

2932.1 1589.9 1010.6 5864.2 3179.8 2021.2 4522.0 3942.7 2600.5 2153.9 1573.8 780.1 4307.8 3147.6 1560.2 3727.7 2934.0 2353.9 2952.1 1566.7 971.3 5904.2 3133.4 1942.6 4518.8 3923.4 2538.0 2169.5 1542.8 751.2 4339.0 3085.6 1502.4 3712.3 2920.7 2294.0

2755.6 1564.8 982.1 5338.1 3107.7 1949.6 4327.6 3723.5 2533.1 2046.8 1553.7 763.7 3997.6 3085.4 1515.2 3595.5 2793.2 2326.2 2788.3 1538.8 939.4 5428.3 3056.5 1867.9 4330.8 3701.3 2464.1 2060.5 1522.7 733.1 4037.4 3023.5 1454.5 3567.4 2761.3 2276.0

2758.1 1564.7 980.3 5375.0 3107.1 1942.3 4330.0 3721.6 2528.2 2049.0 1552.1 763.0 4004.1 3087.0a 1513.8 3597.0 2797.2 2317.3 2789.9 1538.4 938.2 5433.8 3055.0 1863.4 4329.3 3702.7 2459.2 2064.3 1521.4 732.5 4046.9 3026.4 1453.3 3573.5 2768.4 2263.5

2931.6 1589.5 1010.4 5863.2 3179.0 2020.8 4521.1 3942.0 2599.9 2153.5 1573.4 780.0 4307.0 3146.8 1560.0 3726.9 2933.5 2353.4 2951.8 1566.4 971.2 5903.6 3132.8 1942.4 4518.2 3923.0 2537.6 2169.3 1542.5 751.1 4338.6 3085.0 1502.2 3711.8 2920.4 2293.6

2755.2 1563.7 984.2 5337.2 3105.4 1956.0 4325.8 3726.3 2533.8 2046.3 1553.0 764.8 3996.4 3083.9 1518.7 3594.2 2794.4 2326.5 2788.2 1539.0 939.4 5428.0 3057.1 1867.3 4331.2 3701.7 2464.7 2060.4 1522.7 733.1 4037.2 3023.6 1454.2 3567.5 2761.6 2276.3

2757.9 1563.7 982.4 5376.0 3104.9 1948.1 4328.5 3724.8 2528.8 2048.6 1551.6 764.1 4003.0 3087.4b 1516.9 3595.8 2798.6 2318.0 2789.6 1538.6 937.9 5432.9 3055.3 1862.2 4329.6 3702.3 2459.3 2064.4 1521.7 732.6 4046.9 3027.6 1453.4 3574.6 2769.0 2264.2

2923.7 1581.4 1007.6 5847.4 3162.8 2015.2 4505.1 3931.3 2589.0 2147.6 1565.4 777.7 4295.2 3130.8 1555.4 3713.0 2925.3 2343.1 2946.0 1558.9 970.4 5892.0 3117.8 1940.8 4504.9 3916.4 2529.3 2165.1 1535.1 750.5 4330.2 3070.2 1500.9 3700.2 2915.6 2285.6

2748.4 1556.0 981.0 5325.0 3090.2 1949.4 4311.0 3715.7 2522.8 2040.9 1546.6 762.4 3986.4 3071.3 1512.4 3582.3 2786.2 2320.1 2783.4 1531.8 938.4 5419.8 3043.1 1865.5 4318.8 3695.5 2456.5 2056.6 1516.4 732.4 4030.3 3011.5 1451.9 3557.0 2756.5 2271.0

2750.9 1555.9 979.2 5360.6 3089.7 1941.6 4313.6 3714.3 2518.1 2043.2 1544.1 761.6 3993.1 3051.2c 1511.7 3582.7 2790.4 2308.0 2785.0 1531.5 937.3 5427.3 3041.6 1861.6 4317.3 3697.0 2451.9 2060.5 1514.5 731.7 4040.1 3014.3 1451.3 3562.8 2763.7 2256.2

The lower state composed primarily of ν2 + 2ν3 and secondarily of 2ν2 is 3063.6 cm−1. See text for discussion. bSimilar to footnote a but here is 3064.9 cm−1. cThe higher state composed primarily of ν2 + 2ν3 and secondarily of 2ν2 is 3051.2 cm−1. Again, see text for discussion.

a

QFFs. The ν1 C−H stretch varies by 2.5 cm−1 between VPT and VCI for each of the QFFs, and the bending fundamental is consistently 1.8 cm−1 lower for VCI than VPT. The overtones, again, are not as well-behaved, especially 2ν1. VPT with the cCR QFF computes a 5338.1 cm−1 frequency whereas cCR VCI puts this value at 5375.0 cm−1, a difference of 37.1 cm−1. Similar discrepancies are present for this state with the other QFFs. Inclusion of more basis functions does not rectify this difference between VPT and VCI for 2ν1. The difference results from the excitation contributions present in the VCI wave function that VPT cannot treat. The ν1 + ν2 + ν3 transition has a secondary yet large coefficient contribution to the VCI wave function for this state in all QFFs. Hence, the mixing of states in the VCI wave functions raises the frequncy of 2ν1 relative to VPT and should give a more complete description of this frequency. The behavior of the vibrational frequencies for 1 3A′ DCN is similar to that of the main isotopologue with the notable exception that VPT and VCI give more comparable results for the 2ν1 frequency. They differ by 6.5 cm−1 for the cCR QFF

