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.     

Effect of histidine on the sensitized generation of singlet oxygen in the complexes with chlorophyll

The energies of the intermolecular interactions of an O₂ molecule in the ground and excited states with the electron-excited and non-excited model complexes of chlorophyll were calculated using the DFT, CASSCF, SA-CASSCF, MCQDPT2, and XMCQDPT2 methods. The activation energies of formation and dissociation of the oxygen complexes were estimated. The radiative electric dipole moments of (0 → 0) spin-allowed S → S, T → T, and spin-forbidden S → T transitions were calculated taking into account the spin-orbit coupling, and rate constants of nonradiative transitions that determine the generation and deactivation of the O₂ molecule (¹Δ_g) were evaluated. The effect of histidine on the probability of singlet oxygen generation sensitized by the model chlorophyll complex was considered in detail.     

Vibronic spectral behavior of molecules. XIII. Theoretical contribution to the vibronic coupling and the dushinsky effect on the S1 ← S0 absorption and the S1 → S0, S2 → S1, and S2 → S0 fluorescences of azulene

Based on the completely optimized S₀, S₁, and S₂ molecular geometries of azulene, the vibronic structure of the S₁ ← S₀ absorption as well as of the S₁ → S₀, S₂ → S₁, and S₂ → S₀ fluorescences is investigated theoretically within the adiabatic approximation. By means of theory-experiment comparisons, the influence of non-Condon terms and of the Dushinsky effect on the vibronic structure of azulene spectral behavior is discussed. Typical for the S₁ ← S₀ absorption and the S₁ → S₀ fluorescence are vibronic transition moment contributions of Condon type, whereas the interpretation of azulene S₂ → S₁ and S₂ → S₀ fluorescences is successful only within the scope of the Herzberg–Teller approach by taking into account vibronic coupling terms and, additionally, the Dushinsky effect in the latter case. An analysis of the relevant vibrational modes is given.     

Radiationless decay of the second excited singlet states of aromatic thiones: Experimental verification of the energy gap law

S₂ → S₀ fluorescence quantum yields and S₂ lifetimes of eight aromatic thiones in inert perfluoroalkane solutions at room temperature have been measured using picosecond laser techniques. Photostable, structurally rigid thiones undergo S₂ → S₁ internal conversion at rates consistent with the energy gap law of radiationless transitions. An average electronic coupling matrix element of 1.9 × 10² cm^?1 is found.     

The phosphorescence of benzene obtained byab initio and semi-empirical calculations

Summary Radiative decay and phosphorescence of triplet stare benzene is doubly -orbital and spin- forbidden and is only activated through vibronic coupling among the manifold of triplet states. For this reason the determination of lifetime and transition moments for the decay of triplet benzene has posed a considerable challenge to both theory and experiment. In the present work we have addressed the triplet benzene problem at several levels of theory; by truncated perturbation theory and semiempirical, CNDO/S-CI, calculations; by complete sum-over-state calculations as implemented in recentab initio multiconfiguration quadratic response (MCQR) theory; and by direct MCQR calculations of vibronic phosphorescence. The vibronic coupling is in the two former cases treated by the Herzberg-Teller (H-T) perturbation theory, involving four main mechanisms for the phosphorescent decay of triplet benzene. The results and interpretations given by these approaches as well as their merits and limitations are presented and discussed in some detail. Our calculations indicate that the phosphorescent decay of the³ B _1u state takes place predominantly through vibronic coupling along thee _2g mode. We obtain a phosphorescence that is almost completely out-of-plane polarized, which is in line with more recent measurements by the microwave-induced delayed phosphorescence technique, and could reproduce quite well the intensity ratios for different vibronic bands obtained in that experiment. The final triplet state lifetime is the result of a delicate sum of contributions from several vibronic degenerate and non-degenerate modes. The direct vibronic phosphorescence calculations predict a long lifetime, about one minute — 68 seconds for the best wavefunction — and seem to focus on a doubling of the assumed, albeit not established, best experimental value for the radiative lifetime of triplet benzene; 30 seconds.Dedicated to Inga Fischer-Hjalmars on her 75th birthday     

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.     

Discrimination of s-cis/s-trans conformers of jet-cooled methyl cinnamate by population labelling spectroscopy

The S₁−S₀ electronic spectrum of methyl cinnamate in a supersonic jet has been investigated to discriminate the transitions of the s-cis/s-trans conformers. Population labelling spectroscopy was applied to the conformer discrimination, and vibronic bands belonging to each conformer were identified. The relative population was estimated from the fluorescence quantum yields obtained by lifetime measurements. It was found that both conformers exist almost equally in a supersonic jet. The conformer identification of the vibronic bands was carried out based on the difference of the red-shift of their hydrogen-bonded complexes with methanol.     

