Full-Dimensional Quantum Dynamics of Vibrational Mediated

Article pubs.acs.org/JPCA

Full-Dimensional Quantum Dynamics of Vibrational Mediated Photodissociation of HOD in Its B Band Linsen Zhou† and Daiqian Xie*,†,‡ †

Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China ‡ Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ABSTRACT: The photodissociation dynamics for the ground and three fundamental vibrational states of HOD were explored from quantum dynamical calculations including the electronic X̃ , Ã , and B̃ states. The calculations were based on a Chebyshev real wave packet method. Due to the different shapes of the initial vibrational wave functions and isotopic effect, the calculated absorption spectra, product state distributions, and branching ratios show different dynamic features. The initial bending excited vibtaional state (0, 1, 0) generates a bimodal behavior on the absorption spectrum and an inverted vibrational population of OD(X̃ ) fragment at some total energies. The rotational state distributions from four vibrational states have two different behaviors. One has a single broad peak, whereas the other one has a bimodal structure. Large OD(Ã )/OD(X̃ ) ratios are found for photodissociation from four vibrational states at high total energies, which indicate that the H atom dissociates mainly via the adiabatic pathway. We also calculated the OD/OH isotopic branching ratios from four vibrational states and found that the OD + H production channel is dominant over the OH + D channel in the energy range considered. The calculated results are consistent with the available observed ones.

I. INTRODUCTION The photodissociation dynamics of H2O in the vacuum ultraviolet have been extensively studied experimentally and theoretically, due to their importance in atmospheric and interstellar chemistry.1−3 Its A and B bands have served as prototypes for understanding adiabatic and nonadiabatic dynamics in polyatomic systems.4 The Ã 1B1 state photodissociation around 150−200 nm was found to proceed on a single repulsive potential energy surface (PES) and lead to the H atom and OH(X̃ 2 Π) radical with a little internal excitation,5−9 which is an excellent example of direct photodissociation. Dissociation of H2O on the B̃ 1A1 state centered at 128 nm is much more complicated. The B̃ 1A1 state not only correlates adiabatically to the OH(Ã 2Σ+) + H asymptote but also has nonadiabatic couplings with two lower singlet electronic states. In the collinear geometry, there exist two nonadiabatic pathways to the OH(X̃ 2Π) + H fragments, via the Renner−Teller coupling (RT) between B̃ and Ã states and two competitive conical intersections (CIs) between B̃ and X̃ states at the linear HOH and HHO geometries, which lead to interesting quantum interference.10−13 Therefore, a quantitative description of photodissociation via the B band should include three electronic states and nonadiabatic couplings.14 The substitution of a hydrogen in H2O by one deuterium little changes the electronic character but often influences the photodissociation dynamics significantly, in particular where the nonadiabatic couplings are involved. This isotopic © XXXX American Chemical Society

substitution results in symmetry breaking and opens two distinct D + OH and H + OD dissociation channels. It has been reported that the quantitative outcome of dissociation of HOD is not the average of those for H2O and D2O.15,16 Momentum balance between the recoiling H and D atoms of HOD results in a tendency for a 2:1 sharing of the available energy and an unequal branching ratio of (H + OD)/(D + OH). In addition, the vibrationally mediated photodissociation (VMP) with OD or OH bond pre-excitation accesses different regions of the excited-state PES, which might lead to mode or isotopic selectivity.17−19 For example, the theoretical predictions20−24 and experiments25−34 of HOD in the A band have verified that OH/OD branching ratio can been “steered” by choosing the appropriate initial vibrational state and photon wavelength. Compared with the extensive studies of the A band, the studies for photodissociation of HOD in its B band are scarce. In 1982, Segev and Shapiro35 performed the first dynamical calculations for the B band photodissociation of HOD at the ground (0, 0, 0) and bending (0, 1, 0) vibrational states. But they used the two-dimensional ab initio PES of Flouquet and Horsley,36 and completely ignored the nonadiabatic transitions, Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics Received: May 26, 2015 Revised: July 21, 2015

