Experimental observation of nonadiabatic bifurcation dynamics at resonances in the continuum

Dynamic Role of the Intramolecular Hydrogen Bonding in the S1 State Relaxation Dynamics Revealed by the Direct Measurement of the Mode-Dependent Internal Conversion Rate of 2-Chlorophenol and 2-Chlorothiophenol

The dynamic role of the intramolecular hydrogen bond in the S1 relaxation of cis-2-chlorophenol (2-CP) or cis-2-chlorothiophenol (2-CTP) has been investigated in a state-specific manner. Whereas ultrafast internal conversion is dominant for 2-CP, the H-tunneling competes with internal conversion for 2-CTP even at the S1 origin. The S0-S1 internal conversion rate of 2-CTP could be directly measured from the S1 lifetimes of 2-CTP-d1 (Cl-C6H4-SD) as the D-tunneling is kinetically blocked, allowing distinct estimations of tunneling and internal conversion rates with increasing the energy. The internal conversion rate of 2-CTP increases by two times at the out-of-plane torsional mode excitation, suggesting that the internal conversion is facilitated at the nonplanar geometry. It then sharply increases at ∼600 cm-1, indicating that the S1/S0 conical intersection is readily accessible at the extended C-Cl bond length. The strength of the intramolecular hydrogen bond should be responsible for the distinct dynamic behaviors of 2-CP and 2-CTP.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

πσ*-Mediated Nonadiabatic Tunneling Dynamics of Thiophenols in S1: The Semiclassical Approaches

The S-H bond tunneling predissociation dynamics of thiophenol and its ortho-substituted derivatives (2-fluorothiophenol, 2-methoxythiophenol, and 2-chlorothiphenol) in S₁ (ππ*) where the H atom tunneling is mediated by the nearby S₂ (πσ*) state (which is repulsive along the S-H bond extension coordinate) have been investigated in a state-specific way using the picosecond time-resolved pump-probe spectroscopy for the jet-cooled molecules. The effects of the specific vibrational mode excitations and the SH/SD substitutions on the S-H(D) bond rupture tunneling dynamics have been interrogated, giving deep insights into the multidimensional aspects of the S₁/S₂ conical intersection, which also shapes the underlying adiabatic tunneling potential energy surfaces (PESs). The semiclassical tunneling rate calculations based on the Wentzel-Kramers-Brillouin (WKB) approximation or Zhu-Nakamura (ZN) theory have been carried out based on the ab initio PESs calculated in the (one, two, or three) reduced dimensions to be compared with the experiment. Though the quantitative experimental results could not be reproduced satisfactorily by the present calculations, the qualitative trends among different molecules in terms of the behavior of the tunneling rate versus the (adiabatic) barrier height or the number of PES dimensions could be rationalized. Most interestingly, the H/D kinetic isotope effect observed in the tunneling rate could be much better explained by the ZN theory compared to the WKB approximation, indicating that the nonadiabatic coupling matrix elements should be invoked for understanding the tunneling dynamics taking place in the proximity of the conical intersection.

Substitution-induced Nonplanarity of 3-Fluorothioanisole in the First Electronically Excited State

Vibronic spectra of 3-fluorothioanisole (3FTA) in the first electronic excited state (S₁) and the cationic ground state (D₀) have been obtained by one-color resonant two-photon ionization (1C-R2PI) and mass-analyzed threshold ionization (MATI) spectroscopy. Spectroscopic measurements and theoretical calculations indicate that both cis- and trans-rotamers of the 3FTA molecule are stable and coexist in the S₀ (the electronic ground state) and D₀ states, and the cis-rotamer is shown to be slightly more stable than the trans-rotamer. In the S₁ state, theoretical calculations predict a stable gauche-structure of 3FTA, manifested by the observation of strong activation of the vibrational modes involving the motion of the -SCH₃ group in the low-frequency regions of the 1C-R2PI and MATI spectra. The electronic excitation energy from the S₀ state to the S₁ state (E₁) and the adiabatic ionization energy (IE) are respectively determined to be 34 820 ± 3 and 65 468 ± 5 cm^-1 for cis-3FTA, and those of the trans-rotamer are respectively determined to be 35 047 ± 3 and 65 644 ± 5 cm^-1. The structural properties of the stable rotamers of 3FTA and their comparison with other F- and Cl-substituted thioanisole derivatives are discussed as well.

