Condon Transition Research Articles

Low-lying Dipole Resonances in FeCN−: A Viable Formation Pathway for FeCN− in Space

A low-lying resonance in FeCN− anion was identified through abrupt changes in the spectral dependence of the photoelectron angular distribution. Non-Franck–Condon transitions from the resonance to the neutral FeCN (4Δ), and the corresponding photoelectron angular distributions revealed that the resonance is a dipole scattering state. Significant thermionic electron emission was observed in the resonant photoelectron spectra, indicating a strong coupling of the resonance with the ground state of this triatomic anion and its competition over autodetachment. This low-lying resonance is identified to be an efficient pathway for the formation of FeCN− anion in the outer envelope of IRC+10216. The results in general reveal formation pathways in space for anions with low-lying resonances and large permanent dipole moment.

On-the-Fly Ring-Polymer Molecular Dynamics Calculations of the Dissociative Photodetachment Process of the Oxalate Anion.

The dissociative photodetachment dynamics of the oxalate anion, C2O4H− + hν → CO2 + HOCO + e−, were theoretically studied using the on-the-fly path-integral and ring-polymer molecular dynamics methods, which can account for nuclear quantum effects at the density-functional theory level in order to compare with the recent experimental study using photoelectron–photofragment coincidence spectroscopy. To reduce computational time, the force acting on each bead of ring-polymer was approximately calculated from the first and second derivatives of the potential energy at the centroid position of the nuclei beads. We find that the calculated photoelectron spectrum qualitatively reproduces the experimental spectrum and that nuclear quantum effects are playing a role in determining spectral widths. The calculated coincidence spectrum is found to reasonably reproduce the experimental spectrum, indicating that a relatively large energy is partitioned into the relative kinetic energy between the CO2 and HOCO fragments. This is because photodetachment of the parent anion leads to Franck–Condon transition to the repulsive region of the neutral potential energy surface. We also find that the dissociation dynamics are slightly different between the two isomers of the C2O4H− anion with closed- and open-form structures.

Unspecified verticality of Franck-Condon transitions, absorption and emission spectra of cyanine dyes, and a classically inspired approximation.

The computed vertical energy, Ev,a/f, from the equilibrium geometry of the initial electronic state is frequently considered as representative of the experimental excitation/emission energy, Eabs/fl = hc/λmax. Application of the quantum mechanical version of the Franck–Condon principle does not involve precise specification of nuclear positions before, after, or during an electronic transition. Moreover, the duration of an electronic transition is not experimentally accessible in spectra with resolved vibrational structure. It is shown that computed vibronic spectra based on TDDFT methods and application of quantum mechanical FC analysis predict Eabs = hc/λmax with a 10-fold improvement in accuracy compared to Ev,a for nine cyanine dyes. It is argued that part of the reason for accuracy when this FC analysis is compared to experiment as opposed to Ev,a/f is the unspecified verticality of transitions in the context of the quantum version of the FC principle. Classical FC transitions that preserve nuclear kinetic energy before and after an electronic transition were previously found to occur at a weighted average of final and initial electronic state molecular geometries known as the r-centroid. Inspired by this approach a qualitative method using computed vertical and adiabatic energies and the harmonic approximation is developed and applied yielding a 5-fold improvement in accuracy compared to Ev,a. This improvement results from the dominance of low frequency vibronic transitions in the cyanine dye major band. The model gives insight into the nature of the redshift when qPCR dye EvaGreen is complexed to λDNA and is applicable to the low frequency band of similar non cyanine dyes such as curcumin. It is found that the computed vibronic cyanine dye spectra from time-dependent FC analysis at 0 K and 298 K show decreased intensity at higher temperature suggestive of increased intensity with restricted motion shown when cyanine dyes are used in biomedical imaging. A 2-layer ONIOM model of the DNA minor groove indicates restricted motion of the TC-1 dye excited state in this setting indicative of enhanced fluorescence.

