Ergodic collision theory of intermolecular energy transfer

We present a simple theory of collisional energy transfer between molecules based on the assumption of ergodic collisions, i.e., the final state distri     

Theory of excitation energy transfer regarded as nonadiabatic transition 2: Calculational evidence of nonadiabatic interaction causing intermolecular excitation energy transfer

To clarify whether the excitation energy transfer from a donor molecule or aggregate to a remote acceptor molecule or aggregate can be caused by nonadiabatic interaction as expected in our previous studies 4 ; 5 , we carried out ab initio calculations for three donor–acceptor systems. Even when the acceptor is separated from the donor by 15 Å, it was found that nonadiabatic coupling elements have moderately large values in the nuclear configuration region where the potential energy surfaces at two excited states for the donor–acceptor system are close to each other; otherwise, the conical intersection between the two excited‐state potential energy surfaces appears. In addition, it was found that the adiabatic approximation for the donor–acceptor system holds in the nuclear configuration region in which the initial and final wave packets in the process of the excitation energy transfer lie. These findings lead to the conclusion that the excitation energy transfer between two remote molecules or aggregates can be caused by the nonadiabatic interaction. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 36–43, 2003     

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.     

Control of emission by intermolecular fluorescence resonance energy transfer and intermolecular charge transfer

Control of emission by intermolecular fluorescence resonant energy transfer (IFRET) and intermolecular charge transfer (ICT) is investigated with the quantum-chemistry method using two-dimensional (2D) and three-dimensional (3D) real space analysis methods. The work is based on the experiment of tunable emission from doped 1,3,5-triphenyl-2-pyrazoline (TPP) organic nanoparticles (Peng, A. D.; et al. Adv. Mater. 2005, 17, 2070). First, the excited-state properties of the molecules, which are studied (TPP and DCM) in that experiment, are investigated theoretically. The results of the 2D site representation reveal the electron-hole coherence and delocalization size on the excitation. The results of 3D cube representation analysis reveal the orientation and strength of the transition dipole moments and intramolecular or intermolecular charge transfer. Second, the photochemical quenching mechanism via IFRET is studied (here "resonance" means that the absorption spectrum of TPP overlaps with the fluorescence emission spectrum of DCM in the doping system) by comparing the orbital energies of the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) of DCM and TPP in absorption and fluorescence. Third, for the DCM-TPP complex, the nonphotochemical quenching mechanism via ICT is investigated. The theoretical results show that the energetically lowest ICT state corresponds to a pure HOMO-LUMO transition, where the densities of the HOMO and LUMO are strictly located on the DCM and TPP moieties, respectively. Thus, the lowest ICT state corresponds to an excitation of an electron from the HOMO of DCM to the LUMO of TPP.     

Helicity induction and two-photon absorbance enhancement in zinc(II) meso-meso linked porphyrin oligomers via intermolecular hydrogen bonding interactions

Helicity has been induced in meso-meso linked oligomers by hydrogen bonding host-guest interactions with cyclic urea. Helical porphyrin arrays thus formed exhibit chirality amplification and enhanced two-photon absorption properties.     

Calculations of vibrational energy transfer using semi-classicals matrix theory

We utilize an extension of Miller's semi-classical S matrix theory to calculate resonant and non-resonant vibrational energy transfer probabilities. The collisions under study are collinear D₂D₂ interactions at energies below and above the classical dynamic transition threshold and collinear H₂D₂ interactions above the dynamic threshold. Below threshold we employ an initial angle representation. We find that the computed probabilities are in substantial agreement with exact quantum mechanical computations and represent a major improvement over quasi-classical results. At energies above threshold we apply the first order and the classical semi-classical versions of the theory. The results indicate fair agreement with quantum mechanical calculations, but no significant improvement over quasi-classical results.     

Excitation energy transfer in atom—molecule interactions of sodium and potassium vapours

The mechanism of energy transfer, from optically excited sodium and potassium molecules to sodium and potassium atoms has been investigated by the method of sensitized fluorescence. The rate constants of collisional energy transfer have been determined.     

Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain delta-type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and removes a numerical divergence problem. The discrete Fourier transformation and filter diagonalization of the first-order dipole moment are implemented to determine the excited state energies. It is found that the filter diagonalization leads to highly accurate values for the excited state energies. Finally, the density matrix based time-dependent density functional is generalized to calculate the energies of singlet-triplet excitations.     

