Single switch surface hopping for a model of pyrazine

The single switch trajectory surface hopping algorithm is tested for numerical simulations of a two-state three-mode model for the internal conversion of pyrazine through a conical intersection of potential energy surfaces. The algorithm is compared to two other surface hopping approaches, namely, Tully's method of the fewest switches [J. Chem. Phys. 93, 1061 (1990)] and the method by Voronin et al. [J. Phys. Chem. A 102, 6057 (1998)]. The single switch algorithm achieves the most accurate results. Replacing its deterministic nonadiabatic branching condition by a probabilistic accept-reject criterion, one obtains the method of Voronin et al. without momentum adjustment. This probabilistic version of the single switch approach outperforms the considered algorithms in terms of accuracy, memory requirement, and runtime.     

Coherent switching with decay of mixing: an improved treatment of electronic coherence for non-Born-Oppenheimer trajectories

The self-consistent decay-of-mixing (SCDM) semiclassical trajectory method for electronically nonadiabatic dynamics is improved by modifying the switching probability that determines the instantaneous electronic state toward which the system decoheres. This method is called coherent switching with decay of mixing (CSDM), and it differs from the previously presented SCDM method in that the electronic amplitudes controlling the switching of the decoherent state are treated fully coherently in the electronic equations of motion for each complete passage through a strong interaction region. It is tested against accurate quantum mechanical calculations for 12 atom-diatom scattering test cases. Also tested are the SCDM method and the trajectory surface hopping method of Parlant and Gislason that requires coherent passages through each strong interaction region, and which we call the "exact complete passage" trajectory surface hopping (ECP-TSH) method. The results are compared with previously presented results for the fewest switches with time uncertainty and Tully's fewest switches (TFS) surface hopping methods and the semiclassical Ehrenfest method. We find that the CSDM method is the most accurate of the semiclassical trajectory methods tested. Including coherent passages improves the accuracy of the SCDM method (i.e., the CSDM method is more accurate than the SCDM method) but not of the trajectory surface hopping method (i.e., the ECP-TSH method is not more accurate on average than the TFS method).     

A coherent state approach to semiclassical nonadiabatic dynamics

A semiclassical (SC) approximation to the quantum mechanical propagator for nonadiabatic systems is derived. Our derivation starts with an exact path integral expression that uses canonical coherent states for the nuclear degrees of freedom and spin coherent states for the electronic degrees of freedom. A stationary path approximation (SPA) is then applied to the path integral to obtain the SC approximation. The SPA results in complex classical trajectories of both nuclear and electronic degrees of freedom and a double ended boundary condition. The root search problem is solved using the previously proposed "real trajectory local search" algorithm. The SC approximation is tested on three simple one dimensional two-state systems proposed by Tully [J. Chem. Phys. 93, 1061 (1990)], and the SC results are compared to Ehrenfest and surface hopping predictions. Excellent agreement with quantum results is reached when the SC trajectory is far away from caustics. We discuss the origin of caustics in this SC formalism and the strengths and weaknesses of this approach.     

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.     

Simultaneous-trajectory surface hopping: a parameter-free algorithm for implementing decoherence in nonadiabatic dynamics

In this paper, we introduce a trajectory-based nonadiabatic dynamics algorithm which aims to correct the well-known overcoherence problem in Tully's popular fewest-switches surface hopping algorithm. Our simultaneous-trajectory surface hopping algorithm propagates a separate classical trajectory on each energetically accessible adiabatic surface. The divergence of these trajectories generates decoherence, which collapses the particle wavefunction onto a single adiabatic state. Decoherence is implemented without the need for any parameters, either empirical or adjustable. We apply our algorithm to several model problems and find a significant improvement over the traditional algorithm.     

