Genetic algorithm optimization of laser pulses for molecular quantum state excitation.

Conventionally optimal control theory has been used in the theoretical design of laser pulses through the direct variation in the electric field of the laser pulse as a function of time. This often leads to designed laser pulses which contain a broad and seemingly arbitrary frequency structure that varies in time in a manner which may be difficult to realize experimentally. In contrast, the experimental design of laser pulses has used a genetic algorithm (GA) approach, varying only those laser parameters actually available to the experimentalist. We investigate in this paper the possibility of using GA optimization methods in the theoretical design of laser pulses to bring about quantum state transitions in molecules. This allows us to select only a small limited number of parameters to vary and to choose these parameters so that they correspond to those available to the experimentalist. In the paper we apply our methods to the vibrational-rotational excitation of the HF molecule. We choose a small limited number of frequencies and vary only the associated electric field amplitudes and pulse envelopes. We show that laser pulses designed in this way can lead to very high transition probabilities.

Design of an infrared laser pulse to control the multiphoton dissociation of the Fe-CO bond in CO-heme compounds.

Optimal control theory is used to design a laser pulse for the multiphoton dissociation of the Fe-CO bond in the CO-heme compounds. The study uses a hexacoordinated iron-porphyrin-imidazole-CO complex in its ground electronic state as a model for CO liganded to the heme group. The potential energy and dipole moment surfaces for the interaction of the CO ligand with the heme group are calculated using density functional theory. Optimal control theory, combined with a time-dependent quantum dynamical treatment of the laser-molecule interaction, is then used to design a laser pulse capable of efficiently dissociating the CO-heme complex model. The genetic algorithm method is used within the mathematical framework of optimal control theory to perform the optimization process. This method provides good control over the parameters of the laser pulse, allowing optimized pulses with simple time and frequency structures to be designed. The dependence of photodissociation yield on the choice of initial vibrational state and of initial laser field parameters is also investigated. The current work uses a reduced dimensionality model in which only the Fe-C and C-O stretching coordinates are explicitly taken into account in the time-dependent quantum dynamical calculations. The limitations arising from this are discussed in Sec. IV.

Design of infrared laser pulses for the vibrational de-excitation of translationally cold Li2 molecules.

In connection with attempts to form molecular Bose-Einstein condensates, there have been reports in the literature of the preparation of samples of translationally cold alkali metal dimers. The molecules in these samples are generally in excited vibrational levels. To form a stable Bose-Einstein condensate, the molecules must be de-excited to their lowest vibrational state. In this paper, we demonstrate that through the use of optimal control theory, it is possible to design a sequence of infrared laser pulses that will de-excite a sample of (7)Li2 molecules from the v = 10 vibrational level of their (1)Sigma(g)+ ground electronic state to their lowest v = 0 vibrational level with an overall efficiency of 91.1%.

Vector correlation analysis for inelastic and reactive collisions between partners possessing spin and orbital angular momentum.

A general reactive collision of the type A + B --> C + D is considered where both the collision partners (A and B) or the products (C and D) may possess internal, i.e., spin, orbital or rotational, angular momenta. Compact expressions are derived using a rigorous quantum mechanical analysis for the angular momentum anisotropy of either of the products (C or D) arising from an initially polarized distribution of the reactant angular momentum. The angular momentum distribution of the product is expressed in terms of canonical spherical tensors multiplied by anisotropy-transforming coefficients c(K(i)q(k))(K)(K(r),L). These coefficients act as transformation coefficients between the angular momentum anisotropy of the reactants and that of the product. They are independent of scattering angle but depend on the details of the scattering dynamics. The relationship between the coefficients c(K(i)q(k))(K)(K(r),L) and the body-fixed scattering S matrix is given and the methodology for the quantum mechanical calculation of the anisotropy-transforming coefficients is clearly laid out. The anisotropy-transforming coefficients are amenable to direct experimental measurement in a similar manner to vector correlation and alignment parameters in photodissociation processes. A key aspect of the theory is the use of projections of both reactant and product angular momenta onto the product recoil vector direction. An important new conservation rule is revealed through the analysis, namely that if the state multipole for reactant angular momentum distribution has a projection q(k) onto the product recoil vector the state multipoles for the product angular momentum distribution all have this same projection. Expressions are also presented for the distribution of the product angular momentum when its components are evaluated relative to the space-fixed Z-axis. Notes with detailed derivations of all the formulas are available as Supporting Information.

