Quantum Wave Packet Propagation Study of the Photochemistry of Phenol: Isotope Effects (Ph-OD) and the Direct Excitation to the 1πσ* State

Mode-dependent H atom tunneling dynamics of the S1 phenol is resolved by the simple topographic view of the potential energy surfaces along the conical intersection seam

Mode-dependent H atom tunneling dynamics of the O-H bond predissociation of the S₁ phenol has been theoretically analyzed. As the tunneling is governed by the complicated multi-dimensional potential energy surfaces that are dynamically shaped by the upper-lying S₁(ππ*)/S₂(πσ*) conical intersection, the mode-specific tunneling dynamics of phenol (S₁) has been quite formidable to be understood. Herein, we have examined the topography of the potential energy surface along the particular S₁ vibrational mode of interest at the nuclear configurations of the S₁ minimum and S₁/S₂ conical intersection. The effective adiabatic tunneling barrier experienced by the reactive flux at the particular S₁ vibrational mode excitation is then uniquely determined by the topographic shape of the potential energy surface extended along the conical intersection seam coordinate associated with the particular vibrational mode. The resultant multi-dimensional coupling of the specific vibrational mode to the tunneling coordinate is then reflected in the mode-dependent tunneling rate as well as nonadiabatic transition probability. Remarkably, the mode-specific experimental result of the S₁ phenol tunneling reaction [K. C. Woo and S. K. Kim, J. Phys. Chem. A 123, 1529-1537 (2019)] (in terms of the qualitative and relative mode-dependent dynamic behavior) could be well rationalized by semi-classical calculations based on the mode-specific topography of the effective tunneling barrier, providing the clear conceptual insight that the skewed potential energy surfaces along the conical intersection seam (strongly or weakly coupled to the tunneling reaction coordinate) may dictate the tunneling dynamics in the proximity of the conical intersection.

Nuclear wave-packet-propagation-based study of the electron-coupled, proton-transfer process in the charge-transfer state of FHCl exhibiting three electronic states in full-dimensional space

The charge-transfer (CT) excited state of FHCl (F⁺H-Cl^-), generated by the photodetachment of an electron from its precursor anion (FHCl^-) by a photon energy of ∼9.5 eV, is a realistic prototype of two bidirectional-coupled reaction pathways, namely the proton-transfer (PT) and electron-transfer (ET) channels, that produce F + HCl and FH + Cl combinations, respectively. The early-time dynamics of the CT was studied via the time-dependent propagations of nuclear wave packets comprising three nonadiabatically coupled electronic states defined within a three-dimensional space. The detailed analyses of the early-time dynamics revealed an interesting phenomenon in which the onset of PT was ∼80 fs earlier than that of ET, indicating that PT dominated ET in this case. A more significant finding was that the proper adjustment of the electronic-charge distribution for the onset of ET was obtained ∼80 fs after the onset of PT; this adjustment was mediated by the initial movement of the H atom, i.e., the F-H vibration mode. To avail experimental observables, the branching ratio, χ = PT/(PT + ET), and absorption spectrum generating the neutral FHCl molecule from its precursor anion were also simulated. The results further demonstrated the dependences of the χs and spectrum on the change in the initial vibration level of the precursor anion, as well as the isotopic substitution of the connecting H atom with deuterium, tritium, and muonium.

Wavepacket propagations for the early time dynamics of proton-coupled electron transfer in the charge-transfer state of NH3Cl complex

