Excitonic coupling in polythiophenes: Comparison of different calculation methods

Molecular modeling of two-photon absorption and third-order nonlinearities of polymethine dyes for all-optical switching

Stimulated by a recent experimental report [Hales JM et al. (2010) Science 327:1485-1488], two-photon absorption and third-order optical nonlinearities of selenopyrylium- and bis(dioxaborine)-terminated polymethine dyes (called SE-7C and DOB-9C) used for all-optical switching were investigated theoretically with time-dependent DFT (TD-DFT) and response theory as well as visualized real-space analysis. The calculated results for the first hyperpolarizability and second hyperpolarizability demonstrated that the two molecules both have large third-order optical nonlinearities. Using real-space analysis, we were able to visually determine that in the one-photon absorption (OPA) process, the first singlet excited state of SE-7C and DOB-9C is an intramolecular charge transfer (ICT) excited state with strong absorption, while the second excited state of these dyes (also termed the "ICT state") shows weak absorption. However, in the two-photon absorption (TPA) process, a larger TPA absorption cross-section was predicted for the second excited state. In this paper, we describe the properties of the S2 excited state, incorporating charge transfer and the transition moment, via real-space analysis, which was very important for understanding the TPA characteristics of the S(2) state.

Effect of nanoparticle dimensionality on fluorescence resonance energy transfer in nanoparticle-dye conjugated systems

Fluorescence resonance energy transfer (FRET) involving a semiconductor nanoparticle (NP) acting as a donor, attached to multiple acceptors, is becoming a common tool for sensing, biolabeling, and energy transfer applications. Such nanosystems, with dimensions that are in the range of FRET interactions, exhibit unique characteristics that are related to the shape and dimensionality of the particles and to the spatial distribution of the acceptors. Understanding the effect of these parameters is of high importance for describing the FRET process in such systems and for utilizing them for different applications. In order to demonstrate these dimensionality effects, the FRET between CdSe/CdS core/shell NPs with different geometries and dimensionalities and Atto 590 dye molecules acting as multiple acceptors covalently linked to the NP surface is examined. Steady-state emission and temporal decay measurements were performed on the NPs, ranging from spherical to rod-like shaped systems, as a function of acceptor concentration. Changes in the NP geometry, and consequently in the distributions of acceptors, lead to distinctively different FRET behaviors. The results are analyzed using a modified restricted geometries model, which captures the dimensionality of the acceptor distribution and allows extracting the concentration of dye molecules on the surface of the NP for both spherical and elongated NPs. The results obtained from the model are in good agreement with the experimental results. The approach may be useful for following the spatial dynamics of self-assembly and for a wide variety of sensing applications.

CHARGE AND ENERGY TRANSFER IN BINAPHTHALENE MOLECULE WITH TWO SPIROPYRAN UNITS USED FOR CHIRAL MOLECULAR SWITCHES AND LOGIC GATES

A new binaphthalene molecule with two spiropyran units used for chiral molecular switches and logic gates was synthesized and characterized.12 In this paper, charge and energy transfer in binaphthalene molecule with two spiropyran units are theoretically investigated with quantum chemistry method, as well as 2D and 3D real space analysis methods, since molecule construction with photoinduced electron transfer or charge transfer is one of the most frequently used pathways for building useful sensors and molecular machines. The orientation and strength of transition dipole moment in absorption spectra are obtained by 3D transition density. The orientation and results of intramolecular charge transfer on the excitation are obtained with 3D charge difference densities. The electron-hole coherence and excitation delocalization in absorption spectra are investigated with 2D contour plots of transition density matrix. Overall, the computed results remain in good agreement with the relevant experimental data, and the theoretical results reveal the relationship between the function of sensor and the excited state properties of the structure and transformation of the compound, upon addition of acid and base in absorption spectra.

