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Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories Lorquet, Jean-Claude in Journal of Chemical Physics (2015), 143 The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the ... [more ▼] The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of this series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet. [less ▲] Detailed reference viewed: 12 (1 ULg)Information processing in parallel through directionally resolved molecular polarization components in coherent multidimensional spectroscopy ; Fresch, Barbara ; et al in Journal of Chemical Physics (2015), 143(6), 064106 Detailed reference viewed: 19 (0 ULg)Photodissociation of the carbon monoxide dication in the 3 Sigma- manifold: Quantum control simulation towards the C2+ + O channel ; ; et al in Journal of Chemical Physics (2015), 143 The photodissociation and laser assisted dissociation of the carbon monoxide dication X3Π CO2+ into the 3Σ− states are investigated. Ab initio electronic structure calculations of the adiabatic potential ... [more ▼] The photodissociation and laser assisted dissociation of the carbon monoxide dication X3Π CO2+ into the 3Σ− states are investigated. Ab initio electronic structure calculations of the adiabatic potential energy curves, radial nonadiabatic couplings, and dipole moments for the X 3Π state are performed for 13 excited 3Σ− states of CO2+. The photodissociation cross section, calculated by time-dependent methods, shows that the C+ + O+ channels dominate the process in the studied energy range. The carbon monoxide dication CO2+ is an interesting candidate for control because it can be produced in a single, long lived, v = 0 vibrational state due to the instability of all the other excited vibrational states of the ground 3Π electronic state. In a spectral range of about 25 eV, perpendicular transition dipoles couple this 3Π state to a manifold of 3Σ− excited states leading to numerous C+ + O+ channels and a single C2+ + O channel. This unique channel is used as target for control calculations using local control theory. We illustrate the efficiency of this method in order to find a tailored electric field driving the photodissociation in a manifold of strongly interacting electronic states. The selected local pulses are then concatenated in a sequence inspired by the “laser distillation” strategy. Finally, the local pulse is compared with optimal control theory. [less ▲] Detailed reference viewed: 39 (3 ULg)Crossing the dividing surface of transition state theory. I. Underlying symmetries and motion coordination in multidimensional systems Lorquet, Jean-Claude in Journal of Chemical Physics (2014), 140(13), 134303 The objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum ... [more ▼] The objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a transition state is constrained by symmetry properties. Trajectories that all cross the plane R = Ro at time t = 0 (where Ro denotes the position of the saddle point) with the same positive translational momentum PRo can be partitioned into two sets, denoted "gerade" and "ungerade," which coordinate their motions. Both sets have very close average equations of motion. This coordination improves tremendously rapidly as the number of degrees of freedom increases. This property can be traced back to the existence of time-dependent constants of the motion. © 2014 AIP Publishing LLC. [less ▲] Detailed reference viewed: 22 (3 ULg)Erratum: Crossing the dividing surface of transition state theory. I. Underlying symmetries and motion coordination in multidimensional systems (J. Chem. Phys. 140 (2014) (134303)) Lorquet, Jean-Claude in Journal of Chemical Physics (2014), 140(16), 169902 [No abstract available] Detailed reference viewed: 14 (6 ULg)Exciton dissociation at donor-acceptor heterojunctions: Dynamics using the collective effective mode representation of the spin-boson model ; ; et al in Journal of Chemical Physics (2014), 140 Detailed reference viewed: 13 (0 ULg)Crossing the dividing surface of transition state theory. II. Recrossing times for the atom-diatom interaction Lorquet, Jean-Claude in Journal of Chemical Physics (2014), 140(13), 134304 We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of ... [more ▼] We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a saddle point is constrained by symmetry properties. At short times and at not too high energies, recrossing dynamics is largely determined by elementary local structural parameters and thus can be described in configuration space only. Conditions for recrossing are given in the form of inequalities involving structural parameters only. Explicit expressions for recrossing times, valid for microcanonical ensembles, are shown to obey interesting regularities. In a forward reaction, when the transition state is nonlinear and tight enough, one-fourth of the trajectories are expected to recross the plane R = R o (where Ro denotes the position of the saddle point) within a short time. Another fourth of them are expected to have previously recrossed at a short negative time, i.e., close to the saddle point. These trajectories do not contribute to the reaction rate. The reactive trajectories that obey the transition state model are to be found in the remaining half. However, no conclusion can be derived for them, except that if recrossings occur, then they must either take place in the distant future or