A theoretical study of the non-adiabatic charge transfer process Ar2+ (3 P) + He(1 S) → Ar+(2 P) + He+(2 S)

CI calculation with a large basis have been used to calculate the two lowest ³Π adiabatic potential energy curves for the title reaction. These potentials have been transformed to diabatic potentials by employing a recipe based on the CI coefficients. Quantum mechanical close coupling calculations in the diabatic basis have produced total and differential cross sections which are in good agreement with experimental data. Full quantum mechanical and Landau-Zener calculations of the total cross section are in fair agreement with recent experimental measures and by small changes to the diabatic potentials can be brought into essentially exact agreement.     

Multi-channel scattering problems: an analytically solvable model

We have proposed a general method for finding an exact analytical solution for the multi-channel scattering problem in the presence of a delta function coupling. Our solution is quite general and is valid for any set of potentials, if the uncoupled diabatic potential has an exact solution. We have also discussed a few examples, where our method can easily be applied.     

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 (cosγ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2γ in nitromethane and cos3γ 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.     

Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation I. Tunnelling at small relaxation

Basic equations of the perturbational theory of nonradiative multiphonon transitions are reformulated in semiclassical approximation. They are specialized for the mechanisms of static (diabatic) and adiabatic coupling corresponding to the polar alternatives of crossing versus non-crossing oscillator potentials in a two-level-one-mode system. Tunnelling rates are calculated on the basis of contour integrals in the complex co-ordinate plane. These rates for static coupling are proportional to the square of the off-diagonal electron-oscillator interaction as commonly expected. For the alternative of adiabatic coupling we have obtained a non-monotonous (oscillating) pre-exponential transition rate factor. This unfamiliar result is based on a certain beyondnon-Condon procedure consisting in a consequent observation both of the familiarnon-Condon effect represented by the Lorentz function behaviour of the non-adiabaticity term and the associatedavoided- crossing (hyperbolic) behaviour of adiabatic potentials in the classical transition region. Present results confirm both the general non-equivalence of both alternative coupling mechanisms and a certain asymptotic approach between mechanism-specific tunnelling rates at small off-diagonal interactions.     

Enhancement of macroscopic quantum tunneling by Landau-Zener transitions

Motivated by recent realizations of qubits with a readout by macroscopic quantum tunneling in a Josephson junction, we study the problem of barrier penetration in the presence of coupling to a spin-1 / 2 system. It is shown that, when the diabatic potentials for fixed spin intersect in the barrier region, Landau-Zener transitions lead to an enhancement of the tunneling rate. The effect of these spin flips in imaginary time is in qualitative agreement with experimental observations.     

Eigenmodes of triaxial ellipsoidal acoustical cavities with mixed boundary conditions

The linear acoustics problem of resonant vibrational modes in a triaxial ellipsoidal acoustic cavity with walls of arbitrary acoustic impedance has been quasi-analytically solved using the Frobenius power-series expansion method. Eigenmode results are presented for the lowest two eigenmodes in cases with pressure-release, rigid-wall, and lossy-wall boundary conditions. A mode crossing is obtained as a function of the specific acoustic impedance of the wall; the degeneracy is not symmetry related. Furthermore, the damping of the wave is found to be maximal near the crossing.     

Spectroscopic effects of conical intersections of molecular potential energy surfaces

A simple vibronic coupling model involving two electronic states and two vibrational modes is considered. The model is based on harmonic diabatic potentials and linear coupling of the diabatic electronic states. It is shown that the adiabatic electronic potential energy surfaces exhibit, in general, a conical intersection. The well known E × E and E × B Jahn-Teller problems are contained as special cases. Using numerical methods the optical absorption spectrum is calculated exactly. Extremely complex vibronic spectra are obtained when the conical intersection occurs within the Franck-Condon (FC) zone. The exact vibronic spectra are compared with spectra calculated in the adiabatic and FC approximation. The genuine spectroscopic effects of conical intersections are revealed by a comparison with the results of standard one-dimensional vibronic coupling calculations. The presence of a conical intersection limits the applicability of the adiabatic and FC approximations much more strongly than in the one-dimensional case. The upper adiabatic electronic state is strongly affected by non-adiabatic coupling even when the point of intersection lies outside the FC zone. The relevance of these results for the calculation of molecular electronic spectra is briefly discussed.     

Introduction to the theory of electronic non-adiabatic coupling terms in molecular systems

The Born–Oppenheimer treatment leads to the adiabatic framework where the non-adiabatic terms are the physical entities responsible for the coupling between adiabatic states. The main disadvantage of this treatment is in the fact that these coupling terms frequently become singular thus causing difficulties in solving the relevant Schroedinger equation for the motion of the nuclei that make up the molecular systems. In this review, we present the line integral approach which enables the formation of the adiabatic-to-diabatic transformation matrix that yields the friendlier diabatic framework. The review concentrates on the mathematical conditions that allow the rigorous derivation of the adiabatic-to-diabatic transformation matrix and its interesting physical properties. One of the findings of this study is that the non-adiabatic coupling terms have to be quantized in a certain manner in order to yield single-valued diabatic potentials. Another important feature revealed is the existence of the topological matrix, which contains all the topological features of a given molecular system related to a closed contour in configuration space. Finally, we present an approximation that results from the Born–Oppenheimer treatment which, in contrast to the original Born–Oppenheimer approximation, contains the effect of the non-adiabatic coupling terms. The various derivations are accompanied by examples which in many cases are interesting by themselves.     

