State-Resolved Quantum Dynamics of Photodetachment of HCO2

Article pubs.acs.org/JPCA

State-Resolved Quantum Dynamics of Photodetachment of HCO2−/ DCO2− on an Accurate Global Potential Energy Surface Lindong Zou,† Jun Li,‡,∥ Hui Wang,§ Jianyi Ma,*,†,‡ and Hua Guo*,‡ †

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan 610065, China Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States § National Key Laboratory for Reactor Fuel and Materials, Nuclear Power Institute of China, Chengdu, Sichuan 610041, China ‡

ABSTRACT: Full-dimensional quantum dynamics studies of the photodetachment of HCO2− and DCO2− are reported using a wave-packet method on an accurate global potential energy surface of the neutral HOCO/HCO2 system. The calculated photoelectron spectra reproduced both the positions and widths of the main HCO2 and DCO2 peaks observed in experiment. Specifically, both the 2A1 and 2B2 resonance peaks of the neutral radicals were identified in our simulations thanks to the adiabatic PES that captures both the 2A1 and 2B2 minima. The narrow widths and isotope effect of the lowest resonances are indicative of tunneling-facilitated predissociation. Furthermore, the dissociation product CO2 was found to be excited in both its symmetric stretching and bending modes, which are coupled via a strong Fermi resonance, but rotationally cold, in good agreement with the recent photoelectron−photodetachment coincidence experiments. The photodetachment of HCO2− and its deuterated isotopomer was first investigated by Neumark and coworkers.11 The photoelectron spectra indicate the involvement of three close-lying electronic states (2A1, 2B2, and 2A2), as previously predicted by theory.17,18 More recently, the Neumark group reported higher resolution data on the photodetachment process using the slow photoelectron velocity-map imaging (SEVI) technique.13 These authors found that the photoelectron spectra for the HCO2− and DCO2− species are highly structured and quite complicated, involving the lowest two near-degenerate electronic states of the neutral species.19 Their experiment established that the 2A1 band origin is slightly lower than that of the 2B2 state. Assisted by the high-level theory of Stanton and coworkers,19 many of the vibrational features in the photoelectron spectra of both HCO2− and DCO2− have been assigned.13 Furthermore, the dissociation dynamics of these species have been investigated using the photoelectronphotodetachment coincidence (PPC) method by the Continetti group, which showed strong vibrational excitations in the rotationally cold CO2 product.12,14 An accurate global potential energy surface (PES) is the prerequisite for understanding reaction dynamics and kinetics. The previous PESs for the HOCO/HCO2 system, such as the

I. INTRODUCTION The HO + CO → H + CO2 reaction is a prototypical complexforming reaction for a number of reasons. As a major heatrelease step in hydrocarbon combustion, it is considered to be the “second most important combustion reaction”.1 It also plays an important role in atmospheric chemistry as the key CO oxidation mechanism.2 This highly exothermic reaction features an entrance channel bottleneck, a relatively stable HOCO intermediate with two isomers, and an exit channel barrier that is almost isoenergetic with the reactant asymptote.3 Despite numerous experimental and theoretical studies on the spectroscopy, kinetics, and reaction dynamics of this system, a complete understanding of the dynamics of this important reaction has still not been achieved.4,5 A unique approach to probe the reaction dynamics of the HO + CO → H + CO2 reaction is by photodetachment of the HOCO− anion, which places the system vertically on the neutral PES by ejecting an electron.5 Extensive experimental studies of the HOCO− and DOCO− photodetachment have been carried out by Continetti and coworkers, which revealed a wealth of information on the HOCO/DOCO vibration and its tunneling facilitated dissociation.6−10 Interestingly, HOCO has a higher energy and metastable isomer formyloxyl radical (HCO2), which can also be accessed by photodetachment of the corresponding anion HCO2−.11−14 This elusive species predissociates rapidly to H + CO2. Although HCO2 is of minor importance for the HO + CO → H + CO2 reaction, it might significantly impact the reactive and inelastic collisions between a fast H and CO2.15,16 Thus, a better understanding of its stability and dissociation dynamics helps to provide a comprehensive picture of the HOCO system. © XXXX American Chemical Society

Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: December 16, 2014 Revised: January 20, 2015