A

DOI: 10.1021/acs.jpca.5b05029 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A which was demonstrated to be too simple.37−39 In 2001, Harich et al.40 employed a high-resolution Rydberg “tagging” time-offlight (TOF) technique to study the HOD photodissociation at 121.6 nm and found “Super-rotationally excited” rotational states in OH(X̃ , v = 0). These extreme rotational states are slightly above its dissociation limit and are only supported through large centrifugal barriers. In another experiment,41 they revealed a strong preference for OD(Ã , v = 0) with single rotational quantum number N = 28 labeled as “single rotational product phenomenon”. The classical-quantum calculations by van Harrevelt et al.42 demonstrated that this abnormal inverted distribution can be attributed to a dynamically constrained threshold effect on the B̃ 1A1 PES. In 2004, Cheng et al.43 measured the room temperature absorption spectra of H2O and its isotopomers D2O and HOD in the 125−145 nm region using the synchrotron radiation together with a theoretical calculation. The observed and calculated amplitudes of the indirect cross section of HOD are astonishingly larger than those of H2O and D2O. The agreement between the experiment and theory was excellent for H2O and D2O, but for HOD a large discrepancy had been found. Even though much information has been obtained from these studies, a whole picture of HOD photodissociation in the B band is still lacking. Recently, we reported full-dimensional quantum mechanical studies of H2O and D2O photodissociation in the B band.13,44−48 The calculated total cross sections (TCSs), product state distributions, branching ratios, and differential cross sections showed excellent agreement with the latest experimental results. To get a deeper understanding of the isotope effect in the B band photodissociation dynamics of water, we used a three-state model13,46 to explore the VMP of HOD at its ground and three fundamental vibrational states in this work. This article is organized as follows. Section II provides a short description of the quantum mechanical method for the three-state model. Section III presents the numerical details of the calculations. The calculation results are presented and discussed in section IV. Finally, a brief summary is given in section V.

To describe the different dissociation channels of HOD, two sets of product Jacobi coordinates (R, r, γ) were chosen as OH−D and OD−H. R represents the distance between the dissociated atom to the diatomic fragment, r is the bond length of the diatomic fragment, and γ is the enclosed angle between the vectors R and r. In our model, the z-axis of the body-fixed (BF) frame is defined along the R vector (R-embedding), and the HOD molecule was fixed in the x−z plane. Following the proposal of Petrongolo 49 and Goldfield et al., 50 the Hamiltonian can be conveniently given in a quasi-diabatic representation as

H = T̂ I + Hdel

in which I is the three-dimensional identity matrix. Hdel is the 3 × 3 potential energy matrix defined in diabatic representation.13,46 Expressions of the nuclear kinetic operator in the Jacobi coordinates (R, r, γ) can be given as (ℏ = 1 hereafter), T̂ = −

1 ∂2 1 ∂2 ̂ − + Trot 2μR ∂R2 2μr ∂r 2

(2)

2 ⎡ Nẑ ⎤⎥ ̂ = (BR + br )⎢ − 1 ∂ sin γ ∂ + Trot ⎢⎣ sin γ ∂γ ∂γ sin 2 γ ⎥⎦

⎡ 2 2 2 + BR ⎢J ̂ − 2Jẑ − Lẑ + 2Jẑ Lẑ ⎣ ⎛ ⎛ ∂⎞ ∂ ⎞⎤ + J+̂ ⎜cot γNẑ + ⎟ + J−̂ ⎜cot γNẑ − ⎟⎥ ∂γ ⎠ ∂γ ⎠⎦ ⎝ ⎝

(3)

with br = 1/2μrr2 and BR = 1/2μRR2. μr and μR are the reduced masses for two radial Jacobi coordinates, respectively. In the above equations, the BF nuclear angular momentum operator N̂ = J ̂ − L̂ is defined as the difference between the total angular momentum (J)̂ and the electronic angular momentum (L̂ ). The raising/lowering operators J±̂ represent the Coriolis terms. The quasi-diabatic representation can minimizes the derivative coupling and could be expressed as46

II. THEORY The photodissociation of HOD via the B band is depicted as follows,

⎛|λ = 0⟩ ⎞ ⎜ ⎟ ⎜|λ = −1⟩⎟= ⎜ ⎟ ⎝|λ = +1⟩⎠

HOD(X,̃ (v1 , v2 , v3), JK K ) a c

hv

→ HOD(B)̃ adiabatic

(1)

̃2 +

⎯⎯⎯⎯⎯⎯⎯→ D + OH/H + OD(A Σ , v , j)

⎛ cos α sin α 0 ⎞ ⎜ ⎟ α α sin cos i ⎟ ⎛⎜|1A′⟩ ⎞⎟ ⎜− − ⎜ 2 2 2 ⎟ ⎜|2A′⟩ ⎟ ⎜ ⎟ ⎜ ⎟ α α sin cos i ⎜⎜− ⎟⎟ ⎝|1A″⟩⎠ ⎝ 2 2 2 ⎠

