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Feb 3, 2017 - by MULTIMODE with ab Initio Potential Energy and Dipole. Moment ... The current spectra for cis-HOCO, while not of “spectroscopic” a...
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The Rovibrational Spectra of trans- and cis-HOCO, Calculated by MULTIMODE with ab Initio Potential Energy and Dipole Moment Surfaces Stuart Carter, Yimin Wang, and Joel M. Bowman* Cherry L. Emerson Center for Scientific Computation, Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States S Supporting Information *

ABSTRACT: The code MULTIMODE is used in its reaction path version, along with ab initio potential energy and dipole moment surfaces introduced earlier, to predict the infrared spectra of both trans and cis forms of HOCO at temperatures 296 and 15 K. All six fundamentals are isolated for each isomer and temperature, and their main features examined, paying particular attention to the OH stretch fundamental, whose spectrum has been reported experimentally for trans-HOCO. The current spectra for cis-HOCO, while not of “spectroscopic” accuracy, should be sufficient to aid in new experimental efforts to record the spectrum of this isomer.

I. INTRODUCTION The chemical reaction OH + CO → H + CO2 is of central importance in hydrocarbon combustion chemistry; for recent reviews, see refs 1 and 2. The reaction is of fundamental interest as well because of the complexity of the potential energy surface (PES),3,4 which contains, among other features, the trans- and cis-HOCO isomers. Thus, the spectroscopic characterization of these isomers has received considerable attention over the years. Experimentally, there have been several reports of the IR spectrum of the more stable transHOCO.5−8 The high-resolution spectrum of trans-DOCO in the ground vibrational state was recently reported in a direct study of stabilization of the reactants OD + CO.9 This paper confirms in a direct way that trans-DOCO is formed in thirdbody stabilizing collisions in this reaction. The role of the cis isomer in the ultimate formation of the products is also clear from experimental work by Continetti and co-workers.2 However, the detailed dynamics underlying the formation of these isomers and the possible role of isomerization between these isomers in the reaction is not totally clear. Theoretically, there has been a flurry of activity over the past five years. This includes the generation of high-level quartic force fields of both isomers, used in VPT2 calculations of the vibrational fundamentals,10−13 to the construction of high-level, ab initio global and semiglobal PESs.14−17 Less is known experimentally about the cis isomer. The microwave spectrum has been reported for cis-HOCO, cis-DOCO,18,19 and for various isotopic variations of cis-HOCO.19 A low-resolution photodetachment spectrum of DOCO− provided information about several vibrational states of cis-DOCO.10 © 2017 American Chemical Society

Of particular relevance to a calculation of the (ro-)vibrational spectra of these isomers, we reported an ab initio (UCCSD(T)-F12/ aug-cc-pVDZ) dipole moment surface (DMS) that spans the region of both isomers and the isomerization barrier separating them.17 To the best of our knowledge this is the only DMS that can be used in large-scale quantum simulations of the rovibrational spectra of these two isomers and also the isomerization dynamics. In addition to this DMS, we reported a high-level (UCCSD(T)-F12/aug-cc-pVTZ) semiglobal PES that spans the same region. We used this PES in coupled-mode anharmonic calculations of the fundamentals and a variety of overtone and combination bands of the two isomers as well as a number of low-lying states that span both minima. The calculations were done using three independent methods including the “reaction path” version of the code MULTIMODE (MM-RPH).20 Roughly 20 vibrational band intensities (zero total angular momentum) were also reported for cis- and trans-HOCO using MM-RPH. Since this paper was the latest in a series reporting anharmonic vibrational calculations for both isomers, comparisons of results from two earlier VPT2 calculations were made with the MULTIMODE calculations and also those done with an exact four-atom Hamiltonian in CO−OH Jacobi coordinates. These comparisons are significant for the present paper, as they give an assessment of the possible systematic uncertainties in the various calculations. These are mainly from differences in the potentials, although all Received: December 27, 2016 Revised: January 31, 2017 Published: February 3, 2017 1616

