Excited-state Equilibrium Research Articles

CASPT2//CASSCF and TDDFT//CASSCF Mapping of the Excited State Isomerization Path of a Minimal Model of the Retinal Chromophore

In this work we explore the validity of the application of TDDFT methods to the study of excited state reactivity problems. Accordingly, TDDFT//CASSCF calculations have been used to evaluate the excited state isomerization path of a retinal chromophore model and have been compared with the path obtained at the more expensive CASPT2//CASSCF level. We show that the TDDFT and CASPT2 excited state energy profiles are qualitatively similar. Indeed, remarkably, the TDDFT//CASSCF strategy achieves a qualitatively correct description of the intersection region, which is a basic mechanistic feature of photochemical processes. Quantitative differences are found in the region of the energy profile characterized by a coupled stretching−twisting deformation. This discrepancy reflects the difference in the equilibrium values of the bond lengths of the planar excited state structures when evaluated at the TDDFT and CASPT2 levels. We stress that our results support the use of TDDFT for the evaluation of energy profiles along CASSCF reaction coordinates. Thus, in no way shall such results be considered as indicative of the validity of TDDFT for the calculation of excited state equilibrium structures or reaction coordinates.

Excited State Trapping and the Stepanov Relation with Reference to Photosystem I

It has been previously demonstrated that the Stepanov equation provides a rather good description of the absorption/fluorescence spectra in Photosystem I, even though excited state equilibration is not rapid with respect to the excited state decay. In the present article this apparent contradiction is examined analytically for two-state systems and numerically for many-state systems. It is demonstrated that, in the special case of the trapping process being associated with the initially populated state, neither very rapid excited state equilibration nor a transfer equilibrium, which approximates a true Boltzmann distribution, are prerequisites to obtaining a very close approximation to a correct Stepanov result. This interesting conclusion is discussed in terms of plant Photosystem I (PSI-200). It is concluded that whereas, in compartmental modeling, photochemical trapping may be formally associated with the bulk antenna pigments due to the strong energy coupling between them and the trap pigments, this is not the case for the red spectral forms.

Hole transfer in a C-shaped molecule: conformational freedom versus solvent-mediated coupling.

The electronic coupling matrix elements attending the charge separation reactions of a C-shaped molecule containing an excited pyrene as the electron acceptor and a dimethylaniline as the donor are determined in aromatic, ether, and ester solvents. Band shape analyses of the charge-transfer emission spectra (CT --> S(0)) provide values of the reaction free energy, the solvent reorganization energy, and the vibrational reorganization energy in each solvent. The free energy for charge separation in benzene and toluene solvents is independently determined from the excited state equilibrium established between the locally excited pyrene S(1) state and the charge-transfer state. Analyses of the charge separation kinetics using the spectroscopically determined reorganization energies and reaction free energies indicate that the electronic coupling is solvent independent, despite the presence of a cleft between the donor and acceptor. Hence, solvent molecules are not involved in the coupling pathway. The orientations of the donor and acceptor units, relative to the spacer, are not rigidly constrained, and their torsional motions decrease solvent access to the cleft. Generalized Mulliken-Hush calculations show that rotation of the pyrene group about the bond connecting it to the spacer greatly modulates the magnitude of through-space coupling between the S(1) and CT states. The relationship between the torsional dynamics and the electron-transfer dynamics is discussed.

Quantum-Chemical Analysis of Electronic Excitation and Reactivity of Olefins and Dienes

Results obtained in studying the structure of olefin and diene molecules, and complexes of these, in the ground and lower excited states by RHF, ROHF, GVB/DN, and 6-31G* quantum-chemical methods are presented. Attention is paid to the identity of the main structural and electronic parameters of triplet T1 and singlet S1 states forming a reactive fourfold spin-degenerate diradical equilibrium excited state (S·T)1 having the lowest energy. A new mechanism of cyclodimerization of ethylene and tetrafluoroethylene and anionic polymerization of dienes, involving the (S·T)1 states, is suggested.

Theoretical study of the ground and first excited singlet state potential energy surfaces of disulphur monoxide (S2O)

An extended region of the ground state potential energy surface (PES) in the vicinity of the experimentally observed isomer of disulphur monoxide (S2O) has been characterized using second-order generalized Van Vleck perturbation theory (GVVPT2) and the cc-pVDZ basis set. The corresponding region of the PES of the first excited singlet state, [Ctilde] 1A′, was analysed in order to elucidate the nature of the experimentally observed dissociation of the excited state S2O. Our calculations support experimental results suggesting the existence of several quasi-bound vibrational energy levels on the excited state PES. The second excited singlet state, [Dtilde] 1A′, was also examined. Our results corroborate the hypothesis that the cause of the predissociation of excited state S2O into its ground state dissociation products is due to the interaction of the lowest two excited state PESs at elongated S-S bond distances. Additional GVVPT2 calculations for the ground and excited state equilibrium structures were performed with the cc-pVTZ basis, and are in good agreement with experimental and CI results.

