Full-dimensional characterization of photoelectron spectra of HOCO− and DOCO− and tunneling facilitated decay of HOCO prepared by anion photodetachment Jun Wang, Jun Li, Jianyi Ma, and Hua Guo Citation: The Journal of Chemical Physics 140, 184314 (2014); doi: 10.1063/1.4874975 View online: http://dx.doi.org/10.1063/1.4874975 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in An investigation into low-lying electronic states of HCS2 via threshold photoelectron imaging J. Chem. Phys. 140, 214318 (2014); 10.1063/1.4879808 Vibrationally resolved photoelectron imaging of platinum carbonyl anion Pt(CO) n − (n = 1-3): Experiment and theory J. Chem. Phys. 137, 204302 (2012); 10.1063/1.4768004 High-resolution photoelectron spectroscopy of linear ← bent polyatomic photodetachment transitions: The electron affinity of CS2 J. Chem. Phys. 137, 144304 (2012); 10.1063/1.4757726 Slow photoelectron velocity-map imaging spectroscopy of C 3 O − and C 3 S − J. Chem. Phys. 131, 054312 (2009); 10.1063/1.3200927 Photodetachment spectrum of OHF − : Three-dimensional study of the heavy–light–heavy resonances J. Chem. Phys. 121, 309 (2004); 10.1063/1.1756581
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THE JOURNAL OF CHEMICAL PHYSICS 140, 184314 (2014)
Full-dimensional characterization of photoelectron spectra of HOCO− and DOCO− and tunneling facilitated decay of HOCO prepared by anion photodetachment Jun Wang,1,2 Jun Li,3 Jianyi Ma,1,3,a) and Hua Guo3,a) 1
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan 610065, China School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China 3 Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA 2
(Received 14 March 2014; accepted 23 April 2014; published online 12 May 2014) The photodetachment of both the HOCO− and DOCO− anions is investigated using full-dimensional quantum wave packets on new ab initio based global potential energy surfaces for both the neutral and anionic species. The calculated electron affinities and neutral fundamental vibrational frequencies of both isotopomers are in good agreement with available experimental data. The measured photoelectron spectra are also accurately reproduced, further validating the accuracy of the potential energy surfaces. In addition, strong mode specificity is found in the lifetimes of the HOCO vibrational features and the tunneling facilitated predissociation rates to H + CO2 are rationalized using the recently proposed sudden vector projection model. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874975] I. INTRODUCTION
HO + CO → H + CO2 is one of the most important combustion reactions1 and it also plays a key role in atmospheric chemistry.2 The kinetics of the reaction have been investigated extensively and found to be pressure dependent and non-Arrhenius.3, 4 In the low pressure limit, the rate coefficient is nearly temperature independent below 500 K, but increases exponentially at higher temperatures. The unique kinetics has been attributed to the complex-forming nature of the reaction,5 which features a stable HOCO intermediate6, 7 supported by potential wells flanked by entrance channel bottlenecks and a nearly isoenergetic exit channel barrier,8 as shown in Fig. 1. Simulations of the kinetics with explicit inclusion of the HOCO intermediate and tunneling have generally been satisfactory.4, 9–12 In addition, the dynamics of this important bimolecular reaction has been investigated experimentally,13–15 but a clear understanding of the dynamics has not emerged due to several theory-experiment disagreements. Despite the existence of numerous previous theoretical studies of the reaction dynamics,16 it has recently been recognized17 that the potential energy surfaces (PESs) used in most dynamics studies8, 18, 19 were not sufficiently accurate. As a result, efforts have been devoted to the development of an accurate global HOCO PES,17, 20–22 and to the dynamical studies on new PESs using both quasi-classical trajectory and quantum mechanical methods.17, 20–27 Because of its central role in the HO + CO → H + CO2 reaction, the HOCO intermediate (and its deuterated isotopomer (DOCO)) has been studied spectroscopically.28–37 HOCO is known to have two isomers, and the more stable a) Authors to whom correspondence should be addressed. Electronic
addresses: [email protected] and [email protected]
0021-9606/2014/140(18)/184314/7/$30.00
trans-HOCO isomer is separated from the cis-HOCO isomer by a significant isomerization barrier. Both isomers have been spectroscopically identified and characterized, although most previous studies have been focused on the trans-isomer. The spectroscopic studies have stimulated several theoretical investigations of the structure and vibrational dynamics of these isomers,38–43 and the overall agreement with the experimental data has been quite satisfactory. An alternative approach to explore the HO + CO → H + CO2 reaction is by photodetaching the stable HOCO− negative ion,44 which brings the system onto the neutral PES near the exit channel barrier, as shown in Fig. 1. Typically, the configuration space accessed by photodetachment is larger than that probed by conventional microwave and infrared spectroscopy, thus providing complementary information on the PES. In addition, the fact that the cis-HOCO− is the more stable anionic isomer helps to explore the cis-region of the neutral PES that has seldom been studied spectroscopically. Indeed, the photodetachment of the HOCO− and DOCO− anions has been extensively investigated by Continetti and coworkers.44–50 In particular, the photodetachment of HOCO− was found to yield the HO + CO, H + CO2 , and HOCO species, and the dissociation to the H + CO2 products is dominated by tunneling.48, 49 Although an earlier theoretical study found little tunneling,51 our recent work on a much more accurate PES17, 20 confirmed the experimental observation,52 and attributed the lack of tunneling in the earlier theoretical work to the artificially “thick” dissociation barrier in previous PESs. In addition, vibrationally resolved photoelectron spectra of HOCO− and DOCO− have been determined experimentally, and reproduced by theoretical calculations on an ab initio quartic force field.50 These photoelectron spectra complement the ro-vibrational spectra of HOCO and provide a different perspective to the vibrational dynamics in
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MOLPRO 2010.1.55 The ab initio points were then fit using the permutation invariant polynomial-neural network (PIPNN) approach.56, 57 Specifically, 17 symmetrized monomials were used as the input layer of a two-hidden-layer NN with 20 interconnected neurons in each layer. The feed-forward NN was trained with the Levenberg-Marquardt algorithm58 to minimize the root mean square error (RMSE) of the fit. The final PES is an average of three best fits. A unique property of the anion PES, as well as the neutral PES,22 is that they are invariant under exchange of like atoms. III. DYNAMICS
A six-dimensional (6D) non-rotating (J = 0) Hamiltonian for the tetra-atomic system is defined using the diatom-diatom Jacobi coordinates shown in Fig. 1,
FIG. 1. Energetics for the HO + CO → H + CO2 reaction and the diatomdiatom Jacobi coordinates for HOCO. The Jacobi coordinates are defined in the inset.
