Excited state dynamics and spectroscopy of the 1A″ state of NSF vapor — comparisons with SO2

The fluorescence emission spectrum and analysis of NSF vapor is presented. Single vibronic level excitation near the S₁ origin gives rise to a 10 μs radiative decay. The fluorescence lifetime for excitation of levels with ? 4500 cm^?1 excess vibrational energy becomes controlled by a unimolecular radiationless process which is likely photodissociation; the dependence of this radiationless rate on energy and vibrational mode is investigated. The perturbations resulting from coupling of zero-order S₁ states with other vibronic levels which control the excited state dynamics of SO₂ are apparently not operative for NSF. Attempts are made to rationalize the grossly different dynamic behavior of the S₁ levels of these two otherwise very similar systems.     

Non-condon scheme of radiationless transitions for the morse oscillator model

The non-adiabatic coupling matrix elements responsible for radiationless deactivation of an electronically excited molecule are calculated without invoking the Condon approximation. Assuming the Morse potential surfaces for vibrational motion along the local and totally symmetric normal coordinates, the vibronic part of the radiationless rate constant is calculated. It is shown that the rate constant in the non-Condon scheme exceeds that obtained in the Condon approximation by about two orders of magnitude. The calculated dependence of the radiationless rate constant on the energy gap is in good agreement with the experimentally observed energy gap law for intersystem crossing T₁ → S₀ rate constants in aromatic hydrocarbons.     

On the role of intramolecular vibrations in the nonradiative decay of excited charge-transfer states of molecular complexes

An attempt for a theoretical treatment of radiationless transitions from excited charge-transfer states in molecular complexes is made within the framework of the statistical limit of radiationless transitions theory. This work deals with the S₁ → S₀ internal conversion in charge-transfer complexes of tetracyanoethylene (an electron acceptor) with benzene and toluene and their perdeuterated analogues. A dominant role of the high-frequency totally symmetric intramolecular vibrational modes in the nonradiative decay of excited charge-transfer states is assumed (this was inferred from the experimentally observed deuterium isotope effect on radiationless S₁ → S₀ transitions). Calculated absolute rate constants for internal conversion are found to be in good agreement with experimental ones. The results of our calculations reflect very well the observed moderate deuterium isotope effect.     

The energy and isotope dependence of electronic relaxation in dilute vapors of fluorene and β-naphthylamine

The excitation energy and isotope dependence of fluorescence lifetimes and quantum yields in dilute vapors of fluorene and β-naphthylamine are discussed in relation to the manner in which different channels of radiationless transitions are affected by the vibrational energy content of the molecule. Evidence is presented which shows that vibrational relaxation is slow compared with electronic relaxation for molecules with low excess energies and that the rate of S₁ → S₀ internal conversion is greater in the deuterated compound than in the corresponding protonated species for very large excess energies.     

Benzonitrile and its van der waals complexes studied in a free jet. III. Enhancement of the intersystem crossing rate in the benzonitrile dimer and other complexes

By using the sensitized phosphorescence spectroscopy, the intensity of the phosphorescence has been recorded upon excitation of the benzonitrile dimer to the S₁ vibronic states in a free jet. The results indicate that the strong vibrational energy dependence of the fluorescence quantum yield, reported previously, is attributable to the increasing rate of intersystem crossing with increasing vibrational energy. Similar behavior is also observed in other van der Waals complexes of benzonitrile though the increase is less obvious. The enhancement of the intersystem crossing can be correlated with the state density of van der Waals modes in the S₁ electronic state. In case of the benzonitrile trimer and benzonitrile-Kr complex, intersystem crossing is found to be fully efficient even without vibrational excitation.     

Theory of radiationless transitions in a crystalline host material

Consistent calculations of the rate constant of radiationless electron transition are reported for a diatomic molecule in a crystal at zero temperature. The transition between electronic states occurs due to nonadiabaticity. Relaxation of the vibrational energy is stimulated by the interaction of the molecule with the crystal. The calculations have been carried out under the assumption that perturbation theory with respect to the nonadiabaticity operator is applicable. The vibrational interaction of the molecule with the environment is assumed not to be small. The electronic terms of the molecule are approximated by Morse potentials.     

