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.     

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.     

Oscillating laminar electrokinetic flow in infinitely extended circular microchannels

This article addresses the problem of oscillating laminar electrokinetic liquid flow in an infinitely extended circular microchannel. Based on the Debye-Huckel approximation for low surface potential at the channel wall, a complex variable approach is used to obtain an analytical solution for the flow. The complex counterparts of the flow rate and the current are linearly dependent on the pressure gradient and the external electric field. This property is used to show that Onsager's principle of reciprocity continues to be valid (involving the complex quantities) for the stated problem. During oscillating pressure-driven flow, the electroviscous effect for a given value of the normalized reciprocal electrical double-layer (EDL) thickness is observed to attain a maximum at a certain normalized frequency. In general, an increasing normalized frequency results in a reduction of EDL effects, leading to (i). a volumetric flow rate in the case of streaming potential approaching that predicted by the theory without EDL effects, and (ii). a reduction in the volumetric flow rate in the case of electroosmosis.     

Phase control over decaying molecular states in intense laser pulses

A time-dependent approach to study phase control over molecular photoabsorption, provided by intense laser pulses, is elaborate. The method allows for the decay linewidth of molecular states and frequency bandwidth of the controlling laser field, and can be applied in weak and strong laser fields where the perturbation theory is invalid. It is shown that a frequency mismatch between the fundamental laser wave and its third harmonic can destroy control. For the example of the one-photon versus three-photon control a simple picture of interference from two monochromatic absorption pathways is not enough to explain phase control and one needs to consider a nonlinear temporal interference of multiquantum transitions. In the perturbation-theory limit an elegant generalization of the famous Shapiro-Hepburn-Brumer equation for the one-photon versus three-photon control is derived. Various numerical calculations illustrate the dependence of phase control on molecular linewidth, fundamental laser wavelength, pulse duration, and peak intensity. It is obtained, that the one-photon versus three-photon control is productive if the molecular state populations, individually produced by each laser wave, have beats of approximately the same frequency. The calculations demonstrate that an enough intense optical pulse can suppress molecular decay and may be used in order to keep stable the state population of a decaying molecule for a long time. The available experimental results for the one-photon versus three-photon control over simple and large polyatomic molecules are analyzed and recommendations for the experimental improvement of control are formulated.     

Monotone Chemical Reaction Networks

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result.     

用非线性非平衡热力学讨论动电效应

本文用非线性非平衡热力学讨论了动电效应.首先,解释了实验值与旧理论不符的问题.其次,给出了旧理论处理动电效应的近似条件.最后,提出了一个新看法,在一定条件下,对某种液体和某个膜,当△P、△φ达一定值时,动电效应也可能出现耗散结构.     

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.     

Magnetic field controlled optical phase retardation in a hybrid nematic cell

We have studied the phase retardation of linearly polarized light in a hybrid nematic liquid crystal cell. For a certain range of directions of the applied magnetic field the phase retardation is found to change non-monotonically with the magnetic induction. The observed behaviour is described rather well by the standard Frank elastic theory. The corrections resulting from subsurface deformations, which are characteristic both for second order elasticity approach and for surface field theory, are also considered. The analysis of the experimental data suggests that the presence of distortions in the zero-field director configuration is the necessary condition for the non-monotonic phase retardation, which implies that such an experiment could be used for the detection of misalignment of the effective pretilts in a nematic cell.     

A Systems Theory for Chemistry

A systems theory for chemistry is proposed in order to provide a general framework, which covers different theoretical approaches used in the molecular sciences.The basic elements of systems theory are introduced and discussed.By construction, this systems chemistry offers classification and categorizationschemes that will help to identify the range of applicability of certain theoretical approachesas well as to find yet unanswered fundamental questions. Consequently, it will be of value not only to thosewho want to understand and study the structure of chemistry, but it might also be of importance to daily research in chemistry.     

Frequency Characteristics of a Spatially-Confined Electrochemical Cell under Conditions of Convective Diffusion

A theory for the transfer function of an electrochemical cell under conditions of convective diffusion is constructed. The variational principle for the integration of the convective-diffusion equation is developed, which reduces the problem solution to selecting adequate trial functions. With the diffusion frequency exceeded, the decay in the frequency dependence of the transfer function is defined by the system geometry. At a certain balance between parameters of the electrode system the frequency dependence of the transfer function can be strictly analytical, i.e. of the ^–1 type.     

Free Energies in the Landau and Molecular Field Approaches

An expression for the entropy as a power series in the order parameter is derived in the context of molecular field theory. The expression is valid both at and away from equilibrium. It is a unique generalization of molecular field theory to non-equilibrium situations. Discrepancies with certain expressions which have appeared in the literature are resolved. Analysis of the radius of convergence of the power series indicates that in certain cases, including the Maier-Saupe model of liquid crystals, molecular field theory and Landau theory cannot be made to agree over the entire range of possible values of the order parameter.     

Damped response theory description of two-photon absorption

Damped response theory is applied to the calculation of two-photon absorption (TPA) spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPA spectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent. Both exact damped response theory and its application within density functional theory are discussed. The latter is implemented using an atomic-orbital based density matrix formulation, which makes the approach especially suitable for studies on large systems. A test preliminary study is presented for the TPA spectrum of R-(+)-1,1'-bi(2-naphtol).     

