Quantum Energy Flow and trans-Stilbene Photoisomerization: an Example of a Non-RRKM Reaction

On the intramolecular vibrational energy redistribution dynamics of aromatic complexes: A comparative study on C6H6-C6H5Cl, C6H6-C6H3Cl3, C6H6-C6Cl6 and C6H6-C6H5F, C6H6-C6H3F3, C6H6-C6F6

Chemical dynamics Simulation studies on benzene dimer (Bz2) and benzene-hexachlorobenzene (Bz-HCB) as performed in the past suggest that the coupling between the monomeric (intramolecular) vibrational modes and modes generated due to the association of two monomers (intermolecular) has to be neither strong nor weak for a fast dissociation of the complex. To find the optimum coupling, four complexes are taken into consideration in this work, namely, benzene-monofluorobenzene, benzene-monochlorobenzene, benzene-trifluorobenzene (Bz-TFB), and benzene-trichlorobenzene. Bz-TFB has the highest rate of dissociation among all seven complexes, including Bz2, Bz-HCB, and Bz-HFB (HFB stands for hexafluorobenzene). The set of vibrational frequencies of Bz-TFB is mainly the reason for this fast dissociation. The mass of chlorine in Bz-HCB is optimized to match its vibrational frequencies similar to those of Bz-TFB, and the dissociation of Bz-HCB becomes faster. The power spectrum of Bz-TFB, Bz-HCB, and Bz-HCB with the modified mass of chlorine is also computed to understand the extent of the said coupling in these complexes.

Electronic-state chaos, intramolecular electronic energy redistribution, and chemical bonding in persisting multidimensional nonadiabatic systems

We study the chaotic, huge fluctuation of electronic state, resultant intramolecular energy redistribution, and strong chemical bonding surviving the fluctuation with exceedingly long lifetimes of highly excited boron clusters. Those excited states constitute densely quasi-degenerate state manifolds. The huge fluctuation is induced by persisting multidimensional nonadiabatic transitions among the states in the manifold. We clarify the mechanism of their coexistence and its physical significance. In doing so, we concentrate on two theoretical aspects. One is quantum chaos and energy randomization, which are to be directly extracted from the properties of the total electronic wavefunctions. The present dynamical chaos takes place through frequent transitions from adiabatic states to others, thereby making it very rare for the system to find dissociation channels. This phenomenon leads to the concept of what we call intramolecular nonadiabatic electronic-energy redistribution, which is an electronic-state generaliztion of the notion of intramolecular vibrational energy redistribution. The other aspect is about the peculiar chemical bonding. We investigate it with the energy natural orbitals (ENOs) to see what kind of theoretical structures lie behind the huge fluctuation. The ENO energy levels representing the highly excited states under study appear to have four robust layers. We show that the energy layers responsible for chaotic dynamics and those for chemical bonding are widely separated from each other, and only when an event of what we call "inter-layer crossing" happens to burst can the destruction of these robust energy layers occur, resulting in molecular dissociation. This crossing event happens only rarely because of the large energy gaps between the ENO layers. It is shown that the layers of high energy composed of complex-valued ENOs induce the turbulent flow of electrons and electronic-energy in the cluster. In addition, the random and fast time-oscillations of those high energy ENOs serve as a random force on the nuclear dynamics, which can work to prevent a concentration of high nuclear kinetic energy in the dissociation channels.

Post-Transition-State Direct Dynamics Simulations on the Ozonolysis of Catechol

On-the-fly dynamics simulations are performed for the reaction of catechol + O₃. The post transition state (TS) dynamics is studied at temperatures of 400 and 500 K. The PM7 semiempirical method is employed for calculating the potential energy gradient needed for integrating Hamilton's equations of motion. This semiempirical method provides excellent agreement in terms of energy and geometry of the TSs as well as minimum energy states of the system with respect to B3LYP/6-311+G (2df, 2p) calculated results. In the dynamics, first, a peroxyacid is formed, which further dissociates to different fragments. Four major channels forming CO, CO₂, H₂O, and small carboxylic acid (SCA) fragments are seen in this reaction. Rates of each of the channels and the overall unimolecular reaction are calculated at both temperatures. Branching ratios of all these product channels are calculated and compared with experiment. The minimum energy profile of CO₂, CO, and H₂O channels are calculated. A qualitative estimate of activation energies for all the channels are obtained and compared with the explicit TS energies of three product channels, which ultimately correlate with the reaction probabilities.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