Nonadiabatic quantum dynamics in O(3P)+H2→OH+H: a revisited study

To investigate the extent of nonadiabatic effects in the title reaction, quasi-classical trajectory and nonadiabatic quantum scattering as well as the nonadiabatic quantum-classical trajectory calculations were performed on the accurate ab initio benchmark potential energy surfaces of the lowest (3)A' and (3)A" electronic states [Rogers et al., J Phys Chem A 2000, 104, 2308], together with the spin-orbit coupling matrix [Maiti and Schatz, J Chem Phys 2003, 119, 12360] and the lowest singlet (1) A' potential energy surface [Dobby and Knowles, Faraday Discuss 1998, 110, 247]. Comparison of the calculated total cross sections from both adiabatic and nonadiabatic calculations has demonstrated that for adiabatic channels including (3)A'→(3)A' and (3)A"→(3)A", difference does exist between the two kinds of adiabatic and nonadiabatic calculations, showing nonadiabatic effects to some extent. Such nonadiabatic effects tend to become more conspicuous at high collision energies and are found to be more pronounced with trajectories/quantum wave packet initiated on (3)A' than on (3)A". Furthermore, the present study also showed that nonadiabatic effects can bring the component of forward-scattering in the product angular distributions.     

The role of the excited electronic states in the C+ + H2O reaction

The electronic excited states of the [COH2]+ system have been studied in order to establish their role in the dynamics of the C+ + H2O-->[COH]+ +H reaction, which is a prototypical ion-molecule reaction. The most relevant minima and saddle points of the lowest excited state have been determined and energy profiles for the lowest excited doublet and quartet electronic states have been computed along the fragmentation and isomerization coordinates. Also, nonadiabatic coupling strengths between the ground and the first excited state have been computed where they can be large. Our analysis suggests that the first excited state could play an important role in the generation of the formyl isomer, which has been detected in crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], but could not be explained in quasiclassical trajectory computations [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003); J. R. Flores, J. Chem. Phys. 125, 164309 (2006)].     

Rate constant for OH(2 Pi)+O(3P)-->H(2S)+O2(3 Sigma g-) reaction on an improved ab initio potential energy surface and implications for the interstellar oxygen problem

The authors report a global potential energy surface for the ground electronic state of HO(2)(X (2)A(")), which improves upon the XXZLG potential [Xu and et al., J. Chem. Phys. 122, 244305 (2005)] with additional high-level ab initio points for the long-range interaction potential in the O+OH channel. Exact J=0 quantum mechanical reaction probabilities were calculated on the new potential and the rate constant for the title reaction was obtained using a J-shifting method. The calculated rate constant is in good agreement with available experimental values and our results predict a significantly lower rate at temperature range below 30 K, offering a possible explanation for the "interstellar oxygen problem."     

Broad shape resonance effects in CaF Rydberg states

Results of ab initio R-matrix calculations [S. N. Altunata et al., J. Chem. Phys. 123, 084319 (2005)] indicate the presence of a broad shape resonance in electron-CaF(+) scattering for the (2)Sigma(+) electronic symmetry near the ionization threshold. The properties of this shape resonance are analyzed using the adiabatic partial-wave expansion of the scattered electron wave function introduced by Le Dourneuf et al. [J. Phys. B 15, L685 (1982)]. The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion. Mulliken's rule for the structure of the Rydberg state wave functions [R. S. Mulliken, J. Am. Chem. Soc. 86, 3183 (1964)] specifies that, except for an (n*)(-32) amplitude scale factor, every excited state wave function within one Rydberg series is built on an innermost lobe that remains invariant in shape and nodal position as a function of the excitation energy. Mulliken's rule implies a weak energy dependence of the quantum defects for an unperturbed molecular Rydberg series, which is given by the Rydberg-Ritz formula. This zero-order picture is violated by a single (2)Sigma(+) CaF Rydberg series at all Rydberg state energies (n*=5-->infinity, more so with increasing n*) below the ionization threshold, under the broad width of the shape resonance. Such a violation is diagnostic of a global "scarring" of the Rydberg spectrum, which is distinct from the more familiar local level perturbations.     

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.     

Real wave packet and quasiclassical trajectory studies of the H+ + LiH reaction

Time-dependent real wave packet (RWP) and quasiclassical trajectory (QCT) calculations have been carried out to study the H(+) + LiH reaction on the ab initio potential-energy surface of Martinazzo et al. [J. Chem. Phys., 2003, 119, 11241]. Total initial state-selected and final state-resolved reaction probabilities for the two possible reaction channels, H(2)(+) + Li and LiH + H(+), have been calculated for total angular momentum J=0 at a broad range of collision energies. Integral cross sections and thermal rate coefficients have been calculated using the QCT method and from the corresponding J=0 RWP reaction probabilities by means of a capture model. The calculated thermal rate coefficients are found to be nearly independent of temperature in the 100-500 K interval with a value of approximately 10(-9) cm(3) s(-1), which is in good agreement with estimates used in evolutionary models of early-Universe lithium chemistry. The RWP results are found to be in good agreement overall with the corresponding QCT calculations.     

