Zhi-Qiang You

Triplet-triplet energy-transfer coupling: theory and calculation.

Triplet-triplet (TT) energy transfer requires two molecular fragments to exchange electrons that carry different spin and energy. In this paper, we analyze and report values of the electronic coupling strengths for TT energy transfer. Two different methods were proposed and tested: (1) Directly calculating the off-diagonal Hamiltonian matrix element. This direct coupling scheme was generalized from the one used for electron transfer coupling, where two spin-localized unrestricted Hartree-Fock wave functions are used as the zero-order reactant and product states, and the off-diagonal Hamiltonian matrix elements are calculated directly. (2) From energy gaps derived from configuration-interaction-singles (CIS) scheme. Both methods yielded very similar results for the systems tested. For TT coupling between a pair of face-to-face ethylene molecules, the exponential attenuation factor is 2.59 A(-1)(CIS6-311+G(**)), which is about twice as large as typical values for electron transfer. With a series of fully stacked polyene pairs, we found that the TT coupling magnitudes and attenuation rates are very similar irrespective of their molecular size. If the polyenes were partially stacked, TT couplings were much reduced, and they decay more rapidly with distance than those of full-stacked systems. Our results showed that the TT coupling arises mainly from the region of close contact between the donor and acceptor frontier orbitals, and the exponential decay of the coupling with separation depends on the details of the molecular contacts. With our calculated results, nanosecond or picosecond time scales for TT energy-transfer rates are possible.

Experimental benchmark data and systematic evaluation of two a posteriori, polarizable-continuum corrections for vertical excitation energies in solution.

We report the implementation and evaluation of a perturbative, density-based correction scheme for vertical excitation energies calculated in the framework of a polarizable continuum model (PCM). Because the proposed first-order correction terms depend solely on the zeroth-order excited-state density, a transfer of the approach to any configuration interaction-type excited-state method is straightforward. Employing the algebraic-diagrammatic construction (ADC) scheme of up to third order as well as time-dependent density-functional theory (TD-DFT), we demonstrate and evaluate the approach. For this purpose, we assembled a set of experimental benchmark data for solvatochromism in molecules (xBDSM) containing 44 gas-phase to solvent shifts for 17 molecules. These data are compared to solvent shifts calculated at the ADC(1), ADC(2), ADC(3/2), and TD-DFT/LRC-ωPBE levels of theory in combination with state-specific as well as linear-response type PCM-based correction schemes. Some unexpected trends and differences between TD-DFT, the levels of ADC, and variants of the PCM are observed and discussed. The most accurate combinations reproduce experimental solvent shifts resulting from the bulk electrostatic interaction with maximum errors in the order of 50 meV and a mean absolute deviation of 20-30 meV for the xBDSM set.

The mediated excitation energy transfer: Effects of bridge polarizability.

The observation of bridge-mediated excitation energy transfer (EET) has raised questions on the physical origin of such an effect. In this work, we studied the effect of bridge fragments in the Coulomb coupling, the major contribution to the electronic coupling in an EET process. For a series of ortho-phenyleneethynylene oligomers spaced donor-acceptors, we found that a large influence of the bridge fragment in EET coupling is through changes in the Coulomb couplings. Both enhancement and screening effects of the bridge were observed as the EET rates were modified by a factor of 0.3-23 with an intervening bridge in our calculations. The dependency of EET couplings on the orientation of transition dipoles of the donor and acceptor from quantum mechanical computations is very similar to that of a simple classical dielectric model. Our work shows that the bridge fragments can modify the Coulomb coupling with their polarizability by providing an optical dielectric medium between the donor and acceptor. In particular, when the transition dipoles of the donor and acceptor were longitudinal to a polarizable bridge, the EET rates were enhanced by one order of magnitude, as compared to the values of through-space models. Our results offer important insights into the design of efficient energy transfer systems.

Ab Initio Implementation of the Frenkel−Davydov Exciton Model: A Naturally Parallelizable Approach to Computing Collective Excitations in Crystals and Aggregates

A fragment-based method for computing vertical excitation energies of molecular clusters is introduced based on an ab initio implementation of a Frenkel-Davydov exciton model consisting of singly excited monomer basis states. Our strategy is to construct and diagonalize the exact Hartree-Fock Hamiltonian in such a basis. Matrix elements between nonorthogonal determinants are computed via the corresponding orbital transformation and the resulting generalized eigenvalue problem is solved to determine collective excitation energies and wave functions. The basis may be expanded to include higher-lying fragment excited states in order to account for interfragment polarization effects. Absolute errors of ≲0.1 eV (relative to supersystem methods) are achievable for systems such as water clusters and crystalline arrays of organic chromophores such as pentacene and napthalenediimide. Preliminary tests for a nine-chromophore subunit of an organic nanotube suggest that it is possible to target the optically bright state, even when it is a high-lying excitation, by using carefully selected basis states. The highly parallel nature of this method provides a foundation for further developments to treat collective excitations in large molecular assemblies.

