Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH

Pump-probe spectroscopy of chiral vibrational dynamics

A planar molecule may become chiral upon excitation of an out-of-plane vibration, changing its handedness during half a vibrational period. When exciting such a vibration in an ensemble of randomly oriented molecules with an infrared laser, half of the molecules will undergo the vibration phase-shifted by π compared to the other half, and no net chiral signal is observed. This symmetry can be broken by exciting the vibrational motion with a Raman transition in the presence of a static electric field. Subsequent ionization of the vibrating molecules by an extreme ultraviolet pulse probes the time-dependent net handedness via the photoelectron circular dichroism. Our proposal for pump-probe spectroscopy of molecular chirality, based on quantum-chemical theory and discussed for the example of the carbonyl chlorofluoride molecule, is feasible with current experimental technology.

Circularly polarized light-induced potentials and the demise of excited states

In the presence of strong electric fields, the excited states of single-electron molecules and molecules with large transient dipoles become unstable because of anti-alignment, the rotation of the molecular axis perpendicular to the field vector, where bond hardening is not possible. We show how to overcome this problem by using circularly polarized electromagnetic fields. Using a full quantum description of the electronic, vibrational, and rotational degrees of freedom, we characterize the excited electronic state dressed by the field and analyze its dependence on the bond length and angle and the stability of its vibro-rotational eigenstates. Although the dynamics is metastable, most of the population remains trapped in this excited state for hundreds of femtoseconds, allowing quantum control. Contrary to what happens with linearly polarized fields, the photodissociation occurs along the initial molecular axis, not perpendicular to it.

Effective discrimination of chiral molecules in a cavity

We present a scheme to realize precise discrimination of chiral molecules in a cavity. Assisted by additional laser pulses, cavity fields can evolve into different coherence states with contrary-sign displacements according to the handedness of molecules. Consequently, the handedness of molecules can be read out with homodyne measurement on the cavity, and the successful probability is nearly unity without very strong cavity fields. Numerical results show that the scheme is insensitive to errors, noise, and decoherence. Therefore, the scheme may provide helpful perspectives for accurate discrimination of chiral molecules.

Highly Efficient Detection and Separation of Chiral Molecules through Shortcuts to Adiabaticity

A highly efficient method for optical or microwave detection and separation of left- and right-handed chiral molecules is proposed. The method utilizes a closed-loop three-state system in which the population dynamics depends on the phases of the three couplings. Because of the different signs of the coupling between two of the states for the opposite chiralities the population dynamics is chirality dependent. By using the "shortcuts to adiabaticity" concept applied to the stimulated Raman adiabatic passage technique, one can achieve 100% contrast between the two enantiomers in the population of a particular state. It can be probed by light-induced fluorescence for large ensembles or through resonantly enhanced multiphoton ionization for single molecules.

Breaking dynamic inversion symmetry in a racemic mixture using simple trains of laser pulses

Recent advances in ultrafast laser technology hint at the possibility of using shaped pulses to generate deracemization via selective enantiomeric conversion; however, experimental implementation remains a challenge and has not yet been achieved. Here, we describe an experiment that can be considered an accessible intermediate step on the road towards achieving laser induced deracemization in a laboratory. Our approach consists of driving a racemic mixture of 3D oriented 3,5-difluoro-3', 5'-dibromobiphenyl (F₂H₃C₆-C₆H₃Br₂) molecules with a simple train of Gaussian pulses with alternating polarization axes. We use arguments related to the geometry of the field/molecule interaction to illustrate why this will increase the amplitude of the torsional oscillations between the phenyl rings while simultaneously breaking the inversion symmetry of the dynamics between the left- and right-handed enantiomeric forms, two crucial requirements for achieving deracemization. We verify our approach using numerical simulations and show that it leads to significant and experimentally measurable differences in the internal enantiomeric structures when detected by Coulomb explosion imaging.

Generating laser-pulse enantiomers

We present an optical setup capable of mirroring an arbitrary, potentially time-varying, polarization state of an ultrashort laser pulse. The incident beam is split up in two and the polarization of one beam is mirrored by reflection off a mirror in normal incidence. Afterwards, both beams are recombined in time and space such that two collinear ultrashort laser pulses with mutually mirrored polarization, i.e., laser-pulse enantiomers, leave the setup. We employ the Jones formalism to describe the function of the setup and analyze the influence of alignment errors before describing the experimental implementation and alignment protocol. Since no wave plates are utilized, broadband pulses in a large wavelength range can be processed. In particular, we show that the setup outperforms broadband achromatic wave plates. Furthermore, since the two beams travel separately through the optical system they can be blocked independently. This opens the possibility for circular dichroism, ellipsometry, and anisotropy spectroscopy with shot-to-shot chopping and detection schemes as well as chiral coherent control applications.