Theoretical study on contribution of charge transfer effect to surface-enhanced Raman scattering spectra of pyridine adsorbed on Ag(n) (n = 2-8) clusters

We investigate surface-enhanced Raman scattering (SERS) spectra of pyridine-Ag(n) (n = 2-8) complexes by density functional theory (DFT) and time-dependent DFT (TDDFT) methods. In simulated normal Raman scattering (NRS) spectra, profiles of pyridine-Ag(n) (n = 2-8) complexes are analogical with that of isolated pyridine. Nevertheless, calculated pre-SERS spectra are strongly dependent on electronic transition states of new complexes. Wavelengths at 335 nm, 394.8 nm, 316.9 nm and 342.6 nm, which are nearly resonant with pure charge transfer excitation states, are adopted as incident light when simulating pre-SERS spectra for pyridine-Ag(n) (n = 2-8) complexes, respectively. We obtain enhancement factors from 10(3) to 10(5) in pre-SERS spectra compared with corresponding NRS spectra. The obvious increase in Raman intensities mainly result from charge transfer resonance Raman enhancement. A charge difference densities (CDDs) methodology is adopted in describing chemical enhancement mechanism. This methodology aims at visualizing charge transfer from Ag(n) (n = 2-8) clusters to pyridine on resonant electronic transition, which is one of the most direct evidences for chemical enhancement mechanism.

Electronic energy migration on different time scales: concentration dependence of the time-resolved anisotropy and fluorescence quenching of Lumogen Red in poly(methyl methacrylate)

Electronic energy transfer plays an important role in many types of organic electronic devices. Forster-type theories of exciton diffusion provide a way to calculate diffusion constants and lengths, but their applicability to amorphous polymer systems must be evaluated. In this paper, the perylenediimide dye Lumogen Red in a poly(methyl methacrylate) host matrix is used to test theories of exciton motion over Lumogen Red concentrations (C(LR)'s) ranging from 1 x 10(-4) to 5 x 10(-2) M. Two experimental quantities are measured. First, time-resolved anisotropy decays in films containing only Lumogen Red provide an estimate of the initial energy transfer rate from the photoexcited molecule. Second, the Lumogen Red lifetime decays in mixed systems where the dyes Malachite Green and Rhodamine 700 act as energy acceptors are measured to estimate the diffusive quenching of the exciton. From the anisotropy measurements, it is found that theory accurately predicts both the C(LR)(-2) concentration dependence of the polarization decay time tau(pol), as well as its magnitude to within 30%. The theory also predicts that the diffusive quenching rate is proportional to C(LR)(alpha), where alpha ranges between 1.00 and 1.33. Experimentally, it is found that alpha = 1.1 +/- 0.2 when Malachite Green is used as an acceptor, and alpha = 1.2 +/- 0.2 when Rhodamine 700 is the acceptor. On the basis of the theory that correctly describes the anisotropy data, the exciton diffusion constant is projected to be 4-9 nm(2)/ns. By use of several different analysis methods for the quenching data, the experimental diffusion constant is found to be in the range of 0.32-1.20 nm(2)/ns. Thus the theory successfully describes the early time anisotropy data but fails to quantitatively describe the quenching experiments which are sensitive to motion on longer time scales. The data are consistent with the idea that orientational and energetic disorder leads to a time-dependent exciton migration rate, suggesting that simple diffusion models cannot accurately describe exciton motion within this system.

Effect of annealing on P3HT:PCBM charge transfer and nanoscale morphology probed by ultrafast spectroscopy

We employ sub-picosecond TA spectroscopy on operating P3HT:PCBM devices to probe the effect of annealing on charge transfer dynamics and nanoscale morphology. Our measurement configuration allows us to remove the effect of high excitation densities that would otherwise dominate. Charge transfer in pristine P3HT:PCBM devices proceeds on a sub-picosecond time scale, implying molecular level intermixing and explaining the more localized character of excitons and charges. In annealed devices, annealing results in diffusion-limited charge generation with a half-life time of approximately 3 ps, complete only after 30 ps. This is the result of exclusion of PCBM molecules and ordering of P3HT domains and is correlated with improved photovoltaic efficiency. We are able to use the spectra and dynamics of optical excitations themselves to interpret blend morphologies on the appropriate time- and length scales of photoinduced charge generation.

