Ahren W. Jasper

Fewest-switches with time uncertainty: A modified trajectory surface-hopping algorithm with better accuracy for classically forbidden electronic transitions

We present a modification of Tully’s fewest-switches (TFS) trajectory surface-hopping algorithm (also called molecular dynamics with quantum transitions) that is called the fewest-switches with time uncertainty (FSTU) method. The FSTU method improves the self-consistency of the fewest-switches algorithm by incorporating quantum uncertainty into the hopping times of classically forbidden hops. This uncertainty allows an electronic transition that is classically forbidden at some geometry to occur by hopping at a nearby classically allowed geometry if an allowed hopping point is reachable within the Heisenberg interval of time uncertainty. The increased accuracy of the FSTU method is verified using a challenging set of three-body, two-state test cases for which accurate quantum-mechanical results are available. The FSTU method is shown to be more accurate than the TFS method in predicting total nonadiabatic quenching probabilities and product branching ratios.

Non-Born-Oppenheimer trajectories with self-consistent decay of mixing

A semiclassical trajectory method, called the self-consistent decay of mixing (SCDM) method, is presented for the treatment of electronically nonadiabatic dynamics. The SCDM method is a modification of the semiclassical Ehrenfest (SE) method (also called the semiclassical time-dependent self-consistent-field method) that solves the problem of unphysical mixed final states by including decay-of-mixing terms in the equations for the evolution of the electronic state populations. These terms generate a force, called the decoherent force (or dephasing force), that drives the electronic component of each trajectory toward a pure state. Results for several mixed quantum-classical methods, in particular the SCDM, SE, and natural-decay-of-mixing methods and several trajectory surface hopping methods, are compared to the results of accurate quantum mechanical calculations for 12 cases involving five different fully dimensional triatomic model systems. The SCDM method is found to be the most accurate of the methods tested. The method should be useful for the simulation of photochemical reactions.

The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations

A family of four weakly coupled electronically nonadiabatic bimolecular model photochemical systems is presented. Fully converged quantum mechanical calculations with up to 25 269 basis functions were performed for full-dimensional atom–diatom collisions to determine the accurate scattering dynamics for each of the four systems. The quantum mechanical probabilities for electronically nonadiabatic reaction and for nonreactive electronic deexcitation vary from 10−1 to 10−5. Tully’s fewest-switches (TFS) semiclassical trajectory surface-hopping method (also called molecular dynamics with quantum transitions or MDQT) is tested against the accurate quantal results. The nonadiabatic reaction and nonreactive deexcitation events are found to be highly classically forbidden for these systems, which were specifically designed to model classically forbidden electronic transitions (also called frustrated hops). The TFS method is shown to systematically overestimate the nonadiabatic transition probabilities due to the...

Nitrous Oxide Dimer: A New Potential Energy Surface and Rovibrational Spectrum of the Nonpolar Isomer

The spectrum of nitrous oxide dimer was investigated by constructing new potential energy surfaces using coupled-cluster theory and solving the rovibrational Schrödinger equation with a Lanczos algorithm. Two four-dimensional (rigid monomer) global ab initio potential energy surfaces (PESs) were made using an interpolating moving least-squares (IMLS) fitting procedure specialized to describe the interaction of two linear fragments. The first exploratory fit was made from 1646 CCSD(T)/3ZaP energies. Isomeric minima and connecting transition structures were located on the fitted surface, and the energies of those geometries were benchmarked using complete basis set (CBS) extrapolations, counterpoise (CP) corrections, and explicitly correlated (F12b) methods. At the geometries tested, the explicitly correlated F12b method produced energies in close agreement with the estimated CBS limit. A second fit to 1757 data at the CCSD(T)-F12b/VTZ-F12 level was constructed with an estimated fitting error of less than 1.5 cm(-1). The second surface has a global nonpolar O-in minimum, two T-shaped N-in minima, and two polar minima. Barriers between these minima are small and some wave functions have amplitudes in several wells. Low-lying rovibrational wave functions and energy levels up to about 150 cm(-1) were computed on the F12b PES using a discrete variable representation/finite basis representation method. Calculated rotational constants and intermolecular frequencies are in very close agreement with experiment.

Predictive a priori pressure-dependent kinetics.

