Condon Effects Research Articles

Simulating Vibronic Spectra without Born-Oppenheimer Surfaces.

We show how linear vibronic spectra in molecular systems can be simulated efficiently using first-principles approaches without relying on the explicit use of multiple Born–Oppenheimer potential energy surfaces. We demonstrate and analyze the performance of mean-field and beyond-mean-field dynamics techniques for the H2 molecule in one dimension, in the later case capturing the vibronic structure quite accurately, including quantum Franck–Condon effects. In a practical application of this methodology we simulate the absorption spectrum of benzene in full dimensionality using time-dependent density functional theory at the multitrajectory Ehrenfest level, finding good qualitative agreement with experiment and significant spectral reweighting compared to commonly used single-trajectory Ehrenfest dynamics. These results form the foundation for nonlinear spectral calculations and show promise for future application in capturing phenomena associated with vibronic coupling in more complex molecular and potentially condensed phase systems.

Modeling TADF in organic emitters requires a careful consideration of the environment and going beyond the Franck-Condon approximation.

The origin of the thermally-activated delayed fluorescence (TADF) of three organic emitters is investigated, focusing on the nature of the lowest excited states, their transition properties, as well as the role of the environment. For this purpose, the algebraic-diagrammatic construction for the polarization propagator at second order of perturbation theory [ADC(2)], time-dependent density-functional theory in the Tamm-Dancoff approximation (TDA) and unrestricted Kohn-Sham DFT in combination with the maximum-overlap method (ΔDFT) are employed. The influence of the dielectric environment is rigorously included using different variants of the polarizable continuum model. The calculations reveal the lowest excited singlet and triplet states of all studied emitters to be dominated by charge-transfer (CT) character already in the most apolar environment corresponding to cyclo-hexane. The dielectric stabilization entails a drastic reduction of the singlet-triplet gaps, increasing the calculated TADF rates by several orders of magnitude. Another ingredient for accurate TADF rates is hidden in the excited-state potential-energy surfaces along the donor-acceptor twisting angle. A presence of large, shallow plateaus in apolar environments causes the transition properties to be governed by thermal fluctuations rather than the minimum-energy geometries. This leads to a large increase of the oscillator strengths, as well as a breakdown of the Franck-Condon approximation. The last ingredient is a small but significant spin-orbit coupling (SOC) between the singlet and triplet CT states, which is traced back to a delocalization of the excitation hole or excited electron of the triplet CT state. Taking into account all of these effects, a reasonable agreement with experimental TADF and fluorescence lifetimes is obtained. For this, it proves to be sufficient to consider only the lowest lying singlet and triplet excited states.

Reactivity and properties of dications generated by photoionization of 2,5-norbornadiene

The production of C7Hn2+ (with n=6, 8) dications from 2,5-norbornadiene (NBD) and their reactivity toward Xe and N2 are studied using multipole-based tandem mass spectrometry techniques coupled with ionization either by collisions with energetic electrons or with tunable VUV photons coming from the SOLEIL synchrotron facility. From the photoionization studies, an apparent double photoionization energy of 2AE(NBD)=(22.80±0.08)eV is derived, while the appearance energy of the C7H62+ fragment is only slightly higher at (23.08±0.10)eV and the hydrogen-depleted dication dominates the mass spectrum at photon energies above about 24eV. Theoretical calculations predict the adiabatic 2IE(NBD) as about 1.26eV lower than the experimental value, which is attributed to the occurrence of significant Franck–Condon effects. Concerning the formation of C7H62+, theory and experiment indicate that the dehydrogenation product corresponds to the cycloheptatrienylidene dication, as is formed upon dissociative double ionization of previously studied C7H8 isomers (namely toluene and cycloheptatriene, CHT). The C7H62+ formation results from the overall exothermic rearrangement of NBD2+ into CHT2+ and thus only little extra energy is required to afford dehydrogenation. Further, the NBD2+/CHT2+ isomerization affects the reactivity of C7H82+ and C7H62+ dications toward Xe and N2, leading to the formation of the dications C7H6Xe2+ and C7H6N22+, respectively. The high efficiency of formation of the diazo dication C7H6N22+ suggests that reactions of organic dications with N2 may play an important role in the chemistry of nitrogen and hydrocarbon-rich atmospheres of planets and moons.