Quasiclassical trajectories on a finite element density functional potential energy surface: The C++H2O reaction revisited

A new method for the representation of potential energy surfaces (PESs) based on the p version of the finite element method is presented and applied to the PES of the [COH2]+ system in order to study the C++H2O-->[COH]++H reaction through the quasiclassical trajectory method. Benchmark ab initio computations have been performed on the most relevant stationary points of the PES through a procedure that incorporates basis set extrapolations, the contribution of the core correlation energy, and scalar relativistic corrections. The electronic structure method employed to compute the many points needed to construct the PES is a hybrid density functional approach of the B3LYP type with geometry-dependent parameters, which improves dramatically the performance with respect of the B3LYP method. The trajectory computations shed light on the behavior of the COH2+ complex formed in the collision. At a fixed relative translational energy of 0.62 eV, which corresponds to the crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], the complex dissociates significantly into the reactants (37%). However, the behavior for a thermal sampling at T=300 K is significantly different because only 9% of the trajectories where capture occurs lead to dissociation into the reactants. The latter kind of behavior is coherent with the view that simple ion-molecule reactions proceed quite often at the capture rate provided it is corrected by the fraction of the electronic states which, being nearly degenerate for the reactants, become attractive at short distances. For both T=300 K and crossed beam conditions, the trajectory computations indicate that COH2+ is the critical intermediate, in agreement with a recent work [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003)] and in contrast with the interpretation of the crossed beam experiments. Besides, virtually all trajectories generate COH++H (>99%), but a significant proportion of the isoformyl cation is formed with enough vibrational energy as to surmount the COH+-HCO+ isomerization barrier, about 37% at T=300 K.     

Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies

We report quantum wave packet calculations of state-to-state reaction probabilities and cross sections for the reaction H+H(2)(v(0)=0,j(0)=0)-->H(2)(v,j)+H, at total energies up to 4.5 eV above the ground state potential minimum. The calculations are repeated using (i) the ground electronic state only, (ii) the ground state plus the diagonal non-Born-Oppenheimer correction, (iii) the ground state, diagonal non-Born-Oppenheimer correction and geometric phase (GP), and (iv) both electronic states including all nonadiabatic couplings, using the diabatic potential approach of Mahapatra et al. [J. Phys. Chem. A 105, 2321 (2001)]. The results for calculations (iii) and (iv) are in very close agreement, showing that the upper electronic state makes only a very small contribution to the state-to-state dynamics, even at energies much higher than the conical intersection minimum (at 2.74 eV). At total energies above 3.5 eV, many of the state-to-state reaction probabilities show strong GP effects, indicating that they are dominated by interference between one- and two-transition-state (1-TS and 2-TS) reaction paths. These effects survive the coherent sum over partial waves to produce features in the state-to-state differential cross sections which could be detected in an experiment with an angular resolution of approximately 20 degrees . Efficient dephasing of the interference between the 1-TS and 2-TS contributions causes almost complete cancellation of the GP in the integral cross sections, thus continuing a trend observed at lower energies in earlier work.     

Quantum wave packet dynamics of N(2D)+H2 reaction

The quantum wave packet dynamics of the title reaction within the coupled state approximation is examined here and initial state-selected reaction probabilities, integral reaction cross sections, and thermal rate constants are reported. The ab initio potential energy surface of the electronic ground state (1(2)A(")) of the system recently reported by Ho et al. [J. Chem. Phys., 119, 3063 (2003)] is employed in this investigation. All partial wave contributions up to the total angular momentum J=55 were necessary to obtain converged integral reaction cross sections up to a collision energy of 1.0 eV. Thermal rate constants are calculated from the reaction cross sections and compared with the available theoretical and experimental results. Typical resonances formed during the course of the reaction and elucidating the insertion type mechanism for the product formation are calculated. Vibrational energy levels supported by the deep well (approximately 5.5 eV) of the 1(2)A(") potential energy surface of NH(2) are also calculated for the total angular momentum J=0. A statistical analysis of the spacing between the adjacent levels of this energy spectrum is performed and the extent of irregularity in the spectral sequence is assessed.     