Hˆ =
1 1 ∂2 1 ∂2 − + − + V (r ) 2 2 2μi ∂ri2 2μ2 ∂r22 i=0 +
the HOCO wells. However, we note that the theoretical calculations have been performed using a semi-local PES near the potential minima.50 As discussed above, photodetachment often accesses a large configuration space on the neutral PES and its dynamics (and the resulting photoelectron spectrum) should be treated with a global PES. This is particularly important if the lifetimes of the metastable vibrational levels are to be determined. In this publication, we report a full-dimensional simulation of the photoelectron spectra for the photodetachment of both the HOCO− and DOCO− anions using our recently developed global PES for the HOCO radical22 and a new semi-global PES for the anion. These wave packet calculations also provide estimate of predissociative lifetimes for several prominent HOCO vibrational features in the photoelectron spectrum, which confirms the tunneling facilitated predissociation pathway. This work is organized as follows. The ab initio calculation and fitting of the anion PES is described in Sec. II and the quantum wave packet method used to calculate the photoelectron spectra and predissociation lifetimes is outlined in Sec. III. The results are presented and compared with the experimental data in Sec. IV, with a discussion on the mode-specific tunneling rates. The conclusions are given in Sec. V. II. PES of HOCO−
As in our previous work on the neutral HOCO PES,17, 20 the HOCO− (X1 A ) PES was developed from ab initio points using the F12b version of the coupled-cluster method53 with singles, doubles, and perturbative triples based on restricted Hartree-Fock reference wave functions (RHFCCSD(T)-F12b) with the augmented correlation-consistent polarized valence triple zeta (aug-cc-pVTZ, or AVTZ) basis set.54 The frozen-core approximation for the 1s electrons of the non-hydrogen atoms in the correlation calculations was used. All calculations have been carried out using
2 jˆi2 + [V (r0 , r1 , r2 , θ1 , θ2 , φ) − V2 (r2 )], 2μi ri2 i=0
(1)
where r0 is the distance between two centers of mass while r1 and r2 the diatomic bond lengths of HO/DO and CO, respectively. Their corresponding reduced masses are denoted μi . θ 1 , θ 2 are the Jacobi angles, with jˆ1 , jˆ2 as the corresponding angular momentum operators. Note that jˆ02 = (jˆ1 + jˆ2 )2 . The out-of-plane torsion angle is given by φ. V is the PES and V2 is the reference potential for the non-reactive radial coordinate of r2 . The neutral PES on which the dynamics is followed represents the most accurate HOCO PES to date.22 The 6D wave function is expressed as follows: p i0 i1 i2 j1 j2 m |i0 |i1 |i2 |j1 j2 m, p, (2) = i0 i1 i2 j1 j2 m p
where i0 i1 i2 j1 j2 m is the wave function in the discrete representation. Here, i0 and i1 denote the plane-wave DVR (discrete variable representation)59 grid index for the radial coordinates of r0 and r1, while i2 labels the PODVR (potential optimized DVR)60, 61 for the non-reactive radial coordinate r2 . |j1 j2 m, p is the angular FBR (finite basis representation) defined by parity-adapted products of the spherical harmonics |JM, |j1 j2 m, p = (2 + 2δm,0 )−1/2 (|j1 m|j2 − m +p|j1 − m|j2 m),
p = ±1.
(3)
As discussed below, the anionic PES has two minima corresponding to the cis- and trans-isomers of the HOCO− anion. The ground vibrational states of these two isomers were first determined using the iterative Lanczos algorithm.62 Following our recent work,52, 63, 64 the Condon model was assumed for photodetachment, in which the vibrational eigenfunction on the anionic PES is placed vertically on the neutral PES. The propagation of the wave packet, k , on the neutral PES was performed with the Chebyshev propagator:16 k = 2D Hˆ s k−1 − D 2 k−2 ,
k≥2
(4)
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TABLE I. Parameters in the quantum dynamics calculations of the photoelectron spectra. Parameters (in a.u.) Grid/basis ranges and sizes
Largest value of j1 Largest value of j2 Largest value of m Damping for r0 a Damping for r1 a Propagation step a
HOCO r0 ∈ (2.7, 9.35), N0 = 110 for i0 ≤ 35, r1 ∈ (1.1, 5.4), N1 = 28 for i0 > 35, 5 vibrational basis r2 , PODVR, N2 = 5 30 55 30 Cabs = 0.01, r0,abs = 6.0 Cabs = 0.01, r1,abs = 3.3 300 000
r0 ∈ (2.7, 9.35), N0 = 116 for i0 ≤ 40, r1 ∈ (1.1, 5.4), N1 = 34 for i0 > 40, 6 vibrational basis r2 , PODVR, N2 = 5 36 55 36 Cabs = 0.01, r0,abs = 6.0 Cabs = 0.01, r1,abs = 3.3 360 000
The damping term is defined as D = exp [−Cabs (r − rabs )2 ], r ≥ rabs .