A

DOI: 10.1021/jp512557k J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Lakin−Troya−Schatz−Harding (LTSH) PES,20 were instrumental in permitting detailed theoretical studies of the reaction. However, these PESs are not quantitatively accurate because they are based on relatively small numbers of ab initio points. As a result, a previous full-dimensional quantum dynamical study of the HOCO− photodetachment on the LTSH PES failed to show significant tunneling21 apparently due to the artificially “thick” wall between cis-HOCO and the dissociation products H + CO2. Similarly, our previous full-dimensional study of the HCO2− photodetachment using the LTSH PES also showed a poor agreement with experimental observations.22 In the past few years, several new and more accurate PESs have been developed. For example, Li et al.23,24 reported a much improved PES by fitting a large number of ab initio points calculated with an explicitly correlated coupled cluster singles, doubles, and perturbative triples method with the augcc-pVTZ basis set (UCCSD-F12/AVTZ)25,26 using the permutation invariant polynomial (PIP) method of Bowman and coworkers.27 Dynamical calculations using this PES indicated an improved agreement with many experimental data.23,24,28−31 Subsequently, Chen et al.32 developed an even more accurate fit of a larger set of points generated using essentially the same ab initio theory but fitted with a neural network (NN) method.33 This NN PES was further improved by Li et al.34 by rigorously adapting the permutation symmetry using the permutation invariant polynomial−neural network (PIP-NN) method35,36 using the same set of ab initio data of the NN PES.32 Several recent dynamical studies using the NN or PIP-NN PES have been reported.32,34,37−40 The PIP-NN PES has recently been used to simulate the photodetachment dynamics of HOCO− and DOCO− in full dimensionality,39 and the agreement with experimental photoelectron spectra10 was excellent. In addition, the calculated HOCO vibrational energy levels were also in good agreement with those obtained on accurate semiglobal PESs for this species.41−43 These results suggest that the PIP-NN PES is very accurate in the HOCO region. However, it is not clear if the same PES can accurately describe the HCO2 region given the complexity in the electronic structure of this species.19 The vibronic Hamiltonian of Stanton and coworkers19 is semiglobal and cannot thus be used to simulate the dissociation dynamics, despite its accurate description of the photoelectron spectra. In this work, we report a full-dimensional quantum dynamical study of the photodetachment of HCO2− and its deuterated isotopomer using the PIP-NN PES, and the results suggest that the PIP-NN PES does provide a reasonably accurate representation for the photoelectron spectra of the HCO2− and DCO2− species. In addition, our model also yields the final product state distributions at several different energies, which can be directly compared with the PPC experiment.14 This publication is organized as follows. The next section (Section II) outlines the theoretical method used in the calculation. The results are presented in Section III and the conclusions are given in Section IV.

Figure 1. Jacobi−Radau coordinates used to describe the HCO2/ DCO2 systems.

relative azimuthal angle between r1 and r2 in the body-fixed (BF) frame, which has the z axis is along r0. The rotationless (J = 0) Hamiltonian in this coordinate system is given below (ℏ = 1) 2

2

ĵ ĵ 1 ∂2 1 ∂2 1 ∂2 − − + 1 2 + 2 2 Ĥ = − 2 2 2 2μ0 ∂r0 2μ1 ∂r1 2μ2 ∂r2 2μ1r1 2μ2 r2 2

+

j0̂

2μ0 r02

+ V (r0 , r1 , r2 , θ1 , θ2 , φ)

(1)

where μ0 = mH(mC + 2mO)/(mH + mC + 2mO), μ1 = μ2 = mO. (The hydrogen mass needs be replaced by that of deuterium for DCO2−.) j1̂ and j2̂ are the angular momentum operators for r1 and r2, respectively, and j20̂ = (j1̂ + j2̂ )2. V is the six-dimensional potential energy function. The Hamiltonian is discretized using a mixed grid-basis representation45 in which the radial coordinates are discretized in grids and angular coordinates by basis functions. The action of the potential energy operator is evaluated using a pseudospectral method.46 Following our recent work,22,29,39,47 the initial wave packet on the neutral PES was assumed to arise from a vertical transition from an anion vibrational state. The anion wave functions for the three lowest-lying vibrational levels were obtained by diagonalizing the anion Hamiltonian using the PES of Krekeler et al.,48 developed at the CCSD(T)/aug-cc-pVQZ level of theory. For the neutral HOCO/HCO2 species, the global PIP-NN PES was used.34 Note that this PES was based 80 000 ab initio points at the UCCSD(T)-F12/AVTZ level, and it covers not only the HOCO region but also all relevant configuration space.32 In Figure 2, the minimal energy path for the dissociation of HCO2 on PIP-NN PES is shown with the vibrational energy levels of the CO2 product. The energy zero is chosen to be that of the HO + CO asymptote. Interestingly, the PIP-NN PES captures both the 2A1 and 2B2 minima of HCO2, thanks apparently to the fact that the CCSD(T) method follows the lowest adiabatic electronic state. From the Figure, it is also clear that there is a small barrier of 0.06 eV between the 2 A1 and 2B2 minima due to the conical intersection between the two states.19 The former dissociates via a moderate barrier of ∼0.2 eV to H + CO2. It can thus be expected that the lowestlying vibrational states of HCO2 below the classical barrier would be predissociative facilitated by tunneling. Assuming a Condon transition in photodetachment, the initial wave packet on the neutral state (|Ψi⟩) is simply a rovibrational eigenstate on the anion PES. In our calculations,

