Diabatic Approximation Research Articles

High-Temperature Optical Spectra of Diatomic Molecules: Influence of the Avoided Level Crossing

In this study, we analyzed the light absorption by diatomic molecules or colliding atoms in a spectral region dominated by an avoided crossing of adiabatic state levels or crossing of the corresponding diabatic state levels. Our attention was focused on the low-resolution spectrum at a higher gas temperature under local thermodynamic equilibrium conditions. The absorption measurements of mixed vapors of potassium (≈80%) and cesium (≈20%) were made in the temperature range of 542–715 K and the infrared spectral range 900–1250 nm. In this area, the main spectral contributions were the broad A 1 Σ ( u ) + ( 0 ( u ) + ) − X 1 Σ ( g ) + ( 0 ( g ) + ) bands of K2, Cs2, and KCs molecules. There was a crossing of A 1 Σ ( u ) + ( 0 ( u ) + ) and b 3 Π ( u ) ( 0 ( u ) + ) state potential curves and the coupling of this state was due to the matrix element ⟨ A 1 Σ ( u ) + ( 0 ( u ) + ) | H s o | b 3 Π ( u ) ( 0 ( u ) + ) ⟩ of the spin–orbit interaction. Using data for relevant electronic potential curves and transition dipole moments existing in the literature, the spectra of the A 1 Σ ( u ) + ( 0 ( u ) + ) − X 1 Σ ( g ) + ( 0 ( g ) + ) molecular bands of K2, Cs2, and KCs molecules were calculated. Full quantum mechanical and semi-quantum coupled channel calculations were done and compared with their non-coherent adiabatic or diabatic approximations. Through the comparison of our theoretical and experimental spectra, we identified all observed spectral features and determined the atoms’ number density and gas temperature.

Oscillation of channel branching ratios and g−u -symmetry state mixing in the direct photodissociation of HD

For the direct photodissociation of HD in the second threshold, there are four open channels $\mathrm{H}(2s)+\mathrm{D}(1s), \mathrm{H}(2p)+\mathrm{D}(1s), \mathrm{D}(2s)+\mathrm{H}(1s)$, and $\mathrm{D}(2p)+\mathrm{H}(1s)$. We measured the channel branching ratios and found that the ratios oscillate with the wave vectors of the photofragments. However, the population ratios $[\mathrm{H}(2s)]/[\mathrm{H}(2s)+\mathrm{D}(2s)]$ and $[\mathrm{H}(2p)]/[\mathrm{H}(2p)+\mathrm{D}(2p)]$ are nearly constant \ensuremath{\sim}0.6. The results can be explained by assuming that the photodissociation in the Franck-Condon region follows mechanisms similar to those of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$, i.e., the excitations are to the $3p\ensuremath{\sigma}{B}^{\ensuremath{'}}{}^{\phantom{\rule{0.16em}{0ex}}1}{{\mathrm{\ensuremath{\Sigma}}}_{u}}^{+}$ and $2p\ensuremath{\sigma}B{}^{\phantom{\rule{0.16em}{0ex}}1}{{\mathrm{\ensuremath{\Sigma}}}_{u}}^{+}$ states that are interfered with due to the phase differences between the two states. For HD, near the dissociation limits, the $g\ensuremath{-}u$ pair states that are valid in the Born-Oppenheimer approximation are mixed almost completely in the corrected adiabatic approximation. A diabatic approximation would thus predict that the ratios $[\mathrm{H}(2s)]/[\mathrm{H}(2s)+\mathrm{D}(2s)]$ and $[\mathrm{H}(2p)]/[\mathrm{H}(2p)+\mathrm{D}(2p)]$ are 0.5.

Exact relations for the differential conductance and rectification ratio of the tunnel current in the redox-mediated tunneling junctions and demonstration within the fully diabatic approximation for electron transitions

Exact relations for the differential conductance and rectification ratio of the tunnel current through a single one-level redox-active molecule in the electrochemical metal-molecular-metal tunneling junction are obtained in the wide-band approximation. These relations are valid at any temperatures, strengths of the redox molecule-electrodes coupling, arbitrary interaction of the valence electrons with arbitrary phonon modes, arbitrary positions of the redox-molecule valence level and any energies of the Coulomb repulsion U between electrons at the valence level. These relations have the particular physical importance because they permit to reveal in the general form the parameters which determine values of the differential conductance and rectification ratio. The obtained relations also permit to consider the differential conductance/overpotential and rectification ratio/overpotential characteristics only in the specific regions of the parameter space. In order to demonstrate the obtained relations, we calculate and interpret the differential conductance/overpotential and rectification ratio/overpotential characteristics for the case when the redox-mediated tunneling junction has only the classical phonon modes and is described within the fully diabatic approximation.