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that the normal coordinate vectors do so as well. This means paying particular attention to a possible switching of vectors at near-degeneracies in the normal-mode eigenvalues. In the case of HOCO, no such switching takes place at any point along the RP, and dot products of both goemetries and vectors confirm that both quantities do indeed form smooth continuous sets. Product wave functions are built, commencing with harmonic oscillator (HO) primitives in the five normal coordinates at the minimum-energy trans structure and sin(mτ) and cos(mτ) functions in the repeating torsional coordinate τ. These are first improved by performing one-dimensional variational calculations in both Qk and τ by picking only the relevant onedimensional terms from the complete Hamiltonian in turn. Next a vibrational self-consistent field (VSCF) analysis is performed, but here, advantage is taken of the hierarchical expansion of the potential V(Q) and the inverse moment of inertia tensor μαβ(Q).20 In practice, this means that integration is performed over 1, 2, 3, ... normal modes in turn, while integrating fully over τ in all cases. We refer to this as nMR and nMC coupling, where nMR refers to the number of normal coordinates Qk appearing in the integration over V(Q), and nMC refers to the number of normal coordinates Qk appearing in the integration over μαβ(Q), respectively. In this way, nMR and nMC need only be taken as far as is necessary for convergence in the energy levels under consideration. This VSCF procedure yields the final one-dimensional basis for use in the ensuing vibrational configuration interaction (VCI) analysis, where again the nMR and nMC coupling is used with the complete vibrational (J = 0) Hamiltonian. The rovibrational basis uses the same VSCF basis, but now this is multiplied by the symmetric top rotational basis D0ka(±), where Ka is the projection of J along the principal Z-axis. Finally, following Flaud et al.,31 we orientate the principal axes according to the Ir representation. Also note that, in his study of hydrogen peroxide, Flaud et al.31 used a half-integral τ basis for odd Ka, to maintain continuity of the total wave function at τ = 2π. In HOCO, however, the geometries at τ = 0 and τ = 2π are identical, and so only an integral τ basis is required for all Ka. Rovibrational energies and wave functions are obtained by performing vibrational-like calculations for fixed values of Ka (and Kc) in turn. These correspond to a particular rotational basis function D0ka(±). Only those terms diagonal in Ka are used during these steps. Finally, subsets of the functions produced by these steps are mixed under operations of the complete (J > 0) Hamiltonian. Once the rovibrational calculations have been performed, the corresponding wave functions can be used in calculations of the line intensities, providing that a dipole moment surface (DMS) for the molecule is available. An ab initio DMS surface was developed in our earlier study.17 We are therefore able to perform intensity studies of both trans- and cis-HOCO, since both the PES and DMS are valid throughout the complete torsional range covering the cis−trans−cis isomerization. Again, this procedure has been outlined fully earlier.20−22 The temperature-dependent line intensity Si at temperature T (K) is calculated using the following expression:22,32

were obtained at the CCSD(T) level of theory with large basis sets. Results from those comparisons are largely satisfyingly consistent, with quantitative differences in the range of a few wavenumbers, with, however, differences with VPT2 for the OH stretch of cis-HOCO being 14−20 cm−1 owing to strong mixing found in the variational calculations. Unfortunately, that band has not been reported experimentally. Three of the six fundamental bands were reported in recent photodetachment experiments, and these are reviewed and discussed below. In this paper, we report calculated rovibrational line-list spectra for cis- and trans-HOCO at 296 and 15 K, using the PES and DMS of Wang et al.,17 mentioned above. The calculations make use of an exact formalism for arbitrary total angular momenta (currently ignoring any possible spin-rotation effects). Such calculated spectra have not been reported previously for these isomers. (Indeed, for tetraatomic or larger molecules, there have only been a handful of such line-list calculations.20−28) Experimentally, the pure microwave spectrum has been reported for cis-HOCO,18,19 as noted already, but no rovibrational spectra have been reported, to the best of our knowledge. For trans-HOCO a high-resolution spectrum at 13 K was recently reported by Nesbitt and co-workers for the OH stretch.8 The paper is organized as follows. In the next section, a brief review of the methods used in MM-RPH is given, with special attention given to J > 0 calculations. Specifics about the present calculations are given in the preamble to Section III, which is then divided into two subsections, one for each isomer. Results and Discussion are given in that section, and we conclude with a summary and conclusions.

II. THEORY The code MULTIMODE(MM) performs quantum mechanical rovibrational energy calculations of polyatomic molecules by two distinct procedures. For semirigid molecules such as formaldehyde, for example, where there are no large-amplitude motions, the method is based on the Watson normal coordinate Hamiltonian,29 where the normal coordinates are centered at this single minimum. We refer to this method as MM-Single Reference (MM-SR). For molecules that contain a single large-amplitude vibration in the form of a torsion-like motion such as hydrogen peroxide, the method is based on the Miller−Handy−Adams reaction path Hamiltonian,30 where now the torsional (reaction path) coordinate is curvilinear in nature, and 3N − 7 normal coordinates orthogonal to the path are generated at discrete intervals along the path. We refer to this method as MM-Reaction Path (MM-RP). Both of these procedures have been outlined fully in several papers; see, in particular, refs 20, 21, and 22. Because of the nature of the cis−trans isomerization of HOCO, we use the version MM-RP in this work,20 using a slightly modified version of the PES, which was introduced in an earlier study.17 It is necessary only to cover the main topics of the MM-RP algorithm in this paper, since full details can be found elsewhere.20 The reaction path (RP) is represented by 720 equally spaced points at half-degree intervals, and at each point, the geometry of HOCO is optimized to give a smooth minimumenergy path, where each geometry is rotated to a principal axis (PA) system of coordinates, as required by the theory given in ref 30. At each PA geometry, a set of 3N − 7 = 5 normal coordinates Qk are calculated by projecting the torsional motion.30 It must be guaranteed that not only do the RP points form a smooth continuous set along the complete RP but also

Si = 3054.6gNSνi |R |2

exp( −Er /kT ) [1 − exp( −νi /kT )] Q (T ) (1)

where gNS is the nuclear spin statistical weight, Er is the energy of the lower state, νi is the transition wavenumber (in cm−1), 1617

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The Journal of Physical Chemistry A Table 1. Fundamentals and Zero-Point Energy (cm−1) of trans-HOCO

a

MM-RP

ref 17

ZPE

description

4547.5

4547.4

expt

ν1 ν2 ν3 ν4 ν5 ν6

OH stretch CO′ stretch HOC bend OC stretch OCO′ bend torsion

3641.8 1855.6 1208.5 1050.7 613.4 499.7

3639.9 1855.5 1210.0 1049.4 612.4 500.3

3635.7a 1852.6b 1194c 1048c 629c

Reference 7. bReference 6. cReference 10.