with 1 = D Hˆ s 0 and 0 = i , in which i represents the anionic wavefunction. The Hamiltonian in Eq. (4) was scaled to the spectral range of (−1,1) via Hˆ s = (Hˆ − H + )/H − . The spectral medium (H+ = (Hmax + Hmin )/2) and half width (H− = (Hmax − Hmin )/2) were determined by the spectral extrema, Hmax and Hmin , which can be readily estimated. Finally, the wave packet was damped near the edge of the grids in radial coordinates of r0 and r1 , and the damping functions (D) and parameters are listed in Table I. The energy spectra were obtained from the discrete cosine Fourier transform of the Chebyshev autocorrelation functions Ck ≡ 0 | k :65 S(E) =
DOCO
1 (2 − δk,0 ) cos(kϑ)Ck , π H − sin ϑ k=0
(5)
where ϑ = arccosE is the Chebyshev angle, and k is the Chebyshev order. The threshold region is treated with the Wigner threshold law,66 approximated with a function of the form a + beKE0.5 + ceKE1.5 (a = 0.005, b = 0.1, c = 1.0).50 For narrow resonances, we have also determined their complex energies (En − i n /2) using a low-storage filter diagonalization method,67 in which the Chebyshev autocorrelation function is doubled based on the scheme discussed in our earlier work.68, 69
1.361 eV, respectively. The calculated EAs of the transspecies for both HOCO and DOCO match experimental results (1.38 ± 0.01 and 1.37 ± 0.01 eV).50 Similarly, the corresponding values for the cis-isomers of the two isotopomers are also in good accord with the experimental values (1.51 ± 0.01 eV and 1.51 ± 0.01 eV). These values are also in agreement with theoretical values (1.373, 1.371, 1.501, and 1.501 eV) obtained with the HEAT345-(Q) protocol.50 The fundamental vibrational frequencies of the neutral species were also computed for both the HOCO and DOCO isotopomers. As expected, they are in excellent agreement with the frequencies reported in recent work on the same PES but using a different quantum method.22 The theoretical frequencies listed in Table II are close to known experimental results and previous calculation results using several semi-global PESs.42, 43, 50, 70 Note that some of the experimental values were obtained either in matrices or with large uncertainties. Interestingly, the theoretical values appear to converge better among themselves than with the experimental values, suggesting the uncertainties of the PESs used in these
IV. RESULTS AND DISCUSSION
A total of 13 352 points were calculated for the anion PES, and fit accurately using the PIP-NN approach56, 57 (RMSE = 0.3 cm−1 ). The contour plot of the anion PES is given in Fig. 2 with the equilibrium geometries for both cis- and trans-isomers. The cis-minimum is 0.067 eV lower than the trans counterpart, and the isomerization barrier is 0.411 eV. The geometry and energies are in good agreement with previous ab initio studies.45 The zero-point energies for the cis- and trans-HOCO− are 0.506 and 0.507 eV, and the corresponding values for DOCO- are 0.419 and 0.423 eV. The adiabatic electron affinities (EAs) can be determined by the energy differences between the ground vibrational states in the neutral and anion PES minima. For the cis- and trans-isomers of HOCO, the calculated EAs are 1.517 and 1.367 eV, respectively. For the DOCO isotopomer, the calculated EAs for the cis- and trans-isomers are 1.498 and
FIG. 2. Contour plot of the anion PES as in θ 1 and φ with all other coordinates optimized and the structures of the cis- and trans-HOCO− isomers. The contours are in the unit of eV and the bond length and bond angles are in Å and degrees, respectively.
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TABLE II. Comparison of calculated vibrational frequencies (cm−1 ) for cis- and trans-HOCO and DOCO with experimental and previous theoretical results. cis-HOCO
cis-DOCO
mode
Theo.a
Theo.b
Theo.c
Theo.d
Theo.e
Expt.
Theo.a
Theo.b
Theo.d
Theo.e
Expt.
v1 , O–H stretch v2 , C–O stretch v3 , H–O–C bend v4 , O–C stretch v5 , O–C–O bend v6 , torsion
3438 1809 1272 1038 595 548
3452 1824 1280 1042 601 540
3438 1819 1271 1040 597 554
3458 1815 1282 1042 596 545
3461 1825 1278 1059 600 543
3316f 1797f 1290d , 1261f 1040d , 1088f 605d , 620f ...
2544 1818 1118 955 534 457
2552 1827 1123 961 540 447
2555 1814 1121 949 535 454
2258 1829 1132 961 539 452
... ... 1145d ... 557d ...
trans-HOCO
v1 , O–H stretch v2 , C–O stretch v3 , H–O–C bend v4 , O–C stretch v5 , O–C–O bend v6 , torsion
Theo.a 3636 1852 1204 1048 612 503
Theo.b 3641 1862 1213 1052 616 475
Theo.c 3640 1856 1210 1050 613 502
Theo.d 3641 1854 1217 1057 614 507
trans-DOCO Theo.e 3648 1863 1217 1061 617 507
Expt. 3636g , 3628i 1853j , 1848i 1194d 1048d , 1050i 629d , 615f 508i
Theo.a 2685 1842 1080 898 587 392
Theo.b 2685 1860 1086 903 590 368
Theo.d 2688 1845 1081 900 588 395
Theo.e 2691 1859 1092 906 593 396
Expt. 2684h , 2678i 1852j , 1846i 1081d , 1083i ... 597d ...
a
Present work. Reference 43. c Reference 42. d Photodetachment and theory.50 e Reference 41. f CO matrix IR spectroscopy.28 g Gas phase IR spectroscopy.31 h Gas phase IR spectroscopy.32 i Ne matrix IR spectroscopy.35 j Gas phase IR spectroscopy.30 b
calculations are minimal, at least near the equilibrium geometries of the two HOCO isomers. Fig. 3 shows energy spectra of HOCO prepared by photodetaching HOCO− from its cis- and trans-minima, respectively. The cis-HOCO− spectrum is dominated by four primary sequences, the 50-5 , 31 50-5 , 41 50-5 , and 42 50-4 , consistent with the previous simulation of Johnson et al.50 The intensities of these progressions are determined by the
FIG. 3. Photoelectron spectra of HOCO− arising from cis-(upper panel) and trans-species (bottom panel).
Franck-Condon overlaps, which underscore the changes of the equilibrium geometry from the anion to neutral species. For the planar cis-HOCO− and cis-HOCO, the corresponding geometries are {R, rOH , rCO , θ OH , θ CO } = {3.44, 1.85, 2.24, 83.4◦ , 130.9◦ } and {3.48, 1.84, 2.32, 93.7◦ , 144.7◦ }, respectively. As a result, it is not surprising that the HOC bending (v3 ), CO stretching (v4 ) and OCO bending (v5 ) modes of the latter are excited during the transition. The trans-spectrum is shown as the bottom panel in Fig. 3, which is dominated by four sequences: 40-4 , 40-4 51 , and 31 40-4 . The v4 progression represents the strongest excitation, different from cisspectrum dominated by the v5 progression. The intensities can also be explained by the differences in the equilibrium geometries of the anionic and neutral trans-HOCO species. The energy spectra of the DOCO− isomers shown in Fig. 4 are very different from those of the HOCO− isomers. These spectra are dominated by the 3n 5m progressions. The excitation of the v3 and v5 modes can be attributed to the relatively large changes of the OCO and HOC angles. The strong isotope effect in the photoelectron spectra observed here is in good agreement with the experimental observations of Johnson et al.50 To compare with the recent vibrationally resolved photoelectron spectra of internally cold HOCO− and DOCO− at 660 nm,50 we have simulated the electron kinetic energy distribution in Fig. 5. Both the cis- and trans-isomers were included, but the latter is assumed to contribute only slightly: 5% for HOCO− and 4% for DOCO− , as assumed for the anions produced and stored in very cold temperatures.50 As a result, the cis-isomers dominate the spectra for both
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FIG. 4. Photoelectron spectra of DOCO− arising from cis-(upper panel) and trans-species (bottom panel).