The ability to predict the pressure dependence of chemical reaction rates would be a great boon to kinetic modeling of processes such as combustion and atmospheric chemistry. This pressure dependence is intimately related to the rate of collision-induced transitions in energy E and angular momentum J. We present a scheme for predicting this pressure dependence based on coupling trajectory-based determinations of moments of the E,J-resolved collisional transfer rates with the two-dimensional master equation. This completely a priori procedure provides a means for proceeding beyond the empiricism of prior work. The requisite microcanonical dissociation rates are obtained from ab initio transition state theory. Predictions for the CH4 = CH3 + H and C2H3 = C2H2 + H reaction systems are in excellent agreement with experiment. A purely theoretical method for predicting gas-phase chemical reaction rates shows strong agreement with experiment. [Also see Perspective by Pilling] Theoretical chemistry can withstand the pressure Theoretical methods can predict the chemical consequences of a discrete molecular collision in exquisite detail. However, practical chemistry, whether in a flame, in Earths atmosphere, or in an industrial reactor, involves billions of trillions of such collisions. Predicting the aggregate reaction rate requires an accurate means of treating the pressure dependence. Jasper et al. present such a method, which shows strong agreement with experimental measurements (see the Perspective by Pilling). Unlike past approaches that require parameters derived from empirical fits to data, the new technique relies strictly on simulations. Science, this issue p. 1212; see also p. 1183

Improved treatment of momentum at classically forbidden electronic transitions in trajectory surface hopping calculations

Abstract We present a new prescription (called the ∇ V prescription) for treating classically forbidden surface hops in semiclassical trajectory surface hopping simulations. The new method uses gradient information about the target electronic surface to determine the nuclear dynamics at a frustrated hopping event. We have tested this prescription, along with previously suggested prescriptions, against accurate quantum dynamics for 21 cases. We find that the fewest switches with time uncertainty (FSTU) algorithm with the ∇ V prescription for momentum changes at frustrated hops is the most accurate of the six variants of the surface hopping approach that we tested.

Electronic decoherence time for non-Born-Oppenheimer trajectories.

An expression is obtained for the electronic decoherence time of the reduced density electronic matrix in mixed quantum-classical molecular-dynamics simulations. The result is obtained by assuming that decoherence is dominated by the time dependence of the overlap of minimum-uncertainty packets and then maximizing the rate with respect to the parameters of the wave packets. The expression for the decay time involves quantities readily available in non-Born-Oppenheimer molecular-dynamics simulations, and it is shown to have a reasonable form when compared with two other formulas for the decay time that have been previously proposed.

Detection and Identification of the Keto-Hydroperoxide (HOOCH2OCHO) and other Intermediates during Low-Temperature Oxidation of Dimethyl Ether

In this paper we report the detection and identification of the keto-hydroperoxide (hydroperoxymethyl formate, HPMF, HOOCH2OCHO) and other partially oxidized intermediate species arising from the low-temperature (540 K) oxidation of dimethyl ether (DME). These observations were made possible by coupling a jet-stirred reactor with molecular-beam sampling capabilities, operated near atmospheric pressure, to a reflectron time-of-flight mass spectrometer that employs single-photon ionization via tunable synchrotron-generated vacuum-ultraviolet radiation. On the basis of experimentally observed ionization thresholds and fragmentation appearance energies, interpreted with the aid of ab initio calculations, we have identified HPMF and its conceivable decomposition products HC(O)O(O)CH (formic acid anhydride), HC(O)OOH (performic acid), and HOC(O)OH (carbonic acid). Other intermediates that were detected and identified include HC(O)OCH3 (methyl formate), cycl-CH2-O-CH2-O- (1,3-dioxetane), CH3OOH (methyl hydroperoxide), HC(O)OH (formic acid), and H2O2 (hydrogen peroxide). We show that the theoretical characterization of multiple conformeric structures of some intermediates is required when interpreting the experimentally observed ionization thresholds, and a simple method is presented for estimating the importance of multiple conformers at the estimated temperature (∼100 K) of the present molecular beam. We also discuss possible formation pathways of the detected species: for example, supported by potential energy surface calculations, we show that performic acid may be a minor channel of the O2 + ĊH2OCH2OOH reaction, resulting from the decomposition of the HOOCH2OĊHOOH intermediate, which predominantly leads to the HPMF.

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10(-8). For such low-probability events the anteater sampling scheme requires a large number of trajectories ( approximately 10(10)) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10(5) trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm.

Identification of tetrahydrofuran reaction pathways in premixed flames

Abstract Premixed low-pressure tetrahydrofuran/oxygen/argon flames are investigated by photoionization molecular-beam mass spectrometry using vacuum-ultraviolet synchrotron radiation. For two equivalence ratios (φ = 1.00 and 1.75), mole fractions are measured as a function of distance from the burner for almost 60 intermediates with molar masses ranging from 2 (H2) to 88 (C4H6O2), providing a broad database for flame modeling studies. The isomeric composition is resolved by comparisons between experimental photoionization efficiency data and theoretical simulations, based on calculated ionization energies and Franck-Condon factors. Special emphasis is put on the resolution of the first reaction steps in the fuel destruction. The photoionization experiments are complemented by electron-ionization molecular-beam mass-spectrometry measurements that provide data with high mass resolution. For three additional flames with intermediate equivalence ratios (φ = 1.20, 1.40 and 1.60), mole fractions of major species and photoionization efficiency spectra of intermediate species are reported, extending the database for the development of chemical kinetic models.