(4)

where α is the mixing angle. 1A′(X̃ ), 1A″(Ã ), and 2A′(B̃ ) are the adiabatic representation of HOD, which give rise to the adiabatic PESs. For the diabatic representation, we further assume that the electronic angular mometum along R is diagonal even in nonlinear configurations. The diabatic representations are thus assumed to be eigenfunctions of L̂ z and L̂ z2 at linear configurations: L̂ z|λ⟩ = λ|λ⟩, L̂ z2|λ⟩ = λ2|λ⟩. In this work, we use the approximation that the matrix elements of L̂ z and L̂ z2 are constant for the two different Jacobi coordinate systems. This means that the calculations using the coordinates OH−D and OD−H are not strictly equivalent. But the effect is probably small, because the RT and CI couplings are only important near linear geometries.51 The total wave function is expressed as

CI/RT

̃ ̃ ⎯⎯⎯⎯⎯⎯→ HOD(X/A) → D + OH/H + OD(X̃ 2Π, v , j)

where (v1, v2, v3) and JKaKc designate a ro-vibrational state of HOD(X̃ ). The three vibrational quantum numbers represent the OD stretching, HOD bending, and OH stretching modes, respectively. J, Ka, and Kc are the total angular momentum and its projections on the a and c axes in the prolate and oblate symmetric limits. The OH/OD(X̃ /Ã ) fragments are labeled by the vibrational (v) and rotational (j) quantum numbers. The electronic and spin momenta of the fragments were ignored in this study. B


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Ψ=

∑ ∑ ∑ ∑ ∑ ψnp,m,j ,K , l|n⟩|m⟩|j , K , l ; J , M , p⟩ n

m

K

l

TvjJKλp(E)

j =|l|

K−j

= i( −1)

(5)

(12)

where n and m are grid indices for the R and r coordinates. K and M are the z component of J in the SF and BF frames, respectively. p is the rotational parity. The parity-adapted electron-rotational basis is defined by 1 [|jl⟩|J , K , M ⟩|λ⟩ 2 J+K +l+p + (−1) |j − l⟩|J , −K , M ⟩|−λ⟩]

with E = Ei + hv and Es = (E − H̅ )/ΔH. |v, j, l⟩ = χvj(r)Plj(γ) is the product ro-vibrational wave function. kλvj is the corresponding wave vector, and R∞ is the point where the final state projection is performed. The integral cross section (ICS) can be calculated as57,58

| j , K , l ; J , M , p⟩ =

for λ = ±1, 0; K ≠ 0

σvjλ(E) =

(6)

with l = K − λ. |j, l⟩ ≡ Θlj(γ) is a normalized associated Legendre function, and |J, K, M⟩ = [(2J + 1)/8π2]1/2DJM,K * is a Wigner rotation matrix. This definition is similar to that of van Harrevelt and van Hemert.52 For K > 0, the excited molecule can dissociate via both CI and RT coupling routes. For K = 0, RT coupling is switched off, eq 7 is then equal to that in the two-state model.45,47 The matrix elements of the Hamiltonian in diabatic representation have been given in our previous work.46 The propagation of the diabatic wave packet was performed in the Chebyshev order (ξ) domain via the three-term recursion relation,53−55 for ξ > 1

σtot(E) = =

1 2π ΔH 1 − Es 2

3

J = Ji − 1 K

*

TvjJKλp TvjJKλp

∑ σv ,j(E) πω 1 × cε0 ΔHπ 1 − E 2 nrom ∞

ξ=0

(14)