A charge-transfer (CT) excited state of NH₃Cl, generated by photo-detachment of an electron from the anionic NH₃Cl^- precursor, can be represented as H₂N⁺-H-Cl^- and proceeds to two chemical reactions: one reaction generating NH₂ and HCl resulting from a proton transfer (PT) and the other reaction producing NH₃ and a Cl atom resulting from an electron transfer (ET); both are coupled to form a typical proton-coupled electron transfer (PCET) process. The early time dynamics of this CT were studied using time-dependent wavepacket propagation on three nonadiabatically coupled electronic states in a reduced three-dimensional space. The electronic states were treated using the XMS-CASPT2/aug-cc-pVTZ ab initio methodology. The population dynamics of the three coupled electronic states were analyzed in detail to reveal the initial stage of the PCET process up to ∼100 fs, while the branching ratio, χ = PT/(ET+PT), was determined after wavepacket propagations of up to 2000 fs. Another main result is the dependence of χ on the vibration levels of the initial precursor anion and the isotope substitution of the connecting H atom with deuterium and tritium. Our study reveals the detailed microscopic features of the PCET process embedded in the CT state of the NH₃Cl complex and certain systematic dependences of the branching ratio χ on the above factors.

Revealing the role of excited state proton transfer (ESPT) in excited state hydrogen transfer (ESHT): systematic study in phenol-(NH3) n clusters

Excited State Hydrogen Transfer (ESHT), proposed at the end of the 20th century by the corresponding authors, has been observed in many neutral or protonated molecules and become a new paradigm to understand excited state dynamics/photochemistry of aromatic molecules. For example, a significant number of photoinduced proton-transfer reactions from X–H bonds have been re-defined as ESHT, including those of phenol, indole, tryptophan, aromatic amino acid cations and so on. Photo-protection mechanisms of biomolecules, such as isolated nucleic acids of DNA, are also discussed in terms of ESHT. Therefore, a systematic and up-to-date description of ESHT mechanism is important for researchers in chemistry, biology and related fields. In this review, we will present a general model of ESHT which unifies the excited state proton transfer (ESPT) and the ESHT mechanisms and reveals the hidden role of ESPT in controlling the reaction rate of ESHT. For this purpose, we give an overview of experimental and theoretical work on the excited state dynamics of phenol–(NH₃)_n clusters and related molecular systems. The dynamics has a significant dependence on the number of solvent molecules in the molecular cluster. Three-color picosecond time-resolved IR/near IR spectroscopy has revealed that ESHT becomes an electron transfer followed by a proton transfer in highly solvated clusters. The systematic change from ESHT to decoupled electron/proton transfer according to the number of solvent molecules is rationalized by a general model of ESHT including the role of ESPT.

A general model of excited state hydrogen transfer (ESHT) which unifies ESHT and the excited state proton transfer (ESPT) is presented from experimental and theoretical works on phenol–(NH₃)_n. The hidden role of ESPT is revealed.

Photolysis dynamics of m- and o-fluorophenol: Substitution effects on tunneling mechanism

The photolysis dynamics of m-fluorophenol (m-FPhOH) and o-fluorophenol (o-FPhOH) have been investigated with time-resolved velocity map imaging (TR-VMI) and time-resolved ion-yield (TR-IY) techniques. Following excitation to the origin of S₁ (ππ∗) state of m- and o-FPhOH, H atoms elimination mediated by tunneling through the potential barrier under the S₁ (ππ∗)/S₂ (πσ∗) conical intersection (CI) has been observed as a Gaussian feature signal centered at a total kinetic energy release (TKER) of ∼6000 cm^-1 for both molecules. The quantum tunneling mechanism has been identified as the main decay pathway of S₁ state for m-FPhOH, and the tunneling lifetime of 2.1 ns has been obtained from the TR-VMI measurements of H fragments. This tunneling mechanism is further confirmed by the studies on the selective O-H deuterated species, m-FPhOD, and consolidated by our theoretical calculations. However, the photolysis dynamics is quite different for the photoexcited o-FPhOH. The much lower yield of the H atoms originating from tunneling hinders the extraction of a reliable tunneling lifetime for o-FPhOH. Our theoretical calculations exhibit a broader and higher potential barrier exists beneath the S₁/S₂ CI of o-FPhOH, which increase the difficulty for tunneling. Furthermore, the special existence of intramolecular hydrogen bond in o-FPhOH is probably also the key factor that affects the tunneling rate, which would restrict the O-H stretch motion.

