Nonadiabatic Dynamics in Photodissociation of Hydroxymethyl in the

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Nonadiabatic Dynamics in Photodissociation of Hydroxymethyl in the 3A(3p) Rydberg State: A Nine-Dimensional Quantum Study 2

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Changjian Xie, Christopher L Malbon, Daiqian Xie, David R. Yarkony, and Hua Guo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b12184 • Publication Date (Web): 21 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry

Submitted to J. Phys. Chem. A (Reisler Special Issue), 12/18/2018, revised 2/16/2019

Nonadiabatic Dynamics in Photodissociation of Hydroxymethyl in The 32A(3px) Rydberg State: A Nine-Dimensional Quantum Study Changjian Xie,a Christopher L. Malbon,b Daiqian Xie,c David R. Yarkony,b and Hua Guoa,* aDepartment

of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM, 87131, USA

bDepartment

cInstitute

of Chemistry, Johns Hopkins University, Baltimore, MD 21218, USA of Theoretical and Computational Chemistry, Key Laboratory of

Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China

*: corresponding author. [email protected] 1

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The nonadiabatic predissociation dynamics of the hydroxymethyl radical (CH2OH) in its 32A(3px) state is investigated using a nine-dimensional quantum mechanical model based on an ab initio three coupled diabatic state potential energy matrix. The calculated absorption spectrum, which is dominated by predissociative resonances, is in excellent agreement with experiment. The predissociation is facilitated by two conical intersection seams formed between the 32A(3px) and 22A(3s) states near the Franck-Condon region. The h and g vectors of energy minimized points on these seams are analyzed using the normal modes of the 32A equilibrium structure. The low-lying predissociative resonances have been assigned and their lifetimes are less than 100 fs and moderately mode specific. The absorption spectrum is dominated by a CO vibrational progression, due apparently to the promotion of an electron from the ground state antibonding π*CO orbital to the carbon Rydberg orbital, which effectively reduces the C-O bond order.

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I. Introduction The breakdown of the venerable Born-Oppenheimer adiabatic approximation is now known to be quite prevalent for molecular systems, particularly in electronically excited states.1-6 It is responsible for a wide array of physical and chemical processes that are certain to impact future science and technology. However, a clear understanding of electronically nonadiabatic dynamics in these processes is still far from being achieved. The difficulties are two-fold. First, it requires not only an accurate description of potential energy surfaces (PESs) of multiple electronic states, but also the nonadiabatic couplings between those states. While direct-dynamics approaches, in which these quantities are computed on the fly along classical or semi-classical trajectories, can provide valuable insights,7,

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the ultimate characterization of

nonadiabatic dynamics, an intrinsically quantum phenomenon, requires the accurate ab initio determination of the electronic structure quantities in a multidimensional space, as well as their global analytic representations.9 Despite the challenges, much progress has been made in this direction in the past few years.10-22 Second, even with the availability of highly accurate multidimensional PESs and their couplings, an accurate description of the nonadiabatic nuclear dynamics requires a fully coupled multidimensional quantum description,23, 24 which generally scales exponentially with nuclear dimensions. Photodissociation has long been considered a prototype in studying nonadiabatic dynamics.24, 25 In the past, fully coupled quantum dynamics studies of nonadiabatic 3



