Electronic Coherence and Collective Optical Excitations of Conjugated Molecules

Abstract

Optical spectroscopy of conjugated molecules is described by using collective electronic coordinates, which represent the joint dynamics of electron-hole pairs. The approach relates the optical signals directly to the dynamics of charges and bond orders (electronic coherences) induced by the radiation field and uses only ground-state information, thus avoiding the explicit calculation of excited molecular states. The resulting real-space picture is reminiscent of the normal-mode analysis of molecular vibrations and offers a unified framework for the treatment of other types of systems including semiconductor nanostructures and biological complexes. Spatial coherence displayed in two-dimensional plots of the five electronic normal modes that dominate the optical response of poly( p-phenylene vinylene) oligomers with up to 50 repeat units (398 carbon atoms) in the 1.5-to 8-electronvolt frequency range suggests a saturation to bulk behavior at about five repeat units. Spectroscopy allows chemists and physiciststo probe of the dynamics of vibrations and electronic excitations within molecules and solids. The theoretical models used for interpreting molecular spectra compared with those for extended solids are usually quite different, and certain systems, such as clusters and polymers, are not readily treated by either of these limiting cases. There is particular interest to understand the optical spectra of large polymers, which are extended conjugated molecules such as poly(p-phenylene vinylene) (PPV) oligomers (Fig. 1) that have interesting optical applications.Electronic and optical properties of small conjugated chains can be interpreted molecularly in terms of their global manyelectron eigenstates obtained from quantum-chemistry methods (1, 2). Large polymers also can be analyzed with semiconductor band theories that focus on the dynamics of electron-hole pairs (3). The size-scaling of the optical response and the transition between these two regimes has not been fully explored for the lack of adequate theoretical methods. It is very hard to obtain the complete set of eigenstates, which carry considerably more information than necessary for the calculation of spectra, for large molecules with strong electron correlations (as occurs in conjugated chains). Band theories, however, neglect electronic correlation effects, and because they are formulated in momentum (k) space, they do not lend themselves easily to real-space chemical intuition.The collective-electronic oscillator (CEO) representation (4, 5) provides a hybrid formulation that bridges the gap between the chemical and semiconductor points of view. This model uses an electronhole picture in real space, overcomes many of the difficulties associated with the former approaches, and provides a physically intuitive link between electronic structure and optical properties, that is, the optical properties are related directly to the motions of charges and electronic coherences, thus avoiding the need to calculate the global (many-electron) eigenstates. The elec...

Reaction dynamics of photochromic dithienylethene derivatives

“…6 . w x We employed the CEO technique [16][17][18] to compute and analyze the optical spectra using as r an input. The molecular transition dipole is a singleelectron operator which may be expanded in the form P s Ý m c q c , where m is the transition m n m n m n m n dipole moment matrix element.…”

Localized and Delocalized Electronic Excitations in Biological and Artificial Antenna Complexes

“…The numerical CEO-INDO/S procedure for calculating electronic structure has been described in detail elsewhere 12,13 . The ZINDO code was first applied to generate the INDO/S hamiltonian using geometries obtained from crystal structures of LH2 complex of Rs.…”

“…We next calculated the Hartree-Fock ground-state density matrices which are the input to the following CEO calculation. The CEO procedure 12,13 was finally applied to compute the linear-absorption spectra and the relevant transition density matrices (denoted the electronic normal modes ξ ν ), which connect the optical response with the underlying electronic motions. Each mode is a matrix representing the electronic transition between the ground state |g> and an electronically excited state |ν>: ξ ν =<ν|c m + c n |g>, where c m + (c m ) are creation (annihilation) operators of an electron at the m'th atomic orbital.…”

“…In this paper we apply the collective electronic oscillator (CEO) approach 12,13 to study the electronic excitations of Bchl-a aggregates of LH2 complex of Rs. molischianum and dendrimers made up of phenylacetylene repeat unit in a self-similar fashion around the core.…”

Optical and Electronic Properties of Organoboron Compounds in Solvent

“…By using 3D real-space analysis [19][20][21][22][23][24], we studied the properties of charge and energy transfer, transition of the dipole moment, electron-hole coherence and delocalization of compounds in different solvents at excited states. From the absorption spectra, emission spectra and analysis of the 3D real-space, we found that significant red shift or blue shift of both absorption maxima and fluorescence maxima of compounds 1-4 in more polar solvents, indicating a strong intramolecular charge transfer (ICT) feature and suggests that the bigger the polarity of the solvent, the greater the shift in red or blue.…”