Nonradiative decay processes in benzene

We investigate the behavior of single vibronic level nonradiative decay rates in benzene and benzene-d₆. The effects of excitation in a promoting mode which undergoes frequency and geometry changes in the S₁ relaxation (to T₁ or S₀) are considered in detail. Calculated relative nonradiative decay rates are compared with experimental values and are used to assign triplet state vibrational frequencies to the ν_s, ν₁₀ and ν₁₆ vibrations. This comparison also indicates that none of these modes, nor the modes ν₁ and ν6, are likely to be the dominant promoting modes for the S₁ → T₁ decay. Some simple expressions are given which provide good estimates of the vibronic state dependence of the non-radiative decay rates. In conjuction with experimental decay rate data, these estimates can aid in guiding spectral assignments of vibronic bands. Simple but general theoretical criteria are derived which are useful in determining those vibrations which are poor (or good) accepting modes. Our previous theory is generalized to consider absolute nonradiative decay rates. The results are used to suggest a possible mechanism for the “channel three” decay process observed by Callomon . Although the numerical applications presented here are to benzene electronic relaxation processes, the theoretical developments also apply to and the calcultions illustrate general features of nonradiative decay in the statistical limit.     

Nonradiative transitions in benzene

Calculations of nonradiative rates from excess energy levels of theS ₁ singlet state in benzene and deuterobenzene are presented. It is shown that calculations with a complete basis set lead to non-Condon effects which lie in the range of a factor of about 2–3 for theS ₁?S ₀ transition. Non-Condon matrix elements as well as non-Condon generating functions are developed. The results suggest that the development of more elaborate and more far-reaching concepts of the non-Condon models is necessary.     

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 influence of “communicating states” on the dissociation yield in theS 1 of benzene

Non-radiative communicating states rate calculations forS ₁ S ₀ transitions in benzene are presented. The contribution ofC ₆ H ₅+H predissociation to the non-radiative rates with varying excess energy is investigated. Local modes with Morse oscillators for CH-stretch vibrations are introduced. In the channel-three region one finds that much less than 1% of the initial excited energy is found to be of discrete continuum character.C ₆ H ₅+H vibrational predissociation does not conform to the strong increase of pure internal conversion for high excess energies. The steep decrease of the dissociation yield at still higher excess energies is found to be closely related to the energy acceptor behaviour of the (harmonic) out-of-plane modes.     

Franck—condon factors of the T1 ↷ S0 radiative and nonradiative transitions of naphthalene-h8 and -d8-a correlation function analysis

Franck—Condon factors for the T₁ ? S₀ transition in naphthalene-h₈ and naphthalene-d₈ are calculated employing the correlation function approach which allows us to investigate the distribution of the released electronic energy among the normal modes of the Final ground state. The relevant coupling parameters relating to geometry, frequency and anharmonicity changes due to excitation are included. Those related to geometry changes are obtained from the vibronic intensities of the phosphorescence spectrum as well as from a calculation implementing a semi-empirical relation between bond order and bond length. The calculated nonradiative rates compare well with the experimental rates in terms of absolute magnitude and deuterium effect. The semi-empirical calculations of the ribtonic intensities provide detailed information about force fields that are otherwise indistinguishable on the basis of their ability to reproduce infrared frequencies.     

Photophysics and photochemical dynamics of methylanisole molecules in a supersonic jet

