Andrew S. Petit

Infrared-driven unimolecular reaction of CH3CHOO Criegee intermediates to OH radical products

Breaking down a Criegee intermediate Ozones damaging role in the upper atmosphere is well known, but ozone is also quite active closer down to where we live. In particular, ozones run-ins with airborne unsaturated hydrocarbons, from natural or anthropogenic sources, produce even more-reactive OH radicals. Liu et al. used vibrational spectroscopy to study how OH emerges from a so-called Criegee intermediate formed when ozone attacks 2-butene. The results suggest that OH production is easier than current theory predicts. Science, this issue p. 1596 Spectroscopy in the laboratory elucidates key steps in ozone’s atmospheric reaction with unsaturated hydrocarbons. Ozonolysis of alkenes, an important nonphotolytic source of hydroxyl (OH) radicals in the troposphere, proceeds through energized Criegee intermediates that undergo unimolecular decay to produce OH radicals. Here, we used infrared (IR) activation of cold CH3CHOO Criegee intermediates to drive hydrogen transfer from the methyl group to the terminal oxygen, followed by dissociation to OH radicals. State-selective excitation of CH3CHOO in the CH stretch overtone region combined with sensitive OH detection revealed the IR spectrum of CH3CHOO, effective barrier height for the critical hydrogen transfer step, and rapid decay dynamics to OH products. Complementary theory provides insights on the IR overtone spectrum, as well as vibrational excitations, structural changes, and energy required to move from the minimum-energy configuration of CH3CHOO to the transition state for the hydrogen transfer reaction.

Understanding the Surface Hopping View of Electronic Transitions and Decoherence

We present a current, up-to-date review of the surface hopping methodology for solving nonadiabatic problems, 25 years after Tully published the fewest switches surface hopping algorithm. After reviewing the original motivation for and failures of the algorithm, we give a detailed examination of modern advances, focusing on both theoretical and practical issues. We highlight how one can partially derive surface hopping from the Schrödinger equation in the adiabatic basis, how one can change basis within the surface hopping algorithm, and how one should understand and apply the notions of decoherence and wavepacket bifurcation. The question of time reversibility and detailed balance is also examined at length. Recent applications to photoexcited conjugated polymers are discussed briefly.

Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories

We report a surface hopping approach for modeling the full time- and frequency-resolved differential absorbance spectra (beyond the inhomogenous limit) obtained in ultrafast pump-probe experiments. In our approach, we combine dynamical information obtained from ensembles of classical trajectories propagated on the ground and on the excited potential energy surfaces to directly calculate optical response functions and hence spectral lineshapes. We demonstrate that our method is exact for the model problem of two shifted harmonic potentials with identical harmonic frequencies in the absence of electronic relaxation. We then consider a model three state system with electronic relaxation and show that our method is able to capture the effects of nonadiabatic excited state dynamics on the time-dependent differential absorbance spectra. Furthermore, by comparing our spectra against those spectra calculated with either an (1) inhomogenous expression, (2) ground-state Kubo theory, or (3) excited-state Kubo theory, we show that including dynamical information from both the ground and excited potential energy surfaces significantly improves the reliability of the semiclassical approximations. As such, our surface hopping method should find immediate use in modeling the time-dependent differential abosrbance spectra of ultrafast pump-probe experiments.

How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: A simple generalization of ground-state Kubo theory

In this paper, we develop a surface hopping approach for calculating linear absorption spectra using ensembles of classical trajectories propagated on both the ground and excited potential energy surfaces. We demonstrate that our method allows the dipole-dipole correlation function to be determined exactly for the model problem of two shifted, uncoupled harmonic potentials with the same harmonic frequency. For systems where nonadiabatic dynamics and electronic relaxation are present, preliminary results show that our method produces spectra in better agreement with the results of exact quantum dynamics calculations than spectra obtained using the standard ground-state Kubo formalism. As such, our proposed surface hopping approach should find immediate use for modeling condensed phase spectra, especially for expensive calculations using ab initio potential energy surfaces.

Diffusion Monte Carlo Approaches for Evaluating Rotationally Excited States of Symmetric Top Molecules: Application to H3O+ and D3O+†

An approach is described for evaluating energies and wave functions for rotationally excited states of symmetric top molecules using diffusion Monte Carlo methods. The approach is based on the fact that, for many systems, the rotation/vibration Hamiltonian can be modeled by terms that depend on the vibrational coordinates and powers of the components of the rotational angular momentum vector, J. In the case of symmetric top molecules with M = 0, the rotational part of the wave function is given by the tesseral harmonics. We construct rotationally excited states within the diffusion Monte Carlo approach by imposing nodal surfaces that are obtained from the roots of the tesseral harmonics. Results are presented for H(3)O(+) and D(3)O(+) with J <or= 10. Where comparisons to previous calculations can be made, the agreement is excellent.

Appraisal of Surface Hopping as a Tool for Modeling Condensed Phase Linear Absorption Spectra.