Table 2. Fundamentals and Zero-Point Energy (cm−1) of cis-HOCO′ ZPEa

a

description

ν1

OH stretch

ν2 ν3 ν4 ν5 ν6

CO′ stretch HOC bend OC stretch OCO′ bend torsion

MM-RP

ref 17

PES-NN ref 15

5099.2

5101.1

5090.2

b

3440.6 3442.9b 1816.9 1270.4 1035.9 595.6 549.6

b

3438.4 3444.7b 1817.6 1268.7 1037.6 594.5 552.5

exptc

b

3427.6 3443.5b 1816.5 1277.0 1042.4 595.7 557.0

1290 1040 605

Relative to trans-HOCO′. bHeavy mixing of states. cReference 10.

Figure 2. Relative intensities (cm/mol) of transitions in the overview spectra of trans- and cis-HOCO at 15 K.

is a conversion factor to give an intensity in centimeters per mole. We took both gNS and Q(T) to be unity, so we are only able to calculate relative intensities here. We are unable, at present, to deal with electron spin states other than singlets. II.A. Computational Details. This subsection can be skipped by readers who wish to go to results and discussion. The first step in calculating the spectrum is to ensure that the energy levels are converged to some allowed tolerance up to the maximum energy required. In this paper, we are interested in the six fundamentals of both trans- and cis-HOCO. With the PES and MM-RP method used in this work, the zero point of cis-HOCO is calculated as a torsional excited state of trans-HOCO at 551.71 cm−1 above the trans-HOCO zero point. This means that, to calculate the OH fundamental of cis-HOCO (∼3400 cm−1), it is necessary for our calculations to be converged to ∼4000 cm−1. There are two reasonably small frequencies in HOCO; the torsion at 499.66 cm−1 and the OCO′ bend at 613.41 cm−1. The presence of these low-frequency vibrations means that we anticipate that the complete direct product vibrational basis required for this problem would be very large. In all versions of MM20−22 the vibrational basis can be fine-tuned by building a basis of functions in NMAX blocks of differing consecutive mode excitations, to a maximum of 6-mode excitations. In this work, we use all possible blocks of 1-mode, 2-mode, ..., 6-mode excitations. Each block has a parameter MAXBAS(NMODE,NMAX) associated with it, which determines the maximum excitation quantum for mode NMODE in block NMAX. Finally, for each block there is a further parameter MAXSUM(NMAX) that determines the maximum sumoverquanta for block NMAX. For the torsional mode (mode 1

Figure 1. Relative intensities (cm/mol) of transitions in the overview spectra of trans- and cis-HOCO at 296 K.

|R|2 is the squared transition dipole matrix element (in Debye squared), Q(T) is the partition function, and k is the Boltzmann constant, where hc/k = 1.4388 cm K. Finally, the constant 3054.6 1618

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Figure 3. Relative intensities (cm/mol) of transitions in the fundamental bands of trans-HOCO at 296 K.

For J > 0 calculations, we must save a minimum of 150 vibrational functions from each Ka step to ensure the inclusion of the OH fundamental of cis-HOCO. We also save 150 × (2J + 1) rovibrational eigenfunctions from the final rovibrational mixing stage, where 150 stands for an equivalent J = 0 calculation, which is scaled by 2J + 1. This means that at J = 1 we must save 450 functions, etc. Given this large growth in effort with J, the maximum J in the calculations is 9. This maximum is certainly beyond what is needed for well-converged spectra at 15 K; however, for 296 K it is probably not sufficient for benchmark results, which is not our goal. Finally, for both vibrational and rovibrational parts, the matrix elements are integrated numerically, first by Gauss integration for the 1-mode optimizations, and by HEG33 integration thereafter, except for torsion, which is always integrated by Gauss quadrature. For torsion, we use 46 primitives integrated by 60 G points, and for the remaining Qk we use 31 harmonic oscillator

in our normal coordinate analysis), we used a maximum excitation quantum of 24 for 1-mode excitations (MAXBAS(1,1) = 24) and a maximum of eight excitation quanta for all other modes (MAXBAS(m,1) = 8). These are all reduced by one for block 2 and again by one for block 3, etc. With such a difference in excitational quanta between Q1 and the remaining Qk, one final step is required. The basis is initially split into two parts, with each part having its own MAXSUM(NMAX). Hence, we choose MAXSUM(NMAX) = 24 for Q1, and MAXSUM(NMAX) = 8 for all remaining Qk. The resulting expansion sets of 1 and 5 modes, respectively, are then amalgamated block by block, with the restriction that MAXSUM(NMAX) = 24. Such a basis leads to two vibrational expansion sets in Cs symmetry of 11 553 and 10 762 for A′ and A″, respectively. For convergence of the J = 0 levels also requires 3MR and 2MC, which is equivalent to 4MR and 3MC for MM-SR calculations because of the presence of the torsional mode.20 1619

