Nonadiabatic Quantum Dynamics Research Articles

Nonadiabatic quantum reactive scattering of the OH(A Σ2+)+D2

The seams of conical intersection exist between the ground (1 (2)A(')) and the first-excited (2 (2)A(')) electronic potential energy surfaces (PESs) of OH(A (2)Σ(+),X (2)Π) + H(2) system. This intersection induces the nonadiabatic quenching of OH(A (2)Σ(+)) by D(2). We present nonadiabatic quantum dynamics study for OH(A (2)Σ(+)) + D(2) on new five-dimensional coplanar PESs. The ab initio calculations of PESs are based on multireference configuration interaction (MRCI)/aug-cc-pVQZ level. A back-propagation neural network is utilized to fit the PESs and nonadiabatic coupling. High degrees of rotational excitation of quenched OH(X (2)Π) products are found in nonreactive quenching channel, and the quenched D(2) products are vibrationally excited up to quantum number v(2) (')=8. The theoretical results of nonadiabatic time-dependent wave-packet calculation are in good agreement with the existing experimental data.

Quantum calculations of nonadiabatic 2A1– 2B2 conical-intersection effects in the reactions [formula omitted] and N( 4S) + O 2( A3Δ u)

We present both the Born–Oppenheimer (BO) and the nonadiabatic (NA) conical-intersection quantum dynamics of the title reactions, (1) and (2), respectively. BO or NA calculations are carried out using adiabatic or diabatic electronic states, respectively, and we consider some vibrational ( v 0) and rotational ( j 0) states of O 2, taking into account the Pauli principle. The results reflect the barrier or barrierless nature of reaction (1) or (2), respectively, and the former is, thus, much less reactive than the latter. Reaction (1) is direct and its probabilities and cross sections increase with the collision energy from a threshold value, are slightly affected by NA couplings only at high energies, increase with v 0, and are essentially unchanged by j 0. On the contrary, reaction (2) is indirect and its probabilities and cross sections decrease with the collision energy without any threshold, are significantly lowered by NA couplings at low energies, and decrease with both v 0 and j 0.

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.

Nonadiabatic quantum dynamics calculations for the N + NH → N2 + H reaction

Nonadiabatic quantum dynamics calculations on the two coupled potential energy surfaces (PESs) (1(2)A' and 2(2)A') and also adiabatic quantum calculations on the lowest adiabatic PES are reported for the title reaction. Reaction probabilities for total angular momenta, J, varying from 0 to 160, are calculated to obtain the integral cross section (ICS) for collision energies ranging from 0.05 to 1.0 eV. Calculations using both the close coupling and the Centrifugal Sudden (CS) approximation are carried out to evaluate the role of Coriolis coupling effects for this reaction. The results of the nonadiabatic calculations show that the nonadiabatic effects in the title reaction for the initial state of NH (v = 0, j = 0) could be neglected, at least in the collision energy range considered in this study.

Nonadiabatic Hybrid Quantum and Molecular Mechanic Simulations of Azobenzene Photoswitching in Bulk Liquid Environment

A nonadiabatic hybrid quantum and molecular mechanical (na-QM/MM) molecular dynamics scheme has been implemented recently combining the nonadiabatic Car-Parrinello molecular dynamics method by Doltsinis and Marx [Phys. Rev. Lett. 2002, 88, 166402] with the QM/MM coupling approach by Laio et al. [J. Chem. Phys. 2002, 116, 6941]. Here an extensive validation of the underlying, density functional theory based, electronic structure methods by comparison to CASPT2 ab initio data is presented for the case of azobenzene. The "on the fly" na-QM/MM method is then applied to study Z-->E and E-->Z photoisomerization of azobenzene in a bulk liquid environment. The isomerization mechanism is found to be a pedal motion of the central CN horizontal lineNC group in both cases. While the Z-->E reaction is barely affected by the environment, E-->Z photoisomerization is slowed down considerably in the liquid compared to the gas phase. This effect is due to the fact that reorientation of the phenyl rings is significantly hindered in the liquid by steric nearest neighbor interactions. Nonradiative decay is found to be substantially faster for Z-AB (subpicosecond regime) than for E-AB (picosecond regime). The main molecular motions responsible for nonadiabatic coupling have been identified as the oscillations in the NN and CN bond lengths, the CNN bond angles, and the CNNC dihedral angle.

