Vibronic Band Shapes Research Articles

Insights into the Early-Time Excited-State Dynamics of Structurally Inhomogeneous Rhodopsin KR2.

The light-driven sodium-pump rhodopsin KR2 exhibits ultrafast photoisomerization dynamics of its all-trans protonated Schiff-base retinal (PSBR). However, the excited-state decay of KR2 also shows slow picosecond time constants, which are attributed to nonreactive states. The mechanism that produces long-lived states is unclear. Here, by using molecular dynamics simulations and large-scale XMCQDPT2-based QM/MM modeling, we explore the origin of reactive and nonreactive states in KR2. By calculating the S0-S1 vibronic band shapes, we gain insight into the early-time excited-state dynamics of PSBR and show that the protein environment can significantly alter vibrational modes that are active upon photoexcitation, thus facilitating photoisomerization from all-trans to 13-cis PSBR. Importantly, we reveal structural heterogeneity of the retinal-binding pocket of KR2, characterized by three distinct conformations, and conclude that the formation of a strong hydrogen bond between the retinal Schiff base and its counterion is essential for the ultrafast reaction dynamics.

Optical Absorption by Charge-Transfer Molecules.

An analytical formalism is developed for the calculation of absorption of radiation by charge-transfer molecules with electronic density delocalized between the donor and acceptor parts. The theory consistently incorporates both the vibronic coupling to quantum intramolecular vibrations and electrostatic interactions with a classical polarizable medium. The formulation operates in terms of basis-invariant parameters and can be used for calculations based on both the localized diabatic states and delocalized adiabatic wave function produced by standard quantum-chemistry algorithms. The basis-invariant reorganization energy is particularly important, since it determines observable spectroscopic parameters, in contrast to the adiabatic reorganization energy based on the molecular charge distributions in the adiabatic vacuum states. Analytical formulas are derived for the charge-transfer absorption band and first two spectral moments connecting spectroscopy to properties of charge-transfer molecules. Electronic delocalization requires a new definition of the Huang-Rhys factor traditionally used to construct vibronic band shapes. Theory's performance is illustrated by application to experimental data for self-exchange charge-transfer optical absorption and for metal-to-ligand emission transitions.

Franck-Condon Models for Simulating the Band Shape of Electronic Absorption Spectra.

Band shape is an essential ingredient in the simulation of electronic absorption spectra. The excitation of multiple series of vibrational levels during an electronic excitation is a main contributor to band shapes. Here we present two simple models based on the Franck-Condon displaced-harmonic-oscillator model. The models are both derived from the time-dependent formulation of electronic spectroscopy. They assume that the transition dipoles do not depend on geometry and that the potential energy surfaces are locally quadratic; one model is second order in time and is called LQ2, and the other is third order in time and is called LQ3. These models are suitable for simulating the unresolved vibronic band shapes of electronic spectra that involve many vibrational modes. The models are straightforward and can be easily applied to simulate absorption spectra that are composed of many electronic transitions. As compared to carrying out molecular dynamics simulations, they require relatively few electronic structure calculations, and the additional cost for constructing the spectra is negligible. Therefore, the models are suitable for simulating the spectra of complex systems such as transition-metal complexes.

Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route.

We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.

Relation of molecular structure to Franck–Condon bands in the visible-light absorption spectra of symmetric cationic cyanine dyes

A Franck–Condon (FC) model is used to study the solution-phase absorbance spectra of a series of seven symmetric cyanine dyes having between 22 and 77 atoms. Electronic transition energies were obtained from routine visible-light absorbance and fluorescence emission spectra. Harmonic normal modes were computed using density functional theory (DFT) and a polarizable continuum solvent model (PCM), with frequencies corrected using measured mid-infrared spectra. The model predicts the relative energies of the two major vibronic bands to within 5% and 11%, respectively, and also reproduces structure-specific differences in vibronic band shapes. The bands themselves result from excitation of two distinct subsets of normal modes, one with frequencies between 150 and 625cm−1, and the other between 850 and 1480cm−1. Vibronic transitions excite symmetric in-plane bending of the polymethine chain, in-plane bends of the polymethine and aromatic C–H bonds, torsions and deformations of N-alkyl substituents, and in the case of the indocyanines, in-plane deformations of the indole rings. For two dyes, the model predicts vibronic coupling into symmetry-breaking torsions associated with trans–cis photoisomerization.

