Laser induced fluorescence of Sb2. I. Visible B–X system

Diatomic antimony molecules have been produced in a heat-pipe oven at pressures from 10^?2 to 10 Torr. Laser induced fluorescence of Sb₂ has been studied in the spectral range 420–730 nm with various laser sources. In order to investigate different isotopic molecules and to enhance fluorescence intensity, intracavity measurements have been performed. For the isotopic molecules rotational and vibrational constants of the ground state X(¹Σ_g⁺) and for the excited state B(O_u⁺) have been determined. RKR potential curves have been calculated and used to comput Franck—Condon factors.     

The potential energy curves and probability density distributions of the X1Σ+ and A1Σ+ states of RBH

The potential energy curves PMO—RKR—van der Waals of the electronic A¹Σ⁺ and X₁Σ⁺ states of RbH have been determined. The potentials obtained are self-consistent with the experimental data because they have been tested by direct numerical solution of the radial Schrödinger equation. From exact vibrational eigenfunctions probability density distributions and Franck—Condon factors have been calculated over the range of vibrational levels observed. It is observed that the anomalous behaviour of the A¹Σ⁺ state arises in the υ′ = 1, 2 and 3 levels with probability density functions similar to those of a harmonic oscillator.     

Algebraic approximation to the Franck–Condon factors for the Morse oscillator

An algebraic approach is proposed to calculate the Franck–Condon factors for the Morse potential of diatomic molecules. The Morse oscillator is approximated by means of a fourth-order anharmonic oscillator. In the second-quantized formalism, this anharmonic Hamiltonian is diagonalized by way of the Bogoliubov–Tyablikov transformation. The Franck–Condon factors are estimated using the harmonic frequency equivalent and the recurrence relations for the Franck–Condon factors of the harmonic oscillator. Overlap integrals are shown for three band systems and compared with values calculated with an RKR potential. Excellent agreement is achieved.     

Translational spectroscopy of N+ fragments from 5 keV collision-induced dissociation of N2+ ions by helium

Collision-induced dissociation of a 5–10 keV N₂⁺ beam impinging on a helium target has been reinvestigated by translational spectroscopy. The laboratory kinetic energy distribution of N⁺ fragments exhibits height structures on a continuum. They correspond to N⁺ and N fragments ejected in the c.m. frame with kinetic energies W of 4.75, 6.4, 6.8 and 8.1 eV and they are interpreted as transitions into excited states of N₂⁺ lying at more than 30 eV above the ground state of N₂. The experimental W distribution extending over 12 eV is compared to distributions calculated using the model of vertical Franck—Condon electronic excitation with different assumptions for the initial and final states.     

Dominant channels of vibronic transitions in molecules with several identical modes

Weak-coupling radiationless transitions (internal conversion or inter system crossing) are studied assuming separability and symmetry over N identical modes. Franck–Condon factors control the branching ratios between exciting just one of the equivalent modes, or equally distributing the available energy. The dominant process can be predicted by an exact quantum mechanical solution if the wavefunctions are known (Gaussian initial distributions and accepting Morse or Poeschl-Teller oscillators, for example); or more generally by a Wigner phase space surface-jumping analysis based on a classical limit of the Wigner function, using only the donor distribution and the acceptor potential surface.     

The potential energy curve of the B 1Πu state of Na2

We have used the experimental energy levels of the B state of Na₂ to determine the shape of the potential curve. The potential curve obtained has been used to determine the Franck—Condon overlap of the continuum vibrational levels in the B state with bound levels in the ground electronic state.     

Das Franck‐Condon‐Prinzip

The quantum mechanical model is fully recognized and used for rotational and vibronic transitions in molecules, where according to the model, transitions occur between discrete, the resonance condition matching states, only. It is also accepted that selection rules are implied for rotational and vibronic transitions. Why is it so hard to recognize that this established quantum mechanical model is also valid for vibronic transitions, where the Franck‐Condon principle instead of a selection rule applies to the population of vibronic states in the electronic excitation state? In any case, supposed illustrative and comfortable but wrong explanations, also if they are widely used, must not replace more sophisticated, correct quantum mechanical models. In scientific publications as well as in teaching only the quantum mechanical version of the Franck‐Condon principle should be used. Terms like “Franck‐Condon point” or ”Franck‐Condon region of the photochemical reaction" should be avoided in the future.     

Time resolved fluorescence of anthracene in mixed crystals at 2K

An optical Kerr shuttered spectrograph has been used to time resolve the spontaneous fluorescence of aromatic mixed crystal systems at low temperature with moderate resolution. Transient effects on the fluorescence of anthracene in naphthalene excited with 614 cm^?1 vibrational excess energy in ¹B_2u have been observed that may signal measurable vibrational relaxation pathways. A model consistent with these observations is presented: it implicates a strong interaction between the intramolecular Franck—Condon and non-Franck—Condon modes in the relaxation process for specific excitation in the region of large excess lattice energy. Examination of the fluorescence for several aromatic systems integrated over the interval 0 to 30 ps following excitation high in the S₁ vibrational manifold failed to reveal evidence of non-Boltzmann vibrational distributions, although other largely unexplained effects have been observed.     

