Naseem Rahman

A new approach to molecular classical optimal control: Application to the reaction HCN→HC+N

We present a new method for classical control theory of Hamiltonian systems. This approach is based on a special treatment of the adjoint or Lagrange multiplier equations of motion. The latter function is only asked to preserve the mean of the ensemble of molecular trajectories. In the present case only four such equations are involved greatly simplifying the field design process and making it faster and more stable. Good results are obtained for the selective photodissociation of HCN. The objective is to control the intramolecular reaction HCN→HC+N (i.e., break the stronger bond). Hamilton’s equations of motion are employed to model the HCN molecule, initially in its ground state. The control equations are integrated to obtain a high degree of selectivity in the unimolecular dissociation. The robustness of the results to changes in the initial conditions and pulse durations are investigated. An increase of the pulse duration beyond a certain point makes it more difficult to dissociate the N atom due to strong intramolecular coupling. The resultant pulse fields may serve as a basic indicator for future experimental selective dissociation of HCN→HC+N using high power lasers.

A simplified approach to optimally controlled quantum dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously [J. Botina, H. Rabitz, and N. Rahman, J. Chem. Phys. 102, 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory [S. Shi and H. Rabitz, Comp. Phys. Comm. 63, 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reacti...

Effect of the increase of molecular complexity on statistical properties of vibrational spectra

Abstract We present for the first time a study on the influence of the increase in the number of molecular vibrational degrees of freedom on level statistics. A model of three Morse oscillators coupled by Wilson terms has been considered for tetratomic molecules and the level statistics of its spectra have been studied in comparison with that of an analogous two-oscillator model for triatomics. The nearest-neighbor level spacing distribution for three oscillators is essentially a Wigner distribution, while for two oscillators it is a Brody distribution, which is intermediate between a Poisson and a Wigner distribution.

Dynamic dipole polarizabilities of He, Ne and Ar by multiconfigurational linear response

Abstract The frequency-dependent electric dipole polarizabilities of He, Ne and Ar are computed using multiconfigurational linear response (MCLR/MCTDHF). MCTDHF provides the correct linear response to optimized multiconfigurational wavefunctions, thus properly accounting for a large part of the correlation effects in response properties. The calculations are performed with extended basis sets. The results compare well with both experiment and other theoretical calculations and are particularly relevant to understanding the role of the polarizability in the recently observed generation of high-order harmonics with intense radiation.

Statistics of energy levels in the quantum treatment of an elementary reaction

Abstract Statistical tests (NNLSD, Δ 3 of Dyson and Mehta, correlation coefficients) are applied to the adiabatic energy level distribution of the prototypical reaction F+H 2 → HF+H, depending parametrically on the three-body total inertia measured by the hyperradius ρ . As a function of ρ (proposed as a natural control variable for the quantum mechanical three-body problem), a transition can be identified. At high ρ , the situation of separate partners of the reaction shows a Poissonian behavior while, at low ρ , the transition state (where the triatom can be viewed as a system of coupled oscillators) exhibits some Wigner-like features as signatures of quantum chaos.

Effect of the increase in molecular complexity on the statistical properties of vibrational spectra. Four coupled Morse oscillators

Energy level statistics are presented for the vibrational levels of polyatomic molecules utilizing a local mode Hamiltonian made of four coupled Morse oscillators. The nearest-neighbour level spacing distribution shows a progressive transition towards a Wigner distribution. The Δ3 statistics of Dyson—Mehta and correlation coefficients also lead to the same conclusion. The effect of the model-independent kinetic (Wilson) coupling is found to be overwhelmingly predominant over coordinate coupling.

Bound-bound and bound-free X2Σg+ → A 2Πu transitions in Na2+ relevant for experiments in above threshold dissociation

Abstract A preliminarystudy on above threshold dissociation is presented. The specific example is based on the Na 2 + molecular ion, for which accurate potential energy curves and transition dipoles are available. The first step of the process is examined, with a comparison of the bound-bound and bound-free portions of the spectrum.

Quantum wavepacket dynamics simulations of above-threshold dissociation in Na2+

Abstract We present a theoretical study of above-threshold dissociation in the Na2+ molecular ion, based on quantum wavepacket dynamics simulations. A two-photon mechanism for the photodissociation in the first 2Πg state, leading to Na+ + Na(3p), is found to be quite efficient. The best conditions to observe this process (radiation frequency, intensity and pulse length) have been determined.

Isotopic mass as discrete control variable in chaotic processes. The case of molecular vibrations

Abstract The dynamics of CO 2 and HCN molecules are studied with isotopic mass as a control variable thereby introducing a discrete control variable in chaos theory. An interesting variation of threshold energy for chaos is obtained with computation of Poincare sections and Lyapunov exponent. On extending the mass range beyond these two molecules, highly non-monotonic behaviour (with various maxima and minima) for the threshold energy is found. The quantal correspondence is explored with NNLSD, Dyson—Mehta statistics and correlation coefficients. A correlation between symmetry (brought about with the isotopic mass variation) and the transition from Poisson distribution to Wigner—Dyson distribution is found for the CO 2 molecule.

Coupled logistic maps in physico-chemical processes: coexisting attractors and their implications

Abstract Coexisting multiply periodic stable solutions have been found numerically for a coupled logistic map with symmetric coupling. These correspond to period 4 and period 6 attractors. The evolution towards chaos of the period 6 attractor, as well as the basins of attraction in the space of the initial conditions, have been studied. A threshold value for the transition from singly periodic to multiply periodic solutions has been determined. Connections between these results and processes of interest in chemical physics are discussed.