Characterization and quantification of the role of coherence in ultrafast quantum biological experiments using quantum master equations,atomistic simulations,and quantum process tomography

Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.     

Ultrafast photo-induced charge transfer unveiled by two-dimensional electronic spectroscopy

The interaction of exciton and charge transfer (CT) states plays a central role in photo-induced CT processes in chemistry, biology, and physics. In this work, we use a combination of two-dimensional electronic spectroscopy (2D-ES), pump-probe measurements, and quantum chemistry to investigate the ultrafast CT dynamics in a lutetium bisphthalocyanine dimer in different oxidation states. It is found that in the anionic form, the combination of strong CT-exciton interaction and electronic asymmetry induced by a counter-ion enables CT between the two macrocycles of the complex on a 30 fs timescale. Following optical excitation, a chain of electron and hole transfer steps gives rise to characteristic cross-peak dynamics in the electronic 2D spectra, and we monitor how the excited state charge density ultimately localizes on the macrocycle closest to the counter-ion within 100 fs. A comparison with the dynamics in the radical species further elucidates how CT states modulate the electronic structure and tune fs-reaction dynamics. Our experiments demonstrate the unique capability of 2D-ES in combination with other methods to decipher ultrafast CT dynamics.     

A simple method for the preparation of pseudopure states in nuclear magnetic resonance quantum information processing

The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of pseudopure states (POPS) as a basis for QIP is very convenient because of the simplicity in experimental execution. It is now further demonstrated that the product of the NMR spectra corresponding to two sets of POPS that share a common pseudopure state has the same peak frequencies as those of the common (single) pseudopure state. Examples of applying two different quantum logic gates to a 5-qubit system are given.     

Coherence quantum beats in two-dimensional electronic spectroscopy

We study the coherence quantum beats in two-dimensional (2D) electronic spectroscopy of a coupled dimer system using a theoretical method based on a time-nonlocal quantum master equation and a recently proposed scheme for the evaluation of the third-order photon echo polarization [Gelin, M. F.; Egorova, D.; Domcek, W. J. Chem. Phys. 2005, 123, 164112]. The simulations show that the amplitude and peak shape beating in the 2D spectra is a result of the interplay between the rephasing and non-rephasing contributions to the 2D signals and can be used to elucidate the coherence dynamics in a multichromophoric system. In addition, the results suggest that the rephasing and non-rephasing 2D spectra contain complementary information, and a study of both of them could provide more dynamical information from 2D electronic spectroscopy.     

PHOTO-CIDNP STUDY OF PYRIMIDINE DIMER SPLITTING II: REACTIONS INVOLVING PYRIMIDINE RADICAL ANION INTERMEDIATES

A series of photo-CIDNP (chemically induced dynamic nuclear polarization) experiments were performed on pyrimidine monomers and dimers, using the electron-donor Nα-acetyltryptophan (AcTrp) as a photosensitizer. The CIDNP spectra give evidence for the existence of both the dimer radical anion, which is formed by electron transfer from the excited AcTrp* to the dimer, and its dissociation product, the monomer radical anion. The AcTrp spectra are completely different from those obtained with an oxidizing sensitizer like anthraquinone-2-sulfonate, because of different unpaired electron spin density distributions in pyrimidine radical anion and cation. In the spectra of the anti (1,3-dimethyluracil) dimers, polarization is detected that originates from a spin-sorting process in the dimer radical pair, pointing to a relatively long lifetime of the dimer radical anions involved. Although the dimer radical anions of the 1,1′-trimethylene-bridged pyrimidines may have a relatively long lifetime as well, their protons have only very weak hyperfine interaction, which explains why no polarization originating from the dimer radical pair is detected. In the spectra of the bridged pyrimidines, polarized dimer protons are observed as a result of spin sorting in the monomer radical pair, from which it follows that the dissociation of dimer radical anion into monomer radical anion is reversible. A study of CIDNP intensities as a function of pH shows that a pH between 3 and 4 is optimal for observing monomer polarization that originates from spin-sorting in the monomer radical pair. At higher pH the geminate recombination polarization is partly cancelled by escape polarization arising in the same product.     

