Nonadiabatic State Research Articles

Scattering mechanism of integer quantum Hall conductance in a model system

We consider a large class of two-dimensional systems of charged particles in crossed electric and strong magnetic fields in the presence of a static substrate potentialV(x,y), which contains disorder. The time dependence of the single-particle Schroedinger functions are investigated. It is found on general grounds, that adiabatic states are dc-insulating and, that the macroscopic Hall current is carried by the non-adiabatic states. Hall conductance plateaus correspond to spectral domains, which contain only adiabatic states. The plateaus disappear, when these states become non-adiabatic at sufficiently high electric fields, i.e., at sufficiently large Hall currents. An explicit model system is investigated with a substrate potential composed of disorder and of a sequence of smooth barriers and wells. Here the non-adiabatic states can be calculated in a weak-disorder approximation, whenever the electric field (and hence the Hall current) is sufficiently low. In this case the quantum mechanical scattering process leading, to the quantisation of the Hall conductance can be understood in detail. Non-classical particle propagation plays a crucial role in this process. Our analysis opens new perspectives for the theory of the integer quantum Hall effect.

A simple determination of the potential energy curves and couplings for long-range charge-transfer reactions. Application to the system (ArN 2) +

An original method is presented for calculating long-range energies and couplings of the two (non-adiabatic) states A +–B and A–B + of a charge-transfer system (AB) +. This method is applied to the calculation of the charge-exchange cross sections in the system (ArN 2) +. Concerning the reaction from N 2 +, we show that the errors made in approximating the interaction energy and the couplings do not affect strongly the values of the cross sections, that most transitions are well described by the Demkov model, and that the evolution of the cross section is governed by the radius R D (where the coupling is equal to the separation of the states) rather than by the transition probability. We have also obtained qualitative information for the reaction from Ar +.

Semiclassical eigenvalues for a non-adiabatic system

We have performed a semiclassical quantization of the Meyer-Miller classical analog Hamiltonian for the Jahn-Teller E × e system, in the regime of small linear coupling. The primitive semiclassical energies are in good qualitative and reasonable quantitative agreement with the exact quantum-mechanical solution to this problem. These results demonstrate that such a classical model is able to accurately describe the behavior of non-adiabatic bound state systems, but that uniformization will be necessary to obtain more precise agreement with quantum mechanics.

The intra-atomic coulomb repulsion and the distribution of charge states of atoms leaving metal surfaces

The final charge state of an atom leaving a metal surface is calculated, assuming an N-fold degenerate atomic orbital which is in resonance with the conduction band of the metal. The theory is based on an Anderson Hamiltonian approach, and an expansion into states with a small number of e-h pairs is used. The intra-atomic Coulomb repulsion is taken into account by not allowing double occupation of the atomic orbital, i.e. it is taken as infinite. For exponentially decreasing interaction matrix elements and if the atom moves sufficiently slowly the probability that the non-adiabatic charge state will result has the form exp (− c/ν), where ν is the velocity of the adatom motion away from the surface. When the atom valence level ϵ a is above the Fermi level the constant c is found to be larger than in the non-interacting (or N = 1) case, and when ϵ a lies below ϵ F it is found to be smaller. The relevance of the effect for the charge distribution observed in atom scattering and sputtering is discussed.

Vibronic structure of nonadiabatic and fluxional states: Two-photon absorption spectroscopy of jet isolated 3s 1E′ s y m-triazine