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Figure 4. Relative intensities (cm/mol) of transitions in the fundamental bands of trans-HOCO at 15 K.

primitives integrated by 46 G points, resulting in 9 contracted functions integrated by 24 HEG points. It is very important that we can correctly assign both the vibrational (J = 0) and rovibrational (J > 0) levels, since this assignment is a crucial feature in our analysis of the spectrum to be calculated. For low-lying levels (or to be more precise, levels near the minima of the six one-dimensional cuts), the fact that we use normal coordinates will ensure that the J = 0 matrix will almost certainly be nearly diagonal for the six fundamentals. Our method of assignment is merely to look for the largest coefficient in the complete vibrational wave function and work backward from this to the component basis functions. This has been very successful in most of our earlier work.20−22 The calculation of the rovibrational dipole transition moment matrix elements is virtually identical to those of the vibrational matrix elements themselves, and also requires integration as before. We use the same 3MR for the dipole matrix element

calculations. The integration over the rotational D0ka(±) functions takes place analytically,20 and so the collection of vibrational and rovibrational wave functions, together with their assignments, is sufficient to calculate labeled values of |R2| given in expression (1). For all intensities Si calculated via this expression, therefore, we can assign both the vibrational parts in terms of the normal modes Qk, and the rovibrational parts in terms of J, ka, and kc. We write all this information to a file, together with the intensity Si, the energy of the lower state Er, and the transition frequency νi.

III. RESULTS AND DISCUSSION Before presenting the rovibrational line spectra, we give the J = 0 vibrational energies of trans- and cis-HOCO. These are given in Tables 1 and 2, along with results from other, indicated sources. First, note that the current results, denoted MM-RP, are marginally (at ∼1 cm−1) different from the values given in ref 17. 1620

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Figure 5. Relative intensities (cm/mol) of transitions in the fundamental bands of cis-HOCO at 296 K.

trans-HOCO, especially at 15 K. From Tables 1 and 2, it is seen that, with few exceptions, all of the fundamentals are clearly visible at 296 K, for both trans- and cis-HOCO. The exceptions are ν5 for both isomers and ν3 for cis-HOCO. For trans-HOCO, however, ν5 is just about visible at ∼600 cm−1. At 296 K, there are also a couple of overtones (2ν6 at ∼900 cm−1, and 2ν4 at ∼2200 cm−1). Many of these lines do not appear at 15 K, due to the Boltzmann distribution, and we must resort to other methods of identifying transitions at these temperatures. Since we believe that we have correctly assigned the levels, we can split our output files further into trans and cis parts by searching for all transitions with zero quanta for the lower state in any mode (for trans), and those with two quanta of torsion and zero quanta elsewhere (for cis), and write these as two separate files. Furthermore, we can scan each of these files and look for upper states corresponding to each fundamental in turn. In this way, we produce a total of 24 files; 12 at 296 K and

In Table 2 we include new calculations using the accurate PES of Zhang and co-workers,15 denoted PES-NN. We include these to indicate the range of possible systematic uncertainties from the PES. But, equally importantly, we see that the MM calculations using two accurate PESs both predict strong mixing for the cis-HOCO OH-stretch, more so for PES-NN. However, the prediction that this fundamental is mixed is the important point. Plots of the calculated rovibrational spectra at 296 and 15 K are shown in Figures 1 and 2, respectively. These are given as four individual 296 K spectra; those arising from the ground states of both trans- and cis-HOCO at 296 K are given in Figure 1, and the equivalent spectra at 15 K are given in Figure 2. Since these spectra arise from calculations along the global RP of HOCO, the Boltzmann distributions will all be relative to the zero-point energy of trans-HOCO. Therefore, lines corresponding to cis-HOCO will appear to be much weaker than those for 1621

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Figure 6. Relative intensities (cm/mol) of transitions in the fundamental bands of cis-HOCO at 15 K.

12 at 15 K, with 6 for trans-HOCO and 6 for cis-HOCO at each temperature. Each file corresponds exclusively to transitions involving a single fundamental. III.A. trans-HOCO Spectra. The spectra of the six fundamentals of trans-HOCO at 296 and 15 K are shown in Figures 3 and 4, respectively. Very little is known experimentally about the spectroscopy of this molecule, although very recently an attempt has been made to measure the spectra of trans-HOCO at 13 K.8 This work was successful in producing assigned P, Q, and R branch transitions for the OH stretch for the first time. The spectra in Figure 3 at 296 K are presented for comparison purposes only, and also to comply with the data usually associated with the HITRAN database.32 But we will concentrate more on the spectra at 15 K and, in particular, on our predicted spectrum of the OH stretch in trans-HOCO, since this is now an observed transition with which to compare. In Table 2 we present several progressions in some of the more intense P, Q, R branches, in an attempt to make such a