II. THEORY The full-dimensional quantum dynamical calculations of the photodetachment of the HCO2− (and DCO2−) were carried out using the (2 + 1) Radau−Jacobi coordinates,44 denoted as (r0, r1, r2, θ1, θ2, φ) and illustrated in Figure 1. r0 is radial Jacobi coordinate between H and the center of mass of CO2, r1 and r2 are two Radau radial coordinates for the CO2 species, θ1 (θ2) is r 1 (⇀ r 2) and ⇀ r 0, and φ is the the angle between vectors ⇀ B


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The Journal of Physical Chemistry A

determined from the Chebyshev correlation functions using our version of low-storage filter diagonalization (LSFD) method.52,53 Following our recent work,22,54 the CO2 product rotational and vibrational populations were computed as the squared Fourier transform of the Chebyshev cross-correlation functions Cfk = ⟨χf |Ψk⟩ computed in the product channels51,55 2

Pf (E) =

2πH̅ 1 − E2

∑ (2 − δ0k)e−ik arccos ECkf (4)

k=0

In particular, the asymptotic wave packet χf is expressed as a product of the CO2 internal state wave function and a delta function defined at R = 9.5 a.u.. All of the numerical parameters used in the dynamics calculations, including the sizes of the grids and bases as well as the position of the analysis plane, have been tested for convergence, and the final values are collected in Table 1. All results were obtained with 20 000 Chebyshev steps, which are sufficient to resolve the widths of the peaks. However, this propagation length is not long enough to converge the product state distributions for some long-lived resonances.

Figure 2. Minimal energy path for HCO2 dissociation along the dissociation coordinate in (2 + 1) Radau−Jacobi frame (r0). The transition state is denoted as TS3 based on convention.23 The barrier between 2A1 and 2B2 minima is included as an orange dashed line. The C−O bond length at the stationary points is shown in atomic units while the angles are shown in degrees. The vibrational levels of CO2 are denoted by (n1n2ln3, r) and diad quantum number of p, where n1, n2, and n3 are quantum numbers for the symmetric stretching, bending, and antisymmetric stretching modes with l as the vibrational angular momentum. Within each diad, the states are ranked by r.

III. RESULTS AND DISCUSSION As previously mentioned, the PIP-NN PES provides a globally accurate description of the system, including the HCO2 region. However, this adiabatic PES does not contain all of the vibronic interactions necessary for a full description of the HCO2 system. Previous theoretical studies have pointed to a complicated picture due to two strongly interacting neardegenerate electronic states.17−19,56−61 The latest 2 × 2 vibronic model of Stanton and coworkers predicted two minima on the lower adiabat, corresponding to the 2A1 and 2B2 states.19 Although both electronic states have C2v minima in the diabatic representation, the adiabatic equilibrium geometry of the latter is C2v, but the former is near C2v due to pseudo-Jahn− Teller distortion. Nevertheless, Stanton and coworkers have pointed out that the photoelectron spectra can be understood without considering the small distortion of the 2A1 equilibrium geometry.13 The question is whether the adiabatic PIP-NN PES is capable of capturing key features on the lowest adiabat of the vibronic Hamiltonian. The answer to the above question is affirmative. The geometries corresponding to the C2v 2A1 and 2B2 minima of HCO2 on the PIP-NN PES are compared in Table 2 with the accurate values reported by Klein et al.,19 along with the geometry of the sole C2v minimum on the LTSH PES. It is clear that the geometries of the 2A1 and 2B2 minima on the PIP-NN PES are very close to the minima reported by Klein et al., but the LTSH minimum is significantly different. In addition, the energy difference between the two minima is ∼0.0663 eV with

several lowest-lying rotationless vibrational states were used. The wave packet is propagated using the Chebyshev propagator49 |Ψk⟩ = 2DĤ s|Ψk − 1⟩ − D2|Ψk − 2⟩, k ≥ 2