The nature of nonadiabatic effects in the Rydberg and ground ionic states of jet-cooled sym-triazine is investigated by means of ultraviolet two-photon absorption spectroscopy. A highly resolved band system is observed in the region from 55 000 to 60 000 cm−1, which can be associated with excitation from an e′ lone pair to the 3s Rydberg orbital. A complete assignment of the low-energy bands of this system, as determined by isotope effects and comparison to model calculations, reveals a clear example of the dynamical Jahn–Teller effect for the case where only one mode, the ν6 ring distortion, is significantly active. On the basis of simple limiting models we derive approximate vibronic coupling parameters and present a quantitative description of vibronic motion in terms of adiabatic molecular coordinates. We conclude that sym-triazine, in its ground state one of the most rigid of medium-sized polyatomics, becomes strikingly fluxional in its Rydberg and ground ionic states, as the dynamic Jahn–Teller effect introduces a ring-distortion vibronic pseudorotation which can be characterized adiabatically in terms of a rotor frequency no greater than 80 cm−1. This is a limit, however, which the data shows is valid only well below a vibronic energy of 1100 cm−1, at which point the conical intersection is reached and all levels become intrinsically nonadiabatic.

The determination of radial non-adiabatic coupling: HeNe2+as a case study

The matrix elements of the operator d/dR between the first three 1 Sigma + singlets of HeNe2+ have been calculated by the rigorous finite differences technique and by Levy's projection method, based on the determination of the effective Hamiltonian in a quasi-diabatic basis. A numerical diabatisation procedure based on the knowledge of the d/dR matrix elements has also been applied. The results of the two methods for determining non-adiabatic couplings and quasidiabatic states have been compared. The nature of the avoided crossing between the A and B 1 Sigma + states of HeNe2+ is discussed.

Adiabatic vs. non-adiabatic state of a heavy particle in a metal

We discuss a heaby particle moving in an arbitrary potential in a metal. Special attention is paid to whether the interaction with metallic electrons causes a mass shift and/or induces an effective potential. The adiabatic approximation, in which the wave function of the metallic electrons follows the instantaneous position of the particle, involves a difficulty due to the orthogonality catastrophe. We propose a modified adiabatic scheme valid in the ground state to overcome the difficulty, where the particle can be viewed as moving in the unmodified potential with the unmodified mass. When the potential is such that the particle is very localized, this scheme breaks down. The condition for this to occur is k 2 F b 2 ≦̸ ( m/ M) ln( M/ m), where b is the effective range of the particle wave function and m/ M the mass ratio. The possibility of self-trapping of the particle is examined.

Nonadiabatic treatment of the intensity distribution in the V–N bands of ethylene

The V–N band system of ethylene between 6.0 and 8.5 eV has been investigated through ab initio nonadiabatic vibronic calculations. The N1(π2), V1(π,π*), and Ry1(π,3py) electronic states and energies involved in this transition have been calculated as functions of the torsional angle around the CC bond, at an extended CI level and the adiabatic torsional states have been expanded in a free-rotor basis. The nonadiabatic states corresponding to the V and Ry species have then been expanded in the adiabatic electronic–torsional basis with the help of explicit calculations of the vibronic coupling functions. The V and Ry electronic states undergo a sharply avoided crossing and configurational mixing during the torsion and have a significant contribution from (π,ndπ) species, the lower state changing from Ry at D2h to V at the D2d conformation and the upper showing the opposite variation. The V–Ry vibronic couplings are thus quite large in the region of the avoided crossing and the nonadiabatic states above 7.5 eV are strongly mixed; by contrast the lowest-lying species derive mainly from the π→π*V excitation. The computed 0–0 torsional origin at 6.00 eV and the following two levels are in very good agreement with the locations of the first three observed bands, whereas the deviations increase for higher levels in a regular way owing to a small overestimation of the computed ω4′ value; the discrete portion of the V–N system is well reproduced by the present calculations provided a renumbering of the observed bands is undertaken. The nonadiabatic coupling of the V and Ry states is very important near the intensity maximum of the V–N system, yielding a very diffuse intensity distribution in good agreement with the observed broad continuum. A theoretical progression shows two intensity maxima at 7.78 and 8.06 eV, somewhat above that deduced experimentally at 7.66 eV, which has been estimated by subtracting off the intensity of the sharp R 1(π, 3s)–N bands superimposed on the apparent continuum. Numerical tests show that the maximum at 8.06 eV is shifted to about 7.9 eV by taking into account some limitations of the present investigation. Finally, calculated vertical transition energies to various excited states of ethylene, obtained with a large AO basis set indicate that other Rydberg states should have nonadiabatic couplings in the 7.0–8.5 eV region with the electronic species here considered when antisymmetric vibrations are excited, thus leading to a further broadening of the V–N band system; accordingly a vibronically mixed Rx1(π,3px)–V1(π,π*) species is indicated as being the upper state in Wilkinson’s R′–N transition of T0 = 8.26 eV, as has earlier been suggested by various authors.