III. CALCULATION DETAILS All calculations reported here employed our own PESs and transition dipole functions, which were computed at the dynamically weighted Davidson corrected MRCI+Q level with the AVQZ basis set.45 These PESs are more reliable than previous Leiden PESs52,59 and Dobbyn−Knowles (DK) PESs,60 because many more ab initio points were included and the electronic structure calculations involved a larger active space and a larger basis set. The BF Hamiltonian including all the Coriolis coupling is represented with a mixed discrete variable representation (DVR) and finite basis representation (FBR). The action of the radial kinetic energy operators are calculated using the sine fast Fourier transform.61 The evaluation of the action of the rotational kinetic energy operator is straightforward in the FBR as the operator can be expressed as a tridiagonal matrix. A pseudospectral transformation62 between the FBR and DVR was performed to calculate the action of the potential energy operator, in which the DVR is defined by the angular Gauss− Legendre quadrature points associated with the rotational basis ΘΩ=0 (γ).63 l Extensive convergence tests were carried out to determine the size of grid and the propagation steps. For the radial coordinates r and R, 95 and 255 equidistant points were used between 1.2 and 6.0 a0 and between 1.2 and 20.0 a0, respectively, and 100 angular basis functions were used. The wave packet was propagated for 30 000 steps, and the analysis line was placed at R∞ = 11.5a0. In this work, we considered the dissociation from the ground and three fundamental vibrational states of HOD(X̃ ,(v1, v2, v3), 000), and the corresponding wave function was calculated by diagonalizing the ground state Hamiltonian with the Lanczos algorithm.64 The calculated energies for the (1, 0, 0), (0, 1, 0),

(x = r , R ) (9)

In the asymptotic region, the diabatic state |0⟩ dissociates to the product OH/OD(Ã 2Σ+), whereas both diabatic states |−1⟩ and |1⟩ correlate to the product OH/OD(X̃ 2Π). The T matrix elements can be derived using the relations as follows,46,56

A vjJKλp(E) =

δ(JJi 1)

∑ (2 − δξ0) cos(n arccos Es)⟨Ψ0|Ψξ⟩

(8)

CvjJKλp(ξ) = ⟨v , j , l = K − λ|Ψξλ(R =R ∞)⟩

J

v ,j

with Ψλ1 = DHsΨλ0. The adiabatic initial wave packet placed on the 2A′ state is given by the initial ro-vibrational wave functions of HOD multiplied by the B̃ ← X̃ transition dipole moment function μ̂ as (ê × μ̂ )|ΦvJi1K,vip2,vi 3,X(r, R, γ, Ei)⟩,45 where ê is the electric field direction of the photolysis photon. The adiabatic initial wave packet is then transformed to the diabatic representation in the form of eq 4 for the subsequent propagation with the normalized Hamiltonian, which was scaled to the spectral range (−1, +1) via Hs = (H − H̅ I)/ΔH. The spectral half-width and mean H̅ = (Hmax + Hmin)/2, ΔH = (Hmax − Hmin)/2 of the Hamiltonian are easily obtained from the spectral extrema. The wave packet was damped near the edge of the radial coordinates with a damping function D defined as ⎧ 1 for x < xd ⎪ D(x) = ⎨ ⎪ −α(x − xd)2 for x ≥ xd ⎩e

Ji + 1

∑ ∑

where ω is the frequency of excitation photon and c is the speed of light. δ(JJi1) was defined in ref 57. The total cross section (absorption spectrum) can be readily obtained using a cosine Fourier transform of the Chebyshev autocorrelation function,55

(7)

Ψξλ+ 1 = 2DHsΨξλ − D2 Ψξλ− 1

4π 2ω 1 c 2Ji + 1

(13)

|j , 0, l ; J , M , p⟩ 1 [|jl⟩|J , 0, M ⟩|λ⟩ + (−1) J + l + p |j − l⟩|J , 0, M ⟩|−λ⟩] = 2(1 + δl 0) for λ = 0, −1; K = 0

⎛ πk λ ⎞1/2 λ vj ⎟ e−ikvjR∞A vjJKλp(E) 1 + δ0K ⎜⎜ ⎟ ⎝ μR ⎠

(10)