A walk through the approximations of ab initio multiple spawning

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

Detecting reactive islands using Lagrangian descriptors and the relevance to transition path sampling

It has been known for sometime now that isomerization reactions, classically, are mediated by phase space structures called reactive islands (RI). RIs provide one possible route to correct for the nonstatistical effects in the reaction dynamics. In this work, we map out the reactive islands for the two dimensional Müller-Brown model potential and show that the reactive islands are intimately linked to the issue of rare event sampling. In particular, we establish the sensitivity of the so called committor probabilities, useful quantities in the transition path sampling technique, to the hierarchical RI structures. Mapping out the RI structure for high dimensional systems, however, is a challenging task. Here, we show that the technique of Lagrangian descriptors is able to effectively identify the RI hierarchy in the model system. Based on our results, we suggest that the Lagrangian descriptors can be useful for detecting RIs in high dimensional systems.

Failure and Redemption of Statistical and Nonstatistical Rate Theories in the Hydroboration of Alkenes

Our previous work found that canonical forms of transition state theory incorrectly predict the regioselectivity of the hydroboration of propene with BH3 in solution. In response, it has been suggested that alternative statistical and nonstatistical rate theories can adequately account for the selectivity. This paper uses a combination of experimental and theoretical studies to critically evaluate the ability of these rate theories, as well as dynamic trajectories and newly developed localized statistical models, to predict quantitative selectivities and qualitative trends in hydroborations on a broader scale. The hydroboration of a series of terminally substituted alkenes with BH3 was examined experimentally, and a classically unexpected trend is that the selectivity increases as the alkyl chain is lengthened far from the reactive centers. Conventional and variational transition state theories can predict neither the selectivities nor the trends. The canonical competitive nonstatistical model makes somewhat better predictions for some alkenes but fails to predict trends, and it performs poorly with an alkene chosen to test a specific prediction of the model. Added nonstatistical corrections to this model make the predictions worse. Parametrized Rice-Ramsperger-Kassel-Marcus (RRKM)-master equation calculations correctly predict the direction of the trend in selectivity versus alkene size but overpredict its magnitude, and the selectivity with large alkenes remains unpredictable with any parametrization. Trajectory studies in explicit solvent can predict selectivities without parametrization but are impractical for predicting small changes in selectivity. From a lifetime and energy analysis of the trajectories, "localized RRKM-ME" and "competitive localized noncanonical" rate models are suggested as steps toward a general model. These provide the best predictions of the experimental observations and insight into the selectivities.

Thermalization and Thermal Transport in Molecules

The nature and rate of thermal transport through molecular junctions depend on the length over which thermalization occurs. For junctions formed by alkane chains, in which thermalization occurs only slowly, measurements reveal that thermal resistance is controlled by bonding with the substrates, whereas fluorination can introduce thermal resistance within the molecules themselves, although the mechanism remains unclear. Here we present results of quantum-mechanical calculations of elastic and inelastic scattering rates, the length over which thermalization occurs, and thermal conductance in alkane and perfluoroalkane junctions. The contribution to thermalization of quantum effects that give rise to many-body localization (MBL) in isolated molecules is examined. While MBL does not occur due to dephasing, thermalization is typically too slow to establish local temperature if the same molecule in isolation exhibits MBL. The results indicate limitations on the applicability of classical molecular simulations in modeling thermal transport in molecular junctions.

