A simplified approach for the coupling of excitation energy transfer

A simplified approach for computing the electronic coupling of nonradiative excitation-energy transfer is proposed by following Scholes et al.’s construction on the initial and final states [G.D. Scholes, R.D. Harcourt, K.P. Ghiggino, J. Chem. Phys. 102 (1995) 9574]. The simplification is realized through defining a set of orthogonalized localized MOs, which include the polarization effect of the charge densities. The method allows calculating the coupling of both the singlet-to-singlet and triplet-to-triplet energy transfer. Numerical tests are performed for a few of dimers with different intermolecular orientations, and the results demonstrate that Coulomb term are the major contribution to the coupling of singlet-to-singlet energy transfer whereas in the case of triplet-to-triplet energy transfer, the dominant effect is arisen from the intermolecular charge-transfer states. The present application is on the Hartree-Fock level. However, the correlated wavefunctions which are normally expanded in terms of the determinant wavefunctions can be employed in the similar way.     

Theory and calculation for the electronic coupling in excitation energy transfer

Excitation energy transfer (EET) is a process where the electronically excitation is transferred from a donor to an acceptor. EET is widely seen in both natural and in artificial systems, such as light‐harvesting in photosynthesis, the fluorescence resonance energy transfer technique, and the design of light‐emitting molecular devices. In this work, we outline the theories describing both singlet and triplet EET (SEET and TEET) rates, with a focus on the physical nature and computational methods for the electronic coupling factor, an important parameter in predicting EET rates. The SEET coupling is dominated by the Coulomb coupling, and the remaining short‐range coupling is very similar to the TEET coupling. The magnitude of the Coulomb coupling in SEET can vary much, but the contribution of short‐range coupling has been found to be similar across different excited states in naphthalene. The exchange coupling has been believed to be the major physical contribution to the short‐range coupling, but it has been pointed out that other contribution, such as the orbital overlap effect is similar or even larger in strength. The computational aspects and the subsequent physical implication for both SEET and TEET coupling values are summarized in this work. © 2013 The Authors. International Journal of Quantum Chemistry Published by Wiley Periodicals, Inc.     

Advanced theory of excitation energy transfer in dimers

Previously, we developed a unified theory of the excitation energy transfer (EET) in dimers, which is applicable to all of the cases of excitonic coupling strength (Kimura, A.; Kakitani, T.; Yamato, T. J. Phys. Chem. B 2000, 104, 9276). This theory was formulated only for the forward reaction of the EET. In the present paper, we advanced this theory so that it might include the backward reaction of the EET as well as the forward reaction. This new theory is formulated on the basis of the generalized master equation (GME), without using physically unclear assumptions. Comparing the present result with the previous one, we find that the excitonic coupling strengths of criteria between exciton and partial exciton and between hot transfer and hopping (F?rster) mechanisms are reduced by a factor of 2. The critical coherency eta c is also reduced significantly.     

Excitation energy transfer in ion pairs of polymethine cyanine dyes: efficiency and dynamics

The present work deals with singlet excitation energy transfer (EET) occurring in contact ion pairs (CIPs) of several anionic oxonol analogues (acting as EE donors) and cationic cyanines (acting as acceptors) characterized by off resonance individual transitions. Combining conductometric and spectroscopic measurements with decreasing solvent polarity, we were able to observe a progressive ion pairing leading first to solvent-separated ion pairs (SSIPs) and then to CIPs. Analysis of the absorption spectra of three selected salts (A2,C1, A2,C2, and A1,C4) in chloroform-toluene mixtures showed that the transformation of SSIP into CIP involves the appearance of a certain exciton coupling, the extent of which decreases regularly with increasing gap between the local excitation energies. Fluorescence excitation spectra showed that EET occurs in CIP, and EET efficiencies were evaluated with a procedure expressly devised for weakly emitting donors. These were between 0.2 and 0.65 for the examined ion pairs involving anions A1 and A2. The spectroscopic study was complemented by a theoretical investigation aimed at establishing the dynamic regime of the observed EET. From classical MD simulations and local full geometry optimizations, A2,C1 and A2,C2 were found to form rather stable sandwich-type CIP structures with interchromophore distances (R) of about 0.45-0.50 nm. The donor-acceptor electronic coupling was calculated in terms of Coulombic interactions between atomic transition charges. For CIP, the electronic coupling was decidedly beyond the limit of the weak coupling required for an incoherent F?rster-type mechanism. Thus, we tried to arrange the EET dynamics within the theory developed by Kimura, Kakitani, and Yamato (J. Phys. Chem. B 2000, 104, 9276) for the intermediate coupling case, which provides analytical expressions of time-dependent occupation probability, EET rate, and coherency in terms of two basic quantities: the electronic coupling and a correlation time related to the Franck-Condon factor. The latter was shown to be primarily modulated by F?rster's spectral overlap integral (related in turn to the excitation energy gap). Calculations were carried out for the three sample systems using three values of the electronic coupling roughly corresponding to CIP, 1.0, and 2.0 nm interchromophore distances. At the CIP distance, EET in both A2,C1 and A2,C2 was predicted to occur with a partial exciton mechanism, very short transfer times (about 10 fs), and high degree of coherence. In A1,C4 (having the largest energy gap), EET was found to occur with a hot-transfer mechanism. More or less hot-transfer dynamics appeared to be retained by all three systems at R = 1.0 nm. Fully incoherent EET appeared to become operative only at distances larger than 2.0 nm.     