Beyond Förster resonance energy transfer in biological and nanoscale systems

After photoexcitation, energy absorbed by a molecule can be transferred efficiently over a distance of up to several tens of angstroms to another molecule by the process of resonance energy transfer, RET (also commonly known as electronic energy transfer, EET). Examples of where RET is observed include natural and artificial antennae for the capture and energy conversion of light, amplification of fluorescence-based sensors, optimization of organic light-emitting diodes, and the measurement of structure in biological systems (FRET). Forster theory has proven to be very successful at estimating the rate of RET in many donor-acceptor systems, but it has also been of interest to discover when this theory does not work. By identifying these cases, researchers have been able to obtain, sometimes surprising, insights into excited-state dynamics in complex systems. In this article, we consider various ways that electronic energy transfer is promoted by mechanisms beyond those explicitly considered in Forster RET theory. First, we recount the important situations when the electronic coupling is not accurately calculated by the dipole-dipole approximation. Second, we examine the related problem of how to describe solvent screening when the dipole approximation fails. Third, there are situations where we need to be careful about the separability of electronic coupling and spectral overlap factors. For example, when the donors and/or acceptors are molecular aggregates rather than individual molecules, then RET occurs between molecular exciton states and we must invoke generalized Forster theory (GFT). In even more complicated cases, involving the intermediate regime of electronic energy transfer, we should consider carefully nonequilibrium processes and coherences and how bath modes can be shared. Lastly, we discuss how information is obscured by various forms of energetic disorder in ensemble measurements and we outline how single molecule experiments continue to be important in these instances.

DFT study of adsorption site effect on surface-enhanced Raman scattering of neutral and charged pyridine-Ag4 complexes

Density functional theory (DFT) and time-dependent DFT (TDDFT) methods have been used to investigate the adsorption site effect of Raman scattering for neutral and charged pyridine-Ag4 complexes. The calculated results show that the SERS spectra are strongly dependent on adsorption site and the configuration of new complexes. The normal Raman spectra of neutral and charged pyridine-Ag4 complexes are similar with that of isolated pyridine but with an enhancement factor below 10 times. This enhancement is ascribed to ground state chemical enhancement. The pre-surface-enhanced Raman scattering (SERS) spectra were calculated at 1256 nm, 769 nm and 744.3 nm, which are nearly resonant with the charge transfer excited states S2 for neutral and charged pyridine-Ag4 complexes, respectively. We obtain the enhancement factor about 10(4) to 10(5) in pre-SERS spectra which is mainly caused by charge transfer resonance Raman enhancement. The three-dimensional cube representation is also applied to describe the photoinduced CT, which are considered as direct evidence of chemical enhancement, between pyridine and two isomers of Ag4 clusters.

Electronic Energy Transfer in Condensed Phase Studied by a Polarizable QM/MM Model

We present a combined quantum mechanics and molecular mechanics (QM/MM) method to study electronic energy transfer (EET) in condensed phases. The method introduces a quantum mechanically based linear response (LR) scheme to describe both chromophore electronic excitations and electronic couplings, while the environment is described through a classical polarizable force field. Explicit treatment of the solvent electronic polarization is a key aspect of the model, as this allows account of solvent screening effects in the coupling. The method is tested on a model perylene diimide (PDI) dimer in water solution. We find an excellent agreement between the QM/MM method and "exact" supermolecule calculations in which the complete solute-solvent system is described at the QM level. In addition, the estimation of the electronic coupling is shown to be very sensitive to the quality of the parameters used to describe solvent polarization. Finally, we compare ensemble-averaged QM/MM results to the predictions of the PCM-LR method, which is based on a continuum dielectric description of the solvent. We find that both continuum and atomistic solvent models behave similarly in homogeneous media such as water. Our findings demonstrate the potential of the method to investigate the role of complex heterogeneous environments, e.g. proteins or nanostructured host materials, on EET.

