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 non adiabatic 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 photo-switch 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 Multi Target 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 modelled 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.Comment: 29 pages, 7 figure

N-atom molecular systems: bunch of relative position vectors, local coordinates and quantum-mechanical kinetic energy operators

After elimination of the centre of mass translation, a vector parametrization for an N-atom molecular system, consisting of N-1 relative position vectors, is used. Sets of 3N-6 local coordinates well suited for describing the system are introduced: they are all made up of the N-1 vector lengths, N-2 planar angles of vector pairs and N-3 dihedral angles for vector triplets. In addition, three Euler angles describe the orientation of the body-fixed frame: the first two angles allow one to orient the z-BF axis, either parallel to one vector or perpendicular to the plane of two vectors; the third angle is for rotation around z, completing the link between the molecule (i.e. the vectors) and the BF axes. The three Euler angles, together with the 3N-6 local coordinates, make up a set of N-1 triplets of spherical coordinates for the relative position vectors, with respect to various frames. This property is used to derive exact expressions of general quantum mechanical kinetic energy operators, and also to propose a polyspherical-harmonics representation in which the kinetic energy matrix may take a relatively simple form (i.e. prediagonalized to a large extent). (C) 1997 Elsevier Science B.V

A harmonic adiabatic approximation to calculate highly excited vibrational levels of "floppy molecules"

The harmonic adiabatic approximation (HADA), an efficient and accurate quantum method to calculate highly excited vibrational levels of molecular systems, is presented. It is well-suited to applications to "floppy molecules" with a rather large number of atoms (N >3). A clever choice of internal coordinates naturally suggests their separation into active, slow, or large amplitude coordinates q('), and inactive, fast, or small amplitude coordinates q('), which leads to an adiabatic (or Born-Oppenheimer-type) approximation (ADA), i.e., the total wave function is expressed as a product of active and inactive total wave functions. However, within the framework of the ADA, potential energy data concerning the inactive coordinates q(') are required. To reduce this need, a minimum energy domain (MED) is defined by minimizing the potential energy surface (PES) for each value of the active variables q('), and a quadratic or harmonic expansion of the PES, based on the MED, is used (MED harmonic potential). In other words, the overall picture is that of a harmonic valley about the MED. In the case of only one active variable, we have a minimum energy path (MEP) and a MEP harmonic potential. The combination of the MED harmonic potential and the adiabatic approximation (harmonic adiabatic approximation: HADA) greatly reduces the size of the numerical computations, so that rather large molecules can be studied. In the present article however, the HADA is applied to our benchmark molecule HCN/CNH, to test the validity of the method. Thus, the HADA vibrational energy levels are compared and are in excellent agreement with the ADA calculations (adiabatic approximation with the full PES) of Light and Bacic [J. Chem. Phys. 87, 4008 (1987)]. Furthermore, the exact harmonic results (exact calculations without the adiabatic approximation but with the MEP harmonic potential) are compared to the exact calculations (without any sort of approximation). In addition, we compare the densities of the bending motion during the HCN/CNH isomerization, computed with the HADA and the exact wave function. (C) 2001 American Institute of Physics

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). (C) 2002 Elsevier Science B.V. All rights reserved

Quantum-mechanical description of rigidly or adiabatically constrained molecular systems

Whereas model constraints (namely, internal degrees of freedom either frozen or stepwise adjusted by gradient methods) are often imposed for calculating the potential energies of polyatomic molecules by quantum-chemical methods, the derivation of exact expressions for the corresponding kinetic energy operators is difficult because of the changes of metrics of the configuration spaces, which modify the differential operators but not the multiplicative operators. An appropriate method for overcoming this difficulty has been designed in the case of rigid constraints (e.g., frozen groups) (M. Menou and X. Chapuisat, J. Mel. Spectrosc. 159, 300-328, 1993). In this article, it is generalized to the case of adiabatic constraints; i.e., the variations of certain internal degrees of freedom are adjusted to those of other degrees of freedom. Exact kinetic energy operators are derived. An example is analyzed. (C) 1997 Academic Press