The polarisation of two-photon excited fluorescence in rotating molecules

Abstract

We report a general theory of the two-photon excited fluorescence (TPEF) of rotating molecules under the condition of anisotropic depolarisation. The obtained expressions for the TPEF intensity are based upon the spherical tensor approach and valid for any symmetric, or asymmetric top molecule and for any photon polarisation. The expressions are written in terms of the molecular parameters M K (R, R 0 , t) which have clear tensor notation and contain all molecular information that can be extracted from the TPEF experiments. Two important extreme cases are discussed. If the molecular rotation period is much larger than the excited state lifetime, the obtained expressions describe the TPEF in non-rotating molecules under the condition of isotropic relaxation. The time-independent part of these expressions is in agreement with the earlier results of McClain [J. Chem. Phys., 58, 324 (1973)]. The relationship between McClain's molecular parametersQ i and the parameters M K (R, R 0 , 0) is presented and analysed. If the molecular rotation period is much smaller than the excited state lifetime, the expressions describe anisotropy of fluorescence from isolated ro-vibrational molecular states. As shown, under certain approximations the expression still can be written in terms of the M-parameters which are reduced due to molecular rotation by about a factor of (2K þ 1). This result manifests that the fluorescence anisotropy is reduced, but not lost due to the molecular rotation.

Two-color two-photon excited fluorescence of indole: Determination of wavelength-dependent molecular parameters

“…As already stated in the Introduction, the polarized fluorescence intensity in TPEF experiments for any experimental geometry depends on a number of time-dependent molecular parameters which contain all information on the two-photon excitation step and the subsequent evolution of the molecular excited state. In this paper, we used the set of molecular parameters M K (R, R ′ , t) (M-parameters) based on the irreducible representation of the transition tensors, 15 where the parameter rank K is limited to 0, 2 and the arguments R, R ′ are limited to 0, 1, and 2, where |R − R ′ | ≤ K. At t = 0, these parameters can be presented as linear combinations of the McClain's molecular parametersQ i based on the Cartesian tensor representation. 10,11 Three zero-rank M-parameters describe the two-photon absorbance related to the isotropic part of the fluorescence and four second-rank M-parameters are responsible for fluorescence anisotropy.…”

“…Note that the zeroth-rank parameters are positive by definition. 15 Moreover, the parameters with R(R ′ ) = 1 can be determined only in two-color experiments. An advantage of the irreducible representation is that it allows to recognize the identically zero M-parameters from the molecular point group symmetry.…”

“…This paper presents the study of indole at seven effective excitation wavelengths in the spectral region 268-294 nm using the theory and experimental setup developed in our previous studies. 15,17,18 Indole (C 8 H 7 N), the chromophore of the amino acid tryptophan, attracted much attention of theoretical and experimental groups all over the world during latest decades as an important fluorescent marker responsible for most of the UV absorption in proteins. 19 The indole excitation properties and fluorescence behavior in various media are governed by two close-lying lowest excited states conventionally noted as 1 L a and 1 L b .…”

“…In this paper, the TPEF polarization technique was used for obtaining detailed photodynamic information on indole dissolved in propylene glycol. Using the experimental procedure and method of the experimental data analysis developed in our previous papers, 15,17 we experimentally determined and analyzed seven molecular parameters M K (R,R ′ ), the two-photon polarization ratio Ω, and the components of the two-photon excitation tensor S Rγ containing important information on the principal tensor axes and the anisotropy of indole two-photon absorptivity. The results obtained are in perfect agreement with the analysis by Callis 29 who theoretically reconstructed the two-photon excitation tensors for 1 L a and 1 L b states.…”

On the analyses of fluorescence depolarisation data in the presence of electronic energy migration. Part I: Theory and general description

“…The theory of fluorescence depolarisation induced by TPE has been developed previously (10,17). Recently the theory of TPE fluorescence has been extended to two-colour excitation (18). However, so far no theory of fluorescence depolarisation is available that accounts for electronic energy transport upon TPE in the presence of molecular reorientation.…”