Fluctuations of work in nearly adiabatically driven open quantum systems.

We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.

The adiabatic approximation as a diagnostic tool for torsion–vibration dynamics

The adiabatic separation of large-amplitude torsional motion from small-amplitude vibrations is applied as an aid in interpreting the results of fully coupled quantum calculations on a model methanol Hamiltonian. Comparison is made with prior work on nitromethane [D. Cavagnat, L. Lespade, J. Chem. Phys. 106 (1997) 7946]. Even though the torsional potentials are very different, both molecules show a transition from adiabatic to diabatic behavior when the CH stretch is excited to ν CH = 4 or higher. In the adiabatic approximation, the effective torsional potentials for the various CH stretch vibrational states do not cross, but the CH vibrational amplitude moves from one bond to the next as a function of torsional angle. In the diabatic approximation, the effective torsional potentials do cross, but the distribution of the CH vibrational amplitude remains approximately constant in the vicinity of the crossing. The transition to diabatic behavior is promoted by the normal mode to local mode transition, and the relevant adiabatic and diabatic effective torsional potentials are determined by the torsion–vibration coupling. The torsion–vibration couplings in the four overtone manifolds considered (methanol OH, CH, nitromethane CH, and hydrogen peroxide OH) are large, reaching 265–500 cm −1 by ν XH = 6, and are of generally similar magnitude. The largest torsion–vibration couplings involve the first Fourier term in the torsional angle (cos γ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2 γ in nitromethane and cos3 γ for the OH stretch of methanol) result in somewhat weaker coupling. Nonadiabatic matrix elements in methanol couple the torsional and vibrational energies and they exhibit a slow fall-off with coupling order.

Stochastic Dynamics of Release Unit in a Cardiac Cell in Electron-Conformational Model

To further understand the role of stochastic dynamics of ryanodine receptor (RyR) channels on spark generating process we studied the stochastic RyR's cluster gating in calcium release unit (RU) in cardiomyocytes under steady-state conditions. We apply a simple biophysically-reasonable electron-conformational (EC) model [Moskvin ea, PBMB, 2006] for the RyR channel. Single RyR channels are characterized by fast electronic and slow classical conformational degrees of freedom. The RyR gating implies calcium induced electronic transitions between two branches of a conformational potential, a conformational Langevin dynamics, thermoactivated transitions and quantum tunneling. The sarcoplasmic (SR) load is incorporated into the model through the effective conformational strain.We examined different model dependencies of the electronic transition probability on the calcium ion concentration and effective temperature in dyadic space to reproduce all the features observed in lipid bilayer experiments. The 11 × 11 RyR cluster was build into a simple RU dynamic unit. Model simulations performed in frames of a diabatic approximation with a conformational inter-RyR coupling have revealed different gating regimes with a single RyR channel openings generating a Ca2+ synapse (quark) and a cooperative cluster mode, due to a step-by-step opening of a fraction of coupled RyR channels. We have found and analyzed the spark generating openings of groups of channels, providing for a sufficient release. The SR overload was shown to lead to the autooscillation regime with nearly periodical openings-closings of RyR-channels.The RU functioning was examined under different rates of SR load and different strength of the inter-RyR coupling. The EC model was shown to provide an adequate description of the cardiomyocite RU dynamics with valid prediction abilities.Supported by RFBR Grants 05-04-48352, 07-04-96126.

The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σu−1(c4Σu−), v vibrational states of the O2+ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ0 = 0.054 meV and Γ1 = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O2 molecule. About 99% of the O2+ ions in the 2σu−1(c4Σu−), v states were found to decompose to the O(1D) + O+(4S) dissociation products.

Vibrational relaxation on the mixed vibronic levels of the [formula omitted] and [formula omitted] states in all- trans-neurosporene as revealed by subpicosecond time-resolved, stimulated emission and transient absorption spectroscopy

In all- trans-neurosporene, whose 1 B u - ( 0 ) level is lower than the 1 B u + ( 0 ) level by one vibrational quantum, the following two steps of vibrational relaxation from the mixed vibronic states were identified, in the order, 1 B u + ( 1 ) + 1 B u - ( 2 ) stimulated emission → 1 B u + ( 0 ) + 1 B u - ( 1 ) stimulated emission → 1 B u - ( 0 ) transient absorption. The stimulated emission patterns were simulated by the use of Franck–Condon factors in the transitions from the pair of mixed vibronic levels down to the ground 1 A g - ( υ ″ ) vibronic levels. The vibronic levels of the mixed 1 B u + and 1 B u - state were characterized theoretically based on the diabatic approximation.

