Dear Shudong,
Please take a look at the following papers:
Madrid, A. B.; Hyeon-Deuk, K.; Habenicht, B. F.; Prezhdo, O. V. Phonon-Induced Dephasing of Excitons in Semiconductor Quantum Dots: Multiple Exciton Generation, Fission, and Luminescence. ACS nano 2009, 3 (9), 2487–2494. (methodology section)
Akimov, A. V.; Prezhdo, O. V. Persistent Electronic Coherence Despite Rapid Loss of Electron–Nuclear Correlation.
The Journal of Physical Chemistry Letters 2013,
4 (22), 3857–3864.
It is actually the other way around - you first compute the ACF of the energy gap fluctuation dE_ij = E_ij - <E_ij>, where E_ij = E_i - E_j. Then, you compute an FT of the ACF and that gives you the influence spectrum.
Best,
Alexey