Mechanisms of Franck–Condon breakdown over a broad energy range in the valence photoionization of N2 and CO

The molecular photoionization of N2 leading to the 3σg−1, 2σu−1 ion states and CO leading to the valence isoelectronic 5σ−1, 4σ−1 ion states has been studied using both theory and experiment. Vibrational branching ratios have been obtained in the 15–200eV photoelectron energy range. The analysis of the branching ratios for these processes shows a breakdown in the Franck–Condon approximation in the range of energies studied. Some of the deviations at lower energies are well documented as due to shape resonances, and in such cases we found good agreement between the present work and previous experimental and theoretical investigations of these photoionization channels. For both N2 and CO ionization, we also found that the partial wave cross sections have an interference pattern similar to a Young-type interference, which are related to molecular Cooper minima. Such features were also seen to induce non-Franck–Condon effects in the vibrational branching ratios at higher energies. The comparison of theory and experiment was facilitated by the introduction of an electronic factor (F) that is the logarithmic derivative of the cross section with respect to bond length and which could be directly related to the branching ratios.

Energy Partitioning in Single-Electron Transfer Events between Gaseous Dications and Their Neutral Counterparts

Electron-transfer reactions between hydrocarbon dications and neutral hydrocarbons lead to an unequal deposition of the excess energy from the reaction in the pair of monocations formed. The initial observation of this phenomenon was explained by the different states accessible upon single-electron capture by a dication compared to single-electron ejection from a neutral compound. Alternatively, however, isomeric structures of the dicationic species, pronounced Franck-Condon effects, as well as excess energy in the dicationic precursors could cause the asymmetric energy partitioning in such dication/neutral collisions. Here, the investigation of this phenomenon in an interdisciplinary cooperation is described, shedding light not only upon a possible solution of the problem at hand, but also providing an example for the synergistic benefits of international research networks applying complementary approaches.

ChemInform Abstract: The Energy of N2H2 and Related Compounds

Ab initio molecular orbital theory at the G2 level has been used to study the energy of N2H2 and related compounds. Overall, the agreement between theory and experiment is good. The G2 enthalpy of formation ΔH0f0(N2H2) of 49.6 kcal/mol supports the experimental estimate of ≥46.6 kcal/mol derived by Ruscic and Berkowitz [J. Chem. Phys. 95, xxx4 (1991)] in a recent photoionization study. Predicted dissociation energies are D0(HN■NH)=122.8 kcal/mol, D0(HNNH–H)=43.6 kcal/mol, and D0(H2N■NH–H)=82.1 kcal/mol. The G2 value for the proton affinity (PA) of N2 at 298 K is PA298=118.1 kcal/mol. The G2 ionization potential of N2H3 of 7.54 eV is in agreement with the new value of ≤7.61 eV reported by Ruscic and Berkowitz. The G2 results for the ionization potential of N2H4 and the appearance potential of N+2 from N2H2 are in disagreement with experimental results suggesting that detection of the origins in these cases are thwarted by large geometry changes and significant Franck–Condon effects.

Lattice coupling and Franck–Condon effects in K-edge resonant inelastic x-ray scattering

In this paper, we discuss our recent Cu K-edge resonant inelastic x-ray scattering (RIXS) results for CuB2O4, a model system consisting of electronically isolated CuO4 plaquettes, which exhibits anomalies in the incident photon energy dependence that are not captured by electron-only models. We show that these anomalous features can be qualitatively described by extending the electron-only considerations to include the lattice degrees of freedom. Our findings have important general implications for the interpretation of K-edge RIXS results for electronically higher-dimensional transition metal oxides.

Spectral distributions of vibrational excitations accompanying 1s shell photoionization in small molecules

Distribution of vibrational excitations accompanying inner-shell ionization in small molecules is investigated. Within the vibrationally dependent-fixed-nuclei and the harmonic oscillator models the distribution is presented as a product of the Franck–Condon distribution and the interferential factor. It is shown that this factor varies strongly in the shape resonance vicinity and oscillates far above the core-ionization threshold. Analytical relationships between the spectral distributions and the potential functions of initial and final molecular states as well as intramolecular interference of scattered photoelectron waves are obtained and applied for the description of C 1s ionization in CO. The extended oscillations of the intensity ratio of vibrational components v′ = 0 and v′ = 1 of C 1s photoelectron spectrum of CO far above the threshold are discussed in more detail. The non-Franck–Condon, chemical and multi-electron effects on the distributions are also examined.