Phase-Modulated Nonresonant Laser Pulses Can Selectively Convert Enantiomers in a Racemic Mixture

Deracemization occurs when a racemic molecular mixture is transformed into a mixture containing an excess of a single enantiomer. Recent advances in ultrafast laser technology hint at the possibility of using shaped pulses to generate deracemization via selective enantiomeric conversion; however, experimental implementation remains a challenge and has not yet been achieved. Here we suggest a simple, yet novel approach to laser-induced enantiomeric conversion based on dynamic Stark control. We demonstrate theoretically that current laser and optical technology can be used to generate a pair of phase-modulated, nonresonant, linearly polarized Gaussian laser pulses that can selectively deracemize a racemic mixture of 3D-oriented, 3,5-difluoro-3',5'-dibromobiphenyl (F₂H₃C₆-C₆H₃Br₂) molecules, the laser-induced dynamics of which are well studied experimentally. These results strongly suggest that designing a closed-loop coherent control scheme based on this methodology may lead to the first-ever achievement of enantiomeric conversion via coherent laser light in a laboratory setting.

Optical discrimination of racemic from achiral solutions

We demonstrate purely optical discrimination between achiral and racemic solutions by selectively triggering an asymmetric photoreaction with femtosecond laser pulses.

Distinguishability and chiral stability in solution: effects of decoherence and intermolecular interactions

We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energies, and the decoherence in determining: the distinguishability as measured by a population difference between the initially pure and mixed states, and the decoherence process; the chiral stability as measured by the purity decay; and the stationary state of the system at times long relative to the time scales of the system dynamics and of the environmental effects.

Effects of initial coherence on distinguishability of pure/mixed states and chiral stability in an open chiral system

We examine how initial coherences in open chiral systems affect distinguishability of pure versus mixed states and purity decay. Interaction between a system and an environment is modeled by a continuous position measurement and a two-level approximation is taken for the system. The resultant analytical solution is explored for various parameters, with emphasis on the interplay of initial coherences of the system and dephasing rate in determining the purity decay and differences in the time evolution of pure versus mixed initial states. Implications of the results for several fundamental problems are noted.

Interferometric polarization pulse shaper stabilized by an external laser diode for arbitrary vector field shaping

We achieved reliable and stable generation of pulses with all possible polarization states by a Mach-Zehnder pulse shaper. This was realized by incorporating a stabilization mechanism using an external laser diode in the interferometric pulse shaper. This stabilization mechanism has overcome an inherent instability in the Mach-Zehnder interferometer, which caused serious distortion of shaped pulses. For a demonstration of polarization shaping, we generated and measured chiral pulses with a rotating major axis of polarizing orientations at arbitrary frequencies. We expect these chiral pulses enables us to study on new chirality-related light-matter interactions.

Manipulating the torsion of molecules by strong laser pulses

We demonstrate that strong laser pulses can induce torsional motion in a molecule consisting of a pair of phenyl rings. A nanosecond laser pulse spatially aligns the carbon-carbon bond axis, connecting the two phenyl rings, allowing a perpendicularly polarized, intense femtosecond pulse to initiate torsional motion accompanied by an overall rotation about the fixed axis. We monitor the induced motion by femtosecond time-resolved Coulomb explosion imaging. Our theoretical analysis accounts for and generalizes the experimental findings.

Stereoselective isomerization of an ensemble of adsorbed molecules with multiple orientations: stochastic laser pulse optimization for selective switching between achiral and chiral atropisomers

We present quantum dynamical simulations for the laser driven isomerization of an ensemble of surface mounted stereoisomers with multiple orientations. The model system 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers upon torsion around the C-C single bond connecting phenyl ring and ethylene group. An infrared picosecond pulse is used to excite the internal rotation around the chiral axis, thereby controlling the chirality of the molecule. In order to selectively switch the molecules--independent of their orientation on a surface--from their achiral to either their left- or right-handed form, a stochastic pulse optimization algorithm is applied. The stochastic pulse optimization is performed for different sets of defined orientations of adsorbates corresponding to the rotational symmetry of the surface. The obtained nonlinearly polarized laser pulses are highly enantioselective for each orientation.

Wave packets in a bifurcating region of an energy landscape: Diels-Alder dimerization of cyclopentadiene

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-Parr6-31G* 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.

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.