Tuning the photoinduced electron-transfer thermodynamics in 1,3,5-triaryl-2-pyrazoline fluorophores: X-ray structures, photophysical characterization, computational analysis, and in vivo evaluation.

A series of donor-substituted 1,3,5-triaryl-2-pyrazoline fluorophores were structurally characterized by X-ray analysis, and their photophysical properties studied by steady-state absorption and emission spectroscopy. The photoinduced electron-transfer thermodynamics of the derivatives was estimated on the basis of the spectroscopic data and redox potentials of the fluorophores. The aryl substituents in the 1- and 3-position of the pyrazoline ring influence the photophysical properties of the fluorophores in distinctly different ways. The excited-state equilibrium energy DeltaE(00) is primarily influenced by changes of the substituent in the 1-position, whereas the reduction potential of the fluorophore is essentially determined by the 3-aryl group. Density functional calculations were used to probe the electronic structure and energy ordering of the emissive and the electron-transfer state. The results from the computational analysis agree qualitatively well with the experimental data. In addition, we have evaluated a water soluble pyrazoline derivative in vivo as a potential intracellular pH probe. Membrane permeability, low toxicity, and high quantum yield render the fluorophore attractive for biological applications.

Absorption Spectra and Photophysical Properties of a Series of Polypyridine Ligands Containing Appended Pyrenyl and Anthryl Chromophores and of Their Ruthenium(II) and Osmium(II) Complexes

The absorption spectra and luminescence properties (both in fluid solution at room temperature and in rigid matrix at 77 K) of four polypyridine ligands substituted with pyrenyl and anthryl chromophores have been investigated, together with the same properties of 15 Ru(II) and Os(II) complexes prepared using the same ligands. Absorption spectroscopy revealed that the various chromophores contribute to the overall absorption spectra of the mixed-chromophore species in a roughly additive way. The photophysical investigations allowed us to obtain information on several aspects. For example, in the mixed pyrene−anthracene bipyridine-based systems, efficient singlet−singlet pyrene-to-anthracene energy transfer takes place, whereas the same process involving the triplet states is apparently not efficient, unless a metal-to-ligand charge-transfer (MLCT) excited-state mediates the process. The luminescence properties of the Ru(II) complexes are dominated by 3MLCT levels at room temperature (with a few exceptions, that is, the anthracene-containing species) and by pyrene- and/or anthracene-based triplet states at 77 K. However, at room-temperature, equilibration between 3MLCT and pyrene triplets levels is established, and as a consequence, the luminescence lifetimes of the complexes are significantly prolonged (up to 18 μs for the species containing six pyrenyl chromophores). This excited-state lifetime prolongation is linearly related to the number of pyrenyl chromophores and is independent of connectivity. The photophysical properties of the Os(II) complexes are dominated by 3MLCT levels both at room temperature and at 77 K. However, the anthryl chromophores clearly influence the excited-state lifetime of these complexes at room temperature. Indeed, although the anthracene-based triplet states lie at higher energy than the 3MLCT levels, an excited-state equilibration process is also established, as clearly demonstrated by transient absorption spectroscopy, and the luminescence lifetime is (slightly) extended.

Multiple emission in coumarins with heterocyclic substituents

The photophysical behavior of three coumarin dyes with heterocyclic substitution in 3-position and an electron-withdrawing cyano group in 4-position, Scheme 1b, have been studied in solvents of different polarity. The results are compared with those for rotation-inhibited coumarin 153 and coumarin 6, Scheme 1a. It is concluded that the dyes undergo an excited-state equilibrium reaction from an emissive intramolecular charge transfer (ICT) state to a twisted intramolecular charge transfer (TICT) state with forbidden emission in strongly polar solvents. In coumarins I and II this reaction acts as nonradiative decay involving the rotation about the bond joining the coumarin and the heterocyclic substituent in the 3-position because the TICT state reached is nonemissive. In contrast, coumarin III shows emission from two species with the longer wavelength emitting species being preferred in polar solvents. This is characteristic for an emissive TICT state. The donor strength of the heterocyclic substituent in 3-position plays a major role in increasing the CT character of coumarins I and II when compared to C153. Coumarin III possesses significantly larger Stokes shifts and a correspondingly higher excited state dipole moment than the comparable coumarin 6 lacking the electron-withdrawing cyano group in 4-position.

