Theoretical Study of the State-to-State Photodissociation Dynamics of

Article pubs.acs.org/JPCA

Theoretical Study of the State-to-State Photodissociation Dynamics of the Vibrationally Excited Water Molecule in the B Band Guang-Shuang-Mu Lin,† 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, Jiangsu 210093, China ‡ Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ABSTRACT: The state-to-state photodissociation dynamics for the vibrationally excited H2O in its second absorption band has been investigated on the recent three-dimensional potential energy surfaces based on a large number of high-level ab initio points. The photodissociassion dynamics from three fundamental vibrational states of H2O were explored from quantum dynamical calculations including the electronic X̃ and B̃ states on the basis of a Chebyshev real wave packet method. Because of the different shapes of various initial vibrational wave functions, the photoexcited wavepackets access different portions of the upper-state potential energy surface, which yields different absorption spectra, ro-vibrational distributions, and branching ratios. The bending excited vibrational state (0,1,0) generates two lobes with a shallow minimum on the absorption spectrum, a dominant vibrational inverted population OH(X̃ , ν = 1) fragment at higher energy, and a nearly single rotational product propensity. The bond-stretching vibrational states (0,0,1) and (1,0,0) show a high OH(Ã )/OH(X̃ ) ratio at short photon wavelength, which indicates that dissociation proceeds mainly via the adiabatic channel.

I. INTRODUCTION Photodissociation of H2O in its second (B) band near 130 nm has served as a prototype for understanding nonadiabatic dynamics in polyatomic systems. It is well-established that the B1̃ A′ state of H2O correlates adiabatically to OH( Ã 2 Σ+) + H but has nonadiabatic couplings with two lower singlet electronic states, which correlate diabatically to the ground OH(X̃ 2 Π) + H asymptote. There exist two nonadiabatic pathways, via the conical intersections (CIs) between B̃ and X̃ states and the Renner−Teller (RT) coupling between B̃ and Ã states at collinear HOH/OHH geometries. In the past decades, the system has attracted extensive theoretical1−21 and experimental22−36 studies. However, the investigations on the photodissociation dynamics from the excited vibrational states of H2O are scarce. Photodissociation of a vibrationally exicted molecule may be a feasible way to control the fragmentation dynamics toward a specific target. This is due to the fact that excitation of excited ro-vibrational states of the parent molecule accesses different portions of the potential energy surface (PES), which significantly affects the molecule dissociation dynamics. For example, photodissociation of H2O in |01⟩−, |13⟩−, and |40⟩− polyads via the A band show strong propensity for special rotational and vibrational fragments. The theoretical predictions37−41 and vibrationally mediated photodissociation (VMP) experiments42−48 on the bond selectively in the A band of HOD are more exciting, where the OH/OD branching ratio can be “steered” by choosing the advisible initial state and the appropriate photon wavelength. Similar interesting phenomena © XXXX American Chemical Society

of mode-selective dynamics can also be found in the VMP studies from the dissociation of several vibrationally excited states of NH3 and its isotopologues,49−61 which also involves CI coupling between the excited-state and ground-state surface. To the best of our knowledge, there are still no VMP experiments on the dissociation of H2O via the B band. On the theoretical side, Segev and Shapiro17 first reported quantummechanical calculations of the UV photodissociation of H2O and HOD in the bending (0,1,0) vibrational states in 1982, but they used a 2-dimensional model including only the rotational and translational degrees of freedom and ignored the nonadiabatic coupling to other states. The purpose of this work is to further examine the state-to-state photodissociation dynamics of excited vibrational states of H2O in the B band with three-dimensional quantum mechanical calculations. Because the RT nonadiabatic coupling has been found to play only a relatively minor role in the dissociation dynamics and is partly compensated by the CI channel,15,16,62 we did not include the RT channel and involved only the X̃ and B̃ electronic states, the PESs of which have been previously reported by our group.13,14 This paper is organized as follows. In Section II, we briefly give the quantum mechanical method used to compute the absorption spectrum and final state Special Issue: International Conference on Theoretical and High Performance Computational Chemistry Symposium Received: March 27, 2014 Revised: May 7, 2014

A

dx.doi.org/10.1021/jp503062s | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

Article

The spectral half-width and mean, H̅ = (Hmax + Hmin)/2 and ΔH = (Hmax − Hmin)/2, are obtained from the spectral extrema of the Hamiltonian (Hmax and Hmin), which are estimated from the grid. One can calculate the T matrix elements by using the correlation functions as follow65,66

distributions. The calculated results are presented and discussed in Section III. Section IV contains a brief summary.