Photoionization Spectroscopic and Theoretical Study on the Molecular Structures of cis- and trans-3-Chlorothioanisole

Resonance-enhanced two-photon ionization (R2PI) and mass-analyzed threshold ionization (MATI) spectra are measured for the cis- and trans-3-chlorothioanisole (3ClTA). The first electronic excitation energy (E ₁) and the adiabatic ionization energy (IE) of the cis-rotamer are determined to be 33 959±3 and 65 326±5 cm^-1, respectively, and those of the trans-rotamer are determined to be 34102±3 and 65 471±5 cm^-1, respectively. Density functional theory (DFT) calculations confirm that both the cis- and trans-rotamers of 3ClTA are stable and coexist in their respective S₀, S₁, and D₀ states. Both rotamers adopt planar structures with cis- being slightly more stable than trans- in the respective S₀, S₁, and D₀ states. The conformation, substitution, and isotope effects on the molecular structure, active vibrations, and electronic transition and ionization energies of 3ClTA are analyzed.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

S1-State Decay Dynamics of Benzenediols (Catechol, Resorcinol, and Hydroquinone) and Their 1:1 Water Clusters

The S₁-state decaying rates of the three different benzenediols, catechol, resorcinol, and hydroquinone, and their 1:1 water clusters have been state-specifically measured using the picosecond time-resolved parent ion transients obtained by the pump (excitation) and probe (ionization) scheme. The S₁ lifetime of catechol is found to be short, giving τ ∼ 5.9 ps at the zero-point level. This is ascribed to the H-atom detachment from the free OH moiety of the molecule. Consistent with a previous report (J. Phys. Chem. Lett. 2013, 4, 3819-3823), the S₁ lifetime gets lengthened with low-frequency vibrational mode excitations, giving τ ∼ 9.0 ps for the 116 cm^-1 band. The S₁ lifetimes at the additional vibronic modes of catechol are newly measured, showing the nonnegligible mode-dependent fluctuations of the tunneling rate. When catechol is complexed with water, the S₁ lifetime is enormously increased to τ ∼ 1.80 ns at the zero-point level while it shows an unusual dip at the intermolecular stretching mode excitation (τ ∼ 1.03 ns at 146 cm^-1). Otherwise, it is shortened monotonically with increasing the internal energy, giving τ ∼ 0.67 ns for the 856 cm^-1 band. Two different asymmetric or symmetric conformers of resorcinol give the respective S₁ lifetimes of 4.5 or 6.3 ns at their zero-point levels according to the estimation from our transients taken within the temporal window of 0-2.7 ns. When resorcinol is 1:1 complexed with H₂O, the S₁ decaying rate is slightly accelerated for both conformers. The S₁ lifetimes of trans and cis forms of hydroquinone are measured to be more or less same, giving τ ∼ 2.8 ns at the zero-point level. When H₂O is complexed with hydroquinone, the S₁ decaying process is facilitated for both conformers, slightly more efficiently for the cis conformer.

Femtosecond Wavepacket Dynamics Reveals the Molecular Structures in the Excited (S1) and Cationic (D0) States

Molecular structures in the electronically excited (S₁) and cationic (D₀) states of 2-fluorothioanisole (2-FTA) have been precisely refined from the real-time dynamics of the femtosecond (fs) wavepacket prepared by the coherent excitation of the Franck-Condon active out-of-plane torsional modes in the S₁ ← S₀ transition at 285 nm. The simulation to reproduce the experiment in terms of the beating frequencies gives the nonplanar geometry of 2-FTA in S₁, where the out-of-plane dihedral angle (φ) of the S-CH₃ moiety is 51° with respect to the molecular plane. The behavior of the fs wavepacket in terms of the amplitudes and phases with the change of the probe (ionization) wavelength (λ_probe = 300-330 nm) provides the otherwise veiled structure of the cationic D₀ state. While the 2-FTA cation adopts the planar geometry (φ = 0°) at the global minimum, it is found to have a vertical minimum at φ ≈ 135° from the perspective of the D₀ ← S₁ vertical transition. Ab initio calculations support the experiment quite well although the simulation using the model potentials could improve the match with the experiment, giving the new interpretation for the previously disputed photoelectron spectroscopic results.

Diabatization by Machine Intelligence

Understanding nonadiabatic dynamics is important for chemical and physical processes involving multiple electronic states. Direct nonadiabatic dynamics simulations are often employed to observe such processes on a femtosecond time scale. One often needs to do the simulation on a longer time scale, but direct simulation based on electronic structure calculations of the surfaces and couplings is expensive due to the large number of electronic structure calculations needed for ensemble averaging or simulation of longer-time processes. An alternative approach is to construct an analytical representation of potential energy surfaces (PESs) and couplings, which allows for faster dynamics calculations. Diabatic representations are preferred for such purposes because of the smoothness of the surfaces and couplings and the scalar nature of the couplings. However, many diabatization procedures are complicated by the need to consider orbitals or vector coupling elements, and these can make the process very labor-intensive. To circumvent these difficulties, we here propose diabatization by a deep neural network (DDNN) based on a new architecture for a deep neural network that requires neither orbital input nor vector input. The DDNN method allows convenient and semiautomatic diabatization, and it is demonstrated here for a model problem and for producing diabatic potential energy matrices for thiophenol.