Theory of Photoinduced Phase Transitions: From Semiclassical to Quantum Aspects

We review recent progress of theoretical studies for the photoinduced phase tran- sitions (PIPTs) to clarify what the PIPTs are. There are two types of the PIPTs: (a) global change via optically excited states and (b) new material phase creation in optically excited states. First, concerning (a), photoinduced structural phase transitions via excited electronic states are discussed using a minimal one-dimensional model composed of localized electrons and lattices. We show that the global structural change by photoexcitation only at a single site is possible under the adiabatic or diabatic approximation. This dynamics of the domain bound- aries (domain walls) is called the “photoinduced domino process,” which is the photoinduced nucleation in nonequilibrium first-order phase transition. Second, concerning (b), we discuss quantum orders of electron-hole (e-h) systems, which are optically excited states of insulators consisting of many electrons and holes in two bands. In particular, the “exciton Mott transi- tion,” i.e., the “from-insulator-to-metal” transition of the e-h systems as the particle density increases is introduced. We stress that this transition depends strongly on dimensionality of the system.

Theory of Photoinduced Domino Processes.

Photoinduced phase transitions via excited electronic states are discussed theoretically using a one-dimensional model composed of localized electrons and lattices under the adiabatic or diabatic approximation. We show that the global phase change by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such phenomena. In the adiabatic regime, depending on the intersite interaction, an initial local photoinduced change (i) remains locally, (ii) induces cooperatively a global phase change, or (iii) disappears and the system returns to the initial phase. Dynamical features of the case (ii) are characterized by the “deterministic domino” processes of the domain walls; the domain walls between the two phases move deterministically with a constant velocity without spontaneous emissions. In the diabatic regime, similar three types of photoinduced change are possible. The domain-wall dynamics is described as the “stochastic domino” process with a random velocity, which is accompanied by the successive radiative transitions. Related topics of the photoinduced domino theory are also introduced.

Coupling between fragment radial motion and the transversal degrees of freedom in cold fission

The tunneling of a quasibound dinuclear system along the main radial mode is studied for the case of cold fission when the very small excitation energy present in the decaying system is distributed among molecular type transversal collective degrees of freedom. Such a collective mode has typical oscillation periods much smaller than the tunneling time of the main radial mode and, therefore, we discuss various approaches that are suitable in dealing with this problem. The modified penetrabilities are obtained at first by solving the coupled set of Schr\"odinger equations in the adiabatic and the diabatic approximations. The comparison with the one-dimensional penetrability is done also in the frame of the Feynman path integral formalism for a very large inertial mass and small transversal vibrations frequency. In all cases the coupling of the radial(fission) mode to the transversal degrees of freedom leads to a change in the tunneling probability that is, however, not so strong to determine significant variations in the fission lifetime.

Domino mechanisms in photoinduced phase transitions

Photoinduced structural phase transitions via excited electronic states are discussed theoretically using a one-dimensional model composed of localized electrons and lattices under the adiabatic or diabatic approximation. We show that the global structural change by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such phenomena. Spatiotemporal dynamics of nonequilibrium first-order phase transitions is also investigated in detail in terms of photoinduced nucleations and domino processes of the domain boundaries (domain walls), which are in striking contrast to the mean-field dynamics. In the adiabatic regime, after the spontaneous emission of a photon, an initial local structural change (i) remains locally, (ii) induces cooperatively a global structural change, or (iii) disappears and returns to the initial phase. Dynamical features of the case (ii) are characterized by the deterministic (semichaotic) domino process; domain walls between the two phases move determinis-tically at a constant velocity (with changing speed) without further spontaneous emissions in the case of strong (weak) dissipation. In the diabatic regime, similar three types of structural change exist. The domain-wall dynamics is described as the stochastic domino process, which is accompanied by the successive radiative transitions. A new theoretical treatment is also proposed to study crossover between the adiabatic and diabatic regimes.

Theory of Domino Processes in Photoinduced Cooperative Phenomena

Photoinduced phase transitions via excited electronic states are discussed theoretically using a minimal model composed of localized electrons and one-dimensional lattices under the adiabatic and diabatic approximations. We show that the global structural transition by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such cooperative phenomena. Spatiotemporal dynamics of nonequilibrium first-order phase transitions is also investigated in terms of the domino process in photoinduced nucleations.