Large Raman-scattering activities for the low-frequency modes of substituted benzenes: Induced polarizability and stereo-specific ring-substituent interactions

The large nonresonant Raman-scattering activities of the out-of-plane bending and torsional modes of monosubstituted benzene analogs are studied by low-frequency Raman experiments and B3LYP6-31++G(d,p) calculations. Electronic interactions between the sigma orbitals of the substituent and the pi orbitals of the ring are found to enhance the Raman activities, depending on the substituent and its conformation. In the case of tert-butylbenzene [C6H5C(CH3)3] and trimethylphenylsilane [C6H5Si(CH3)3], three single bonds which are linked to the alpha atom of the substituent have low rotational barriers around the joint bond. Nearly free rotation of the substituents leads to a significant probability for one of the single bonds to occupy a conformation close to the vertical configuration with respect to the ring at room temperature. The resultant sigma-pi electronic interaction gives rise to the large Raman activities. In contrast, those possessing a single bond in a coplanar (or nearly coplanar) configuration at the most stable equilibrium state, i.e., anisole (C6H5OCH3), thioanisole (C6H5SCH3), and N-methylaniline (C6H5NHCH3), display no prominent Raman bands for the low-frequency vibrational modes. In these molecules, the sigma-pi conjugation does not take place due to the orthogonal orientation of the orbitals. Strong conformational dependence of the sigma-pi Raman enhancement is clearly obtained for the metastable vertical conformer of thioanisole, for which Raman activities are one-order magnitude greater than those of the coplanar conformer.

Density Functional Theoretical Study on Enantiomerization of 2,2‘-Biphenol

The S-R enantiomerization processes of 2,2'-biphenol (biphenol) have been investigated using density functional theory (DFT). Five isomers for biphenol were identified: I0, which is the most stable isomer; I1a and I1b, which are formed by a restricted rotation of one OH group; and I2a and I2b, which are formed by a restricted rotation of the two OH groups where a and b denote cis and trans configurations, respectively. Each isomer has R- and S-enantiomers. The energies relative to the most stable isomer I0 are 1.6, 3.3, 5.3, and 5.5 kcal mol(-1) for I1a, I1b, I2a, and I2b, respectively. The direct enantiomerization of I0, in which the phenol-ring rotation is considered to be the reaction coordinate while the OH rotations are frozen, is forbidden because of the repulsion between the two OH groups. The transition states for isomerizations of I0 to other isomers (I1a, I1b, I2a, or I2b) were calculated as well as those for the other direct enantiomerizations except for that of I0. From the viewpoint of the least number of the transition states and their low energy levels, the probable S-R enantiomerization of I0 is expressed as a sequential process of isomerization: I0,S --> I1a,S, a direct enantiomerization induced by one of the two OH rotations, I1a,S --> I1a,R, and another isomerization, I1a,R --> I0,R, that is, I0,S --> I1a,S --> I1a,R --> I0,R as the whole process. This process is effective in quantum control of the enantiomerization of biphenol and can be carried out by a sequence of a pump-dump IR laser-pulse scheme.

Optimal control of photoisomerization

We report on optimal control of the photoisomerization of 3,3-diethyl-2,2-thiacyanine iodide dissolved in methanol. Enhancement and reduction of the relative yield of cis to trans isomers are achieved; i.e., the quantum efficiency of the photoisomerization is controlled with optimally phase and amplitude shaped 400 nm femtosecond laser pulses. Single-parameter control schemes, like chirp or intensity variation, fail to change the ratio of the photoproducts. The successful modification of the molecular structure can be regarded as a first step towards controlled stereoselectivity in photochemistry.

Nontrivial polarization shaping of femtosecond pulses by reference to the results of dual-channel spectral interferometry

Adaptive shaping of time-dependent polarization pulses is performed by reference to the analyzed results of dual-channel spectral interferometry. The desired pulses can be generated only by use of such a polarization-characterization technique. We demonstrate the generation of shaped femtosecond pulses whose ellipticity increases at a constant rate. The relative error between the shaped pulse and the target pulse is less than 6% over the main part of the pulse. Shaped time-dependent polarization pulses have many potential applications.

Quantum control by ultrafast polarization shaping

We demonstrate that the use of time-dependent light polarization opens a new level of control over quantum systems. With potassium dimer molecules from a supersonic molecular beam, we show that a polarization-shaped laser pulse increases the ionization yield beyond that obtained with an optimally shaped linearly polarized laser pulse. This is due to the different multiphoton ionization pathways in K2 involving dipole transitions which favor different polarization directions of the exciting laser field. This experiment is a qualitative extension of quantum control mechanisms which opens up new directions giving access to the three-dimensional temporal response of molecular systems.