Theoretical DFT study of phosphorescence from porphyrins

Geometrical structure of free-base porphin (H₂P) and Mg- and Zn-porphyrins together with their vibrational frequencies and vibronic intensities in phosphorescence are investigated by density functions theory (DFT) with the standard B3LYP functional. These molecules have a closed-shell singlet ground state (S₀) and low-lying triplet (T₁) excited states of ππ* type. The S₀–T₁ transition probability and radiative lifetime of phosphorescence (τ_p) of these molecules are calculated by time-dependent DFT utilizing quadratic response functions for account of spin–orbit coupling (SOC) and electric-dipole transition moments including displacements along active vibrational modes. The infrared and Raman spectra in the ground singlet and first excited triplet states are also studied for proper assignment of vibronic patterns. The long radiative lifetime of free-base porphin phosphorescence (τ_p ∼ 360 s at low temperature limit, 4.2 K) gets considerably shorter for the metalloporphyrins. An order of magnitude reduction of τ_p is predicted for Mg-porphyrin but no change of phosphorescence polarization is found. A forty times enhancement of the radiative phosphorescence rate constant is obtained for Zn-porphyrin in comparison with the H₂P molecule which is accompanied by a strong change of polarization and spin-sublevel radiative activity. A strong vibronic activity of free-base porphin phosphorescence is found for the b_2g mode at 430 cm⁻¹, while the 679 and 715 cm⁻¹ vibronic bands of b_3g symmetry are less active. These and other out-of-plane vibrations produce considerable changes in the radiative constants of different spin sublevels of the triplet state; they also promote the S₁ → T₁ intersystem crossing. Among the in-plane vibrations the a_g mode at 1614 cm⁻¹ is found very active; it produces a long progression in the phosphorescence spectrum. The time-dependent DFT calculations explain the effects of the transition metal atom on phosphorescence of porphyrins and reproduce differences in their phosphorescence and EPR spectra.     

Vibronisches Spektralverhalten von Molekülen: XIV. Zum Einfluß der vibronischen Kopplung auf die S0-S1-Absorption und Fluoreszenz von ausgewählten 1,3-Diketonato-bor-komplexen im Rahmen der Herzberg-Teller-Näherung

Summary Based upon completely-optimized S₀ and S₁ molecular geometries the vibrational structures of S₀-S₁ absorption and fluorescence transitions of selected 1,3-diketonato boron complexes being differently substituted, are calculated within the Herzberg-Teller approach taking into account vibronic coupling contributions. In dependence on substituted diketone as well as on the co-ligand, the influence of vibronic coupling and the consequences of intensity borrowing on the spectral behaviour in absorption and fluorescence are found to be quite different for the studied boron complexes. Consequently, for some complexes their spectroscopic properties may be interpreted exclusively by means of the Herzberg-Teller approach. An analysis of the relevant vibrational modes is given.

     

Some comments on vibronic intensities of naphthalene fluorescence spectra from single vibronic levels

It is shown that some features of intensity distribution among certain vibronic transitions in naphthalene molecule can be understood, when one takes into account adiabatic and nonadiabatic interaction between S₁(¹B_3u), S₂(^tB_2u), and S₃(^IB_3u) electronic states. the vibronic activity of the $\text{6}\text{?}$(b_1g) mode in naphthalene-d₈ can be explained in terms of an anharmonic coupling with the $\text{7}\text{?}$(b_1g) mode. The theoretical analysis suggests reinterpretation of some vibronic transitions.     

Influence of an identified dimer vibration on the emission spectrum of [2,2]paracyclophane

The emission spectrum of polycrystalline [2,2]paracylophane shows a resolved vibronic structure with a 241 cm^?1 progression at He temperatures. The dependence of the energy of this mode upon selective deuteration in combination with results from FIR and Raman spectra could be used to identify the mode as a torsional dimer vibration. The emission spectra could be simulated assuming a linear coupling of the torsional mode to the electronic transitions with coupling strengths of S = 10 (fluorescence) and S = 13 (phosphorescence). This corresponds to an equilibrium displacement of the benzene rings under electronic excitation by a torsional angle of 10.6° (S₁) and 12.1° (T₁), in addition to the small torsion in the ground state S₀ by about 3°.     