The fluorescence excitation, dispersed fluorescence and hole burning spectra, and fluorescence lifetimes of jet-cooled o-, m-, and p-methylanisoles (MA) were measured. The low-frequency ring methyl internal rotational bands observed for their S₀ and S₁ states were assigned. In the case of m-MA, the rotational isomers of cis and trans conformers, which arise from the orientation of the OCH₃ group with respect to the CH₃ group, were assigned by hole-burning spectroscopy. The observed level energies and relative intensities of the methyl internal rotation were reproduced by a calculation using a free rotor basis set. Furthermore, their potentials in the S₀ and the S₁ states were determined. The potential barrier heights for the S₀ states of m- and p-MA were quite low, suggesting that the methyl groups are freely rotating, while changing from S₀ to S₁ states, the potential barrier height increases. The potential barrier heights of o-MA drastically decreased in going from S₀ to S₁ states. The decrease would be due to the hydrogen bonding between O atom and one H atom of the methyl group. The torsional bands of the methoxy group (–OCH₃) were also observed for p- and o-MA. The –OCH₃ modes are found to couple with the level of the e species for the methyl internal rotation.Fluorescence lifetimes (τ_f) of the methyl internal rotational bands in the S₁ states of o-, m-, and p-MA were measured in order to investigate the photochemical dynamics. The values of the nonradiative rate constant (k_nr) were estimated from the τ_f values and Franck–Condon factors. The k_nr values drastically increased with the excitation of methyl internal rotation. Accordingly, the methyl internal rotation should enhance the nonradiative process, presumably intersystem crossing (ISC). The enhancement should be caused by the increase of the state density (ρ) effectively coupled with triplet manifolds. The drastic increase in the ρ value should be caused by level mixing. In addition, the methyl internal rotational motion may enhance the increase of the coupling matrix elements through the vibronic coupling between the excited singlet states. The remarkable rotational quantum species dependence on the ISC rate constant (k_ISC) value clearly appeared in m-MA. The dependence should result from the difference of the ρ value between a₁ and e species, since the e species are doubly degenerate. The species dependence was apparently related to the potential barrier height, suggesting that the large barrier height should have an influence on the ρ value of the triplet states.     

The n-π transitions of the pyrazine molecule: II. Polarized spectrum in benzene crystal,and anharmonicity in the upper singlet state potential function

The polarized absorption spectra of pyrazine (h₄ and d₄) in single benzene crystals have been measured at high resolution at 2 K. Vibrational assignments in the ¹Ag → ¹B_3u (nπ^*) transition have been confirmed and considerably extended. The quartic potential component of hydrogen bending mode :Oa has been found to originate primarily from vibronic coupling with the nearby ¹B_2u (ππ^*). The coupling between in-plane 6a and out-of-plane 10a modes is described theoretically, and leads to further spectral assignments. Other out-of-plane modes 4 and 5 are identified and shown to have combination defects with 6a. A quartic component found for the out-of-plane ring bending mode 4 could not be explained by vibronic coupling.     

The effect of molecular distortions on spin–orbit coupling in simple hydrocarbons

Recent work [D.N.S. Parker et al., Chem. Phys. Lett. 469 (2009) 43–49] has found intersystem crossing (ISC) on an ultrafast timescale in electronically excited benzene, a surprise as hydrocarbons generally have small spin–orbit coupling. In this paper, the effect of molecular distortions on spin–orbit coupling (SOC) is calculated for cyclobutadiene and benzene. At equilibrium the SOC in both molecules is negligible, and therefore terms arising from molecular distortions must play a significant role in any fast ISC. We show that out-of-plane C–H bends, which leads to the hybridisation of σ and π orbitals, are responsible for the most significant effect. The S₁/S₀ conical intersection is an important feature for understanding the photochemistry of these molecules. We examine the SOC along the vector from the Franck–Condon point to the lowest energy point on the crossing seam and discuss the potential importance of the SOC to the ultrafast dynamics.     

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.     

Substituent effect on the nonradiative decay rates from 3MLCT excited state of ruthenium(II) complexes: A quantum chemical treatment

The radiationless transition rates from metal-to-ligand charge-transfer excited states of [Ru(phen)₃]²⁺ (phen = 1,10-phnanthroline) and its analogues were investigated in terms of the Huang–Rhys factors (S) using luminescence measurements and quantum chemical calculations. From the luminescence spectral fitting, it was found that not only S_M for medium frequency mode but also S_L for low frequency mode was significant for the nonradiative process. Huang–Rhys factors predicted by the conventional quantum chemical method were in agreement with the experimental values, S_M and S_L.     