Manifestation of Molecular Chromophore Polymorphism in Diffuse Vibronic Spectra

The location of the purely electronic 0–0-transition v0 for homomorphic chromophores is defined in the transition cross-section spectrum σ(ν) by the extremum (∂φ/∂v = 0) of the function [σ(ν)/ν] exp ((∓hv/2kT) = φ(|v − v0|) and "–" for absorption, ν < ν0 and "+" for emission) for the dipole Frank–Condon transition with thermal distribution among the initial-state sublevels. The observed effective cross section and spectrum with polymorphism are formed by partial contributions of electronic transitions of the separate species with different νi0. In this instance, the homomorphic extremum is distorted, i.e., broadened, weakened, or absent, which is also indicative of a polymorphic chromophore. Examples of these distortions of the functions calculated from the experimental spectra are given.

Evaluation of State-Resolved Reaction Probabilities and Their Application in Population Models for He, H, and H2

Population models are a prerequisite for performing qualitative analysis of population densities measured in plasmas or predicting the dependence of plasma emission on parameter variations. Models for atomic helium and hydrogen as well as molecular hydrogen in low-pressure plasmas are introduced. The cross-sections and transition probabilities used as input in the atomic models are known very accurately, and thus a benchmark of these models against experiments is very successful. For H2, in contrast, significant deviations exist between reaction probabilities taken from different literature sources. The reason for this is the more complex internal structure of molecules compared to atoms. Vibrationally resolved models are applied to demonstrate how these deviations affect the model results. Steps towards a consistent input data set are presented: vibrationally resolved Franck–Condon factors, transition probabilities, and ionization cross-sections have been calculated and are available now. Additionally, ro-vibrational models for selected transitions are applied successfully to low-density, low-temperature plasmas. For further improving the accuracy of population models for H2, however, it is necessary to establish a comprehensive data set for ro-vibrationally resolved excitation cross-sections based on the most recent calculation techniques.

Polaronic exciton in self-organized assemblies of protonated meso-tetraphenylporphine dimers and water at room temperature

Assemblies consisting of protonated meso-tetraphenylporphine (TPP) dimers and water have been investigated by UV–vis and infrared (IR) spectroscopy and by atomic force microscopy (AFM) in thin layers. Features of electronic absorption spectra of the assemblies are interpreted in terms of hole polaron combined with exciton theory using quantum well with parameters obtained from the dimer structure. It appears to be hole polaron moving defines kinetic energy of polaronic exciton confined in a quantum well when the electron absorbs photon. Hole polaron characteristics such as polaron self-energy, energy of Frank–Condon transitions, and radius of hole polaron moving through water are found to be 1.38 eV, 0.2445 eV, and 0.246 Å, respectively. A doublet at 1944, 1960 cm−1 (0.2412, 0.2432 eV) observed in IR spectra matches the energy of Frank–Condon transitions. Excitation energies estimated using molecular parameters for polaronic excitons in pure water and in the TPP dimers are found in a good agreement with the experimental data.

Hole polaron of small radius in assemblies of hydrated mono-protonated meso-tetraphenylporphine dimers at 77 K

Polaron theory is often used for the study of electrons and holes mobility in semiconductors when longitudinal optical (LO) phonons are generated upon the charge carriers moving. The polaron theory was applied to explain long-wavelength absorptions observed nearby Soret band in the electronic spectra of assemblies of mono-protonated meso-tetraphenylporphine dimer (TPP2H+) that are interpreted as LO-phonons originated due to proton movement. The energy of hole polaron is found to be 1.50eV at 77K. Energy of Franck–Condon transitions of LO-phonons generated by hole polaron moving through water confined in the assemblies with distortions of O–H bonds is 0.2653eV (2138cm−1). A broad band around 2127cm−1 corresponding the same energy of O–H bonds vibrations is observed in IR spectra of the assemblies consisting of water and mainly of TPP2H+ species in the solid state indicating the presence of similar distortions of the hydrogen bonds. The radius of protonic sphere of 0.202Å, which was estimated as a polaron quasiparticle moving through the confined water at 77K, is found in agreement with earlier evaluated one of 0.265Å that was obtained for proton diffusion at 298K in similar assemblies.