The potential energy surfaces and the radiationless dynamics of excited states of benzene and pyrazine

The potential energy surfaces of the lowest excited states of benzene and pyrazine are investigated as a function of some of the symmetry-adapted internal coordinates by means of the INDO/S method. A large stabilization of the T₂ (ππ*) state of pyrazine (≈ 0.5 eV) along the S_8b vibrational coordinate is found. The calculated potential energy in some excited states (T₁ in benzene, T₂ and S₂ in pyrazine) is a very flat function of the S_16b vibrational coordinate, leading to a crossing with the potential energy of the ground state at relatively small excess of vibrational energy (≈ 1 eV). Thus the ν_16b vibrational mode is postulated to play an important role in the radiationless relaxation to the ground states of these systems. No such crossing has been found near the “channel three” threshold of benzene.     

Vibrational analysis of the electronic spectrum of ethylene based onab initio SCF-CI calculations

Ab initio calculations for CH₂ twisting and CC stretching vibrational wavefunctions and energy levels are reported for various electronic states of ethylene C₂H₄. Electronic transition moments between these states are also obtained to allow a calculation of the oscillator strengths for vibrational transitions involved in various electronic band systems; from this study it is concluded that thevertical electronic energy differenceΔE _e may differ significantly from the energy of the absorption maximumΔE _max with which it is often equated. In particular it is found in the case of theπ→π ^* singlet-singlet excitation of ethylene that theΔE _e value overestimates the most probable vibrational transition energy (7.89 eV) by some 0.4 eV, thereby offering an explanation for the fact that previous attempts to predict the location of theV-N Franck-Condon absorption maximum have consistently obtained substantially higher results than the 7.66 eV value actually observed. Similar calculations for various Rydberg species and for theN-T transition are also found to obtain a quite consistent representation of the electronic spectrum of this system.     

Competition between intersystem crossing and internal conversion in isolated large molecules

The excess energy and deuteration dependence of the radiationless decay rate in “isolated” aromatic hydrocarbons (anthracene, 9,10-dimethylanthracene, phenanthrene and fluorene) suggest that S₁→S₀ internal conversion dominates over S₁→T intersystem crossing for molecules with very large excess vibrational energies.     

Cross sections and rate coefficients for electronic excitation of the triplet states of the hydrogen molecule in different vibrational levels

Cross sections for the excitation of the triplet state of H₂ from different vibrational levels of the ground electronic state have been calculated by using the Gryzinski approximation. The results for the ground vibrational level are in satisfactory agreement with the corresponding values obtained by the quantum mechanical close coupling method. The calculated cross sections have been used to generate rate coefficients for the excitation of the triplet states by using a self-consistent electron energy distribution function, obtained by numerical integration of the Boltzmann equation. The results show a strong increase of the different rate coefficients with increasing the vibrational quantum number.     

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin–orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the 2|H_so|S₁>, 1|H_so|S₁>, and 1|H_so|S₀> spin–orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S₁→T₁ population transfer is found to proceed at a rate of ≈10⁷ s⁻¹ in the isolated molecule.     

Model study of the abrupt excess-energy dependence of radiationless decay in benzene and azabenzenes

Model studies are reported aimed at accounting for the abrupt dependence of radiationless decay-rate constants on excess energy (known as channel-three decay in the case of S₁ benzene) in singlet and triplet manifolds of benzene and azabenzenes. The favored model involves L_a(ππ*) state, strongly distorted along an out-of-plane coordinate, crossing the ground-state potential at an energy close to the minimum of the lowest excited state. The results are compared with experimental observations on benzene and three azabenzenes. Implications for photochemical reactions are also discussed.     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

Trajectory surface-hopping study of the K + O2 collision: Energy transfer in neutral and ionic products

The K + O₂ collision has been studied at low energy by three-dimensional trajectory surface-hopping calculations. The diabatic potential energy surfaces used to describe the electronic states involved in the collision have been built using an analytical semi-empirical model and have not been fitted to experimental results. The double-peak structure experimentally observed in the energy-loss spectrum for K⁺ production is confirmed; but it appears that the high-energy-loss peak is due to efficient T-V energy transfer and not to electronic excitation of the O₂^? molecular ion. The energy transfer mechanism is explained by a comparison between the vibrational period of the target and the collision time which depends upon the collision energy.     

