Diabatic Limit Research Articles

Solution to a class of multistate Landau-Zener model beyond integrability conditions

We study a class of multistate Landau-Zener model which cannot be solved by integrability conditions or other standard techniques. By analyzing analytical constraints on its scattering matrix and performing fitting to results from numerical simulations of the Schrödinger equation, we find nearly exact analytical expressions of all its transition probabilities for specific parameter choices. We also determine the transition probabilities up to leading orders of series expansions in terms of the inverse sweep rate (namely, in the diabatic limit) for general parameter choices. We further show that this model can describe a Su-Schrieffer-Heeger chain with couplings changing linearly in time. Our work presents a new route, i.e., analytical constraint plus fitting, to analyze those multistate Landau-Zener models which are beyond the applicability of conventional solving methods.

Observation of rotationally dependent fine-structure branching ratios near the predissociation threshold N(2D5/2,3/2) + N(2D5/2,3/2) of 14N2.

Photofragment spin-orbit fine-structure branching ratios have long been predicted to depend on the rotational quantum number J' by theory near the dissociation thresholds of several diatomic molecules, while this has rarely been observed in any photodissociation experiments yet. Here, we measured the fine-structure branching ratios N(2D5/2)/N(2D3/2) produced in the N(2D5/2,3/2) + N(2D5/2,3/2) channel at the b'1Σu +(v = 20) state of 14N2 by using our vacuum ultraviolet (VUV)-pump-VUV-probe time-sliced velocity-mapped ion imaging setup. It is found that 14N2 almost exclusively dissociates into the spin-orbit channel N(2D5/2) + N(2D3/2) at low rotational levels and gradually approaches the statistical or diabatic limit by distributing all possible spin-orbit channels at higher rotational levels. The strongly rotationally dependent fine-structure branching ratios should be due to the increasing strength of nonadiabatic Coriolis interaction among various dissociative states in the so-called "recoupling zone" as J' increases. They are supposed to provide unprecedented information on the near threshold photodissociation dynamics of 14N2.

Born-Oppenheimer and non-Born-Oppenheimer contributions to time-dependent electron momenta.

Using a model system for a coupled electron-nuclear motion, we calculate time-dependent expectation values of the electronic momentum operator. Whereas, within the velocity form, this quantity vanishes if the Born-Oppenheimer (BO) approximation is applied, it differs from zero if the calculation employs the length form of the expectation value. Using the adiabatic expansion of the total wave function, it is analyzed which terms contribute to the mean electronic momentum. For an adiabatic motion, where the BO approximation holds, it is shown that in the length form, the BO wave function yields an excellent estimate of the momentum. On the other hand, in the velocity form, it is necessary to include non-BO terms to calculate its value. This illustrates the different convergence behavior of the matrix elements in the two formulations. In the diabatic limit where the electron density does only marginally change upon the nuclear motion, both approaches converge to a vanishing mean electronic momentum.

Theoretical study of amplification of the tunnel current in the redox-mediated tunneling junctions for the symmetric and asymmetric electron-molecular coupling in the case of the adiabatic transport regime

Dependence of amplification A of the tunnel current in the electrochemical bridged tunneling junction on the bias voltage Vb, reorganization free energy Er, the broadening Δ of the electronic level of the redox molecule (RM) and intensity of the Debye screening in the tunneling gap is studied for the cases of the fully adiabatic and partially adiabatic electron transitions. We consider a one–level single RM within the spin-less model and assume the wide-band approximation for the electronic structure of the working electrodes. It is shown that amplification in the fully and partially adiabatic limits is appreciably smaller than that in the diabatic limit studied earlier [I.G. Medvedev, Electrochim. Acta 186 (2015) 613–623] due to the sufficiently large values of the broadening Δ. It is also shown that, in contrast to the diabatic limit, amplification depends weekly on the asymmetry of the coupling of the RM to the working electrodes. On the other hand, similar to the diabatic limit, amplification as a function of the bias voltage Vb approaches to relatively large values at large values of Vb in the case of the full Debye screening while, in the realistic case of the intermediate Debye screening, amplification increases at first with the increase of Vb, then reaches a maximum value Amax at some value Vb max and, when Vb farther increases, decreases to A = 1. The functions A(Vb) are calculated for different values of the parameters of the tunneling junction and it is shown that Amax increases with the increase of Er and the intensity of Debye screening and decrease with the increase of Δ. The approximate analytical expression which shows in the explicit form the dependence of A on the parameters of the system is presented.