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.     

Quasiclassical trajectory study of the reaction H+CH4(nu3 = 0,1)-->CH3+H2 using a new ab initio potential energy surface

Detailed quasiclassical trajectory calculations of the reaction H+CH4(nu3 = 0,1)-->CH3 + H2 using a slightly updated version of a recent ab initio-based CH5 potential energy surface [X. Zhang et al., J. Chem. Phys. 124, 021104 (2006)] are reported. The reaction cross sections are calculated at initial relative translational energies of 1.52, 1.85, and 2.20 eV in order to make direct comparison with experiment. The relative reaction cross section enhancement ratio due to the excitation of the C-H antisymmetric stretch varies from 2.2 to 3.0 over this energy range, in good agreement with the experimental result of 3.0 +/- 1.5 [J. P. Camden et al., J. Chem. Phys. 123, 134301 (2005)]. The laboratory-frame speed and center-of-mass angular distributions of CH3 are calculated as are the vibrational and rotational distributions of H2 and CH3. We confirm that this reaction occurs with a combination of stripping and rebound mechanisms by presenting the impact parameter dependence of these distributions and also by direct examination of trajectories.     

Photo-induced desorption of NO from NiO(100): calculation of the four-dimensional potential energy surfaces and systematic wave packet studies

The velocity distributions of the laser-induced desorption of NO molecules from an epitaxially grown film of NiO(100) on Ni(100) have been studied [Mull et al., J. Chem. Phys., 1992, 96, 7108]. A pronounced bimodality of velocity distributions has been found, where the NO molecules desorbing with higher velocities exhibit a coupling to the rotational quantum states J. In this article we present simulations of state resolved velocity distributions on a full ab initio level. As a basis for this quantum mechanical treatment a 4D potential energy surface (PES) was constructed for the electronic ground and a representative excited state, using a NiO5Mg(18+)13 cluster. The PESs of the electronic ground and an excited state were calculated at the CASPT2 and the configuration interaction (CI) level of theory, respectively. Multi-dimensional quantum wave packet simulations on these two surfaces were performed for different sets of degrees of freedom. Our key finding is that at least a 3D wave packet simulation, in which the desorption coordinate Z, polar angle theta and lateral coordinate X are included, is necessary to allow the simulation of experimental velocity distributions. Analysis of the wave packet dynamics demonstrates that essentially the lateral coordinate, which was neglected in previous studies [Klüner et al., Phys. Rev. Lett. 1998, 80, 5208], is responsible for the experimentally observed bimodality. An extensive analysis shows that the bimodality is due to a bifurcation of the wave packet on the excited state PES, where the motion of the molecule parallel to the surface plays a decisive role.     

Portably parallel construction of a configuration-interaction wave function from a matrix–product state using the Charm++ framework

The construction of configuration-interaction (CI) expansions from a matrix product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations in a large Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS employing the parallel object-oriented Charm++ programming framework, upon which automatic load-balancing and object migrating facilities can be employed. This procedure was employed in the MPS-to-CI utility (Moritz et al., J. Chem. Phys. 2007, 126, 224109), the sampling-reconstructed complete active-space algorithm (SR-CAS, Boguslawski et al., J. Chem. Phys. 2011, 134, 224101), and the entanglement-driven genetic algorithm (EDGA, Luo et al., J. Chem. Theory Comput. 2017, 13, 4699). It enhances productivity and allows the sampling programs to evolve to their population-expansion versions, for example, EDGA with population expansion (PE-EDGA). Further, examples of 1,2-dioxetanone and firefly dioxetanone anion (FDO⁻) molecules demonstrated the following: (a) parallel efficiencies can be persistently improved by simply by increasing the proportions of the asynchronous executions and (b) a sampled CAS-type CI wave function of a bi-radical-state FDO⁻ molecule utilizing the full valence (30e,26o) active space can be constructed within a few hours with using thousands of cores.