1

(2)

where |Ψ1⟩ = DĤ s|Ψ0⟩ and |Ψ0⟩ = |Ψi⟩. D is a damping function defined in the edges of the grid to impose outgoing boundary conditions.50 The scaled Hamiltonian is defined as Ĥ s = (Ĥ − H̅ )/ΔH to avoid the divergence of the Chebyshev propagator outside the range [−1, 1]. Here the mean and half-width of the Hamiltonian are determined as H̅ = (Hmax + Hmin)/2 and ΔH = (Hmax − Hmin)/2, where Hmax and Hmin define the spectral range of the Hamiltonian and can be estimated from the kinetic and potential energies on the grid/basis. The photoelectron spectra for HCO2− and DCO2− were computed from the cosine Fourier transform of the autocorrelation functions defined in the Chebyshev order domain Ck = ⟨Ψ0|Ψk⟩51 1 S(E ) = ∑ (2 − δk ,0) cos(k arccos E)Ck πH̅ 1 − E2 k = 0 (3)

where E is the total energy of the system. For the few narrow resonances, their complex energies (E − iΓ/2) were

Table 1. Numerical Parameters (in a.u.) Used in Wave-Packet Calculations system grid/basis ranges and sizes largest values of j1, j2, and m damping potential for r0a position of the product projection propagation steps a

HCO2

DCO2

r0 ∈ (1.8, 13.5) N0 = 65 7 point PODVR for r1 and r2 55, 55, 55 αabs = 0.01, r0,abs = 10.0 r0,p = 9.5 20 000

r0 ∈ (1.8, 13.5) N0 = 85 7 point PODVR for r1 and r2 55, 55, 55 αabs = 0.01, r0,abs = 10.0 r0,p = 9.5 20 000

Damping function is defined as D = exp[−αabs(r − rabs)2], r ≥ rabs. C


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The Journal of Physical Chemistry A Table 2. Equilibrium Structure of the 2A1 and 2B2 States of HCO2 and the of HCO2− (in a.u. and deg.) PIP-NNa 2

A1

H−C O−C ∠OCO a

2.200 2.313 145.1

diabatic minimab 2

B2

2.035 2.381 110.6

2

B2

LTSHc

aniond

2.065 2.375 112.5

2.090 2.400 124.1

2.133 2.368 130.2

2

A1

2.192 2.321 144.8

Ref 34. bRef 19. cRef 20. dRef 48.

a lower 2B2 minimum, also in excellent agreement with the previous theoretical estimate (0.0668 eV).19 (The larger vibrational frequencies of the 2B2 state lead to a higher zeropoint energy, rendering a lower 2A1 band origin, as observed experimentally.13) As a result, the PIP-NN PES should be sufficient to provide information on the photoelectron spectra of HCO2− and DCO2− and perhaps more importantly their dissociation dynamics. For comparison, the equilibrium structure of HCO2− is also included in the Table. The calculated photoelectron spectra of HCO2− and DCO2− on the PIP-NN PES are compared with the corresponding experimental results in Figures 3 and 4, respectively. The

