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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. [ABSTRACT FROM AUTHOR]

We compare the strategy found by the optimal control theory in a complex molecular system according to the active subspace coupled to the field. The model is the isomerization during a Cope rearrangement of Thiele's ester that is the most stable dimer obtained by the dimerization of methyl-cyclopentadienenylcarboxylate. The crudest partitioning consists in retaining in the active space only the reaction coordinate, coupled to a dissipative bath of harmonic oscillators which are not coupled to the field. The control then fights against dissipation by accelerating the passage across the transition region which is very wide and flat in a Cope reaction. This mechanism has been observed in our previous simulations [Chenel et al., J. Phys. Chem. A 116, 11273 (2012)]. We compare here, the response of the control field when the reaction path is coupled to a second active mode. Constraints on the integrated intensity and on the maximum amplitude of the fields are imposed limiting the control landscape. Then, optimum field from one-dimensional simulation cannot provide a very high yield. Better guess fields based on the two-dimensional model allow the control to exploit different mechanisms providing a high control yield. By coupling the reaction surface to a bath, we confirm the link between the robustness of the field against dissipation and the time spent in the delocalized states above the transition barrier. [ABSTRACT FROM AUTHOR]

We present a theoretical approach which consists of applying the strategy of local control to projectors based on asymptotic scattering states. This allows to optimize final state distributions upon laser excitation in cases where strong non-adiabatic effects are present. The approach, despite being based on a time-local formulation, can take non-adiabatic transitions that appear at later times fully into account and adopt a corresponding control strategy. As an example, we show various dissociation channels of HeH+, a system where the ultrafast dissociation dynamics is determined by strong non-Born-Oppenheimer effects. [ABSTRACT FROM AUTHOR]

Following the scheme recently proposed by Remacle and Levine [Phys. Rev. A 73, 033820 (2006)], we investigate the concrete implementation of a classical full adder on two electronic states (X 1A1 and C 1B2) of the SO2 molecule by optical pump-probe laser pulses using intuitive and counterintuitive (stimulated Raman adiabatic passage) excitation schemes. The resources needed for providing the inputs and reading out are discussed, as well as the conditions for achieving robustness in both the intuitive and counterintuitive pump-dump sequences. The fidelity of the scheme is analyzed with respect to experimental noise and two kinds of perturbations: The coupling to the neighboring rovibrational states and a finite rotational temperature that leads to a mixture for the initial state. It is shown that the logic processing of a full addition cycle can be realistically experimentally implemented on a picosecond time scale while the readout takes a few nanoseconds. [ABSTRACT FROM AUTHOR]

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 24 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Quantum dynamics in a valley ridge inflection (VRI) point region is analyzed in the case of the Diels-Alder endo-dimerization of cyclopentadiene pointed out recently by [Caramella et al., J. Am. Chem. Soc. 124, 1130 (2002)]. The VRI point is located along the reaction path connecting the bispericyclic symmetrical transition structure put in evidence by Caramella et al. and the transition state of the Cope rearrangement. Dynamics is carried out by using constrained Hamiltonian methodology. The active coordinates are the first formed C–C bond length and the difference between the two other C–C bond lengths which achieve the dimerization as 4+2 or 2+4 adducts. A two-dimensional (2D) minimum-energy surface have been computed at the Becke 3 Lee–Yong–Parr/6-31G* level. The energy landscape can be classified as an uphill ridge-pitchfork VRI bifurcation according to a recent classification of bifurcation events [W. Quapp, J. Mol. Struct. 695–696, 95 (2004)]. Dynamics does not describe the thermal reaction but concerns wave packets which could be prepared by pulse reagents, i.e., by coherent control. We analyze how the shape and initial location on the ground potential-energy surface are linked to the synchronous or asynchronous mechanism of the final step after the first transition state. We use a one-dimensional model of optimum control theory to check the feasibility of such a coherent preparation. The wave-packet evolution in the VRI domain is well explained by semiclassical predictions even with the negative curvature of the unstable ridge. Finally, a crude model of dissipation has been introduced to test the stability of the 2D predictions. [ABSTRACT FROM AUTHOR]