Nonadiabatic effects in the H + H2 exchange reaction: accurate quantum dynamics calculations at a state-to-state level.

Real wave packet propagations were carried out on both a single ground electronic state and two-coupled-electronic states of the title reaction to investigate the extent of nonadiabatic effects on the distinguishable-atom reaction cross sections. The latest diabatic potential matrix of Abrol and Kuppermann [J. Chem. Phys. 116, 1035 (2002)] was employed in the present nonadiabatic quantum state-to-state scattering calculations over a total energy range-from threshold (the zero point of the reagent H(2)) to 3.0 eV. Based on the assumption that the hydrogen atoms are distinguishable in the collisions where the inelastic and elastic ones are excluded, no significant nonadiabatic effects have been found in the calculations of the full state-to-state integral and differential cross sections up to a total energy of 3.0 eV for product vibrational levels v(')=0, 1, 2, 3. Our results therefore confirm the recent and the previous studies of the geometric phase effects in H+H(2) employing a different diabatic double many-body expansion potential matrix or a different BKMP2 potential energy surface.

Quantum mechanical calculation of energy dependence of OCl/OH product branching ratio and product quantum state distributions for the O(1D) + HCl reaction on all three contributing electronic state potential energy surfaces.

OCl/OH product branching ratios are calculated as a function of total energy for the O( (1) D) + HCl reaction using quantum wavepacket methods. The calculations take account of reaction on all the three electronic state potential energy surfaces which correlate with both reactants and products. Our results show that reaction on the excited electronic state surfaces has a large effect on the branching ratio at higher energies and that these surfaces must therefore be fully taken into account. The calculations use the potential energy surfaces of Nanbu and co-workers. Product vibrational and rotational quantum state distributions are also calculated as a function of energy for both product channels. Inclusion of the excited electronic state potential energy surfaces improves the agreement of the predicted product vibrational quantum state distributions with experiment for the OH product channel. For OCl agreement between theory and experiment is retained for the vibrational quantum state distributions when the excited electronic state potential energy surfaces are included in the analysis. For the rotational state distributions good agreement between theory and experiment is maintained for energies at which experimental results are available. At higher energies, above 0.7 eV of total energy, the OCl rotational state distributions predicted using all three electronic state potential energy surfaces shift to markedly smaller rotational quantum numbers.

Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses.

We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

Design of laser pulses for selective vibrational excitation of the N6-H bond of adenine and adenine-thymine base pair using optimal control theory.

Time dependent quantum dynamics and optimal control theory are used for selective vibrational excitation of the N6-H (amino N-H) bond in free adenine and in the adenine-thymine (A-T) base pair. For the N6-H bond in free adenine we have used a one dimensional model while for the hydrogen bond, N6-H(A)...O4(T), present in the A-T base pair, a two mathematical dimensional model is employed. The conjugate gradient method is used for the optimization of the field dependent cost functional. Optimal laser fields are obtained for selective population transfer in both the model systems, which give virtually 100% excitation probability to preselected vibrational levels. The effect of the optimized laser field on the other hydrogen bond, N1(A)...H-N3(T), present in A-T base pair is also investigated.

Dynamics of molecules in strong oscillating electric fields using time-dependent Hartree-Fock theory.

Restricted and unrestricted forms of time-dependent Hartree-Fock theory have been implemented and used to study the electronic dynamics of ethene, benzene, and the formaldehyde cation subjected to both weak and strong oscillating electric fields. Absorption spectra and frequency-dependent polarizabilities are calculated via the instantaneous dipole moment and its derivative. In the weak field limit the computed excitation energies agree very well with those obtained using linearized time-dependent Hartree-Fock theory, which is valid only in the low-field perturbation limit. For strong fields the spectra show higher-order excitations, and a shift in the position of the excitations, which is due to the nonadiabatic response of the molecules to the field. For open-shell systems in the presence of strong oscillating electric fields, unrestricted time-dependent Hartree-Fock theory predicts the value of S(2) to vary strongly with time.