photodissociation dynamics including all internal degrees of freedom (DOFs) have largely been restricted to molecules with at most four atoms, such as ammonia,26-29 which have six DOFs. In this contribution, we report a quantum dynamics study of the photodissociation of a prototypical penta-atomic radical, hydroxymethyl (CH2OH), which has nine internal DOFs, using a full-dimensional diabatic potential energy matrix (PEM) based on fitting a large number of ab initio data. The hydroxymethyl radical (CH2OH) is an important combustion intermediate. Consequently, it has received much recent attention.30-39 Reisler and coworkers have systematically investigated the UV photochemistry of this radical in its 22A(3s), 32A(3px), and 52A(3pz) states.40-46 The absorption spectrum of the first Rydberg state (22A(3s)) is essentially structureless, evidence of rapid dissociation dominated by the H2CO + H channel.42 This dissociation is strongly influenced by a conical intersection (CI) seam with the ground (12A) electronic state along the O-H coordinate, although two CIs seams exist between the two electronic states along the C-H coordinates at higher energies.47 Both the higher 32A(3px) and 52A(3pz) Rydberg states, on the other hand, are quasi-bound. Predissociation of the 32A(3px) state is facilitated by two CI seams with the lower 22A(3s) state,47, 48 which results in a series of vibronic resonances. The decay of these resonances leads to multiple product channels resulting from the cleavage of the O-H or C-H bonds.43-46 Indeed, this system serves as an excellent testing ground for understanding nonadiabatic multichannel, multistate dynamics.49

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A full-dimensional diabatic PEM for the three lowest-lying electronic states has recently been developed by Malbon and Yarkony based on a large set of ab initio data.50, 51

Previous work based on this PEM has identified five energy minimized CIs

among

the three electronic states, denoted as 1,2-form, 1,2-cis, 1,2-trans, 2,3-cis, and 2,3-trans, respectively. Using this PEM, surface-hopping50 and reduced-dimensional quantum dynamics studies52,

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have been carried out for the direct nonadiabatic

photodissociation of hydroxymethyl upon excitation to the 22A(3s) state, which leads predominantly to the rapid formation of formaldehyde (H2CO) and H.42 The agreement between the measured and computed kinetic energy release spectra is excellent, underscoring the accuracy of the PEM. More importantly, these studies provided valuable insights into the role of the CI in the dissociation dynamics. In the current work, we report a nine-dimensional (9D) quantum dynamics study of the nonadiabatic dynamics of the same radical upon excitation to the higher 32A(3px) state, based on the same diabatic PEM. The nonadiabatic dissociation produces both H2CO + H and HCOH + H products.43,

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Here, we focus on the absorption spectrum of this

predissociative process. As discussed below, the quantum dynamical model accurately reproduces the experimental spectrum. In addition, some low-lying predissociative resonances in the absorption spectrum are assigned and their lifetimes are determined. The resonance lifetimes suggest moderate mode specificity in the nonadiabatic dynamics. These results not only validate the PEM, but also shed valuable light on the nonadiabatic dynamics of this system.

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II. Theory In this work, we use a full 9D model to study the absorption spectrum of CH2OH (3px) based on the three-state diabatic PEM constructed by Malbon and Yarkony.51 The nuclear Hamiltonian of the system in the diabatic representation is given as follows:

Hˆ  T  Η

d ,(3)

 1    V11 V12 V13   Tˆ  0     V21 V22 V23  ,  0    V V V     31 32 33 

(1)

in which Η d ,(3) is the 3×3 diabatic PEM. This 9D PEM was determined using multireference configuration interaction with single and double excitations (MRCISD) wave functions which employed cc-pVTZ bases augmented with Rydberg functions on both oxygen and carbon.50, 51 The fitting method, based on nuclear permutation-inversion symmetry adapted functions,54 was detailed in an earlier publication.51 Specifically, it fits energies, energy gradients, and derivative couplings from ab initio calculations at 9785 nuclear configurations. using a diabatic Hamiltonian. The diagonal terms in the PEM represent the PESs of three diabatic states, which are denoted below as D1, D2, and D3.51 These three states have B1, A1, and A1 symmetry, respectively, within the complete nuclear permutation inversion group isomorphic to C2v. The three corresponding diabatic states are coupled by the off-diagonal terms in the PEM. The 12A, 22A(3s), and 32A(3px) adiabatic PESs are obtained by diagonalizing this threestate diabatic PEM, and they form the five CIs previously noted.51 To achieve better agreement with experimental excitation energy, the D1 diabat is shifted energetically by -1500 cm-1.51 6


