Franck-Condon Contributions Research Articles

Electrochemical Analysis in Charge-Transfer Science: Things Are Not Always What They Seem

Charge transfer (CT) and charge transport (CTr) are essential for supporting life on Earth and for making our modern ways of living possible [Phys. Chem. Chem. Phys. 2020, 22, 21583-21629]. Electrochemical analysis, while relying on heterogeneous electron transfer (ET), is of key importance for characterizing CT systems and process [Curr. Opin. Electrochem. 2022, 31, 100862]. The huge difference between the timescales of electrochemical measurements and the picosecond CT reactions of interests places inherent demands for reliable interpretations of voltammetry analyses [J. Electrochem. Soc. 2019, 166, H3175-H3187]. Concurrently, the ubiquity of electric dipole warrants deep understanding of how they affect CT thermodynamics and kinetics [J. Am. Chem. Soc. 2014, 136, 12966-12973]. The localized dipole-generated fields affect the electrochemical potentials of donors and acceptors and, thus, the Franck-Condon contribution to the CT kinetics [Angew. Chem. Intnl. Ed. 2018, 57, 12365-12369]. In the context of our latest developments in electrochemical analysis, this presentation focuses on how molecular dipoles affect not only the potentials, but also the reorganization energy and the donor-acceptor coupling. Understanding the multifaceted nature of the effects of dipoles on charge transfer and charge transport drives the emergence of new paradigms for electronics, photonics and energy science and engineering.

First-principles study on the luminescence property of a single-molecule near metallic nanoclusters

In this work we investigate the influence of a silver nano-cluster on the luminescence properties of porphine by using combined first-principles calculations and Franck–Condon (FC) and Herzberg-Teller (HT) simulations. Density functional theory (DFT) calculations indicate that the nano-cluster starts to interact with the molecule at cluster-molecule distance less than 0.8 nm and a stable configuration can form at distances around 0.2–0.3 nm depending on the contact positions. Electronic transition properties obtained with time-dependent DFT and luminescence spectra calculated from FC and HT simulations demonstrate that the nano-cluster starts to have significant influence on the luminescence properties of the molecule when the cluster-molecule distance was decreased to be smaller than 0.5 nm. The changes to the luminescence spectra are found to be caused by the variations of the electronic transition properties at short cluster-molecule distances which could affect the relative intensities of the FC and HT contributions to the total spectra.

(Invited) Why Do Dipole Effects on Charge Transfer Matter?

Charge transfer (CT) and charge transport (CTr) are by far among the most important processes for sustaining life on Earth and for making our modern ways of living possible (Phys. Chem. Chem. Phys. 2020, 22, 21583-21629). In natural and manmade sensing systems, for example, well synchronized CT processes drive the conversion of mechanical, optical, chemical and thermal signals into electric outputs, which is essential for interfacing with processing modules. Concurrently, electric dipoles are everywhere and therefore, understanding how they affect CT and CTr is of principal importance for attaining and controlling the functionality of a wide range of materials and devices. Discussions of the idea about dipole effects on CT date back to the mid 20th century and reported experimental evidence from the 1990s and 2000s demonstrated their key importance. The dipole-generated localized electric fields induce Stark effects and modulate the electronic properties of the CT moieties in their vicinity. The notion for such effects focusses on dipole-induced changes in the reduction potentials of the donor and the acceptor, affecting the CT driving forces and thus, the Franck-Condon (FC) contributions to the CT kinetics. We recently demonstrated that to harness such effects, which are inherently enormous, (1) the dipoles should be placed as closed as possible to the electron donor and acceptor, and (2) the media polarity should be lowered (Angew. Chem. 2018, 57, 12365-12369). Polar media, indeed, stabilize charged states and in general enhances the rates of CT. Polar media, however, screen the field permeation and damps the dipole effect on the electron donor and acceptor. Using hydrocarbons as a medium, results in electron transfer rates along the dipole that are six times larger than the rates for the same system when in polar solvents, such as acetonitrile. The same localized field effects in non-polar medium completely shut down the electron transfer against the dipole. While in the vicinity of dipoles, the electric fields can reach GV/m, they fall of rapidly with distance. In our work, we incorporate the dipoles in the electron donors. This geometry provides the closest possible placement of the dipole to the CT moieties. Most importantly, it has also allowed us to discover for the first time dipole effects on donor-acceptor electronic coupling that dominate and oppose the established notion about effects on the FC contributions to the CT kinetics. These discoveries change the ways of thinking about dipole effects on CT and CTr, and set unprecedented paradigms for the development of electronic materials and devices.