Whereas surface hopping is usually used to study populations and mean-field dynamics to study coherences, in two recent papers, we described a procedure for calculating dipole-dipole correlation functions (and therefore absorption spectra) directly from ensembles of surface hopping trajectories. We previously applied this method to a handful of one-dimensional model problems intended to mimic the gas phase. In this article, we now benchmark this new procedure on a set of multidimensional model problems intended to mimic the condensed phase and compare our results against other standard semiclassical methods. By comparison, we demonstrate that methods that include only dynamical information from one PES (the standard Kubo approaches) exhibit large discrepancies with the results of exact quantum dynamics. Furthermore, for model problems with nonadiabatic excited state dynamics but no quantized vibrational structure in the spectra, our surface hopping approach performs comparably to using Ehrenfest dynamics to calculate the electronic coherences. That being said, however, when quantized vibrational structures are present in the spectra but the electronic states are uncoupled, performing the dynamics on the mean PES still outperforms our present method. These benchmark results should influence future studies that use ensembles of independent semiclassical trajectories to model linear as well as multidimensional spectra in the condensed phase.

Diffusion Monte Carlo in internal coordinates.

An internal coordinate extension of diffusion Monte Carlo (DMC) is described as a first step toward a generalized reduced-dimensional DMC approach. The method places no constraints on the choice of internal coordinates other than the requirement that they all be independent. Using H(3)(+) and its isotopologues as model systems, the methodology is shown to be capable of successfully describing the ground state properties of molecules that undergo large amplitude, zero-point vibrational motions. Combining the approach developed here with the fixed-node approximation allows vibrationally excited states to be treated. Analysis of the ground state probability distribution is shown to provide important insights into the set of internal coordinates that are less strongly coupled and therefore more suitable for use as the nodal coordinates for the fixed-node DMC calculations. In particular, the curvilinear normal mode coordinates are found to provide reasonable nodal surfaces for the fundamentals of H(2)D(+) and D(2)H(+) despite both molecules being highly fluxional.

Simultaneous Evaluation of Multiple Rotationally Excited States of H3+, H3O+, and CH5+ Using Diffusion Monte Carlo

An extension to diffusion Monte Carlo (DMC) is proposed for simultaneous evaluation of multiple rotationally excited states of fluxional molecules. The method employs an expansion of the rotational dependence of the wave function in terms of the eigenstates of the symmetric top Hamiltonian. Within this DMC approach, each walker has a separate rotational state vector for each rotational state of interest. The values of the coefficients in the expansion of the rotational state vector associated with each walker, as well as the locations of the walkers, evolve in imaginary time under the action of a propagator based on the imaginary-time time-dependent Schrödinger equation. The approach is first applied to H3(+), H2D(+), and H3O(+) for which the calculated energies can be compared to benchmark values. For low to moderate values of J the DMC results are found to be accurate to within the evaluated statistical uncertainty. The rotational dependence of the vibrational part of the wave function is also investigated, and significant rotation–vibration interaction is observed. Based on the successful application of this approach to H3(+), H2D(+), and H3O(+), the method was applied to calculations of the rotational energies and wave functions for CH5(+) with v = 0 and J ≤ 10. Based on these calculations, the rotational energy progression is shown to be consistent with that for a nearly spherical top molecule, and little evidence of rotation–vibration interaction is found in the vibrational wave function.

Using fixed-node diffusion Monte Carlo to investigate the effects of rotation-vibration coupling in highly fluxional asymmetric top molecules: Application to H2D+

A fixed-node diffusion Monte Carlo approach for obtaining the energies and wave functions of the rotationally excited states of asymmetric top molecules that undergo large amplitude, zero-point vibrational motions is reported. The nodal surfaces required to introduce rotational excitation into the diffusion Monte Carlo calculations are obtained from the roots of the asymmetric top rigid rotor wave functions calculated using the systems zero-point, vibrationally averaged rotational constants. Using H(2)D(+) as a model system, the overall accuracy of the methodology is tested by comparing to the results of converged variational calculations. The ability of the fixed-node diffusion Monte Carlo approach to provide insights into the nature and strength of the rotation-vibration coupling present in the rotationally excited states of highly fluxional asymmetric tops is discussed. Finally, the sensitivity of the methodology to the details of its implementation, such as the choice of embedding scheme, is explored.

Unraveling rotation-vibration mixing in highly fluxional molecules using diffusion Monte Carlo: applications to H3+ and H3O+.

A thorough examination of the use of fixed-node diffusion Monte Carlo for the study of rotation-vibration mixing in systems that undergo large amplitude vibrational motions is reported. Using H(3)(+) as a model system, the overall accuracy of the method is tested by comparing the results of these calculations with those from converged variational calculations. The effects of the presence of a large amplitude inversion mode on rotation-vibration mixing are considered by comparing the H(3)(+) results with those for H(3)O(+). Finally, analysis of the results of the fixed-node diffusion Monte Carlo calculations performed in different nodal regions is found to provide clear indications of when some of the methodologys underlying assumptions are breaking down as well as provide physical insights into the form of the rotation-vibration coupling that is most likely responsible.