Theoretical insight into the aggregation induced emission phenomena of diphenyldibenzofulvene: a nonadiabatic molecular dynamics study

The diphenyldibenzofulvene (DPDBF) molecule appears in two forms: ring open and ring closed. The former fluoresces weakly in solution, but it becomes strongly emissive in the solid phase, exhibiting an exotic aggregation-induced emission phenomenon. The latter presents a normal aggregation quenching phenomenon, as is expected. We implement nonadiabatic molecular dynamics based on the combination of time-dependent Kohn-Sham (TDKS) and density functional tight binding (DFTB) methods with Tully's fewest switches surface hopping algorithm to investigate the excited state nonradiative decay processes. From the analysis of the nonadiabatic coupling vectors, it is found that the low frequency twisting motion in the ring open DPDBF couples strongly with the electronic excitation and dissipates the energy efficiently. While in the closed form, such motion is blocked by a chemical bond. This leads to the nonradiative decay rate for the open form (1.4 ps) becoming much faster than the closed form (24.5 ps). It is expected that, in the solid state, the low frequency motion of the open form will be hindered and the energy dissipation pathway by nonradiative decay will be slowed, presenting a remarkable aggregation enhanced emission phenomenon.     

The energy gap law for triplet states in Pt-containing conjugated polymers and monomers

The energy gap law established for aromatic hydrocarbons and rare earth ions relates the nonradiative decay rate to the energy gap of a transition through a multiphonon emission process. We show that this energy gap law can be applied to the phosphoresce of a series of conjugated polymers and monomers for which the radiative decay rate has been enhanced through incorporation of a heavy metal. We find that the nonradiative decay rate from the triplet state T(1) increases exponentially with decreasing T(1)-S(0) gap for the polymers and monomers at 300 and 20 K. Comparison of the nonradiative decay of polymers with that of their corresponding monomers highlights the role of electron-lattice coupling.     

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate: Formalism and Application to Azulene?

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.     

How the central torsion angle affects the rates of nonradiative decay in some geometrically restricted p-quaterphenyls

A small series of p-quaterphenyl derivatives has been prepared in which the dihedral angle (phi) for the two central rings is constrained by dialkoxy spacers of varying length. The photophysical properties of these compounds remain comparable, but there is a clear correlation between the rate constants for nonradiative decay of both singlet and triplet excited states and phi in fluid solution. The rates tend toward a minimum as phi approaches 90 degrees . These effects are attributed to the general phenomenon of extended delocalization and can be traced to a combination of changes in the Huang-Rhys factor and the electron-vibrational coupling matrix element, both relating to displacement of the relevant potential energy surfaces and to the medium-frequency vibronic mode coupled to decay. The latter effect arises because of different levels of conjugation in the ground-state molecule. Such findings might have important implications for the design of improved light-emitting diodes. A similar angle dependence is noted for the yield of the pi-radical cation formed on photoionization in a polar solvent, but here, the effect is due to variations in the respective energy gaps between the relevant excited states.     

Spectroscopic and photophysical properties of hexanuclear rhenium(III) chalcogenide clusters

The electronic, vibrational, and excited-state properties of hexanuclear rhenium(III) chalcogenide clusters based on the [Re(6)(mu(3)-Q)(8)](2+) (Q = S, Se) core have been investigated by spectroscopic and theoretical methods. Ultraviolet or visible excitation of [Re(6)Q(8)](2+) clusters produces luminescence with ranges in maxima of 12 500-15 100 cm(-)(1), emission quantum yields of 1-24%, and emission lifetimes of 2.6-22.4 microseconds. Nonradiative decay rate constants and the luminescence maxima follow the trend predicted by the energy gap law (EGL). Examination of 24 clusters in solution and 14 in the solid phase establish that exocluster ligands engender the observed EGL behavior; clusters with oxygen- or nitrogen-based apical ligands achieve maximal quantum yields and the longest lifetimes. The excited-state decay mechanism was investigated by applying nonradiative decay models to temperature-dependent emission experiments. Solid-state Raman spectra were recorded to identify vibrational contributions to excited-state deactivation; spectral assignments were enabled by normal coordinate analysis afforded from Hartree-Fock and DFT calculations. Excited-state decay is interpreted with a model where normal modes largely centered on the [Re(6)Q(8)](2+) core induce nonradiative relaxation. Hartree-Fock and DFT calculations of the electronic structure of the hexarhenium family of compounds support such a model. These experimental and theoretical studies of [Re(6)Q(8)](2+) luminescence provide a framework for elaborating a variety of luminescence-based applications of the largest series of isoelectronic clusters yet discovered.     

