Diabatic Approximation Research Articles

Semiadiabatic treatment of photodissociation in strong laser fields.

A semiadiabatic treatment of the matter-field coupling is presented that accounts for the nonlinear variations affecting the widths and positions of laser-induced resonances in photodissociation as a function of the electromagnetic-field intensity. The procedure developed here goes beyond the widely used decoupled electronic-plus-field adiabatic treatment by retaining two ``semiadiabatic'' potentials that result from partial diagonalization of several blocks in the Floquet Hamiltonian. All closed channels lead to a unique multiphoton-dressed adiabatic closed channel that crosses a unique dressed adiabatic open channel. The remaining nondiagonal interaction is treated diabatically within a two-coupled-channel frame. The relative merits of diabatic approximations and of the semiadiabatic scheme are discussed within a large range of laser intensities and wavelengths on the example of ${\mathrm{H}}_{2}^{+}$(1s${\mathrm{\ensuremath{\sigma}}}_{\mathit{g}}$, v=0, J=1\ensuremath{\rightarrow}2p${\mathrm{\ensuremath{\sigma}}}_{\mathrm{u}}$) photodissociation. Uniformally accurate results are reached for the semiadiabatic approach. This is very promising for studying field-induced nonlinearities for very intense lasers operating at rather short wavelengths where many electronic states including rotational structures may play a role.

Energy levels and dynamics of vibrational predissociation of NeCl 2: Approximate quantum mechanical calculations.

Metastable energy levels and rates for vibrational predissociation of NeCl 2 (B, v 1 = 11) complex are investigated. The potential energy surface is represented by the sum of atom-atom pairwise interactions. Due to the large vibrational spacing of Cl 2 (B), a diabatic distorted-wave approximation is used to describe diatomic vibrations. Discrete energy levels are then calculated by separating adiabatically the fast stretching motion in the weak bond from the slow rotational motions within the complex. Continuum states are described in the “infinite order sudden” (I.O.S.) approximation, and rates for vibrational predissociation are evaluated using the corresponding discrete-continuum potential couplings in the frame of the Fermi's golden rule.

Two-photon sequential absorption spectroscopy of the E(0 +) state of iodine monofluoride

The energy levels of a new state of iodine monofluoride lying 5 eV above the ground state have been measured using the two-photon sequential absorption technique. Eleven vibrational levels of the state were measured. A vibrational and rotational analysis gives the spectroscopic constants as T e = 41291.96 cm −1, ω e = 248.76 cm −1, ω eχ e = 0.4951 cm −1 and B e = 0.12920 cm −1. The state has 0 + character, and dissociates to I + + F − in the diabatic approximation.

Theoretical spectroscopic study of van der Waals systems

In this paper we discuss the application of three dimensional quantum models, in order to study the dynamics of vibrational predissociation of van der Waals molecules. In the first model the vibrations are described in the distorted-wave diabatic approximation while rotations are treated in the sudden approximation. The second model is related to the “Infinite order sudden approximation” and after a close coupling formalism for the vibrations, the bending motion is considered in an approximate way. We present the 3D quasibound levels and the rates for vibrational predissociation in a test case, the HeI 2.

Dynamics of nonadiabatic reactions (theory). I. Branching ratios for early and late seams