(Invited) Why Do Dipole Effects on Charge Transfer Matter?

Charge transfer (CT) and charge transport (CTr) are by far among the most important processes for sustaining life on Earth and for making our modern ways of living possible. In natural and manmade sensing systems, for example, well synchronized CT processes drive the conversion of mechanical, optical, chemical and thermal signals into electric outputs, which is essential for interfacing with processing modules. Conversely, electric dipoles are everywhere and therefore, understanding how they affect CT and CTr is of principal importance for attaining and controlling the functionality of a wide range of devices. Discussions of the idea about dipole effects on CT date back to the mid 20th century and reported experimental evidence from the 1990s and 2000s demonstrated their key importance. The dipole-generated localized electric fields induce Stark effects and modulate the electronic properties of the CT moieties in their vicinity. The notion for such effects focusses on dipole-induced changes in the reduction potentials of the donor and the acceptor, affecting the CT driving forces and thus, the Franck-Condon (FC) contributions to the CT kinetics. We recently demonstrated that to harness such effects, which are inherently enormous, (1) the dipoles should be placed as closed as possible to the electron donor and acceptor, and (2) the media polarity should be lowered. Polar media, indeed, stabilize charged states and in general enhances the rates of CT. Polar media, however, screen the field permeation and damps the dipole effect on the electron donor and acceptor. Using hydrocarbons as a medium, results in electron transfer rates along the dipole that are six times larger than the rates for the same system when in polar solvents, such as acetonitrile. The same localized field effects in non-polar medium completely shut down the electron transfer against the dipole. While in the vicinity of dipoles, the electric fields can reach GV/m, they fall off rapidly with distance. In our work, we incorporate the dipoles in the electron donors. This geometry provides the closest possible placement of the dipole to the CT moieties. Most importantly, it has also allowed us to discover for the first time dipole effects on donor-acceptor electronic coupling that dominate and oppose the established notion about effects on the FC contributions to the CT kinetics. These discoveries change the ways of thinking about dipole effects on CT and CTr, and set unprecedented paradigms for the development of electronic materials and devices.

Vibrationally resolved electronic circular dichroism and circularly polarized luminescence spectra of a boron-fused double helicene: A theoretical study.

In this work, we present the theoretical study of the vibrationally resolved absorption (ABS), electronic circular dichroism (ECD), emission (EMI), and circularly polarized luminescence (CPL) spectra of a boron-fused double helicene, with a detailed and complete discussion of the alternative possible approximate methods. Given the fact that few examples of CPL calculations exist, the potential energy surfaces (PESs) have been constructed and compared with Adiabatic (AH) and Vertical Hessian (VH) models. All the vibronic calculations have accounted for Duschinsky mixings, Franck-Condon (FC) effect and Herzberg-Teller (HT) contribution. Moreover, different HT expansions have been checked and compared, by computing the derivatives of the electric and magnetic dipole transition moments around the equilibrium geometries of the initial and final states. Our results show that both AH and VH models have well reproduced the experimental vibronic structures and VH model shows a better performance in the simulation of spectral lineshapes. They also show that HT effects dominate the shapes of EMI and CPL, tuning the relative heights of the different vibronic peaks, improving the agreement with the experiment for EMI. Moreover, HT effects are the main reason for the mirror-symmetry breaking between ECD and CPL spectra. Furthermore, interesting interference effects between FC and HT contributions have also been addressed.

On the spectral profile change in the Q band absorption spectra of metalloporphyrins (Mg, Zn, and Pd): A first-principles study.