Vibronic bandshape of the absorption spectra of dibenzoylmethanatoboron difluoride derivatives: analysis based on ab initio calculations.

The nature of absorption bandshapes of dibenzoylmethanatoboron difluoride (DBMBF2) dye substituted in ortho-, meta-, and para-positions of the phenyl ring is investigated using DFT and TDDFT with the range-separated hybrid CAM-B3LYP functional and the 6-311G(d,p) basis set. The solvent effects are taken into account within the polarized continuum model. The vibronic bandshape is simulated using a time-dependent linear coupling model with a vertical gradient approach through an original code. For flexible chromophores, the spectra of individual conformers are summed up with Boltzmann factors. It is shown that the long-wavelength absorption bandshape of DBMBF2 derivatives is determined by three factors: the relative statistical weights of conformers with different electronic absorption patterns, the relative position and intensity of the second low-energy electronic transition, and the vibronic structure of individual electronic peaks. The latter is governed by the relationship between the hard vibrational modes, which contribute to vibronic progression, and soft modes, which provide broadening of the peaks. The simulated spectra of the dyes in the study are generally consistent with the available experimental data and explain the observed spectral features.

Vibronic-structure tracking: a shortcut for vibrationally resolved UV/Vis-spectra calculations.

The vibrational coarse structure and the band shapes of electronic absorption spectra are often dominated by just a few molecular vibrations. By contrast, the simulation of the vibronic structure even in the simplest theoretical models usually requires the calculation of the entire set of normal modes of vibration. Here, we exploit the idea of the mode-tracking protocol [M. Reiher and J. Neugebauer, J. Chem. Phys. 118, 1634 (2003)] in order to directly target and selectively calculate those normal modes which have the largest effect on the vibronic band shape for a certain electronic excitation. This is achieved by defining a criterion for the importance of a normal mode to the vibrational progressions in the absorption band within the so-called "independent mode, displaced harmonic oscillator" (IMDHO) model. We use this approach for a vibronic-structure investigation for several small test molecules as well as for a comparison of the vibronic absorption spectra of a truncated chlorophyll a model and the full chlorophyll a molecule. We show that the method allows to go beyond the often-used strategy to simulate absorption spectra based on broadened vertical excitation peaks with just a minimum of computational effort, which in case of chlorophyll a corresponds to about 10% of the cost for a full simulation within the IMDHO approach.

Electronic Band Shapes Calculated with Optimally Tuned Range-Separated Hybrid Functionals.

Using a set of 20 organic molecules, we assess the accuracy of both the absorption and emission band shapes obtained by two optimally tuned range-separated hybrid functionals possessing 0% (LC-PBE*) and 25% (LC-PBE0*) of short-range exact exchange as well as by four other hybrid functionals including or not dispersion and long-range corrections (APF-D, PBE0-1/3, SOGGA11-X, and ωB97X-D). The band topologies are compared to experimental data and to previous time-dependent density functional theory calculations. It turns out that both optimally tuned functionals vastly improve the vibronic band shapes obtained with the non-tuned LC-PBE approach but, statistically, do not yield more accurate topologies than standard hybrid functionals. In other words, optimal tuning allows to obtain more accurate excited-state energies without degrading the description of band shapes. In addition, the LC-PBE0* 0-0 energies have been determined for a set of 40 compounds, and it is shown that the results are, on average, less accurate than those obtained by LC-PBE* for the same panel of molecules. The correlation between the optimal range-separation parameters determined for LC-PBE* and LC-PBE0* is discussed as well.

Optical Properties of Diarylethenes with TD-DFT: 0-0 Energies, Fluorescence, Stokes Shifts, and Vibronic Shapes.

This contribution is an investigation of both the structures and optical properties of a set of 14 diverse, recently synthesized diarylethenes using Time-Dependent Density Functional Theory (TD-DFT) at the ωB97X-D/6-31G(d) level of theory. The linear response (LR) and state-specific (SS) versions of the Polarizable Continuum Model (PCM) have been adopted to account for the bulk solvation effects and their relative performances were critically accessed. It is shown, for the first time in the case of nontrivial diarylethenes, that TD-DFT provides good agreement between the experimental absorption-fluorescence crossing points (AFCPs) and their theoretical counterparts when a robust model accounting for both geometrical relaxation and vibrational corrections is used instead of the vertical approximation. On the other hand, the theoretical estimates for the Stokes shifts based on the vertical transition energies were found to be in disagreement with respect to experiment, prompting us to simulate the absorption/emission vibronic band shapes. It is proved that difficulties associated with the breakdown of the harmonic approximation in Cartesian coordinates exist for the investigated system, and we show how they can be at least partially overcome by means of a vertical approach including Duschinsky effects. Our results provide a valuable basis to rationalize the experimental vibronic structure of both emission and absorption bands and are expected to be a significant asset to the understanding of the optical properties of diarylethene derivatives.