The Franck—Condon principle for radiationless transitions in molecules and a selection rule for morse oscillators

The Franck—Condon (FC) principle for the tunnel radiationless transition (RT) is formulated. It reads that the RT occurs at constant values of the nuclear coordinates q* and of the classical momenta p*. However, unlike the optical transitions, q* and p* take non-physical values since the tunnel RT is a classically forbidden process. As a result of energy conservation, the potential surfaces of two given electronic states cross with one another at the nuclear configuration q*. It is concluded that the electronic-orbital selection rules and the numerical values of the purely electronic matrix elements are governed by the configuration q* rather than by the equilibrium nuclear configuration as was supposed previously. The configuration q* for the T₁ → S₀ intersystem crossing in aromatic hydrocarbons is described in terms of a large displacement of only one H atom from its equilibrium position along the CH bond (perhaps, there is also some out-of-plane displacement). Using the FC principle, it is found that the anharmonicity of the local CH bond vibrations results in a strong dependence of the T₁ → S₀ intersystem crossing rates upon the sign of the CH bond-length change between two given electronic states, Δq = R_T1 - R_S0. Namely, the following “selection rule” holds: these RTs are allowed at Δq < 0 and they are forbidden at Δq > 0, the prohibition factor being of the order of 10²–10⁴. Finally, an oscillatory dependence of the FC factors upon Δq is explained, using the FC principle, in terms of quantum interference in the total transition probability, of which the amplitude is a sum of the transition amplitudes due to different crossing points q*. The interference effects are believed to be insignificant for RTs in molecules with large energy gaps and so they are eliminated in the usual manner by adding up the partial probabilities rather than the partial amplitudes. The classical FC factor thus obtained smoothly depends upon Δq (and upon other parameters as well). This procedure also provides an analytical continuation of the FC factor to non-integral quantum numbers.     

Spectroscopy of benzene complexes with perylene and other aromatic species

The fluorescence excitation spectra are reported of complexes of benzene with perylene and anthracene. Some correlations are established between the results of simple potential energy calculations and the experimental data, in regard to the structures and binding energies of a number of different complexes. In particular, while the anthracenebenzene complex is somewhat similar to one postulated form of the benzene dimer where parallel, but displaced rings are found, benzene appears to occupy a center-of-mass position on perylene. The spectrum of perylenebenzene also shows evidence of strong coupling between internal modes of the two molecules near 1600 cm⁻¹. The other major perturbation of the spectrum involves damping of the out-of-plane “butterfly” motion of perylene by the adsorbed benzene molecule. The principal low-frequency mode, known to be a v = 0 → v = 2 transition in the bare molecule, at 95 cm⁻¹, is replaced in the benzene 1:1 and 2:1 complexes by a transition, at 68 cm⁻¹. Furthermore, unlike the bare molecule, the ground state frequency of the perturbed out-of-plane mode is very similar to that of the excited state. Indications from these data support the idea that the equilibrium out-of-plane distortion of perylene in a complex with benzene is rather different from that observed in the bare perylene molecule.     

Structure and properties of a model of deoxyheme,an ab initio SCF calculation

Ab initio SCF calculations have been used to study the structure and the electronic properties of four- and five-coordinate Fe(II) porphyrins. The following systems have been considered: FeP (P = porphine dianion) (S = 1 and S = 2) and Fe(NH₂)₄ (S = 1) as four-coordinate systems. FePNH₃, Fe(NH₂)₄NH₃ and Fe(NH₂)₄1m as models of the deoxyheme (S = 2). Fe(NH₂)₄SH (S = 2) as a model of the reduced cytochrome P450. The basis sets used are either of the split-valence type or of double-zeta quality. The ground-state electronic configurations have been assigned. The potential energy curve of FePNH₃, as a function of the out-of-plane displacement of the iron atom, has a minimum for a displacement of 0.32 Å. a value significantly smaller than the accepted value of 0.6 Å in human deoxyhemoglobin. The out-of-plane displacement is larger, by ≈ 0.2 Å, when a mercaptide ligand replaces the ammonia or imidazole ligand. The electric field gradient tensor, the quadrupole splitting and the asymmetry parameter have been calculated and compared with the experimental values derived from the ⁵⁷Fe Mössbauer spectra.     