Including anharmonicity in the calculation of rate constants. 1. The HCN/HNC isomerization reaction

A method for calculating anharmonic vibrational energy levels in asymmetric top and linear systems that is based on second-order perturbation theory in curvilinear coordinates is extended to the bound generalized normal modes at nonstationary points along a reaction path. Explicit formulas for the anharmonicity coefficients, x(ij), and the constant term, E0, are presented, and the necessary modifications for resonance cases are considered. The method is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the HCN/HNC isomerization reaction. Although the results for this system are not very sensitive to the choice of coordinates, we find that the inclusion of anharmonicity leads to a substantial improvement in the vibrational energy levels. We also present detailed comparisons of rate constants computed with and without anharmonicity, with various approximations for incorporating tunneling along the reaction path, and with a more practical approach to calculating the vibrational partition functions needed for larger systems.     

FC≡CF→F~2C=C:重排反应的动态学理论研究

本文用从头算方法, 在RHF/3-21G分子轨道从头算法的水平上, 得到了重排反应F-C≡C-F→F~2C=C:的内禀反应坐标(IRC)。沿着IRC, 计算了体系各简正模所对应的频率(ω)以及沿IRC运动与垂直于IRC运动的简正模之间的耦合常数(BK,F); 根据传统过渡态理论、变分过渡态理论及相应的隧道效应校正, 计算了本重排反应的反应速率常数。     

Identification of the optically active vibrational modes in the photoluminescence of MEH-PPV films

The temperature dependence of the photoluminescence properties of a thin film of poly[2-methoxy-5-(2(')-ethylhexyloxy)-p-phenylene-vinylene], MEH-PPV, fabricated by spin coating, is analyzed. The evolution with temperature of the peak energy of the purely electronic transition, of the first vibronic band, of the effective conjugation length, and of the Huang-Rhys factors are discussed. The asymmetric character of the pure electronic transition peak and the contribution of the individual vibrational modes to the first vibronic band line shape are considered by a model developed by Cury et al. [J. Chem. Phys. 121, 3836 (2004)]. The temperature dependence of the Huang-Rhys factors of the main vibrational modes pertaining to the first vibronic band allows us to identify two competing vibrational modes. These results show that the electron coupling to different vibrational modes depends on temperature via reduction of thermal disorder.     

The effects of supramolecular assembly on exciton decay rates in organic semiconductors

We present time-resolved photoluminescence measurements on two series of oligo-p-phenylenevinylene (OPV) materials that are functionalized with quadruple hydrogen-bonding groups. These form supramolecular assemblies with thermotropic reversibility. The morphology of the assemblies depends on the way that the oligomers are functionalized; monofunctionalized OPVs (MOPVs) form chiral, helical stacks while bifunctionalized OPVs (BOPVs) form less organized structures. These are therefore model systems to investigate the effects of supramolecular assembly, the effects of morphology, and the dependence of oligomer length on the radiative and nonradiative rates of pi-conjugated materials. The purpose of this work is to use MOPV and BOPV derivatives as model systems to study the effect of intermolecular interactions on the molecular photophysics by comparing optical properties in the dissolved phase and the supramolecular assemblies. A simple photophysical analysis allows us to extract the intrinsic radiative and nonradiative decay rates and to unravel the consequences of interchromophore coupling with unprecedented detail. We find that interchromophore coupling strongly reduces both radiative and intrinsic nonradiative rates and that the effect is more pronounced in short oligomers.     