Insights into the Mechanism of Nonadiabatic Photodissociation from Product Vibrational Distributions. The Remarkable Case of Phenol

The fate of a photoexcited molecule is often strongly influenced by electronic degeneracies, such as conical intersections, which break the Born-Oppenheimer separation of electronic and nuclear motion. Detailed information concerning internal energy redistribution in a nonadiabatic process can be extracted from the product state distribution of a photofragment in photodissociation. Here, we focus on the nonadiabatic photodissociation of phenol and discuss the internal excitation of the phenoxyl fragment using both symmetry analysis and wave packet dynamics. It is shown that unique and general selection rules exist, which can be attributed to the geometric phase in the adiabatic representation. Further, our results provide a reinterpretation of the experimental data, shedding light on the impact of conical intersections on the product state distribution.

Multidimensional H Atom Tunneling Dynamics of Phenol: Interplay between Vibrations and Tunneling

Multidimensional facets of the hydrogen tunneling dynamics of phenol excited in S₁ (ππ*) have been unraveled to give particular S₁ vibronic states strongly coupled or actively decoupled to the O-H tunneling coordinate. Strong mode-dependent variation of the tunneling rate measured with picosecond lasers indicates that tunneling probability is extremely sensitive to low-frequency vibrational modes seemingly orthogonal to the O-H elongation coordinate unless the rate of energy randomization exceeds that of tunneling. The multidimensional nature of tunneling has also been manifested in efficient internal-to-translational energy transfers observed at S₁ vibronic modes strongly coupled to the tunneling coordinate, giving insights into otherwise the formidable multidimensional map of tunneling process. The nonadiabatic bifurcation dynamics in the later stage of the chemical reaction has been disentangled by analyzing picosecond time-resolved product state distributions, resolving a long controversial issue regarding the origin of high or low kinetic energy component of the product translational energy distributions.

Excited-state dissociation dynamics of phenol studied by a new time-resolved technique

Phenol is an important model molecule for the theoretical and experimental investigation of dissociation in the multistate potential energy surfaces. Recent theoretical calculations [X. Xu et al., J. Am. Chem. Soc. 136, 16378 (2014)] suggest that the phenoxyl radical produced in both the X and A states from the O-H bond fission in phenol can contribute substantially to the slow component of photofragment translational energy distribution. However, current experimental techniques struggle to separate the contributions from different dissociation pathways. A new type of time-resolved pump-probe experiment is described that enables the selection of the products generated from a specific time window after molecules are excited by a pump laser pulse and can quantitatively characterize the translational energy distribution and branching ratio of each dissociation pathway. This method modifies conventional photofragment translational spectroscopy by reducing the acceptance angles of the detection region and changing the interaction region of the pump laser beam and the molecular beam along the molecular beam axis. The translational energy distributions and branching ratios of the phenoxyl radicals produced in the X, A, and B states from the photodissociation of phenol at 213 and 193 nm are reported. Unlike other techniques, this method has no interference from the undissociated hot molecules. It can ultimately become a standard pump-probe technique for the study of large molecule photodissociation in multistates.

Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only

A very simple equation, F_ij^App=[(∂²(V_i^a-V_j^a)/∂Q²)/(V_i^a-V_j^a)]^1/2/2, giving a reliable magnitude of non-adiabatic coupling terms (NACTs, F_ij's) based on adiabatic potential energies only (V_i^a and V_j^a) was discovered, and its reliability was tested for several prototypes of same-symmetry interstate crossings in LiF, C₂, NH₃Cl, and C₆H₅SH molecules. Our theoretical derivation starts from the analysis of the relationship between the Lorentzian dependence of NACTs along a diabatization coordinate and the well-established linear vibronic coupling scheme. This analysis results in a very simple equation, α=2κ/Δ_c, enabling the evaluation of the Lorentz function α parameter in terms of the coupling constant κ and the energy gap Δ_c (Δ_c=|V_i^a-V_j^a|_Qc ) between adiabatic states at the crossing point Q_C. Subsequently, it was shown that Q_C corresponds to the point where F_ij^App exhibit maximum values if we set the coupling parameter as κ=[(V_i^a-V_j^a)⋅(∂²(V_i^a-V_j^a)/∂Q²)]_Qc^1/2/2. Finally, we conjectured that this relation could give reasonable values of NACTs not only at the crossing point but also at other geometries near Q_C. In this final approximation, the pre-defined crossing point Q_C is not required. The results of our test demonstrate that the approximation works much better than initially expected. The present new method does not depend on the selection of an ab initio method for adiabatic electronic states but is currently limited to local non-adiabatic regions where only two electronic states are dominantly involved within a nuclear degree of freedom.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.

