Ab initio nonadiabatic dynamics study of ultrafast radiationless decay over conical intersections illustrated on the Na3F cluster

We present a theoretical approach for the ultrafast nonadiabatic dynamics based on the ab initio molecular dynamics carried out "on the fly" in the framework of the configuration interaction method combined with Tully's surface hopping algorithm for nonadiabatic transitions. This approach combined with our Wigner distribution approach allows us to perform accurate simulations of femtosecond pump-probe spectra in the systems where radiationless transitions among electronic states take place. In this paper we illustrate this by theoretical simulation of ultrafast processes and nonradiative relaxation in the Na(3)F cluster, involving three excited states and the ground electronic state. Furthermore, we show that our accurate simulation of the photoionization pump-probe spectrum is in full agreement with the experimental signal. Based on the nonadiabatic dynamics at high level of accuracy and taking into account all degrees of freedom, the nonradiative lifetime for the 1 (1)B(1) excited state of Na(3)F has been determined to be approximately 900 fs.     

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron-transfer rate processes

In this work, we revisit the electron-transfer rate theory, with particular interests in the distinct quantum solvation effect and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theor. Comput. Chem. 2006, 5, 685. Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier crossing to tunneling and from barrierless to quantum barrier crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.     

利用基于直接动力学的轨线面跳跃方法处理非绝热过程

势能面交叉引起的非绝热过程广泛存在于光化学和光物理中。对这一过程进行描述是理论化学的重要挑战之一。非绝热过程涉及原子核与电子之间的耦合运动,因此量子化学的基本假设之一"玻恩-奥本海默"近似被打破,所以对其进行描述需要发展新的动力学理论方法。在这些方法中,Tully发展的最少轨线面跳跃方法凭借易于程序化、便于计算等优点已经发展成为处理非绝热问题的主要动力学方法之一。其中原子核以经典的方式在单一势能面上进行演化,电子以量子的方式沿着同一轨线进行演化。在整个演化过程中,非绝热跃迁通过轨线在不同势能面间的跃迁来描述,其中跳跃发生的几率与电子的演化有关。如果将该方法与从头算直接动力学相结合,可以在全原子水平上研究实际分子体系的非绝热动力学,给出其激发态寿命、非绝热动力学中分子的主要运动方式、反应通道以及分支比等重要信息。本文旨在讨论最少面跳跃直接动力学方法研究非绝热问题的一些进展,包括动力学基本理论,特别关注将最少面跳跃方法和直接动力学结合的数值实现细节,同时讨论该方法在研究实际体系当中的一些应用,并对轨线面跳跃方法下一步发展的一些方向进行合理的展望。     

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.     

Semiclassical treatment of thermally activated electron transfer in the inverted region under the fast dielectric relaxation

The previously formulated semiclassical theory (Zhao, Liang, and Nakamura, J. Phys. Chem. A 2006, 110, 8204) is used to study electron transfer in the Marcus inverted case by considering multidimensional potential energy surfaces of donor and acceptor. The Zhu-Nakamura formulas of nonadiabatic transition in the case of Landau-Zener type are incorporated into the approach. The theory properly takes into account the nonadiabatic transition coupled with the nuclear tunneling and can cover the whole range from weak to strong coupling regime uniformly under the assumption of fast solvent relaxation. The numerical calculations are performed for the 12-dimensional model of shifted harmonic oscillators and demonstrate that the reaction rate with respect to the electronic coupling shows a maximum, confirming the adiabatic suppression in the strong coupling limit. The adiabatic suppression is dramatically reduced by the effect of nuclear tunneling compared to the case that the Landau-Zener formula is used. The possible extension and applications to the case of the slow solvent dynamics are discussed.     

Communication: Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution

An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

Reduced dimensionality spin-orbit dynamics of CH3 + HCl ⇌ CH4 + Cl on ab initio surfaces

A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH(3) + HCl ? CH(4) + Cl((2)P(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions.     