FIG. 5. Photoelectron spectra of HOCO− (upper panel) and DOCO− (bottom panel) at 660 nm (1.878 eV). Blue (red) lines denote cis (trans) transitions. Black lines show the experimental spectrum. The assignments of the main peaks on the spectrum show by their sequences.
HOCO− and DOCO− , due to their lower energies. All of the experimentally observed peaks match with our theoretical simulations and the agreement is excellent, further validating the accuracy of the PESs. It should be pointed out that only the vibrational ground state of trans-HOCO or trans-DOCO is a true bound state. All higher ones are in principle predissociative, because their energies are higher than the H/D + CO2 asymptote. As a result, the vibrationally excited peaks in Figs. 3 and 4 have finite lifetimes. The lifetimes for the HOCO resonances have been estimated before based on reduced-dimensional models.48, 52, 71
Here, the lifetimes of the prominent features in the cis-HOCO spectra are re-estimated by filter-diagonalization based on full-dimensional wave packet propagation and the results are listed in Table III. The propagations have been carried out with ∼300 000 steps, which are roughly equivalent to about 30 ps. Due to the exceedingly long lifetimes of these resonances, only a few predissociation rates have been determined with certainty. The lifetimes of the cis-DOCO features are too long to be determined accurately. As expected, the lifetime typically decreases with the increase of energy for each primary progression, as the tunneling probability
TABLE III. Lifetimes of main peaks in photoelectron spectrum of cis-HOCO and cis-DOCO anions. cis-HOCO Lifetime (s) States
Energy (cm−1 )
6Da
1Db
0 51 52 53 54 55 41 41 51 41 53 41 54 41 55 41 56d 42 42 51 42 52 42 53 42 54
0 595 1192 1790 2388 2987 1038 1627 2809 3403 3990 4582 2061 2643 3226 3810 4394
... ... ... ... ... ∼4 × 10−3 ... ... ... ... 1.2 × 10−4 4.8 × 10−5 ... ... ∼3 × 10−3 2.6 × 10−4 1.4 × 10−5
... ... ... ... 9.5 × 10−3 6.6 × 10−4 ... ... 6.6 × 10−4 4.4 × 10−6 4.4 × 10−7 6.2 × 10−8 ... ... 9.6 × 10−6 4.8 × 10−7 4.4 × 10−7
cis-DOCO 5Dc
States
Energy (cm−1 )
> μs > μs > μs > μs > μs ∼ns τ > μs τ > μs ∼ns ∼ns ∼ns ∼ns τ > μs τ > μs ∼ns ∼ns ∼ns
0 51 52 53 54 55 56 31 31 51 31 52 31 53 31 54 31 55 31 56 31 57 31 58
0 534 1072 1611 2151 2709 3232 1118 1646 2176 2692 3243 3771 4303 4830 5374
τ τ τ τ τ
a
Present work. Reference 72. c Reference 52. d Assignment tentative. b
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increases as the energy approaches the saddle point. Interestingly, the lifetimes of the prominent HOCO vibrational features are longer than the μs flight time in the experimental set up,49 and these resonances would thus be classified as “stable” HOCO molecules. It is also noted that the 5D results reported in our earlier reduced-dimensional work52 are not quantitatively accurate. These observations underscore the full-dimensional nature of the tunneling dynamics. It is clear that strong mode-specificity exists in the predissociation lifetimes. Although there is no experimental data on the predissociation rates, the trend is consistent with that observed in the recent work by Wang and Bowman,72 who have estimated the lifetimes using a modespecific model.73 Although the absolute magnitudes differ from our full-dimensional results, their model correctly captured the trend. The mode-specific model of Bowman and coworkers considers both the energetic factor and the projection of the reactant normal mode vector onto the reaction coordinate vector at the tunneling transition state.73 In the latter aspect, it is conceptually similar to the Sudden Vector Projection (SVP) model recently proposed by us.74, 75 To understand the mode specificity in the tunneling lifetime reported here, we resort to an adaptation of the SVP model to unimolecular dissociation reactions,76 which attributes mode-specific unimolecular decay reactivity to the strength of the coupling of the reactant normal mode with the reaction coordinate at the transition state. This coupling is determined in the sudden limit as the projection of the normal mode vector on to the reaction coordinate vector at the reactive saddle point, which possesses an imaginary frequency. As we demonstrated recently,76 the SVP model provides much insight into modespecificity in unimolecular dissociation reactions for systems with weak intermodal coupling and slow intramolecular vibrational energy redistribution (IVR). To compute the coupling, we first determine the normal modes for both cisHOCO and cis-DOCO as well as the reaction coordinate at the i and Q RC . The projectransition state leading to H + CO2 : Q RC , namely, Pi = Q i · Q RC /|Q i |/|Q RC | ∈ i onto Q tion of Q [0, 1], is then computed, using the protocol outlined in Ref. 76. As shown in Table IV, the SVP values for HOCO suggest that in addition to the H–O stretch (v1 ), the C–O stretch (v4 ) and O–C–O bend (v5 ) also promote the dissociation, thanks to their large couplings with the reaction coordinate. These numbers are consistent with the trend observed in Table III. For DOCO, the SVP model predicts that the D–O–C bend TABLE IV. Harmonic frequencies (cm−1 ) for cis-HOCO and cis-DOCO and their SVP values (Pi ). cis-HOCO
cis-DOCO
Vibrational mode
vi
Pi
vi
Pi
1, H–O stretch 2, C–O stretch 3, H–O–C bend 4, C–O stretch 5, O–C–O bend 6, torsion
3651.5 1855.6 1309.6 1080.7 603.7 575.6
0.839 0.052 0.008 0.475 0.259 0.006
2654.6 1854.9 1152.6 980.7 544.9 474.0
0.820 0.081 0.350 0.302 0.323 0.004
(v3 ) is also involved, in addition to the D–O stretch (v1 ), the C–O stretch (v4 ), and O–C–O bend (v5 ). These predictions are to be verified. V. CONCLUSIONS
In this work, we report a full-dimensional quantum mechanical characterization of the photoelectron spectra of both HOCO− and DOCO− , using the most accurate global potential energy surfaces to date. The theoretical vibrational frequencies of the neutral radicals are in good agreement with those obtained using highly accurate semi-global PESs, and with known experimental values. In addition, the experimental electron affinities and photoelectron spectra of both isotopomers are reproduced. These results lend strong support for the accuracy of the PESs used in the calculations. Most importantly, our full-dimensional quantum calculations allowed us to provide estimations of the tunneling lifetimes for several HOCO vibrational states populated by photodetachment of the corresponding anions. The decay of these low-lying metastable states facilitated by tunneling is modespecific. The mode specificity is explained by the large coupling strengths of the O–C stretching and OCO bending modes with the reaction coordinate, according to the SVP model. The positions and widths of these vibrational states should serve as benchmarks for approximate treatments of tunneling induced unimolecular decay. ACKNOWLEDGMENTS
This work was supported by Department of Energy (Grant No. DE-FG02-05ER15694 to H.G.). J.M. thanks the National Natural Science Foundation of China (21303110) for partial support. We thank Joel Bowman for sending us Ref. 72 prior to publication, Bob Continetti for sharing with us the experimental photoelectron spectra, and Al Wagner for many stimulating discussions on tunneling. 1 J.