Dynamic Symmetry Breaking Hidden in Fano Resonance of a Molecule: S1 State of Diazirine Using Quantum Wave Packet Propagation

Fano resonance in the predissociation of the S1 state of diazirine was studied by applying a time-dependent wave packet propagation method, and dynamic symmetry breaking (DSB) around the stationary structure of S1 was disclosed in a detailed analysis of this theoretical result. The DSB was found to originate in coupling between the asymmetric C-N2 stretching and CH2 wagging modes, suggesting that there is a slight time gap between ring opening and the concurrent dragging of two H atoms of the CH2 moiety. Although the depth of the double well due to DSB is just 0.011 eV, its presence noticeably affects the early time dynamics and observed spectrum.

Accurate nonadiabatic dynamics

This Perspective addresses the use of coupled diabatic potential energy surfaces (PESs) together with rigorous quantum dynamics in full or reduced dimensional coordinate spaces to obtain accurate solutions to problems in nonadiabatic dynamics.

Comparing the electronic relaxation dynamics of aniline and d7-aniline following excitation at 272–238 nm

Femtosecond studies of electronic relaxation in aniline reveal evidence for a 3-state conical intersection and show that tunnelling is unimportant.

Branching Ratio between Proton Transfer and Electron Transfer Channels of a Bidirectional Proton-Coupled Electron Transfer

Rigorous quantum dynamical study of concerted proton-coupled electron transfer (PCET) on the time scale of a few femtoseconds (fs) has been rarely reported. Herein, a time-dependent quantum wavepacket propagation method was applied to the dynamics of the charge-transfer excited electronic state of FHCl corresponding to F(+)HCl(-). The dynamics corresponds to a bidirectional PCET with two dissociation channels: the electron transfer (ET, generating FH+Cl) and proton transfer (PT, generating F+HCl) paths. The calculated branching ratio (Cl/F), 0.78, implies a surprising fact: PT prevails over ET. A detailed analysis of the proton movement and electron readjustment suggests that the proton movement starts ∼3 fs earlier than the electron movement, and the electron readjustment is triggered by the initial movement of the proton. The branching ratio drastically inverts to 1.24 because of a reduced nonadiabatic effect in the isotope-substituted system, FDCl.

Full-dimensional potentials and state couplings and multidimensional tunneling calculations for the photodissociation of phenol

Full-dimensional potentials and state couplings were developed for the photodissociation of phenol. We also present multidimensional tunneling calculations at the transition state on the shoulder of the first conical intersection.

Direct Observation of Hydrogen Tunneling Dynamics in Photoexcited Phenol

The excited-state dynamics of phenol following ultraviolet (UV) irradiation have received considerable interest in recent years, most notably because they can provide a model for understanding the UV-induced dynamics of the aromatic amino acid tyrosine. Despite this, there has been some debate as to whether hydrogen tunneling dynamics play a significant role in phenol's excited-state O-H bond fission when UV excitation occurs below the (1)ππ*/(1)πσ* conical intersection (CI). In this Letter, we present direct evidence that (1)πσ*-mediated O-H bond fission below the (1)ππ*/(1)πσ* CI proceeds exclusively through hydrogen tunneling dynamics. The observation of hydrogen tunneling may have some parallels with proton tunneling dynamics from tyrosine residues (along the O-H bond of the phenol moiety) in a wide range of natural enzymes, potentially adding further justification for utilizing phenols as model systems for investigating tyrosine-based dynamics.