theoretical spectra were obtained with the same photon energies used in the experiment:13 31 745 cm−1 = 3.94 eV and 32 023 cm−1 = 3.97 eV for HCO2− and DCO2−, respectively. Our simulations involve the photodetachment for the ground and first two excitation states of the v3 mode of HCO2−/DCO2−. The contributions of the three lowest-lying vibrational states of the anions are weighted by the Boltzmann factor at the experimental temperature of 400 K. For the positions, intensities, and widths of the peaks, the simulation results match both the observed and previous theoretical spectra very well. The calculated peaks are labeled by the same characters as the experimental spectra reported in ref 13. The assignments, positions, and lifetimes of the labeled peaks for HCO2− and DCO2− species are collected in Tables 3 and 4, respectively. On the basis of the nodal structure and position of the wave function, peak A in the HCO2 spectrum is assigned to the vibrational ground state of the 2A1 state. The much less intense and narrower peak labeled C, lying 325 cm−1 above A, is assigned to the vibrational ground state of the 2B2 state. The widths of the A and C peaks are, respectively, 0.72 and 0.03 cm−1, which correspond to lifetimes longer than 10 ps, due apparently to tunneling. The longer lifetime of the latter can be attributed to the fact that the 2B2 minimum has a smaller OCO angle, as shown in Figure 2, and thus it is more difficult to go through the barrier at TS3. The D, F, G, and H peaks in Figure 3 are assigned to the 310, 320, 620, and 310620 excitations of the 2A1 state of HCO2, while peak E is assigned to the 310 excitation of the 2B2 state. These assignments agree with the previous assignments very well.13 In our simulation, peak J, which was not previously assigned, belongs to the 520 excitation of the 2A1 state of HCO2. Interestingly, the wave function of peak D has some 2B2 character, despite its assignment to the 2A1 state. Peak E has a similar mixed character as well. This is not surprising because the barrier between two minima is only 0.06 eV. The D to J peaks have shorter lifetimes compared with the vibrational ground states of the 2A1 and 2B2 states due to their high energies. The most intense peaks correspond to the v3 progression on both electronic states, apparently due to the differences in the O−C−O bending angle of the anionic and neutral equilibrium geometries, as indicated in Figure 2. For the DCO2 species, the A and B peaks are assigned to the 2 A1 and 2B2 ground vibrational states, respectively. As expected, the deuteration increases the lifetimes significantly: the lifetime of B is ∼10 ns, much longer than other peaks. The D, F, and I peaks in Figure 4 are assigned to the 310, 320, and 620 excitations of the 2A1 state. Interestingly, the assignments of F and I were difficult based on the corresponding wave functions. This is consistent with the PPC experiment, in which the vibrational state distribution of CO2 of peak I has a mixed electronic character.14 Several weaker peaks in the low-energy wing of the spectra, labeled by lower case letters, stem from the 310 and 311 excitations of the HCO2− and DCO2− anions, weighted by

Figure 3. Comparison between the calculated and measured photoelectron spectrum for the HCO2− species at the photon wavenumber of 31 745 cm−1.13 The same labels as those in ref 13 are used to mark the simulation peaks.

Figure 4. Comparison between the calculated and measured photoelectron spectrum for the DCO2− species at the photon wavenumber of 32 023 cm−1.13 The same labels as those in ref 13 are used to mark the simulation peaks.

D


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The Journal of Physical Chemistry A Table 3. Assignments of the Labeled Peaks in the Photoelectron Spectrum of HCO2−a peaks

present work

assign.

e f g A C D E F

−739.1 −413.3 −243.7 0.0 325.8 504.4 773.5 1008.7 1063.2 1369.0 1829.4 1937.7

301(2A1) 301(2B2) 311(2A1) 000(2A1) 000(2B2) 310(2A1) 310(2B2) 320(2A1) 210(2A1) 620(2A1) 310620(2A1) 520(2A1)

G H J

Γ

0.72 0.03 9.59 10.20 50.14 9.38 3.11 18.63 12.19

positions (exptl)b

positions (theor)b

assign.b

−743 −435 −196 0 318 564 877 1086

−752 −442 −182 0.0 310.2 569.7 880.1 1058.8 1145.4 1337.1 1872.1

301(2A1) 301(2B2) 311(2A1) 000(2A1) 001(2B2) 310(2A1) 310(2B2) 320(2A1) 210(2A1) 620(2A1) 310620(2A1)

1363 1910 2109

Energies in cm−1 relative to origin peak A and Γ in cm−1. For the assignment of vpq, v denotes the vibrational modes of HCO2. (See figure 1 in ref 13 for a detailed definition.) p and q denote the corresponding quantum numbers for the neutral and anion species of HCO2, respectively. bExperiment and the simulation values in ref 13. a

Table 4. Assignments of the Labeled Peaks in the Photoelectron Spectrum of DCO2−a

a

peaks

present work

d e f g A B D F I J K O

−733.0 −634.6 −267.1 −105.1 0.0 98.4 465.9 901.1 983.5 1431.5 1906.4 2350.4

assign. 301(2A1) 301(2B2) 311(2A1) 311(2B2) 000(2A1) 000(2B2) 310(2A1) 320(2A1) 620(2A1) mixed 310620(2A1) mixed

Γ

positions (exptl)b

positions (theor)b

assign.b

0.90 0.03 0.00057 0.47 6.24 0.50 1.65 6.28 11.6

−742 −642 −155 −68 0 87 563 948 1193 1520 2023 2583

−745 −645 −180 −67 0.0 100.5 564.8 910.0 1199.7 1478.1 1997.4

301(2A1) 301(2B2) 311(2A1) 311(2B2) 000(2A1) 000(2B2) 310(2A1) 310610(2A1) 320(2B2) 110(2A1)

Energies in cm−1 relative to origin peak A and Γ in cm−1. bExperiment and the simulation values in ref 13.