We performed a systematic study of the vibrationally resolved absorption spectra in the Q band of three metalloporphyrins (Mg, Zn, and Pd) to understand the spectral changes in this series, including both the Franck-Condon (FC) and Herzberg-Teller (HT) contributions. The ground (S0) and the lowest singlet excited (S1) states were, respectively, simulated by the static and time-dependent density functional theory, with which the Duschinsky rotation effect was considered. Different functionals and basis sets were tested and compared with experiment. Results show that the long-range corrected functional CAM-B3LYP can nicely describe the spectral fingerprints of these metalloporphyrins, while the B3LYP functional significantly underestimates the FC contributions. We found that the absorption fine structures of these molecules are mainly caused by the HT vibronic couplings. The experimentally observed enhancements to the on-site 0-0 absorption peak in the series of Mg, Zn, and Pd are nicely reproduced. Enhanced absorption intensity is caused by larger FC contributions of molecules with heavier metal ions. The structure-spectroscopy relationship was analyzed, and it was found that the smaller cavity size of the porphyrin ring can significantly enhance the oscillator strength of the S0 → S1 transition.

First-principles study on vibrationally resolved fluorescence of fused 5,15-(diphenyl)-10,20-(dibromo)porphyrin molecule.

The vibrationally resolved fluorescence spectrum of a narrow-line single-molecule transducer, fused 5,15-(diphenyl)-10,20-(dibromo)porphyrin (fused-H2P) molecule, has been calculated by time-dependent density functional theory with the inclusion of both Franck-Condon and Herzberg-Teller contributions. Analytical transition dipole derivatives are used for the calculations of Herzberg-Teller terms to eliminate the possible errors caused by numerical differentials. The performance of different exchange-correlation functionals including B3LYP, ωB97X-D, and M06-2X has been examined. The comparison with the high-resolution experimental emission spectrum indicates that all three functionals can satisfactorily describe the fluorescence spectral profile, while ωB97X-D and M06-2X give slightly better excitation energy than B3LYP. Detailed analysis shows that the fluorescence spectrum is dominated by the Franck-Condon contribution, while the Herzberg-Teller term contributes mostly to its low energy tail. It is found that the size of the basis set has limited influence on the fluorescence spectrum, and a standard 6-31G(d, p) basis set is adequate for the purpose. The substitution of terthiophene side chains is found to have minor effects on the fluorescence spectrum. Our study provides unambitious assignments for all the vibronic structures in the experimental spectrum.

The role of Herzberg-Teller effects on the resonance Raman spectrum of trans-porphycene investigated by time dependent density functional theory.

The S1 excited state properties as well as the associated absorption and resonance Raman (RR) spectra of trans-porphycene are investigated by means of time dependent density functional theory calculations. The relative magnitude of the Franck-Condon (FC) contribution and of the Herzberg-Teller (HT) effects is evaluated for both the absorption and RR intensities. The accuracy of the calculated spectra is assessed by employing different theoretical approximations and by comparing with experimental data. The obtained results show that Duschinsky effects lead to noticeable modifications in the absorption intensities but are nearly negligible in the RR spectrum. By contrast, the HT effects are stronger for the RR intensities compared to the absorption intensities, and these effects significantly improve the agreement with the experimental RR spectrum. Moreover, the HT effects produce different values of the RR depolarization ratios, which can be used to quantify the relative importance of the FC and HT contributions. Generally, it is found that the HT effects have a significant role on the RR spectrum of trans-porphycene and that their inclusion in the computational scheme is mandatory to accurately predict the RR intensities.

A combined theoretical and experimental study of the valence and Rydberg states of iodopentafluorobenzene.

A new ultraviolet (UV) and vacuum ultraviolet (VUV) spectrum for iodopentafluorobenzene (C6F5I) using synchrotron radiation is reported. The measurements have been combined with those from a recent high-resolution photoelectron spectroscopic study. A major theoretical study, which includes both Franck-Condon (FC) and Herzberg-Teller (HT) analyses, leads to conclusions, which are compatible with both experimental studies. Our observation that the VUV multiplet at 7.926 eV in the VUV spectrum is a Rydberg state rather than a valence state leads to a fundamental reassignment of the VUV Rydberg spectrum over previous studies and removes an anomaly where some previously assigned Rydberg states were to optically forbidden states. Adiabatic excitation energies (AEEs) were determined from equations-of-motion coupled cluster with singles and doubles excitation; these were combined with time dependent density functional theoretical methods. Frequencies from these two methods are very similar, and this enabled the evaluation of both FC and HT contributions in the lower valence states. Multi-reference multi-root configuration interaction gave a satisfactory account of the principal UV+VUV spectral profile of C6F5I, with vertical band positions and intensities. The UV spectral onset consists of two very weak transitions assigned to 11B1 (πσ*) and 11B2 (σσ*) symmetries. The lowest unoccupied molecular orbital of a σ*(a1) symmetry has a significant C-I* antibonding character. This results in considerable lengthening of the C-I bond for both these excited states. The vibrational intensity of the lowest 11B1 state is dominated by HT contributions; the 11B2 state contains both HT and FC contributions; the third band, which contains three states, two ππ*(11A1, 21B2) and one πσ*(21B1), is dominated by FC contributions in the 1A1 state. In this 1A1 state, and the spectrally dominant bands near 6.7 (1A1) and 7.3 eV (1A1 + 1B2), the C-I bond length is in the normal range, and FC components dominate.