Quantum dynamical study of the O(1D)+HCl reaction employing three electronic state potential energy surfaces.

Quantum dynamical calculations are reported for the title reaction, for both product arrangement channels and using potential energy surfaces corresponding to the three electronic states, 1 1A', 2 1A', and 1 1A", which correlate with both reactants and products. The calculations have been performed for J=0 using the time-dependent real wavepacket approach by Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. Reaction probabilities for both product arrangement channels on all three potential energy surfaces are presented for total energies between 0.1 and 1.1 eV. Product vibrational state distributions at two total energies, 0.522 and 0.722 eV, are also presented for both channels and all three electronic states. Product rotational quantum state distributions are presented for both product arrangement channels and all three electronic states for the first six product vibrational states.

Vibrationally selective optimal control of alignment and orientation using infrared laser pulses: application to carbon monoxide.

Optimal control methods are used to study molecular alignment and orientation using infrared laser pulses. High order molecule-field interactions are taken into account through the use of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. High degrees of alignment and orientation are achieved by optimized infrared laser pulses of duration on the order of one rotational period of the molecule. It is shown that, through the incorporation of a vibrational projection operator into the optimization procedure, it is possible not only to maximize the alignment and orientation but also to bring the whole system into a single prescribed vibrational manifold. Numerical calculations are performed for carbon monoxide using ab initio potential energies computed in the presence of external electric fields.

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction.

The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation.

Ab initio design of picosecond infrared laser pulses for controlling vibrational-rotational excitation of CO molecules.

Optimal control of rovibrational excitations of the CO molecule using picosecond infrared laser pulses is described in the framework of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. The potential energy surface of the CO molecule in the presence of an electric field is calculated using coupled cluster theory with a large orbital basis set. The quantum dynamics of the process is treated using a full three dimensional treatment of the molecule in the laser field. The detailed mechanisms leading to efficient control of the selected excitation processes are discussed.

Quantum control of molecular vibrational and rotational excitations in a homonuclear diatomic molecule: a full three-dimensional treatment with polarization forces.

The optimal control of the vibrational excitation of the hydrogen molecule [Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)] utilizing polarization forces is extended to three dimensions. The polarizability of the molecule, to first and higher orders, is accounted for using explicit ab initio calculations of the molecular electronic energy in the presence of an electric field. Optimal control theory is then used to design infrared laser pulses that selectively excite the molecule to preselected vibrational-rotational states. The amplitude of the electric field of the optimized pulses is restricted so that there is no significant ionization during the process, and a new frequency sifting method is used to simplify the frequency spectrum of the pulse. The frequency spectra of the optimized laser pulses for processes involving rotational excitation are more complex than those relating to processes involving only vibrational excitation.

Design of infrared laser pulses for the deexcitation of highly excited homonuclear diatomic molecules.

We explore the possibility of using shaped infrared laser pulses to deexcite a homonuclear diatomic molecule from its highest vibrational state down to its ground vibrational state. The motivation for this study arises from the need to deexcite alkali metal dimers in a similar way so as to stabilize molecular Bose-Einstein condensates. We demonstrate that for the case of the H(2) molecule, where it is possible to evaluate all the necessary high accuracy ab initio data on the interaction of the molecule with an electric field, we are able to successfully design a sequence of infrared laser pulses to accomplish the desired deexcitation process in a highly efficient manner.

Analytical control of molecular excitations including strong field polarization effects.

An analytical scheme is presented for designing a laser pulse to excite H2 from one specified vibrational-rotational state to another. The scheme is based on an adiabatic two-state approximation in a Floquet picture. By continuously and smoothly changing the laser frequency, we explicitly harness the dynamic Stark shifts and maintain resonance between the dressed diabatic states during laser-molecule interaction. The explicit time-dependent solution of the Schrödinger equation confirms the validity and efficacy of the analytically designed laser pulses. The scheme depends on the molecular polarizability to achieve its control objectives.

State-to-state reactive differential cross sections for the H+H2-->H2+H reaction on five different potential energy surfaces employing a new quantum wavepacket computer code: DIFFREALWAVE.