The 3D classical trajectory surface hopping (TSH) method has been applied in a ‘‘model’’ study of factors governing nonadiabatic reaction, A+BC→AB+C* and →AB+C. In the diabatic approximation the potential-energy surfaces (pes) were a LEPS surface for F+H2 (→AB+C*) and a repulsive pes Vrep (→AB+C). These intersected in the exit valley to give an early or a late seam (E or L, perpendicular to the exit valley). The splitting at the avoided crossing 2ε was adjusted to ε=1.26 or 5.02 kcal/mol. The ratio of reactive cross sections onto the upper and lower adiabatic pes ρ* was investigated for mass combinations H+HL, L+HL, L+HH, and H+LL with E and L seams, and for small and large ε. The effect on ρ* of reapportioning a constant total energy (ETOT=13.84 kcal/mol) between reagent translation T and vibration V was examined for these 16 cases. Since the velocity in the coordinate of separation increased with increased T (yielding increased product translation; ΔT→ΔT′) ρ* also tended to increase with T. The extreme mass combinations H+HL and L+HH exhibited modified ρ* due to markedly differing widths in the entry and exit valley. The strongly skewed pes for H+LL led to multiple crossing of the seam which reduced ρ*. For other mass combinations ρ* was reduced by the inability of the low T′ component of the product to hop across the 2ε gap. In all cases ρ* was an index of the local dynamics at the seam, and hence shed light on the intermediate motions en route to the asymptotic outcome V′, R′, T′.

Resonances in the photodissociation of OH by absorption into coupled 2Π states: Adiabatic and diabatic formulations

The bound 3 2Π and repulsive 2 2Π states of OH are strongly coupled by the action of the nuclear kinetic energy operator. The process of photodissociation by absorption into the coupled 2Π states is studied theoretically. The adiabatic electronic eigenfunctions and potential energy curves of the 2 2Π and 3 2Π states are calculated using large configuration-interaction (CI) representations and the nuclear radial coupling matrix elements are obtained by numerical differentiation. The coupled equations for the nuclear wave functions of the two states are set up in an adiabatic and in a diabatic formulation and are solved by numerical integration. The electric dipole transition moments connecting the ground X 2Π state to the 2 2Π and 3 2Π states are computed from the CI wave functions and the resulting photodissociation cross sections of OH arising from absorption into the coupled 2 2Π and 3 2Π states are obtained. Two alternative sets of potential curves, coupling matrix elements, and transition moments are employed to provide an assessment of the accuracy of the results. The photodissociation cross section shows a series of resonances superimposed on a broad continuous background. The resonances are located near to the vibrational levels of the uncoupled bound diabatic potential curve. They have asymmetric Beutler–Fano profiles and vary in width from 50 cm−1 for the lowest levels to 2 cm−1 for the higher levels. The accuracy of adiabatic and diabatic approximations, carried to first order in the coupling, is explored and it is demonstrated that the diabatic approximation provides a more satisfactory representation of the photodissociation process. The discrete-continuum configuration interaction theory of Fano is applied in the diabatic formulation and the resonance structures are calculated. The discrete-continuum interaction theory yields profile parameters and level shifts which agree well with the accurate values obtained by solving the coupled equations but its application is considerably more laborious. The contribution of absorption into the coupled 2Π states to the interstellar photodissociation rate is evaluated. In the optically thin limit, the rate is1.5×10−10 s−1. The total rate is 4×10−10 s−1.

Dissipative diabatic dynamics: A shell-model approach to large-amplitude collective nuclear motion

Starting from the discussion of isoscalar giant vibrations as small-amplitude diabatic modes, a time-dependent shell-model approach is introduced which simultaneously treats coherent and incoherent aspects of large-amplitude collective nuclear motion. The coherent coupling of the single-particle motion to the time-dependent mean field is treated in a diabatic approximation. The incoherent aspect is represented by residual two-body collisions which lead to statistical equilibrium within the intrinsic degrees of freedom (local equilibrium). An important consequence of the combined effects from diabatic single-particle motion and dissipative two-body collisions is a significant retardation of the friction force for realistic values of the mean free path of nucleons. The retarded-friction term describes an elastic response of the nucleus for perturbations fast compared to the local equilibration time, and a dissipative response for slow perturbations. This elastoplastic behaviour represents an interesting dynamical property of nuclear matter. A diabatic two-center shell model is introduced and results on diabatic single-particle levels and potentials are given and compared with corresponding quantities from TDHF calculations. Effects on cross-sections of nucleus-nucleus collisions (deeply inelastic reactions, extra-push for capture and fusion) are discussed. A specific finger print for the diabatic single-particle motion is the preequilibrium emission of neutrons from unbound diabatic levels in central nucleus-nucleus collisions.