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The rotationless (Jtot=0) kinetic energy operator Tˆ for the nuclear motion can be written in the normal mode approximation as ( h  1 hereafter): 9 i  2 ˆ T   , 2 Qi2 i 1

(2)

where Qi denote the nine mass-scaled normal mode coordinates of the ground (12A) state of CH2OH and ɷi are the corresponding harmonic frequencies. These modes are O-H stretch (v1), C-H asymmetric stretch (v2), C-H symmetric stretch (v3), CH2 scissor (v4), in-phase HCOH bend (v5), C-O stretch (v6), out-of-phase HCOH bend (v7), HCOH torsion (v8), and CH2 wag (v9), respectively. These normal mode vectors are shown in Figure 1. It is noted that these normal modes are different from those on the excited 32A(3px) state, but they are close and related by a simple transformation. While the kinetic energy operator in Eq. (2) is not designed for describing dissociation, it is sufficient for the determination of the absorption spectrum, as the short time dynamics following photoexcitation is mostly restricted to the FranckCondon region. Note in particular that non-adiabatic transitions via all CI seams are covered by this model. However, the resolution of product states is not considered as the wave packets reaching the long O-H and C-H bond distance regions are damped. This approach bears some resemblance to the multimode vibronic model of Köppel, Domcke, and Cederbaum,55 but it is important to recognize that intermodal couplings are included here to the highest possible order because of the use of the fully coupled PEM. 7



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The diabatic nuclear wavefunctions associated with the three electronic states are:

 1       2  .  3   

(3)

Each nuclear wavefunction is expanded in a direct-product grid:

l 



i1i2i3i4i5i6i7i8i9

Cil1i2i3i4i5i6i7i8i9 i1 i2 i3 i4 i5 i6 i7 i8 i9 , l  1, 2,3 ,

(4)

in which Cil1i2i3i4i5i6i7i8i9 are the expansion coefficients, in denotes the potential optimized discrete variable representation (PODVR)56,

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grid indices for the corresponding

normal mode Qin . An orthogonal matrix connects the PODVR grid for each mode to the corresponding eigen-bases of the one-dimensional potential optimized Hamiltonian. The 32A(3px)←12A photo-excitation was simulated using the Condon approximation, in which the initial wave packet on the excited state is directly taken as the ground ro-vibrational state eigenfunction on the ground state PES. The neglect of transition dipole in the Condon approximation is justified by the small nuclear configuration space occupied by the ground vibrational state wavefunction, in which the dipole changes only mildly with nuclear coordinates. The initial wave packet is then propagated with Hˆ in the Chebyshev order (k) domain:58

 k  2dHˆ s  k 1  d 2  k 2 , k  2 ,

(5)

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with 1  dHˆ s  0 where  0 is the initial wave packet. The Hamiltonian defined in Eq. (5) is scaled to the spectral range of (-1,1) via Hˆ s  ( Hˆ  H  ) / H  , in which the spectral medium ( H   ( H max  H min ) / 2 ) and half width ( H   ( H max  H min ) / 2 ) were determined by the spectral extrema, H max and H min , which can be readily estimated. To avoid reflection, damping functions (d, with a form given in Table 1) were used at the edges of three (v1, v2, and v3) normal mode grids. These damping functions thus impose the outgoing boundary conditions. The numerical parameters used in the calculations are summarized in Table 1. The absorption spectrum, S(E), was obtained from the discrete cosine Fourier transform of the Chebyshev autocorrelation function Ck   0  k ,59

S(E) 

1  (2   k ,0 ) cos(k )Ck ,  H sin  k 0 

(6)

where E is the total energy and   arccos E is the Chebyshev angle. When needed, the time-dependent wavefunction and correlation functions can be readily obtained by expanding the time propagator in terms of the Chebyshev polynomials.60 To accurately determine decay lifetimes of the predissociative resonances, the lowstorage filter diagonalization (LSFD) method58 was used to extract the positions and widths of the resonance. To this end, a small complex-symmetric Hamiltonian matrix is constructed from the Chebyshev autocorrelation function and then diagonalized to provide an estimate of the complex eigenvalues (Ei - ii/2) of the resonances. III. Results and Discussion 9