Energy migration as related to the mutual position and orientation of donor and acceptor molecules in LH1 and LH2 antenna complexes of purple bacteria

Many approaches to discovering the interaction energy of molecular transition dipoles use the well-known coefficient xi(phi, psi (1) psi (2)) = (cos phi - 3 cos psi (1) cos psi (2))(2), where phi, Psi (1), and Psi (2) are inter-dipole angles. Unfortunately, this formula often yields rather approximate results, in particular, when it is applied to closely positioned molecules. This problem is of great importance when dealing with energy migration in photosynthetic organisms, because the major part of excitation transfers in their chlorophyllous antenna proceed between closely positioned molecules. In this paper, the authors introduce corrected values of the orientation factor for several types of mutual orientation of molecules exchanging with electronic excitations for realistic ratios of dipole lengths and spacing. The corrected magnitudes of interaction energies of neighboring bacteriochlorophyll molecules in LH2 and LH1 light-absorbing complexes are calculated for the class of photosynthetic purple bacteria. Some advantageous factors are revealed in their mutual positions and orientations in vivo.

Visualizations of transition dipoles, charge transfer, and electron-hole coherence on electronic state transitions between excited states for two-photon absorption

The one-photon absorption (OPA) properties of donor-pi-bridge-acceptor-pi-bridge-donor (D-pi-A-pi-D)-type 2,1,3-benzothiadiazoles (BTD) were studied with two dimensional (2D) site and three dimensional (3D) cube representations. The 2D site representation reveals the electron-hole coherence on electronic state transitions from the ground state. The 3D representation shows the orientation of transition dipole moment with transition density, and the charge redistribution on the excited states with charge difference density. In this paper, we further developed the 2D site and 3D cube representations to investigate the two-photon absorption (TPA) properties of D-pi-A-pi-D-type BTD on electronic transitions between excited states. With the new developed 2D site and 3D cube representations, the orientation of transition dipole moment, the charge redistribution, and the electron-hole coherence for TPA of D-pi-A-pi-D-type BTD on electronic state transitions between excited states were visualized, which promote deeper understanding to the optical and electronic properties for OPA and TPA.

Insights into excitons confined to nanoscale systems: electron-hole interaction, binding energy, and photodissociation

The characteristics of nanoscale excitons--the primary excited states of nanoscale systems like conjugated polymers, molecular aggregates, carbon nanotubes, and nanocrystalline quantum dots--are examined through exploration of model systems. On the basis of a valence bond-type model, an intuition is developed for understanding and comparing nanoscale systems. In particular, electron-hole interactions are examined in detail, showing how and why they affect spectroscopy and properties such as binding energy. The relationship between the bound exciton states and the nanoscale analogue of free carriers (charge-transfer exciton states) is developed. It is shown why the electron and hole act as independent particles in this manifold of states. The outlook for the field is discussed on the basis of the picture developed in the paper, with an emphasis on exciton binding and photodissociation.

Conformational disorder of conjugated polymers

Conformational disorder of conjugated polymers is an important issue to be understood and quantified. In this paper we present a new method to assess the chain conformation of conjugated polymers based on measurements of intrachain energy transfer. The chain conformation is modeled on the basis of monomer-monomer interactions, such as torsion, bending, and stretching of the connecting bond. The latter two potentials are assumed to be harmonic, while the torsional potential was calculated by density functional theory using B3-LYP functional with the SVP basis set. The energy transfer dynamics of excitons on these chains are quantitatively simulated using Forster-type line-dipole energy transfer. This allows us to compare the simulated ground state conformation of single polymer chains to ultrafast depolarization experiments of poly [3-(2,5-dioctylphenyl)thiophene] in solution. We identify torsional rotation as the main contributor to conformational disorder and find that this disorder is mainly controlled by the energy difference between syn and anti bonds.