Vibrational predissociation of highly vibrationally excited van der Waals molecules. A quantum-mechanical distorted-wave treatment for vibration and sudden approximation for rotation

In this paper a three-dimensional quantum model to study vibrational predissociation of van der Waals molecules is applied to the I 2He complex for very high vibrational (50 ≤ υ 1 ≤ 64) of the I 2 subunit. The vibrations are described in the distorted-wave diabatic approximation while rotations are treated in the sudden approximation. The rates for vibrational predissociation as a function of the initial diatomic (I 2) vibrational excitation show a maximum at ν 1 ≈ 57, which is found to be in good agreement with recent experimental data.

Diabatic aspects of single-particle motion within the time-dependent Hartree-Fock theory

Time-dependent Hartree-Fock (TDHF) calculations for central collisions of86Kr on166Er are investigated with respect to quasi-stationary properties for various energies in the center-of-mass system. A quasi-stationary potential as well as quasi-stationary single-particle levels are extracted as functions of the relative distance between the two nuclei. A quantitative comparison with the diabatic two-center shell-model yields surprising agreement with the results from TDHF-calculations for both the nucleus-nucleus potential and the single-particle levels. From this we conclude that the approach phase of a nucleus-nucleus collision can be well described within a diabatic approximation for the single-particle motion.

Two-photon sequential absorption spectroscopy of iodine monobromide in the 5 eV region

Two-photon high resolution absorption spectroscopy was used to determine accurately the frequencies of sharp rotational lines in the B′(0 +) -X 1σ + transition for both I 79 Br and I 81 Br. These lines were then pumped with a high resolution dye laser, and an independently tunable probe laser used to excite transitions from the populated B′ state levels to an “E” state at 4.90 eV. A combined isotopic analysis established the E state constants for I 79Br as T c = 39491.35 cm −1, ω c = 119.158 cm −1, ω cx c = 0.2063 cm −1 and B c = 0.03069 cm −1. The state probably has O + symmetry, and dissociates into ions in diabatic approximation.

Dynamics of ligand binding to heme proteins

The dynamics of CO or O 2 binding to myoglobin are examined theoretically with particular emphasis on the effect of the globin on the barriers along possible reaction paths. By use of a diabatic representation, in which a model ligand moves in the potential of a rigid protein, two paths in or out of the heme pocket are found in myoglobin; one is by the E helix near the distal histidine and the other near the intersection of the B, D and E helices. Classical trajectories calculated for a photo-dissociated ligand in the diabatic approximation yield complicated motion; the ligand tends to spend considerable time undergoing multiple collisions with the protein matrix in the wells between barriers. To investigate the height of the barriers, the adiabatic limit is used; that is, the protein is allowed to relax in the presence of a perturbation due to the ligand-protein interaction. A detailed description is obtained for the displacements of residues required for the ligand to enter or leave the globin. The barrier heights calculated in this manner are found to be in qualitative agreement with observed values. Some differences between myoglobin and hemoglobin are described. Although the present calculations make use of a simplified model of the ligand-myoglobin system, they provide a useful first step in the analysis of the effect of the globin matrix on the binding process.

Theoretical studies of inelastic atomic collisions in a two-state model problem

A two-state scattering problem in which two non-crossing Morse curves are coupled by an exponential potential is discussed theoretically in both the diabatic and adiabatic approximations. Inelastic cross sections are estimated by various approximate analytical formulas, which are expressed in terms of the distorted wave matrix elements. The Landau (steepest descent) method is applied to estimate the distorted wave matrix element. The previously proposed separable potential approximation in the adiabatic method is found to be best among others by comparing with the exact numerical results. Transition probability as a function of l (angular momentum of relative motion) is well reproduced by this approximation. A glory effect in the velocity dependence of the cross section is found in the low energy region, and the adiabatic approximation reproduces this undulation phenomenon well.