Combined theoretical and experimental study of the valence, Rydberg, and ionic states of chlorobenzene.

New photoelectron (PE) and ultra violet (UV) and vacuum UV (VUV) spectra have been obtained for chlorobenzene by synchrotron study with higher sensitivity and resolution than previous work and are subjected to detailed analysis. In addition, we report on the mass-resolved (2 + 1) resonance enhanced multiphoton ionization (REMPI) spectra of a jet-cooled sample. Both the VUV and REMPI spectra have enabled identification of a considerable number of Rydberg states for the first time. The use of ab initio calculations, which include both multi-reference multi-root doubles and singles configuration interaction (MRD-CI) and time dependent density functional theoretical (TDDFT) methods, has led to major advances in interpretation of the vibrational structure of the ionic and electronically excited states. Franck-Condon (FC) analyses of the PE spectra, including both hot and cold bands, indicate much more complex envelopes than previously thought. The sequence of ionic states can be best interpreted by our multi-configuration self-consistent field computations and also by comparison of the calculated vibrational structure of the B and C ionic states with experiment; these conclusions suggest that the leading sequence is the same as that of iodobenzene and bromobenzene, namely: X(2)B1(3b1 (-1)) < A(2)A2(1a2 (-1)) < B(2)B2(6b2 (-1)) < C(2)B1(2b1 (-1)). The absorption onset near 4.6 eV has been investigated using MRD-CI and TDDFT calculations; the principal component of this band is (1)B2 and an interpretation based on the superposition of FC and Herzberg-Teller contributions has been performed. The other low-lying absorption band near 5.8 eV is dominated by a (1)A1 state, but an underlying weak (1)B1 state (πσ(∗)) is also found. The strongest band in the VUV spectrum near 6.7 eV is poorly resolved and is analyzed in terms of two ππ(∗) states of (1)A1 (higher oscillator strength) and (1)B2 (lower oscillator strength) symmetries, respectively. The calculated vertical excitation energies of these two states are critically dependent upon the presence of Rydberg functions in the basis set, since both manifolds are strongly perturbed by the Rydberg states in this energy range. A number of equilibrium structures of the ionic and singlet excited states show that the molecular structure is less subject to variation than corresponding studies for iodobenzene and bromobenzene.

Interpretation of the photoelectron, ultraviolet, and vacuum ultraviolet photoabsorption spectra of bromobenzene by ab initio configuration interaction and DFT computations.

New photoelectron, ultraviolet (UV), and vacuum UV (VUV) spectra have been obtained for bromobenzene by synchrotron study with higher sensitivity and resolution than previous work. This, together with use of ab initio calculations with both configuration interaction and time dependent density functional theoretical methods, has led to major advances in interpretation. The VUV spectrum has led to identification of a considerable number of Rydberg states for the first time. The Franck-Condon (FC) analyses including both hot and cold bands lead to identification of the vibrational structure of both ionic and electronically excited states including two Rydberg states. The UV onset has been interpreted in some detail, and an interpretation based on the superposition of FC and Herzberg-Teller contributions has been performed. In a similar way, the 6 eV absorption band which is poorly resolved is analysed in terms of the presence of two ππ* states of (1)A1 (higher oscillator strength) and (1)B2 (lower oscillator strength) symmetries, respectively. The detailed analysis of the vibrational structure of the 2(2)B1 ionic state is particularly challenging, and the best interpretation is based on equation-of-motion-coupled cluster with singles and doubles computations. A number of equilibrium structures of the ionic and singlet excited states show that the molecular structure is less subject to variation than corresponding studies for iodobenzene. The equilibrium structures of the 3b13s and 6b23s (valence shell numbering) Rydberg states have been obtained and compared with the corresponding ionic limit structures.