Ground- and excited-state intramolecular proton transfer in 3,5-dibromosalicylic acid

The existence of both ground- and excited-state proton transfer equilibrium between the enolic and keto tautomers of 3,5-dibromosalicylic acid has been investigated in aqueous solution using electronic absorption and luminescence emission spectroscopies, together with ab initio and semiempirical MO/CI calculations. The compound provides an example of a room temperature phosphorescence triplet-state emission from a phototautomer (ketonic) form. The interference from radiationless paths, which may in principle avoid the observation of the phosphorescence signal, was overcome by using a protective micellar medium and the presence of an external heavy atom.

Rotationally Resolved LIF Spectra of the A2Σ +– X2Π r Transition of Jet-Cooled 74Ge 35Cl

The A 2Σ +– X 2Π r band system of 74Ge 35Cl has been rotationally resolved for the first time using isotopically enriched 74GeCl 4 as the precursor in a pulsed discharge jet experiment. The previous vibrational analysis of W. J. Balfour and K. S. Chandrasekhar (1986, J. Phys. B 19, L187–L191) has been verified from the observed isotopic splittings of both the chlorine and germanium isotopomers. The 2Π 1/2 components of three vibronic bands have been rotationally analyzed leading to revised values for the ground state rotational constant B″ 0=0.154165(35) cm −1 and the lambda-doubling constant p″ 0=6.560(97)×10 −3 cm −1. We have experimentally determined the value of B′ e=0.118710(24) cm −1 for the A 2Σ + state leading to an excited state equilibrium bond length of 2.44581(25) Å.

Equilibrium and pressure-jump relaxation studies of the conformational transitions of P13MTCP1.

The conformational transitions of a small oncogene product, p13(MTCP1), have been studied by high-pressure fluorescence of the intrinsic tryptophan emission and high-pressure 1D and 2D 1H-15N NMR. While the unfolding transition monitored by fluorescence is cooperative, two kinds of NMR spectral changes were observed, depending on the pressure range. Below approximately 200 MPa, pressure caused continuous, non-linear shifts of many of the 15N and 1H signals, suggesting the presence of an alternate folded conformer(s) in rapid equilibrium (tau<<ms) with the basic native structure. Above approximately 200 MPa, pressure caused a sharp decrease in the intensity of the folded proteins signals, while the peaks corresponding to disordered structures increased, yielding a free energy of unfolding change of 6.0 kcal/mol and associated volume change of -100 ml/mol, in agreement with the fluorescence result. Differential scanning calorimetry also reveals two transitions between 21 and 65 degrees C, confirming the existence of an additional species under mildly denaturing conditions. We report here a real-time observation of pressure-jump unfolding kinetics by 2D NMR spectroscopy on P13MTCP1 made possible due to its very long relaxation times at high pressure revealed by fluorescence studies. Within the dead-time after the pressure-jump, the NMR spectra of the native conformer changed to those of the transient conformational species, identified in the equilibrium studies, demonstrating the equivalence between a transient species and an equilibrium excited state. After these rapid spectral changes, the intensities of all of the individual 15N-1H cross-peaks decreased gradually, and those of the disordered structure increased, consistent with the slow relaxation to the unfolded form at this pressure. Rate constants of unfolding monitored at individual amide sites within the beta-barrel were similar to those obtained from fluorescence and from side-chain protons in the hydrophobic core region, consistent with nearly cooperative unfolding. However, some heterogeneity in the apparent unfolding rate constants is apparent across the sequence and can be understood as non-uniform effects of pressure on the unfolding rate constant due to non-uniform hydration.

Dual fluorescent polyaniline model compounds: steric and temperature effects on excited state charge separation.

Low temperature dual fluorescence of several derivatives of 4-aminodiphenylamine is investigated quantitatively. A strong thermochromic and solvatochromic redshift is indicative of the high dipole moment of the CT state emitting at long wavelength. The combination of steady state and time-resolved data allowed the calculation of the excited-state equilibrium. The absence of CT-risetimes in diethyl ether and their presence in butyronitrile points to the complication by additional ground state conformational equilibria. Both ground and excited state equilibria depend on solvent polarity and temperature. High solvent polarity favours one of the ground state conformers.

Dynamic study of excited state hydrogen-bonded complexes of harmane in cyclohexane-toluene mixtures.