Exciton propagation via quantum walks based on non-Hermitian coin flip operations

We examine the coherent propagation of the one-dimensional Frenkel exciton (correlated electron-hole pair system) based on a model of a quantum walker in multi-dimensional Hilbert space. The walk is governed by a non-Hermitian coin flip operation coupled to a generalized shift process. The dissipative coin flip operation is associated with amplitude leakages at occupied sites, typical of processes which occur when an exciton is transferred along dimer sites in photosynthetic protein complexes. We analyze the characteristics probability distribution of the one-dimensional quantum walk for various system parameters, and examine the complex interplay between non-Markovian signatures and amplitude leakages within the Hilbert position subspace. The visibility of topological defects such as exceptional points, and non-Markovian signatures via quantum tomography based spectroscopic measurements is discussed.     

Vibrational averaging of the chemical shift in crystalline α‐glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane‐wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born–Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower‐frequency vibrational modes. Temperature excitations of the lowest‐frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data. © 2012 Wiley Periodicals, Inc.     

PHOTO-CIDNP STUDY OF PYRIMIDINE DIMER SPLITTING I: REACTIONS INVOLVING PYRIMIDINE RADICAL CATION INTERMEDIATES

The light-induced splitting of pyrimidine dimers was studied using the electron acceptor anthraquinone-2-sulfonate (AQS) as a photosensitizer. To this end, photochemically induced dynamic nuclear polarization (photo-CIDNP) experiments were performed on a series of pyrimidine monomers and dimers. The CIDNP spectra demonstrate the existence of both the dimer radical cation, which is formed by electron transfer from the dimer to the photoexcited sensitizer AQS*, and its dissociation product, the monomer radical cation. In spectra of 1,1′-trimethylene bridged cis,syn pyrimidine dimers, polarization is observed that originates from a spin-sorting process in the dimer radical pair. This points to a relatively long lifetime of the dimer radical cation involved, which is presumably due to stabilization by the trimethylene bridge. Polarization originating from a dimer radical pair is detected in the spectrum of trans,anti (1,3-dimethyluracil) dimer as well. The spectra of the bridged pyrimidines also demonstrate the reversibility of the dissociation of dimer radical cation into monomer radical cation, which is concluded from the observation of polarization in the dimer as a result of spin sorting in the monomer radical pair.     

Aggregation-driven,re-entrant isotropic phase in a smectic liquid crystal material

An azobenzene-core chiral mesogen designed for a photoactive ferroelectric liquid crystal system with switchable polarisation displays a highly unusual phase sequence, with a re-entrant, optically isotropic, fluid phase found below smectic phases in mixtures with high enantiomeric purity. The re-entrant isotropic phase is found on the basis of X-ray scattering and freeze-fracture transmission electron microscopy experiments not to be a cubic or other highly ordered phase but instead a translationally disordered liquid. The material also forms a gel under a wide range of concentrations in 50:50 ethanol/chloroform solutions. Ultraviolet/visible and infrared spectroscopy and quantum chemistry calculations suggest that the primary unit in the re-entrant isotropic and gel phases is a dimer composed of molecules crossed by about 90°, which hinders the formation of crystal phases and forms tubules of helical aggregates in the gel phase.     

Quantitative analysis of backbone dynamics in a crystalline protein from nitrogen-15 spin-lattice relaxation

A detailed analysis of nitrogen-15 longitudinal relaxation times in microcrystalline proteins is presented. A theoretical model to quantitatively interpret relaxation times is developed in terms of motional amplitude and characteristic time scale. Different averaging schemes are examined in order to propose an analysis of relaxation curves that takes into account the specificity of MAS experiments. In particular, it is shown that magic angle spinning averages the relaxation rate experienced by a single spin over one rotor period, resulting in individual relaxation curves that are dependent on the orientation of their corresponding carousel with respect to the rotor axis. Powder averaging thus leads to a nonexponential behavior in the observed decay curves. We extract dynamic information from experimental decay curves, using a diffusion in a cone model. We apply this study to the analysis of spin-lattice relaxation rates of the microcrystalline protein Crh at two different fields and determine differential dynamic parameters for several residues in the protein.     