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THE JOURNAL OF CHEMICAL PHYSICS 140, 184314 (2014)
Full-dimensional characterization of photoelectron spectra of HOCO− and DOCO− and tunneling facilitated decay of HOCO prepared by anion photodetachment Jun Wang,1,2 Jun Li,3 Jianyi Ma,1,3,a) and Hua Guo3,a) 1
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan 610065, China School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China 3 Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA 2
(Received 14 March 2014; accepted 23 April 2014; published online 12 May 2014) The photodetachment of both the HOCO− and DOCO− anions is investigated using full-dimensional quantum wave packets on new ab initio based global potential energy surfaces for both the neutral and anionic species. The calculated electron affinities and neutral fundamental vibrational frequencies of both isotopomers are in good agreement with available experimental data. The measured photoelectron spectra are also accurately reproduced, further validating the accuracy of the potential energy surfaces. In addition, strong mode specificity is found in the lifetimes of the HOCO vibrational features and the tunneling facilitated predissociation rates to H + CO2 are rationalized using the recently proposed sudden vector projection model. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874975] I. INTRODUCTION
HO + CO → H + CO2 is one of the most important combustion reactions1 and it also plays a key role in atmospheric chemistry.2 The kinetics of the reaction have been investigated extensively and found to be pressure dependent and non-Arrhenius.3, 4 In the low pressure limit, the rate coefficient is nearly temperature independent below 500 K, but increases exponentially at higher temperatures. The unique kinetics has been attributed to the complex-forming nature of the reaction,5 which features a stable HOCO intermediate6, 7 supported by potential wells flanked by entrance channel bottlenecks and a nearly isoenergetic exit channel barrier,8 as shown in Fig. 1. Simulations of the kinetics with explicit inclusion of the HOCO intermediate and tunneling have generally been satisfactory.4, 9–12 In addition, the dynamics of this important bimolecular reaction has been investigated experimentally,13–15 but a clear understanding of the dynamics has not emerged due to several theory-experiment disagreements. Despite the existence of numerous previous theoretical studies of the reaction dynamics,16 it has recently been recognized17 that the potential energy surfaces (PESs) used in most dynamics studies8, 18, 19 were not sufficiently accurate. As a result, efforts have been devoted to the development of an accurate global HOCO PES,17, 20–22 and to the dynamical studies on new PESs using both quasi-classical trajectory and quantum mechanical methods.17, 20–27 Because of its central role in the HO + CO → H + CO2 reaction, the HOCO intermediate (and its deuterated isotopomer (DOCO)) has been studied spectroscopically.28–37 HOCO is known to have two isomers, and the more stable a) Authors to whom correspondence should be addressed. Electronic
addresses: [email protected] and [email protected]
0021-9606/2014/140(18)/184314/7/$30.00
trans-HOCO isomer is separated from the cis-HOCO isomer by a significant isomerization barrier. Both isomers have been spectroscopically identified and characterized, although most previous studies have been focused on the trans-isomer. The spectroscopic studies have stimulated several theoretical investigations of the structure and vibrational dynamics of these isomers,38–43 and the overall agreement with the experimental data has been quite satisfactory. An alternative approach to explore the HO + CO → H + CO2 reaction is by photodetaching the stable HOCO− negative ion,44 which brings the system onto the neutral PES near the exit channel barrier, as shown in Fig. 1. Typically, the configuration space accessed by photodetachment is larger than that probed by conventional microwave and infrared spectroscopy, thus providing complementary information on the PES. In addition, the fact that the cis-HOCO− is the more stable anionic isomer helps to explore the cis-region of the neutral PES that has seldom been studied spectroscopically. Indeed, the photodetachment of the HOCO− and DOCO− anions has been extensively investigated by Continetti and coworkers.44–50 In particular, the photodetachment of HOCO− was found to yield the HO + CO, H + CO2 , and HOCO species, and the dissociation to the H + CO2 products is dominated by tunneling.48, 49 Although an earlier theoretical study found little tunneling,51 our recent work on a much more accurate PES17, 20 confirmed the experimental observation,52 and attributed the lack of tunneling in the earlier theoretical work to the artificially “thick” dissociation barrier in previous PESs. In addition, vibrationally resolved photoelectron spectra of HOCO− and DOCO− have been determined experimentally, and reproduced by theoretical calculations on an ab initio quartic force field.50 These photoelectron spectra complement the ro-vibrational spectra of HOCO and provide a different perspective to the vibrational dynamics in
140, 184314-1
© 2014 AIP Publishing LLC
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MOLPRO 2010.1.55 The ab initio points were then fit using the permutation invariant polynomial-neural network (PIPNN) approach.56, 57 Specifically, 17 symmetrized monomials were used as the input layer of a two-hidden-layer NN with 20 interconnected neurons in each layer. The feed-forward NN was trained with the Levenberg-Marquardt algorithm58 to minimize the root mean square error (RMSE) of the fit. The final PES is an average of three best fits. A unique property of the anion PES, as well as the neutral PES,22 is that they are invariant under exchange of like atoms. III. DYNAMICS
A six-dimensional (6D) non-rotating (J = 0) Hamiltonian for the tetra-atomic system is defined using the diatom-diatom Jacobi coordinates shown in Fig. 1,
FIG. 1. Energetics for the HO + CO → H + CO2 reaction and the diatomdiatom Jacobi coordinates for HOCO. The Jacobi coordinates are defined in the inset.