State-to-state differential cross sections have been calculated for the hydrogen exchange reaction, H+H2-->H2+H, using five different high quality potential energy surfaces with the objective of examining the sensitivity of these detailed cross sections to the underlying potential energy surfaces. The calculations were performed using a new parallel computer code, DIFFREALWAVE. The code is based on the real wavepacket approach of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. The calculations are parallelized over the helicity quantum number Omega' (i.e., the quantum number for the body-fixed z component of the total angular momentum) and wavepackets for each J,Omega' set are assigned to different processors, similar in spirit to the Coriolis-coupled processors approach of Goldfield and Gray [Comput. Phys. Commun. 84, 1 (1996)]. Calculations for J=0-24 have been performed to obtain converged state-to-state differential cross sections in the energy range from 0.4 to 1.2 eV. The calculations employ five different potential energy surfaces, the BKMP2 surface and a hierarchical family of four new ab initio surfaces [S. L. Mielke, et al., J. Chem. Phys. 116, 4142 (2002)]. This family of four surfaces has been calculated using three different hierarchical sets of basis functions and also an extrapolation to the complete basis set limit, the so called CCI surface. The CCI surface is the most accurate surface for the H3 system reported to date. Our calculations of differential cross sections are the first to be reported for the A2, A3, A4, and CCI surfaces. They show that there are some small differences in the cross sections obtained from the five different surfaces, particularly at higher energies. The calculations also show that the BKMP2 performs well and gives cross sections in very good agreement with the results from the CCI surface, displaying only small divergences at higher energies.

Photodissociation of HBr. 1. Electronic structure, photodissociation dynamics, and vector correlation coefficients.

Ab initio potential energy curves, transition dipole moments, and spin-orbit coupling matrix elements are computed for HBr. These are then used, within the framework of time-dependent quantum-mechanical wave-packet calculations, to study the photodissociation dynamics of the molecule. Total and partial integral cross sections, the branching fraction for the formation of excited-state bromine atoms Br(2P(1/2)), and the lowest order anisotropy parameters, beta, for both ground and excited-state bromine are calculated as a function of photolysis energy and compared to experimental and theoretical data determined previously. Higher order anisotropy parameters are computed for the first time for HBr and compared to recent experimental measurements. A new expression for the Re[a1(3) (parallel, perpendicular)] parameter describing coherent parallel and perpendicular production of ground-state bromine in terms of the dynamical functions is given. Although good agreement is obtained between the theoretical predictions and the experimental measurements, the discrepancies are analyzed to establish how improvements might be achieved. Insight is obtained into the nonadiabatic dynamics by comparing the results of diabatic and fully adiabatic calculations.

Velocity map imaging study of BrCl photodissociation at 467 nm: determination of all odd-rank (K = 1 and 3) anisotropy parameters for the Cl(2P(3/2)0) photofragments.

Resonance-enhanced multiphoton ionization and velocity map imaging of the Cl(2P(3/2)0) fragments of BrCl photolysis at 467.16 nm have been used to obtain a complete set of orientation parameters (with ranks K = 1 and 3) describing the polarization of the electronic angular momentum. The experiments employ two geometries distinguished only by the circular or linear polarization of the photolysis laser beam. Normalized difference images constructed from the data accumulated using a right or left circularly polarized probe-laser beam, counterpropagating with the photolysis laser, were fitted to basis images corresponding to contributions from various odd-rank anisotropy parameters. Expressions are given for the difference images in terms of the K = 1 and 3 anisotropy parameters, which describe coherent and incoherent parallel and perpendicular excitation and dissociation mechanisms. The nonzero values of the anisotropy parameters are indicative of nonadiabatic dissociation dynamics, with likely contributions from flux on the A 3Pi1,B 3Pi(0+),C 1Pi1, and X 1sigma+(0+) states as well as one further omega = 1 state, all of which correlate adiabatically to Cl(2P(3/2)0) + Br(2P(3/2)0) photofragments. The magnitudes of the parameters depend both on the amplitudes of dissociative flux in these states, and also on the phases accumulated by the nuclear wave functions for different dissociation pathways.