Excited state intramolecular proton transfer (ESIPT) in 2-(2'-hydroxyphenyl)benzoxazole and its naphthalene-fused analogs: a TD-DFT quantum chemical study

The intramolecular proton transfer reactions in 2-(2'-hydroxyphenyl)benzoxazole (HBO) and its naphthalene-fused analogs, (HNB1-3) in both S0 and S1 states at the PBE1PBE/6-311++G(2d,2p) level of theory in the gas phase and water have been investigated to find the effects of extension of aromaticity on the intramolecular proton transfer and photophysical properties. The results show that the ground state intramolecular proton transfer (GSIPT) in the studied species is impossible. Excited states potential energy surface calculations support the existence of ESIPT process. Structural parameters, relative energy of isomers, H-bonding energy, adsorption and emission bands, vertical excitation and emission energies, oscillator strength, fluorescence rate constant, dipole moment, atomic charges and electron density at critical points were calculated. Orbital analysis shows that vertical S0→S1 transition in the studied molecules corresponds essentially to the excitation from HOMO (π) to LUMO (π(*)). The potential of HNB2 molecule as an emissive and electron transport material in designing improved organic white light emitting diodes is predicted in this work. Our calculations are also supported by the experimental observations.

Photoisomerization of Stilbene: The Detailed XMCQDPT2 Treatment

We report the detailed XMCQDPT2/cc-pVTZ study of trans-cis photoisomerization in one of the core systems of both experimental and computational photochemistry-the stilbene molecule. For the first time, the potential energy surface (PES) of the S1 state has been directly optimized and scanned using a multistate multiconfiguration second-order perturbation theory. We characterize the trans-stilbene, pyramidalized (phantom), and DHP-cis-stilbene geometric domains of the S1 state and describe their stationary points including the transition states between them, as well as S1/S0 intersections. Also reported are the minima and the activation barriers in the ground state. Our calculations correctly predict the kinetic isotope effect due to H/D exchange at ethylenic hydrogens, the dynamic behavior of excited cis-stilbene, and trans-cis branching ratio after relaxation to S0 through a rather unsymmetric conical intersection. In general, the XMCQDPT2 results confirm the qualitative adequacy of the TDDFT (especially SF-TDDFT) picture of the excited stilbene but also reveal quantitative discrepancies that deserve further exploration.

Hybrid quantum/classical simulations of the vibrational relaxation of the amide I mode of N-methylacetamide in D2O solution

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

Photoisomerization of stilbene: a spin-flip density functional theory approach

The photoisomerization process of 1,2-diphenylethylene (stilbene) is investigated using the spin-flip density functional theory (SFDFT), which has recently been shown to be a promising approach for locating conical intersection (CI) points (Minezawa, N.; Gordon, M. S. J. Phys. Chem. A2009, 113, 12749). The SFDFT method gives valuable insight into twisted stilbene to which the linear response time-dependent DFT approach cannot be applied. In contrast to the previous SFDFT study of ethylene, a distinct twisted minimum is found for stilbene. The optimized structure has a sizable pyramidalization angle and strong ionic character, indicating that a purely twisted geometry is not a true minimum. In addition, the SFDFT approach can successfully locate two CI points: the twisted-pyramidalized CI that is similar to the ethylene counterpart and another CI that possibly lies on the cyclization pathway of cis-stilbene. The mechanisms of the cis--trans isomerization reaction are discussed on the basis of the two-dimensional potential energy surface along the twisting and pyramidalization angles.

Electronic effects on photochemistry: the diverse reaction dynamics of highly excited stilbenes and azobenzene

Ultrafast time-resolved mass spectrometry and structural dynamics experiments on trans-stilbene, cis-stilbene, and azobenzene, with excitation to high-lying electronic states, reveal a rich diversity of photochemical reaction dynamics. All processes are found to be quite unlike the well-known photochemistry on lower electronic surfaces. While in trans-stilbene, excitation at 6 eV induces a phenyl twisting motion, in cis-stilbene it leads to an ultrafast ring-closing to form 4a,4b-dihydrophenanthrene. Azobenzene dissociates on an ultrafast time scale, rather than isomerizing as it does on a lower surface. The photochemical dynamics of the sample molecules proceed along steep potential energy surfaces and conical intersections. Because of that, the dynamics are much faster than vibrational relaxation, the randomizing effects from vibrational energy scrambling are avoided, and excitation-energy specific reaction dynamics results.