(3997.6 cm−1 for VPT and 4004.1 cm−1 for VCI), and this is consistent with the other QFFs, as well. However, the ν2 + ν3 combination band varies between VPT and VCI more than it does in HCN: 8.5 cm−1 for the core correlating QFFs and 11.9 cm−1 for the CR QFF. The ν1 C−D fundamental stretch varies between methods to a much lesser degree by 2.2 cm−1 for the cCR QFF (2046.8 cm−1 for VPT and 2049.0 cm−1 for VCI), and the other two fundamentals give even better agreement between methods. Still, the difference between VPT and VCI is roughly consistent between QFFs indicating that these effects result from the methods and not the QFFs themselves. Agreement for a given frequency between the cCR and CcCR QFFs is better for DCN than for HCN. The largest discrepancy present is again 2ν3, but here it is only 3.5 cm−1 for VPT and 3.1 cm−1 for VCI. Most other states have agreement to 1 cm−1 or better. The CR QFF fundamentals are once more lower than the values for either of the core correlating treatments. The 1544.1 cm−1 CR VCI ν2 is 8.0 cm−1 less than its 1552.1 cm−1 cCR VCI counterpart, for example. On the extreme, 9328



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the CR VCI 2ν2 overtone is fully 35.8 cm−1 less at 3051.2 cm−1 than the 3087.0 cm−1 frequency from cCR VCI. Again, mixing of states in the CR VCI wave function affects the reported frequencies of the 2ν2 frequency. For each of the QFFs, there exist two frequencies that have large wave function coefficients for the 2ν2 basis. These also have large contributions from ν2 + 2ν3, as well. For the cCR and CcCR QFFs, the higher frequency has a larger wave function coefficient for 2ν2. The cCR higher frequency 2ν2 coefficient is 0.76 whereas the ν2 + 2ν3 coefficient is 0.60. For the CR QFF, however, the lower frequency 2ν2 coefficient (0.75) is larger than the ν2 + 2ν3 coefficient (0.56). Hence, the state with more 2ν2 character and the subsequent eponymous label differs between QFFs. Furthermore, the VCI frequencies should be more accurate than VPT because a more complete description of the vibrational behavior is included in the formulation, and the CR QFF has shown to be more accurate in the prediction of frequencies for comparable systems of first-row atoms.31 HCO+ and DCO+. The fundamentals, overtones, and combination bands are much better behaved between QFFs for 1 3A′ HCO+ compared to the isoelectronic HCN. The best example is that the cCR and CcCR QFFs differ by no more than 1.2 cm−1 for VCI 2ν3 with most states varying between QFFs by 0.3 cm−1 or less. The CR QFF again computes its frequencies to be lower in energy than the other two QFFs, especially for the stretches. Agreement between the VPT and VCI methods is more consistent for HCO+, as well. The overtones give the largest discrepancies, but the fundamentals differ within a given QFF by 1.6 cm−1 or less. DCO+ also improves on all fronts relative to HCN, especially between the core correlating basis sets. VPT and VCI produce nearly identical results for most of the frequencies between the cCR and CcCR QFFs. The CR QFF is still as much as 12.1 cm−1 below its corresponding cCR frequency for VCI 2ν2 (3014.3 and 3026.4 cm−1, respectively), but the fundamental frequencies are more consistent between QFFs, especially for ν1 and ν2. VPT and VCI still differ by several cm−1 in their descriptions of the frequencies for the overtones and combination bands. This is once more due to the mixing of states and resonances in the VCI wave functions but, on the whole, is much less than that observed for DCN.

frequencies for these systems and their deuterated counterparts. This will help to inform currently ongoing laboratory studies of these small, common molecules and give insight to interstellar studies of these systems in environments where they may be found.

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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.

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ACKNOWLEDGMENTS The NASA Postdoctoral Program administered by Oak Ridge Associated Universities through a contract with NASA funded the work done by R.C.F. T.D.C. and R.C.F. acknowledge support from the National Science Foundation Multi-User Chemistry Research Instrumentation and Facility (CRIF:MU) award CHE-0741927, which provided the computational hardware utilized in this study. X.H. acknowledges funding from the NASA/SETI Institute Cooperative Agreement NNX12AG96A. NASA Grant 10-APRA10-0167 funded the work done by T.J.L. Drs. John C. Pearson and Shanshan Yu of the Jet Propulsion Laboratory deserve the authors’ thanks for broaching the importance of this project and for engaging in beneficial discussions related to the work. The CheMVP program was utilized in the creation of the figures. T.J.L. thanks Professor Takeshi Oka for his encouragement and insight in the study of astrochemistry over much of the last 30 years.

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REFERENCES

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CONCLUSIONS Consistent with previous studies, the use of explicit core correlation or a core correlation correction in a QFF produces rotational constants within 1% agreement of one another and vibrational frequencies that are often within 1 cm−1 of each other. Core correlation is definitely a factor in the computation of the spectroscopic constants or vibrational frequencies. The CR QFF reports lower frequencies than either the cCR or CcCR QFFs, and the rotational constants vary by a few hundred megahertz without core correlation. The fundamental frequencies vary relatively little between VPT and VCI and even between QFFs. We are providing data for those states which may prove insightful in future studies. Furthermore, the use of Morse-cosine coordinates in the VCI computations should make those frequencies more trustworthy than their VPT counterparts. Rovibrational data for the 1 3A′ states of the HCN and HCO+ systems is pertinent to the analysis of these species in various interstellar and terrestrial environments where excitations from the linear ground states are possible. In this work we are providing the first spectroscopic constants and vibrational 9329



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HCO+ Vibrational Frequencies and Spectroscopic Constants from

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