Molecular‐Level Understanding of Ground‐ and Excited‐State O?H⋅⋅⋅O Hydrogen Bonding Involving the Tyrosine Side Chain: A Combined High‐Resolution Laser Spectroscopy and Quantum Chemistry Study

The present study combines both laser spectroscopy and ab initio calculations to investigate the intermolecular O? H???O hydrogen bonding of complexes of the tyrosine side chain model chromophore compounds phenol (PH) and para‐cresol (pCR) with H₂O, MeOH, PH and pCR in the ground (S₀) state as well as in the electronic excited (S₁) state. All the experimental and computational findings suggest that the H‐bond strength increases in the S₁ state and irrespective of the hydrogen bond acceptor used, the dispersion energy contribution to the total interaction energy is about 10–15 % higher in the S₁ state compared to that in the S₀ state. The alkyl‐substituted (methyl; +I effect) H‐bond acceptor forms a significantly stronger H bond both in the S₀ and the S₁ state compared to H₂O, whereas the aryl‐substituted (phenyl; ?R effect) H‐bond donor shows a minute change in energy compared to H₂O. The theoretical study emphasizes the significant role of the dispersive interactions in the case of the pCR and PH dimers, in particular the C? H???O and the C? H???π interactions between the donor and acceptor subunits in controlling the structure and the energetics of the aromatic dimers. The aromatic dimers do not follow the acid–base formalism, which states that the stronger the base, the more red‐shifted is the X? H stretching frequency, and consequently the stronger is the H‐bond strength. This is due to the significant contribution of the dispersion interaction to the total binding energy of these compounds.     

Magnetic rotational strengths of higher states in benzene: evidence for the existence of an out-of-plane transition

Calculations of magneto-optical B values in equilibrium benzene, were carried out in the CNDO/S CI approximation. The calculations demonstrate that the apparent B term feature just on the low energy edge of the E_1u absorption in the MCD spectrum of benzene vapor may arise from an electric dipole allowed, out-of-plane polarized transition to an A_2u state. Although the A_1g ? A_2u transition has a very low oscillator strength, it can have a non-trivial magnetic rotational strength via magnetic coupling with the close lying E_1u state. Signs and magnitudes of the rotational strength are sensitive to details of the calculation. The B value of the E_1u state is also discussed.     

The study of the intramolecular heavy atom effect in 9,10-dichlorophenanthrene and 1,2,3,4-tetrachloronaphthalene using PMDR techniques

Using PMDR techniques, the top two zero-field triplet levels in 9,10-dichlorophenanthrene and 1,2,3,4-tetrachloronaphthalene are shown to be most favoured by S₁ → T₁ ISC and T₁ → S₀ phosphorescence. Spin—orbit vibronic coupling via CCl out-of-plane modes and static distortions of the heavy atom are responsible for such behaviour respectively.     

Resonance CARS spectra of 9,9′-bianthryl in the excited states

Resonance CARS spectra of 9,9′-bianthryl in the twisted intramolecular charge-transfer (TICT), locally excited (LE)-S₁ and T₁ states were obtained in solution at room temperature. Observed Raman frequencies were compared with those of the S₀ state, the values of anthracene in the S₁, T₁ and radical ion states. The results show those vibrational modes of bianthryl not only in the S₀ state but also in the LE-S₁, TICT and T₁ states more or less consist of those of anthracene moieties. The inter-moiety CC stretching vibrational mode was not observed in the excited states.     