On the performance of molecular polarization methods. II. Water and carbon tetrachloride close to a cation

Our initial study on the performance of molecular polarization methods close to a positive point charge [M. Masia, M. Probst, and R. Rey, J. Chem. Phys. 121, 7362 (2004)] is extended to the case in which a molecule interacts with a real cation. Two different methods (point dipoles and shell model) are applied to both the ion and the molecule. The results are tested against high-level ab initio calculations for a molecule (water or carbon tetrachloride) close to Li+, Na+, Mg2+, and Ca2+. The monitored observable is in all cases the dimer electric dipole as a function of the ion-molecule distance for selected molecular orientations. The moderate disagreement previously obtained for point charges at intermediate distances, and attributed to the linearity of current polarization methods (as opposed to the nonlinear effects evident in ab initio calculations), is confirmed for real cations as well. More importantly, it is found that at short separations the phenomenological polarization methods studied here substantially overestimate the dipole moment induced if the ion is described quantum chemically as well, in contrast to the dipole moment induced by a point-charge ion, for which they show a better degree of accord with ab initio results. Such behavior can be understood in terms of a decrease of atomic polarizabilities due to the repulsion between electronic charge distributions at contact separations. It is shown that a reparametrization of the Thole method for damping of the electric field, used in conjunction with any polarization scheme, allows to satisfactorily reproduce the dimer dipole at short distances. In contrast with the original approach (developed for intramolecular interactions), the present reparametrization is ion and method dependent, and corresponding parameters are given for each case.     

Velocity profiles in simple shear flow of liquid-crystalline polymers

The velocity profiles of isotropic and anisotropic solutions of hydroxypro-pylcellulose in water have been measured by a tracer method. The velocity profile is the usual linear one for steady state experiments and also for transient experiments if a short waiting time (less than 3 hours) is left between loading and the experiment. For long waiting times (more than 12 hours), the profile is S-shaped. This could be due to the establishment of a cholesteric superstructure.     

Photo-reversible liquid crystal alignment using azobenzene-based self-assembled monolayers: comparison of the bare monolayer and liquid crystal reorientation dynamics

Photosensitive surfaces treated to have in-plane structural anisotropy by illumination with polarized light can be used to orient liquid crystals (LCs). Here we report a detailed study of the dynamic behavior of this process at both short and long times, comparing the ordering induced in the bare active surface with that of the LC in contact with the surface using a high-sensitivity polarimeter that enables detailed characterization of the anisotropy of the active surface. The experiments were carried out using self-assembled monolayers (SAMs) made from dimethylaminoazobenzene covalently bonded to a glass surface through a triethoxysilane terminus. This surface gives planar alignment of the liquid crystal director with an azimuthal orientation that can be controlled by the polarization of actinic light. We find a remarkable long-term collective interaction between the orientationally ordered SAM and the director field of the LC: while an azobenzene based SAM in contact with an isotropic gas or liquid relaxes to an azimuthally isotropic state in the absence of light due to thermal fluctuations, an orientationally written SAM in contact with LC in the absence of light can maintain the LC director twist permanently, that is, the SAM is capable of providing azimuthal anchoring to the LC even in the presence of a torque about the surface normal. We find that the short-time, transient LC reorientation is limited by the weak azimuthal anchoring strength of the SAM and by the LC viscosity.     

Internal noise coherent resonance for mesoscopic chemical oscillations: a fundamental study.

The effect of internal noise for a mesoscopic chemical oscillator is studied analytically in a parameter region outside, but close to, the supercritical Hopf bifurcation. By normal form calculation and a stochastic averaging procedure, we obtain stochastic differential equations for the oscillation amplitude r and phase theta that is solvable. Noise-induced oscillation and internal noise coherent resonance, which has been observed in many numerical experiments, are reproduced well by the theory.     

Polarization dependence of transition intensities in double resonance experiments: unresolved spin doublets

The polarization dependence of transition intensities in multiple resonance spectroscopic experiments can provide information useful for making rotational assignments. A formalism to describe the polarization dependence of transition intensities in multiple resonance experiments, particularly for cases when two rotational/fine structure quantum numbers are needed to specify the state of the system, is presented. The formalism is presented in a form usable both when the transitions between the underlying fine structure components are experimentally resolved, as well as when they are unresolved, to form composite lines. This sort of treatment is necessary for cases when the two quantum numbers that specify the fine structure differ significantly, such as is the case at low N, when the difference between J and N becomes comparable to the value of J. Ratios of transition intensities in different experimentally convenient polarization arrangements are evaluated for the case of composite N transitions formed by combining the spin components of a doublet system. The formalism is expressed in a form easily extendable to accommodate experimental cases of more than two excitation steps, or a combination of excitation steps and an external static electric field. This polarization diagnostic has been experimentally applied to assign spectral features in double resonance Rydberg spectra of CaF.     