The vibronic effects in the 1 1B 2 and 2 1A 1 states of 1,3-dicyanomethylene croconate dianion: The resonance Raman study in terms of CASSCF and DFT methods

Franck–Condon (FC) and vibronic coupling effects in the excited 1 1B 2 and 2 1A 1 states of the 1,3-dicyanomethylene croconate (LD) dianion are studied using CASSCF and B3LYP methods on the aug-cc-pVDZ basis set level. The study concerns with the resonance Raman spectra measured for the laser excitation energies corresponding to the low-energy 1 1A 1 → 1 1B 2 and 1 1A 1 → 2 1A 1 transitions in the LD dianion absorption. It is shown that the main features of the empirical Raman spectra are clearly due to FC effect in the 1 1B 2 and 2 1A 1 states. We argue that certain features, like these observed at 495 cm −1 and 760 cm −1 may represent fundamentals of b 2-symmetry modes enhanced because of vibronic coupling between 1 1B 2 and 2 1A 1.

Electron Super-Rich Radicals in the Gas Phase. A Neutralization−Reionization Mass Spectrometric and ab Initio/RRKM Study of Diaminohydroxymethyl and Triaminomethyl Radicals

Diaminohydroxymethyl (1) and triaminomethyl (2) radicals were generated by femtosecond collisional electron transfer to their corresponding cations (1+ and 2+, respectively) and characterized by neutralization-reionization mass spectrometry and ab initio/RRKM calculations at correlated levels of theory up to CCSD(T)/aug-cc-pVTZ. Ion 1+ was generated by gas-phase protonation of urea which was predicted to occur preferentially at the carbonyl oxygen with the 298 K proton affinity that was calculated as PA = 875 kJ mol-1. Upon formation, radical 1 gains vibrational excitation through Franck-Condon effects and rapidly dissociates by loss of a hydrogen atom, so that no survivor ions are observed after reionization. Two conformers of 1, syn-1 and anti-1, were found computationally as local energy minima that interconverted rapidly by inversion at one of the amine groups with a <7 kJ mol-1 barrier. The lowest energy dissociation of radical 1 was loss of the hydroxyl hydrogen atom from anti-1 with ETS = 65 kJ mol-1. The other dissociation pathways of 1 were a hydroxyl hydrogen migration to an amine group followed by dissociation to H2N-C=O* and NH3. Ion 2+ was generated by protonation of gas-phase guanidine with a PA = 985 kJ mol-1. Electron transfer to 2+ was accompanied by large Franck-Condon effects that caused complete dissociation of radical 2 by loss of an H atom on the experimental time scale of 4 mus. Radicals 1 and 2 were calculated to have extremely low ionization energies, 4.75 and 4.29 eV, respectively, which belong to the lowest among organic molecules and bracket the ionization energy of atomic potassium (4.34 eV). The stabilities of amino group containing methyl radicals, *CH2NH2, *CH(NH2)2, and 2, were calculated from isodesmic hydrogen atom exchange with methane. The pi-donating NH2 groups were found to increase the stability of the substituted methyl radicals, but the stabilities did not correlate with the radical ionization energies.

Electron-Rich Radicals by Neutralization—Reionization Mass Spectrometry. Generation, Dissociations and Energetics of the Hydrogen Atom Adduct to Acetamide

Protonated acetamide exists as two planar conformers, the more stable anti-form (anti-1(+)) and the syn-form (syn-1(+)), DeltaG(degree) (298) (anti-->syn) = 10.8 kJ mol(-1). Collisional neutralization of 1(+) produces 1-hydroxy-1-amino-1-ethyl radicals (anti-1 and syn-1) which in part survive for 3.7 micros. The major dissociation of 1 is loss of the hydroxyl hydrogen atom (approximately 95%) which is accompanied by loss of one of the methyl hydrogen atoms (approximately 3%) and loss of the methyl group (approximately 2%). The most favorable dissociation of the OH bond is calculated to be only 34 kJ mol(1) endothermic but requires 88 kJ mol(-1) in the transition state. Other dissociations of 1, e.g., loss of one of the amide hydrogens, methyl hydrogens, and loss of ammonia are calculated to proceed through higher- energy transition states and are not kinetically competitive if proceeding from the ground doublet electronic state of 1. The unimolecular dissociation of 1 following collisional electron transfer is promoted by large Franck-Condon effects that result in 8090 kJ mol(-1) vibrational excitation in the radicals. Radicals 1 are calculated to exoergically abstract hydrogen atoms from acetamide in water, but not in the gas phase. The different reactivity is due to solvent effects that favor the products, (.)CH(2)CONH(2) and CH(3)CH(OH)NH(2), over the reactants.