Ab Inito Study on Triplet Excitation Energy Transfer in Photosynthetic Light-Harvesting Complexes

We have studied the triplet energy transfer (TET) for photosynthetic light-harvesting complexes, the bacterial light-harvesting complex II (LH2) of Rhodospirillum molischianum and Rhodopseudomonas acidophila, and the peridinin-chlorophyll a protein (PCP) from Amphidinium carterae. The electronic coupling factor was calculated with the recently developed fragment spin difference scheme (You and Hsu, J. Chem. Phys. 2010, 133, 074105), which is a general computational scheme that yields the overall coupling under the Hamiltonian employed. The TET rates were estimated based on the couplings obtained. For all light-harvesting complexes studied, there exist nanosecond triplet energy transfer from the chlorophylls to the carotenoids. This result supports a direct triplet quenching mechanism for the photoprotection function of carotenoids. The TET rates are similar for a broad range of carotenoid triplet state energy, which implies a general and robust TET quenching role for carotenoids in photosynthesis. This result is also consistent with the weak dependence of TET kinetics on the type or the number of π conjugation lengths in the carotenoids and their analogues reported in the literature. We have also explored the possibility of forming triplet excitons in these complexes. In B850 of LH2 or the peridinin cluster in PCP, it is unlikely to have triplet exciton since the energy differences of any two neighboring molecules are likely to be much larger than their TET couplings. Our results provide theoretical limits to the possible photophysics in the light-harvesting complexes.

A Structural Model for a Self-Assembled Nanotube Provides Insight into Its Exciton Dynamics

The design and synthesis of functional self-assembled nanostructures is frequently an empirical process fraught with critical knowledge gaps about atomic-level structure in these noncovalent systems. Here, we report a structural model for a semiconductor nanotube formed via the self-assembly of naphthalenediimide-lysine (NDI-Lys) building blocks determined using experimental 13C–13C and 13C–15N distance restraints from solid-state nuclear magnetic resonance supplemented by electron microscopy and X-ray powder diffraction data. The structural model reveals a two-dimensional-crystal-like architecture of stacked monolayer rings each containing ∼50 NDI-Lys molecules, with significant π-stacking interactions occurring both within the confines of the ring and along the long axis of the tube. Excited-state delocalization and energy transfer are simulated for the nanotube based on time-dependent density functional theory and an incoherent hopping model. Remarkably, these calculations reveal efficient energy migration from the excitonic bright state, which is in agreement with the rapid energy transfer within NDI-Lys nanotubes observed previously using fluorescence spectroscopy.

Calculating Electron-Transfer Coupling with Density Functional Theory: The Long-Range-Corrected Density Functionals

The density functional theory (DFT) with commonly used functionals is known to be incorrect for charge-transfer problems. With long-range-corrected (LC) density functionals, the asymptotic exchange potential is gradually switched to the Hartree-Fock exchange at a long range, and the prediction for charge-transfer states is greatly improved. In this work, we test LC-DFTs performance on charge-transfer couplings. The range-separation parameter can be tuned nonempirically for properties of a generalized DFT. We propose to minimize the difference of highest-occupied Kohn-Sham orbital energy and the ionization potential (for hole transfer) or the lowest-unoccupied orbital energy and the electron affinity (for electron transfer). For photoinduced charge transfer, the minimum in the sum of such differences for the donor and the acceptor is proposed. With the range-separation parameters optimized, we found that ET couplings derived from the LC-DFT are close to those derived from coupled cluster with singles and doubles. When compared with experimentally derived Mulliken-Hush couplings, LC-DFT couplings are greatly improved as well. We also found that the couplings from BNL and LC-BLYP functionals are generally better than those from LC-ωPBE and LC-ωPBE0. LC-DFT is suitable for calculating ET coupling, especially with this nonempirical approach for the range-separation parameter.

Theoretical characterization of photoinduced electron transfer in rigidly linked donor–acceptor molecules: the fragment charge difference and the generalized Mulliken–Hush schemes

We calculate the electron transfer (ET) rates for a series of heptacyclo[6.6.0.02,6.03,13.014,11.05,9.010,14]-tetradecane (HCTD) linked donor–acceptor molecules. The electronic coupling factor was calculated by the fragment charge difference (FCD) [19] and the generalized Mulliken–Hush (GMH) schemes [20]. We found that the FCD is less prone to problems commonly seen in the GMH scheme, especially when the coupling values are small. For a 3-state case where the charge transfer (CT) state is coupled with two different locally excited (LE) states, we tested with the 3-state approach for the GMH scheme [30], and found that it works well with the FCD scheme. A simplified direct diagonalization based on Rusts 3-state scheme was also proposed and tested. This simplified scheme does not require a manual assignment of the states, and it yields coupling values that are largely similar to those from the full Rusts approach. The overall electron transfer (ET) coupling rates were also calculated.

Reparameterization of an Accurate, Few-Parameter Implicit Solvation Model for Quantum Chemistry: Composite Method for Implicit Representation of Solvent, CMIRS v. 1.1

CMIRS (composite method for implicit representation of solvent) is a relatively new implicit solvation model that adds terms representing solute-solvent dispersion, Pauli repulsion, and hydrogen bonding to a continuum treatment of electrostatics. A small error in the original implementation of the dispersion term, but one that can modify dispersion energies by up to 8 kcal/mol in some cases, necessitates refitting the parameters in the model, which we do here. We refer to the modified implementation and parameter set as CMIRS v. 1.1. While the dispersion energies change in nontrivial ways, an increase in the attractive dispersion term in the new implementation is largely offset by an increase in the Pauli repulsion during the fitting process, such that overall statistical errors are virtually unchanged with respect to v. 1.0 of the model, for a large database of experimental solvation free energies for molecules and ions. Overall, we obtain mean unsigned errors of <0.7 kcal/mol when the solvent is cyclohexane or benzene, <1.5 kcal/mol for water, and <2.8 kcal/mol for dimethyl sulfoxide and acetonitrile, despite using no more than five empirical parameters per solvent. For the important but difficult case of ionic solutes in water, mean unsigned errors are <2.9 kcal/mol.