Density functional theory study of the properties of N-H...N, non-cooperativities, and intermolecular interactions in linear trans-diazene clusters up to ten molecules

We investigate aspects of N-H...N hydrogen bonding in the linear trans-diazene clusters (n=2-10) such as the N...H and N-H lengths, n(N) --> sigma(N-H) interactions, N...H strengths, and frequencies of the N-H stretching vibrations utilizing the DFT/B3LYP theory, the natural bond orbital (NBO) method, and the theory of atoms in molecules (AIM). Our calculations indicate that the structure and energetics are qualitatively different from the conventional H-bonded systems, which usually exhibit distinct cooperative effects, as cluster size increases. First, a shortening rather than lengthening of the N-H bond is found and thus a blue rather than red shift is predicted. Second, for the title clusters, any sizable cooperative changes in the N-H and N...H lengths, n(N) --> sigma(N-H) charge transfers, N...H strengths, and frequencies of the N-H stretching vibrations for the linear H-bonded trans-diazene clusters do not exist. Because the n(N) --> sigma(N-H) interaction hardly exhibits cooperative effects, the capability of the linear trans-diazene cluster to localize electrons at the N...H bond critical point is almost independent of cluster size and thereby leads to the noncooperative changes in the N...H lengths and strengths and the N-H stretching frequencies. Third, the dispersion energy is sizable and important; more than 30% of short-range dispersion energy not being reproduced by the DFT leads to the underestimation of the interaction energies by DFT/B3LYP. The calculated nonadditive interaction energies show that, unlike the conventional H-boned systems, the trans-diazene clusters indeed exhibit very weak nonadditive interactions.     

Resonance energy transfer from a fluorescent dye molecule to plasmon and electron-hole excitations of a metal nanoparticle

The authors study the distance dependence of the rate of electronic excitation energy transfer from a dye molecule to a metal nanoparticle. Using the spherical jellium model, they evaluate the rates corresponding to the excitation of l=1, 2, and 3 modes of the nanoparticle. The calculation takes into account both the electron-hole pair and the plasmon excitations of the nanoparticle. The rate follows conventional R(-6) dependence at large distances while small deviations from this behavior are observed at shorter distances. Within the framework of the jellium model, it is not possible to attribute the experimentally observed d(-4) dependence of the rate to energy transfer to plasmons or electron-hole pair excitations.     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Dispersion-corrected energy decomposition analysis for intermolecular interactions based on the BLW and dDXDM methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.     

Communication: Density functional theory overcomes the failure of predicting intermolecular interaction energies

Density-functional theory (DFT) revolutionized the ability of computational quantum mechanics to describe properties of matter and is by far the most often used method. However, all the standard variants of DFT fail to predict intermolecular interaction energies. In recent years, a number of ways to go around this problem has been proposed. We show that some of these approaches can reproduce interaction energies with median errors of only about 5% in the complete range of intermolecular configurations. Such errors are comparable to typical uncertainties of wave-function-based methods in practical applications. Thus, these DFT methods are expected to find broad applications in modelling of condensed phases and of biomolecules.     

Single-particle detection of cholesterol based on the host-guest recognition induced plasmon resonance energy transfer

Plasmon resonance energy transfer (PRET) occurs between the plasmonic nanoparticles (NPs) and organic dyes forming donor-acceptor pairs, which has great potential in quantitative analytical chemistry because of its excellent sensitivity under dark-field microscopy (DFM). Herein, we introduce supramolecular β-cyclodextrin (β-CD) to design a host-guest recognition plasmonic nano-structure modified gold nanoparticles (GNPs), while GNPs and rhodamine molecule (RB) act as the donor and acceptor, respectively. In the presence of the target cholesterol, due to the stronger binding of cholesterol with β-CD, RB molecules are released, inducing the inhibition of PRET, as well as the increase of the scattering intensity of GNPs. The proposed strategy achieves a linear range from 0.02 µmol/L to 2.0 µmol/L for cholesterol detection, and reaches a limit of detection (LOD) of 6.7 nmol/L. This host-guest recognition strategy can easily integrate receptor-donor pair into one nanoparticle, which simplifies the construction of the PRET platform, and further provides an effective approach for PRET-based analytical applications. Afterwards, the proposed PRET strategy was successfully applied for the detection of cholesterol in serum samples with high sensitivity and specificity. The proposed method provides an effective clinically potential means for the detection of cholesterol and other disease-related biomarkers.     

Density functional theory study of triphenyl phosphite: molecular flexibility and weak intermolecular hydrogen bonding

The high conformational flexibility of triphenyl phosphite (TPP) is investigated by density functional theory (DFT) calculations. First, through a scan of the molecular potential energy surface, we bring to light a new stable conformation of an isolated molecule, not yet encountered in the crystal states of TPP. Different relevant conformations of the TPP monomer in the gas state are further presented and discussed in terms of molecular structure, relative energy, and dipole moments. Second, we considered dimer and trimer of TPP starting from their structural topology within the hexagonal crystal, which is characterized by the existence of molecular rods. It is shown that weak C-H...O intermolecular hydrogen bonds in TPP cannot definitely be excluded, and finally this point is discussed in the scope of the glacial state problem.     