Direct Observation of the Forbidden Hydrogen Atom Adduct to Acetonitrile: A Neutralization−Reionization Mass Spectrometric and CCSD(T) ab Initio/RRKM Study

Collisional neutralization of protonated acetonitrile (6+) generates (E)- and (Z)-1-azapropen-2-yl radicals, CH3C•N−H, (3 and 4, respectively) that represent the kinetically and thermodynamically forbidden adducts of hydrogen atoms to acetonitrile. Radicals 3 and 4 are formed with an excess of internal energy due to Franck−Condon effects and rapidly dissociate by loss of the imine hydrogen atom, a methyl hydrogen, and by CH3---CN−H bond cleavage. The branching ratios for the loss of the imine hydrogen (H or D) and methyl group (CH3 or CD3) were determined for CH3C•N−H, CD3C•N−H, CH3C•N−D, and CD3C•ND as 70/30, 66/34, 43/57, and 61/39, respectively. Ab initio calculations with coupled clusters with single, double, and perturbative triple excitations/aug-cc-pVTZ predict the loss of the imine hydrogen from 4 to have the lowest transition-state energy. The calculated branching ratios that were based on Rice−Ramsperger−Kassel−Marcus (RRKM) unimolecular rate constants agreed with the mass spectrometric data wit...

The Franck–Condon and Dushinsky effects in the lowest energy 1 2B 3u doublet of the tetracyanoquinodimethane (TCNQ) monoanion: the absorption and resonance Raman studies in terms of the density functional theory (DFT) and complete active space self-consistent field (CASSCF) methods

The absorption and resonance Raman excitation profiles of ν 4=1389 and ν 5=1195 cm −1 fundamentals are studied in the excitation region corresponding to the 1 2 B 2 g →1 2 B 3 u transition in the tetracyanoquinodimethane (TCNQ) monoanion. Both Franck–Condon (FC) and mode-mixing (Dushinsky) effects in the 1 2 B 3 u electronic state are considered. These effects are discussed in terms of B3LYP and CASSCF methods. It is shown that both absorption and excitation profiles discussed in the 1 2 B 2 g →1 2 B 3 u excitation region are in excellent agreement with those available from the experiment. The computations confirm D 2h symmetry of the TCNQ − molecule in its lowest energy 1 2 B 3 u doublet. On the other hand in at least one of two states 2 2 B 3 u or 1 2 A u , the computations suggest that the symmetry of TCNQ monoanion is unstable being reduced from the D 2h to the C 2h symmetry.

Effect of medium relaxation on the acidity constants of electronically excited states obtained by the Förster cycle method

The theoretical basis for the calculation of acid dissociation constants in the lowest excited singlet or triplet state of organic compounds has been reexamined in light of a recent study on solvatochromism. A mathematical analysis based on the Onsager cavity model reveals that the absorption or emission frequency of an acid and its conjugate base, as they appear in the Förster equation, should be replaced with the averages of absorption and emission frequencies corresponding to the 0–0 transition of acid and base, respectively, in order to account for Franck–Condon effects on the free energy balance. The free energy of spontaneous medium relaxation is found to be the same for absorption and emission, and proportional to one-half of the Stokes shift. The main premise of the proposed method, besides the obvious requirement that both the acid and its conjugate base should fluoresce or phosphoresce, is that each excited state exists long enough for equilibrium with the medium to be established prior to emission.

Autoionisation of superexcited states in N 2 to the N 2+ B state

Vibrationally resolved N 2 + (B–X) (1–2) and (0–1) emission bands were recorded after photoexcitation of N 2 in the 20–46 eV energy range. The branching ratio between these transitions reveals strong non-Franck–Condon effects. Ab initio calculations using a configuration interaction method based on Kohn–Sham orbitals indicate that the autoionisation of certain superexcited states is responsible for some structures present in the branching ratio curve.

Hydrogen Atom Adducts to the Amide Bond. Generation and Energetics of Amide Radicals in the Gas Phase

The 1-hydroxy-1-(N-methyl)aminoethyl radical (1) represents a simple model system for hydrogen atom adducts to the amide bond in gas-phase peptide and protein ions relevant to electron capture dissociation (ECD). Radical 1 was generated in the rarefied gas phase by femtosecond electron transfer to the stable cation prepared by selective O-protonation of N-methylacetamide. The main dissociations of 1 were loss of the hydroxyl hydrogen atom and the N-methyl group in a 1.7:1 ratio, as deduced from product analysis and deuterium labeling. The dissociations that occur on the 4.1 microsecond time scale are driven by large Franck−Condon effects on collisional electron transfer that deposit 93−103 kJ mol-1 in the nascent radicals. Detailed analysis of the potential energy surface for dissociations of 1 revealed several conformers and isomeric transition states for dissociations of the O−H and N−CH3 bonds. The experimental branching ratio is in quantitative agreement with RRKM calculations within the accuracy of t...