Predissociation dynamics of D2 + hv→ D(1s1/2) + D(2p1/2,3/2, 2s1/2) revealed by the spin-orbit state resolved fragment branching ratios and angular distributions.

For molecular photodissociations, the spin-orbit state resolved fragment branching ratios and angular distributions provide deep insight into the dynamics. For the first excited state of the H(2p1/2,3/2) atom, a branching ratio measurement is a challenge because of small energy spacing between them. For the D(2p1/2,3/2) fragments from the predissociation of D2 + 14.76 eV → D(1s) + D(2s, 2p1/2,3/2) in the 2pπC1Πu (υ = 19) state, we made such measurements by pumping the D(2s, 2p1/2,3/2) fragments to high-lying Rydberg states that are subsequently ionized by a delayed-pulse electric field. In the 2pπC1Πu (υ = 19) state, the D2 molecule dissociates via both shape and Feshbach resonances correlating to the channels D(1s) + D(2p3/2) and D(1s) + D(2p1/2), respectively. The measured spin-orbit branching ratios, 2p3/2/(2p1/2 + 2p3/2), correspond to the diabatic limit, 2/3, which indicates strong spin-orbit state mixings near the dissociation limits. The spin-orbit state resolved fragment angular distributions also support the diabatic dissociation mechanism and illustrate simultaneous shape and Feshbach resonances for the R(0) transition.

Potential energy surfaces and nonadiabatic transitions in the asymptotic regions of ICN photodissociation to study the interference effects in the F1 and F2 spin-rotation levels of the CN products.

One of the most spectacular yet unsolved problems for the ICN -band photodissociation is the non-statistical spin-rotation F1 = N + 1/2 and F2 = N - 1/2 populations for each rotation level N of the CN fragment. The F1 /F2 population difference function f(N) exhibits strong N and λ dependences with an oscillatory behavior. Such details were found to critically depend on the number of open-channel product states, namely, whether both I (2 P3/2 ) and I (2 P1/2 ) are energetically available or not as the dissociation partner. First, in the asymptotic region, the exchange and dipole-quadrupole inter-fragment interactions were studied in detail. Then, as the diabatic basis, we took the appropriate symmetry adapted products of the electronic and rotational wavefunctions for the F1 and F2 levels at the dissociation limits. We found that the adiabatic Hamiltonian exhibits Rosen-Zener-Demkov type nonadiabatic transitions reflecting the switch between the exchange interaction and the small but finite spin-rotation interaction within CN at the asymptotic region. This non-crossing type nonadiabatic transition occurs with the probability 1/2, that is, at the diabatic limit through a sudden switch of the quantization axis for CN spin S from the dissociation axis to the CN rotation axis N. We have derived semiclassical formulae for f(N) and the orientation parameters with a two-state model including the 3A' and 4A' electronic states, and with a four-state model including the 3A' through 6A' electronic states. These two kinds of interfering models explain general features of the F1 and F2 level populations observed by Zare's group and Hall's group, respectively. © 2018 Wiley Periodicals, Inc.