Curve crossing problem with Gaussian type coupling: analytically solvable model

We give a general method for finding an exact analytical solution for the two state curve crossing problem. The solution requires the knowledge of the Green's function for the motion on the uncoupled potentials. We use the method to find the solution of the problem in the case of parabolic potentials coupled by Gaussian interaction. Our method is applied to this model system to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.     

A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics

We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1-4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.     

Optical potential discrete variable representation method in the adiabatic representation

The optical potential discrete variable representation method (OP-DVR) has been applied recently to calculate resonances in the framework of the diabatic representation [J. Chem. Phys. 101, 7580 (1994)]. This method is based on the conjoint use of the discrete variable representation (DVR) method and the properties of a complex absorbing potential (CAP). The OP-DVR method is the DVR version of the CAP stabilization method initially proposed by Jolicard and Austin [Chem. Phys. Lett. 121, 106 (1985)]. In the present study, we show that this efficient and accurate method can also be applied within the adiabatic representation since it allows one to overcome in a simple way, numerical difficulties associated with the first derivative operator which appears in the expression of non adiabatic couplings. Within the OP-DVR method, the choice of the representation (diabatic or adiabatic) is governed by physical arguments and by the fact that the potentials and the couplings are known in one or the other of these two representations. In the case where the potentials and the couplings are obtained in the adiabatic representation, we show in this paper that the transformation into the diabatic framework is not necessary. We demonstrate that the discrete variable representation can be a simple and an efficient way to deal with the adiabatic representation. Received: 30 April 1998 / Revised: 29 September 1998 /Accepted: 21 October 1998     

On the coupling impedance for particles with opposite velocities

As already shown by several authors, the reciprocity theorem can be rewritten as a simple formula connecting the longitudinal coupling impedances of a particle travelling in the positive and negative directions of an infinitely long vacuum chamber crossing a scattering structure (cavity, step junction, iris, etc.) of general shape. The formula is valid for any particle velocity. As an example, we consider the case of two semi-infinite circular vacuum chambers with different radii; for this case we give the explicit difference between the coupling impedances and the wake potentials. Received: 27 March 2002 / Revised version: 5 December 2002 / Published online: 26 February 2003     

Diabatic states from nodal structure conservation

For a Hamiltonian H(q), given in a suitable set of basis states, we construct diabatic states from requiring conservation of their nodal structure. The diabatic states and energies are single-valued functions for an arbitrary number of parameters q equivalent to {q1,q2,...q(f)}. The method is illustrated for nucleons moving in a deformed Woods-Saxon potential.     

Diabatization of the reactive F + H<Subscript>2</Subscript> system employing rigorous Berry phases

In this article are presented the first ever derived single-valued diabatic potentials for the reactive H₂ +  F system based on a rigorous study of the conical intersection (ci) and Born-Oppenheimer non-adiabatic coupling terms (BO NACTs). This study revealed the existence of a Jahn-Teller (1, 2) ci located at a point on the collinear axis and a Renner-Teller (2, 3) ci along this axis. The diabatic potentials were calculated employing the rigorous adiabatic-to-diabatic transformation (ADT) angles (also known as mixing angles) which possess integer Berry phases along any closed contour at the region of interest in configuration space. The ADT angles were calculated employing BO NACTs and line integrals.     

Inter-state coupling and definitions of bright and dark states

Contrary to a standard definition of diabatic states (i.e., those without momentum-dependent coupling), based on the construction from adiabatic ones, we defined diabatic states as bright and dark states of a given experiment. Namely, they are defined as states providing maximum, respectively, zero value of electronic transition dipole moments projected to a given polarization vector. Second, the state from (or to) which the optical transition is performed is not from the space of investigated electronic excited state manifold, but it is chosen by the observer. It is shown, for this case, that the inter-state coupling is a general function of vibrational coordinates. The explicit dependence of the inter-state coupling on vibrational coordinates is particularly important for system with strong Stokes shift. The role of exact definitions of bright and dark states as well as the inter-state coupling is discussed with respect to the coherent structure of electronic population observed in optical spectroscopy.     

Infinite hierarchies of exact solutions of the einstein and einstein-maxwell equations for interacting waves and inhomogeneous cosmologies

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so-called "monodromy transform" approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous cosmological models or gravitational and electromagnetic waves and their interactions, include a number of important known solutions as particular cases.     

Predissociation resonances in CO and IBr. Smooth exterior scaling combined with the discrete variable representation

Smooth exterior scaling (SES) and the discrete variable representation (DVR) are combined to accurately compute predissociation resonances of a bound state non-adiabatically coupled to a dissociative state. For the CO( predissociation interaction good agreement is found with approaches based on optical potentials and complex scaling. The comparison is done both in the diabatic and the adiabatic representation. The effect of the coupling strength in the IBr predissociation interaction and the transition from the diabatic to the adiabatic picture was studied by computing resonances for coupling strengths from up to . The transition from weak (diabatic) to strong (adiabatic) coupling was clearly seen. The intermediate case leads to a complicated resonance distribution. Comparison was made with recent studies using pump-probe spectroscopy [M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110, 2465 (1999)]. It was found that the overall features of the experiment could be explained from the resonance distribution, but for a detailed comparison more accurate potential energy surfaces and couplings are needed. Received 12 July 1999 and Received in final form 6 December 1999     

A Numerical Method for the Calculation of Transmission Coefficient

A numerical method is presented for calculating the quantum-mechanical transnmission coefficient of one-dimensional problems with potentials of arbitrary shapes. The method is demonstrated to give very accurate results on two solvabie examples. The numerical error in the calculated transmission coefficient is proportional to the second power of integration step size for potentials without discontinuities; for potentials with discontinuities, the dependence is linear.