Analysis of vibronic intensities in the phosphorescence spectrum of dimethylbenzaldehydes in durene

An attempt is reported to explain the main intensity patterns in the phosphorescence spectra of 2,4-, 2,5- and 3,4-dimethyl-benzaldehyde-1h₁ and -1d₁, observed previously. The analysis is based on CNDO and MINDO calculations of (transition) dipole moments, spin-orbit couplings, vibronic couplings, state energies, normal coordinates and vibrational frequencies. Where possible these quantities are empirically checked and corrected. Additional information, especially about the separation of the closely spaced T₁(³ππ^*) and T₂(³nπ^*) states, is obtained from phosphorescence excitation spectra reported here for all six isomers. The phosphorescence spectra consist of two components, an “allowed” component of ³ππ^* and a “forbidden” component of ³nπ^* symmetry. It is concluded that the allowed component is partly induced by the crystal field. The forbidden component is vibronically induced by out-of-plane vibrations among which the aldehydic CH(CD)-wag mode is the most active. The observed intensity patterns for this component are ascribed to interference between two mechanisms, one involving vibronic coupling between S₀ and S₁(¹nπ^*) and spin-orbit coupling between S₁ and T₁, the other involving vibronic coupling between T₁ and T₂ and spin-orbit coupling between S₀ and T₂. Within the groups of either 1h₁ or 1d₁ isomers, the main changes in the spectrum are shown to be due to the change in T₁–T₂ energy separation. The changes observed upon deuterium substitution in the aldehyde group involve, in addition to changes in the T₁–T₂ gap, changes in vibronic coupling due to normal-coordinate mixing. All these spectral changes are reproduced by calculations based on a mixture of theoretical and empirical input parameters, derived from, or at least consistent with, other observations, including excitation spectra, dipole moments and zero-field splittings. It is concluded that the mechanisms underlying these calculations offer a satisfactory explanation of the observed intensity patterns in the phosphorescence spectra of dimethylbenzaldehydes.     

Spin-forbidden electronic transitions in non-planar aromatic amines

Evidence is presented which indicates that the direct spin—orbit coupling between low-lying ππ^* states is largely responsible for the efficient S₁ → T₁ intersystem crossing and T₁ → S₀ radiative transition in non-planar aromatic amines.     

S1←S0 Vibronic spectrum and structure of 2,2-difluoroethanal in the S1 state

The vibronic spectrum of the 2,2-difluoroethanal vapor was recorded using a multipass optical cell with an optical length of at least 140 m. The spectrum in the region of 300—364 nm was assigned to the S₁S₀ electronic transition (from the ground S₀ to the first excited singlet S₁ electronic state); the vibrational structure of the spectrum was analyzed. The spectrum bands were assigned to two systems of vibronic transitions, namely, transitions between the levels of the cis-conformer (S₀) and of the S₁ conformers, with the origins (0₀ ⁰ transitions between the zero vibrational levels of conformers) at 29192 and 29087 cm^–1, respectively. Analysis of the spectrum showed that the S₁S₀ electronic excitation of the cis-conformer was followed by rotation of the CHF₂ top and pyramidal distortion of the carbonyl fragment. A number of fundamental frequencies were found for S₁ conformers, in particular, torsion and inversion energy levels. The experimental data are in satisfactory agreement with the results of quantum-chemical calculations for the 2,2-difluoroethanal molecule in the S₀ and S₁ states.     

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.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.     

Excitation-energy dependence of the radiative decay rate of s-triazine vapor: Participation of a higher singlet electronic state than S1 in the fluorescence emission

Emission spectra, quantum yields and decays of the fast emission component of s-triazine vapor following excitation into various vibronic levels in S₁ are reported. A monotonic increase of the radiative decay constant with increasing excitation energy suggests that a singlet electronic state higher than S₁ should participate in the fluorescence emission.     

Spectroscopic studies of the electronic and vibrational spectra of tetramethylammonium fluorochromate(VI)

The electronic and vibrational spectra of tetramethylammonium fluorochromate(VI) have been measured. The observed electronic transitions correlated simply and directly with those of CrO ₄ ²⁻ . The electronic spectrum shows a weak band at about 450 nm and the edge of a very strong, broad band which extends beyond 344 nm. The intervening band has been identified with o oxygen-to-chromium charge transfer. This band exhibits a partially resolved vibrational progression or vibronic coupling due to excitation of a symmetric stretching mode in the CrO₃ group. This vibronic coupling is analyzed completely due to spectral correlation and symmetry of transitions, the Duschinsky effect, vibronic-spin-orbit coupling, environmental effect, anharmonicity order, vibrational intervals, and electronic rearrangement. The text was submitted by the authors in English.     

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.     

Vibronisches Spektralverhalten von Molekülen, 10. Mitt. Theoretische Molekülgeometrien und Spektrumstruktur der S0-S1-Absorption und Fluoreszenz des 2,5-Diphenylfurans

Summary Completely-optimized S₀ and S₁ molecular geometries of 2,5-diphenylfurane and the theoretical vibronic line spectra for its absorption and fluorescence are presented. The experimental spectroscopic peaks are reasonably reproduced by the calculated vibronic transitions.