Classical Trajectory Surface Hopping Research Articles

Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry

We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived Gomer-Noyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important state-specific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, cyclic-C(2)H(4)O-->(*)CH(2)CH(2)O(*). This is followed by hopping to the electronic ground state where hot (4000 K) dynamics leads to further reactions, namely, (*)CH(2)CH(2)O()-->CH(3)CHO-->(*)CH(3)+(*)CHO and CH(4)+CO. We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true (S(0),S(1)) conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to approximate a conical intersection in this system.

The triplet channel in the photodissociation of ozone in the Hartley band: Classical trajectory surface hopping analysis

The triplet channel in the photodissociation of ozone in the Hartley band, O3 + hv-->O(3P) + O2(3sigma), is investigated by means of a classical trajectory surface hopping method using ab initio diabatic potential energy surfaces for the B and the R states. Because of the strong recoil in the R state along the breaking O-O bond, O2(3sigma) is produced with a high rotational energy. The nonadiabatic transition probability depends markedly on the coordinate along the crossing seam. As a consequence a unique correlation is found between the internuclear geometry at the crossing and the final vibrational state of O2(3sigma). The calculated distribution of the translational energy is in good accord with the measured distribution.

Theory of dissociative charge exchange in ion-molecule collisions

Dissociative charge exchange is one of the many processes resulting from vibronic transitions in ion-molecule collisions. Its particular interest lies in the molecular breakup that accompanies in specific conditions as electron-transfer process. The available theoretical descriptions of such reactions are surveyed. The salient findings of (i) the classical trajectory surface hopping model, (ii) the high-energy sudden approximation, (iii) the complex local potential, and (iv) the complex local interaction matrix approaches, as well as (v) an unprecedented exact coupled wavepackets description, are put to the fore. Attention is paid to the fundamental concepts conveyed by each treatment and emphasis is put on the relative importance of the various dynamical parameters of the considered reaction.

A comparison of two classical trajectory surface hopping methods for Na(2P)+H2,D2 quenching

Trajectory surface hopping calculations were performed on optimized diatomics-in-molecules surfaces to study Na(2P) collisions with H2 and D2 molecules (v=0, j=1) at four different translational energies (0.039, 0.062, 0.101, and 0.140 eV). Two methods were used to predict surface hopping: (1) transformation of the multidimensional surface intersection to a local one-dimensional curve crossing and calculation of the Landau–Zener transition probability, and (2) integration of the coefficients of the adiabatic electronic states to determine transition probability. For all initial conditions used in this work, we found that method (2) gave significantly larger quenching cross sections. Also in this paper we present results that show nonadiabatic coupling terms calculated by the diatomics-in-molecules method are in good agreement with ab initio values.

Observation of vibrationally resolved charge transfer in H++H2 at ECM=20 eV

The doubly differential cross sections for both the scattered protons and H atoms have been measured at ELAB=30 eV (ECM=20 eV) from θLAB=0° to 12° (θCM=0° to 18°) for the reactions H++H2(v=0)→H++H2(vf) and →H+H+2(vf) . The energy resolution is sufficient to resolve final vibrational states in both channels. The comparison of both the angular and energy loss distributions for the two product channels provides the first clear experimental evidence of a two-step charge transfer mechanism: Vibrational excitation on the lower H++H2 surface is followed by charge transfer in the outgoing collision for only those H2 molecules which are excited vibrationally high enough (vf≥4) to overcome the endoergic barrier (ΔE=1.83 eV). The final vibrational distributions of H+2 appear to be very similar to those of H2 for vf≥4 indicating that for the angular range observed the charge transfer probability is the same for all vibrational states with vf≥4. The comparison with classical trajectory surface hopping (TSH) calculations points to some disagreement which probably can be attributed to the potential surface used.

On the multidimensional surface intersection problem and classical trajectory surface hopping

We comment on a paper [J. R. Stine and J. T. Muckerman, J. Chem. Phys. 65, 3975 (1976)] of the same title. We point out that their attempted reduction of a locally avoided intersection of two potential energy surfaces to a one-dimensional problem is incorrect.

A classical trajectory surface hopping approach to non-adiabatic molecule-surface processes

Scattering processes of diatomic molecules from solid surfaces in which the molecular affinity level crosses the surface Fermi level thus enabling charge transfer back and forth between the metal and molecule are considered here. The nuclei are assumed to move classically on a single model potential energy surface until a diabatic potential energy surface crossing is reached. At such points the trajectory is split into branches, each of which follows a different potential surface. The probability for hopping onto a new potential energy surface or remaining on the initial one is determined within the Landau-Zener-Tully-Preston picture. The phase averaged outgoing vibrational energy as well as the average residence time of the molecular ion resonances have been calculated as a function of the incident kinetic energy treating the off-diagonal matrix element within the Landau-Zener branching probabilities parametrically.

Dynamics of nonadiabatic reactions (theory). I. Branching ratios for early and late seams

The 3D classical trajectory surface hopping (TSH) method has been applied in a ‘‘model’’ study of factors governing nonadiabatic reaction, A+BC→AB+C* and →AB+C. In the diabatic approximation the potential-energy surfaces (pes) were a LEPS surface for F+H2 (→AB+C*) and a repulsive pes Vrep (→AB+C). These intersected in the exit valley to give an early or a late seam (E or L, perpendicular to the exit valley). The splitting at the avoided crossing 2ε was adjusted to ε=1.26 or 5.02 kcal/mol. The ratio of reactive cross sections onto the upper and lower adiabatic pes ρ* was investigated for mass combinations H+HL, L+HL, L+HH, and H+LL with E and L seams, and for small and large ε. The effect on ρ* of reapportioning a constant total energy (ETOT=13.84 kcal/mol) between reagent translation T and vibration V was examined for these 16 cases. Since the velocity in the coordinate of separation increased with increased T (yielding increased product translation; ΔT→ΔT′) ρ* also tended to increase with T. The extreme mass combinations H+HL and L+HH exhibited modified ρ* due to markedly differing widths in the entry and exit valley. The strongly skewed pes for H+LL led to multiple crossing of the seam which reduced ρ*. For other mass combinations ρ* was reduced by the inability of the low T′ component of the product to hop across the 2ε gap. In all cases ρ* was an index of the local dynamics at the seam, and hence shed light on the intermediate motions en route to the asymptotic outcome V′, R′, T′.

Non-adiabatic processes in alkali metal-alkyl halide molecule collisions

The mechanism for vibronic excitation and ion pair production in alkali metal-alkyl halide collisions is investigated. A classical trajectory surface hopping model is developed to account for the fourteen exit channels for which data is available. It is shown that the ground ionic intermediate accounts for the observed A state excitation in CH3I as well as the production of excited alkali atoms. It is further shown that the other, more highly excited, processes can be understood on the basis of an electron harpoon to form one of a sequence of strongly ionic doorway states. Each doorway state connecting to a manifold of exit channels. The nature of these doorway states and the role of vacancy production in their excitation is discussed.

More on the multidimensional surface intersection problem and classical trajectory surface hopping

We respond to the previous Comment by Mead and Truhlar pointing out a circularity in our published analysis of a trajectory passing through a locally avoided intersection of potential energy surfaces in a two state system. We did not distinguish clearly in that analysis between properties of the physical system and those of our model for it. Our ‘‘reduction’’ to a one-dimensional problem is rather a ‘‘mapping’’ onto a one-dimensional model. We present a clearer description of the actual procedures we used to demonstrate that our method is valid for the types of systems to which we have applied it.