Difluorocarbene Studied with Threshold Photoelectron Spectroscopy (TPES): Measurement of the First Adiabatic Ionization Energy (AIE) of CF2

The first photoelectron band of difluorocarbene CF₂, has been studied by threshold photoelectron (TPE) spectroscopy. CF₂ was prepared by microwave discharge of a flowing mixture of hexafluoropropene, C₃F₆, and argon. A vibrationally resolved band was observed in which at least twenty‐two components were observed. In the first PE band of CF₂, the adiabatic ionization energy differs significantly from the vertical ionization energy because, for the ionization CF₂⁺ (X?²A₁)+e^? ← CF₂ (X?¹A₁), there is an increase in the FCF bond angle (by ≈20°) and a decrease in the C? F bond length (by ≈0.7 Å). The adiabatic component was not observed in the experimental TPE spectrum. However, on comparing this spectrum with an ab initio/Franck–Condon simulation of this band, using results from high‐level ab initio calculations, the structure associated with the vibrational components could be assigned. This led to alignment of the experimental TPE spectrum and the computed Franck–Condon envelope, and a determination of the first adiabatic ionization energy of CF₂ as (11.362±0.005) eV. From the assignment of the vibrational structure, values were obtained for the harmonic and fundamental frequencies of the symmetric stretching mode (ν₁′) and symmetric bending mode (ν₂′) in CF₂⁺ (X?²A₁).     

Lifetime measurements of two-photon excited vibronic levels in the low pressure limit: naphthalene

Single vibronic lifetimes of two-photon excited states are measured in the low pressure limit for naphthalene. The two-photon spectrum, besides yielding new states in S₁, is also free of the interference from the neighborhood of the S₂, known from one-photon experiments, and hence unperturbed lifetimes can be measured to higher excess energies. The overall pattern of lifetimes with excess energy including both one-photon and two-photon states shows that the vibronic structure is subordinate to an overall monotonic decrease, much as found earlier for β-naphthylamine. This indicates, at least for naphthalene, that radiationless processes into triplets are dominated by Franck—Condon factors and not by vibronic inductions and promoting modes.     

Potential‐Energy Surfaces,the Born–Oppenheimer Approximations,and the Franck–Condon Principle: Back to the Roots

The concept of a potential‐energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as “adiabatic”, “Born–Oppenheimer”, or “Born–Oppenheimer adiabatic” approximation. Concerning the closely relevant and important Franck–Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as “Franck–Condon (excited) state”, or a vertical transition to the “Franck–Condon point” with the “Franck–Condon geometry” that relaxes to the excited‐state equilibrium geometry. The Born–Oppenheimer approximation and the “classical” model of the Franck–Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts.     

Theoretical evaluation of the radiative lifetimes of LiCs and NaCs in the A<Superscript>1</Superscript>Σ<Superscript>+</Superscript> state

Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A¹Σ⁺) and the first excited (A¹Σ⁺) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs⁺, Li⁺ and Na⁺ cores, parameterized l-dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A⁺Σ⁺ state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A⁺Σ⁺ state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.     

Theoretical Study of Origin of Triple Fluorescences of a Squaraine Dye, Bis[4-(N,N-dimethylamino)phenyl]-squaraine

A new scheme of photo‐fluorescent emission origin, described as S₀ (relaxed state)→S_n (Frank‐Condon state)→ S_m (relaxed state)→S₀ (Frank‐Condon state), is presented to explain the multiple fluorescent emissions of squaraine dyes observed experimentally according to the configuration interaction singles calculations of relaxed excited states of a model compound, bis[4‐(N,N‐dimethylamino)phenyl]squaraine (SQ). It is exhibited that all triple fluorescent emissions of SQ have their significant origin in vertical electron transitions of different relaxed excited states. In addition, some important absorption peaks appearing in higher energy region are most likely to be responsible for the higher energy band observed in solid states of many squaraine dyes.     

Nuclear coordinate dependence of electronic matrix elements for radiationless transitions

The nuclear coordinate dependence of the electronic matrix elements for radiationless transitions (in the weak coupling limit) is investigated by the use of a Q-centroid approximation. This approach bears a similarity to the familiar r-centroid method in diatomic spectroscopy, but has a wholy different physical character. Because the Q-centroid for electronic relaxation is obtained as an average with density of states weighted Franck—Condon factors, it is not restricted to geometries near the equilibrium position of the initial electronic state as it is in the case of radiative transitions (in the weak coupling limit). For totally symmetric vibrations, it is shown that the Q-centroids for poor accepting modes are in the vicinity of the equilibrium positions for this vibration, while those for good accepting modes tend towards the surface crossing along those vibrational modes. Thus, in the case of dominant accepting modes, the electronic matrix element reflects a Teller surface crossing mechanism for electronic relaxation, even though the density of states weighted Franck—Condon factors reflect a tunnelling mechanism. For non-totally symmetric vibrations, Q-centroids may be large or small independent of their accepting mode capabilities. Thus, coupling mechanisms, which are “forbidden” at the equilibrium geometry in aromatic hydrocarbons, may become allowed and even dominant because of very distorted Q-centroid configurations. This leads to another possible reason for the absence of observation of a vibration that is clearly assignable as a promoting mode in the single vibronic level fluorescence studies of benzene-like molecules. The results underscore previous warnings as to the enormous errors incurred by using the Condon approximation for the nuclear coordinate dependent energy denominators that appear in the electronic matrix elements.     

