Few-state Model Research Articles

Designing a Propellane-based Nonlinear Optically Active System Absorbing in Three Different Wavelength Regions.

The aim of this work is to demonstrate the possibility of using propellane in designing a molecule that can absorb in three different wavelength regions and their nonlinear optical (NLO) activity can be fine-tuned by varying the three wings. We considered 22 tailor-made propellane derivatives consisting of phenyl, naphthyl, and biphenyl wings for this purpose. Using the state-of-the-art linear and quadratic response methods within TD-DFT and RI-CC2 theories and a suitable generalized few-state model that quantifies the effect of orientation of different transition moments on NLO properties, we discussed how and why the linear and nonlinear optical activity of propellane vary when the three wings are assembled successively to construct a full-propellane.

Thermally Activated Delayed Fluorescence: Polarity, Rigidity, and Disorder in Condensed Phases.

We present a detailed and comprehensive picture of the photophysics of thermally activated delayed fluorescence (TADF). The approach relies on a few-state model, parametrized ab initio on a prototypical TADF dye, that explicitly accounts for the nonadiabatic coupling between electrons and vibrational and conformational motion, crucial to properly address (reverse) intersystem crossing rates. The Onsager model is exploited to account for the medium polarity and polarizability, with careful consideration of the different time scales of relevant degrees of freedom. TADF photophysics is then quantitatively addressed in a coherent and exhaustive approach that accurately reproduces the complex temporal evolution of emission spectra in liquid solvents as well as in solid organic matrices. The different rigidity of the two environments is responsible for the appearance in matrices of important inhomogeneous broadening phenomena that are ascribed to the intertwined contribution from (quasi)static conformational and dielectric disorder.

Much of a Muchness: On the Origins of Two- and Three-Photon Absorption Activity of Dipolar Y-Shaped Chromophores.

The molecular origin of two- (2PA) and three-photon absorption (3PA) activity in three experimentally studied chromophores, prototypical dipolar systems, is investigated. To that end, a generalized few-state model (GFSM) formula is derived for the 3PA transition strength for nonhermitian theories and employed at the coupled-cluster level of theory. Using various computational techniques such as molecular dynamics, linear and quadratic response theories, and GFSM, an in-depth analysis of various optical channels involved in 2PA and 3PA processes is presented. It is found that the four-state model involving the second and third excited singlet states as intermediates is the smallest model among all considered few-state approximations that produces 2PA and 3PA transition strengths (for S0 → S1 transition) close to the reference results. By analyzing various optical channels appearing in these models and involved in studied multiphoton processes, we found that the 2PA and 3PA activities in all the three chromophores are dominated and hence controlled by the dipole moment of the final excited state. The similar origins of the 2PA and the 3PA in these prototypical dipolar chromophores suggest transferability of structure–property relations from the 2PA to the 3PA domain.

Two-Photon Absorption Activity of BOPHY Derivatives: Insights from Theory

We present a theoretical study of a two-photon absorption (2PA) process in dipolar and quadrupolar systems containing two BF2 units. For this purpose, we considered 13 systems studied by Ponce-Vargas et al. [J. Phys. Chem. B2017, 121, 10850−1085829136383] and performed linear and quadratic response theory calculations based on the RI-CC2 method to obtain the 2PA parameters. Furthermore, using the recently developed generalized few-state model, we provided an in-depth view of the changes in 2PA properties in the molecules considered. Our results clearly indicate that suitable electron-donating group substitution to the core BF2 units results in a large red-shift of the two-photon absorption wavelength, thereby entering into the desired biological window. Furthermore, the corresponding 2PA strength also increases significantly (up to 30-fold). This makes the substituted systems a potential candidate for biological imaging.

Designing curcumin-based non-linear optically active compounds

ABSTRACT Curcumin – an active composition of turmeric – is well-known for its various therapeutic uses. In this work, the authors aim to design a curcumin-based highly active non-linear optical compound. For this purpose, the authors propose 18 chemically modified curcumin-based molecules and theoretically study their non-linear optical properties such as two-photon absorption and static first hyperpolarisability. The solvent effect has also been taken into account by calculating the said properties in two different solvents too. The results reveal that the non-linear optical property of curcumin can be enhanced significantly by placing an electron donor at the two extremes of curcumin. The microscopic origin of the respective changes in non-linear optical properties are explained using the generalised few-state model developed by Alam et al. [M.M. Alam, M. Chattopadhyaya and S. Chakrabarti, Phys. Chem. Chem. Phys. 14, 1156–1165 (2012). doi:10.1039/C1CP22849H; M.M. Alam, M.T.P. Beerepoot and K. Ruud, J. Chem. Phys. 146, 244116 (2017). doi:10.1063/1.4990438].