Photoinduced proton transfer reactions of harmane or 1-methyl-9H-pyrido[3,4-b]indole (HN) in the presence of the proton donor hexafluoroisopropanol (HFIP) in cyclohexane-toluene mixtures (CY-TL; 10% vol/vol of TL) have been studied. Three excited state species have been identified: a 1:2 hydrogen-bonded proton transfer complex (PTC), between the pyridinic nitrogen of the substrate and the proton donor, a hydrogen-bonded cation-like exciplex (CL*) with a stoichiometry of at least 1:3 and a zwitterionic exciplex (Z*). Time-resolved fluorescence measurements evidence that upon excitation of ground state PTC, an excited state equilibrium is established between PTC* and the cationlike exciplex, CL*, lambdaem approximately/= 390 nm. This excited state reaction is assisted by another proton donor molecule. Further reaction of CL* with an additional HFIP molecule produces the zwitterionic species, Z*, lambda(em) approximately/= 500 nm. From the analysis of the multiexponential decays, measured at different emission wavelengths and as a function of HFIP concentration, the mechanism of these excited state reactions has been established. Thus, three rate constants and three reciprocal lifetimes have been determined. The simultaneous study of 1,9-dimethyl-9H-pyrido[3,4-b]indole (MHN) under the same experimental conditions has helped to understand the excited state kinetics of these processes.

The Excited State Equilibrium between Two Rotational Conformers of a Sterically Restricted Donor−Acceptor Biphenyl As Characterized by Global Fluorescence Decay Analysis

A global fluorescence decay analysis approach has been employed to characterize the conformational relaxation in the excited state of a sterically hindered twisted donor−acceptor biphenyl (III) dissolved in diethyl ether (EOE). A temperature dependent population ratio of two conformationally different charge-transfer species CT and CTR is found for which the thermodynamic equilibration (reversible photoreaction) is reached above 265 K. The separated fluorescence bands of CT and CTR as well as kinetic and thermodynamic parameters associated with the adiabatic (forward and backward) photoreaction could be determined (ΔH = −2.5 kJ/mol, ΔS = −0.7 J/(mol K) with activation barriers Ea(CT → CTR) = 14.3 kJ/mol and Ea(CT←CTR) = 16.8 kJ/mol). The derived excited state dipole moments (μCT = 26D; μCTR = 30D) and their kf ratio (kfCTR/kfCT ≈ 0.7) are consistent with a photoreaction from a more planar (CT) to a more twisted (CTR) conformer.

Kinetic Study of Hydrogen Bonded Exciplex Formation of N9-methyl Harmane

The kinetics of exciplex formation of N9-methyl-1-methyl-9H-pyrido[3,4-b]indole, MHN, in the presence of the proton donor hexafluoro2-propanol, HFIP, in cyclohexane has been studied by UV-vis, steady-state, and time-resolved fluorescence measurements. The results conclusively show the formation of a 1:2 ground-state proton-transfer hydrogen bonded complex, PTC, between the pyridinic nitrogen of the substrate and the proton donor. The formation of these complexes is a necessary prerequisite for the exciplex to be observed. Thus, upon excitation of PTC, an excited-state equilibrium is established between PTC* and a cation like exciplex, CL*, λem. 410 nm. This excited-state reaction is assisted by a proton donor molecule. From the analysis of the multiexponential decays, measured at different emission wavelengths and as a function of HFIP concentration, the excited-state kinetics of this phototautomeric process has been analyzed in detail.

New Ru(II) chromophores with extended excited-state lifetimes.

We describe the synthesis, electrochemical, and photophysical properties of two new luminescent Ru(II) diimine complexes covalently attached to one and three 4-piperidinyl-1,8-naphthalimide (PNI) chromophores, [Ru(bpy)(2)(PNI-phen)](PF(6))(2) and [Ru(PNI-phen)(3)](PF(6))(2), respectively. These compounds represent a new class of visible light-harvesting Ru(II) chromophores that exhibit greatly enhanced room-temperature metal-to-ligand charge transfer (MLCT) emission lifetimes as a result of intervening intraligand triplet states ((3)IL) present on the pendant naphthalimide chromophore(s). In both Ru(II) complexes, the intense singlet fluorescence of the pendant PNI chromophore(s) is nearly quantitatively quenched and was found to sensitize the MLCT-based photoluminescence. Excitation into either the (1)IL or (1)MLCT absorption bands results in the formation of both (3)MLCT and (3)IL excited states, conveniently monitored by transient absorption and fluorescence spectroscopy. The relative energy ordering of these triplet states was determined using time-resolved emission spectra at 77 K in an EtOH/MeOH glass where dual emission from both Ru(II) complexes was observed. Here, the shorter-lived higher energy emission has a spectral profile consistent with that typically observed from (3)MLCT excited states, whereas the millisecond lifetime lower energy band was attributed to (3)IL phosphorescence of the PNI chromophore. At room temperature the data are consistent with an excited-state equilibrium between the higher energy (3)MLCT states and the lower energy (3)PNI states. Both complexes display MLCT-based emission with room-temperature lifetimes that range from 16 to 115 micros depending upon solvent and the number of PNI chromophores present. At 77 K it is apparent that the two triplet states are no longer in thermal equilibrium and independently decay to the ground state.