Toward assessment of density functionals for vibronic coupling in two-photon absorption: A case study of 4-nitroaniline.

In this study, we predict vibronic two-photon absorption (TPA) spectra for 4-nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second-order coupled-cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium-sized systems. A special focus is put on the geometric derivatives of the second-order transition moment and the dipole moment difference between the charge-transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4-nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck-Condon contribution.

Nonadiabatic anharmonic electron transfer

The effect of an inner sphere, local mode vibration on an electron transfer is modeled using the nonadiabatic transition probability (rate) expression together with both the anharmonic Morse and the harmonic oscillator potential. For an anharmonic inner sphere mode, a variational analysis uses harmonic oscillator basis functions to overcome the difficulties evaluating Morse-model Franck-Condon overlap factors. Individual matrix elements are computed with the use of new, fast, robust, and flexible recurrence relations. The analysis therefore readily addresses changes in frequency and/or displacement of oscillator minimums in the different electron transfer states. Direct summation of the individual Boltzmann weighted Franck-Condon contributions avoids the limitations inherent in the use of the familiar high-temperature, gaussian form of the rate constant. The effect of harmonic versus anharmonic inner sphere modes on the electron transfer is readily seen, especially in the exoergic, inverted region. The behavior of the transition probability can also be displayed as a surface for all temperatures and values of the driving force/exoergicity Δ = -ΔG. The temperature insensitivity of the transfer rate is clearly seen when the exoergicity equals the collective reorganization energy (Δ = Λ(s)) along a maximum ln (w) vs. Δ ridge of the surface. The surface also reveals additional regions for Δ where ln (w) appears to be insensitive to temperature, or effectively activationless, for some kinds of inner sphere contributions.

Vibronic fine-structure in the S0 → S1 absorption spectrum of zinc porphyrin: A Franck–Condon simulation incorporating Herzberg–Teller theory and the Duschinsky effect

Although zinc porphyrin is a suitable specimen for studying the electronic structures and fine optical spectra of large molecules, few theoretical investigations have been performed to simulate and assign the vibrational bands in highly resolved spectra. On the basis of density functional theory and its TD extension, the S0→S1 absorption spectrum (that is, the Q band) of zinc porphyrin was simulated using the Franck–Condon (FC) approximation and incorporating the Herzberg–Teller (HT) and Duschinsky contributions to electronic transition dipole moments. Our theoretical results fit well with the optical spectrum obtained by experimental observations. The spectral profile of the Q band of zinc porphyrin is primarily described by the transition of the vibrational normal modes v8, v18, v49, v56, v57, v63, v64 and v87. Comparison of the FC and FCHT spectra with experimental results indicate that the S0→S1 absorption spectrum of zinc porphyrin is primarily due to the HT mechanism. In this regard, for the vibronically allowed or very weak transitions like those of the Q band in zinc porphyrin, the results indicate that the HT effect is more dominant than the FC contribution. In addition, we have tentatively assigned the vibrational lines in the simulated absorption spectrum. When compared with the available experimental spectra, our simulated results accurately reproduce most of the dominant transitions.

Vibronic induced one- and two-photon absorption in a charge-transfer stilbene derivate

Both the electronic and the vibronic contributions to one- and two-photon absorption of a D-pi-D charge-transfer molecule (4-dimethylamino-4'-methyl-trans stilbene) are studied by means of density functional response theory combined with a linear coupling model. Vibronic profiles of the first four excited states are fully explored. The dominating vibrational modes for both Franck-Condon and Herzberg-Teller contributions are identified. The Franck-Condon contribution dominates the spectra of first, second, and fourth excited states. The Herzberg-Teller contribution is on the other hand of comparable size for the third excited state, where its inclusion leads to a blueshift with respect to the vertical transition. A similar vibronic coupling behavior is found for both one- and two-photon absorptions.