Dynamic scaling at classical phase transitions approached through nonequilibrium quenching

We use Monte Carlo simulations to demonstrate generic scaling aspects of classical phase transitions approached through a quench (or annealing) protocol where the temperature changes as a function of time with velocity $v$. Using a generalized Kibble-Zurek ansatz, we demonstrate dynamic scaling for different types of stochastic dynamics (Metropolis, Swendsen-Wang, and Wolff) on Ising models in two and higher dimensions. We show that there are dual scaling functions governing the dynamic scaling, which together describe the scaling behavior in the entire velocity range $v\ensuremath{\in}[0,\ensuremath{\infty})$. These functions have asymptotics corresponding to the adiabatic and diabatic limits, and close to these limits they are perturbative in $v$ and $1/v$, respectively. Away from their perturbative domains, both functions cross over into the same universal power-law scaling form governed by the static and dynamic critical exponents (as well as an exponent characterizing the quench protocol). As a by-product of the scaling studies, we obtain high-precision estimates of the dynamic exponent $z$ for the two-dimensional Ising model subject to the three variants of Monte Carlo dynamics: for single-spin Metropolis updates ${z}_{\mathrm{M}}=2.1767(5)$, for Swendsen-Wang multicluster updates ${z}_{\mathrm{SW}}=0.297(3)$, and for Wolff single-cluster updates ${z}_{\text{W}}=0.30(2)$. For Wolff dynamics, we find an interesting behavior with a nonanalytic breakdown of the quasiadiabatic and diabatic scalings, instead of the generic smooth crossover described by a power law. We interpret this disconnect between the two scaling regimes as a dynamic phase transition of the Wolff algorithm, caused by an effective sudden loss of ergodicity at high velocity.

Communications: Evaluation of the nondiabaticity of quantum molecular dynamics with the dephasing representation of quantum fidelity

We propose an approximate method for evaluating the importance of non-Born-Oppenheimer effects on the quantum dynamics of nuclei. The method uses a generalization of the dephasing representation (DR) of quantum fidelity to several diabatic potential energy surfaces and its computational cost is the cost of dynamics of a classical phase space distribution. It can be implemented easily into any molecular dynamics program and also can utilize on-the-fly ab initio electronic structure information. We test the methodology on three model problems introduced by Tully and on the photodissociation of NaI. The results show that for dynamics close to the diabatic limit, the decay of fidelity due to nondiabatic effects is described accurately by the DR. In this regime, unlike the mixed quantum-classical methods such as surface hopping or Ehrenfest dynamics, the DR can capture more subtle quantum effects than the population transfer between potential energy surfaces. Hence we propose using the DR to estimate the dynamical importance of diabatic, spin-orbit, or other couplings between potential energy surfaces. The acquired information can help reduce the complexity of a studied system without affecting the accuracy of the quantum simulation.

Correlated fine structure branching ratios arising from state-selected predissociation of ClO (A2Π3/2)

We have extended our investigation of the v'-dependent predissociation dynamics of the ClO A(2)Pi(3/2) state using velocity-map ion imaging. Correlated fine-structure branching ratios are reported for v' = 0-5. The measured branching ratios are non-statistical and are qualitatively inconsistent with adiabatic dissociation dynamics. The coupling constants between the A(2)Pi(3/2) state and several dissociative excited state potentials have been optimized, as have the locations of the crossing points, based on comparison to previously reported v'-dependent predissociation rates. Using these optimized potentials we have modeled the branching ratios in the diabatic limit but the lack of agreement with experiments suggests the importance of exit channel coupling. Coupled channel calculations including 9 coupled potentials provide modest improvement with experiment but differences remain.

Origin of the Temperature Dependence of Isotope Effects in Enzymatic Reactions: The Case of Dihydrofolate Reductase

The origin of the temperature dependence of kinetic isotope effects (KIEs) in enzyme reactions is a problem of general interest and a major challenge for computational chemistry. The present work simulates the nuclear quantum mechanical (NQM) effects and the corresponding KIE in dihydrofolate reductase (DHFR) and two of its mutants by using the empirical valence bond (EVB) and the quantum classical path (QCP) centroid path integral approach. Our simulations reproduce the overall observed trend while using a fully microscopic rather than a phenomenological picture and provide an interesting insight. It appears that the KIE increases when the distance between the donor and acceptor increases, in a somewhat counter intuitive way. The temperature dependence of the KIE appears to reflect mainly the temperature dependence of the distance between the donor and acceptor. This trend is also obtained from a simplified vibronic treatment, but as demonstrated here, the vibronic treatment is not valid at short and medium distances, where it is essential to use the path integral or other approaches capable of moving seamlessly from the adiabatic to the diabatic limits. It is pointed out that although the NQM effects do not contribute to catalysis in DHFR, the observed temperature dependence can be used to refine the potential of mean force for the donor and acceptor distance and its change due to distanced mutations.