Rigorous Franck–Condon absorption and emission spectra of conjugated oligomers from quantum chemistry

A harmonic Condon approach is used to calculate excitation and emission band shapes for the lowest dipole-allowed electronic transitions in conjugated oligomers: polyenes, oligorylenes, and para-phenylenevinylenes. Ground- and excited-state adiabatic energies, equilibrium structures, and vibrational modes are obtained within standard all-valence-electron molecular Hamiltonian incorporating extended configuration interaction. The interstate distortion is cast in normal coordinates and used to calculate transition probabilities from the zero-phonon initial state to the vibrational manifold of the final state. Spectral profiles are obtained as a superposition of Lorentzian line shapes. Theoretical band shapes reproduce prominent features in the absorption and fluorescence spectra of the oligomers in question. The strength of the bond-stretching vibronic progression increases with oligomeric length in polyenes, but decreases in para-phenylenevinylenes. In line with experiment, absorption and emission band shapes of para-phenylenevinylenes are obtained intrinsically nonsymmetric due to stiffening of the accepting vibrational modes in the excited state. The Stokes shifts of the apparent 0-0 features in the latter are reproduced and traced back to relaxations in slow, ring-torsional motions.

A Brownian Oscillator Approach to the Kennard−Stepanov Relation

The Kennard−Stepanov (KS) relation, also known as the reciprocity relation, connects the absorption and fluorescence spectra of homogeneous complex systems under the assumption of thermal equilibration of the emitting electronic state. A recent elaboration of the theory by Sawicki and Knox (SK) [Phys. Rev. A, 1996 54, 4837] introduces a spectral temperature that is a sensitive indicator of the failure of the relation. Studies using the SK formalism, which have been limited almost exclusively to experimental cases, reveal various failures that may be due to incomplete equilibration, inhomogeneity, or both. Using the Brownian oscillator model for nuclear dynamics, we investigate the KS relation theoretically with the aid of the SK spectral temperature. The spectral temperature is again found to be a sensitive indicator, this time of the accuracy of the numerical methods necessary for the multiple integrations. The original KS relation appears to hold regardless of the memory effects of the bath, a result which is not totally unexpected considering the assumptions of excited-state equilibrium implicit in the theory. We extend the theory to the nonequilibrated case of time-resolved fluorescence, where a time-dependent temperature can be defined.

Intramolecular photo-induced electron transfer between pyrene and a xanthene dye

The bi-exponential fluorescence decay of a rhodamine substituted with two 4-(1-pyrenyl)-butyl moieties is attributed to a reversible intramolecular photo-induced electron transfer. The additional decay channel is confirmed by a decrease of the fluorescence quantum yield. Global compartmental analysis of fluorescence decays obtained at different scales allowed the determination of the different rate constants of the excited state equilibrium. Transient absorption indicates that the decay of the charge transfer state populates the locally excited triplet state of the rhodamine.

A Theoretical Study of the Low-Lying Excited States of trans- and cis-Urocanic Acid

A multiconfigurational second-order perturbation theory (CASPT2) study of the lowest lying states in the gas-phase electronic spectra of trans- and cis-urocanic acid is presented. Geometries of both isomers have been optimized at the MP2/6-31G(d) and π-CASSCF/ANO-L(4s3p1d,2s) levels of theory. The geometries are found to differ considerably between the two levels. The vertical and 0−0 excitation spectra were calculated for each isomer. Both singlet and triplet states are described for each, including the lowest lying ππ* excitations and the nOπ* excitations. Remarkably, in the trans spectrum, it is found that the nOπ* state has a higher vertical excitation energy than the lowest ππ* (5.12 vs 4.93 eV), but a lower band origin (4.10 vs 4.66 eV). Thus, the ππ* and nOπ* surfaces cross at a coordinate between that of the ground-state structure and the equilibrium excited state structure. The trans vertical spectrum consists of three intense (ππ*) electronic transitions at 4.93, 5.40, and 6.00 eV, whereas the cis spectrum is dominated by a single intense transition at 4.15 eV and a weaker one at 5.85 eV. The wave functions of the excitations typically show a multiconfigurational character, with the weighting of doubly excitated configurations exceeding 20% in a number of instances. The lowest lying Rydberg states (π3s) were found at 5.47 and 5.67 eV for the trans and cis isomers, respectively.