A generalized few-state model for the first hyperpolarizability.

The properties of molecules depend on their chemical structure, and thus, structure-property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability β, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure-property relationship for β and can hence be used to fine-tune the magnitude of β in a molecule.

Attosecond Time-Domain Measurement of Core-Level-Exciton Decay in Magnesium Oxide.

Excitation of ionic solids with extreme ultraviolet pulses creates localized core-level excitons, which in some cases couple strongly to the lattice. Here, core-level-exciton states of magnesium oxide are studied in the time domain at the Mg L_{2,3} edge with attosecond transient reflectivity spectroscopy. Attosecond pulses trigger the excitation of these short-lived quasiparticles, whose decay is perturbed by time-delayed near-infrared pulses. Combined with a few-state theoretical model, this reveals that the infrared pulse shifts the energy of bright (dipole-allowed) core-level-exciton states as well as induces features arising from dark core-level excitons. We report coherence lifetimes for the two lowest core-level excitons of 2.3±0.2 and 1.6±0.5 fs and show that these are primarily a consequence of strong exciton-phonon coupling, disclosing the drastic influence of structural effects in this ultrafast relaxation process.

Tunable linear and nonlinear optical properties of chromophores containing 3,7-(di)vinylquinoxalinone core by modification of receptors moieties

To study the linear and nonlinear optical properties of chromophores with 3,7-(di)vinylquinoxalinone core, excitation energies, dipole moments, polarizabilities, the first and second hyperpolarizabilities as well as TPA cross-sections of four chromophores with different receptors in vacuum and chloroform solvent were calculated by DFT method and response theory. Two methods of the Hellmanne-Feynman theorem and the McRae equation were used to estimate the difference of the dipole moment between the excited state and the ground state. The linear polarizability and the first hyperpolarizability were calculated by the derivative method, and the second hyperpolarizability was calculated by the finite difference method. It is found that the numerical size and order of the above polarizability and hyperpolarizability were verified by using the few-state model. By studying charge-transfer excited states and the transition matrix element, the internal mechanism of TPA and transition channels were revealed. Results demonstrated that chromophore TCP with acceptor [5-dicyanomethylene-2-oxo-4-cyano-2,5-dihydropyrrol-3-yl] possesses a more obvious NLO coefficient value, and TCF with 5,5-dimethyl-2- dicyanomethylene-3-cyano-2,5-dihydrofuran-4-yl possesses the largest TPA cross-section. The current investigation is expected to provide theoretical support for the development of chromophores with 3,7-(di)vinylquinoxalinone π-electron bridge in NLO materials.

Two-photon absorption properties of D-A-D type chromophores containing tetraphenylethylene and triphenylamine moieties: a close look at the effects of the strength, position and number of donors

ABSTRACTThe two-photon absorption (TPA) properties of a series of D-A-D type chromophores containing tetraphenylethylene (TPE) and triphenylamine moieties have been investigated employing the density functional response theory in combination with the polarisable continuum model. Special emphases are placed on the effects of the strength, position and number of donors on TPA. Our calculations demonstrate that the TPA intensity enhances with the increase of the electron-donating ability of the substituents on the triphenylamine unit, which is consistent with experimental observations. It is shown that the position of donors has an important effect on TPA. The donor on the side position of TPE unit decreases the TPA cross section, thereby more donors could not necessarily produce stronger TPA. The cis-trans isomerism effect is also explored and it is found that all the cis structures have lower TPA intensities than those of corresponding trans forms. By considering a different number of donors on TPE and triphenylamine unit respectively, it is interesting to find that the structure with one terminal donor on TPE and two donors on triphenylamine unit has the largest TPA cross section. The few-state model and the natural bond orbital charge analysis are used to explore the reason behind it.

Benchmarking the Performance of Exchange-Correlation Functionals for Predicting Two-Photon Absorption Strengths.