∞

∑ (2 − δξ0)e−iξarccosE CvjJKλp(ξ) s

ξ=0

(11) C


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amplitude of the resonance structures appears on the TCS from the (0, 0, 0) state, followed by that from the (0, 0, 1), (0, 1, 0), and (1, 0, 0) states. And the structures from the initial (0, 1, 0) state become more pronounced than others in the low energy tail. It is well understood that such diffuse structures are related to the predissociation of many resonances on the excited state by the CI coupling with the ground state near the HOD linearity. The scattering wave functions for the resonances contain complicated bending-stretching coupling and have not been exactly identified so far.45,52,67,68 Similar to the case of the VMP of H2O,48 the various features of the TCSs are mainly due to the different shapes of the initial vibrational wave functions. According to the well-known classical reflection principle,69 the bimodal behaviors of the (0, 1, 0) TCS reflects the nodal pattern of the corresponding wave function along the coordinate of the angle γ where the excited PES is repulsive. This is similar to the TCS of CH2 (X̃ 3B1, (0, 1, 0)) in its second absorption band.70 B. Product State Distributions for OH(X̃ ) and OD(X̃ ). Figure 2 displays the calculated vibrational state distributions for OH(X̃ ) and OD(X̃ ) productions from four vibrational states at six total energies, corresponding to the peaks at the theoretical TCS from the ground vibrational state of HOD. In Figure 2a, all the populations are similar for different initial vibrational states and different total energies. The ground vibrational state of OH(X̃ ) dominates in all the cases, although many vibrationally excited states are also populated. This trend persists in those of OD(X̃ ) from the (0, 0, 0), (1, 0, 0), and (0, 0, 1) states in Figure 2b. As pointed out from the classical calculations,11,42 the ground vibrational fragments are mainly formed by fast and direct trajectories passing through the linear HO−D CI and RT channels, with the nonreactive OH bond still maintaining its initial length, whereas the excited vibrational fragments are presumably due to the indirect events spending a long time on the upper adiabatic PES. On the contrary, the maximal distribution of OD(X̃ ) from the (0, 1, 0) state appears at v = 0 for the total energies of 9.420, 9.568, and 9.725 eV but shifts to v = 1 for the other three total energies. The vibrational inversion also appears in the OH(X̃ ) from the H2O (0, 1, 0) state at high energies,48 which stems from indirect dissociation via HHO CI and RT channels. The inverted vibrational distributions of OD(X̃ ) at some total energies should stem from the indirect dissociation of HOD. The calculated rotational state distributions of OH(X̃ , v = 0) and OD(X̃ , v = 0) products from four vibrational states at six total energies are depicted in Figure 3. For the OH(X̃ , v = 0) fragment, all the rotational state distributions at each energy are highly inverted and have similar peaks near the highest allowed rotational states, implying that most of the available energy is deposited into the purely rotational excitation. It is clear that the high excitation is attributed to the large torque from large angular anisotropy on the PESs of both B̃ and X̃ states along the linear HO−D CI nonadiabatic pathway. Thus, the rotational state distributions depend weakly on the initial states. One interesting feature is that the distributions show intense oscillations around j = 40, which is quite similar to that of HOD at 121.6 nm explained in terms of quantum interference between two linear HOD and HDO CI nonadiabatic pathways.40 However, the rotational state distributions of OD(X̃ , v = 0) are sensitive to the initial vibrational state of HOD, as shown in Figure 3b. For the initial (1, 0, 0) state, the rotational state distributions have a asymmetric bell shape peaked near j = 40, which is much lower than the highest

and (0, 0, 1) vibrational states are found to be 2716.86, 1403.90, and 3697.32 cm−1, respectively, which agree well with the corresponding experimental values of 2727, 1402, and 3707 cm −1.65 The parallel transition B̃ ← X̃ leads to the spectroscopic selection rules: J = 1, P = 1 ← Ji = 0, Pi = 0, giving rise to an excited state of mixed K = 0 and K = 1 compositions.

IV. RESULTS AND DISCUSSION A. Total Cross Section. Although we used two sets of coordinates to describe the photodissociation dynamics of HOD, the calculated total absorption cross section should be independent of the coordinate system employed. Due to the approximations made in the electronic angular momentum terms in the Hamiltonian (see section II), the calculations using two Jacobi coordinates are not strictly equivalent. However, the discrepancies between two Jacobi coordinates are surely small and can be ignored.51 Figure 1 presents the calculated TCSs

Figure 1. Calculated total cross sections from four vibrational states of HOD as a function of total energy together with the experiment spectrum from the ground vibrational state. The arrows indicate the energies at which product state distributions are calculated.

from four vibrational states together with the experimental absorption spectrum from the ground vibrational state of HOD.43 To facilitate the comparison, the spectra are plotted as a function of the total energy, which is defined as Etot = Eint(H2O) + hv, where Eint(H2O) is the vibrational energy of the initial state, hv is the photon energy. It can be seen from this figure that our calculated TCS for HOD(X̃ , (0, 0, 0), 000) state correctly predicts positions of the six strongest peaks in the experimental spectrum at room temperature. The good agreement between theory and experiment indicates the high accuracy of our ab initio PESs and transition dipole moments in the Franck−Condon region. On the contrary, the experimental spectrum shows a more regular vibrational progression with a spacing of about 0.08 eV and less pronounced structures than those of the theoretical one, in particular below 9.3 eV. It was already demonstrated that the differences between the theoretical and experimental spectra can be attributed to the effect of initial molecular rotation.66 In Figure 1, all four calculated TCSs show some diffuse structures superimposed on a broad band, which indicates that the dissociation on the B̃ state occurs in a few vibrational periods (tens of femtoseconds).4 The most pronounced D