Investigation of nonadiabatic effects in molecular-hydrogen Rydberg states by electric field ionization

The technique of electric field ionization has been used to study molecular Rydberg states of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ formed by electron capture of ${\mathrm{H}}_{2}^{+}$ or ${\mathrm{D}}_{2}^{+}$ beams in ${\mathrm{H}}_{2}$. The neutral molecules were passed through two intense electric field ionization regions in tandem, separated by an \ensuremath{\sim} ${10}^{\ensuremath{-}7}$-sec drift region. Up to 15% of the Rydberg population removed by the first ionization region was repopulated during transit through the drift region. This result has been interpreted in terms of nonadiabatic state mixing of nearly degenerate adiabatic molecular states. A difference in the state repopulation between Rydberg states of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ was observed, indicating the importance of the rovibrational spectrum on the repopulation mechanism. By comparison, similar studies on atomic Rydberg states showed no difference between H and D. Moreover, the atoms exhibited only a small repopulation effect, consistent with the contribution due to $\stackrel{\ensuremath{\rightarrow}}{1}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$ coupling.

Rovibronic two-photon transitions of symmetric top molecules

Rotational line strengths of two-photon absorption (TPA) processes in symmetric top molecules in the gas phase are developed by angular momentum theory. Experimentally accessible polarization states and frequencies of the photons are considered case by case. For TPA processes of identical photon frequency, parallel linearly polarized photons and same-sense circularly polarized photons form a complete polarization study. In the absence of resonance-enhanced intermediate states, TPA of nonidentical photon frequencies normally does not give new spectral features which are forbidden in identical TPA, because of the highly unfavorable weighting factors involving the intermediate state energies. High resolution studies of TPA, especially in the Doppler-free regime where features can be further resolved, is an alternative and can be more fruitful than polarization study for excited state assignments. A more general selection rule for TPA is that the initial and final states must have identical overall rovibronic symmetry. The Jahn–Teller effect induced, j-type doubling can be probed directly by TPA. As resonance condition is approached, features of different rotational structures (ΔK selection rules) within a two-photon allowed electronic band can occur through a nonadiabatic intermediate state. The polarization ratios for near-resonant TPA, which is useful for both intermediate and final state assignments, are also presented.

Non-adiabatic 2s-2p state mixing in metastable hydrogen by electric fields

The evolution of a (n=2) hydrogen atom passing through a linearly increasing or decreasing electric field is calculated in a three-state approximation. The observable fraction of 2p1/2, 2s1/2 and 2p3/2 quantum state in the resulting coherent mixture is calculated. The amplitude of the oscillations, which appear when the field parameters are varied, is shown to depend only on the rate of change of the field, as seen by the atom. Maps of oscillation amplitudes and average values are given for the metastable atom. Comparison is made with the sudden and adiabatic approximations.

Some accurate results for three-particle systems

Results of a variational calculation of the nonadiabatic ground state energy of H 2 + are presented. Diagonal corrections for nuclear motion have also been calculated for the electronic ground state of H 2 + . The adiabatic potential energy curve has been employed to calculate the rotational and vibrational levels for the H 2 + ion and for muonic molecules. Nonadiabatic energy corrections are discussed. Forpμd the adiabatic wave function is compared with the corresponding nonadiabatic result.