Chemoselective quantum control of carbonyl bonds in Grignard reactions using shaped laser pulses

Grignard reactants like methylmagnesium chloride are not selective with respect to different carbonyl bonds. We present a theoretical study where shaped laser pulses are utilized to prefer specific bonds in a mixture of more than one carbonyl reactant. A mixture of cyclohexanone and cyclopentanone has been chosen as a representative example. The light pulse is supposed to provide the activation energy and to adopt the function of a protecting group. The control aim is to stretch exclusively the C-O bond of one compound to the length required in the Grignard transition state. To guarantee an experimentally realizable bandwidth for the unshaped pulse, we use our recently developed optimal control theory algorithm, which allows the simultaneous optimization of the light field in the time and frequency domain. Highly selective picosecond control pulses could be optimized in the infrared regime suggesting that laser assisted chemoselectivity is possible to a large extent. To obtain control not only on the final product but also on the excitation mechanism, various initial conditions and frequency restrictions were investigated.     

A site-renormalized molecular fluid theory

The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.     

Conformational studies utilizing asymmetric torsional frequencies

The utility of asymmetric torsional frequencies, obtained from low frequency infrared and/or Raman spectra of the gas phase, for conformational studies is presented. Vibrational spectroscopy may well be the most generally applicable method to be used in the study of the conformations of certain types of small molecules with few substituents because infrared and Raman spectra can be recorded in all phases, and variable temperature experiments can also be conducted. Additionally, gas phase band contours in both the infrared and Raman spectra, along with Raman depolarization data, provide considerable structural information and lend confidence to conclusions arrived at from vibrational studies. The theory and experimental difficulties involved in the determination of potential functions governing internal rotation is presented, and illustrated by a few examples.     

Free Energies in the Landau and Molecular Field Approaches

Abstract

An expression for the entropy as a power series in the order parameter is derived in the context of molecular field theory. The expression is valid both at and away from equilibrium. It is a unique generalization of molecular field theory to non-equilibrium situations. Discrepancies with certain expressions which have appeared in the literature are resolved. Analysis of the radius of convergence of the power series indicates that in certain cases, including the Maier-Saupe model of liquid crystals, molecular field theory and Landau theory cannot be made to agree over the entire range of possible values of the order parameter.     

Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms

Optimal control theory has recently been introduced to nuclear magnetic resonance (NMR) spectroscopy as a means to systematically design and optimize pulse sequences for liquid- and solid-state applications. This has so far primarily involved numerical optimization using gradient-based methods, which allow for the optimization of a large number of pulse sequence parameters in a concerted way to maximize the efficiency of transfer between given spin states or shape the nuclear spin Hamiltonian to a particular form, both within a given period of time. Using such tools, a variety of new pulse sequences with improved performance have been developed, and the NMR spin engineers have been challenged to consider alternative routes for analytical experiment design to meet similar performance. In addition, it has lead to increasing demands to the numerical procedures used in the optimization process in terms of computational speed and fast convergence. With the latter aspect in mind, here we introduce an alternative approach to numerical experiment design based on the Krotov formulation of optimal control theory. For practical reasons, the overall radio frequency power delivered to the sample should be minimized to facilitate experimental implementation and avoid excessive sample heating. The presented algorithm makes explicit use of this requirement and iteratively solves the stationary conditions making sure that the maximum of the objective is reached. It is shown that this method is faster per iteration and takes different paths within a control space than gradient-based methods. In the present work, the Krotov approach is demonstrated by the optimization of NMR and dynamic nuclear polarization experiments for various spin systems and using different constraints with respect to radio frequency and microwave power consumption.     

Classical aspects emerging from local control of energy and particle transfer in molecules

The question in how far classical mechanics can be used to describe coherent control processes in molecules is addressed within the framework of local control theory. Therefore, quantum and classical calculations are compared for a model proton transfer process and also for the multi-photon infrared dissociation of the HOD molecule. It is shown that control fields can be derived classically as long as wave packet dispersion is not too large. This hints at further applications which might be helpful to devise control fields for complex molecular systems being present in biological processes.     

Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy

Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen M?ller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.     

Three-dimensional-IR spectroscopy: beyond the two-point frequency fluctuation correlation function

Three-dimensional-IR spectroscopy is proposed as a new spectroscopic technique that is sensitive to three-point frequency fluctuation correlation functions. This will be important when the statistics of the underlying stochastic process is non-Gaussian, and hence when the system does not follow the linear response hypothesis. Furthermore, a very general classification of nonlinear spectroscopy in terms of higher order frequency fluctuation correlation functions is introduced, according to which certain moments of a multidimensional spectrum are related to certain frequency fluctuation correlation functions. The classification is rigorous in the so-called inhomogeneous limit, but remains valid approximately also when motional narrowing becomes important. The work also puts a recent paper [J. Bredenbeck et al., Phys. Rev. Lett. 95, 083201 (2005)] onto solid theoretical grounds, where we have shown for the first time that fifth-order spectroscopy--in this case transient two-dimensional spectroscopy--is indeed sensitive to the three-point frequency fluctuation correlation function.