Hˆ =
1 1 ∂2 1 ∂2 − + − + V (r ) 2 2 2μi ∂ri2 2μ2 ∂r22 i=0 +
the HOCO wells. However, we note that the theoretical calculations have been performed using a semi-local PES near the potential minima.50 As discussed above, photodetachment often accesses a large configuration space on the neutral PES and its dynamics (and the resulting photoelectron spectrum) should be treated with a global PES. This is particularly important if the lifetimes of the metastable vibrational levels are to be determined. In this publication, we report a full-dimensional simulation of the photoelectron spectra for the photodetachment of both the HOCO− and DOCO− anions using our recently developed global PES for the HOCO radical22 and a new semi-global PES for the anion. These wave packet calculations also provide estimate of predissociative lifetimes for several prominent HOCO vibrational features in the photoelectron spectrum, which confirms the tunneling facilitated predissociation pathway. This work is organized as follows. The ab initio calculation and fitting of the anion PES is described in Sec. II and the quantum wave packet method used to calculate the photoelectron spectra and predissociation lifetimes is outlined in Sec. III. The results are presented and compared with the experimental data in Sec. IV, with a discussion on the mode-specific tunneling rates. The conclusions are given in Sec. V. II. PES of HOCO−
As in our previous work on the neutral HOCO PES,17, 20 the HOCO− (X1 A ) PES was developed from ab initio points using the F12b version of the coupled-cluster method53 with singles, doubles, and perturbative triples based on restricted Hartree-Fock reference wave functions (RHFCCSD(T)-F12b) with the augmented correlation-consistent polarized valence triple zeta (aug-cc-pVTZ, or AVTZ) basis set.54 The frozen-core approximation for the 1s electrons of the non-hydrogen atoms in the correlation calculations was used. All calculations have been carried out using
2 jˆi2 + [V (r0 , r1 , r2 , θ1 , θ2 , φ) − V2 (r2 )], 2μi ri2 i=0
(1)
where r0 is the distance between two centers of mass while r1 and r2 the diatomic bond lengths of HO/DO and CO, respectively. Their corresponding reduced masses are denoted μi . θ 1 , θ 2 are the Jacobi angles, with jˆ1 , jˆ2 as the corresponding angular momentum operators. Note that jˆ02 = (jˆ1 + jˆ2 )2 . The out-of-plane torsion angle is given by φ. V is the PES and V2 is the reference potential for the non-reactive radial coordinate of r2 . The neutral PES on which the dynamics is followed represents the most accurate HOCO PES to date.22 The 6D wave function is expressed as follows: p i0 i1 i2 j1 j2 m |i0 |i1 |i2 |j1 j2 m, p, (2) = i0 i1 i2 j1 j2 m p
where i0 i1 i2 j1 j2 m is the wave function in the discrete representation. Here, i0 and i1 denote the plane-wave DVR (discrete variable representation)59 grid index for the radial coordinates of r0 and r1, while i2 labels the PODVR (potential optimized DVR)60, 61 for the non-reactive radial coordinate r2 . |j1 j2 m, p is the angular FBR (finite basis representation) defined by parity-adapted products of the spherical harmonics |JM, |j1 j2 m, p = (2 + 2δm,0 )−1/2 (|j1 m|j2 − m +p|j1 − m|j2 m),
p = ±1.
(3)
As discussed below, the anionic PES has two minima corresponding to the cis- and trans-isomers of the HOCO− anion. The ground vibrational states of these two isomers were first determined using the iterative Lanczos algorithm.62 Following our recent work,52, 63, 64 the Condon model was assumed for photodetachment, in which the vibrational eigenfunction on the anionic PES is placed vertically on the neutral PES. The propagation of the wave packet, k , on the neutral PES was performed with the Chebyshev propagator:16 k = 2D Hˆ s k−1 − D 2 k−2 ,
k≥2
(4)
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TABLE I. Parameters in the quantum dynamics calculations of the photoelectron spectra. Parameters (in a.u.) Grid/basis ranges and sizes
Largest value of j1 Largest value of j2 Largest value of m Damping for r0 a Damping for r1 a Propagation step a
HOCO r0 ∈ (2.7, 9.35), N0 = 110 for i0 ≤ 35, r1 ∈ (1.1, 5.4), N1 = 28 for i0 > 35, 5 vibrational basis r2 , PODVR, N2 = 5 30 55 30 Cabs = 0.01, r0,abs = 6.0 Cabs = 0.01, r1,abs = 3.3 300 000
r0 ∈ (2.7, 9.35), N0 = 116 for i0 ≤ 40, r1 ∈ (1.1, 5.4), N1 = 34 for i0 > 40, 6 vibrational basis r2 , PODVR, N2 = 5 36 55 36 Cabs = 0.01, r0,abs = 6.0 Cabs = 0.01, r1,abs = 3.3 360 000
The damping term is defined as D = exp [−Cabs (r − rabs )2 ], r ≥ rabs .
with 1 = D Hˆ s 0 and 0 = i , in which i represents the anionic wavefunction. The Hamiltonian in Eq. (4) was scaled to the spectral range of (−1,1) via Hˆ s = (Hˆ − H + )/H − . The spectral medium (H+ = (Hmax + Hmin )/2) and half width (H− = (Hmax − Hmin )/2) were determined by the spectral extrema, Hmax and Hmin , which can be readily estimated. Finally, the wave packet was damped near the edge of the grids in radial coordinates of r0 and r1 , and the damping functions (D) and parameters are listed in Table I. The energy spectra were obtained from the discrete cosine Fourier transform of the Chebyshev autocorrelation functions Ck ≡ 0 | k :65 S(E) =
DOCO
1 (2 − δk,0 ) cos(kϑ)Ck , π H − sin ϑ k=0
(5)
where ϑ = arccosE is the Chebyshev angle, and k is the Chebyshev order. The threshold region is treated with the Wigner threshold law,66 approximated with a function of the form a + beKE0.5 + ceKE1.5 (a = 0.005, b = 0.1, c = 1.0).50 For narrow resonances, we have also determined their complex energies (En − i n /2) using a low-storage filter diagonalization method,67 in which the Chebyshev autocorrelation function is doubled based on the scheme discussed in our earlier work.68, 69
1.361 eV, respectively. The calculated EAs of the transspecies for both HOCO and DOCO match experimental results (1.38 ± 0.01 and 1.37 ± 0.01 eV).50 Similarly, the corresponding values for the cis-isomers of the two isotopomers are also in good accord with the experimental values (1.51 ± 0.01 eV and 1.51 ± 0.01 eV). These values are also in agreement with theoretical values (1.373, 1.371, 1.501, and 1.501 eV) obtained with the HEAT345-(Q) protocol.50 The fundamental vibrational frequencies of the neutral species were also computed for both the HOCO and DOCO isotopomers. As expected, they are in excellent agreement with the frequencies reported in recent work on the same PES but using a different quantum method.22 The theoretical frequencies listed in Table II are close to known experimental results and previous calculation results using several semi-global PESs.42, 43, 50, 70 Note that some of the experimental values were obtained either in matrices or with large uncertainties. Interestingly, the theoretical values appear to converge better among themselves than with the experimental values, suggesting the uncertainties of the PESs used in these
IV. RESULTS AND DISCUSSION
A total of 13 352 points were calculated for the anion PES, and fit accurately using the PIP-NN approach56, 57 (RMSE = 0.3 cm−1 ). The contour plot of the anion PES is given in Fig. 2 with the equilibrium geometries for both cis- and trans-isomers. The cis-minimum is 0.067 eV lower than the trans counterpart, and the isomerization barrier is 0.411 eV. The geometry and energies are in good agreement with previous ab initio studies.45 The zero-point energies for the cis- and trans-HOCO− are 0.506 and 0.507 eV, and the corresponding values for DOCO- are 0.419 and 0.423 eV. The adiabatic electron affinities (EAs) can be determined by the energy differences between the ground vibrational states in the neutral and anion PES minima. For the cis- and trans-isomers of HOCO, the calculated EAs are 1.517 and 1.367 eV, respectively. For the DOCO isotopomer, the calculated EAs for the cis- and trans-isomers are 1.498 and
FIG. 2. Contour plot of the anion PES as in θ 1 and φ with all other coordinates optimized and the structures of the cis- and trans-HOCO− isomers. The contours are in the unit of eV and the bond length and bond angles are in Å and degrees, respectively.