Absorption and emission spectra of the lowest triplet state in hexachloroacetone

T₁ ← S₀ absorption and T₁ → S₀ phosphorescence spectra of neat cystalline hexachloroacetone have been analyzed at 4.2°K. From the lifetime and energy the upper state is assigned as ³nπ^*. The spectra are sharp compared to other aliphatic ketones, with the 0-0 band at 26 248 ± 2 cm ^?1. The phosphorescence shows two strong progressions; one involving the CO stretching mode at 1784 cm^?1 (x), the other a long progression of at least 8 bands involving a mode at 143 cm^t-1 (a). The 143 cm^?1 progression forming mode can best be asigned to the CO out-of-plane wagging vibration. The absorption shows the same two strong progressions, reduced in frequency to 1270 cm^t-1 and 123 cm^?1, respectively, but with the progression in mode a broadened with increasing n. The broadening is interpreted as arising from inversion doublets; the close harmonicity up to n = 5 allowing the potential barrier to inversion to be estimated as > 700 cm^?1. A feature of the spectra is the absence of low frequency torsional modes suggesting lack of pseudo Jahn-Teller distortion of the triplet state potential surface. For comparison, the phosphorescence of crystalline hexafluoroacetone was also studied at 4.2°K. The spectrum exhibits broad bandedness with a 00 band tentatively assigned at 26 870 ± 20 cm^?1.     

The harmonic force field and absolute infrared intensities of butyne-2

The frequencies, harmonic force field and absolute IR intensities for butyne-2-d₀ and butyne-2-d₆ are reported. The final set of “harmonized” fundamental frequencies for butyne-2-d₀ and butyne-2-d₆ obeys the Teller—Redlich product rule very well. Starting values for the force constants were obtained from the harmonic force field of propyne, and diagonal force constants were adjusted in order to reproduce the experimental “harmonized” frequencies for the d₀ and d₆ compounds.The integrated IR intensities were measured according to the Wilson—Wells—Penner—Weber method, using nitrogen as a broadening gas. Thirteen sets of ?μ/?S values were obtained from the experimental intensities, using an iterative least-squares fitting procedure. This number could be reduced to one by use of several selection criteria. The signs of the remaining set appeared to be in complete agreement with the best set for propyne as reported both by Kondo and Koga and by Bode et al. The final ?μ/?S parameters were transformed into atomic polar tensors. Both kinds of intensity parameters are discussed and compared with corresponding parameters for related molecules.     

Photophysical properties and vibrational structure of ladder-type penta p-phenylene and carbazole derivatives based on SAC-CI calculations

The ??-conjugated ladder-type molecules constitute an attractive field of organic photoactive materials. In this work, the photophysical properties of ladder-type penta-p-phenylene (LPP) and carbazole derivatives (bisindenocarbazole and diindolocarbazole) have been investigated theoretically using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. The equilibrium geometries in the ground (S ₀) and first excited (S ₁) states were calculated to be planar, and the excitation is delocalized over the molecules. SAC-CI/DZP calculations have been applied to the absorption and emission spectra of these molecules. The absorption spectra were well reproduced in both peak positions and the shape of the absorption bands. The strong absorption is attributed to the highest occupied molecular orbital to the lowest unoccupied molecular orbital (H?CL) transition; however, in carbazoles, the H?C1??L transition is located below the H?CL transition. The vibrational structure in the S ₀?CS ₁ absorption band of LPP was analyzed by calculating the Franck?CCondon (FC) factors based on the potential energy surfaces (PESs) along the normal coordinates that are relevant to the geometry change. The vibrational structure was well reproduced by the theoretical simulation. The C?CC stretching mode dominantly contributes to the vibrational structure, while the breathing motion of the molecular frame does not influence the structure. The emission energies calculated by the SAC-CI method also agree well with the experimental values. The vibrational structure in the fluorescence band was also examined by the FC analysis; the theoretical spectrum is satisfactory for the two carbazoles, while the 0?C0 transition is overestimated in LPP. In diindolocarbazole, the S ₂ state has a large oscillator strength, while the S ₁ state has a small oscillator strength.