Transient dynamics in the Anderson–Holstein model with interfacial screening

We study the combined effects of electron---phonon coupling and dot-lead repulsion in the transport properties of the Anderson---Holstein model. We employ a recently proposed nonperturbative method to calculate the transient response of the system. By varying the initial conditions for the time propagation the current exhibits transient oscillations of different nature. We are able to disentangle two dynamical processes, namely the local charge rearrangement due to the dot-lead contacting and the establishment of the nonequilbrium many-body state due to the application of the external bias. These processes involve either Franck---Condon excitations or transitions between the resonant level and the Fermi energy of the leads.

The Lifshitz-Kosevich-Shoenberg theory of relativistic electronic gas in neutron stars

Similar to the de Haas-van Alphen magnetic oscillatory in some normal metals when the Landau quantization is predominant, the magnetic oscillation can also occur in highly degenerate and relativistic electron gas in neutron stars. At large Landau quantum number (Landau quantum number r≥2), we generalize the Lifshitz-Kosevich-Shoenberg theory in non-relativistic electron gas to relativistic gas. At small Landau quantum number (r<2), we expand the grand potential into Fourier series and get similar harmonic oscillatory formula of magnetization. These results indicate that magnetic phase transition similar as Condon transition observed in metals can appear in neutron stars when the differential susceptibility exceeds 1/4π.

Accurate spectroscopic calculations on the X2Σ +, A2Π, and 22Σ + electronic states of the BeAr+ cation including spin-orbit coupling

The complete active space self-consistent field/internally contracted multireference configuration interaction calculations with the correlation-consistent basis sets have been made to characterize all of the states of BeAr+ cation, which are attributed to the first two dissociation channels. The effect on the potential energy curves by Davidson correction, core-valence correlation, and scalar relativistic corrections is included. The spin-orbit coupling effect is taken into account by the state interaction method with the Breit–Pauli Hamiltonian. Our calculations can provide some useful guidelines for the future experimental work of band system 22[Formula: see text]+1/2-X2[Formula: see text]+1/2. For the first time, the transition properties including Franck−Condon factors and transition dipole moments have been derived for all of the Ω states. Some transition probabilities and radiative lifetimes have been estimated.

Theoretical study of ClH2− electron detachment spectroscopy revisited

Electron detachment spectroscopy of ClH2− and ClD2− is revisited in this paper. Franck–Condon transition from the ground vibrational level of the electronic ground state of the anion to the coupled electronic manifold of the neutral species is investigated by a time-dependent wave packet (WP) approach. Rich vibronic structures due to Cl…H2 continuum states at higher energies appeared in the photodetachment band in our previous study [Chem. Phys. Lett. 394 (2004) 207] are eliminated on improving the representation of the anionic wavefunction and the WP propagation algorithm. The theoretical findings are compared with the available experimental and theoretical results.

Theoretical study of potential energy curves, spectroscopic constants, and radiative lifetimes of low-lying states in an SeO molecule

The low-lying potential energy curves of the SeO molecule are computed by means of an ab initio multireference configuration interaction technique, taking into account relativistic (scalar plus spin—orbit coupling) effects. The spectroscopic constants of Ω states for X3Σ−, a1Δ, b1Σ+, A3Π, A′3Δ, and A″ 3Σ+ states are obtained, and they are in good accordance with available experimental values. The Franck—Condon factors and transition dipole moments to the ground state are computed, and the natural radiative lifetimes of low-lying Ω states are theoretically obtained. Comparisons of the natural lifetimes of Ω states with previous experimental results and those of isovalent TeO molecule are made.