Figure 5. Simulated photoelectron−photofragment coincidence spectrum for HCO2−→ H + CO2 + e− and DCO2−→ D + CO2 + e− at 290 nm. The simulation data are convoluted with Gaussian function (σ = 10 meV) for both of eKE and translational energy.

4. Although most of the features observed in the experiments are reproduced by our simulations, intensity discrepancies of several peaks between the experimental and computational spectra are visible. The main reason is probably that our adiabatic PES loses some diabatic effects and a more accurate description of the spectral intensities requires a diabatic representation of the PESs. The overall good agreement with experimental photoelectron spectra suggests that the PIP-NN PES is capable of

the Boltzmann factor at 400 K. The assignments of these weak hot bands agree with the previous assignments13 as well. The 301 and 311 excitations of the HCO2− and DCO2− anions are stronger than the band origin of the 2B2 state due to the fact that the OCO angle of the anions is closer to the angle of the 2 A1 minimum than that of the 2B2 state. We note that there are several weak unassigned peaks in both the experimental and computational spectra. There are mostly mixed states between the two electronic states and thus not included in Tables 3 and E


Article


Figure 6. CO2 rovibrational state distributions for different resonance peaks of the photoelectron spectrum of HCO2−, labeled by the diad quantum number, p.

Figure 7. CO2 rovibrational state distributions for different resonance peaks of the photoelectron spectrum of DCO2−, labeled by the diad quantum number p.

included in the simulations, and the temperature of the anion is assumed to be 500 K based on the experimental estimate.14 To plot in two-dimensional contours, the peaks are convoluted by a Gaussian with a width of 10 meV in both the electronic and translational energies. Because an accurate energy of the anion state related to the neutral state is not known in our calculation, due to the use of different ab initio methods in the determination of the respective PESs, we shifted the maximum of the electronic kinetic (eKE) maxima to the experimental values of 1.34 and 1.30 eV for HCO2− and DCO2−,

describing the dynamics near the HCO2 minima. This is very encouraging because the global PES also allows the characterization of the dissociation dynamics, which is not possible for the vibronic Hamiltonian of Klein et al.19 Recently, Ray et al. reported results of a state-resolved PPC experiment for the DCO2− anion at 290 nm (4.27 eV).14 The photon energy allows the access of most of the 2A1 and 2B2 resonance features in Figure 4. In Figure 5, our simulated PPC spectra for both the HCO2− and DCO2− anions are presented. Again, the lowest three states of the v3 mode of HCO2− and DCO2− anions were F