already have taken place in the remote past, i.e., far away from the saddle point. Trajectories that all cross the plane R = Ro at time t = 0, with the same positive translational momentum P can be partitioned into two sets, distinguished by the parity of their initial conditions; both sets have the same average equation of motion up to and including terms cubic in time. Coordination is excellent in the vicinity of the saddle point but fades out at long (positive or negative) times, i.e., far away from the transition state. © 2014 AIP Publishing LLC. [less ▲] Detailed reference viewed: 17 (3 ULg)Reorientation of the helix of the tryptophan-rich gp41W peptide from HIV-1 at interfaces ; ; Nasir, Mehmet Nail et al in Journal of Chemical Physics (2013), 139 The glycoprotein gp41 from the Human Immunodeficiency Virus type 1 (HIV-1) has an amino acid sequence enriched in tryptophan residues, the so-called gp41W peptide (i.e., KWASLWNWFNITNWLWYIK) and plays a ... [more ▼] The glycoprotein gp41 from the Human Immunodeficiency Virus type 1 (HIV-1) has an amino acid sequence enriched in tryptophan residues, the so-called gp41W peptide (i.e., KWASLWNWFNITNWLWYIK) and plays a crucial role in HIV-1 host cell infection. Using the coupling of Second Harmonic Generation targeting the tryptophan residues with lateral surface tension measurements, we investigate the interaction of gp41W with a neat air/water and a lipid/water interfaces. At the air/water interface, gp41W presents a well-defined orientation and this orientation is strongly modified at the lipid/water interface, depending on the surface pressure. These results show that this strategy is well suited to monitor tryptophan containing α-helices orientation at lipid/water interfaces. [less ▲] Detailed reference viewed: 19 (2 ULg)Hot electron production and diffuse excited states in C70, C82, and Sc3N@C80 characterized by angular-resolved photoelectron spectroscopy ; ; et al in Journal of Chemical Physics (2013), 139 Detailed reference viewed: 12 (2 ULg)Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design ; ; et al in Journal of Chemical Physics (2013), 139 Detailed reference viewed: 7 (0 ULg)Functionality in single-molecule devices: Model calculations and applications of the inelastic electron tunneling signal in molecular junctions ; ; Verstraete, Matthieu et al in Journal of Chemical Physics (2012), 136 We analyze how functionality could be obtained within single-molecule devices by using a combination of non-equilibrium Green's functions and ab initio calculations to study the inelastic transport ... [more ▼] We analyze how functionality could be obtained within single-molecule devices by using a combination of non-equilibrium Green's functions and ab initio calculations to study the inelastic transport properties of single-molecule junctions. First, we apply a full non-equilibrium Green's function technique to a model system with electron-vibration coupling. We show that the features in the inelastic electron tunneling spectra (IETS) of the molecular junctions are virtually independent of the nature of the molecule-lead contacts. Since the contacts are not easily reproducible from one device to another, this is a very useful property. The IETS signal is much more robust versus modifications at the contacts and hence can be used to build functional nanodevices. Second, we consider a realistic model of a organic conjugated molecule. We use ab initio calculations to study how the vibronic properties of the molecule can be controlled by an external electric field which acts as a gate voltage. The control, through the gate voltage, of the vibron frequencies and (more importantly) of the electron-vibron coupling enables the construction of functionality: nonlinear amplification and/or switching is obtained from the IETS signal within a single-molecule device. [less ▲] Detailed reference viewed: 60 (2 ULg)Slow Magnetic Relaxation and Electron Delocalization in an S = 9/2 Iron(II/III) Complex Featuring Two Crystallographically Inequivalent Iron Sites ; ; et al in Journal of Chemical Physics (2011), 134 The magnetic, electronic and Mössbauer spectral properties of [Fe2L(μ-OAc)2]ClO4, 1, where L is the dianion of the tetraimino-diphenolate macrocyclic ligand, H2L, indicate that 1 is a class III mixed ... [more ▼] The magnetic, electronic and Mössbauer spectral properties of [Fe2L(μ-OAc)2]ClO4, 1, where L is the dianion of the tetraimino-diphenolate macrocyclic ligand, H2L, indicate that 1 is a class III mixed valence iron(II/III) complex with an electron that is fully delocalized between two crystallographically inequivalent iron sites to yield a [Fe2]V cationic configuration with a St = 9/2 ground state. Fits of the dc magnetic susceptibility between 2 and 300 K and of the isofield variable-temperature magnetization of 1 yield an isotropic magnetic exchange parameter, J, of –32(2) cm–1 for an electron transfer parameter, B, of 950 cm–1, a zero-field uniaxial D9/2 parameter of –0.9(1) cm–1, and g = 1.95(5). In agreement with the presence of uniaxial magnetic anisotropy, ac susceptibility measurements reveal that 1 is a single-molecule magnet at low temperature with a single molecule magnetic effective relaxation barrier, Ueff, of 9.8 cm–1. At 5.25 K the Mössbauer spectra of 1 exhibit two spectral components, assigned to the two crystallographically inequivalent iron sites with a static effective hyperfine field; as