II. THEORY The photodissociation process under investigation is depicted as follows:

CvjJKp(ξ) = ⟨P jK (γ )χvj (r )|Ψξ⟩

hv

H 2O(X̃ , (v1 , v2 , v3), JK K ) → H 2O(B)̃ a c

2

2 +

→ H + OH(X Π, v , j)/H + OH(A Σ , v , j)

A vjJKp(E) =

(1)

ξ=0

(8)

⎛ πk vj ⎞1/2 ⎟⎟ exp( − ik vjR ∞)A vjJKp(E) TvjJKp(E) = i( − 1)K − j 1 + δ0K ⎜⎜ ⎝ μR ⎠ (9)

where kvj is the corresponding wave vector and R∞ is the grid point where the final state projection is performed. PKj (γ) χvj (r) is the product ro-vibrational wave function. The integral cross section (ICS) can been calculated by66,67

(2)

2 ĵ (J ̂ − j ̂)2 1 ∂2 1 ∂2 − + + 2μR ∂R2 2μr ∂r 2 2μr r 2 2μR R2

σvj(E) =

ξ>1

Ji + 1

J

∑ ∑ J = Ji − 1 K

δ(JJi 1) 3

*

TvjJKp TvjJKp (10)

(3)

σtot(E) =

∑ σvj(E) v ,j

=

πω 1 cε0 ΔHπ 1 − E 2 norm ∞

∑ (2 − δξ0)cos(ξ arccos Enorm)⟨ψ0|ψξ⟩ ξ=0

(11)

with Enorm = (E − H̅ )/ΔH. The grid and basis used here are similar to those in our previous work.13,14,16 For the radial coordinates r and R, 95 points in [1.2, 6.0]a0 and 255 points in [1.2, 20.0]a0 were used, respectively. For the angular degree of freedom, 100 Legendre 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 consider only the photodissociation dynamics of the three fundamental vibrational states of H2O, the vibrational wave functions of which were calculated by diagonalizing the ground-state Hamiltonian with the Lanczos algorithm.

(4)

̂ i (r, R, γ, Ei)⟩, where Φi is with Ψ1 = DĤ Ψ0 and |Ψ0⟩ = e ̂ × μ|Φ a ro-vibrational state of H2O on the ground electronic state and μ̂ is the transition dipole moment of 2A′ − 1A′ in the Franck− Condon region. The damping factor D was applied at the grid edge, defined as ⎧ ⎪1 for x < xd D(x) = ⎨ , ⎪ 2 ⎩ exp[−α(x − xd) ] for x ≥ xd

4π 2ω 1 c 2Ji + 1

where ω is the frequency of excitation photon and c the speed of light. δ(JJi1) was define in ref 67. The total cross section (absorption spectrum) can be simply obtained using a cosine Fourier transform of the Chebyshev autocorrelation function

where μR and μr are the reduced masses for R (H−OH distance) and r (O−H distance), respectively. j ̂ is the diatomic rotational angular momentum operator in the angle (γ) between vectors R and r, and J ̂ is the total angular momentum operator. The z-axis of the body-fixed reference frame is located along R. The photodissociation dynamics of H2O was treated using a Chebyshev real wave packet propagation,63 which is defined by Tξ̂ (Ĥ norm) ≡ cos(ξ Θ̂) with Θ = arccos(Ĥ norm). The damped Chebyshev three-term recursion relation64 was used to propagate the wave packet in the diabatic representation Ψξ + 1 = D(2Ĥ norm Ψξ − DΨξ − 1),

2 2π ΔH 1 − Enorm

∑ (2 − δξ0) exp(−iξ arcos Enorm)CvjJKp(ξ)

where I is the two-dimensional identity matrix and VΣ, VII, and VΣII are the three diabatic potential energy surfaces (PESs).14 The kinetic energy operator is given in the product H−OH Jacobi coordinates (R, r, γ) as T̂ = −

