  A new theoretical method, referred to as Generalized Langevin Mode Analysis
(GLMA), is proposed to analyze the mode of structural fluctuations of a
biomolecule in solution. The method combines the two theories in the
statistical mechanics, or the Generalized Langevin theory and the RISM/3D-RISM
theory, to calculate the second derivative, or the Hessian matrix, of the free
energy surface of a biomolecule in aqueous solution, which consists of the
intramolecular interaction among atoms in the biomolecule and the solvation
free energy. The method is applied to calculate the wave-number spectrum of an
alanine dipeptide in water for which the optical heterodyne-detected
Raman-induced spectroscopy (RIKES) spectrum is available to compare with. The
theoretical analysis reproduced the main features of the experimental spectrum
with respect to the peak positions of the four bands around ~90 cm-1, ~240
cm-1, ~370 cm-1, and 400 cm-1, observed in the experimental spectrum, in spite
that the physics involved in the two spectrum was not exactly the same: the
experimental spectrum includes the contributions from the dipeptide and the
water molecules interacting with the solute, while the theoretical one is just
concerned with the solute molecule, influenced by solvation. Two major
discrepancies between the theoretical and experimental spectra, one in the band
intensity around ~100 cm-1, and the other in the peak positions around ~370
cm-1, are discussed in terms of the fluctuation mode of water molecules
interacting with the dipeptide, which is not taken explicitly into account in
the theoretical analysis.