Combined experimental and theoretical study on the ultraviolet photodissociation dynamics of 1-bromo-2,6-difluorobenzene in 267 nm-234 nm

Thanks to their specific molecular symmetry, aromatic molecules and their derivatives represent ideal model systems in understanding photo-induced chemistry of small molecules. Herein, ultraviolet photodissociation dynamics of the 1-bromo-2,6-difluorobenzene molecule has been visualized via imaging the recoiling velocity distributions of photofragments. The measured recoiling angular distributions of the Br(²P_3/2) product vary significantly with the increasing photon energy, arguing against the simple bond-fission mechanism within the C_2v symmetry. Ab initio calculations reveal that in addition to the C-Br bond cleavage, two additional internal molecular coordinates that break the molecular symmetry are likely involved. The Br out-of-plane bending opens a direct dissociation pathway on the S₁-¹A″ (S₁-¹ππ^*) state, while the asymmetric C-F stretching significantly changes the orientation of the transition dipole moment. The present study sheds new light on the effect of symmetry breaking in the photodissociation dynamics of symmetric aryl halides, highlighting the multi-dimensional feature of excited state potential energy surfaces.

Conformer Specific Excited-State Structure of 3-Methylthioanisole

Trans and cis conformers of 3-methylthioanisole have been spectroscopically investigated to reveal the conformer specific structural changes upon the S₁(ππ*)-S₀ excitation. The conformational cooling during the supersonic expansion is found to be quite efficient in the Ar carrier gas giving the trans conformational isomer exclusively in the molecular beam, whereas both trans and cis conformers are populated in the jet when the sample is carried in Ne. Using the Stark deflector, trans and cis conformers are unambiguously identified, showing the distinct Stark deflection profiles according to their sufficiently different dipole moments of 1.013 or 1.670 D, respectively. For the trans conformer, the methyl moiety on the meta-position adopting the eclipsed geometry in S₀ transforms into the staggered geometry in S₁ to activate a series of the CH₃ torsional mode. A Hamiltonian with the one-dimensional sinusoidal torsional potential is solved using the free-rotor basis set to explain the experiment, giving the 3-fold torsional barrier of 34 and 304 cm^-1 for S₀ and S₁, respectively. For the cis conformer, on the other hand, the CH₃ torsion is little activated in the S₁-S₀ transition as both S₀ and S₁ adopt the staggered geometry at the minimum energy points. The doublet of each band of the cis conformer is ascribed to tunneling split due to the very low CH₃ torsional barrier of 27 cm^-1 in S₀. It is found that the cis conformer undergoes a planar to pseudoplanar structural change upon the S₁-S₀ transition. Theoretical calculation based on the double-well model potential curve could explain the experiment quite well, suggesting that the SCH₃ moiety of the cis conformer in S₁ becomes out-of-plane with respect to the plane of the phenyl moiety. This implies that excited-state predissociation dynamics of trans and cis conformers of the title molecule might be different.

Multidimensional characterization of the conical intersection seam in the normal mode space

Multidimensional conical intersection seam has been characterized by utilizing the dynamic resonances in the nonadiabatic transition probability experimentally observed in the predissociation of thioanisole isotopomers.

Vibronic structure and predissociation dynamics of 2-methoxythiophenol (S1): The effect of intramolecular hydrogen bonding on nonadiabatic dynamics

Vibronic spectroscopy and the S-H bond predissociation dynamics of 2-methoxythiophenol (2-MTP) in the S₁ (ππ^*) state have been investigated for the first time. Resonant two-photon ionization and slow-electron velocity map imaging (SEVI) spectroscopies have revealed that the S₁-S₀ transition of 2-MTP is accompanied with the planar to the pseudoplanar structural change along the out-of-plane ring distortion and the tilt of the methoxy moiety. The S₁ vibronic bands up to their internal energy of ∼1000 cm^-1 are assigned from the SEVI spectra taken via various S₁ vibronic intermediate states with the aid of ab initio calculations. Intriguingly, Fermi resonances have been identified for some vibronic bands. The S-H bond breakage of 2-MTP occurs via tunneling through an adiabatic barrier under the S₁/S₂ conical intersection seam, and it is followed by the bifurcation into either the adiabatic or nonadiabatic channel at the S₀/S₂ conical intersection where the diabatic S₂ state (πσ^*) is unbound with respect to the S-H bond elongation coordinate, giving the excited (Ã) or ground (X̃) state of the 2-methoxythiophenoxy radical, respectively. Surprisingly, the nonadiabatic transition probability at the S₀/S₂ conical intersection, estimated from the velocity map ion images of the nascent D fragment from 2-MTP-d₁ (2-CH₃O-C₆H₄SD) at the S₁ zero-point energy level, is found to be exceptionally high to give the X̃/Ã product branching ratio of 2.03 ± 0.20, which is much higher than the value of ∼0.8 estimated for the bare thiophenol at the S₁ origin. It even increases to 2.33 ± 0.17 at the ν₄₅ ² mode (101 cm^-1) before it rapidly decays to 0.69 ± 0.05 at the S₁ internal energy of about 2200 cm^-1. This suggests that the strong intramolecular hydrogen bonding of S⋯D⋯OCH₃ in 2-MTP at least in the low S₁ internal energy region should play a significant role in localizing the reactive flux onto the conical intersection seam. The minimum energy pathway calculations (second-order coupled-cluster resolution of the identity or time-dependent-density functional theory) of the adiabatic S₁ state suggest that the intimate dynamic interplay between the S-H bond cleavage and intramolecular hydrogen bonding could be crucial in the nonadiabatic surface hopping dynamics taking place at the conical intersection.