1 ∞

where (v1,v2,v3) and Jkakc designate the parent ro-vibrational state of H2O(X̃ ) with three normal mode quantum numbers representing the symmetric stretching, bending, and antisymmetric stretching modes, respectively. The diatomic molecular fragment is labeled by the vibrational (v) and rotational (j) quantum numbers. In this work, all initial states contain pure vibrational states with zero total angular momentum, J = 0. A two-state coupling model was employed to study the stateto-state photodissociation dynamics of H2O in the B band. The spinless triatomic Hamiltonian is given as (ℏ = 1) ⎡ VΣ VΣΠ ⎤ ⎥ Ĥ = T̂ I + ⎢ ⎢⎣ VΣΠ VΠ ⎥⎦

(7)

(x = R , r )

III. RESULTS AND DISCUSSION A. Total Cross Section. Figure 1 shows the calculated total absorption cross sections (TCSs) from four vibrational states as a function of the total energy, which is defined as = Eint(H2O) + hv, where Eint(H2O) is the vibrational energy of a state and hv is the photon energy. As discussed before,13,14 the calculated TCS of the (0,0,0) state agrees well with the experimental absorption spectrum.14 The arrows in Figure 1 indicate the five peaks of diffuse vibronic structures for TCS of the (0,0,0) state, for

(5)

The Hamiltonian is normalized to [-1,1]. ⎛(T̂ + V − H̅ )/ΔH ⎞ VΣΠ/ΔH Σ ⎜ ⎟ ̂ Hnorm = ⎜ ⎟ VΣΠ/ΔH (T̂ + VΠ − H̅ )/ΔH ⎠ ⎝ (6) B



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Figure 1. Calculated total cross sections for four vibrational states of H2O as a function of total energy. The arrows indicate the energies at which final ro-vibrational state distributions are calculated.

which the final vibrational and rotational distributions were calculated in this work. One can see from Figure 1 that all four spectra exhibit more or less pronounced diffuse vibronic structures superimposed on a broad band. The most pronounced amplitude of the undulating structures appears on the TCS of the (0,0,0) state, followed by that of (0,1,0), (1,0,0), and (0,0,1). The pronounced vibronic peaks always appear on the red side of the TCS. The metastable resonances exist in the potential well created by the CI near the HOH linearity and show a complicated coupling of bending and stretching motions;4,6 therefore, the exact mechanism of the resonance structures in the TCS is still unknown. The different absolute values of the broad bands in the four TCSs are mainly due to the different shapes of the initial vibrational wave functions. Another interesting phenomenon is that the broad band in the TCS of (0,1,0) shows clearly two lobes with a shallow minimum, which may be understood by the classical reflection principle:68−71 the (0,1,0) wave function has a node along the dissociation coordinate, which leads to a minimum in the absorption spectrum. B. Product Distribution of OH(X̃). Figure 2 shows the calculated vibrational state distributions for the OH(X̃ ) products from four vibrational states of H2O as a function of the total energy. For (0,0,0), (0,0,1), and (1,0,0) states, the vibrational distributions depend weakly on the energy in the whole energy range. It can be seen that the ground vibrational state distribution of OH(X̃ , v = 0) fragment is dominant because of the fast and direct trajectories passing though the HOH CI intersection located at (ROH1, ROH2, ∠HOH) = (1.853a0, 3.056a0, 180°) where one OH bond length of H2O is similar to that of the free OH fragment.10,13 The same trend of OH(X̃ ) distribution was also found for the bending−stretching state (0,1,0) at the three lower total energies, but the population of OH(X̃ , v = 1) becomes dominant at higher energies of 9.56 and 9.68 eV. This reversion is due to the shape of the (0,1,0) vibrational wave function, which covers a large angular region of the B̃ state surface. As suggested by Harrevelt and Hemert,10 part of the initial wavepacket can easily travel above the barrier between the linear HOH and HHO region at higher total energies and indirectly dissociates via HHO CI

Figure 2. Calculated relative vibrational state distributions of the OH(X̃ ) product from four vibrational states of H2O at five total energies. All the distributions have been normalized to v = 0.

channel, where the O−H band is significantly elongated from its equilibrium geometry. The calculated rotational state distributions for the OH(X̃ , v = 0) products from four vibrational states as a function of the total energy are depicted in Figure 3. One can see from this figure that the rotational state distributions are highly inverted and have similar peaks near the highest allowed rotational states, which means that most of the total energy is deposited into the rotational excitation. The high rotational excitation in the OH(X̃ , v = 0) fragment is due to a strong torque action on the system, which stems from the large anisotropy along the dissociation pathway. The rotational state distributions of the OH(X̃ , v = 0) for the (0,1,0) state at 9.38, 9.56, and 9.68 eV show different behavior, which is a bimodal structure with a strong but narrow high-energy peak and a broader lower-energy C



