Trajectory Surface Hopping Method Research Articles

Nonadiabatic dynamics and photoisomerization of biomimetic photoswitches

N-alkylated indanylidene pyrroline Schiff bases (NAIPs) are of great interest because their photoisomerization mimics the primary photoreactions of the retinal chromophore in rhodopsin. The nonadiabatic dynamics of two NAIP models (OMe-NAIP and dMe-OMe-NAIP) are investigated by trajectory surface-hopping method at the semi-empirical OM2/MRCI level. Both molecules show ultrafast isomerization governed by nonadiabatic dynamics via the S0/S1 conical intersections (CIs). Two CIs, CIα and CIβ, play important roles in the E→Z and Z→E isomerization dynamics, respectively, and are mainly distinguished by different twisting statuses of the central C1′–C4 double bond. Although both compounds show ultrafast nonadiabatic dynamics, the S1 lifetime of dMe-OMe-NAIP is much longer than that of OMe-NAIP. By removing the methyl group, dMe-OMe-NAIP allows less twist at the C1′–C4 double bond than OMe-NAIP. This result in the slower excited-state decay of dMe-OMe-NAIP, providing solid evidence to support a similar hypothesis proposed in a previous study.

Application of particle-mesh Ewald summation to ONIOM theory

We extended a particle mesh Ewald (PME) summation method to the ONIOM (our Own N-layered Integrated molecular Orbitals and molecular Mechanics) scheme (PME-ONIOM) to validate the simulation in solution. This took the form of a nonadiabatic ab initio molecular dynamics (MD) simulation in which the Zhu-Nakamura trajectory surface hopping (ZN-TSH) method was performed for the photoisomerization of a (Z)-penta-2,4-dieniminium cation (protonated Schiff base, PSB3) electronically excited to the S1 state in a methanol solution. We also calculated a nonadiabatic ab initio MD simulation with only minimum image convention (MI-ONIOM). The lifetime determined by PME-ONIOM-MD was 3.483ps. The MI-ONIOM-MD lifetime of 0.4642ps was much shorter than those of PME-ONIOM-MD and the experimentally determined excited state lifetime. The difference eminently illustrated the accurate treatment of the long-range solvation effect, which destines the electronically excited PSB3 for staying in S1 at the pico-second or the femto-second time scale.

Nonadiabatic transition state theory and trajectory surface hopping dynamics: intersystem crossing between (3)B1 and (1)A1 states of SiH2.

The ability of time-independent nonadiabatic transition state theory (NA-TST) to reproduce intersystem crossing dynamics obtained from the more computationally demanding Tully fewest switches trajectory surface hopping method is investigated. The two approaches are applied to the intersystem crossing between the ground (1)A1 state and lowest energy (3)B1 state of SiH2, coupled through the spin-orbit interaction. For NA-TST, the transition probabilities are calculated using the Landau-Zener formula and the Delos formula which accounts for tunneling. The fewest switches method produces rate constants of 7.6 × 10(11) s(-1) for the triplet to singlet transition and 5.2 × 10(11) s(-1) for the singlet to triplet transition, using a first-order kinetics model. This corresponds to a triplet electronic state lifetime of 781 fs. The NA-TST predicted rate constants are 1-2 orders of magnitude smaller, leading to a larger triplet state lifetime, as compared with the fewest switches method. This discrepancy cannot be explained by the difference in transition probabilities obtained from NA-TST and fewest switches molecular dynamics, and it is believed to be a result of the NA-TST semilocal description of nonadiabatic transitions in the vicinity of the intersystem crossing. Also, the larger triplet state lifetime obtained from NA-TST could be a result of the quantum sampling of rovibrational states, which is missing in classical trajectories traversing the crossing seam.

The Theoretical Estimation of the Bioluminescent Efficiency of the Firefly via a Nonadiabatic Molecular Dynamics Simulation.