Uniform analytic description of dephasing effects in two-state transitions

We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, along with several other models, such as a Gaussian model and a Landau-Zener model with a pulsed coupling.

Vibrational state-dependent predissociation dynamics of ClO (A2Π3/2): Insight from correlated fine structure branching ratios

We have studied the v'-dependent predissociation dynamics of the ClO A (2)Pi(3/2) state using velocity-map ion-imaging. Experimental final correlated state branching ratios, i.e. Cl((2)P(J=3/2,1/2)) + O((3)P(J=2,1,0)) channels, have been measured for v' = 6-11. We find that the branching ratios are highly variable and depend strongly on v', providing a window into the v'-dependent predissociation mechanism. A comparison of the experimental results with the recent model of Lane et al. (I. C. Lane, W. H. Howie and A. J. Orr-Ewing, Phys. Chem. Chem. Phys., 1999, 1, 3087) in both the diabatic and adiabatic limits suggests that the dynamics are closer to the diabatic limit. The overall Cl((2)P(J)) branching ratios are in good agreement with the diabatic model results. There are significant differences, however, between theory and experiment at the correlated state level, demonstrating the sensitivity of correlated measurements to the role of the exit channel coupling in the predissociation dynamics. The results highlight the need for more sophisticated quantum dynamical calculations to describe the correlated fine structure branching ratios in this system.

Observation and dynamics of “mixed-valence isomers” and a thermodynamic estimate of electronic coupling parameters

The thermodynamics of mixed-valence isomers – the two limiting charge distributions in a mixed-valence complex – are reviewed and used as a basis for calculating the electronic coupling ( H AB). Infrared spectroscopy is used to determine equilibrium constants between the two mixed-valence isomers in the strongly coupled adiabatic limit. Equilibrium constants in the diabatic ( H AB = 0) limit are independently estimated from electrochemical data for corresponding symmetric complexes. Analysis of these data provide direct measurements of Δ Δ G 0 = Δ G 0 0 - Δ G 1 0 , the difference in thermodynamic driving force for electron transfer in the diabatic and strongly coupled adiabatic limits which it is shown can be interpreted within the framework of appropriate potential energy surfaces for ET to estimate H AB.

Electron transfer rate in the Marcus inverted regime beyond the perturbation theory

Two possible quantum mechanical methods, the flux–flux correlation function formula in time domain and quantum S-matrix approach in energy domain, are used to evaluate the electron transfer rate in the Marcus inverted regime. One dimensional test calculations show that both methods give the same results in the whole range of the coupling strength from adiabatic to diabatic limits. It is also shown that the perturbation theory in the strong coupling regime predicts incorrect electronic transfer rate as expected. Potential application of both quantum methods to complex systems is discussed.

Mechanisms of molecular electronic rectification through electronic levels with strong vibrational coupling

We present a new view and an analytical formalism of electron flow through a donor–acceptor molecule inserted between a pair of metal electrodes. The donor and acceptor levels are strongly coupled to an environmental nuclear continuum. The formalism applies to molecular donor–acceptor systems both in vacuum or air, and in aqueous solution under electrochemical potential control. Multifarious patterns of rectified electron flow from the negatively to the positively biased electrode arise. The electronic interaction between the donor and acceptor fragments, mutually and with the electrodes, can be weak, corresponding to the fully diabatic limit. The rectification process then reduces to a sequence of vibrationally relaxed single-electron transfer steps. In the limits where the interactions are strong, denoted as the partially and fully adiabatic limits, the character of the rectification process is different, and electron flow proceeds coherently, without vibrational relaxation. In still another class of mechanisms the electronic level broadening of either donor or acceptor from the adjacent electrode is so strong that it is comparable to the vibrational broadening. The process then reduces to a three-level transition similar to STM of large redox molecules. Recent data for rectification in hexadecyl-quinolinium tricyanodimethanide monolayers by Metzger and co-workers [J. Am. Chem. Soc. 119, 10455 (1997); Acc. Chem. Res. 32, 950 (1999)], are discussed in terms of the reported views and formalism.