Coherent state-based generating function approach for Franck–Condon transitions and beyond

One-photon and multi-photon absorption, spontaneous and stimulated photon emission, resonance Raman scattering and electron transfer are important molecular processes that commonly involve combined vibrational-electronic (vibronic) transitions. The corresponding vibronic transition profiles in the energy domain are usually determined by Franck-Condon factors (FCFs), the squared norm of overlap integrals between vibrational wavefunctions of different electronic states. FC profiles are typically highly congested for large molecular systems and the spectra usually become not well-resolvable at elevated temperatures. The (theoretical) analyses of such spectra are even more difficult when vibrational mode mixing (Duschinsky) effects are significant, because contributions from different modes are in general not separable, even within the harmonic approximation. A few decades ago Doktorov, Malkin and Man'ko [1979 J. Mol. Spectrosc. 77, 178] developed a coherent state-based generating function approach and exploited the dynamical symmetry of vibrational Hamiltonians for the Duschinsky relation to describe FC transitions at zero Kelvin. Recently, the present authors extended the method to incorporate thermal, single vibronic level, non-Condon and multi-photon effects in energy, time and probability density domains for the efficient calculation and interpretation of vibronic spectra. Herein, recent developments and corresponding generating functions are presented for single vibronic levels related to fluorescence, resonance Raman scattering and anharmonic transition.

Solvent effect on the UV/Vis absorption spectra in aqueous solution: The nonequilibrium polarization with an explicit representation of the solvent environment

An explicit solvation model was presented in this work to estimate the solvent effect on the UV/Vis absorption spectra in aqueous solution. Different from others’ concern, we concentrate on the establishment of proper electrostatic solvation energy formula for nonequilibrium polarization in explicit solvent model with adopting the constrained equilibrium approach, which was originally proposed by Leontovich and firstly introduced by us to cope with the nonequilibrium solvation problem. The formulation of this model was deduced entirely based on the explicit representation of the solvent surrounding with discrete dipoles and polarizability for each solvent molecule. The external field, applied to construct the virtual constrained equilibrium state, can be expressed by the physical quantities before and after the Franck–Condon transition. The newly established solvation energy formulation for nonequilibrium was implemented under the popular QM/MM strategy with modifying the nonequilibrium module in the averaged solvent electrostatic potential/molecular dynamics program to carry out numerical calculations. The new codes were further utilized to study the solvatochromic shift of the n → π ∗ transition in formaldehyde in aqueous solution. Different contributions to the total solvent shift were analyzed and the main component comes from the electrostatic interaction between the solute and solvent and the solvent polarization also has a significant influence. The solute molecule properties and the microscopic solvent structure were also discussed to uncover more details.

Franck–Condon factors for molecule–ion reactions of [formula omitted] and its isotopomers

An existing, systematic, fundamental database of Franck–Condon factors and transition probabilities for all isotopomers of the hydrogen molecule (H 2, D 2, T 2, HD, HT, and DT) has been extended for reactions which connect the molecule with its ion H 2 + ( v ) (or the corresponding ion of the specific isotopomer). The most recent Born–Oppenheimer potential curves were used to calculate the vibrational eigenvalues and eigenfunctions, from which the Franck–Condon factors were obtained by convolution. The accuracy of the results has been assessed and a comparison with results available in the literature was performed.

Dissociative Double Ionization of CO2: Dynamics, Energy Levels, and Lifetime

In a kinematically complete experiment on the dissociative double ionization of CO2 by electron impact, spontaneous and metastable decay have been observed via the channel CO2(2+) --> CO+ + O+. The metastable decay shows a lifetime of 5.8 +/- 1.5 micros. The measured kinetic energy release spectrum of the dissociation shows one broad peak. To understand the observed features, ab initio potential energy surface (PES) for the ground electronic state of CO2(2+) was computed using a multireference configuration interaction method and a correlation-consistent polarized-valence quadruple-zeta basis set, for a range of internuclear distances and O-C-O bond angles, and an analytic fit of the PES was obtained. The computed PES clearly indicates the metastability of the dication and yields a barrier height and an asymptotic limit in fair agreement with the reported data. A time-dependent quantum mechanical approach was used to compute the ground vibrational state wave function of CO2 in its ground electronic state. Assuming a Franck-Condon transition, the same function was taken to be the initial wave function at time t = 0 for the time evolution on the fitted PES for the ground electronic state of CO2(2+). The autocorrelation function was computed and Fourier transformed to obtain the excitation spectrum. Upon convolution with the instrument resolution function, the kinetic energy release spectrum was obtained, in good agreement with the experimental results, particularly at lower energies. The discrepancies at higher energies are attributed to the noninclusion of the excited states of CO2(2+) in the dynamical study.