The 32A(3px) Rydberg state is quasi-bound and its predissociation is facilitated by a combination of the 32A-22A and 22A-12A CI seams.47, 48, 50, 51 Figure 2 shows the mass-weighted g and h vectors at the five previously reported51 energy minimized CIs. As shown in the figure, the g and h vectors are in the molecular plane for the 32A-22A CIs since the electronic states have the same (A) symmetry, while h vectors are outof-plane for the 22A-12A CIs. Two of the reported CIs connect the 32A(3px) and 22A(3s) states and are located along the two C-H coordinates. The geometrical structures of these minimum energy crossings (MEXs) differ significantly. Motion along the g vectors is primarily a cis or trans C-H stretch (see Figure 2), and motion along h is perpendicular to g. Table 2 lists the overlaps between the g and h vectors at the five MEXs and nine normal mode vectors of the 32A(3px) state. These results provide considerable insight into the character of the g and h vectors which span the associated branching or g-h plane which in turn describes the nuclear motion enhanced by the CIs. As shown in the table, for the 1-2 MEXs, the g vectors only have nonzero overlaps with the in-plane normal mode vectors, while the h vectors only have nonzero overlaps with out-of-plane normal mode vectors. For 2-3 MEXs, both g and h vectors only have nonzero overlaps with the inplane normal mode vectors at these Cs geometries as shown in Figure 2. The electronic energies are 37924 and 37366 cm-1 for the cis and trans 3-2 CIs, respectively, which are higher than that (34617 cm-1) of the 32A(3px) state at its equilibrium geometry. When accessed these CIs funnel molecular motion in the g and h directions, and eventually leads, following transit through 2-12A CIs, to the cis- and trans-HCOH + H 10


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product channels. It should be noted, however, that CH2O + H rather than cis- or transHCOH + H is the major product. In this regard, the MEX connecting the 22A(3s) and 12A states is located along the O-H coordinate. For this MEX, g (h) is principally v1 (v8) as their overlaps are close to one, and its electronic energy is 19126 cm-1. The 22A12A MEXs relevant to the cis- and trans-HCOH +H channels are at much higher energies, 34088 and 31905 cm-1, respectively, but are still energetically accessible from the 32A state. In Figure 3, a path leading to the trans-HCOH + H channel is shown as a function of the RCH' and H'COH coordinates. Figure 4 shows the calculated absorption spectrum for CH2OH(3px) as a function of the excitation energy. This spectrum is obtained using the Chebyshev autocorrelation function up to 10000 Chebyshev steps, which is equivalent to 425 fs. The peaks in the low-energy wing of the spectrum are converged in both their positions and widths. The spectrum at excitation energy higher than 41000 cm-1 is not shown as it includes contributions from a higher excited state (the band origin of the 3pz state is 41062 cm1),41

which is not included in the three-state PEM. The experimental action spectrum

measured by Reisler and coworkers is also included in that figure in the measured energies for comparison.41 It should be noted that the D1 diabat surface is shifted down by 1500 cm-1 from its nascent position in the fit to match the excitation energy in experiment.51 No additional shift was performed in our calculated absorption spectrum. It can be seen from Figure 4 that the calculated absorption spectrum is in rather good agreement with the experimental result.41 The larger widths for resonance peaks in the experimental spectrum are presumably due to unresolved rotational contours, which is 11