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Figure 2. Calculated relative vibrational state distributions for (a) OH(X̃ ) and (b) OD(X̃ ) fragments from four vibrational states of HOD at six total energies. All the distributions have been normalized to v = 0.

These two different behaviors also exist for the (0, 1, 0) and (0, 0, 1) states at different energies. Therefore, Figure 3b demonstrates that the initial vibrational state of HOD and total energy have strong dynamical effects on the OD(X̃ , v = 0) product channel.

rotational state. The distributions for the (0, 0, 0) state at 9.420, 9.568, and 9.725 eV show a bimodal structure with a strong but narrow peak near the highest allowed rotational states and present a single broad peak near j = 45 at the other total energies, similar to the distributions from the (1, 0, 0) state. E


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Figure 3. Calculated rotational state distributions for (a) OH(X̃ , v = 0) and (b) OD(X̃ , v = 0) fragments from four vibrational states of HOD at six total energies. The maximum value of the population is set to 1.

C. Product State Distributions for OH(Ã ) and OD(Ã ). For the electronically excited OH(Ã ) and OD(Ã ) fragments dissociated along the adiabatic pathway, only a few low-lying vibrational states are populated over the energy range of the B band, due apparently to the high energy constraint. The calculated vibrational state distributions of the OH(Ã ) and OD(Ã ) fragments as a function of the total energy above the energy threshold for v = 0 are shown in Figure 4. The threshold energies for OH(Ã , v = 1) and OH(Ã , v = 2) are 9.54 and 9.89 eV, respectively. Because the vibrational frequency of OD is

smaller than that of OH, the threshold energies for OD(Ã , v = 1) and OD(Ã , v = 2) are decreased to 9.39 and 9.65 eV, respectively. For both OH and OD fragments, the distributions from four initial vibrational states show similar trends. The populations for v > 0 rise sharply above the energy threshold and then oscillate strongly with the total energy, indicating the existence of many long-lived resonances. At high energies, the oscillations become weaker, as the lifetime of the resonances decrease with increasing energy.39 For the OD fragment, the F


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Figure 4. Calculated vibrational state distributions for (a) OH(Ã ) and (b) OD(Ã ) fragments from four vibrational states of HOD as a function of total energy.

relative populations of v = 0 become dominant above the energy of 10.0 eV for all the four initial vibrational states. Figure 5 presents the calculated rotational state distributions of the OH(Ã , v = 0) and OD(Ã , v = 0) fragments. The electronically excited fragments are only subjected to the smaller torque by the angular gradient on the B state PES, resulting in rotationally much cooler distributions than their ground state counterparts in Figure 3. The rotational distributions resemble a random behavior with significant oscillations as a result of the influence of metastable resonances, which are very sensitive to the energy and initial vibrational state. At 9.420 eV, OD(Ã ,v = 0, j = 11) from four vibrational state has a remarkably enhanced population of about 30% with respect to other rotational states. This phenomenon is somewhat similar to the “single rotational product propensity” at 121.6 nm with a stronger population exceeding 50%, which is attributed to the dynamically constrained threshold effect.41 D. Branching Ratio. The branching ratio of the photodissociation with more than one open channel has been used as an important probe into the reaction mechanism.71 Figure 6 depicts the calculated branching ratios of OH(Ã )/OH(X̃ ) and OD(Ã )/OD(X̃ ) as a function of total energy. In Figure 6a, the branching ratios from the four vibrational states increase steeply once the total energy exceeds the threshold energy and then have strong oscillations, which come from the oscillations in the