Theoretical ab initio study of the water trimer anion: Ground and excited state

The ground and excited state of the water trimer anion, (H2O)3−, are studied via high-level ab initio calculations. A systematic search for the stable (H2O)3− configuration is carried out, based on the configuration formed by the stable (H2O)2− plus one additional water molecule. Four isomers, including three surface structures and one interior structure, are located on the (H2O)3− potential energy surface. While the linear chainlike structure is determined to be the major species detected in supersonic expansion experiments, consistent with previous theoretical studies, the other three isomers may also exist in molecular beams as evidenced by the matches of their vertical detachment energies with high-energy shoulders observed in photoelectron spectra. A significant geometric distortion of water molecules directly interacting with the excess electron indicates that the Franck–Condon effects are the major cause for the experimental observation of the excitation of water vibrational modes upon the photodetachment of (H2O)3−. This is in contrast to the vibronic effects for the case of (H2O)2−. In addition, the excited states of (H2O)3− are also investigated. The results show the existence of electronically bound excited states in surface structures of (H2O)3−. These states possess considerable p character, and therefore, can be regarded as a precursor of three p-like excited states of bulk hydrated electrons.

Non Franck–Condon effects in the photoionization of molecular nitrogen to the [formula omitted] state in the 19–34 eV photon energy region

Photoionization to the N 2 + A 2Π u state is studied using photoelectron spectroscopy. Experimentally, vibrational branching ratios for the v ′=0–3 levels obtained for the first time in the 20–34 eV region, show strong non Franck–Condon effects around 22 eV. Using ab initio many body perturbation theory, branching ratios for ionization to the A 2Π u state are calculated. This study indicates that the Franck–Condon breakdown in the photoionization of the N 2 1π u electron is due to autoionization from Rydberg and valence states of N 2.

Non Franck–Condon effects in the photoionization of molecular oxygen to the [formula omitted] state in the 19–31 eV photon energy region

Photoionization to the O 2 + X 2Π g state is studied using photoelectron spectroscopy. Experimentally, vibrational branching ratios for the v=0 to 3 levels are obtained in the 19–31 eV region which show strong non Franck–Condon effects. Using ab initio many body perturbation theory branching ratios, vibrationally resolved partial cross-sections and total cross-section for ionization to the X 2Π g state are calculated. Molecular states which autoionize to the O 2 + X 2Π g state continuum are discussed. Photoionization of the O 2 π g electron is not fully explained by channel coupling effects and autoionization from known Rydberg series and valence states.

Protonation sites in methyl nitrate and the formation of transient CH 4NO 3 radicals. a neutralization–reionization mass spectrometric and computational study

Protonation sites in methyl nitrate ( 1) were evaluated computationally at the Gaussian 2(MP2) level of ab initio theory. The methoxy oxygen was the most basic site that had a calculated proton affinity of PA = 728–738 kJ mol −1 depending on the optimization method used to calculate the equilibrium geometry of the CH 3O(H)–NO 2 + ion ( 2 +). Protonation at the terminal oxygen atoms in methyl nitrate was less exothermic; the calculated proton affinities were 725, 722, and 712 kJ mol −1 for the formation of the syn–syn, anti–syn, and syn–anti ion rotamers 3a +, 3b +, and 3c +, respectively. Ion 2 + was prepared by an ion–molecule reaction of NO 2 + with methanol and used to generate the transient CH 3O(H)–NO 2 · radical ( 2) by femtosecond collisional electron transfer. Exothermic protonation of 1 produced a mixture of 3a +– 3c + with 2 + that was used to generate transient radicals 3a– 3c. Radical 2 was found to be unbound and dissociated without barrier to methanol and NO 2. Radicals 3a– 3c were calculated to be weakly bound. When formed by vertical neutralization, 3a– 3c dissociated completely on the 4.2 μs time scale of the experiment. The main dissociations of 3a– 3c were formations of CH 3O · + HONO and CH 3ONO + OH ·. The gas-phase chemistry of radicals 3a– 3c and their dissociation products, as studied by neutralization–reionization mass spectrometry, was dominated by Franck–Condon effects on collisional neutralization and reionization. The adiabatic ionization energies of 3a– 3c were calculated as 7.54, 7.57, and 7.66 eV, respectively.