The 3D cumulative isomerization probability N(E) for the transfer of a light particle between two atoms is computed by one time-independent and two time-dependent versions of the transition state wave packet (TSWP) method. The time-independent method is based on the direct expansion of the microcanonical projection operator on Chebyshev polynomials. In the time-dependent TSWP methods, the propagations are carried out by the split operator scheme and the multiconfiguration time-dependent Hartree (MCTDH) algorithm. This is the very first implementation of the TSWP method in the Heidelberg MCTDH package [G. W. Worth, M. H. Beck, A. Jäckle, and H.-D. Meyer, The MCDTH package, Version 8.2 (2000); H.-D Meyer, Version 8.3 (2002). See http://www.pci.uni-heidelberg.de/tc/usr/mctdh/]. The benchmark is the HCN→CNH isomerization for zero total angular momentum. Particular insights are given into the tunneling region. In larger systems, the time-dependent version of TSWP making use of the MCTDH algorithm will permit to treat more and more modes quantum mechanically, for very accurate results. Therefore, it was important to calibrate the implementation. Besides, we also assess the efficiency of a reduced dimensionality approach by comparing the new exact 3D calculations of N(E) for the HCN→CNH isomerization with results obtained via 1D or 2D active subspaces. This suggests that, it should be possible to take directly benefit of the present 3D approaches, adapted for triatomic Jacobi coordinates to compute N(E) for H-transfer in larger systems, via three active coordinates. The prerequisite is then the simplification of the reduced 3D kinetic energy operator with rigid constraint to take the form corresponding to a pseudo triatomic system in Jacobi coordinates with effective masses. This last step is checked in the methoxy radical and malonaldehyde. Finally, different ways to obtain reliable eigenvectors of the flux operator associated with a dividing surface are revisited. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The competitive photodissociation of bromoacetyl chloride BrCH[sub 2]COCl in the first [sup 1]A[sup ″] state (S[sub 1]) by 248 nm photons is investigated by nonadiabatic wave packet simulations. We show that the preferential breaking of the stronger C–Cl bond (α to the excited carbonyl) over the weaker C–Br bond (β) could be explained by a diabatic trapping or nonadiabatic recrossing as previously proposed. Our energy resolved flux analysis agrees fairly well with the experimental branching ratio (C–Cl:C–Br=1.0:0.4). Even if this does not prove the mechanism, this at least prevents to discard it. A reduced dimensionality approach based on constrained Hamiltonian is used. The nonadiabatic dissociation is studied in the two C–O/C–X (X=Br, Cl) subspaces to emphasize the role of the C–O vibration upon [n[sub O]→π[sub CO][sup *]] excitation. The internal torsion and wagging dihedral angles are frozen at their Franck–Condon value, according to preliminary dynamical tests. The other inactive coordinates are optimized at the trans and C[sub s] constrained geometry in the first excited state. Corresponding 2D cuts in the potential energy surfaces have been computed at the CASSCF level. The nonadiabatic kinetic couplings are highly peaked along an avoided crossing seam in both cases. A two-state diabatic model with a constant potential coupling is proposed in the two C–O/C–X subspaces. The inclusion of the C–O stretching in the active coordinates improves the value of the branching ratio over our previous 1D computation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 H[sub 3]CO→H[sub 2]COH. 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 location of VRI points according to an invariant definition is discussed. [ABSTRACT FROM AUTHOR]

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. N[sub nD](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-Ĥ[sub nD]) appearing in the quantum expression of N[sub nD](E) is checked. The method is implemented for the study of tunneling effect in H transfer. The coordinates are three spherical coordinates referred to the frozen or adiabatic skeleton. We compare the quantum corrections brought about by different 2D groups of internal coordinates. [ABSTRACT FROM AUTHOR]