Theory of the Domino Dynamics Via Nonadiabatic Transitions

Photoinduced nucleation processes, called photoinduced domino processes, via excited electronic states are discussed theoretically for a one-dimensional arrangement of deformable molecules using a model composed of localized electrons and lattices. We show that the global structural transition by photoexcitation only at a molecule (site) is possible in the adiabatic and diabatic limits. An intermediate regime between these limits is investigated; an analytical treatment and a numerical calculation are presented taking into account the nonadiabatic electronic transition, i . e ., the Landau-Zener-type transition. In this regime, the domino dynamics can be terminated halfway ( i . e ., a finite - size domain appears) in contrast to the "all-or-nothing" domino dynamics ( i . e ., a photoinduced domain vanishes or grows up to the system size) in the adiabatic and diabatic limits.

Theoretical aspects of electron transfer reactions of complex molecules

Features of electron transfer involving complex molecules are discussed. This notion presently refers to molecular reactants where charge transfer is accompanied by large molecular reorganization, and commonly used displaced harmonic oscillator models do not apply. It is shown that comprehensive theory of charge transfer in polar media offers convenient tools for the treatment of experimental data for such systems, with due account of large-amplitude strongly anharmonic intramolecular reorganization. Equations for the activation barrier and free energy relationships are provided, incorporating vibrational frequency changes, local mode anharmonicity, and rotational reorganization, in both diabatic and adiabatic limits. Systems for which this formalism is appropriate are discussed.

Quantum Wave Packet Study of Nonadiabatic Effects in O(1D) + H2 → OH + H

The authors develop a wave packet approach to treating the electronically nonadiabatic reaction dynamics of O({sup 1}D) + H{sub 2} {yields} OH + H, allowing for the 1{sup 1}A{prime} and 2{sup 1}A{prime} potential energy surfaces and couplings, as well as the three internal nuclear coordinates. Two different systems of coupled potential energy surfaces are considered, a semiempirical diatomics-in-molecules (DIM) system due to Kuntz, Niefer, and Sloan, and a recently developed ab initio system due to Dobbyn and Knowles (DK). Nonadiabatic quantum results, with total angular momentum J = 0, are obtained and discussed. Several single surface calculations are carried out for comparison with the nonadiabatic results. Comparisons with trajectory surface hopping (TSH) calculations, and with approximate quantum calculations, are also included. The electrostatic coupling produces strong interactions between the 1{sup 1}A{prime} and 2{sup 1}A{prime} states at short range (where these states have a conical intersection) and weak but, interestingly, nonnegligible interactions between these states at longer range. The wave packet results show that if the initial state is chosen to be effectively the 1A{prime} state (for which insertion to form products occurs on the adiabatic surface), then there is very little difference between the adiabatic and coupled surface results. Inmore » either case the reaction probability is a relatively flat function of energy, except for resonant oscillations. However, the 2A{prime} reaction, dynamics (which involves a collinear transition state) is strongly perturbed by nonadiabatic effects in two distinct ways. At energies above the transition state barrier, the diabatic limit is dominant, and the 2A{prime} reaction probability is similar to that for 1A{double{underscore}prime}, which has no coupling with the other surfaces. At energies below the barrier, the authors find a significant component of the reaction probability from long range electronic coupling that effectively allows the wave packet to avoid having to tunnel through the barrier. This effect, which is observed on both the DIM and DK surfaces, is estimated to cause a 10% contribution to the room temperature rate constant from nonadiabatic effects. Similar results are obtained from the TSH and approximate quantum calculations.« less

Phase Diagram of a Heisenberg Spin-Peierls Model with Quantum Phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Perfect following in the diabatic limit

We present the theory of optical excitation of a two-level quantum system, using an interaction Hamiltonian that permits both adiabatic following and diabatic following.