The firefly is famous for its high bioluminescent efficiency, which has attracted both scientific and public attention. The chemical origin of firefly bioluminescence is the thermolysis of the firefly dioxetanone anion (FDO(-)). Although considerable theoretical research has been conducted, and several mechanisms were proposed to elucidate the high efficiency of the chemi- and bioluminescence of FDO(-), there is a lack of direct experimental and theoretical evidence. For the first time, we performed a nonadiabatic molecular dynamics simulation on the chemiluminescent decomposition of FDO(-) under the framework of the trajectory surface hopping (TSH) method and theoretically estimated the chemiluminescent quantum yield. The TSH simulation reproduced the gradually reversible charge-transfer initiated luminescence mechanism proposed in our previous study. More importantly, the current study, for the first time, predicted the bioluminescence efficiency of the firefly from a theoretical viewpoint, and the theoretical prediction efficiency is in good agreement with experimental measurements.

On the FCNS ⇆ FC(NS) reaction: A matrix isolation and theoretical study

The FCNS⇆FC(NS) photoisomerization process is a simple model system for molecular switches. Here, we examined the switching processes by experimental and theoretical methods. Prior matrix-isolation IR spectroscopic studies were complemented by matrix-isolation UV spectroscopic measurements to assist the interpretation of the mechanism of the ring closure and opening processes and to verify the accuracy of the computations on the vertical excitation energies. Vertical excitation energies were computed by the EOMEE-CCSD, MCSCF, and MR-CISD methods. Conical intersections were also searched for and three conical intersections along the reaction path FCNS→FC(NS) were located, one conical intersection between the 2A′ and 1A″ state, one between the 1A″ and 1A′ state and one where all three states intersect. The ring opening and closing processes were simulated by non-adiabatic dynamics propagation with the trajectory surface hopping method. The combined computational and experimental results suggest that upon 365nm irradiationthe ring closure FCNS→FC(NS) occurs under participation of all three conical intersections, while 254nm irradiation causes ring opening FC(NS)→FCNS. Both processes, especially the ring opening, are accompanied by fragmentation into FCN+S.

Second-quantized surface hopping.

The trajectory surface hopping method for quantum dynamics is reformulated in the space of many-particle states to include entanglement and correlation of trajectories. Used to describe many-body correlation effects in electronic structure theories, second quantization is applied to semiclassical trajectories. The new method allows coupling between individual trajectories via energy flow and common phase evolution. It captures the properties of a wave packet, such as branching, Heisenberg uncertainty, and decoherence. Applied to a superexchange process, the method shows very accurate results, comparable to exact quantum data and improving greatly on the standard approach.

Generalized trajectory surface-hopping method for internal conversion and intersystem crossing.

Trajectory-based fewest-switches surface-hopping (FSSH) dynamics simulations have become a popular and reliable theoretical tool to simulate nonadiabatic photophysical and photochemical processes. Most available FSSH methods model internal conversion. We present a generalized trajectory surface-hopping (GTSH) method for simulating both internal conversion and intersystem crossing processes on an equal footing. We consider hops between adiabatic eigenstates of the non-relativistic electronic Hamiltonian (pure spin states), which is appropriate for sufficiently small spin-orbit coupling. This choice allows us to make maximum use of existing electronic structure programs and to minimize the changes to available implementations of the traditional FSSH method. The GTSH method is formulated within the quantum mechanics (QM)/molecular mechanics framework, but can of course also be applied at the pure QM level. The algorithm implemented in the GTSH code is specified step by step. As an initial GTSH application, we report simulations of the nonadiabatic processes in the lowest four electronic states (S0, S1, T1, and T2) of acrolein both in vacuo and in acetonitrile solution, in which the acrolein molecule is treated at the ab initio complete-active-space self-consistent-field level. These dynamics simulations provide detailed mechanistic insight by identifying and characterizing two nonadiabatic routes to the lowest triplet state, namely, direct S1 → T1 hopping as major pathway and sequential S1 → T2 → T1 hopping as minor pathway, with the T2 state acting as a relay state. They illustrate the potential of the GTSH approach to explore photoinduced processes in complex systems, in which intersystem crossing plays an important role.