comparison, although this is a very difficult task, as the data in ref 8 are presented only in figures. Nevertheless, some comparisons can be made, and we indicate by footnote b the transitions that are given in Figures 5 and 6 of ref 8. In this reference, the Q branch data are split into two distinct groups, namely, a-type in Figure 5a and b-type in Figure 5b. There then follows R branch data in Figure 6a and P branch data in Figure 6b. In our Table 3, the top four blocks are all Q branch transitions, with the uppermost left-hand block of type-b. The bottom three left-hand blocks are R branch transitions, and the bottom three right-hand blocks are P branch transitions. We restricted our data in Table 3 to include only those transitions in which one of either Kc or Kc is always less than or equal to unity. This restriction therefore excludes two (weak) lines from ref 8, namely, the P branch transitions 322←423 and 321←422 from their Table 6b. Of the remaining transitions, and with the exemption of the two a-type Q branch transitions 220←221 and 221←220, the relative intensities of all the lines in 1622

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The Journal of Physical Chemistry A Table 3. Progressions in the ν1 (OH Stretch) Spectrum of trans-HOCO at 296 and 15 K

a

transitiona

energy

296 K

15 K

transitiona

energy

296 K

15 K

110←101 211←202 312←303 413←404 514←505 615←606 716←707 817←808 918←909 110←111 211←212 312←313 413←414 514←515 615←616 716←717 817←818 918←919 101←000 202←101 303←202 404←303 505←404 606←505 707←606 808←707 909←808 212←111 313←212 414←313 515←414 616←515 717←616 818←717 919←818 211←110 312←211 413←312 514←413 615←514 716←615 817←716 918←817

3647.16 3647.18 3647.21 3647.26 3647.33 3647.43 3647.56 3647.74 3647.97 3641.90 3641.94 3642.00 3642.08 3642.18 3642.31 3642.46 3642.65 3642.86 3642.57 3643.29 3644.02 3644.73

0.4490 0.7958 1.063 1.307 1.474 1.659 1.854 1.907 1.940 1.833 0.9677 0.6639 0.4902 0.4408 0.3632 0.2819 0.2498 0.2286 1.741 2.562 3.671 5.122

0.4202 0.6521 0.7138b 0.6742b 0.5471b 0.4155b 0.2940b 0.1800 0.1025 1.063 0.4921b 0.2774 0.1577 0.1023 0.0571 0.0281 0.0148 0.0076 1.741 2.398b 3.009 3.441

111←110 221←220 331←330 441←440

3641.87 3642.12 3639.61 3640.25

1.833 3.125 3.362 5.664

1.061 0.3763b 0.0303 0.0014

3641.90 3642.13 3639.61 3640.25 3641.87 3641.83 3641.76 3641.68 3641.56 3641.42 3641.25 3641.05 3640.82 3641.11 3640.38 3639.66 3638.93 3638.21

1.833 3.111 3.363 5.664 1.833 0.9675 0.6636 0.4899 0.4405 0.3629 0.2816 0.2495 0.2289 0.8630 2.768 3,657 5.221 9.142

1.063b 0.3747b 0.0303 0.0014 1.061 0.4894b 0.2744 0.1548 0.0995 0.0548 0.0266 0.0138 0.0069 0.8076 2.268 2.457 2.693b 3.393

3646.14 3646.83 3647.50 3648.16 3643.32 3644.04 3644.74 3645.45 3646.15 3646.84 3647.54 3648.22 3643.36 3644.10 3644.83 3645.56 3646.29 3647.02 3647.74 3648.46

7.156 11.24 10.26 9.234 1.845 3.125 4.736 3.162 6.798 10.54 9.761 8.859 1.844 3.124 4.733 3.156 6.786 10.52 9.732 8.806

2.655 2.813 1.628 0.8716 1.069b 1.589 1.979 1.017 1.578 1.655 0.9732 0.5260 1.068b 1.581 1.957 0.997 1.532 1.588 0.919 0.486

110←111 220←221 330←331 440←441 111←110 212←211 313←312 414←413 515←514 616←615 717←716 818←817 919←918 000←101 101←202 202←303 303←404 404←505 505←606 606←707 707←808 808←909 111←212 212←313 313←414 414←515 515←616 616←717 717←818 818←919 110←211 211←312 312←413 413←514 514←615 615←716 716←817 817←918

3636.80 3636.11 3635.43 3640.45 3639.73 3639.01 3638.29 3637.58 3636.87 3636.16 3635.45 3640.41 3639.67 3638.93 3638.19 3637.45 3636.71 3635.98 3635.25

5.488 9.921 9.097 1.989 3.091 4.702 8.745 6.728 5.244 9.455 8.558 1.989 3.089 4.697 8.734 6.712 5.224 9.417 8.514

0.8704 0.9364 0.4808 1.012 1.292 1.513b 2.030 1.057 0.5228 0.5614 0.2840 1.006 1.277 1.484b 1.972 1.013 0.4932 0.5202 0.2576

