A Theory of Intensity Distribution in Band Systems

Condon, E. U.

doi:10.1103/physrev.28.1182

Cited by 550 publications

(290 citation statements)

References 17 publications

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“…The energy calculations carried out up to fourth order led to the complete decoupling of vibrational, rotational and electronic motion and allowed to obtain expressions for the eigenfunctions and the transition intensities (at the zeroth order approximation) that completely agreed with previous findings by Franck (Franck, 1925) and Condon (Condon, 1926;Condon, 1927a;Condon 1927b). Instead, possible couplings between the three basic types of motion had to be introduced only as effects higher than fourth order (and with the inclusion of all degeneracies of the electronic motion), which were not considered by Born and Oppenheimer. A general quantitative theory (Born & Oppenheimer, 1927) was, then, developed, which allowed to classify rotational, vibrational and electronic terms in a molecule with N-atoms.…”

Section: Variational Approachsupporting

confidence: 78%

The Genesis of the Quantum Theory of the Chemical Bond

Esposito¹,

Naddeo²

2014

AHS

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An historical overview is given of the relevant steps that allowed the genesis of the quantum theory of the chemical bond, starting from the appearance of the new quantum mechanics and following later developments till approximately 1931. General ideas and some important details are discussed concerning molecular spectroscopy, as well as quantum computations for simple molecular systems performed within perturbative and variational approaches, for which the BornOppenheimer method provided a quantitative theory accounting for rotational, vibrational and electronic states. The novel concepts introduced by the Heitler-London theory, complemented by those underlying the method of the molecular orbitals, are critically analyzed along with some of their relevant applications. Further improvements in the understanding of the nature of the chemical bond are also considered, including the ideas of one-electron and three-electron bonds introduced by Pauling, as well as the generalizations of the Heitler-London theory firstly performed by Majorana, which allowed the presence of ionic structures into homopolar compounds and provided the theoretical proof of the stability of the helium molecular ion. The study of intermolecular interactions, as developed by London, is finally examined.

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Section: Variational Approachsupporting

confidence: 78%

The Genesis of the Quantum Theory of the Chemical Bond

Esposito¹,

Naddeo²

2014

AHS

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“…The original formalism only considered a harmonic oscillator solution. The R represents the nuclear interdistance, n is the vibrational quantum number of the excited state, and n ′ is the quantum number of the ground state, 21,47 C(n, n…”

Section: Theoretical and Computational Methodsmentioning

confidence: 99%

Ground and excited states of zinc phthalocyanine, zinc tetrabenzoporphyrin, and azaporphyrin analogs using DFT and TDDFT with Franck-Condon analysis

Theisen

Huang

Fleetham

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested inGround and excited states of zinc phthalocyanine, zinc tetrabenzoporphyrin, and azaporphyrin analogs using DFT and TDDFT with Franck-Condon analysis The electronic structure of eight zinc-centered porphyrin macrocyclic molecules are investigated using density functional theory for ground-state properties, time-dependent density functional theory (TDDFT) for excited states, and Franck-Condon (FC) analysis for further characterization of the UV-vis spectrum. Symmetry breaking was utilized to find the lowest energy of the excited states for many states in the spectra. To confirm the theoretical modeling, the spectroscopic result from zinc phthalocyanine (ZnPc) is used to compare to the TDDFT and FC result. After confirmation of the modeling, five more planar molecules are investigated: zinc tetrabenzoporphyrin (ZnTBP), zinc tetrabenzomonoazaporphyrin (ZnTBMAP), zinc tetrabenzocisdiazaporphyrin (ZnTBcisDAP), zinc tetrabenzotransdiazaporphyrin (ZnTBtransDAP), and zinc tetrabenzotriazaporphyrin (ZnTBTrAP). The two latter molecules are then compared to their phenylated sister molecules: zinc monophenyltetrabenzotriazaporphyrin (ZnMPTBTrAP) and zinc diphenyltetrabenzotransdiazaporphyrin (ZnDPTBtransDAP). The spectroscopic results from the synthesis of ZnMPTBTrAP and ZnDPTBtransDAP are then compared to their theoretical models and nonphenylated pairs. While the Franck-Condon results were not as illuminating for every B-band, the Q-band results were successful in all eight molecules, with a considerable amount of spectral analysis in the range of interest between 300 and 750 nm. The π-π * transitions are evident in the results for all of the Q bands, while satellite vibrations are also visible in the spectra. In particular, this investigation finds that, while ZnPc has a D 4h symmetry at ground state, a C 4v symmetry is predicted in the excited-state Q band region. The theoretical results for ZnPc found an excitation energy at the Q-band 0-0 transition of 1.88 eV in vacuum, which is in remarkable agreement with published gas-phase spectroscopy, as well as our own results of ZnPc in solution with Tetrahydrofuran that are provided in this paper. C 2015 AIP Publishing LLC. [http://dx

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“…Franck-Condon factors (FCF) and Franck-Condon densities (FCD) describe the overlap of two vibrational wave functions in a molecule [20,21]. In the Franck-Condon approximation, the internuclear distance is considered to be fixed during an electronic transition.…”

Section: Franck-condon Factors and Franck-condon Densitiesmentioning

confidence: 99%

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule

Wünderlich

2011

Chemical Physics

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Ionization cross sections for the hydrogen molecule have been calculated by applying the classical Gryzinski theory combined with the Franck-Condon theory. It is shown that -if the reaction channels, Franck-Condon factors and Franck-Condon densities are taken into account properly -the calculated cross sections for ionization of the molecular ground state X 1 Σ + g (v ′ = 0) are in almost perfect agreement with the latest and most reliable experimental results. A comprehensive database is established which includes vibrationally resolved cross sections for non-dissociative and dissociative ionization of the molecular ground state as well as for the first five non-repulsive electronically excited states in the molecule.

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A Theory of Intensity Distribution in Band Systems

Cited by 550 publications

References 17 publications

The Genesis of the Quantum Theory of the Chemical Bond

The Genesis of the Quantum Theory of the Chemical Bond

Ground and excited states of zinc phthalocyanine, zinc tetrabenzoporphyrin, and azaporphyrin analogs using DFT and TDDFT with Franck-Condon analysis

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule

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