Excited State and Charge Photogeneration Dynamics in Conjugated Polymers

Conjugated polymers are becoming interesting materials for a range of optoelectronic applications. However, their often complex electronic and structural properties prevent establishment of straightforward property-function relationships. In this paper, we summarize recent results on the photophysics and excited state dynamics of conjugated polymers, in order to paint a picture of exciton formation, quenching, and generation of charge carriers.

Exciton transfer integrals between polymer chains

The line-dipole approximation for the evaluation of the exciton transfer integral J between conjugated polymer chains is rigorously justified. Using this approximation, as well as the plane-wave approximation for the exciton center-of-mass wave function, it is shown analytically that J approximately L when the chain lengths are smaller than the separation between them, or J approximately L-1 when the chain lengths are larger than their separation, where L is the chain length. Scaling relations are also obtained numerically for the more realistic standing wave approximation for the exciton center-of-mass wave function, where it is found that for chain lengths larger than their separation J approximately L-1.8 or J approximately L-2, for parallel or collinear chains, respectively. These results have important implications for the photophysics of conjugated polymers and self-assembled molecular systems, as the Davydov splitting in aggregates and the Forster transfer rate for exciton migration decrease with chain lengths larger than their separation. This latter result has obvious deleterious consequences for the performance of polymer photovoltaic devices.

Control of structure and photophysical properties by protonation and subsequent intramolecular hydrogen bonding

Protonation and subsequent intramolecular hydrogen bonding as methods to control chain structure and tune luminescence in heteroatomic conjugated polymers were reported experimentally [A. P. Monkman et al., J. Am. Chem. Soc. 124, 6049 (2002)]. In this paper, the structure and photophysical properties of the model teraryl compound of phenylene-pyridylene copolymer before and after protonation are theoretically studied with quantum chemistry methods. From the optimized ground states, intramolecular hydrogen bonding to the adjacent oxygen atom in the alkoxy substituent planarizes the backbone of the molecules, and the optimized detailed results of compound 9 before and after protonation, such as the dihedral angles between the central benzene and the two pyridyl rings, the bond lengths, and the bond angles, are consistent with the experimental results. From the results of the calculated excited states, the protonation and subsequent intramolecular hydrogen bonding result in the redshifts of the absorption, the increase of the ionization energy, the increase of the electron affinity, the decrease of the energy difference of the highest occupied molecular orbital and lowest unoccupied molecular orbital, the decrease of the binding gap, and the delocalization of the electron-hole coherence. The photophysical properties of compound 9 before and after protonation are further studied with a three-dimensional real-space analysis method of transition and charge difference densities (study transition dipole moment and charge transfer in the absorption and fluorescence processes) and two-dimensional real-space analysis method of transition density matrices (study the electron-hole coherence and the excitation delocalization). The calculated results show theoretically an insight understanding on the influence of the protonation and subsequent intramolecular hydrogen bonding to chain structure and photophysical properties.

Anomalous energy transfer dynamics due to torsional relaxation in a conjugated polymer

In isolated conjugated polymers two explanations are in discussion for the redshift of the emission on a picosecond time scale-exciton energy transfer (EET) between conjugated segments along the chains and conformational changes of these segments themselves, i.e., torsional relaxation. In order to resolve this question we perform femtosecond time-resolved transient absorption measurements of the energy relaxation of poly[3-(2,5-dioctylphenyl)thiophene] in toluene solution. We show that torsional relaxation can be distinguished from EET by site-selectively exciting low-energy conjugated segments. We present a unified model that integrates EET and torsional dynamics. In particular, comparison to ultrafast depolarization measurements shows that torsional dynamics cannot be neglected when analyzing EET dynamics and furthermore reveals that the exciton extends itself by about 2 monomer units during torsional relaxation.