Nonadiabatic molecular dynamics simulation: An approach based on quantum measurement picture

Mixed-quantum-classical molecular dynamics simulation implies an effective quantum measurement on the electronic states by the classical motion of atoms. Based on this insight, we propose a quantum trajectory mean-field approach for nonadiabatic molecular dynamics simulations. The new protocol provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also bridges two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. Excellent agreement with the exact results is illustrated with representative model systems, including the challenging ones for traditional methods.

Electronic Quenching in N((2)D) + N2 Collisions: A State-Specific Analysis via Surface Hopping Dynamics.

The electronic quenching reaction N((2)D) + N2 → N((4)S) + N2 is studied using the trajectory surface hopping method and employing two doublet and one quartet accurate potential energy surfaces. State-specific properties are analyzed, such as the dependence of the cross section on the initial quantum state of the reactants, vibrational energy transfer, and rovibrational distribution of the product N2 molecule in thermalized conditions. It is found that rotational energy on the reactant N2 molecule is effective in promoting the reaction, whereas vibrational excitation tends to reduce the reaction probability. For initial states and collision energy thermalized in an initial bath, it is found that the products are "hotter", both vibration and rotation wise.

Acetamide as the model of the peptide bond: Nonadiabatic photodynamical simulations in the gas phase and in the argon matrix

The short-time photodynamics of acetamide in the gas phase and in the Ar-matrix starting from the first excited singlet S1 (n–π*) and S2 (π–π*) states was explored by the direct trajectory surface hopping method based on multiconfigurational ab initio calculations. For the n–π* state effect of embedding into Ar matrix employing hybrid QM/MM approach on the lifetime and dissociation paths was also discussed. The calculations show that nonadiabatic deactivation from the S1 to the ground state occurs within 785fs via the crossing seam related to the CN bond stretching MXS. The major products in the gas phase are NH2+CH3CO radicals which partially undergo further dissociation of the CH3CO or recombination to the parent molecule. The embedding of the molecule in the Ar matrix considerably suppresses the CN dissociation and prevents dissociation of the CH3CO radical.

Trajectory surface hopping study of the O((3)P) + C2H2 reaction dynamics: effect of collision energy on the extent of intersystem crossing.

Intersystem crossing (ISC) dynamics plays an important role in determining the product branching in the O((3)P) + C2H2 reaction despite the necessarily small spin-orbit coupling constant values. In this study we investigate the effect of collision energy on the extent of the contribution of a spin non-conserving route through ISC dynamics to the product distributions at the initial collision energies 8.2, 9.5, and 13.1 kcal/mol. A direct dynamics trajectory surface hopping method is employed with potential energy surfaces generated at the unrestricted B3LYP/6-31G(d,p) level of theory to perform nonadiabatic dynamics. To make our calculation simpler, nonadibatic transitions were only considered at the triplet-singlet intersections. At the crossing points, Landau-Zener transition probabilities were calculated using spin-orbit coupling constant values computed at the same geometry. The Landau-Zener model for the title reaction is validated against a more rigorous Tully's fewest switches method and found to be working reasonably well as expected because of weak spin-orbit coupling. We have compared our results with the recent crossed molecular beam experiments and observed a very good agreement with respect to the primary product branching ratios. Our calculation revealed that there is no noticeable effect of the initial collision energy on the overall product distributions that corroborates the recent experimental findings. Our calculation indicates, however, that the extent of intersystem crossing contributions varies significantly with collision energy, needed to be verified, experimentally.

Constraint Trajectory Surface-Hopping Molecular Dynamics Simulation of the Photoisomerization of Stilbene

Combining trajectory surface hopping (TSH) method with constraint molecular dynamics, we have extended TSH method from full to flexible dimensional potential energy surfaces. Classical trajectories are carried out in Cartesian coordinates with constraints in internal coordinates, while nonadiabatic switching probabilities are calculated separately in free internal coordinates by Landau-Zener and Zhu-Nakamura formulas along the seam. Two-dimensional potential energy surfaces of groundS0and excitedS1states are constructed analytically in terms of torsion angle and one dihedral angle around the central ethylenic C=C bond, and the other internal coordinates are all fixed at configuration of the conical intersection. At this conical intersection, the branching ratio from the present simulation is 48 : 52 (33 : 67) initially starting from trans(cis)-Stilbene in comparison with experimental value 50 : 50. Quantum yield for trans-to-cis isomerization is estimated as 49% in very good agreement with experimental value of 55%, while quantum yield for cis-to-trans isomerization is estimated as 47% in comparison with experimental value of 35%.

