Spectral Resemblances of Cata-Condensed Hydrocarbons

Klevens, H. B.; Platt, John R.

doi:10.1063/1.1747291

Cited by 483 publications

(146 citation statements)

References 35 publications

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“…The energy values calculated by using the parameters for the cyclopentadienide anion for benzene are the same as those found experimentally (29)(30)(31). The results are shown in Table 1.…”

supporting

confidence: 71%

Derivation of a formula for the resonance integral for a nonorthogonal basis set

Yim¹,

Eyring²

1981

Proc. Natl. Acad. Sci. U.S.A.

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In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set ofparameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the aielectron approximation are transformed to those for an orthogonal basis set by the I~wdin symmetrical orthogonalization.Semiempirical calculations using the Hartree-Fock equation (1) with a zero differential overlap (2-7) neglect the overlap integrals and assume orthogonality of a set of atomic orbitals. These approaches have been rationalized through the use ofthe Lowdin orthogonalized atomic orbital (8). Explanations of the earlier Pariser-Parr method (2-4) have been given by Gladney (9), Fischer-Hjalmars (10), Berthier et al. (11), and several other authors (12-14); a systematic treatment of the zero differential overlap assumption using the nonorthogonal atomic orbitals has been compared with the procedure using the nonorthogonal Lowdin atomic orbitals by Fischer-Hjalmars (15-18); and further application of the orthogonal transformation has been carried out by Adams and Miller (19,20). Linderberg (21,22) has shown that the equivalence of the dipole length and velocity form of oscillator strength places a condition on the parameters used in the Pariser-Parr model. For the case of two orbitals centered at positions A and B and having a vanishing gradient perpendicular to the axis connecting them, Linderberg has derived Eq. 1. h2 L aS4 mRv OR' [a1] where 4A and 1k are the atomic orbitals on atoms A and B, SAV = (4+,j4,), R AV = (R, -Rv), and f3A is a resonance integral between the orbitals ',, and 4p. This procedure is a diatomic approach and neglects the higher order corrections that would occur in polyatomic molecules. There is not, however, a proper limit when B approaches A in this formula. To compute a, for the diagonal matrix elements of the core Hamiltonian, one needs to know / values for the nonorthogonal basis set, but we now only have /8 values for the orthogonal basis set, as given by Eq. 1. The /8 values for the nonorthogonal basis set can be obtained by the procedure described below. Derivation of the off-diagonal matrix element of the core Hamiltonian The fundamental equations for the self-consistent field method are FC = ESC, IF -ESI = 0, Ci s Cj = 8ij, [2] where F is the Fock matrix, E is the eigenvalue matrix of F, C is the eigenmatrix of F, Bij is the Kronecker delta, and S is the overlap matrix. The zero differential overlap approximation leads to the familiar contradiction of neglecting the overlap integral on the one hand and taking a nonzero value of the resonance integral on the other hand.The L6wdin orthogonalized atomic orbitals and the Mulliken approximation (23) can be combined into a computational method in a self-consistent field calculation. The nonorthogonal orbitals, 4i,, are transformed into the orthogo...

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“…The energy values calculated by using the parameters for the cyclopentadienide anion for benzene are the same as those found experimentally (29)(30)(31). The results are shown in Table 1.…”

supporting

confidence: 71%

Derivation of a formula for the resonance integral for a nonorthogonal basis set

Yim¹,

Eyring²

1981

Proc. Natl. Acad. Sci. U.S.A.

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“…Experimentally, this transition is observed at 3.18 eV (390 nm) 46 and can be assigned unambiguously to 1 L a excited state of the 8-hydroxyquinoline. 47,48 Two critical differences can be observed between the AlQ3 and AlQ2OH traces in Fig. 4b.…”

Section: Neutral Alq3 Hydrolysismentioning

confidence: 95%

Chemical failure modes of AlQ3-based OLEDs: AlQ3 hydrolysis

Knox

Halls

Hratchian

et al. 2006

Phys. Chem. Chem. Phys.

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“…Supersonic beam techniques have made it possible to study the excited-state dynamics and obtain detailed information about geometries and intermolecular interactions in these clusters (8)(9)(10). Naphthalene is one of the most thoroughly studied chromophores in crystals and in the gas phase both theoretically and experimentally (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Calculations provided a test for quantum mechanical theories of molecular electronic structure (16,17).…”

mentioning

confidence: 99%

Excitonic couplings and electronic coherence in bridged naphthalene dimers

Tretiak

Zhang

Chernyak

et al. 1999

Proc. Natl. Acad. Sci. U.S.A.

104

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The electronic excitations of naphthalene and a family of bridged naphthalene dimers are calculated and analyzed by using the Collective Electronic Oscillator method combined with the oblique Lanczos algorithm. All experimentally observed trends in absorption profiles and radiative lifetimes are reproduced. Each electronic excitation is linked to the corresponding real-space transition density matrix, which represents the motions of electrons and holes created in the molecule by photon absorption. Two-dimensional plots of these matrices help visualize the degree of exciton localization and explain the dependence of the electronic interaction between chromophores on their separation. R elating electronic excitations of molecular aggregates to those of the individual chromophores is a long-standing fundamental problem with numerous applications to organic superlattices and biological complexes (1, 2).Considerable effort has been devoted to clusters of the simplest aromatic molecules such as napthalene and benzene (3-7). Supersonic beam techniques have made it possible to study the excited-state dynamics and obtain detailed information about geometries and intermolecular interactions in these clusters (8-10). Naphthalene is one of the most thoroughly studied chromophores in crystals and in the gas phase both theoretically and experimentally (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Calculations provided a test for quantum mechanical theories of molecular electronic structure (16,17). In recent years, detailed information about naphthalene clusters has been obtained through high-resolution rotational spectroscopy analysis (22, 23). For example, structural information on naphthalene trimer has been extracted from rotational coherence spectroscopy (23). Excimer formation dynamics has been studied by Lim's group through fluorescence spectroscopy (24-28). Excitonic interactions depend strongly on the distance and relative orientation of the transition moments of monomer units. The geometry can be obtained from high-resolution vibronic spectra and nonlinear Raman spectroscopy (10,22,29). Extensive study of benzene has been carried out as well. Recent interest focused on the structure and properties of benzene clusters (30-36). Isotopically mixed benzene clusters have been used in the investigation of intermolecular interactions. Discrete exciton spectra were observed for benzene dimers (9, 37).In this paper, we analyze the absorption spectra of naphthalene and a family of naphthalene-bridge-naphthalene systems DN-2, DN-4, and DN-6 (see Fig. 1) (38-41). These molecules may be regarded as naphthalene dimers where pairs of naphthalene chromophores are held at fixed distances and orientations by a rigid polynorbornyl-type bridge of variable length (two, four, or six bonds, respectively). The UV-spectra and radiative decay rates of these dimers have been measured (39-41) and interpreted by using a simple exciton model (42). Within this model, each excited state of the monomer generates two states in the dimer. The interac...

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Spectral Resemblances of Cata-Condensed Hydrocarbons

Cited by 483 publications

References 35 publications

Derivation of a formula for the resonance integral for a nonorthogonal basis set

Derivation of a formula for the resonance integral for a nonorthogonal basis set

Chemical failure modes of AlQ3-based OLEDs: AlQ3 hydrolysis

Excitonic couplings and electronic coherence in bridged naphthalene dimers

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