Importance of anharmonicity, recrossing effects, and quantum mechanical tunneling in transition state theory with semiclassical tunneling. A test case: the H2 + Cl hydrogen abstraction reaction

The hydrogen abstraction reaction from H2 by the Cl atom is studied by means of the variational transition state theory with semiclassical tunneling coefficients on the BW2 potential energy surface. Vibrational anharmonicity and coupling between the bending modes are taken into account. The occurrence of trajectories that recross the transition state is estimated by means of the canonical unified statistical method and by classical trajectories calculations. Different semiclassical methods for tunneling calculations are tested. Our results show that anharmonicity has a small but nonnegligible effect on the thermal rate constants, recrossing can be neglected, and tunneling is adequately described by the least-action approximation, and less successfully by the large-curvature version 3 approximation. However, the large-curvature version 4 and small-curvature approximations lead to a severe underestimation of tunneling. Thermal rate constants calculated using transition state theory including anharmonicity and tunneling agree very well with accurate quantal thermal rate constants over a wide temperature range, although the improvement over the harmonic transition state theory with the microcanonically optimized semiclassical tunneling approximation (based on version 3 of the large-curvature tunneling method) used in a previous study of this reaction is only marginal.     

“Through-space” P spin-spin couplings in ferrocenyl tetraphosphine coordination complexes: Improvement in the determination of the distance dependence of JPP constants

From the analysis of several nickel and palladium halide complexes of a constrained ferrocenyl tetraphosphine, the existence in solution phase of unique ³¹P-³¹P “through-space” nuclear spin-spin coupling constants (J_PP) had been previously evidenced. Due to the blocked conformation of the species in solution, and based on the NMR spectra obtained for the complexes and their corresponding solid state X-ray structures, these J_PP constants had been shown to clearly depend on the mutual spatial position of the corresponding phosphorus atoms. Herein, the quantitative correlation disclosed at that time (P?P distance dependence of coupling constants) is remarkably confirmed, and mathematically refined owing to the study of a new palladium dibromide tetraphosphine complex, for which the synthesis and the solution NMR and solid state X-ray characterizations are reported.     

Relating normal vibrational modes to local vibrational modes with the help of an adiabatic connection scheme

Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [Int. J. Quantum Chem. 67, 29 (1998)] represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.     

Nonradiative transitions in benzene

A symmetric Rosen-Morse potential was assumed for the potential of the out-of-plane vibrations of benzene. Matrix elements and the respectiveS ₁ ?S ₀ nonradiative rates were calculated for several values of the anharmonicity constants and compared with the results obtained with a harmonic potential. Anharmonicities of the out-of-plane modes in benzene are found to decrease the values of the matrix elements and rates, thus leaving unresolved, a discrepancy between experimental and theoreticalS ₁ ?S ₀ rates for benzene. However, in molecules with distorted acceptor modes whose frequencies are higher in the optically excited, as compared to the acceptor state, increases of several orders of magnitude of the nonradiative rate could occur on introduction of Rosen-Morse type anharmonicities.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

Nonradiative relaxation from MLCT excited states of Re(I), Ru(II) and Os(II) complexes: Franck–Condon factors from quantum chemical calculations

The Franck–Condon factors for nonradiative transitions from ³MLCT excited states in 16 complexes of Re(I), Ru(II) and Os(II) with -diimine ligands were estimated using ligand’s geometry, vibrational frequencies and normal modes obtained by ab initio quantum chemical calculations. The linear correlation was obtained between logarithms of experimental constants of nonradiative transitions and theoretical Franck–Condon factors.     

Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: application to solvated electrons in water and methanol

A new, alternative form of the golden rule formula defining the nonadiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the nonadiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via molecular dynamics simulations. The formalism is applied to the problem of the nonadiabatic p-->s relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvents, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated nonadiabatic coupling.     

Excitation wavelength-dependent electron-phonon and electron-vibrational coupling in the CP29 antenna complex of green plants

Electron-phonon and electron-vibrational coupling strengths of a weakly (excitonically) coupled chlorophyll a S1-->S0 transition of the CP29 antenna complex of plant photosystem II were studied by difference fluorescence-line-narrowing spectroscopy at 4.5 K. A strong, almost linear increase of the electron-phonon coupling strength toward longer wavelengths was observed, with Huang-Rhys factors Sph increasing from 0.41+/-0.05 at 680 nm to about 0.66+/-0.07 at 688 nm. The former and latter wavelengths are located close to the peak and on the red edge of the inhomogeneous site distribution function, respectively. The experimentally obtained wavelength dependence of Sph may originate either from an alteration of the electron-phonon coupling strength by the local environment of the fluorescing chromophore and/or from the presence of two isoforms of CP29, which are characterized by different coupling strengths to the protein environment. The one-phonon profile peaks at omegam=22 cm(-1) and is described by an asymmetric function composed of a Gaussian low-energy wing and a Lorentzian high-energy tail with half-widths at half-maximum of 10+/-1 and 60+/-10 cm(-1), respectively. Thirty-nine individual vibrational modes between 90 and 1665 cm(-1) were resolved, and their Huang-Rhys factors were determined, which fall in the range between 0.0004 and 0.032. The broad feature present in the overlap region of phonon and vibrational modes at about 90 cm(-1) is characterized by S=0.048. An integral value of vibrational coupling strengths Svib=0.36+/-0.05 was determined, which is similar to that observed earlier for the trimeric LHC II complex.     

Collision-induced nonadiabatic transitions in the second-tier ion-pair states of iodine molecule: experimental and theoretical study of the I2(f0g+) collisions with rare gas atoms

Nonadiabatic transitions induced by collisions with He, Ar, Kr, and Xe atoms in the I(2) molecule excited to the f0(g)(+) second-tier ion-pair state are investigated by means of the optical-optical double resonance spectroscopy. Fluorescence spectra reveal that the transition to the F0(u)(+) state is a dominant nonradiative decay channel for f state in He, Ar, and Kr, whereas the reactive quenching is more efficient for collisions with Xe atom. Total rate constants and vibrational product state distributions for the f-->F electronic energy transfer are determined and analyzed in terms of energy gaps and Franck-Condon factors for the combining vibronic levels at initial vibrational excitations v(f)=8, 10, 14, and 17. Quantum scattering calculations are performed for collisions with He and Ar atoms, implementing a combination of the diatomics-in-molecule and long-range perturbation theories to evaluate diabatic PESs and coupling matrix elements. Calculated rate constants and vibrational product state distributions agree well with the measured ones, especially in case of Ar. Qualitative comparison is made with the previous results for the second-tier f0(g)(+)-->F0(u)(+) transition in collisions with I(2)(X) molecule and the first-tier E0(g)(+)-->D0(u)(+) transition induced by collisions with the rare gas atoms.     

Temperature dependence of the fluorescence properties of curcumin

Steady-state and time-resolved techniques were employed to study the nonradiative process of curcumin dissolved in ethanol and 1-propanol in a wide range of temperatures. We found that the nonradiative rate constants at temperatures between 175-250 K qualitatively follow the same trend as the dielectric relaxation times of both neat solvents. We attribute the nonradiative process to solvent-controlled proton transfer. We also found a kinetic isotope effect on the nonradiative process rate constant of ~2. We propose a model in which the excited-state proton transfer breaks the planar hexagonal structure of the keto-enol center of the molecule. This, in turn, enhances the nonradiative process driven by the twist angle between the two phenol moieties.