Electronic Quenching of N(2D) by N2: Theoretical Predictions, Comparison with Experimental Rate Constants, and Impact on Atmospheric Modeling

Rate constants for the electronic quenching reaction N(2D) + N2 → N(4S) + N2 are calculated for temperatures over the range of 240 ≤ T/K ≤ 1000 using an accurate set of three global electronic potential energy surfaces for the N3 system (4A″,2A′, and 2A″). The nuclear motion is treated by running quasiclassical trajectories, incorporating spin-forbidden transitions with the trajectory surface hopping method. The exclusively theoretical results are compared with available experimental data for the reaction and contribute to clarify the discrepancies among them. The rate constants at higher temperatures achieved in the atmosphere, for which no experiments have been performed, are presented for the first time. The impact of the results in atmospheric modeling is analyzed, predicting at what altitudes this reaction will play an important role.

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

Photochemical dynamics of indolylmaleimide derivatives

On-the-fly nonadiabatic ab initio molecular dynamics simulations have been carried out for three anionic species of indolylmaleimides (3-(1H-3-indolyl)-2,5-dihydro-1H-2,5-pyrroledione, IM) to clarify the mechanisms of photochemical reactions. The results are obtained for (i) a monovalent anion with a deprotonated indole NH group (IM(-)'), (ii) a monovalent anion with a deprotonated maleimide NH group (IM(-)'') and (iii) a divalent anion with doubly deprotonated indole and the maleimide NH groups (IM(2-)). Quantum chemical calculations are treated at the three state averaged complete-active space self-consistent field level for 6 electrons in 5 orbitals with the cc-pVDZ basis set (CAS (6, 5) SCF/cc-pVDZ). Molecular dynamics simulations are performed with electronically nonadiabatic transitions included using the Zhu-Nakamura version of the trajectory surface hopping (ZN-TSH) method. It is found that the nonadiabatic transitions occur accompanied by the stretching and shrinking motions of the N(7)-C(8) bond in the case of IM(-)' and the C(11)-N(12) bond in IM(2-) rather than the twisting motion of the dihedral angle. We also found that the ultrafast S(2)→ S(1) nonadiabatic transitions occur through the conical intersection (CoIn) right after photoexcitation to S(2) in IM(-)' and IM(2-). Furthermore, the S(1)→ S(0) nonadiabatic transitions are found to take place in IM(-)'. It is concluded that IM(2-) would mainly contribute to the photoemission, because the S(1)← S(0) and S(2)← S(0) transitions of IM(-)'' are dipole-forbidden transitions and, moreover, IM(2-) is found to be the only species to stay in the S(1) state without non-radiative decay.

New Implementation of Semi-classical Dynamic Simulation on the Photoisomerization ofcis- and trans-Isomers of Free Stilbene

New implementation of semi-classical trajectory surface hopping dynamic simulation has been developed and applied to the photoisomerization of cis- and trans- isomers on the gas phase. This method not only uses the exponential model to the modification of the originally analytical non-adiabatic transition probability formula, but also involves the con- strained Hamiltonian system into the constrained molecular dynamic simulation. Two-dimensional potential energy surfaces of ground S0 and excited S1 states are constructed analytically fitting to ab initio calculations in terms of torsion angle and one dihedral angle around the central ethylenic C=C bond as variables, and the other internal coordinates are all fixed at configuration of one-bond flip conical intersection. The analytical PESs are quite accurate and the mean absolute error is less than 2.4 kcalmol -1 , and much less than 1.0 kcalmol -1 around conical intersection region. A straight seam line is found on potential energy surfaces that simply separates the cis-area with the trans-area. The constrained Hamiltonian system is em- ployed to run trajectories in the Cartesian coordinate system and surface hopping in terms of the two internal dihedral angles. Typical trajectories are found in which the torsion angle changes monotonically for both cis- to trans- and trans- to cis- isomerizations. This is an exact picture of one-bond flip mechanism of photoisomerization around the conical intersection. Quantum yield for trans- to cis- isomerization is simulated as 60.45% in very good agreement with experimental value 55.0%, while quantum yield for cis- to trans- isomerization is simulated as 42.3% in comparison with experimental value 35.0%. As the S1 energy in local minimum of cis-area is higher than that in trans-area, and thus cis- to trans- isomerization is quite possible to access to another Hula-Twist conical intersection. These simulation results demonstrate that the computed cumulative quantum yield and reaction mechanism are consistent with the previously experimental and theoretical results. This means that the present trajectory surface hopping method would be good at the dynamic simulation on the large system with or without constraint Hamiltonian in comparison with the quantum molecular dynamics. Keywords new implementation of semi-classical dynamic simulation; constrained Hamiltonian system; Zhu-Nakamura theory; isomerization of cis- and trans-stilbene; two dimensional analytical potential energy surfaces