Monte Carlo simulations of charge transport in molecular solids: a modified Miller Abrahams type jump rate approach

Charge transport properties in disordered organic materials show some universal characteristics which are related to the “intrinsic” degree of disorder both energetically and spatially rather than to the dominance of impurity effects. This behaviour is usually explained in terms of charge transport via elementary hopping processes between localised “sites” in terms of Gaussian Disorder Model. Quantum mechanical models for the charge transfer in donor–acceptor complexes in the diabatic approximation suggest electronic transfer rates which are dependent on the energy difference between initial and final state as well as some reorganisation energy in both directions of the electron transfer, i.e., independent of the sign of the energy difference. This contrasts a ubiquitous factor 1 for jumps downward in energy and gives rise to what we believe is a more accurate description of the dynamic properties of charge transport. In order to clarify the influence of such a modification on the macroscopic charge transport, we set up dynamic MC calculations. The temperature and field dependence of the mobility for both jump rate expressions are compared. We study the effect of spatial and energetic Gaussian disorder and discuss implications for the interpretation of experimental data.

Stochastic and deterministic domino processes in photoinduced structural changes

The photoinduced structural change is discussed theoretically using a one-dimensional model, which is composed of localized electrons and lattices. We clarify the condition for the adiabatic and/or diabatic approximations. The global structural change by one-site excitation is possible in both cases. Under the adiabatic picture, the domain wall between the two phases moves at constant velocity, and the structural change in each site occurs nonradiatively within the time order of the lattice vibration. On the contrary, under the diabatic picture, the motion of the domain wall becomes a stochastic process because the structural change in each site occurs via the radiative transition, which takes a longer time than the lattice vibration.

Low-energy electron - argon scattering in a low-frequency laser field

We have used several non-perturbative Floquet methods to calculate the differential and total cross sections for electron scattering from argon in a laser field. One method utilizes the mixed-gauge R-matrix technique to calculate the scattering cross section. A diabatic approximation adopted from molecular applications is also applied to this low-frequency limit. Results are compared with the well known Kroll - Watson approximation. We find that all three theoretical treatments agree well with each other but do not agree with some experimental results. Possible explanations for the discrepancy between the calculations and experiments are examined.

Equipotential surfaces of the model reaction H+H2: Struggling with three dimensions

The solution of the complete Schrödinger equation for scattering and electronic structure calculations is the objective of this work, focusing on the triatomic systems. The mathematical difficulties of solving the Schrödinger equation are analyzed, what can be done easily and what needs large scale computational work. An overview of basic atomic and molecular quantum mechanics is given, including how adiabatic and diabatic approximations are used in calculating scattering cross sections. Effective interaction potentials are discussed in detail, how to compute them and what they look like. Besides describing how computers have opened the door to real computation of the full spatial behavior of these multicomponent systems, some simple graphical images significantly aid the development of intuition of how the system actually behaves. The graphical representation focuses on the potential energy surfaces of the H3 electronic structure.

From Skyrmions to NN phase shifts.

We study the [ital NN] phase shifts in a Hamiltonian obtained from quantization of the collective modes in the Skyrme model. We show that a combination of an adiabatic and a diabatic approximation gives a good [ital NN] force, with sufficient attraction to produce a bound deuteron. The description of the repulsive core appears to be the main cause for the remaining discrepancies between the Skyrme-model force and phonomenology. Finally we discuss the possibility of finding nonstrange dibaryon resonances in the [ital J][sup [pi]]=3[sup +], [ital T]=0 channel.

The diabatic approximation in the classical frame

The time-dependent version of a Golden Rule treatment for studying vibrational predissociation (VP) of a model triatomic van der Waals (vdW) X ċ BC system shows the VP rate as the Fourier transform of an autocorrelation function. Analytical fits to this time dependent function allow the rewriting of such a rate in terms of the autocorrelation time. This suggests the possibility of using a diabatic vibrational approximation within the classical frame. In particular, it would enable the study of the VP of vdW clusters containing a fast vibrational diatomic subunit, a current bottleneck in quasiclassical trajectory (QCT) calculations.

Potential surface symmetry and vibronic wave functions for methane cation

In attempting to understand the ground vibronic state of CH+4, a new formalism was developed for discussing molecular symmetry groups. Various diabatic basis sets and approximations for Jahn–Teller vibronic problems were examined, using the relatively simple E⊗e case. Finally, the symmetries and form of the ground vibronic states of CH+4 were produced.