The transition between the diabatic and the adiabatic zero order representation when the electronic potential coupling increases, is studied in the partitioning method (PM) and in the complex coordinate method (CCM) implemented in a discrete variable representation (DVR). The model is a C+ type predissociation in a diatomic system with a crossing between a Morse potential energy curve and an exponentially repulsive curve. In the weak coupling regime (isolated diabatic metastable states), both methods confirm the linear variation of the resonance widths with the strength of the electronic interaction, as expected in a perturbative treatment. When the coupling is large in the diabatic representation (strong overlap regime), the formation of narrow resonances supported by the upper adiabatic potential can be related, in PM, to the process of avoided resonance overlapping among interfering states. The complete change of representation can be described in the initial diabatic basis set in PM. However, the full energy dependence of the discrete-continuous matrix elements must then be taken into account. The deformation and the final splitting of a diffuse spectral line with increasing coupling is re-examined in terms of these energy dependent eigenvalues of the effective Hamiltonian. The use of the appropriate representation, either diabatic or adiabatic, according to the strength of the electronic coupling, has been found decisive in CCM so as to observe the correct migration of the resonance positions towards the zero order adiabatic states, and the decrease of their widths. No relevant results have been obtained for the intermediate strength of the coupling in CCM. Analytical expressions for the derivative coupling matrix elements (∂/∂R) in the fixed node DVR (corresponding to the particle-in-a-box wave functions) have been established. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The interaction of overlapping resonances is studied in the case of a vibrational predissociation in a linear molecule. The energy independent approach rests on the neglect of the variation of the coupling elements with the energy in the continuum. It predicts the formation of trapped and short-lived decay modes when resonances overlap. The relevance of this prediction is discussed on the basis of results obtained from two different methods going beyond this energy independent formalism. The first one consists in searching the solutions of the implicit equation derived from the Feshbach partitioning method, taking into account the full energy dependence of the local effective Hamiltonian Heff(E). The second one is the variational complex coordinate method (CCM), implemented in a discrete variable representation (DVR). The results demonstrate that the energy dependency enhances the trapping effect. The distribution of the resonance energies in the complex plane is different from the prediction of the energy independent formalism. The fast modes are found to be slower than expected. Their position is also completely shifted. The mean width is not constrained by a sum rule which is characteristic of the energy independent approximation. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The distribution of the widths of N quasidegenerate metastable states decaying into a large number K of dissociation continua is studied in the framework of the random matrix theory. For strong overlap, the distribution of the imaginary parts of the eigenvalues of the effective Hamiltonian H-iΓ/2 is that of the eigenvalues of the width matrix Γ. The latter is found to belong to a model of random matrices proposed by Wigner and developed by Dyson. The analytical expression of the asymptotic density ρ(γ) for equal partial widths and N=K→∞ is a semicircular law centered at twice the mean width γ times a function 1/γ. It predicts extensive fluctuations around the mean with a high density of small widths. As a result, the average survival probability of the metastable states lying within a narrow energy range decays more slowly than the exponential law which is assumed in the RRKM theory. [ABSTRACT FROM AUTHOR]

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. As an application to a real system, we study the B 2B2 state of H2O+ which is coupled to the A 2A1 state via a conical intersection. State B is found to undergo an ultrafast intramolecular relaxation with a lifetime of (1.6±0.2) 10-14 s. [ABSTRACT FROM AUTHOR]

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 with the loci along which ΔE remains constant. This reference direction in the configuration space corresponds to nuclear trajectories which are unable to bring about a nonadiabatic transition. In the case of avoided crossings, there exists only one nuclear degree of freedom which gives rise to surface hopping. Conical intersections, on the other hand, have two such active degrees of freedom. This creates a qualitative difference between the two cases which makes conical intersections more efficient as funnels than avoided crossings. A two-dimensional extension of the Landau–Zener formula is derived for avoided crossings. It contains a factor of anisotropy. It is possible, at least in favorable cases, to extract approximate diabatic quantities from ab initio calculations and to compare them with the predictions of these models. This has been done for two 2A1 electronic states of the CH+2 ion. The results are found to agree with the... [ABSTRACT FROM AUTHOR]