Yves Justum

Vector parametrization of the N-atom problem in quantum mechanics. I. Jacobi vectors

Within the framework of an adequate spectral representation, the geometrical description of an N-atom molecular system by n = N - 1 Jacobi relative position vectors is shown to be particularly advantageous with regard to the criterion of prediagonalization of the matrix representing the kinetic energy operator

Oxidation kinetics of NADH by heteropolyanions

A series of selected Dawson-type mixed heteropolyanions readily oxidize NADH in buffered aqueous pH 7 medium. The process was monitored by UV-visible spectroscopy, which helps to establish the 2:1 stoichiometry for the oxometalate/NADH couple. The starting system for electrochemistry consists of the one-electron reduction product of the heteropolyanions in the presence of various amounts of NADH. Cyclic voltammetry confirms unequivocally that the oxidized forms of the selected heteropolyanions are capable of catalyzing efficiently the oxidation of NADH. The kinetics were studied quantitatively by double step chronocoulometry. The logarithm of the second order rate constant was a linear function of the Eo of the first redox systems of the heteropolyanions with a slope of 16.4 V−1. This result indicates that the oxidation of NADH proceeds by a multistep mechanism involving an initial rate-limiting one-electron transfer. An estimate of the Eo value for the one-electron NADH/NADH·+ redox couple has been obtained.

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)

Laser control in a bifurcating region

We present a complete analysis of the laser control of a model molecular system using both optimal control theory and adiabatic techniques. This molecule has a particular potential energy surface with a bifurcating region connecting three potential wells which allows a variety of processes such as isomerization, tunneling, or implementation of quantum gates on one or two qubits. The parameters of the model have been chosen so as to reproduce the main features of H{sub 3}CO which is a molecule benchmark for such dynamics. We show the feasibility of different processes and we investigate their robustness against variations of laser field. We discuss the conditions under which each method of control gives the best results. We also point out the relation between optimal control theory and local control.

Cumulative reaction probability by constrained dynamics: H transfer in HCN, H2CO, and H3CO

A strategy to obtain quantum corrections to the cumulative reaction probability from a subspace of active coordinates is analyzed. The kinetic energy operator exactly takes into account the constraints due to inactive coordinates. The geometry of the inactive skeleton is adiabatically adjusted to the dynamical variables or simply frozen according to the coupling to the active space. Dynamics is carried out using the curvilinear coordinates of the Z-matrix so that computation of the potential energy surface and dynamics are coupled. The cumulative reaction probability N(E) is obtained directly in a large range of energy by a time independent formulation of the Zhang and Light transition state wave packet method. NnD(E) is first computed in the active n-dimensional space and then convoluted with a bath. The efficiency of the Chebyshev expansion of the microcanonical projection operator δ(E−ĤnD) appearing in the quantum expression of NnD(E) is checked. The method is implemented for the study of tunneling eff...

NOT gate in a cis-trans photoisomerization model

We numerically study the implementation of a NOT gate by laser pulses in a model molecular system presenting two electronic surfaces coupled by nonadiabatic interactions. The two states of the bit are the fundamental states of the cis-trans isomers of the molecule. The gate is classical in the sense that it involves a one-qubit flip so that the encoding of the outputs is based on population analysis which does not take the phases into account. This gate can also be viewed as a double photoswitch process with the property that the same electric field controls the two isomerizations. As an example, we consider one-dimensional cuts in a model of the retinal in rhodopsin already proposed in the literature. The laser pulses are computed by the multitarget optimal control theory with chirped pulses as trial fields. Very high fidelities are obtained. We also examine the stability of the control when the system is coupled to a bath of oscillators modeled by an ohmic spectral density. The bath correlation time scale being smaller than the pulse duration, the dynamics is carried out in the Markovian approximation.

Vector parametrization of the three-atom problem in quantum mechanics

It is shown that the geometrical description of a three-atom molecular system by two Jacobi relative position vectors is, within the framework of an adequate representation, particularly advantageous with regard to the criterion of maximal pre-diagonalization of the matrix representing the kinetic energy operator

Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design

We simulate the implementation of a 3-qubit quantum Fourier transform gate in the hyperfine levels of ultracold polar alkali dimers in their first two lowest rotational levels. The chosen dimer is (41)K(87)Rb supposed to be trapped in an optical lattice. The hyperfine levels are split by a static magnetic field. The pulses operating in the microwave domain are obtained by optimal control theory. We revisit the problem of phase control in information processing. We compare the efficiency of two optimal fields. The first one is obtained from a functional based on the average of the transition probabilities for each computational basis state but constrained by a supplementary transformation to enforce phase alignment. The second is obtained from a functional constructed on the phase sensitive fidelity involving the sum of the transition amplitudes without any supplementary constrain.

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the e-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308)

One-dimensional quantum description of the bending vibrations of HCN/CNH

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).