the temperature increases from 7 to 310 K the spectra exhibit increasingly rapid relaxation of the hyperfine field on the iron-57 Larmor precession time of 5 × 10–8 s. A fit of the temperature dependence of the average effective hyperfine field yields |D9/2| = 0.9 cm–1. An Arrhenius plot of the logarithm of the relaxation frequency between 5 and 85 K yields a relaxation barrier of 17 cm–1. [less ▲] Detailed reference viewed: 28 (5 ULg)Local control of non-adiabatic dissociation dynamics ; ; et al in Journal of Chemical Physics (2011), 134 Detailed reference viewed: 17 (0 ULg)Beyond quantum microcanonical statistics Fresch, Barbara ; in Journal of Chemical Physics (2011), 134 Detailed reference viewed: 4 (1 ULg)Emergence of Equilibrium Thermodynamic Properties in Quantum Pure States I. Theory. Fresch, Barbara ; in Journal of Chemical Physics (2010), 133 Detailed reference viewed: 9 (4 ULg)Emergence of equilibrium thermodynamic properties in quantum pure states. II. Analysis of a spin model system Fresch, Barbara ; in Journal of Chemical Physics (2010), 133 Detailed reference viewed: 2 (1 ULg)First-Principles conductance of nanoscale junctions from the polarizability of finite systems Verstraete, Matthieu ; ; in Journal of Chemical Physics (2009), 130 Detailed reference viewed: 30 (9 ULg)Adiabatic and diabatic invariants in ion-molecule reactions Lorquet, Jean-Claude in Journal of Chemical Physics (2009), 131(24), A point charge interacting with a dipole (either induced or permanent) constitutes a completely integrable dynamical subsystem characterized by three first integrals of the motion (E, pφ, and either 2 or ... [more ▼] A point charge interacting with a dipole (either induced or permanent) constitutes a completely integrable dynamical subsystem characterized by three first integrals of the motion (E, pφ, and either 2 or a Hamilton-Jacobi separation constant Β). An ion-molecule reaction (capture or fragmentation) can be seen as an interaction between such a subsystem and a bath of oscillators. This interaction is a perturbation that destroys some of the first integrals. However, the perturbation depends on the separation between the fragments and the destruction is gradual. The mathematical simplicity of the long-range electrostatic interaction potential leads to useful simplifications. A first-order perturbation treatment based on the structured and regular nature of the multipole expansion is presented. The separating integrals valid in the asymptotic limit are found to subsist at intermediate distances, although in a weaker form. As the reaction coordinate decreases, i.e., as the fragments approach, the asymptotic range is followed by an outer region where (i) the azimuthal momentum pφ remains a constant of the motion; (ii) the square angular momentum 2 or the separation constant Β transform into a diabatic invariant in regions of phase space characterized by a high value of the translational momentum pr; (iii) for low values of pr, it is advantageous to use the action integral pθ dθ, which is an adiabatic invariant. The conditions under which an effective potential obtained by adding centrifugal repulsion to an electrostatic attractive term can be validly constructed are specified. In short, the dynamics of ion-molecule interactions is still regular in parts of phase space corresponding to a range of the reaction coordinate where the interaction potential deviates from its asymptotic shape. © 2009 American Institute of Physics. [less ▲] Detailed reference viewed: 9 (0 ULg)Adiabatic invariance along the reaction coordinate Lorquet, Jean-Claude in Journal of Chemical Physics (2009), 130(2), 024307 In a two-dimensional space where a point particle interacts with a diatomic fragment, the action integral Φ pθ dθ (where θ is the angle between the fragment and the line of centers and pθ its conjugate ... [more ▼] In a two-dimensional space where a point particle interacts with a diatomic fragment, the action integral Φ pθ dθ (where θ is the angle between the fragment and the line of centers and pθ its conjugate momentum) is an adiabatic invariant. This invariance is thought to be a persistent dynamical constraint. Indeed, its classical Poisson bracket with the Hamiltonian is found to vanish in particular regions of the potential energy surface: asymptotically, at equilibrium geometries, saddle points, and inner turning points, i.e., at remarkable situations where the topography of the potential energy surface is locally simple. Studied in this way, the adiabatic decoupling of the reaction coordinate is limited to disjoint regions. However, an alternative view is possible. The invariance properties of entropy (as defined in information theory) can be invoked to infer that dynamical constraints that are found to operate locally subsist everywhere, throughout the entire reactive process, although with a modified expression. © 2009 American Institute of Physics. [less ▲] Detailed reference viewed: 11 (1 ULg)Vibrational computing: Simulation of a full adder by optimal control ; ; Remacle, Françoise et al in Journal of Chemical Physics (2008), 128(6), 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 ... [more ▼] 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 [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. (C) 2008 American Institute of Physics. [less ▲] Detailed reference viewed: 28 (3 ULg) |
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