Nonadiabatic transitions between lambda-doubling states in the capture of a diatomic molecule by an ion

The low-energy capture of a dipolar diatomic molecule in an adiabatically isolated electronic state with a good quantum number Omega (Hund's coupling case a) by an ion occurs adiabatically with respect to rotational transitions of the diatom. However, the capture dynamics may be nonadiabatic with respect to transitions between the pair of the Lambda-doubling states belonging to the same value of the intrinsic angular momentum j. In this work, nonadiabatic transition probabilities are calculated which define the Lambda-doubling j-specific capture rate coefficients. It is shown that the transition from linear to quadratic Stark effect in the ion-dipole interaction, which damps the T(-1/2) divergence of the capture rate coefficient calculated with vanishing Lambda-doubling splitting, occurs in the adiabatic regime with respect to transitions between Lambda-doubling adiabatic channel potentials. This allows one to suggest simple analytical expressions for the rate coefficients in the temperature range which covers the region between the sudden and the adiabatic limits with respect to the Lambda-doubling states.     

化学反应中的几何相效应

锥形交叉可以通过几何相效应影响核动力学.在过去的一些年里关于锥形交叉的理论有大量的发展和进步,本文综述了分子反应动力学领域针对几何相效应研究的一些理论成果.介绍了分子反应动力学中与几何相效应直接相关的一些最新成果,同时也对这些重要结果进行了解释.我们相信几何相效应将会在非绝热化学中发挥最重要的作用.     

Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: application to solvated electrons in water and methanol

A new, alternative form of the golden rule formula defining the nonadiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the nonadiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via molecular dynamics simulations. The formalism is applied to the problem of the nonadiabatic p-->s relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvents, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated nonadiabatic coupling.     

LAND-map, a linearized approach to nonadiabatic dynamics using the mapping formalism

We present a new approach for calculating quantum time correlation functions for systems whose dynamics exhibits relevant nonadiabatic effects. The method involves partial linearization of the full quantum path-integral expression for the time correlation function written in the nonadiabatic mapping Hamiltonian formalism. Our analysis gives an algorithm which is both numerically efficient and accurate as we demonstrate in test calculations on the spin-boson model where we find results in good agreement with exact calculations. The accuracy of our new approach is comparable to that of calculations performed using other approximate methods over a relatively broad range of model parameters. However, our method converges relatively quickly when compared with most alternative schemes. These findings are very encouraging in view of the application of the new method for studying realistic nonadiabatic model problems in the condensed phase.     

Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuitsplit-operator Fourier-transform (MPSOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MPSOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.     

Dynamics of nonadiabatic chemical reactions

New methods are proposed to treat nonadiabatic chemical dynamics in realistic large molecular systems by using the Zhu-Nakamura (ZN) theory of curve-crossing problems. They include the incorporation of the ZN formulas into the Herman-Kluk type semiclassical wave packet propagation method and the trajectory surface hopping (TSH) method, formulation of the nonadiabatic transition state theory, and its application to the electron transfer problem. Because the nonadiabatic coupling is a vector in multidimensional space, the one-dimensional ZN theory works all right. Even the classically forbidden transitions can be correctly treated by the ZN formulas. In the case of electron transfer, a new formula that can improve the celebrated Marcus theory in the case of normal regime is obtained so that it can work nicely in the intermediate and strong electronic coupling regimes. All these formulations mentioned above are demonstrated to work well in comparison with the exact quantum mechanical numerical solutions and are expected to be applicable to large systems that cannot be treated quantum mechanically numerically exactly. To take into account another quantum mechanical effect, namely, the tunneling effect, an efficient method to detect caustics from which tunneling trajectories emanate is proposed. All the works reported here are the results of recent activities carried out in the author's research group. Finally, the whole set of ZN formulas is presented in Appendix.     

Excited state electronic structures and dynamics of NOCl: a new potential function set, absorption spectrum, and photodissociation mechanism

A set of analytical potential energy surfaces (PESs) for six singlet excited states of NOCl are constructed based on multireference configuration interaction calculations. The total absorption cross section at the energy range of 2-7 eV is calculated by quantum dynamics calculations with the present PESs and transition dipole moments. The calculated absorption spectrum agrees well with the experiment. It is also found that the A band with the absorption maximum at 6.3 eV is attributed to the transition to the 4 1A' state, though the excitations to the 3 1A' and 3 1A" states contribute to the spectrum at the energy range between 4 and 5 eV. The spin-forbidden transitions are concluded to be negligibly weak. The mechanism of photodissociation reaction at the energy region corresponding to the A band is examined. The nonadiabatic transition rates from the 4 1A' state to lower singlet and triplet states are estimated by Fermi's golden rule, and the transitions to the 1 1A' and 3 1A' states induced by vibronic coupling are found to be the predominant dissociation pathways. The experimentally observed energy dependence of the recoil anisotropy of the fragments is discussed based on the calculated nonadiabatic transition rates.