Nonadiabatic Transition Probability Research Articles

On the energy dependence of inelastic cross sections

The new accurate two-state quantum calculations of the inelastic cross sections in H + Li, Na collisions for energies from the thresholds and till 100 eV or 600 eV are performed, and the results are compared with the Landau-Zener model cross sections in both the diabatic and the adiabatic representations. It is found that the low-energy inelastic cross section is very sensitive to nonadiabatic coupling and, hence, the new NaH coupling is computed. The numerical solutions of the coupled channel equations are checked by independent calculations indicating that the quantum results are accurate. These checks are done by means of the analytic formula for a nonadiabatic transition probability derived within the perturbation approach. Both the Landau-Zener-like and the non-Landau-Zener-like behaviour of the excitation cross sections are found. 34.70.+e Charge transfer

Transition probabilities on Ga(P2,S2,andP2)+CH4 reactions

In a previous item the authors reported potential energy surfaces (PESs) of the Ga–CH4 reaction, where no mention was made of transition probabilities on the avoided crossings between curves. Here they tackle this problem by applying the Landau-Zener (LZ) premise to obtain transition probabilities at these crossings and they present new developments based on the LZ theory for avoided crossings by considering the insertion angle θ as the reaction parameter. The nonadiabatic transition probability depends on the angular velocity, which leads to the inertia moment. These developments are applied to the avoided crossings of three A′ PESs of the Ga(P2,S2,andP2)+CH4 interactions.

Nonadiabatic transitions for a decaying two-level system: geometrical and dynamical contributions

We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of \alpha_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a nonuniversal one, involving the full time dependence of E_(+-)(t). This general result is applied to the Akulin-Schleich model where the initial upper level is damped with damping constant $\gamma$. For analytic power-law sweeps we find that Stueckelberg oscillations of P exist for gamma smaller than a critical value gamma_c and disappear for gamma > gamma_c. A physical interpretation of this behavior will be presented by use of a damped harmonic oscillator.

Low-energy capture of antiprotons by helium ions

Low-energy antiproton capture, p+He{sup +}{yields}pHe{sup 2+}+e, is investigated using a wave-packet-propagation full-quantum-mechanical method or a quantum-classical hybrid (i.e., semiclassical) approximation. If the adiabatic picture (i.e., Born-Oppenheinmer separation) is a good approximation, the antiproton capture, which is a typical nonadiabatic process, can rarely occur. It is found that the probability of the nonadiabatic transition is small (at most {approx}0.1). However, even in the zero energy limit (E{yields}0), the antiproton capture always occurs for the total angular momenta J(less-or-similar sign)40. Correspondingly, the cross section for the antiproton capture diverges as E{yields}0. This happens due to the peculiarity that the Coulomb force range is longer than the centrifugal one. The importance of a Rydberg series of resonances in the capture process is emphasized. On the low-energy dynamical feature, some interesting similarities to the e+ion system are also found.

Time-dependent wave packet calculations for the photodissociation of molecular chlorine

The dissociation processes of Cl 2 molecule have been studied at numerous photolysis wavelengths (310–470 nm) using time-dependent wave packet method. The initial wave packets are propagated on the excited state potentials utilizing the splitting operator technique. The optical cross-sections are calculated numerically by extracting the dynamics information at a large internuclear separation. Applying the Rozen–Zener–Demkov model, the radial non-adiabatic transition probabilities from C 1Π u to 1 u(III) electronic state are predicted, the branching ratio of various product channels and anisotropy parameter β(Cl ∗) are determined.

Photodissociation dynamics of n-C5H11Br at 234nm

Abstract The photodissociation of n-C5H11Br at 234 nm has been investigated utilizing the ion velocity imaging technique. The two-dimensional images provide detailed information on the translational energy distributions and anisotropy parameters. The obtained translational energy distributions corresponding to the Br and Br∗ fragments have been fitted by a single Gaussian function, respectively. The anisotropies for the Br and Br∗ channels are measured to be β = 1.08 and 1.84, respectively. The contributions of each electronic state have been estimated and the probability of nonadiabatic transition between 3Q0 and 1Q1 states is determined to be 0.47.

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.

Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization

Reaction mechanisms of the ultrafast photoisomerization between cyclohexadiene and hexatriene have been elucidated by the quantum dynamics on the ab initio potential energy surfaces calculated by multireference configuration interaction method. In addition to the quantum wave-packet dynamics along the two-dimensional reaction coordinates, the semiclassical analyses have also been carried out to correctly estimate the nonadiabatic transition probabilities around conical intersections in the full-dimensional space. The reaction time durations of radiationless decays in the wave-packet dynamics are found to be generally consistent with the femtosecond time-resolution experimental observations. The nonadiabatic transition probabilities among the ground (S0), first (S1), and second (S2) excited states have been estimated by using the semiclassical Zhu-Nakamura formula considering the full-dimensional wave-packet density distributions in the vicinity of conical intersections under the harmonic normal mode approximation. The cyclohexadiene (CHD) ring-opening process proceeds descending on the S1(1 1B) potential after the photoexcitation. The major part of the wave-packet decays from S1(1 1B) to S1(2 1A) by the first seam line crossing along the C2-symmetry-breaking directions. The experimentally observed ultrafast S1-S0 decay can be explained by the dynamics through the S1-S0 conical intersection along the direction toward the five-membered ring. The CHD: hexatriene (HT) branching ratio is estimated to be approximately 5:5, which is in accordance with the experiment in solution. This branching ratio is found to be mainly governed by the location of the five-membered ring S1-S0 conical intersection along the ground state potential ridge between CHD and HT.

Nonadiabatic Trajectory Studies of NaI(H2O)n Photodissociation Dynamics

We have investigated the photodissociation dynamics of NaI(H(2)O)(n) [n = 1-4] clusters using the molecular dynamics with quantum transitions method and a quantum mechanics/molecular mechanics description of NaI(H(2)O)(n), which involves a semiempirical valence-bond approach to describe the NaI electronic structure and classical solvent-solvent and solute-solvent interaction potentials. Our simulation results show that the NaI(H(2)O)(n) excited-state population decay upon reaching the NaI curve-crossing region increases with cluster size due to the stabilization of the ionic branch of the NaI excited state by the surrounding water molecules, and the resulting increase in nonadiabatic transition probability. After reaching the curve-crossing region for the first time, however, the excited-state population decay resembles that of bare NaI because of rapid evaporation of 99% and 95% of the water molecules for NaI(H(2)O) and NaI(H(2)O)(n) [n = 2-4], respectively. This extensive evaporation is due to the reversed NaI polarity in the Franck-Condon region of the NaI first excited state, which causes strong repulsive NaI-H(2)O forces and induces rapid nonstatistical water evaporation, where product water molecules are formed more rotationally than translationally hot. A few water molecules (5% or less) remain transiently or permanently bound to NaI, forming long-lived clusters, when NaI remains predominantly ionic, i.e., remains in the excited state, after reaching the curve-crossing region. To connect simulation results with experiment, we have simulated femtosecond probe signals resulting from two-photon and one-photon excitation to the X and I NaI(+) probe states. In agreement with experimental findings, the probe signals resulting from the two-photon probe scheme, where excitation occurs from the covalent branch of the excited state, decay exponentially over the NaI first excited-state vibrational period, with very little evidence of long-time dynamics. The one-photon probe scheme (not used for experimental cluster studies) is shown to be less sensitive to solvation, in that excitation energies will remain similar over a range of cluster sizes, as the ionic branch of the excited state and the NaI(+) probe states are stabilized to the same extent by the presence of water molecules. The resulting probe signals are also more revealing of the NaI(H(2)O)(n) photodissociation dynamics than the two-photon probe signals, as they may allow monitoring of solvation effects on the NaI nonadiabatic dynamics and of successive evaporation of water molecules. Time-resolved photoelectron spectra provide limited additional information regarding the NaI(H(2)O)(n) photodissociation dynamics. A key consequence of the rapid water evaporation demonstrated here is that experimentally observed signals may arise from the photodissociation of much larger NaI(H(2)O)(n) parent clusters.

Does really Born–Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

Effects of deviation from the Born–Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus–Hush–Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.

Adiabatic mode multiplexer for evanescent-coupling-insensitive optical switching

A novel adiabatic mode multiplexer enables a 2 x 2 optical switch whose operation does not depend on accumulated phase due to evanescent coupling between waveguides. The adiabatic mode multiplexer has a negligible insertion loss over C+L bands and modal cross talk better than -40 dB for any polarization state. Mode multiplexing is achieved by adiabatic transition from the fundamental mode of the single-mode waveguide to the higher mode of the multimode waveguide. Experimental measurement results for a device realized in silica-on-silicon technology are presented. By directly measuring the nonadiabatic transition probability, we show that the adiabatic mode multiplexer operates in the Landau-Zener regime.

Stark slowing asymmetric rotors: Weak-field-seeking states and nonadiabatic transitions

Stark deceleration is one of the few methods that can be used to slow polyatomic molecules. We present calculations of Stark shift energies, a quantitative analysis of nonadiabatic transition probabilities, and orientational distribution functions applicable to typical Stark slowing conditions for the two small asymmetric rotors nitromethane and acetaldehyde. We show that asymmetric polyatomic molecules are good candidates for Stark slowing.