Transition wavenumbers are given in inverse centimeters, and intensities are given in cm/mol × 1017. bObserved in ref 8.

with intensities reaching maxima for increasing J and then fading for even higher J. The remaining P and R branches have progressions that again basically follow this behavior, except in the middle J regions around J = 5, where the transition involving the OH stretch level ν1(505) is completely missing due to heavy mixing with the combination band 2ν3 + 2ν5, and only appears as the second-largest coefficient, which means that we miss assigning this level. On either side (J = 4 and J = 6), there is some evidence that the Ka = 0 level is starting to mix with this combination band. We can therefore only surmise that the slight anomolies in Table 3 are as a result of this apparent mixing, where intensity will be lost to the mixed level. Finally, on inspection of ν2−ν6 in Figure 4, many of the progressions can be seen directly from the figure, without resorting to tables similar to Table 3.

Table 3 indicated by footnote b are in accord with those in Tables 5 and 6 of ref 8. This can most easily be seen by comparing Q(a) transition 212←211 with Q(b) transition 615←606, Q(a) transition 110←111 with R branch transition 212←111, and finally Q(a) transition 110←111 with P branch transition 312←413, and then by comparing the relative intensities in each of the four individual figures of ref 8. The remaining two a-type Q branch transitions 220←221 and 221←220 have energies that differ by only 0.01 cm−1, which means that in Figure 5a of ref 8, the intensities will appear approximately twice as intense as each individual transition. With this in mind, our intensities for these two transitions are on the weak side compared to experiment. We now comment on the progressions given in Table 3. First, the four Q branch blocks all show regular behaviors, 1623

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The Journal of Physical Chemistry A Table 4. Progressions in the ν1 (OH Stretch) Spectrum of cis-HOCO at 296 and 15 K

a

transitiona

energy

296 K

15 K

transitiona

energy

296 K

15 K

110←101 211←202 312←303 413←404 514←505 615←606 716←707 817←808 918←909 110←111 211←212 312←313 413←414 514←515 615←616 716←717 817←818 918←919 101←000 202←101 303←202 404←303 505←404 606←505 707←606 808←707 909←808 212←111 313←212 414←313 515←414 616←515 717←616 818←717 919←818 211←110 312←211 413←312 514←413 615←514 716←615 817←716 918←817

3445.12 3445.12 3445.15 3445.19 3445.27 3445.41 3445.60 3445.89 3446.27 3440.74 3440.78 3440.83 3440.91 3441.01 3441.13 3441.28 3441.46 3441.66 3441.31 3442.04 3442.75 3443.45 3444.13 3444.79 3445.45 3446.14 3446.66 3442.17 3442.89 3443.59 3444.28 3444.95 3445.62 3446.28 3446.89 3442.22 3442.95 3443.66 3444.36 3445.06 3445.74 3446.42 3447.09

0.2507 0.4612 0.6229 0.7804 0.9678 1.071 1.024 1.076 1.078 0.0011 0.0002 0.0001 0.0003 0.0005 0.0005 0.0003 0.0004 0.0005 0.0699 0.0033 0.0015 0.0079 0.0556 0.0090 0.0438 0.0423 0.0103 0.0023 0.0014 0.0074 0.5327 0.0084 0.4362 0.0535 0.0103 0.0023 0.0013 0.0073 0.5496 0.0085 0.4626 0.0554 0.0103

0.2341 0.3759 0.4141 0.3960 0.3514 0.2611 0.1577 0.0986 0.0546 0.0007 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0699 0.0031 0.0012 0.0052 0.2822 0.0033 0.1067 0.0065 0.0009 0.0014 0.0007 0.0033 0.1830 0.0021 0.0721 0.0056 0.0006 0.0014 0.0007 0.0032 0.1837 0.0020 0.0721 0.0053 0.0006

111←110 221←220 331←330 441←440

3440.69 3441.18 3442.26 3440.60

0.0011 0.0090 0.0004 0.0045

0.0007 0.0001 0.0000 0.0000

110←111 220←221 330←331 440←441 111←110 212←211 313←312 414←413 515←514 616←615 717←716 818←817 919←918 000←101 101←202 202←303 303←404 404←505 505←606 606←707 707←808 808←909 111←212 212←313 313←414 414←515 515←616 616←717 717←818 818←919 110←211 211←312 312←413 413←514 514←615 615←716 716←817 817←918

3440.74 3441.19 3442.26 3440.60 3440.69 3440.61 3440.50 3440.35 3440.16 3439.94 3439.68 3439.39 3439.02 3439.82 3439.07 3438.31 3437.55 3436.80 3436.07 3435.37 3434.70 3434.10 3439.25 3438.50 3437.75 3436.99 3436.23 3435.47 3434.72 3433.96 3439.18 3438.39 3437.60 3436.79 3435.99 3435.18 3434.38 3433.59