Modelling solvent effects on the absorption and emission spectra of constrained cyanines with both implicit and explicit QM/EFP models

In this contribution, we have combined Time-Dependent Density Functional Theory with both implicit solvation using variations of the well-known Polarisable Continuum Model (Linear-Response, corrected Linear-Response and State-Specific schemes) and explicit solvation approaches, to investigate the solvatochromic shifts undergone by three recently synthesised dyes. These dyes, an aza-BODIPY, a BODIPY and a so-called NBO fluorophore all present excited-states developing a significant cyanine-like character, that is known to be challenging for density-based theories. Our investigation reveals dramatic influence of the selected environmental model on both the predicted sign and amplitude of the solvent shifts. The impact of solvation on the 0–0 energies and vibronic band shapes is also discussed and comparisons with experimental data are performed.

ChemInform Abstract: Experimental Determination of the S1 Torsional Potential of 9,9′- Bianthryl in 2-Methyl-butane by Simultaneous Franck-Condon and Band Shape Analysis of Temperature Dependent Optical Fluorescence Spectra.

Optical fluorescence spectra of anthracene (AN) and of 9,9’‐bianthryl (BA) have been measured in the apolar solvent 2‐methyl‐butane (2MB) at seven different temperatures in the range 123 K to 298 K. The AN spectra are strongly structured and consist of simple Franck–Condon (FC) progressions. The BA spectra on the other hand are broad and show unusual temperature dependencies. These effects are interpreted within a two state model with five vibrational and one torsional degree of freedom. A FC analysis is carried out using vibronic band shape functions which are convolutions of two functions. The first one is a Gaussian representing the spectral broadening due to librations and intermolecular interactions. The second one results from a semiclassical treatment of the intramolecular torsional mode (large amplitude motion, LAM). Optical transitions are assumed to occur from ensembles which are thermally equilibrated with respect to their nuclear degrees of freedom. The Boltzmann distribution with respect to the LAM potentials in combination with a change of the transition frequency as a function of the torsional angle φ is identified as the predominant broadening mechanism. The LAM potentials in the S0 and S1 state are represented by a three parameter cosine series. A nonlinear least‐squares fit of the experimental spectra leads to a single consistent set of model parameters valid for all temperatures. The S1 double minimum LAM potential of BA in 2MB is found to have minima at φeq=62° (and 118°) and a local barrier at φ=90° of 255 cm−1.

Electron-phonon coupling inNi2+−dopedperovskites:KMgF3andBaLiF3

Electron-phonon (e-ph) coupling has been studied in two ${\mathrm{Ni}}^{2+}\ensuremath{-}\mathrm{d}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{d}$ fluoride crystals: the classical ${\mathrm{KMgF}}_{3}$ perovskite and the inverted perovskite ${\mathrm{BaLiF}}_{3}.$ The purely linear character of the EP coupling is shown through the comparison of emission or excitation vibronic spectra arising from different electronic levels at low temperature and the thermal evolution of the spectra. The $[{\mathrm{NiF}}_{6}{]}^{4\ensuremath{-}}\mathrm{complex}$ is described by using the molecular orbital formalism, and its covalency is estimated from the parameters of the super hyperfine structure observed in electron spin resonance measurements. A modified Pryce model is used to simulate the vibronic band shapes of ${\mathrm{Ni}}^{2+}$ ions in the compounds from their measured phonon density of states and to estimate the Huang-Rhys S parameter. The strength of the crystal field and the strength of the e-ph coupling experienced by the ${\mathrm{Ni}}^{2+}$ ions is shown to increase with the covalency of the bonding. No effect on e-ph coupling has been observed when the concentration of doping ions has been increased.