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TABLE II. Comparison of calculated vibrational frequencies (cm−1 ) for cis- and trans-HOCO and DOCO with experimental and previous theoretical results. cis-HOCO
cis-DOCO
mode
Theo.a
Theo.b
Theo.c
Theo.d
Theo.e
Expt.
Theo.a
Theo.b
Theo.d
Theo.e
Expt.
v1 , O–H stretch v2 , C–O stretch v3 , H–O–C bend v4 , O–C stretch v5 , O–C–O bend v6 , torsion
3438 1809 1272 1038 595 548
3452 1824 1280 1042 601 540
3438 1819 1271 1040 597 554
3458 1815 1282 1042 596 545
3461 1825 1278 1059 600 543
3316f 1797f 1290d , 1261f 1040d , 1088f 605d , 620f ...
2544 1818 1118 955 534 457
2552 1827 1123 961 540 447
2555 1814 1121 949 535 454
2258 1829 1132 961 539 452
... ... 1145d ... 557d ...
trans-HOCO
v1 , O–H stretch v2 , C–O stretch v3 , H–O–C bend v4 , O–C stretch v5 , O–C–O bend v6 , torsion
Theo.a 3636 1852 1204 1048 612 503
Theo.b 3641 1862 1213 1052 616 475
Theo.c 3640 1856 1210 1050 613 502
Theo.d 3641 1854 1217 1057 614 507
trans-DOCO Theo.e 3648 1863 1217 1061 617 507
Expt. 3636g , 3628i 1853j , 1848i 1194d 1048d , 1050i 629d , 615f 508i
Theo.a 2685 1842 1080 898 587 392
Theo.b 2685 1860 1086 903 590 368
Theo.d 2688 1845 1081 900 588 395
Theo.e 2691 1859 1092 906 593 396
Expt. 2684h , 2678i 1852j , 1846i 1081d , 1083i ... 597d ...
a
Present work. Reference 43. c Reference 42. d Photodetachment and theory.50 e Reference 41. f CO matrix IR spectroscopy.28 g Gas phase IR spectroscopy.31 h Gas phase IR spectroscopy.32 i Ne matrix IR spectroscopy.35 j Gas phase IR spectroscopy.30 b
calculations are minimal, at least near the equilibrium geometries of the two HOCO isomers. Fig. 3 shows energy spectra of HOCO prepared by photodetaching HOCO− from its cis- and trans-minima, respectively. The cis-HOCO− spectrum is dominated by four primary sequences, the 50-5 , 31 50-5 , 41 50-5 , and 42 50-4 , consistent with the previous simulation of Johnson et al.50 The intensities of these progressions are determined by the
FIG. 3. Photoelectron spectra of HOCO− arising from cis-(upper panel) and trans-species (bottom panel).
Franck-Condon overlaps, which underscore the changes of the equilibrium geometry from the anion to neutral species. For the planar cis-HOCO− and cis-HOCO, the corresponding geometries are {R, rOH , rCO , θ OH , θ CO } = {3.44, 1.85, 2.24, 83.4◦ , 130.9◦ } and {3.48, 1.84, 2.32, 93.7◦ , 144.7◦ }, respectively. As a result, it is not surprising that the HOC bending (v3 ), CO stretching (v4 ) and OCO bending (v5 ) modes of the latter are excited during the transition. The trans-spectrum is shown as the bottom panel in Fig. 3, which is dominated by four sequences: 40-4 , 40-4 51 , and 31 40-4 . The v4 progression represents the strongest excitation, different from cisspectrum dominated by the v5 progression. The intensities can also be explained by the differences in the equilibrium geometries of the anionic and neutral trans-HOCO species. The energy spectra of the DOCO− isomers shown in Fig. 4 are very different from those of the HOCO− isomers. These spectra are dominated by the 3n 5m progressions. The excitation of the v3 and v5 modes can be attributed to the relatively large changes of the OCO and HOC angles. The strong isotope effect in the photoelectron spectra observed here is in good agreement with the experimental observations of Johnson et al.50 To compare with the recent vibrationally resolved photoelectron spectra of internally cold HOCO− and DOCO− at 660 nm,50 we have simulated the electron kinetic energy distribution in Fig. 5. Both the cis- and trans-isomers were included, but the latter is assumed to contribute only slightly: 5% for HOCO− and 4% for DOCO− , as assumed for the anions produced and stored in very cold temperatures.50 As a result, the cis-isomers dominate the spectra for both
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FIG. 4. Photoelectron spectra of DOCO− arising from cis-(upper panel) and trans-species (bottom panel).
FIG. 5. Photoelectron spectra of HOCO− (upper panel) and DOCO− (bottom panel) at 660 nm (1.878 eV). Blue (red) lines denote cis (trans) transitions. Black lines show the experimental spectrum. The assignments of the main peaks on the spectrum show by their sequences.