A novel spectroscopy using ultrafast two-pulse excitation of large polyatomic molecules

A first infrared pulse at frequency ν₁ interacts with vibrational states in S₀ and a second visible pulse at ν₂ promotes the excited molecules to the S₁ state from where they fluoresce. Tuning the frequency ν₂ over 600 cm^?1 allows the observation of a detailed spectrum which gives information on vibrational states in S₀ and on vibronic states in S₁ together with corresponding Franck—Condon factors. The spectra differ drastically from the common broad and featureless absorption and fluorescence bands.     

Penning ionization optical spectroscopy: Metastable helium (He23S) with nitric oxide

The interaction between NO(X²π) and metastable He(2³S) atoms has been investigated by emission spectrometry. Several reaction channels have been identified, leading to NO⁺(A¹π), or to electronically excited N or O atoms. The NO⁺(A⁺π-X¹Σ⁺) banded emission spectrum was observed in the range 123-190 nm, and it was analyzed for vibrational and rotational populations. The NO⁺(A) state vibrational distribution, determined with a new set of Franck—Condon factors for NO⁺(A–X), is in approximate accord with the calculated NO⁺ (A) - NO(X) Franck—Condon (FC) factors; however the υ' = 2 – 5 levels are overpopulated relative to the FC values. The NO⁺(A) state rotational populations are shifted to higher J-values than the precursor, NO(X). Emission was observed from several excited states of O and N in both the vacuum ultraviolet and red regions of the spectrum. Comparison of total rates from excited atomic fragments with emissions from NO⁺(A) showed that the cross-section for dissociative excitation was similar to that for Penning ionization giving NO⁺(A).     

Optical Spectroscopy of the Au4+ Cluster: The Resolved Vibronic Structure Indicates an Unexpected Isomer

Knowledge of the geometric and electronic structure of gold clusters and nanoparticles is vital for understanding their catalytic and photochemical properties at the molecular level. In this study, we report the vibronic optical photodissociation spectrum of cold and mass‐selected Au₄⁺ clusters measured at a resolution high enough to allow for comparison with Franck–Condon simulations of the excited state transitions based on time‐dependent density functional theory calculations. The three vibrational frequencies identified for the lowest‐lying optically accessible excited state at 2.17 eV stem from the Y‐shaped isomer (C_2v) and not from the rhombic isomer (D_2h) considered to be the ground state structure of Au₄⁺. This study demonstrates that an analysis of low‐resolution electronic spectra by calculations of vertical transitions alone is not sufficient for a reliable isomer assignment of such metal clusters.     

Molecular Mechanism of Diaminomaleonitrile to Diaminofumaronitrile Photoisomerization: An Intermediate Step in the Prebiotic Formation of Purine Nucleobases

The photoinduced isomerization of diaminomaleonitrile (DAMN) to diaminofumaronitrile (DAFN) was suggested to play a key role in the prebiotically plausible formation of purine nucleobases and nucleotides. In this work we analyze two competitive photoisomerization mechanisms on the basis of state‐of‐the‐art quantum‐chemical calculations. Even though it was suggested that this process might occur on the triplet potential‐energy surface, our results indicate that the singlet reaction channel should not be disregarded either. In fact, the peaked topography of the S₁/S₀ conical intersection suggests that the deexcitation should most likely occur on a sub‐picosecond timescale and the singlet photoisomerization mechanism might effectively compete even with a very efficient intersystem crossing. Such a scenario is further supported by the relatively small spin–orbit coupling of the S₁ and T₂ states in the Franck–Condon region, which does not indicate a very effective triplet bypass for this photoreaction. Therefore, we conclude that the triplet reaction channel in DAMN might not be as prominent as was previously thought.     

Vibronic Structures in Absorption and Fluorescence Spectra of Firefly Oxyluciferin in Aqueous Solutions

To elucidate the factors determining the spectral shapes and widths of the absorption and fluorescence spectra for keto and enol oxyluciferin and their conjugate bases in aqueous solutions, the intensities of vibronic transitions between their ground and first electronic excited states were calculated for the first time via estimation of the vibrational Franck–Condon factors. The major normal modes, overtones and combination tones in absorption and fluorescence spectra are similar for all species. The theoretical full widths at half maximum of absorption spectra are 0.4–0.7 eV and those for the fluorescence spectra are 0.4–0.5 eV, except for phenolate‐keto that exhibits exceptionally sharp peak widths due to the dominance of the 0–0′ or 0′–0 band. These spectral shapes and widths explain many relevant features of the experimentally observed spectra.