Mode-to-mode vibrational energy flow in S1 benzene

Resolved fluorescence spectra from low pressures of benzene with nine added gases have been used to follow mode-to-mode vibrational relaxation in the S₁ state of benzene under “single-collision” conditions. Cw pumping of the S₁ fundamental 6¹ (ν″₆ = 522 cm^?1) allows study of collisional vibrational energy flow into each of four channels. Two channels consist of flow into single levels, and the others represent flow into unresolved pairs of levels. The mode-to-mode cross sections are much larger than those usually observed in ground electronic states, being near gas kinetic even for partners transferring energy by VT, R processes alone. The mode-to-mode transfer has highly specific patterns, with roughly seventy percent of the transfer going into the four channels in spite of many other nearby levels. The largest cross sections are always to a level 237 cm^?1 above the initial level rather than to a level nearly resonant (ΔE = 7 cm^?1) with the initia l level. A common pattern of flow occurs for the four gases transferring energy by VT, R processes alone, and another common pattern is established for the five gases which can also use VV transfers. With the exception of one channel, VV resonances with vibrationally complex partners increase cross sections by less than a factor of two over that provided by the VT, R path. VV transfers have a similarly small effect on the overall vibrational relaxation rate out of the initial level 6¹. Both the flow patterns and the VV versus VT, R competitions are accounted for with an extremely simple and general set of propensity rules taken directly from SSH calculations made by others for vibrational relaxation in ground electronic states. The rules are based on the degeneracies of the final levels, the number of vibrational quantum changes, and the amount of energy exchanged between vibrational and translational/rotational degrees of freedom. The rules seem general to relaxation in both ground and excited electronic states, whereas large cross sections seem a special property of the excited state. The cross sections for collision partners SF₆ and perfluorohexane are small relative to those for other partners with similar vibrational complexity and mass.     

Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spectroscopy and decay dynamics of jet-cooled carbazole and N-ethylcarbazole and their homocyclic analogues

Fluorescence excitation spectra of supersonic jet-cooled carbazole (C) and N-ethylcarbazole (EC) are reported together with those of their homocyclic analogues fluorene (F) and 9-ethylfluorene (EF). Fluorescence spectra of C and EC have been measured following excitation at energies up to ≈ 1300 cm⁻¹ above the S₁ origin and reveal that the onset of intramolecular vibrational redistribution occurs at around 900 cm⁻¹ for both molecules, with redistribution being more extensive in the ethylated molecule. In C and EC, a number of modes are active in vibronically coupling the S₁ and S₂ states and Duschinsky mixing of these modes is apparent in the spectra. The fluorescence lifetimes of both C and EC show a slowly decreasing trend with increasing excitation energy in the range 0–1500 cm⁻¹ excess vibrational energy; vibrational redistribution does not appear to enhance the rate of non-radiative decay in either molecule. Comparison of lifetime values under supersonic jet conditions with solution phase results indicates that solvation produces a considerable increase in the rate of intersystem crossing in these molecules.     

“Proximity effects”: the effect of methylation and vibrational excitation on bi-exponential decay in pyrimidine

Experimental data concerning the effect of methylation and vibrational excitation on bi-exponential decay in pyrimidine is analyzed within the framework of a kinetic scheme. A method for the exact determination of the rate constants is given. It is shown that the effect of methylation and vibrational excitation on the internal conversion and intersystem crossing rates is consistent with the results of model studies dealing with the “proximity effect” in radiationless transitions.     

Quantum mechanical study of electronic transitions in collinear atom—diatom collisions

Quantum mechanical calculations are reported for model, nonreactive, collinear collision systems composed of the H₂ diatom and the halogen atom X = F, Cl, Br or I. The model involves two electronic potential energy surfaces, obtained in a diatomics-in-molecules formulation, that correspond asymptotically to the two spin-orbit states of X. On each surface the calculations include as many vibrational states of H₂ as are asymptotically allowed, up to a limiting number of five. The first two collision systems, FH₂ and ClH₂, are characterized by electronic splittings much smaller than any vibrational spacing included in the diatom spectrum, and as a result they show a high degree of vibrational elasticity with essentially all transition activity testricted to spin—orbit switching in the halogen. This pattern is broken for BrH₂ collisions, where the near-equality between electronic and vibrational quanta apparently leads to a resonant exchange of energy between the two modes. The greater spinorbit splitting in iodine (～ 2 vibrational quanta) results in largely elastic behavior in IH₂ collisions for both vibrational and electronic transitions. A modified Massey criterion is exhibited for some of the FH₂ and BrH₂ transitions.