Density functional theory study of vibronic structure of the first absorption Q x band in free-base porphin

Harmonic vibrational frequencies and vibronic intensities in the first S 0→S 1 ( π π ∗ ) absorption band of free-base porphin (H 2 P) are investigated by hybrid density functional theory (DFT) with the standard B3LYP functional. The S 0−S 1 transition probability is calculated using time-dependent DFT with account of Franck–Condon (FC) and Herzberg–Teller (HT) contributions to the electric–dipole transition moments including displacements along all 108 vibrational modes. Two weak wide bands observed in the gas phase absorption spectra of the H 2 P molecule at 626 and 576 nm are interpreted as the 0–0 band of the X 1 A g→1B 3u transition and the 0–1 band with largest contributions from the ν 10 ( a g ) = 1610 cm −1 and ν 19 ( b 1 g ) = 1600 cm −1 modes, respectively, in agreement with previous tentative assignments. Both bands are induced by the HT mechanism, while the FC contributions are negligible. A number of fine structure bands, including combination of two vibrational quanta, are obtained and compared with available spectra from supersonic jet and Shpolskij matrices. Both absorption and fluorescence spectra are interpreted on ground of the linear coupling model and a good fulfillment of the mirror-symmetry rule.

Solvent effects on molecular spectra. II. Simulations of hydrated clusters and dilute solutions of pyrimidine in its lowest (n,π*) singlet excited state

Hydrogen bonding between pyrimidine in its lowest (n,π*) singlet excited state and water in dilute solution is investigated using NPT-ensemble Monte Carlo simulations, and the properties of the pyrimidine–water complex are examined using molecular dynamics. The 1(n,π*) excitation, known experimentally to be delocalized in the gas phase, is shown to remain delocalized when pyrimidine undergoes hydrogen bonding. Assuming that the intermolecular interactions are electronic state independent, Kollman’s Lennard-Jones interactions are combined with molecular charges obtained in four different ways, generating a variety of intermolecular pair potentials. It is found that, in solution, both pyrimidine–water–hydrogen bonds are considerably weakened in the excited state; however, on average, one hydrogen bond per pyrimidine remains. The excited state hydrogen bonding gives rise to structures in the liquid more like those found in van der Waals bonded systems than in strongly hydrogen-bonded systems such as ground-state pyrimidine in water. A blue shift of the absorption band origin is correctly predicted and its magnitude and Franck–Condon contribution are in reasonable agreement with experiment. For pyrimidine–water clusters, minor changes in the intermolecular potential surfaces are shown to cause major qualitative differences in the excited state cluster dynamics, mimicking the observed spectral properties of several different hydrogen-bonded pyrimidine clusters.

On charge transfer-assisted polynucleation reactions. A trinuclear carbonyltungsten complex of ambident 4,4′-bipyrimidine

Coordinative saturation of,the ligand 4,4′-bi- pyrimidine has been achieved in the N 1, N 1′-bis- (pentacarbonyltungsten)- N 3, N 3′-tetracarbonyltungsten complex. Electrochemical and spectroscopic studies of the compound and its anion radical exhibit an MLCT absorption maximum at unexpected high energy, despite a small HOMO/LUMO gap. Inspection of band widths shows that large Franck-Condon contributions from the structurally flexible W(CO) 5 fragments are responsible for the hypsochromic shift relative to the mononuclear chelate system. The propensity of polyfunctional π acceptor ligands towards complete coordinative saturation with electron rich metal fragments is discussed.

On the Franck–Condon behavior of the H+Cl2 reaction

Extended quantum collinear calculations of the H+Cl2 reaction have been compared with model results in order to single out distinctive properties of reactive probabilities for a reaction thought to be governed by a Franck–Condon mechanism. Such an analysis has shown that even a simple model is able to rationalize the Franck–Condon contributions to the product vibrational distribution when the energy dependence of the exact quantum results is taken into account properly. On top of that, it has been shown that the product vibrational distribution of a Franck–Condon driven reaction need not have v+1 peaks (v being the initial vibrational state of reactants).

Vibronic and multimode effects on the raman excitation profile of a totally symmetric fundamental in the soret band of cytochrome c

A detailed, quantitative evaluation is reported of Franck-Condon and vibronic coupling effects on the excitation profile of the 1362 cm−l fundamental of cytochrome c in the Soret-band region. It is shown that the asymmetry of this profile is caused by interference between both effects. A new approximation method is introduced to evaluate multimode Franck-Condon contributions to Raman scattering. Accurate values are derived for several properties of the B state corresponding to the Soret band.