Michèle Desouter-Lecomte

Constructing approximately diabatic states from LCAO‐SCF‐CI calculations

We consider here two approaches which have been proposed in the literature to obtain diabatic states from ab initio calculations. First, by calculating explicitly the coupling vector g=〈ψ2‖∇ψ1〉 which describes the nonadiabatic interaction between two adiabatic states ψ1 and ψ2. Second, by some extrapolation process of the wave functions obtained at a particular reference point. The coupling vector g is the sum of three contributions: g=gCI+gLCAO+gAO. The first two represent the change in character of the adiabatic states in the region of nonadiabatic coupling due to the variation of the CI and LCAO coefficients, whereas gAO results from the translation of the atomic orbitals with the moving nuclear centers. Criteria have been given to recognize when it is possible to transform a set of CI wave functions into a pair of useful diabatic states. A particularly favorable situation is obtained when the interacting electronic states are doubly excited with respect to each other. Within the two‐state approximatio...

Vibrational computing: Simulation of a full adder by optimal control

Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale.

Quantum dynamics of the charge transfer in C+ + S at low collision energies

Following a recent semiclassical investigation by Bacchus-Montabonel and Talbi (2008 Chem. Phys. Lett. 467 28), the C + (2s 2 2p) 2 P + S(3s 2 3p 4 ) 3 P charge transfer process involved in the modellization of the interstellar medium chemistry and its reverse reaction are revisited by combining a wave packet approach and semiclassical dynamics in a quasimolecular approach for doublet and quartet states. New radial non-adiabatic coupling matrix elements have been calculated and the mixed treatment gives access to new precise values of the rate coefficients for the direct and reverse charge transfer processes. For this system, quantum and semiclassical results are in good agreement even at low collision kinetic energies. The dominance of the quartet states in the process is confirmed. In the quantum treatment, the collision matrix elements are extracted from wave packets by the flux method with an absorbing potential. The formation of resonances due to a centrifugal barrier is illustrated. (Some figures in this article are in colour only in the electronic version)

Trapping in competitive decay of degenerate states

Abstract The interference among N degenerate levels which decay into K non-interacting continua generally leads to the formation of N - K bound states in the continuum (BCSs). The total and partial widths of the K resonances can be obtained from an eigenvalue problem in a reduced K X K subspace, instead of in the initial N X N one.

Non-adiabatic interactions in unimolecular decay. I.

Abstract A semi-classical treatment of the non-adiabatic among a set of several interacting states is presented. The electrons are described by a wave function obtained by the integration of a set of coupled differential equations. An expression for the force acting on the nuclei is obtained by requiring the total energy to remain constant. This force is found to be equal to the sum of two contributions. The first one is the average of the forces deriving from each Born-Oppenheimer potential. The second one is an interference term which exhibits oscillations in a region of strong non-adiabatic coupling and vanishes outside. An application to a set of fourteen states of a diatomic molecule is presented. The results are sometimes at variance with those predicted by the Landau-Zener equation.

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment.

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.

Non-adiabatic effects in the photodissociation of bromoacetyl chloride

Abstract The competitive photodissociation of bromoacetyl chloride has been investigated by means of ab initio methods. Quantum dynamics in full dimensionality is prohibitive for such a system and therefore a reduced dimensionality method based on constrained Hamiltonians has been used. A one-dimensional (1-D) non-adiabatic wave packet treatment in the C S optimized geometry (trans Cl and Br) on the first excited states leads to encouraging results when compared to experimental data. The slow relaxation of the torsion angle is assessed by a 2-D dynamics in the subspace including the CO bond length.

Avoided crossings: A study of the nonadiabatic transition probabilities

An approximate solution to the problem of constructing a pair of diabatic states exists only if certain requirements are fulfilled, for example, when the nonadiabatic coupling results from an interaction between two electronic configurations which are doubly excited with respect to one another. It is then possible to build up a model in which the series expansion of the elements of the Hamiltonian matrix is truncated after the first nonzero term. This leads to several conclusions concerning the nonadiabatic transition probability which differentiate conical intersections from avoided crossings. For the latter, the nonadiabatic coupling matrix elements (which are Lorentzians with an area equal to π/2) reach their maximum at the nuclear geometry for which ΔE (the energy gap between adiabatic surfaces) is a minimum. The loci along which the angle θ of the orthogonal transformation which relates adiabatic and diabatic wave functions keeps a constant value are a set of parallel straight lines which coincides w...

Wave packet dynamics along bifurcating reaction paths

The problem of bifurcating reaction paths is revisited by wave packet (WP) dynamics. The pitchfork model connecting five stationary points—a reactive, two transition structures and two enantiomeric products—is characterized by a Valley Ridge inflection point (VRI) where WP could leave the standard intrinsic reaction path. We question the role of such a VRI point to determine whether the mechanism is sequential or concerted. WP simulations on two-dimensional minimum energy surfaces are carried out in the benchmark case of the methoxy radical isomerization H3CO→H2COH. The ab initio potential energy surface (PES) is fitted to an analytical model which is bent to analyze the incidence of geometrical parameters on the WP behavior. For each of these generated PES, the WP width in the entrance valley is the main factor which conditions the behavior on the unstable ridge. The WP evolution is also analyzed in terms of nonadiabatic transitions among adiabatic channels along the reaction coordinate. Finally, the loc...

Extracting laws of decay in the femto–picosecond range from autocorrelation functions

The formalism of the resonance states is used to derive approximate expressions of the unimolecular law of decay resulting from a specific excitation. These expressions contain no cross terms and wash out the quantum interferences. We propose a method to relate them to an experimentally observable quantity, viz., the autocorrelation function C(t) obtained as the Fourier transform of a spectral profile, which is available even when the spectrum is poorly resolved. For a specific excitation, the exact initial rate of decay (valid up to the dephasing time T1) is equal to the initial slope of ‖C(t)‖2. The subsequent time evolution can be obtained by averaging ‖C(t)‖2 over its oscillations. This generates a function ‖C(t)‖2av whose area (from time T1 onwards) is directly related to an average decay lifetime. At times t>T1, a good approximation to the average decay curve Pav(t) can be derived by multiplying ‖C(t)‖2av by an appropriate constant. The method is exemplified on various diatomic and triatomic models....