RESONANCES IN H+HLi SCATTERING FOR NONZERO TOTAL ANGULAR MOMENTUM (J &gt; 0): A TIME-DEPENDENT WAVE PACKET APPROACH

The resonances in H + HLi scattering for nonzero total angular momentum (J &gt; 0) are examined here by a time-dependent wave packet approach employing an ab initio potential energy surface (PES) [Dunne LJ, Murrell JN, Jemmer P, Chem Phys Lett336: 1, 2001] of the system. The resonances are identified by calculating a set of pseudospectra corresponding to the Franck–Condon transition of a hypothetical initial state to the interaction region of the H + HLi PES. The resonances are characterized by calculating their eigenfunctions and linewidth lifetimes. The resonances for J ≠ 0 are discussed in relation to their counterpart for J = 0. The effect of Coriolis coupling on the resonances obtained from the centrifugal sudden approximation for J = 2 and for K = 0,1,2 is examined.

Tailoring model Hamiltonians for dihalogen—rare gas matrix problems

A strategy for reducing the number of electronic states which need to be incorporated into a diatomics-in-molecules description of prototypical condensed phase processes is demonstrated. The selection of a problem-adapted representation is based on symmetry properties of the molecular basis set and its disturbance by the external potential due to the environment. Using the \({B \leftarrow X}\) excitation of Br2 in solid Argon as an example, we show that the energy range accessible via a Franck–Condon transition can approximately be described by 17 instead of all 36 valence states. The approach shall be particularly useful for reducing the numerical effort of semiclassical and quantum dynamics simulations.

Franck–Condon factors, transition probabilities, and radiative lifetimes for hydrogen molecules and their isotopomeres

A systematic fundamental molecular database for all isotopomeres of the hydrogen molecule (H 2, D 2, T 2, HD, HT, DT) is calculated on the basis of the latest Born–Oppenheimer potential curves and the latest electronic dipole transition moments of hydrogen molecules. Vibrational eigenvalues, Franck–Condon factors, and vibrationally resolved transition probabilities are presented for electronic transitions in each multiplet system up to principal quantum number n = 4. Radiative lifetimes of the vibrational levels in the electronically excited states are obtained from the summation over the optically allowed transitions. In a similar manner, effective transition probabilities and effective radiative lifetimes of electronically excited states are determined assuming that only the lowest vibrational level in the ground state is populated, i.e. the data are directly applicable to molecular gases. Differences between the isotopomeres are discussed briefly.

Real-time observation of vibrational revival in the fastest molecular system

After preparing a coherent vibrational wave packet in the hydrogen molecular ion by ionizing neutral H 2 molecules with a 6.5 fs, 760 nm laser pulse at 3 × 10 14 W/cm 2, we map its spatio-temporal evolution by the fragmentation induced with a second 6.5 fs laser pulse of doubled intensity. In this proof-of-principle experiment, we visualize the oscillations of this most fundamental molecular system, observe a dephasing of the vibrational wave packet and its subsequent revival. Whereas the experimental data exhibit an overall qualitative agreement with the results of a simple numerical simulation, noticeable discrepancy is found in the characteristic revival time. The most likely reasons for this disagreement originate from the simplifications used in the theoretical model, which assumes a Franck–Condon transition induced by the pump pulse with subsequent field-free propagation of the H 2 + vibrational wave packet, and neglects the influence of the rotational motion.