The present work investigates the performance of exchange-correlation functionals in the prediction of two-photon absorption (2PA) strengths. For this purpose, we considered six common functionals used for studying 2PA processes and tested these on six organoboron chelates. The set consisted of two semilocal (PBE and BLYP), two hybrid (B3LYP and PBE0), and two range-separated (LC-BLYP and CAM-B3LYP) functionals. The RI-CC2 method was chosen as a reference level and was found to give results consistent with the experimental data that are available for three of the molecules considered. Of the six exchange-correlation functionals studied, only the range-separated functionals predict an ordering of the 2PA strengths that is consistent with experimental and RI-CC2 results. Even though the range-separated functionals predict correct relative trends, the absolute values for the 2PA strengths are underestimated by a factor of 2-6 for the molecules considered. An in-depth analysis, on the basis of the derived generalized few-state model expression for the 2PA strength for a coupled-cluster wave function, reveals that the problem with these functionals can be linked to underestimated excited-state dipole moments and, to a lesser extent, overestimated excitation energies. The semilocal and hybrid functionals exhibit less predictable errors and a variation in the 2PA strengths in disagreement with the reference results. The semilocal and hybrid functionals show smaller average errors than the range-separated functionals, but our analysis reveals that this is due to fortuitous error cancellation between excitation energies and the transition dipole moments. Our results constitute a warning against using currently available exchange-correlation functionals in the prediction of 2PA strengths and highlight the need for functionals that correctly describe the electron density of excited electronic states.

Elucidating the Mechanism of Zn(2+) Sensing by a Bipyridine Probe Based on Two-Photon Absorption.

In this work, we examine, by means of computational methods, the mechanism of Zn(2+) sensing by a bipyridine-centered, D-π-A-π-D-type ratiometric molecular probe. According to recently published experimental data [Divya, K. P.; Sreejith, S.; Ashokkumar, P.; Yuzhan, K.; Peng, Q.; Maji, S. K.; Tong, Y.; Yu, H.; Zhao, Y.; Ramamurthy, P.; Ajayaghosh, A. A ratiometric fluorescent molecular probe with enhanced two-photon response upon Zn(2+) binding for in vitro and in vivo bioimaging. Chem. Sci. 2014, 5, 3469-3474], after coordination to zinc ions the probe exhibits a large enhancement of the two-photon absorption cross section. The goal of our investigation was to elucidate the mechanism behind this phenomenon. For this purpose, linear and nonlinear optical properties of the unbound (cation-free) and bound probe were calculated, including the influence of solute-solvent interactions, implicitly using a polarizable continuum model and explicitely employing the QM/MM approach. Because the results of the calculations indicate that many conformers of the probe are energetically accessible at room temperature in solution and hence contribute to the signal, structure-property relationships were also taken into account. Results of our simulations demonstrate that the one-photon absorption bands for both the unbound and bound forms correspond to the bright π → π* transition to the first excited state, which, on the other hand, exhibits negligible two-photon activity. On the basis of the results of the quadratic response calculations, we put forward a notion that it is the second excited state that gives the strong signal in the experimental nonlinear spectrum. To explain the differences in the two-photon absorption activity for the two lowest-lying excited states and nonlinear response enhancement upon binding, we employed the generalized few-state model including the ground, first, and second excited states. The analysis of the optical channel suggests that the large two-photon response is due to the coordination-induced increase of the transition moment from the first to the second excited state.

Model Hamiltonian Analysis of Singlet Fission from First Principles

We present an approach to accurately construct the few-state model Hamiltonians for singlet fission processes on the basis of an ab initio electronic structure method tailored to dimer wave functions, called an active space decomposition strategy. In this method, the electronic structure of molecular dimers is expressed in terms of a linear combination of products of monomer states. We apply this method to tetracene and pentacene, using monomer wave functions computed by the restricted active space (RAS) method. Near-exact wave functions are computed for π-electrons of dimers that contain up to 7 × 1012 electronic configurations. Our product ansatz preserves the diabatic picture of the minimal dimer model, allowing us to accurately identify model Hamiltonians. The wave functions obtained from the model Hamiltonians account for more than 99% of the total wave functions. The resulting model Hamiltonians are shown to be converged with respect to all the parameters in the model, and corroborate previously reported coupling strengths.

Chelation-Induced Quenching of Two-Photon Absorption of Azacrown Ether Substituted Distyryl Benzene for Metal Ion Sensing.

Imaging of metal ion concentration, distribution, and dynamics can pave the way to diagnose a number of diseases and to identify the normal functioning of the human body. Recently, two-photon microscopy-based imaging of metal ions has become popular due to several favorable factors as compared to fluorescence-based imaging. However, much has to be investigated in order to design probes with large two-photon absorption cross sections and yet with selective binding affinity toward metal ions. In particular, it is crucial to recognize the mechanisms of metal ion-induced changes of the two-photon absorption intensity. The present paper contributes to this effort and reports on the results of extensive studies carried out to define a reliable computational protocol that can account for sampling, solvent, and finite temperature effects for one- and two-photon properties of metal probes, using azacrown ether substituted distyrylbenzene embedded in solvents as a testbed. We employ a selection of theoretical approaches to model the structure of the probe alone and in the presence of Mg(2+) ion in acetonitrile solvent, including static quantum-chemical calculations, rigid- and flexible-body molecular dynamics, and hybrid QM/MM molecular dynamics. For a set of solute-solvent configurations, the one- and the two-photon properties are computed using the recently developed polarizable embedding response approach. It is found that the hybrid QM/MM molecular dynamics based approach is the most successful one among other employed computational strategies, viz. reproduction of the metal ion-induced blue shift in the absorption wavelength and decrease in the two-photon absorption cross section, which actually is in excellent agreement with experimental data. The mechanism for such metal ion-induced changes in the optical properties is put forward using a few-state model. Possible design principles to tune the two-photon absorption properties of probes are also discussed.

