Franck-Condon Analyses Research Articles

Geometries and molecular properties of phosphaethyne cations

Franck-Condon analyses were carried out on vibrational intensity distributions of the first two photoelectron bands of phosphaethyne (HCP). The CH and CP bond lengths of HCP + were found to be respectively 1.073 Å and 1.600 A in the X 2π state and 1.077 Å and 1.572 Å in the A 2Σ + state. The calculated structural parameters were compared with those from experimental work and molecular orbital calculations. In addition, force constants for the first two lowest energy ionic states were determined from observed vibrational frequencies. Bonding properties of the ions are discussed in the light of the molecular parameters obtained.

Determination of geometries and molecular properties of XCN + ions (where X is Cl, Br, I) through Franck—Condon analyses on the corresponding photoelectron spectra

Vibrational intensity calculations were carried out on photoelectron spectra of ClCN, BrCN and ICN to deduce ionic geometries of ClCN and BrCN in the X 2π, A 2Σ +, and B 2π states and ICN in the X 2π states. Results obtained are comapred with the experimental values and with those obtained by other workers. Force constants are also obtained for these ions through normal coordinate analyses on the observed ionic frequencies. The calculated data provide information on changes in structural and bonding properties of the XCN molecules upon ionization.

Calculation of time autocorrelation and spectral functions using locally expanded potentials

We present theory for autocorrelation and spectral functions and for the description of molecular motions on a multidimensional potential energy surface. The basic idea is to express the autocorrelation functions by stepwise series expansions of the molecular surface using only local information. This approach thus presents one way to avoid the dimensionality catastrophe that is associated with dynamic studies using globally calculated and fitted polyatomic energy surfaces. The autocorrelation function is obtained by solving the quantum equations of motions in a set of locally defined internal coordinates uncoupled to rotation and translation. A Fourier transform of the autocorrelation function gives a time-evolved interpretation of the formation of the vibronic spectrum. Locally expanded and quadratically approximated Hamiltonians are assumed throughout the reaction path. The formalism implements in a direct fashion the information obtained from molecular gradient and Hessian techniques, so that the buildup of the spectrum can be followed along with the reaction walks on the molecular hypersurface. The method applies to unbound or quasi-bound as well as to bound potentials. In the latter case, the calculation of the autocorrelation function also provides a cost-effective way to perform Franck–Condon analyses, since, in contrast to conventional Franck–Condon methods, it avoids sum-over-state and basisset procedures completely. A set of 3N – 6 Cartesian coordinates are analyzed for the purpose of translational and rotational-free walks on a locally and quadratically expanded multidimensional potential energy surface without recoursing to the standard Eckart conditions and/or the necessity of performing supplementary transformations on the gradient vector and the Hessian matrix. Demonstrations of the formalism are given by calculations of time autocorrelation and spectral functions using locally expanded potentials corresponding to N22IIu and O22IIg photoionization.

Photoelectron spectroscopy of group IV heavy metal dimers: Sn−2, Pb−2, and SnPb−

Negative ion photoelectron spectra of Sn−2, SnPb−, and Pb−2 are presented for electron binding energies up to 3.35 eV. Each spectrum exhibits multiple electronic bands, most of which contain resolved vibrational structure. Franck-Condon analyses yield spectroscopic parameters (re, ωe, and Te) for the anion ground states and the neutral excited states. Adiabatic electron affinities are determined to be: EA(Sn2)=1.962±0.010 eV, EA(Pb2)=1.366±0.010 eV, and EA(SnPb)=1.569±0.008 eV. The anion dissociation energies D0(Sn−2) and D0(Pb−2) are derived from the electron affinities and the neutral dissociation energies. For SnPb−, the dissociation energy difference D0(SnPb−)−D0(SnPb) is precisely measured. Based on the present data, previous experiments and ab initio calculations, we assign most of the observed bands to the corresponding neutral low-lying electronic states.

A study of the electronic structures of Pd−2 and Pd2 by photoelectron spectroscopy

The ultraviolet negative ion photoelectron spectrum of Pd−2 is presented for electron binding energies up to 3.35 eV. The anion is prepared by sputtering in a flowing afterglow ion source. Multiple low-lying electronic states of Pd2, all unidentified previously, are observed with resolved vibrational structure. The spectrum shows two strong electronic bands, each with similar vibrational progressions. Franck–Condon analyses are carried out on the two transitions and molecular constants are extracted for the anion and the two neutral electronic states. With the help of simple molecular orbital arguments and ab initio calculations, these two electronic bands are assigned as the triplet ground state (3Σ+u) and a singlet excited state (1Σ+u). The adiabatic electron affinity is E.A.(Pd2)=1.685±0.008 eV and the singlet excitation energy T0(1Σ+u) is 0.497±0.008 eV (4008±65 cm−1 ). The bonding in the palladium dimers is discussed and we find that the anion bond strength is 1.123±0.013 eV stronger than that of the neutral. Related studies of Pd− yield an improved electron affinity of E.A.(Pd)=0.562±0.005 eV.