An excited state paired interacting orbital method

A new method for analyzing and visualizing the molecular excited states, named "excited state paired interacting orbital (EPIO)," is proposed. The method is based both on the paired interacting orbital (PIO) proposed by Fujimoto and Fukui [J. Chem. Phys. 60, 572 (1974)] and the natural transition orbital (NTO) by Martin [J. Chem. Phys. 118, 4775 (2003)]. Within the PIO method, orbital interactions between the two fragmented molecules are represented practically only by a few pairs of fragment orbitals. The NTO method is a means of finding a compact orbital representation for the electronic transitions in the excited states. With the method, electronic transitions are expressed by a few particle-hole orbital pairs and a clear picture on the electronic transitions is obtained. EPIO method is designed to have both properties of the preceding two methods: electronic transitions in composite molecular systems can be expressed with a few pairs of EPIOs which are constructed with fragmented molecular orbitals (MOs). Excited state characters, such as charge transfer and local excitations, are analyzed by using EPIOs with their generation probabilities. Thus, the present method gives us clear information on the composition of MOs which play an important role in the molecular excitation processes, e.g., optical processes.     

New reaction simulator "LUMMOX" and its application for prediction of catalytic activities

We developed a new reaction simulator, "LUMMOX." It is an intermolecular interaction analyzer based on the theories of paired interacting orbitals (PIOs) and localized frontier orbitals (LFOs) that have been developed by Fujimoto et al. (Fukui, K.; Koga, N.; Fujimoto, H. J Am Chem Soc 1981, 103, 196; Fujimoto, H.; Koga, N.; Fukui, K. J Am Chem Soc 1981, 103, 7452; Fujimoto, H.; Satoh, S. J Phys Chem 1994, 98, 1436). LUMMOX runs on a Windows PC and displays graphic representation of orbital interactions. Prediction of activities, selectivities, and molecular weight of olefin polymerization catalysts are presented using PIO analysis and LFO calculation. Not only computational chemists but also experimental chemists can easily use this new system for catalyst design or molecular design from the point of view of orbital interaction.     

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Fo?rster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.     

Elastic and charge transfer processes in H+ + CO collisions

Proton and hydrogen atom time-of-flight spectra in collision energy range of E(trans) = 9.5-30 eV show that the endoergic charge transfer process in the H+ + CO system is almost an order of magnitude less probable than the elastic scattering [G. Niedner-Schatteburg and J. P. Toennies, Adv. Chem. Phys. LXXXII, 553 (1992)]. Ab initio computations at the multireference configuration interaction level have been performed to obtain the ground- and several low-lying excited electronic state potential energy curves in three different molecular orientations namely, H+ approaching the O-end and the C-end (collinear), and H+ approaching the CO molecule in perpendicular configuration with fixed CO internuclear distance. Nonadiabatic coupling terms between the ground electronic state (H+ + CO) and the three low-lying excited electronic states (H + CO+) have been computed and the corresponding diabatic potentials have been obtained. A time-dependent wavepacket dynamics study is modeled first involving only the ground and the first excited states and then involving the ground and the three lowest excited states at the collision energy of 9.5 eV. The overall charge transfer probability have been found to be approximately 20%-30% which is in qualitative agreement with the experimental findings.     

Photophysical properties of natural light-harvesting complexes studied by subsystem density functional theory

In this study, we investigate the excited states and absorption spectra of a natural light-harvesting system by means of subsystem density functional theory. In systems of this type, both specific interactions of the pigments with surrounding protein side chains as well as excitation energy transfer (EET) couplings resulting from the aggregation behavior of the chromophores modify the photophysical properties of the individual pigment molecules. It is shown that the recently proposed approximate scheme (J. Chem. Phys. 2007, 126, 134116) for coupled excitations within a subsystem approach to time-dependent DFT is capable of describing both effects in a consistent manner, and is efficient enough to study even the large assemblies of chromophores occurring in the light-harvesting complex 2 (LH2) of the purple bacterium Rhodopseudomonas acidophila. A way to extract phenomenological coupling constants as used in model calculations on EET rates is outlined. The resulting EET coupling constants and spectral properties are in reasonable agreement with the available reference data. Possible problems related to the effective exchange-correlation kernel are discussed.     