Article

The Journal of Physical Chemistry A respectively.14 The agreement with the experimental spectrum of Ray et al. is very good, although the experimental spectrum has much lower resolution. It is clear that the simulated PPC spectra are dominated by discrete peaks. The projection of the PPC spectrum on to the eKE axis results in the photoelectron spectrum for each species, and the peaks are consistent with the ones discussed in Figures 3 and 4. At each eKE value, the peaks correspond to the CO2 product state distributions, which are discussed in more detail later. Detailed dynamical information can be obtained from the CO2 product state distributions. In Figures 6 and 7, the CO2 vibrational−rotational state distributions at some of the resonance peaks described in Figures 3 and 4 are presented. For charity, these product state distributions included only the ground vibrational states of the HCO2− and DCO2− anions. The vibrational states of CO2 are labeled by (n1nl2n3, r), as shown in Figure 2, in which n1, n2, and n3 are quantum numbers for the symmetric stretching, bending, and asymmetric stretching modes with l as the vibrational angular momentum quantum number. Because of the 1:2 Fermi resonance, the symmetric stretch is strongly mixed with the bend. As a result, the CO2 vibrational levels are better described using the diad quantum number p = 2n1 + n2.62 This is clearly shown in Figure 2, where the vibrational states are naturally clusters together, with each cluster corresponding to a specific diad quantum number. Within each diad, the states are distinguished by the ranking number, r. We further note that linear CO2 only allows even bending quanta for even rotational quantum numbers (j = 0, 2, 4, ...) and odd bending quanta for odd rotational quantum numbers (j = 1, 3, 5,...) in our simulations. This is apparently an artifact of the calculation in which the total angular momentum quantum number (J) is set to zero. Similar to our previous results on LTSH PES,22 no population is found in the asymmetric stretching states of CO2 due to the C2v symmetry in the initial wave packet and the transition state. However, much higher excitations of the CO2 vibration are found using the PIP-NN PES. As shown in these Figures, the product state distributions are dominated by populations in several clusters with different diad quantum numbers. Strong vibrational excitation and weak rotational excitation of the CO2 product are apparent for all of the peaks in the photoelectron spectra, although there is somewhat more rotational excitation for peaks H and J of HCO2− and peak M of DCO2−. Specifically, several CO2 vibrational states ranging from p = 0 to 5 with low rotational excitation (j < 6 for peaks A−F) are populated, as shown in Figure 6, for the dissociation of HCO2. The CO2 vibrational distributions for low-energy HCO2 resonances typically peak at the p = 2 or 3 cluster. For the higher energy resonances, the peak position is shifted to higher clusters. A similar vibrational population inversion is present for the DCO2 resonances, as shown in Figure 7. The calculated CO2 product state distributions are typically peaked at p = 1 to 2, which are somewhat lower than the experimental distributions, which peak near p = 3. There are several possible sources of errors in our simulations. First, the rotational excitation of the parent molecule (DCO2), which is quite significant at 400 K, is ignored. Second, most of the simulated peaks in Figure 4 are lower in energy than the experimental ones, which are expected to impart less energy into the product. Third, the propagation time (roughly equivalent to 2 ps) may be too short to completely capture the long-lived tunneling feature for low-lying peaks. Nonetheless, these rovibrational

state distributions of the CO2 product represent a huge improvement over our previous work22 on the LTSH PES in comparing with the experimental observations of Ray et al.14 To understand the CO2 internal excitation, we rely on the recently proposed sudden vector projection (SVP) model.63−66 Assuming an instantaneous dissociation, the extent of vibrational excitation in the product of the unimolecular reaction is related to the coupling of the product vibrational mode with the reaction coordinate at the transition state (TS3 in Figure 2). This coupling can be estimated by projecting the product normal mode vector onto the reaction coordinate vector. On the PIP-NN PES, the SVP values for the symmetric stretching, bending, and asymmetric stretching modes of CO2 are 0.13, 0.31 and 0.00. These values clearly indicate significant coupling of the first two modes with the dissociation reaction coordinate, thus explaining the observed excitation. The antisymmetric stretching mode is by symmetry orthogonal to the C2v dissociation reaction coordinate, thus resulting in the null coupling. Similarly, extensive CO2 rotational excitation can also be ruled out based on the same symmetry argument.

IV. CONCLUSIONS We report exact full-dimensional quantum mechanical studies of the predissociation dynamics of HCO2 and DCO2 prepared by photodetachment of HCO2− and DCO2− using a globally accurate PES for the corresponding neutral species. Our simulations reproduced all of the main features in the experimental results, including peak positions and widths in the photoelectron spectra and the CO2 product state distributions. The assignments of the main peaks and their lifetimes in the photoelectron spectra are consistent with those determined previously using a nonadiabatic vibronic Hamiltonian thanks to the fact that the adiabatic PES captures the main features of the 2A1 and 2B2 state minima. Furthermore, the CO2 products are found to be highly excited in the Fermicoupled symmetric stretching and bending modes, with low rotational excitations, in agreement with experimental observations. The vibrationally hot and rotationally cold product distributions can be readily explained by the SVP model based on the coupling of the product mode with the reaction coordinate at the dissociative transition state. The agreement with experiment provides strong evidence in support of the accuracy of the adiabatic PES used in the calculations.

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AUTHOR INFORMATION

Corresponding Authors

*J.M.: E-mail: [email protected]. *H.G.: E-mail: [email protected]. Present Address ∥

J.L.: School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400030, China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by the National Natural Science Foundation of China (21303110 to J.M. and 21301164 to H.W.), Excellent Young Scholars Foundation of Sichuan University (to J.M.), and U.S. Department of Energy (DEFG02-05ER15694 to H.G.). We thank Bob Continetti and John Stanton for many useful discussions. G


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State-Resolved Quantum Dynamics of Photodetachment of HCO2

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