Model study of the Landau–Zener approximation

We reexamine the accuracy of the Landau–Zener approximation, whose analytic simplicity has made it often cited and applied over the past 70years in describing nonadiabatic transitions. We find that this approximation may be in substantial disagreement with exact numerical results for a model physical system and a wide range of coupling strengths and relative velocities. We conclude that the Landau–Zener approximation should be used with caution for quantitative estimates of nonadiabatic transition probabilities or cross sections.

The triplet channel in the photodissociation of ozone in the Hartley band: Classical trajectory surface hopping analysis

The triplet channel in the photodissociation of ozone in the Hartley band, O3 + hv-->O(3P) + O2(3sigma), is investigated by means of a classical trajectory surface hopping method using ab initio diabatic potential energy surfaces for the B and the R states. Because of the strong recoil in the R state along the breaking O-O bond, O2(3sigma) is produced with a high rotational energy. The nonadiabatic transition probability depends markedly on the coordinate along the crossing seam. As a consequence a unique correlation is found between the internuclear geometry at the crossing and the final vibrational state of O2(3sigma). The calculated distribution of the translational energy is in good accord with the measured distribution.

A theoretical study of cyclohexadiene/hexatriene photochemical interconversion: multireference configuration interaction potential energy surfaces and transition probabilities for the radiationless decays

The overall energetics and the feature of reactive potential energy surfaces for the photochemical interconversion between cyclohexadiene (CHD) and all- cis-hexatriene (cZc-HT) have been investigated using the multireference configuration interaction (MRCI) calculations. The adiabatic and the diabatic potential energy surfaces of the ground and the excited states have been calculated along the Jacobi coordinates. The conical intersections among the states are estimated and the corresponding non-adiabatic transition probabilities are calculated using the semiclassical Zhu–Nakamura formula. The 1 1B–2 1A decay occurs by C 2-symmetry-breaking motion around the conical intersection. The non-adiabatic transition to 1 1A occurs by the motion toward the 5-membered ring.

Evaluation of canonical and microcanonical nonadiabatic reaction rate constants by using the Zhu–Nakamura formulas

We consider a problem of calculating both thermal and microcanonical rate constants for nonadiabatic chemical reactions. Instead of using the conventional transition state theory, we use a generalized seam surface and introduce a concept of a coordinate dependent effective nonadiabatic transition probability based on the Zhu-Nakamura theory which can treat the nonadiabatic tunneling properly. The present approach can be combined with Monte Carlo method so as to be applicable to chemical reactions in complicated systems. The method is demonstrated to work well in wide energy and temperature range. Numerical tests also show that it is very essential for accurate evaluation of the thermal rate constant to use the generalized seam surface and take into account the nonadiabatic tunneling effect.

Nonradiative decay of photoexcited methylated guanine

Radiationless decay of the two most stable methylated guanine tautomers after photoexcitation to the first excited singlet electronic state has been investigated using an “on the fly” nonadiabatic surface hopping approach based on density functional theory. The biologically relevant 9Me-keto guanine exhibits large changes in geometric and electronic structure in the S1 state giving rise to an increased nonadiabatic transition probability and thus a shorter lifetime compared to the 7Me-keto tautomer. A detailed analysis in terms of the excited state topology and individual vibrational modes is presented.

Analytic solution to wave packet dynamics in a laser field: the case of linear chirp

An analytical expression for the nonadiabatic transition probability is derived for the case that two linear potentials in coordinate space are coupled by a linearly chirped time-dependent laser field. This constitutes a solution to the wave packet dynamics in the high energy approximation. Numerical calculations are carried out to demonstrate the applicability of the formula.

Analytical calculation of nonadiabatic transition probabilities from the monodromy of differential equations

The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2x2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy approach. The application of this method to multi-level systems is also discussed.

Theoretical study of nonadiabatic transitions in the photodissociation of Cl 2 and Br 2

Lower-lying potential curves of Br 2 are calculated by the spin–orbit configuration interaction method, and the spin–orbit branching mechanisms in the photodissociation processes are examined. The second absorption band at 227 nm is assigned unambiguously to the transition from the X 1 Σ + g to the 3 Σ + 1 u ( σ g→ σ u *) state. The calculated potential curves and the radial derivative coupling elements of Cl 2 and Br 2 are used to evaluate the nonadiabatic transition probabilities by solving the time-dependent coupled Schrödinger equations semiclassically. The different nonadiabatic behavior in Cl 2 and Br 2 is analyzed in terms of the differences in the electronic factors and the reduced mass.