0.0011 0.0009 0.0003 0.0045 0.0011 0.0002 0.0002 0.0003 0.0005 0.0005 0.0002 0.0003 0.0002 0.1460 0.0031 0.0011 0.0055 0.3614 0.0088 0.6474 0.0424 0.0089 0.0022 0.0010 0.0052 0.3461 0.0081 0.6335 0.0409 0.0096 0.0022 0.0010 0.0051 0.3534 0.0083 0.6636 0.0422 0.0099

0.0007 0.0001 0.0000 0.0000 0.0007 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.1363 0.0025 0.0008 0.0028 0.1312 0.0021 0.0997 0.0039 0.0005 0.0012 0.0004 0.0018 0.0852 0.0013 0.0658 0.0025 0.0003 0.0012 0.0004 0.0017 0.0835 0.0013 0.0638 0.0023 0.0003

Transition wavenumbers are given in inverse centimeters, and intensities are given in centimeters per mole × 1 × 1017.

only 1/√2. The second ν1 entry in Table 2 has the zero-order OH stretch only as the second-highest coefficient. The mixing is with the zero-order state 2ν6 + ν5 + ν2. Because of this, there will be an apparent loss of intensity in our calculations, which will vary as this coefficient varies when the amount of mixing changes. To check that this result is not an artifact of our PES, we ran MULTIMODE calculations using a second PES, independently generated ab initio.15 Results using this PES gave almost identical mixing of the cis-HOCO OH stretch fundamental ν1. We must therefore conclude that this is a real effect. In Table 4, we applied a Boltzmann correction factor of exp(551.7086/kT) to the intensities shown in Figures 5 and 6 to allow for the relative energies of the cis-HOCO and transHOCO zero-point energies. From the table, it appears that all Q branch progressions have basically regular features. Perhaps

III.B. cis-HOCO Spectra. We believe that the comparison of the trans-HOCO at 15 K is sufficiently close to experiment8 that we are able to predict some portions of the cis-HOCO spectrum with a certain degree of confidence. The spectra of the six fundamentals of cis-HOCO at 296 and 15 K are shown in Figures 5 and 6, respectively. In Table 4, we show the same progressions that we gave for trans-HOCO in Table 3. As before, we will concentrate on the 15 K spectra, since this is the temperature currently being investigated experimentally. From Figure 6, we can see that all fundamental transitions except ν3 have some quite regular features, some more than others. Leaving ν3 aside for the moment, we first comment on the transitions within ν1, the OH stretch calculated to be ∼3440 cm−1. From Table 2, we note that at J = 0, the wave function for this fundamental is heavily mixed, where the maximum coefficient is 1624

DOI: 10.1021/acs.jpca.6b13013 J. Phys. Chem. A 2017, 121, 1616−1626

The Journal of Physical Chemistry A

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this is not too surprising, since the amount of mixing will be approximately constant for a given value of J. On the one hand, where different values of J are involved, as in P and R branches, we would expect to see more fluctuations in the coefficients, and hence in the intensities. We would not wish to speculate further than this, but the coefficients within the vibrational parts of the complete rovibrational wave functions are very erratic. On the other hand, ν2, ν4, ν5 and ν6 are much more regular, and may be better transitions to investigate experimentally, if our doubts about ν1 are correct. Finally, a quick inspection of the cis and trans-HOCO spectra at the two temperatures reveals some rough similarities for some bands and significant differences for others. The differences are due both to the differences in the degree of mixing, the ν1 band being a clear example of this, and also differences in the dipole moment surface.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b13013. Readme file explaining in detail what is given (PDF)