product distributions of electronically excited fragments discussed above. The branching ratios from the (0, 1, 0) state are obviously larger than other branching ratios for total energies above 9.9 eV. All the branching ratios decrease slowly at the high energy tail. It can be seen that the branching ratios are lower than 1.0 over the whole energy range, indicating the dominance of the nonadiabatic channels for D atom dissociation. However, the branching ratios of OD(Ã )/ OD(X̃ ) in Figure 6b show much different trends. The branching ratios from the (0, 1, 0) state increase more rapidly than those from the other states just above the threshold energy. All branching ratios have a shallow minimum near 9.3 eV, high fluctuations around a value of 0.2 in the middle energy range, and a growth with different speeds at higher energies. The branching ratios exceed the value of 1.0 at higher energies, especially for the initial vibrational state of (0, 0, 1), which means that the H atom mainly dissociates by direct adiabatic trajectories. Figure 7 displays the calculated branching ratios of OD/OH as a function of total energy together with the experimental value at the photon wavelength of 121.6 nm.72 The calculated isotopic branching ratios convolve together and show rather sharp oscillations in the low energy region. The most pronounced amplitude of the oscillations appears on the isotopic branching ratio from the (0, 0, 0) state, followed by G


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Figure 5. Calculated rotational state distributions for (a) OH(Ã , v = 0) and (b) OD(Ã , v = 0) fragments from four vibrational states of HOD at six total energies. The total populations are normalized.

bond selectivity comparing with that from the (0, 0, 0) vibrational state, which differs from the VMP dynamics of HOD in the A band.20−23 The isotopic branching ratio from the LIF experiment was found to be 1.66 ± 0.5 at 121.6 nm (Etot = 10.2 eV) from the initial (0, 0, 0) state,72 which is smaller than our calculated value of 3.04. The origin of this discrepancy is unclear. Due to the nonadiabatic coupling, longlived resonances and large anisotropy along the reaction

that from (0, 1, 0), (0, 0, 1), and (1, 0, 0). At the higher energy above 10.1 eV, the isotopic branching ratio of the (0, 0, 1) state is steady at about 1.6−2.0, which is much smaller than those from the other vibrational states. All the isotopic branching ratios show a preference for the H + OD channel, due to a smaller mass and more rapid movement of the H atom. It is worth noticing that the VMP of HOD pre-excited to fundamental OH vibration does not significantly enhance the H


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the VMP of HOD in its B band. The calculated absorption spectrum from the initial (0, 0, 0) state is in good agreement with the observed one, indicating the accuracy of our theoretical model and PESs in the Franck−Condon region. The product state distributions of OH(X̃ ) from four vibrational states are highly hot rotational excitation and very cold vibrational excitation, similar to the photodissociation of H2O. For the OD(X̃ ) + H channel, some interesting phenomena are observed. The vibrational state distributions from (0, 1, 0) are inverted with a peak at v = 1 at some total energies. The rotational state distributions from four vibrational states show two different behaviors. One has a single broad peak, whereas the other one has a bimodal structure with a very pronounced peak near the highest allowed rotational state and a broad peak at lower rotational states. The vibrational state distributions of OH(Ã ) and OD(Ã ) have different threshold energies for v > 0 state and display opposite trends at the high energy tail. All the rotational state distributions of OH(Ã , v = 0) and OD(Ã , v = 0) are largely random and very sensitive to the total energy, due to the strong influence of metastable resonances. The calculated branching ratios OH(Ã )/OH(X̃ ) show that the nonadiabatic pathway dominates for the D atom dissociation throughout the whole energy range. This trend also exists for the H atom dissociation at low energy range, but the adiabatic pathway becomes dominant at higher energy. The isotopic branching ratios show a preference of OD fragment. The theoretical isotopic branching ratio OD/OH from the (0, 0, 0) vibrational state is in qualitative agreement with the experimental estimated result at 121.6 nm but has a larger value. Our investigations should stimulate further experimental and theoretical investigations on this important photodissociation process of HOD.

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Figure 6. Calculated (a) OH(Ã )/OH(X̃ ) and (b) OD(Ã )/OD(X̃ ) branching ratios from four vibrational states of HOD as a function of total energy.

AUTHOR INFORMATION

Corresponding Author

*D. Xie. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21133006, 21273104 and 91421315) and the Ministry of Science and Technology (2013CB834601).

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REFERENCES

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Figure 7. Calculated OD/OH isotopic branching ratios from four vibrational states of HOD as a function of total energy.

pathways, the mechanism of this bond-breaking selectivity in the B band is very complicated and obscure.

V. CONCLUSIONS In this work, a three-state coupling model including X̃ , Ã , and B̃ states was used to study the state-to-state quantum dynamics of I


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Full-Dimensional Quantum Dynamics of Vibrational Mediated

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