not considered in our theoretical model (J=0). In particular, the calculated spectrum predicts the positions and intensities of the first two peaks in the experimental spectrum very well. The calculated band origin of CH2OH(3px) is located at 35185 cm-1, which is in good agreement with the experimental value (35063 cm-1).41 The second peak in the calculated absorption is located at 1590 cm-1 above the band origin, which is also in good agreement with the experimental value (1607 cm-1).41 The agreement with higher energy peaks in the experimental spectrum deteriorates somewhat, but reasonable agreement is still achieved. This success of theory in reproducing the vibronic resonances can be attributed to the high accuracy of the PEM. To assign the high intensity peaks in the absorption spectrum, the resonance wavefunctions were calculated at their corresponding total energies. In Figure 5, these wave functions are plotted against two excited-state (32A(3px)) normal mode coordinates while all other normal modes are chosen to be zero, namely at the excited state equilibrium geometry. It is shown in Figure 5(a) that the wavefunction of the lowest peak has no node, confirming it is the ground vibrational state. The wavefunction of the second peak, as shown in Figure 5(b), has a single mode along the C-O stretching mode coordinate, and so is the first excited vibrational state of v6 (61), confirming the experimental assignment.41 The second excited state in this vibrational mode, 62, is found at 38357 cm-1 (3172 cm-1 above the band origin) and is shown in Figure 5(c). The wavefunctions of the other three assigned resonances 51, 82, and 6182 are shown in Figs. 5(d), 5(e), and 5(f), respectively.

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To further confirm the nature of the predissociative resonances in the absorption spectrum, the “bound-state” spectrum was calculated on a single adiabatic PES, S2, which is the third eigenvalue of the PEM in the Franck-Condon region. The comparison with the absorption spectrum obtained using the full diabatic PEM is shown in Figure 6. As expected, the peaks in the adiabatic spectrum match quite well the resonances in the low-energy wing of the absorption spectrum, thus confirming the assignment of the resonance peaks. The nonadiabatic interaction of the 32A(3px) state with the 22A(3s) state is clearly responsible for the broadening of the vibrational levels. To understand the dominance of the CO vibrational (v6) features in the 32A(3px)←12A photoexcitation of CH2OH, we calculated the normal mode displacements of the excited 32A(3px) state with respect to those on the ground electronic state, following our earlier work.53 It can be readily seen from Table 3 that the C-O stretching mode (v6) has the largest amplitude displacement -1.53 a.u., while for the other eight modes the displacements are small. The large displacement of the CO stretching mode coordinate shows that it is an active mode for the photodissociation of CH2OH via the 32A(3px) state. This behavior is similar to the photodissociation via the 3s state,52, 53 in that the CO vibrational mode is excited. The excitation of the CO mode in all Rydberg states in this system can be attributed to the nature of the excitation, which promotes an electron from the half-occupied π*CO antibonding orbital of the CH2OH ground (12A) electronic state to a carbon Rydberg orbital (3s, 3px or 3pz).30 As a result, the Rydberg states have a higher bond order for the CO moiety than does the ground electronic state. In addition, due to the planar and nonplanar equilibrium 13



geometries for the 32A(3px) and 12A ground states, respectively, the HCOH torsion (a″) and CH2 wagging (a″) modes have relatively large amplitude displacements (-0.83 and 0.85 a.u., respectively) as well, but their influence on the dynamics is small. As shown in Figure 4, the resonances have finite and rather broad widths, due to nonadiabatic coupling to lower states. As discussed above, the CIs between the 32A(3px) and 22A(3s) states along the C-H coordinates allow facile transfer of population from the former to the latter, which give rise to the short lifetime of the 32A(3px) resonances. The populations of the three adiabatic states of CH2OH are displayed in Figure 7. It can be readily seen that the decay of the 32A(3px) state is fast, and the populations of the 22A(3s) and 12A states increase with time, due to the nonadiabatic couplings among these three states. After 40 fs, only ~40% of the norm of the initial state remains in the 32A(3px) component. We note in passing that the total norm is less than unity because of the use of absorbing boundary conditions in order to avoid reflection of the wave packet. The convergence of the 32A(3px) population has been tested with various grids and absorption potentials. The calculated lifetime of the 00 state is 74.7 fs, which is consistent with the (nonenergy resolved) decay of the excited state population shown in Figure 7. It is also consistent with the experimental estimate (

Nonadiabatic Dynamics in Photodissociation of Hydroxymethyl in the

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