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REFERENCES

(1) Francisco, J. S.; Muckerman, J. T.; Yu, H. HOCO Radical Chemistry. Acc. Chem. Res. 2010, 43, 1519−1526. (2) Johnson, C. J.; Otto, R.; Continetti, R. E. Spectroscopy and Dynamics of the HOCO Radical: Insights into the OH + CO → H + CO2 Reaction. Phys. Chem. Chem. Phys. 2014, 16, 19091−19105. (3) Lester, M. I.; Pond, B. V.; Marshall, M. D.; Anderson, D. T.; Harding, L. B.; Wagner, A. F. Mapping the OH+CO → HOCO Reaction Pathway Through IR Spectroscopy of the OH-CO Reactant Complex. Faraday Discuss. 2001, 118, 373−385. (4) Lagana, A.; Garcia, E.; Paladini, A.; Casavecchia, P.; Balucani, N. The Last Mile of Molecular Reaction Dynamics Virtual Experiments: the Case of the OH(N = 1−10) + CO(j = 0−3) Reaction. Faraday Discuss. 2012, 157, 415−436. (5) Jacox, M. E. The Vibrational Spectrum of the t-HOCO Free Radical Trapped In Solid Argon. J. Chem. Phys. 1988, 88, 4598. (6) Sears, T. J.; Fawzy, W. M.; Johnson, P. M. Transient Diode Laser Absorption Spectroscopy of the ν2 Fundamental of trans-HOCO and DOCO. J. Chem. Phys. 1992, 97, 3996. (7) Petty, J. T.; Moore, C. B. Transient Infrared Absorption Spectrum of the ν1 Fundamental of trans-HOCO. J. Mol. Spectrosc. 1993, 161, 149. (8) Chang, C.-H.; Buckingham, G. T.; Nesbitt, D. J. Sub-doppler Spectroscopy of the trans-HOCO Radical in the OH Stretching Mode. J. Phys. Chem. A 2013, 117, 13255−13264. (9) Bjork, B. J.; Bui, T. Q.; Heckl, O. H.; Changala, P. B.; Spaun, B.; Heu, P.; Follman, D.; Deutsch, C.; Cole, G. D.; Aspelmeyer, M.; Okumura, M.; Ye, J. Direct Frequency Comb Measurement of OD + CO → DOCO Kinetics. Science 2016, 354, 444−448. (10) Johnson, C. J.; Harding, M. E.; Poad, B. L. J.; Stanton, J. F.; Continetti, R. E. Electron Affinities, Well Depths, and Vibrational Spectroscopy of cis- and trans-HOCO. J. Am. Chem. Soc. 2011, 133, 19606−19609. (11) Fortenberry, R. C.; Huang, X.; Francisco, J. S.; Crawford, T. D.; Lee, T. J. The trans-HOCO Radical: Quartic Force Fields, Vibrational Frequencies, and Spectroscopic Constants. J. Chem. Phys. 2011, 135, 134301. (12) Fortenberry, R. C.; Huang, X.; Francisco, J. S.; Crawford, T. D.; Lee, T. J. Vibrational Frequencies and Spectroscopic Constants From Quartic Force Fields for cis-HOCO: The Radical and the Anion. J. Chem. Phys. 2011, 135, 214303. (13) Huang, X.; Fortenberry, R. C.; Wang, Y.; Francisco, J. S.; Crawford, T. D.; Bowman, J. M.; Lee, T. J. Dipole Surface and Infrared Intensities for the cis- and trans-HOCO and DOCO Radicals. J. Phys. Chem. A 2013, 117, 6932−6939. (14) Li, J.; Wang, Y.; Jiang, B.; Ma, J.; Dawes, R.; Xie, D.; Bowman, J. M.; Guo, H. Communication: A Chemically Accurate Global Potential Energy Surface for the HO + CO → H + CO2 Reaction. J. Chem. Phys. 2012, 136, 041103. (15) Chen, J.; Xu, X.; Xu, X.; Zhang, D. H. Communication: An Accurate Global Potential Energy Surface for the OH + CO → H + CO2 Reaction Using Neural Networks. J. Chem. Phys. 2013, 138, 221104. (16) Mladenović, M. Rovibrational Energies of the Hydrocarboxyl Radical from a RCCSD(T) Study. J. Phys. Chem. A 2013, 117, 7224− 7235. (17) Wang, Y.; Carter, S.; Bowman, J. M. Variational Calculations Of Vibrational Energies and IR Spectra of trans- and cis-HOCO Using New ab initio Potential Energy and Dipole Moment Surfaces. J. Phys. Chem. A 2013, 117, 9343−9352. (18) Oyama, T.; Funato, W.; Sumiyoshi, Y.; Endo, Y. Observation of the Pure Rotational Spectra of trans- and cis-HOCO. J. Chem. Phys. 2011, 134, 174303. (19) McCarthy, M. C.; Martinez, O., Jr.; McGuire, B. A.; Crabtree, K. N.; Martin-Drumel, M.-A.; Stanton, J. F. Isotopic Studies of trans- and cis-HOCO Using Rotational Spectroscopy: Formation, Chemical Bonding, and Molecular Structures. J. Chem. Phys. 2016, 144 (12), 124304.

IV. SUMMARY AND CONCLUSIONS We have calculated the rovibrational spectra of trans-HOCO and cis-HOCO at 296 and 15 K from ab initio PES and DMS data using the code MM-RP. Our trans-HOCO spectrum predicts on the one hand regular patterns in the fundamental transitions, and we also get qualitative agreement of relative intensities within the OH stretch manifold at 15 K. Our cis-HOCO spectrum on the other hand predicts two band systems with erratic behavior; one is the HOC bending fundamental, and the other the OH stretch fundamental. These behaviors are explained by our method of assignment and heavy mixing occurring between wave functions associated with these two fundamentals. We believe that experimental investigations in other regions of the spectra may be one way of overcoming this behavior, as other band systems appear quite regular.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Joel M. Bowman: 0000-0001-9692-2672 Notes

The authors declare no competing financial interest. Zip files containing transition energies, R2, and line intensities for the cis- and trans-HOCO spectra at 296 K are available at https://figshare.com/s/07eff0526ba9b7befbb7.

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ACKNOWLEDGMENTS We thank D. Zhang for sending the PES of ref 15 and the Army Research Office (W911NF1410208) for financial support. NOTE ADDED IN PROOF The following reference was inadvertently omitted: Wang, J.; Li, J.; Ma, J.; Guo, H. Full-dimensional characterization of photoelectron spectra of HOCO− and DOCO− and the tunneling facilitated decay of HOCO and DOCO prepared by anion photodetachment. J. Chem. Phys. 2014, 140, 184314. 1625

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