HOCO− and DOCO− , due to their lower energies. All of the experimentally observed peaks match with our theoretical simulations and the agreement is excellent, further validating the accuracy of the PESs. It should be pointed out that only the vibrational ground state of trans-HOCO or trans-DOCO is a true bound state. All higher ones are in principle predissociative, because their energies are higher than the H/D + CO2 asymptote. As a result, the vibrationally excited peaks in Figs. 3 and 4 have finite lifetimes. The lifetimes for the HOCO resonances have been estimated before based on reduced-dimensional models.48, 52, 71
Here, the lifetimes of the prominent features in the cis-HOCO spectra are re-estimated by filter-diagonalization based on full-dimensional wave packet propagation and the results are listed in Table III. The propagations have been carried out with ∼300 000 steps, which are roughly equivalent to about 30 ps. Due to the exceedingly long lifetimes of these resonances, only a few predissociation rates have been determined with certainty. The lifetimes of the cis-DOCO features are too long to be determined accurately. As expected, the lifetime typically decreases with the increase of energy for each primary progression, as the tunneling probability
TABLE III. Lifetimes of main peaks in photoelectron spectrum of cis-HOCO and cis-DOCO anions. cis-HOCO Lifetime (s) States
Energy (cm−1 )
6Da
1Db
0 51 52 53 54 55 41 41 51 41 53 41 54 41 55 41 56d 42 42 51 42 52 42 53 42 54
0 595 1192 1790 2388 2987 1038 1627 2809 3403 3990 4582 2061 2643 3226 3810 4394
... ... ... ... ... ∼4 × 10−3 ... ... ... ... 1.2 × 10−4 4.8 × 10−5 ... ... ∼3 × 10−3 2.6 × 10−4 1.4 × 10−5
... ... ... ... 9.5 × 10−3 6.6 × 10−4 ... ... 6.6 × 10−4 4.4 × 10−6 4.4 × 10−7 6.2 × 10−8 ... ... 9.6 × 10−6 4.8 × 10−7 4.4 × 10−7
cis-DOCO 5Dc
States
Energy (cm−1 )
> μs > μs > μs > μs > μs ∼ns τ > μs τ > μs ∼ns ∼ns ∼ns ∼ns τ > μs τ > μs ∼ns ∼ns ∼ns
0 51 52 53 54 55 56 31 31 51 31 52 31 53 31 54 31 55 31 56 31 57 31 58
0 534 1072 1611 2151 2709 3232 1118 1646 2176 2692 3243 3771 4303 4830 5374
τ τ τ τ τ
a
Present work. Reference 72. c Reference 52. d Assignment tentative. b
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increases as the energy approaches the saddle point. Interestingly, the lifetimes of the prominent HOCO vibrational features are longer than the μs flight time in the experimental set up,49 and these resonances would thus be classified as “stable” HOCO molecules. It is also noted that the 5D results reported in our earlier reduced-dimensional work52 are not quantitatively accurate. These observations underscore the full-dimensional nature of the tunneling dynamics. It is clear that strong mode-specificity exists in the predissociation lifetimes. Although there is no experimental data on the predissociation rates, the trend is consistent with that observed in the recent work by Wang and Bowman,72 who have estimated the lifetimes using a modespecific model.73 Although the absolute magnitudes differ from our full-dimensional results, their model correctly captured the trend. The mode-specific model of Bowman and coworkers considers both the energetic factor and the projection of the reactant normal mode vector onto the reaction coordinate vector at the tunneling transition state.73 In the latter aspect, it is conceptually similar to the Sudden Vector Projection (SVP) model recently proposed by us.74, 75 To understand the mode specificity in the tunneling lifetime reported here, we resort to an adaptation of the SVP model to unimolecular dissociation reactions,76 which attributes mode-specific unimolecular decay reactivity to the strength of the coupling of the reactant normal mode with the reaction coordinate at the transition state. This coupling is determined in the sudden limit as the projection of the normal mode vector on to the reaction coordinate vector at the reactive saddle point, which possesses an imaginary frequency. As we demonstrated recently,76 the SVP model provides much insight into modespecificity in unimolecular dissociation reactions for systems with weak intermodal coupling and slow intramolecular vibrational energy redistribution (IVR). To compute the coupling, we first determine the normal modes for both cisHOCO and cis-DOCO as well as the reaction coordinate at the i and Q RC . The projectransition state leading to H + CO2 : Q RC , namely, Pi = Q i · Q RC /|Q i |/|Q RC | ∈ i onto Q tion of Q [0, 1], is then computed, using the protocol outlined in Ref. 76. As shown in Table IV, the SVP values for HOCO suggest that in addition to the H–O stretch (v1 ), the C–O stretch (v4 ) and O–C–O bend (v5 ) also promote the dissociation, thanks to their large couplings with the reaction coordinate. These numbers are consistent with the trend observed in Table III. For DOCO, the SVP model predicts that the D–O–C bend TABLE IV. Harmonic frequencies (cm−1 ) for cis-HOCO and cis-DOCO and their SVP values (Pi ). cis-HOCO
cis-DOCO
Vibrational mode
vi
Pi
vi
Pi
1, H–O stretch 2, C–O stretch 3, H–O–C bend 4, C–O stretch 5, O–C–O bend 6, torsion
3651.5 1855.6 1309.6 1080.7 603.7 575.6
0.839 0.052 0.008 0.475 0.259 0.006
2654.6 1854.9 1152.6 980.7 544.9 474.0
0.820 0.081 0.350 0.302 0.323 0.004
(v3 ) is also involved, in addition to the D–O stretch (v1 ), the C–O stretch (v4 ), and O–C–O bend (v5 ). These predictions are to be verified. V. CONCLUSIONS
In this work, we report a full-dimensional quantum mechanical characterization of the photoelectron spectra of both HOCO− and DOCO− , using the most accurate global potential energy surfaces to date. The theoretical vibrational frequencies of the neutral radicals are in good agreement with those obtained using highly accurate semi-global PESs, and with known experimental values. In addition, the experimental electron affinities and photoelectron spectra of both isotopomers are reproduced. These results lend strong support for the accuracy of the PESs used in the calculations. Most importantly, our full-dimensional quantum calculations allowed us to provide estimations of the tunneling lifetimes for several HOCO vibrational states populated by photodetachment of the corresponding anions. The decay of these low-lying metastable states facilitated by tunneling is modespecific. The mode specificity is explained by the large coupling strengths of the O–C stretching and OCO bending modes with the reaction coordinate, according to the SVP model. The positions and widths of these vibrational states should serve as benchmarks for approximate treatments of tunneling induced unimolecular decay. ACKNOWLEDGMENTS
This work was supported by Department of Energy (Grant No. DE-FG02-05ER15694 to H.G.). J.M. thanks the National Natural Science Foundation of China (21303110) for partial support. We thank Joel Bowman for sending us Ref. 72 prior to publication, Bob Continetti for sharing with us the experimental photoelectron spectra, and Al Wagner for many stimulating discussions on tunneling. 1 J.
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