Fluorescence and absorption spectra of oligophenylenevinylenes: Vibronic coupling, band shapes, and solvatochromism

Fluorescence emission and excitation spectra of para-phenylene vinylenes nPV with n=1–4 styryl units are investigated experimentally and theoretically as a function of the temperature and the polarizability of the solvent. At low temperatures, the vibronic structures of the S0↔S1 emission and excitation bands are mirror symmetrical with negligible 0–0 energy gaps. The frequencies of the prominent vibrational modes are assigned to the second longitudinal acoustic phonon modes of the entire molecules and to localized carbon–carbon stretching vibrations. The complete vibronic structures of the spectra are calculated at the ab initio Hartree–Fock (HF/6-311G*) and restricted configuration interaction singles (RCIS/6-311G*) levels of theory assuming planar C2h molecular symmetry. The theoretically predicted spectra are in good agreement with the experiments. At room temperature, a 0–0 energy gap between the first band maxima opens, and the mirror symmetry between absorption and emission is lost. The vibronic band shapes and 0–0 band gaps are successfully simulated with a combination of Gaussian and exponential broadening of the low temperature spectra. The exponential term reflects the differences in thermal population of the phenyl-vinyl torsional modes in the S0 and S1 electronic states. Spectral shifts upon changes in temperature and solvents are quantitatively explained by changes in the refractive index of the environment. From extrapolation of the experimental data the vertical and adiabatic transition energies of the oligomers in vacuo are obtained and compared to RCIS and semiempirical quantum chemical calculations, respectively.

Spectroscopic study and structural characterization of a Li-related photoluminescence center in neutron-irradiated Si

We report on a new Li-related photoluminescence center with zero-phonon line at 879.3 meV. The center is created at 550--600 \ifmmode^\circ\else\textdegree\fi{}C in the final stages of annealing out radiation-induced point defects in float-zone silicon. Isotope and chemical correlation data establish that the center contains Li and C atoms. The isotope shift from ${}^{6}\mathrm{Li}$ to ${}^{7}\mathrm{Li},$ $\ensuremath{\Delta}{E=E(}^{7}\mathrm{Li})\ensuremath{-}{E(}^{6}\mathrm{Li})=0.18\mathrm{meV},$ is similar, per Li atom, to that observed for other Li-related centers in silicon. Uniaxial stress measurements establish the symmetry as monoclinic I, with only small departures from trigonal symmetry. A simple method for the transition is introduced to fit simultaneously the energies, polarizations, and relative intensities of the stress-split components. The transition's dipole is shown to be close to a bonding direction in the plane perpendicular to the characteristic 〈110〉 axis of the monoclinic I center. The vibronic sideband is produced by coupling to modes of 16, 31, and 36 meV, with a Huang-Rhys factor $S=1.1.$ This value can be predicted simply from the uniaxial-stress data. The temperature dependence of the zero-phonon line can be fitted precisely using the spectrum of coupled phonons derived from the vibronic band shape, plus the approximation that the differences in frequencies of the phonons in the ground and excited electronic states are proportional to the phonon frequency. The luminescence from the center is reversibly quenched with increasing temperature, with an activation energy ${E}_{a}=32\ifmmode\pm\else\textpm\fi{}5\mathrm{meV},$ however, we show that this result does not arise from the excited state containing a shallow particle. Although the center is created at 600 \ifmmode^\circ\else\textdegree\fi{}C, it is rapidly destroyed at room temperature through passivation by the capture of one mobile Li atom.

The effects of carbon and nitrogen isotopes on the `N3' optical transition in diamond

The N3 centre in diamond consists of three nitrogen atoms and one vacancy. We show that the N3 zero-phonon line, at 2.985 eV in natural diamond, is shifted by in diamond doped with , with no detectable change in the vibronic bandshape. In diamond, the energies of all the phonons seen in the vibronic band appear to be reduced from diamond in the ratio , and the zero-phonon is shifted by . The carbon isotope shift can be understood in terms of contributions from the lattice expansion, of from the different vibrational frequencies in the ground and excited electronic states, and from the Jahn - Teller effect in the excited state.

Lowest Triplet State of Indole: An ab Initio Study

Ab initio electronic structure calculations at the CIS/3-21G and CIS/6-31G(p,d) levels on the La state of indole confirm that its permanent dipole is much smaller than that of its singlet counterpart, Lasdespite having nearly the same configuration contentsand they predict that it is even smaller than that of the ground state because the electron density shift is opposite that for the La transition. This not only explains why the phosphorescence of indole derivatives, including tryptophan, has well-defined vibronic structure in polar media, whereas the fluorescence from La is broad and nearly featureless, but also suggests that the tryptophan phosphorescence spectrum maximum for proteins at low temperature may be anticorrelated with the fluorescence maximum. Reasons for the difference are traced to interference terms involving minor configurations that have considerable leverage on the permanent dipole because of large transition dipoles between the minor and major configurations. Fluorescence and phosphorescence vibronic band shapes were calculated using these wave functions and are in good qualitative agreement with experimental results.