Spin-orbit coupling in O2(upsilon)+O2 collisions: I. Electronic structure calculations on dimer states involving the X 3Sigmag-, a 1Deltag, and b 1Sigmag+ states of O2

The importance of vibrational-to-electronic (V-E) energy transfer mediated by spin-orbit coupling in the collisional removal of O2(X 3Sigmag-,upsilon>or=26) by O2 has been reported in a recent communication [F. Dayou, J. Campos-Martinez, M. I. Hernandez, and R. Hernandez-Lamoneda, J. Chem. Phys. 120, 10355 (2004)]. The present work provides details on the electronic properties of the dimer (O2)2 relevant to the self-relaxation of O2(X 3Sigmag-,upsilon>0) where V-E energy transfer involving the O2(a 1Deltag) and O2(b 1Sigmag+) states is incorporated. Two-dimensional electronic structure calculations based on highly correlated ab initio methods have been carried out for the potential-energy and spin-orbit coupling surfaces associated with the ground singlet and two low-lying excited triplet states of the dimer dissociating into O2(X 3Sigmag-)+O2(X 3Sigmag-), O2(a 1Deltag)+O2(X 3Sigmag-), and O2(b 1Sigmag+)+O2(X 3Sigmag-). The resulting interaction potentials for the two excited triplet states display very similar features along the intermolecular separation, whereas differences arise with the ground singlet state for which the spin-exchange interaction produces a shorter equilibrium distance and higher binding energy. The vibrational dependence is qualitatively similar for the three studied interaction potentials. The spin-orbit coupling between the ground and second excited states is already nonzero in the O2+O2 dissociation limit and keeps its asymptotic value up to relatively short intermolecular separations, where the coupling increases for intramolecular distances close to the equilibrium of the isolated diatom. On the other hand, state mixing between the two excited triplet states leads to a noticeable collision-induced spin-orbit coupling between the ground and first excited states. The results are discussed in terms of specific features of the dimer electronic structure (including a simple four-electron model) and compared with existing theoretical and experimental data. This work gives theoretical insight into the origin of electronic energy-transfer mechanisms in O2+O2 collisions.     

How solvent controls electronic energy transfer and light harvesting: toward a quantum-mechanical description of reaction field and screening effects

This paper presents a quantum-mechanical study of electronic energy transfer (EET) coupling on over 100 pairs of chromophores taken from photosynthetic light-harvesting antenna proteins. Solvation effects due to the protein, intrinsic waters, and surrounding medium are analyzed in terms of screening and reaction field contributions using a model developed recently that combines a linear response approach with the polarizable continuum model (PCM). We find that the screening of EET interactions is quite insensitive to the quantum-mechanical treatment adopted. In contrast, it is greatly dependent on the geometrical details (distance, shape, and orientation) of the chromophore pair considered. We demonstrate that implicit (reaction field) as well as screening effects are dictated mainly by the optical dielectric properties of the host medium, while the effect of the static properties is substantially less important. The empirical distance-dependent screening function we proposed in a recent letter (Scholes, G. D.; Curutchet, C.; Mennucci, B.; Cammi, R.; Tomasi, J. J. Phys. Chem. B 2007, 111, 6978-6982) is analyzed and compared to other commonly used screening factors. In addition, we show that implicit medium effects on the coupling, resulting from changes in the transition densities upon solvation, are strongly dependent on the particular system considered, thus preventing the possibility of defining a general empirical expression for such an effect.     

DFT performance for the hole transfer parameters in DNA π stacks

Recently, we showed that unoccupied Kohn‐Sham (KS) orbitals stemming from DFT calculations of a neutral system can be used to derive accurate estimates of the free energy and electronic couplings for excess electron transfer in DNA (Félix and Voityuk, J Phys Chem A 2008, 112, 9043). In this article, we consider the propagation of radical cation states (hole transfer) through DNA π‐stacks and compare the performance of different exchange‐correlation functionals to estimate the hole transfer (HT) parameters. Two different approaches are used: (1) calculations that use occupied KS orbitals of neutral π stacks of nucleobases, and (2) the time‐dependent DFT method which is applied to the radical cation states of these stacks. Comparison of the calculated parameters with the reference data suggests that the best results are provided by the KS scheme with hybrid functionals (B3LYP, PBE0, and BH&HLYP). The TD DFT approach gives significantly less accurate values of the HT parameters. In agreement with high‐level ab initio results, the KS scheme predicts that the hole in π stacks is confined to a single nucleobase; in contrast, the spin‐unrestricted DFT method considerably overestimates the hole delocalization in the radical cations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

An Anderson impurity model for efficient sampling of adiabatic potential energy surfaces of transition metal complexes

We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required "on-the-fly" and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U(d) and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron transfer occurring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment. (