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Figure 3. Calculated rotational state distributions of the OH(X̃ , v = 0) fragment from four vibrational states of H2O at five total energies. The maximum value of the population is set to 1.

peak. As discussed above, the HHO CI pathway should be open for the excitation of the (0,1,0) state at the total energies of 9.56 and 9.68 eV. The dissociation via this indirect channel could cause a different rotational excited behavior, as suggested by van Harrevelt and van Hemert.10 C. Product Distribution of OH(Ã ). Because the electronically excited OH(Ã ) fragment can be produced only via the adiabatic pathway and has a high energy threshold, only a few low-lying vibrational states are populated in the energy range of the B band. The calculated vibrational state distributions of OH(Ã ) fragment as a function of the total energy above the OH(Ã , v) threshold are shown in Figure 4. The threshold energy for OH(Ã , v = 1) and OH(Ã , v > 1) is about 9.5 and 9.8 eV, respectively. The computed vibrational excited state

populations (v > 0) rise sharply above the threshold because more energy is available for this adiabatic product at high photon energy. In various energy regimes, the population of the OH(Ã , v > 1) product exceeds that of OH(Ã , v = 1). Figure 5 shows the calculated rotational state distributions of the OH(Ã , v = 0) fragment. When this is compared with Figure 3, the electronically excited OH fragment is rotationally cooler than its ground-state counterpart, due apparently to the smaller torque only by the angular gradient on the B state PES along the adiabatic pathway. All the distributions for different vibrational states show significantly different oscillations, which are sensitive to the energy. As discussed previously, these oscillations stem from the long-lived Feshbach resonances D



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Figure 4. Calculated vibrational state distributions of the OH(Ã ) fragment from four vibrational states of H2O as a function of total energy above the OH(Ã , v) threshold.

Figure 5. Calculated rotational state distributions of the OH(Ã , v = 0) fragment from four vibrational states of H2O at five total energies. The total populations are normalized.

supported by the potential well in the B̃ state along the adiabatic pathway and cannot be accurately characterized.6,13−16 D. Branching Ratio. The branching ratio of OH(Ã )/ OH(X̃ ) plays an important role in photodissociation of H2O because it can serve as an effective probe to the excited PES in the Franck−Condon region. In Figure 6, the calculated branching ratios of different vibrational states are shown as a function of total energy. Similar to the product distributions of OH(Ã ), the calculated branching ratios oscillate with the energy, which is apparently due to the resonances in the adiabatic pathway. The branching ratios of (0,0,1) and (1,0,0) states increase more rapidly than those of the other two states at the beginning above the OH(Ã ) threshold energy. After the quick rise at the threshold, the branching ratio of the ground state is steady at about 0.2−0.25. Whereas over the same energy

range the vibrational excitation leads to at least doubling of the branching ratio in various energy regimes. At higher total energy, the branching ratio of (0,0,1) state exceeds the ratio of 1, which means that direct dissociation becomes dominant.

IV. CONCLUSIONS State-to-state photodissociation dynamics of water in the B band has revealed a wealth of nonadiabatic dynamics phenomena, which arises from the involvement of coupled electronic states with different PESs. One-photon dissociation and VMP conducted at the same total energy often result in different quantum states and branching ratios of photofragments.72 In this work, the state-to-state photodissociation dynamics in the B band from three fundamental vibrational E



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Figure 6. Calculated OH(Ã )/OH(X̃ ) branching ratios from four vibrational states of H2O as a function of total energy.

states of H2O have been theoretically investigated. The quantum dynamics calculations were performed using a wave packet method and included the full Coriolis coupling. We clearly demonstrated that the photoexcitation of bending and bond-stretching modes significantly influences the dissociation dynamics, which yield abnormal absorption spectrum, rovibrational state distributions, and branching ratios. We hope our theoretical prediction reported here will stimulate further experimental studies.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.:+86-2583596383. 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 91221301) and the Ministry of Science and Technology (2013CB834601).

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REFERENCES

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