Role of diffusion in excitation energy transfer and migration

Effect of diffusion on excitation energy transfer and migration in a dye pair sodium fluorescein (donor) and Rhodamine-6G (acceptor) has been studied for different viscosities by both steady state and time domain fluorescence spectroscopic measurements. The donor-donor interaction appears to be weaker as compared to donor-acceptor interaction and thus favors direct Forster-type energy transfer. Interestingly, at low viscosity (water in this case) transfer appears to be controlled by material diffusion/energy migration. Further, acceptor dynamics reveals the fact that direct Forster transfer dominates in viscous media.     

Two-step picosecond UV excitation of polynucleotides and energy transfer

We studied the dependence of the efficiency of two-step photoreactions in several polynucleotides: poly-U, C_spd-phage DNA and TMV RNA, on the chain length and spatial structure of the excited biopolymer under high-intensity picosecond UV irradiation (λ = 266nm, I = 10¹¹ ?10¹⁴ W/m², τ_p = 23 ps). It has been found that the effective energy transfer distance Λ in single-stranded polynucleotides is ≈ 1 or 2 nucleotides. In double-stranded nucleic acids Λ < 170. The lifetime τ₁ of the excited electronic state S₁ and the absorption cross section σ₂ from the level S₁ have been estimated for nucleotide pU (τ > 6.6 ps, σ₂ <1.7 × 10^?16 cm²).     

Irradiation of atactic polystyrene: linear energy transfer effects

Atactic glassy polystyrene (PS) has been irradiated in anoxic conditions by electron and ion beams. The induced modifications were followed, in situ, by Fourier transform infrared spectroscopy (FTIR). In-film modifications and hydrocarbon gas release were followed. In-situ measurements allowed one to avoid any spurious oxidation of the films after irradiation and also permitted studying in detail the evolution with dose of the FTIR spectra. The data were quantitatively analyzed, and we present a complete analysis of the effects of the Linear Energy Transfer (LET) on the radiation chemical yields of several radiation-induced modifications (alkynes, allenes, alkenes, benzene, and disubstituted benzenes). For a better understanding of the LET effects, the in-film modifications are compared to H2 release data from the literature and to our measurements of hydrocarbon gaseous molecule yields obtained by us. The overall destruction yield becomes very significant at high LET, and the radiation sensitivity of this aromatic polymer merges with typical values of aliphatic polymers: the radiation resistance conferred at low LET to polystyrene by the phenyl side groups is lost at high LET. This loss of radiation resistance equally affects the aromatic and aliphatic moieties. Monosubstituted alkynes are created above a LET threshold, whereas the other radiation-induced modifications are observed in the whole LET range. Several observations indicate that the phenyl ring is broken at high LET. Comparison of the alkyne yield in PS, polyethylene, and polycarbonate as well as the formation of nitrile bonds in poly(vinylpyridine- co-styrene) are consistent with a cleavage of the phenyl ring as the prominent source of alkynes. As the competing damage mechanisms do not have the same LET evolution, the relative importance of a specific modification on the global damage depends on LET. Some (benzene and disubstituted benzenes) dominate at low LET, while others (in-film alkyne and acetylene release) dominate at high LET.     

Intramolecular electronic excitation energy transfer in donor/acceptor dyads studied by time and frequency resolved single molecule spectroscopy

Electronic excitation energy transfer has been studied by single molecule spectroscopy in donor/acceptor dyads composed of a perylenediimide donor and a terrylenediimide acceptor linked by oligo(phenylene) bridges of two different lengths. For the shorter bridge (three phenylene units) energy is transferred almost quantitatively from the donor to the acceptor, while for the longer bridge (seven phenylene units) energy transfer is less efficient as indicated by the occurrence of donor and acceptor emission. To determine energy transfer rates and efficiencies at the single molecule level, several methods have been employed. These comprise time-correlated single photon counting techniques at room temperature and optical linewidth measurements at low temperature (1.4 K). For both types of measurement we obtain broad distributions of the rate constants of energy transfer. These distributions are simulated in the framework of Forster theory by properly taking into account static disorder and the flexibility of the dyads, as both effects can substantially contribute to the distributions of energy transfer times. The rate constants of energy transfer obtained from the calculated distributions are smaller on average than those extracted from the experimental distributions, whereby the discrepancy is larger for the shorter bridge. Furthermore, by plotting the experimentally determined transfer rates against the individual spectral overlaps, approximately linear dependencies are found being indicative of a Forster-type contribution to the energy transfer. For a given single molecule such a linear dependence could be followed by spectral diffusion induced fluctuations of the spectral overlap. The discrepancies between measured energy transfer rates and rates calculated by Forster theory are briefly discussed in light of recent results of quantum chemical calculations, which indicate that a bridge-mediated contribution is mainly responsible for the deviations from Forster theory. The availability of the inhomogeneous distributions of donor and acceptor electronic transition frequencies allows for comparing the energy transfer process at liquid helium and room temperature for the same set of molecules via simple simulations. It is found that on average the energy transfer is by a factor of approximately 3 faster at room temperature, which is due to an increase of spectral overlap.