Multivariate curve resolution applied to in situ X-ray absorption spectroscopy data: An efficient tool for data processing and analysis

Large datasets containing many spectra commonly associated with in situ or operando experiments call for new data treatment strategies as conventional scan by scan data analysis methods have become a time-consuming bottleneck. Several convenient automated data processing procedures like least square fitting of reference spectra exist but are based on assumptions. Here we present the application of multivariate curve resolution (MCR) as a blind-source separation method to efficiently process a large data set of an in situ X-ray absorption spectroscopy experiment where the sample undergoes a periodic concentration perturbation. MCR was applied to data from a reversible reduction–oxidation reaction of a rhenium promoted cobalt Fischer–Tropsch synthesis catalyst. The MCR algorithm was capable of extracting in a highly automated manner the component spectra with a different kinetic evolution together with their respective concentration profiles without the use of reference spectra. The modulative nature of our experiments allows for averaging of a number of identical periods and hence an increase in the signal to noise ratio (S/N) which is efficiently exploited by MCR. The practical and added value of the approach in extracting information from large and complex datasets, typical for in situ and operando studies, is highlighted.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Electronic coherence within the semiclassical field-induced surface hopping method: strong field quantum control in K2

We demonstrate that the semiclassical field-induced surface hopping (FISH) method (Mitri?et al., Phys. Rev. A: At., Mol., Opt. Phys., 2009, 79, 053416.) accurately describes the selective coherent control of electronic state populations. With the example of the strong field control in the potassium dimer using phase-coherent double pulse sequences, we present a detailed comparison between FISH simulations and exact quantum dynamics. We show that for short pulses the variation of the time delay between the subpulses allows for a selective population of the desired final state with high efficiency. Furthermore, also for pulses of longer time duration, when substantial nuclear motion takes place during the action of the pulse, optimized pulse shapes can be obtained which lead to selective population transfer. For both types of pulses, the FISH method almost perfectly reproduces the exact quantum mechanical electronic population dynamics, fully taking account of the electronic coherence, and describes the leading features of the nuclear dynamics accurately. Due to the significantly higher computational efficiency of FISH as a trajectory-based method compared to full quantum dynamics simulations, this offers the possibility to theoretically investigate control experiments on realistic systems including all nuclear degrees of freedom.     

Applications of a time correlation function theory for the fifth-order Raman response function I: atomic liquids

Multidimensional spectroscopy has the ability to provide great insight into the complex dynamics and time-resolved structure of liquids. Theoretically describing these experiments requires calculating the nonlinear-response function, which is a combination of quantum-mechanical time correlation functions R5(t1,t2) was expressed with a two-time, computationally tractable, classical TCF. Writing the response function in terms of classical TCFs brings the full power of atomistically detailed molecular dynamics to the problem. In this paper, the new TCF theory is employed to calculate the fifth-order Raman response function for liquid xenon and investigate several of the polarization conditions for which experiments can be performed on an isotropic system. The theory is shown to reproduce line-shape characteristics predicted by earlier theoretical work.     

Experimental and Theoretical Investigation of the First‐Order Hyperpolarizability of Octupolar Merocyanine Dyes

Hyper‐Rayleigh scattering experiments and quantum chemical calculations are combined to investigate the second‐order nonlinear optical responses of a series of three‐arm merocyanine derivatives. They exhibit an octupolar hyperpolarizability response with lower amplitude than crystal violet due to a lower extent of the photoinduced charge transfer and reduced bond length alternation. Strong effects on the second‐order optical response measured close to the two‐photon absorption level are clearly evidenced; for example, the effective measured polarization ratio deviates below the ideal octupolar value of 3/2 even at very low excitation power. These effects are attributed to two‐photon absorption resonance, which we believe modifies dynamically the population of the ground state versus that of the excited state.