Tn Frequency Functions as Energy Contours for Photon Absorbance in Condensed Systems

Spectroscopic absorption contours of condensed systems appear to be described by one of several frequency functions, i.e., Gaussian, Lorentzian ${\mathrm{(T}}_1)$ , or $T_n$ , where $\text{1\hspace{0.17em}<\hspace{0.17em}n\hspace{0.17em}≤\hspace{0.17em}3}$ . A phenomenological explanation is given in terms of a statistical model involving random perturbations on energy levels ${\mathrm{(〈\psi }}_m{\mathrm{|\; H\; |\; \psi }}_n〉$ , ${\mathrm{〈\psi }}_n{\mathrm{|\; H\; |\; \psi }}_n\mathrm{〉)}$ and orthogonal coupling matrix elements ${\mathrm{(〈\psi }}_m{\mathrm{|\; M}}_q{\mathrm{|\; \psi }}_n\mathrm{〉)}$ , where $M_q$ is the light‐coupling operator and $n$ and $m$ are the two states between which transitions occur. If the matrix elements are well shielded from perturbation or strong complexes exist such that only a few relaxations of the same order of duration can occur, Gaussian functions result. If, along with the energy levels, one of the orthogonal components is strongly perturbed by a statistically orientated environment, a Lorentzian function ${\mathrm{(T}}_1)$ results. If two such components are perturbed, the predicted function is $T_2$ , and if all three components are significantly perturbed, then $T_3$ results.