Local control theory in trajectory-based nonadiabatic dynamics

In this paper, we extend the implementation of nonadiabatic molecular dynamics within the framework of time-dependent density-functional theory in an external field described in Tavernelli et al. [Phys. Rev. A 81, 052508 (2010)] by calculating on-the-fly pulses to control the population transfer between electronic states using local control theory. Using Tully's fewest switches trajectory surface hopping method, we perform MD to control the photoexcitation of LiF and compare the results to quantum dynamics (QD) calculations performed within the Heidelberg multiconfiguration time-dependent Hartree package. We show that this approach is able to calculate a field that controls the population transfer between electronic states. The calculated field is in good agreement with that obtained from QD, and the differences that arise are discussed in detail.

Nonadiabatic dynamics with trajectory surface hopping method

AbstractThe trajectory surface hopping (TSH) method is a general methodology for dynamics propagation of nonadiabatic systems. It is based on the hypothesis that the time evolution of a wave packet through a potential‐energy branching region can be approximated by an ensemble of independent semiclassical trajectories stochastically distributed among the branched surfaces. As it was proposed about 40 years ago, the TSH methodology has become one of the main tools for nonadiabatic dynamics propagation in molecular physics and chemistry. One reason for this success lies on its intuitive conceptual background allied to its high computational efficiency when compared to full quantum mechanical propagation. In this work, the TSH method is reviewed and applications from different fields are surveyed. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 620–633 DOI: 10.1002/wcms.64This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

Communications: Direct dynamics study of the O(P3)+C2H2 reaction: Contribution from spin nonconserving route

The importance of intersystem crossing dynamics for the O((3)P)+C(2)H(2) reaction is demonstrated in this work. A direct dynamics trajectory surface hopping method has been employed to study the intersystem crossing effects. Our study reveals that there is a significant contribution from the spin nonconserving route to the chemical dynamics of the O((3)P)+C(2)H(2) reaction, despite small spin-orbit coupling constant values (<70 cm(-1)).

Study of the Mechanism of the N−CO Photodissociation in N,N-Dimethylformamide by Direct Trajectory Surface Hopping Simulations

Photodynamics of N,N-dimethylformamide (DMF) in its low-lying singlet excited n(O)-pi* and pi-pi* states have been explored by the direct trajectory surface hopping method based on multiconfigurational ab initio calculations. The dynamics simulations starting in the first excited singlet state (n(O)-pi*) showed that in 57% of trajectories, S(1) excited DMF decays to the ground via the crossing seam related to the N-CO bond stretching MXS1. In 41% of all trajectories, the relaxation process on the S(1) PES moves the molecule into the minimum, where it stays trapped until the end of simulation time. In simulations starting in the second excited state, all trajectories are found to deactivate through MXS5 (S(2)/S(1)) by very fast N-CO stretching. Because the N-CO dissociation process continues in the S(1) potential energy surface, most of the population overshoots the MXS1 and leads to fully dissociated electronically excited HCO and N(CH(3))(2) radicals. A mechanism for their deactivation by H-C-O and C-N-C bending modes is proposed.