The ultraviolet photoelectron spectrum of SO−

The ultraviolet photoelectron spectrum (hν=3.531 eV) of SO− shows transitions to the three lowest lying electronic states of SO neutral. The electron affinity of SO was determined to be 1.125(5) eV. The harmonic vibrational frequency and the spin-orbit splitting of the SO− electronic ground state (2Π) were also determined. Franck–Condon analyses of the SO vibrational progressions were used in conjunction with the molecular constants of the well-characterized SO neutral molecule to determine the equilibrium bond length of SO− [re=1.570(5) Å].

Ionic geometries of acetylene in the X 2Π u and B 2Σ u+ ionic states

Franck-Condon analyses are applied to the high-resolution photoelectron spectra of C 2H 2 and C 2D 2. From the first photoelectron bands, the CH and CC bond lengths are found to be respectively 1.076 and 1.250 Å for C 2H 2 + and 1.080 and 1.247 Å for C 2D 2 + in the X 2Π u state. Results obtained are compared with those by previous workers. As for the third photoelectron bands, simulated spectra of acetylenes agree well with observed ones. The CH and CC bond lengths thus deduced for the B 2Σ u + state have values of respectively 1.271 and 1.191 Å for C 2H 2 + and 1.276 and 1.178 Å for C 2D 2 +. The long CH bond length obtained for the acetylene ions is discussed.

Franck—Condon analyses on the first photoelectron bands of formaldehyde and its deuterated species

Abstract An iterative Franck—Condon analysis procedure was applied to a three-mode system to deduce ionic geometries of formaldehyde and its deuterated species upon X 2 B 2 ←X 1 A 1 ionization processes. The ionic geometries thus derived agree with one another and are parallel in signs with those predicted from changes in overlap populations and the nodal repulsive forces model. Furthermore, the calculated ionic geometries were found to be insensitive to the Duschinsky matrix relating to the two combining states.

An iterative franck-condon analysis procedure for the determination of ionic geometries for H 2O and H 2S

The pattern search optimization procedure is applied to a Franck-Condon analysis method with the use of the formulation proposed by Kupka and Cribb for evaluating vibrational overlap integrals [H. Kupka and P.H. Cribb, J. Chem. Phys., 85 (1986) 1303; H. Kupka and G. Olbrich, J. Chem. Phys., 80 (1985) 3163]. The method was applied to three different ionization processes accompanied by small to large changes in molecular geometry. It was found that ionic geometries thus deduced for transitions with small structural changes agree well with observation. However, the agreement is poor for transitions with large geometric changes although the method can still account for the observed vibrational intensity distributions to a certain extent. In addition, properties of the pattern search method as well as Kupka and Cribb's formulation for Franck-Condon analyses are discussed.

Validity of Franck—Condon analysis procedures for deduction of excited-state and ionic geometries: Part II. The X2B1 and A2A1 states of hydrogen oxide and hydrogen sulphur

The vibrational intensity distributions observed in the first two photoelectron bands of H 2O, D 2O and H 2S were adopted in studying the validity and limitations of different methods for carrying out Franck—Condon analyses. These methods include the generating function method, Coon et al.'s method, the Duschinsky matrix method and the two approximate methods involving the use of the vibrational quantum number with the maximum intensity as well as vertical and adiabatic ionization potentials within a progression. The geometries thus deduced for the H 2O + and H 2S + ions in the X 2 B 1 and A 2 A 1 states are in good agreement with observed values. Various criteria for the prediction of signs for changes in bond lengths and bond angles were discussed. Furthermore, the Badger's rule and the electrostatic force model were utilized to estimate quantitatively the changes in bond length on ionization.

ChemInform Abstract: The Geometry of Ethylene in the Ground Ionic State (Franck‐Condon analyses on the first photoelectron band).

Chemischer InformationsdienstVolume 17, Issue 11 Physical Organic Chemistry ChemInform Abstract: The Geometry of Ethylene in the Ground Ionic State (Franck-Condon analyses on the first photoelectron band). F. T. CHAU, F. T. CHAUSearch for more papers by this author F. T. CHAU, F. T. CHAUSearch for more papers by this author First published: March 18, 1986 https://doi.org/10.1002/chin.198611040AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume17, Issue11March 18, 1986 RelatedInformation

The geometry of ethylene in the ground ionic state

Franck—Condon analyses were carried out on the first photoelectron band of ethylene to deduce the CC bond length, the CH bond length and the HCH bond angle in the ground ionic state 1 B 3u|to be 1.42 ± 0.01 Å, 1.09 ± 0.01 Å and 120 ± 1° respectively. These structructural parameters have values close to those previously obtained in the 1 B 3u Rydberg state (see ref. 10). With regard to the vibrational energies of the torsional mode of ethylene and its deuterated species in the 2 B 3u and 1 B 3u Rydberg states, they were analysed by using a one-deminsional potential function constructed from the harmonic oscillator term perturbed by a Gaussian barrier. The equilibrium torsional angles of ethylene thus obtained are found to be 28° and 25°, respectively, in the 2 B 3u and 1 B 3u states. In addition, the observed vibrational intensity distributions of the torsional mode accompanying electronic transitions from the ground state to the two 2 B 3u and 1 B 3u states are well reproduced by the proposed potential. Moreover, it is found that these vibrational transition probabilities are sensitive to the magnitude of the barrier heights, the shape of the potentials and the frequency changes upon electronic transitions and thus should be useful in providing structural information about the molecules under study.