Quantum nonadiabatic dynamics of hydrogen exchange reactions

In continuation of our earlier effort to understand the nonadiabatic coupling effects in the prototypical H + H 2 exchange reaction [Jayachander Rao et al. Chem. Phys. 333 (2007) 135], we present here further quantum dynamical investigations on its isotopic variants. The present work also corrects a technical scaling error occurred in our previous studies on the H + HD reaction. Initial state-selected total reaction cross sections and Boltzmann averaged thermal rate constants are calculated with the aid of a time-dependent wave packet approach employing the double many body expansion potential energy surfaces of the system. The theoretical results are compared with the experimental and other theoretical data whenever available. The results re-establish our earlier conclusion, on a more general perspective, that the electronic nonadiabatic effects are negligible on the important quantum dynamical observables of these reactive systems reported here.

Nonadiabatic Quantum Dynamics and Laser Control of Br2 in Solid Argon

A five-dimensional reaction surface-vibronic coupling model is introduced to describe the B- to C-state predissociation dynamics of Br(2) occupying a double substitutional lattice site in a face-centered cubic argon crystal at low temperatures. The quantum dynamics driven by a Franck-Condon vertical excitation is investigated, revealing the role of matrix cage compression for efficient nonadiabatic transitions. Vibrational preexcitation of the Br(2) bond in the electronic ground state can be used to access a different regime of predissociation which does not require substantial matrix compression because the Franck-Condon window shifts into the energetic range of the B-C level crossing. Using optimal control theory, it is shown how vibrational preexcitation can be achieved via a pump-dump-type mechanism involving the repulsive C state.

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2–3%.

Nonadiabatic quantum dynamics of Br 2 in solid Ar: A four-dimensional study of the B to C state predissociation

Quantum dynamics simulations are performed for a diatomics-in-molecules based model of Br 2 in solid Ar which incorporates four nuclear degrees of freedom and four electronic states. The nuclear motions comprise two large amplitude coordinates describing the Br 2 bond distance and an effective symmetry-preserving matrix mode. Two symmetry-lowering harmonic modes are added in the spirit of linear vibronic coupling theory. Initiating the dynamics on the B state by means of an ultrafast laser pulse, nonadiabatic transitions to the two degenerate C states are monitored and the effect of vibrational preexcitation in the electronic ground state is investigated.

Quantum dynamics through conical intersections in macrosystems: Combining effective modes and time-dependent Hartree

We address the nonadiabatic quantum dynamics of (macro)systems involving a vast number of nuclear degrees of freedom (modes) in the presence of conical intersections. The macrosystem is first decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment can be constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. The environment is described by a few effective modes augmented by a residual environment. In practice, the effective modes can be added to the system’s modes and the quantum dynamics of the entire macrosystem can be accurately calculated on a limited time-interval. For longer times, however, the residual environment plays a role. We investigate the possibility to treat fully quantum mechanically the system plus a few effective environmental modes, augmented by the dynamics of the residual environment treated by the time-dependent Hartree (TDH) approximation. While the TDH approximation is known to fail to correctly reproduce the dynamics in the presence of conical intersections, it is shown that its use on top of the effective-mode formalism leads to much better results. Two numerical examples are presented and discussed; one of them is known to be a critical case for the TDH approximation.

Quantum dynamics in macrosystems with several coupled electronic states: Hierarchy of effective Hamiltonians

We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multistate conical intersections. The general situation of an arbitrary number of states and arbitrary number of nuclear degrees of freedom (modes) is considered. The macrosystem is decomposed into a system part carrying a few, strongly coupled modes and an environment, comprising the vast number of remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment is constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. By considering the system's Hamiltonian along with a few members of the hierarchy, it is shown mathematically by a moment analysis that the quantum dynamics of the entire macrosystem can be numerically exactly computed on a given time scale. The time scale wanted defines the number of effective Hamiltonians to be included. The contribution of the environment to the quantum dynamics of the macrosystem translates into a sequential coupling of effective modes. The wave function of the macrosystem is known in the full space of modes, allowing for the evaluation of observables such as the time-dependent individual excitation along modes of interest as well as spectra and electronic-population dynamics.