Optimal control of multiphoton ionization processes in aligned I2 molecules with time-dependent polarization pulses

Multiphoton ionization processes in aligned I2 molecules are actively controlled by the homemade pulse shaping system, with which a time-dependent polarization pulse can be generated and controlled. We find a correlation between a femtosecond time-dependent polarization pulse and the production efficiency of evenly or oddly charged molecular ions. We achieve much better controllability of the correlation with a time-dependent polarization pulse than with a pulse having a fixed ellipticity. The results suggest the existence of an unknown tunnel ionization mechanism which is characteristic of a time-dependent polarization pulse. Our experiments point to new directions in optimal control studies with molecular systems, as discussed in the text.

Quantum control of gas-phase and liquid-phase femtochemistry

Active control of chemical reactions on a microscopic (molecular) level, that is, the selective breaking or making of chemical bonds, is an old dream. However, conventional control agents used in chemical synthesis are macroscopic variables such as temperature, pressure or concentration, which gives no direct access to the quantum-mechanical reaction pathway. In quantum control, by contrast, molecular dynamics are guided with specifically designed light fields. Thus it is possible to efficiently and selectively reach user-defined reaction channels. In the last years, experimental techniques were developed by which many breakthroughs in this field were achieved. Femtosecond laser pulses are manipulated in so-called pulse shapers to generate electric field profiles which are specifically adapted to a given quantum system and control objective. The search for optimal fields is guided by an automated learning loop, which employs direct feedback from experimental output. Thereby quantum control over gas-phase as well as liquid-phase femtochemical processes has become possible. In this review, we first discuss the theoretical and experimental background for many of the recent experiments treated in the literature. Examples from our own research are then used to illustrate several fundamental and practical aspects in gas-phase as well as liquid-phase quantum control. Some additional technological applications and developments are also described, such as the automated optimization of the output from commercial femtosecond laser systems, or the control over the polarization state of light on an ultrashort timescale. The increasing number of successful implementations of adaptive learning techniques points at the great versatility of computer-guided optimization methods. The general approach to active control of light-matter interaction has also applications in many other areas of modern physics and related disciplines.

Two-step enantio-selective optical switch

We present an optical "enantio-selective switch" that, in two steps, turns a ("racemic") mixture of left-handed and right-handed chiral molecules into the enantiomerically pure state of interest. The optical switch is composed of an "enantio-discriminator" and an "enantio-converter" acting in tandem. The method is robust, insensitive to decay processes, and does not require molecular preorientation. We demonstrate the method on the purification of a racemate of (transiently chiral) D2S2 molecules, performed on the nanosecond time scale.

Quantum control of molecular chirality: optical isomerization of difluorobenzo[c]phenanthrene

The results of a theoretical study are presented on quantum control of a chiral exchange reaction of a polyatomic molecule by using infrared laser pulses. Difluorobenzo[c]phenanthrene was chosen to be the simplest model for its helical chirality exchange reaction. This molecule has two stable configurations: M and P forms. From the viewpoint of chemical reaction dynamics, isomerization is regarded as the movement of one of the two representative points that initially correspond to the two forms to the position of the other representative point, while the other representative point remains in its initial position. The ground-state potential energy surface and dipole moment functions required to control this reaction were evaluated at the MP2/6-31+G(d,p) and MP2/TZV+(d,p) levels of molecular orbital (MO) theory. An effective potential energy surface (PES) that is a function of twisting motion of the benzene rings and wagging motion of the CF(2) group was constructed on the basis of the MO results. An analytical expression for the effective PES and that for the dipole moment functions were prepared to make the isomerization control tractable. A quantum control method in a classical way was applied to the isomerization of preoriented difluorobenzo[c]phenanthrene in low temperature limits. The time evolution of the representative point of the M form and that of the P form are separately evaluated to determine the optimal laser fields. This means that the laser control produces pure helical enantiomers from a racemic mixture. Representative points are replaced by the corresponding nuclear wave packets in this treatment. The derived control laser field consists of two linearly polarized E(x)() and E(z)() components that are perpendicular to each other. These components are pi-phase-shifted when the representative point is in the transition-state regions. Under the irradiation of this laser pulse, one of the two representative points of the isomerization is transferred to the target position along the intrinsic reaction path between the enantiomers, while the other representative point remains in its initial potential well. This results in one-way isomerization control, that is, the M(P) to P(M) form. The isomerization is completed with yields of ca. 70% within a few picoseconds. Temporal behaviors of the nuclear wave packet whose center corresponds to the representative point are drawn to see how the desired chiral exchange reaction proceeds in the presence of the control field, while its reverse process is suppressed.