Molecular Vibrations in the Exciton Theory for Molecular Aggregates. IV. Excited States of Weakly-coupled Systems

1963 ◽  
Vol 16 (3) ◽  
pp. 295 ◽  
Author(s):  
EG McRae
Keyword(s):  
Intermolecular Interaction ◽  
Excited States ◽  
Excited Molecule ◽  
Coupled Systems ◽  
General Description ◽  
Molecular Vibrations ◽  
Molecular Aggregates ◽  
Weakly Coupled ◽  
Electronically Excited ◽  
Weakly Coupled Systems

The theory of the vibronic states of an electronically excited molecular aggregate is developed for the case of weak intermolecular interaction. The resulting description is complementary to that derived for the case of strong intermolecular interaction in Parts I-III of this series.1 The intermolecular interaction term in the Hamiltonian is treated as a small perturbation. A particular set of zeroth-order functions for the problem, here called m-m functions, is defined. The interaction integrals between m-m functions are studied and certain of the m-m functions are corrected to the first order of perturbation theory. A criterion for the validity of the perturbation treatment is given. The effect of molecular vibrations in exciton theory is to inhibit intermolecular interaction. Expressions are obtained for the vibrational inhibition factors, and their properties are related to the molecular distortion in the vicinity of the electronically excited molecule. All theoretical results are discussed in comparison with those of Parts I-III. The results of the two methods of treatment are combined to give a general description of the excited states of molecular aggregates. It is shown that an exciton together with the associated molecular distortion in polymeric aggregates may be regarded as a quasiparticle analogous to the polaron in a molecular crystal.

Article

1999 ◽  
Vol 77 (11) ◽  
pp. 1810-1812 ◽  
Author(s):  
Alex D Bain
Keyword(s):  
Spin System ◽  
Coupled System ◽  
Coupled Systems ◽  
Physical Reason ◽  
Strongly Coupled ◽  
System Combination ◽  
First Order ◽  
Weakly Coupled ◽  
Quantum Transitions ◽  
Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

Transport in weakly coupled systems

1973 ◽  
Vol 59 (6) ◽  
pp. 3235-3243
Author(s):  
Gary R. Dowling ◽  
H. T. Davis
Keyword(s):  
Coupled Systems ◽  
Weakly Coupled ◽  
Weakly Coupled Systems

Molecular Vibrations in the Exciton Theory for Molecular Aggregates. V. Electronic Spectra of Weakly-coupled Systems

1963 ◽  
Vol 16 (3) ◽  
pp. 315 ◽  
Author(s):  
EG McRae
Keyword(s):  
Electronic Spectra ◽  
Fluorescence Spectra ◽  
Vibrational Structure ◽  
Coupled Systems ◽  
Quantum Yields ◽  
Molecular Aggregates ◽  
Relative Quantum ◽  
Electronically Excited ◽  
Anthracene Crystal ◽  
Theoretical Results

The theory of the gross vibrational structure in the electronic spectra of molecular aggregates is developed for the case of weak intermolecular interaction. The electronically excited states are represented by a set of m-m functions corrected to first order as described in Part IV of this series. An explicit treatment is given for aggregates with two molecules per unit cell. Formulae are obtained for the relative vibronic intensities, splittings, and polarization ratios in absorption spectra, and for relative quantum yields and polarization ratios in fluorescence spectra. The theoretical results are compared with those of the E-V coupling theory developed in Parts II and III. On the basis of this comparison, a general equation is put forward to relate the theoretical crystal splitting (i.e. the splitting for a rigid model) to observed polarization ratios in spectra. The theoretical results are compared with the observed vibrational structure in the 3800 Ǻ band system of anthracene crystal. The crystal splitting calculated from the observed polarization ratios is 380 cm-1. The theory accounts, within the rather large experimental error, for the observed variations of polarization ratio in both the absorption and the fluorescence spectra of anthracene crystal.

scholarly journals Nonlinear multipoint boundary value problems for weakly coupled systems

1999 ◽  
Vol 60 (1) ◽  
pp. 45-54 ◽  
Author(s):  
H.B. Thompson ◽  
C.C. Tisdell
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Coupled Systems ◽  
Multipoint Boundary ◽  
Weakly Coupled ◽  
Weakly Coupled Systems ◽  
Multipoint Boundary Value Problems

We establish existence results concerning solutions to multipoint boundary value problems for weakly coupled systems of second order ordinary differential equations with fully nonlinear boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document