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The Journal of Chemical Physics

Dipole broadened line shape of impurity chromophores isolated in a transparent matrix

Mikhail A. Ovchinnikov, Charles A. Wight

Published Dec 8, 1995• 3 citations
Publisher

Abstract

The inhomogeneous broadening caused by dipole–dipole interactions between molecules having strongly allowed optical transitions is considered for the case in which the chromophores are randomly distributed at low concentration in a transparent matrix. Model calculations show that absorption in the wings of the spectrum is caused almost exclusively by strongly interacting pairs of chromophores. This result has important implications for the interpretation of recent experiments in which the spectra of single dye molecules have been observed in organic matrices. The generalized lineshape in these wings is shown to be proportional to the inverse square of the detuning from line center. The line shape is also somewhat asymmetric, with the red wing being more intense than the blue.

DOI
10.1063/1.469970

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The inhomogeneous broadening caused by dipole–dipole interactions between molecules having strongly allowed optical transitions is considered for the case in which the chromophores are randomly distributed at low concentration in a transparent matrix. Model calculations show that absorption in the wings of the spectrum is caused almost exclusively by strongly interacting pairs of chromophores. This result has important implications for the interpretation of recent experiments in which the spectra of single dye molecules have been observed in organic matrices. The generalized lineshape in these wings is shown to be proportional to the inverse square of the detuning from line center. The line shape is also somewhat asymmetric, with the red wing being more intense than the blue.
We have carried out a theoretical and numerical study of disorder-induced changes in the absorption line shape of a chromophore embedded in a host matrix. The stochastic sudden jump model is employed wherein the host matrix molecules are treated as noninteracting two-level systems (TLSs) occupying points on a three-dimensional lattice with randomly oriented dipole moments. By systematically controlling the degree of positional disorder (α) attributed to them, a perfectly crystalline (α = 0) or a glassy environment (α = 1) or a combination of the two is obtained. The interaction between the chromophore and the TLSs is assumed to be of the dipole-dipole form. With an increase in α, the broadening of the absorption line shape was found to follow a power-law behavior. More importantly, it is revealed in the long-time limit that the resultant line shape is Gaussian in the absence of disorder but transforms to Lorentzian for a completely disordered environment. For an arbitrarily intermediate value of α, the resultant line shape can be approximately fitted by a linear combination of Gaussian and Lorentzian components. The Lorentzian profile for the disordered medium is attributed to the chomophore-TLS pairs with vanishingly small separation between them.
The effects of intense laser pulse trains in coupled multilevel systems (such as pure or mixed molecular crystals) are analyzed by calculating exact density matrix evolutions. It is shown that two-level approximations are inadequate. The contributions of exchange couplings, inhomogeneous broadening, permanent multipole interactions and transition multipole interactions to absorption and photon echo line shapes are calculated. The absorption line shape of 1,4-dibromonaphthalene (DBN) is shown to be predominantly an isotopic substitution effect, as our Monte Carlo results give quantitative agreement with experiment for this model. Average t-matrix approximations to the Green’s function, which have been used to propose a different mechanism for the DBN line shape are shown to be qualitatively inadequate. Dipole–dipole interactions are shown to be an important photon echo decay mechanism in mixed crystals, with the relative importance of permanent and transition multipole interactions dependent on the resonance frequency distribution. Multiple pulse trains, including multiple pulse echoes and optical multiple-quantum sequences, are shown to be capable of distinguishing different types of interactions in the molecular Hamiltonian and reducing optical density effects. Specific pulse sequences are proposed and their effects are calculated.
When two atoms are in proximity, their resonance lines are broadened because of the formation of molecular potentials, between which photon transitions can occur. The level of experimental refinement in measuring excimer and collisional far-wing spectra calls for interpretive theoretical methods that accurately treat the observed structure in line shapes. Of particular interest are satellites and undulations, for they can give much information on intermolecular potentials. We derive an expression for TTT-matrix elements, based on JWKB wave functions and stationary-phase techniques, that is universally applicable to situations with one, two, or more Condon points. Each transition point is treated individually, with effects of potential shape, wave-function phases, and interference separately highlighted. The expression is tested against quantum-mechanical line shapes of the red and blue wings of the Rb DDD lines broadened by Xe perturbers. Agreement is quite good for both the red-wing undulations and the blue-wing satellite-supernumerary structure.
Reduced absorption coefficients γBaBa were measured for the far-wing absorption of the self-broadened Ba6s2 1S0–5d6p 1P1 line, Ba(6s2 1S0) +Ba(6s2 1S0)+ℏω → Ba*(5d6p 1P1)+Ba(6s21 S0)and the pair absorption Ba(6s2 1S0)+Ba(6s2 1 S0) +ℏω→Ba*(6s6p 1P1 +Ba*(6s5d 1D2). The self-broadening shows the red-shaded asymmetric profile: γBaBa on the red wing is proportional to Δν−3/2, where Δν is the detuning from the line center. The pair absorption shows a broad asymmetric peak having a blue tail and a blue satellite. The estimated γBaBa, which is based on the quasistatic line-broadening theory and the long-range dipole–dipole interaction between the relevant atomic excited levels, shows reasonable agreement for the red wing of the self-absorption whereas it gives larger values by a factor of 3 for the blue tail of the main peak for the pair absorption.
A method is introduced to calculate for a model set of molecular levels the spectral line shapes expected for a variety of conventional laser experiments including absorption, hole burning, fluorescence line narrowing, and Raman scattering. The method allows the incident laser field to have arbitrary intensity. Furthermore, the effects of model Gaussian or Lorenzian inhomogeneous distributions are readily incorporated. Earlier results for a two-level system are easily obtained and new results are presented for inhomogeneously broadened two and three level systems, and for the effects of pure dephasing on the strong field spectra. In particular we have described the differences between fluorescence and Raman in strong fields, and the effect of strong fields on the spontaneous emission of inhomogeneously broadened transitions. Some predictions are made regarding line narrowing experiments in the strong-field limit.
We analyze the early-time development of the spectral transfer of optical excitation in inhomogeneously broadened systems. Previous models for the decay of the narrow-band fluorescence are generalized to include systems with asymmetric energy-dependent transfer rates. It is assumed that the energy splittings of the ions are uncorrelated. An analogous model for the early-time development of the background fluorescence is outlined. Detailed results are presented for spectral transfer over a Gaussian line shape assuming a dipole-dipole mechanism with rates that are inversely proportional to the square of the energy mismatch. Comparison is made with the treatment of Holstein et al.