Significant Nonadiabatic Effects in the S(1D) + HD Reaction

A nonadiabatic quantum dynamics calculation involving four coupled potential energy surfaces (two degenerate 3A' ', one 3A', and one 1A') and the spin-orbit coupling matrix for these states is reported for the title reaction. The results show that the important discrepancy between theoretically calculated and experimentally measured intramolecular isotope effects can at least in part be attributed to significant nonadiabatic effects.

Nonadiabatic quantum dynamics based on a hierarchical electron-phonon model: Exciton dissociation in semiconducting polymers

A hierarchical electron-phonon coupling model is applied to describe the ultrafast decay of a photogenerated exciton at a donor-acceptor polymer heterojunction, via a vibronic coupling mechanism by which a charge-localized interfacial state is created. Expanding upon an earlier Communication [H. Tamura et al., J. Chem. Phys. 126, 021103 (2007)], we present a quantum dynamical analysis based on a two-state linear vibronic coupling model, which accounts for a two-band phonon bath including high-frequency C[Double Bond]C stretch modes and low-frequency ring torsional modes. Building upon this model, an analysis in terms of a hierarchical chain of effective modes is carried out, whose construction is detailed in the present paper. Truncation of this chain at the order n (i.e., 3n+3 modes) conserves the Hamiltonian moments (cumulants) up to the (2n+3)rd order. The effective-mode analysis highlights (i) the dominance of the high-frequency modes in the coupling to the electronic subsystem and (ii) the key role of the low-frequency modes in the intramolecular vibrational redistribution process that is essential in mediating the decay to the charge-localized state. Due to this dynamical interplay, the effective-mode hierarchy has to be carried beyond the first order in order to obtain a qualitatively correct picture of the nonadiabatic process. A reduced model of the dynamics, including a Markovian closure of the hierarchy, is presented. Dynamical calculations were carried out using the multiconfiguration time-dependent Hartree method.

The MP/SOFT methodology for simulations of quantum dynamics: Model study of the photoisomerization of the retinyl chromophore in visual rhodopsin

Rigorous simulations of excited-state nonadiabatic quantum dynamics in polyatomic chromophores are particularly challenging since they require solving the multichannel time-dependent Schrödinger equation describing nuclear wavepackets evolving on electronically coupled potential energy surfaces. This paper presents an overview of the matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method for simulations of nonadiabatic quantum dynamics [X. Chen, V.S. Batista, Matching-pursuit split operator Fourier transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine. J. Chem. Phys., 125 (2006) Art. No. 124313] and its application to the description of the 11- cis/all- trans photoisomerization of the retinyl chromophore in rhodopsin. The underlying nonadiabatic dynamics is described by a 2-state 25-dimensional wave-packet evolving according to an empirical model Hamiltonian with frequencies and excited-state gradients parameterized to reproduce the observed resonance Raman excitations of rhodopsin. The reported results show that the MP/SOFT method is a valuable tool to simulate nonadiabatic dynamics in polyatomic systems and to assess the validity of mixed quantum-classical approaches as applied to simulations of complex (nonintegrable) quantum dynamics in multidimensional systems.

Photoinduced nonadiabatic dynamics of ethene: Six-dimensional wave packet propagations using two different approximations of the kinetic energy operator

The nonadiabatic dynamics of ethene in its N, V and Z valence states is reinvestigated. Wave packet dynamics initiated by a vertical π → π ∗ excitation is studied and particular emphasis is put on the investigation of the evolution of diabatic and adiabatic state populations. A new algorithm for computing the adiabatic state populations from diabatically represented wavefunctions is discussed and applied here for the first time. We have used the potential model of ethene which was derived by Krawczyk et al. [R.P. Krawczyk, A. Viel, U. Manthe, W. Domcke, Photoinduced dynamics of the valence states of ethene: a six-dimensional potential-energy surface of three electronic states with several conical intersections. J. Chem. Phys. 119 (2003) 1397–1411] and the kinetic energy operator derived by Viel et al. [A. Viel, R.P. Krawczyk, U. Manthe, W. Domcke, Photoinduced dynamics of ethene in the N, V and Z valence states: a six-dimensional nonadiabatic quantum dynamics investigation, J. Chem. Phys. 120 (2004) 11000–11010]. However, a second kinetic energy operator, which is more accurate than the first one, was derived and applied. The results of our calculations are in qualitative agreement with the previous ones of Viel et al., but there are marked quantitative differences.

Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit

This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born-Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum classical methods. Specifically, an exact path integral formulation of the quantum nonadiabatic dynamics of Born-Oppenheimer systems is described. Stationary phase approximations to the propagator for full quantum dynamics are derived. It is shown that quantum corrections to mixed quantum classical methods can be obtained through stationary phase approximations to the full quantum dynamics. A rigorous description of the quantum corrections due to electronic nonadiabatic coupling on the nuclear dynamics within the Ehrenfest framework is obtained. The fewest switches surface hopping method is shown to be obtained as a quasiclassical approximation to the dynamics, and natural semiclassical extensions to include classically forbidden nonadiabatic transitions are suggested.

Spin-orbit effect in the energy pooling reaction O2(aΔ1)+O2(aΔ1)→O2(bΣ1)+O2(XΣ3)

Five-dimensional nonadiabatic quantum dynamics studies have been carried out on two new potential energy surfaces of S(2)((1)A(')) and T(7)((3)A(")) states for the title oxygen molecules collision with coplanar configurations, along with the spin-orbit coupling between them. The ab initio calculations are based on complete active state second-order perturbation theory with the 6-31+G(d) basis set. The calculated spin-orbit induced transition probability as a function of collision energy is found to be very small for this energy pooling reaction. The rate constant obtained from a uniform J-shifting approach is compared with the existing theoretical and experimental data, and the spin-orbit effect is also discussed in this electronic energy-transfer process.

Effect of the geometric phase on the dynamics of the hydrogen-exchange reaction

A recent puzzle in nonadiabatic quantum dynamics is that geometric phase (GP) effects are present in the state-to-state opacity functions of the hydrogen-exchange reaction, but cancel out in the state-to-state integral cross sections (ICSs). Here the authors explain this result by using topology to separate the scattering amplitudes into contributions from Feynman paths that loop in opposite senses around the conical intersection. The clockwise-looping paths pass over one transition state (1-TS) and scatter into positive deflection angles; the counterclockwise-looping paths pass over two transition states (2-TS) and scatter into negative deflection angles. The interference between the 1-TS and 2-TS paths thus integrates to a very small value, which cancels the GP effects in the ICS. Quasiclassical trajectory (QCT) calculations reproduce the scattering of the 1-TS and 2-TS paths into positive and negative deflection angles and show that the 2-TS paths describe a direct insertion mechanism. The inserting atom follows a highly constrained "S-bend" path, which allows it to avoid both the other atoms and the conical intersection and forces the product diatom to scatter into high rotational states. By contrast, the quantum 2-TS paths scatter into a mainly statistical distribution of rotational states, so that the quantum 2-TS total ICS is roughly twice the QCT ICS at 2.3 eV total energy. This suggests that the S-bend constraint is relaxed by tunneling in the quantum system. These findings on H+H(2) suggest that similar cancellations or reductions in GP effects are likely in many other reactions.

Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine

A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] to simulations of nonadiabatic quantum dynamics. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S(1)S(2) interconversion of pyrazine after S(0)-->S(2) photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.

Classical description of the dynamics and time-resolved spectroscopy of nonadiabatic cis– trans photoisomerization

The mapping formulation of nonadiabatic quantum dynamics is applied to obtain a classical description of the ultrafast dynamics and time-resolved spectroscopy of a photochemical reaction. Adopting a previously studied dissipative two-state two-mode model of nonadiabatic cis–trans photoisomerization, classical mapping simulations are compared to quantum-mechanical reduced density matrix calculations. Overall, the simple classical method is found to reproduce the quantum reference calculations quite well. In particular, it is studied if the classical approach yields the correct long-time cis/trans localization of the wave packet and therefore the correct quantum yield of the photoreaction. As the long-time behavior of the classical mapping formulation suffers from the well-known zero point energy problem of classical mechanics, a new practical method is proposed to determine a zero point energy correction. Employing a second-order Franck–Condon-type approximation, the capability of the classical method to simulate time- and frequency-resolved pump–probe spectra of the nonadiabatic photoreaction is studied. The potential of the classical approach as a practical method to describe condensed-phase photoreactions is discussed.