Modeling nonlinear optics of nanosystems with sum‐over‐states model

Three-stage strategies (ladder rule, few state model (FSM), and parallelization) were proposed to improve the computational efficiency of the sum-over-states (SOS) model in nonlinear optics (NLO) modeling. Ladder rule decomposes NLO coefficients of the nth state into the (n-1)th term and the contribution from the (n-1)th to the nth state without loss of rigor in theory. FSM singles out the states with substantial contribution to NLO. Those strategies are universal to all (including revised and simplified) SOS models. The computing cost reduces roughly to C/(n(i-1)) (C is a constant and i is the rank (order) of the NLO coefficients).

UV/Vis Absorption, Emission Spectra and Two-Photo Absorption Cross Sections of 4-Dihydroquinolinone Derivatives

A series of 4-dihydroquinolinone derivatives were fully optimized by density functional theory (DFT), Hartree-Fock (HF) and Configuration Interaction Singlet (CIS) approaches. Absorption spectra, emission spectra and two-photon absorption cross sections were calculated by using time-dependent density functional theory and few-state model. Calculations were performed in the presence of solvent by using Conductor polarizable continuum model (CPCM). The molecular geometries, absorption spectra, emission spectra were in good agreement well with those experiment values. The absorption and emission peak red-shifted as a result of the extension of the conjugated structures. The introduction of heteroatoms such as F, Cl and Br gave rise to intramolecular transfer and the blueshift of the absorption and the emission spectra. The introduction of O or S atoms in two sides of molecules propelled the redshift of the absorption and emission maximum.

The theoretical studies on the two-photon absorption properties of symmetric 1,4-bis{2-[4-(2-aryl)phenyl]vinyl}-2,5-bisdialkoxybenzenes

On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-(2-aryl) phenyl]vinyl}-2,5-bisdialkoxybenzenes are studied respectively utilizing the analytic response theory and the few-state model methods. The calculated results show that the planarity of the geometrical structure plays a great role in enhancing the linear and nonlinear optical abilities of the molecule. However the effect of the length of the chain linked to the π-centre on the optical property is very little. For the investigated compounds, the A-π-A type charge-transfer molecules display more superior one- and two-photon absorption characteristics than the D-π-D type ones. Furthermore, the two-photon absorption results by use of few-state model are generally consistent with those by analytic response theory, demonstrating the reliability of the few-state model for evaluating the two-photon absorption cross section. The numerical simulations are in good agreement in tendency with the available experimental measurements.

Maximum caliber inference of nonequilibrium processes

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays.

Quadrupolar Chromophores for Voltage Sensing and White‐Light Generation

A few-state model predicts that spectral properties of some quadrupolar chromophores are affected by the application of static electric fields. These dyes can monitor neuronal activity (action potential), as a sensitive and versatile alternative to classical dipolar dyes and can also be used in organic LEDs: color-tunable and/or white-light emission is obtained by varying the working voltage (see chromaticity diagram).

Predictions of Novel Two-Photon Absorption Bands in Fluorescent Proteins

By means of time-dependent density functional theory, we calculate the two-photon cross-sections for the lowest relevant excitations in some model chromophores of intrinsically fluorescent proteins. The two-photon strength of the first, one-photon active transition varies among the various chromophores, in line with experimental findings. Interestingly, additional transitions with large two-photon cross-sections are found in the 500-700 nm region arising from near-resonant enhancement, as revealed by few-state model analysis. Multiphoton excitation of fluorescent proteins in this spectral region can lead to relevant application for bioimaging.

Two-photon Absorption Properties of Heteroatomic Ring Molecules

The nonlinear optical properties of three benzothiazolyl-derivatives newly synthesized were calculated using few-state model and DFT method. The results showed that a red-shift of the maximum absorption took place when the delocalization of the ?仔 electrons in the organic molecules increases. When the conjugate chain had a longer size, the contribution of the increasing size of the conjugate chain on the increasing cross section was much more important than that of changing of electron drawing group. This kind of molecule had a better TPA (two-photon absorption) characteristic.