Slow emission of the 2.56 eV centre in synthetic diamond

The 2.56 eV luminescence band in synthetic diamond is studied in detail by time resolved photoluminescence and spin resonance measurements. The temperature dependence of the vibronic band shape indicates that between 2 and 20 K there is a noticeable change in relative intensities of the two dominant lines at 2.56 and 2.54 eV, accompanied by a change in lifetime behaviour. Conventional electron paramagnetic resonance experiments show a considerable amount of substitutional Ni − ( g = 2.032) and N donors in the sample. By optically detected magnetic resonance experiments an isotropic line at g = 2.03 ± 0.01 is detected for the 2.56 eV luminescence. The defect responsible for the luminescence is tentatively related to substitutional Ni −.

Vibronic band shapes for indole from scaled bond order changes

The quantum consistent force field (QCFF/PI) method was modified by scaling the it bond order changes by a factor of 1.3, which gives a good fit for the S 1( 1L b) Franck-Condon factors of benzene. Use of the scaled bond orders in calculations of the 1L a, 1L b, and 3L a excited state geometries for indole gives calculated band shapes in good general agreement with the distinctive characteristic shapes known for these bands. Computed spectra at a variety of simulated resolutions provide interesting insights.

Quantitative interpretation of the red edge excitation (REE) effect of 9,9′-bianthryl in polyisobutene by band shape analysis of the temperature-dependent optical fluorescence spectra

Optical fluorescence spectra of 9,9′-bianthryl (BA) in polyisobutene (PIB) were measured as a function of the excitation wavelength at various temperatures between 210 and 293 K. Irradiation at the red edge of the absorption spectra selectively excites distinct conformers with respect to the torsional angle. This leads to a strong dependence of the vibronic band shape of the fluorescence spectra on the excitation wavelength. The marked temperature dependence of the band shape may be attributed to the viscosity-dependent deceleration of the torsional relaxation of BA in the highly viscous polymer which prevents the excited state ensemble from reaching thermal equilibrium. The predominant broadening mechanism affecting the band shape is given by a combination of the S1 torsional distribution and the torsional angle-dependent transition frequency. These effects are interpreted quantitatively within a torsional relaxation model based on the description of the torsional dynamics according to a Smoluchowski equation which is adapted to the steady state case. The band shape analysis of the fluorescence spectra enables the determination of the effective S1 torsional potential as well as the friction coefficient related to the internal torsional motion of BA in the polymer matrix. A value of ΔV = 325 cm−1 is deduced for the local barrier of the S1 double minimum potential at ϕ = 90° while the minimum torsional angle is found to be ϕmin = 61°. Additionally, model calculations on time-resolved fluorescence spectra of BA in apolar solvents are carried out as a function of excitation wavelength and temperature showing the importance of conformational relaxation for the interpretation of transient spectra of flexible molecules.

Luminescence decay time studies and time-resolved cathodoluminescence spectroscopy of CVD diamond

Luminescence decay times of the characteristic electron-beam excited emission systems in CVD diamond were measured for samples grown by the combustion flame and microwave techniques. For the sharp emission lines between 2.3 and 3.0 eV the decay times range from 9.6 ns for the 2.33 eV line to 1.8 μs for the 2.537 eV line. The luminescence intensity of the 1.681 eV silicon-related system initially decreases relatively slowly, followed, after about 3 ns, by a rapid decrease with decay time of 2.4 ± 0.3 ns. This behaviour is attributed to the presence of energy reservoirs coupled to the 1.681 eV excited state. The decay time of the blue band A is relatively short and this allows the bandshapes of vibronic systems superimposed on this band to be studied in more detail using time-resolved spectroscopy. In particular, the system with a zero-phonon line at 2.99 eV is shown to have a different vibronic bandshape to the N3 system (with a zero-phonon line at 2.985 eV) with which it was originally confused. In favourable circumstances the sample-limited spectral resolution in continuously excited measurements is enhanced in the time-resolved spectra.