Anharmonic effects on theoretical IR line shapes of H-bonds

In the spirit of Y. Maréchal and A. Witkowski's J. Chem. Phys. 48 (1968) 2697] work, one revisits, for weak H-bonds, the dependence of the angular frequency ω and of the equilibrium position q_e of the υ_X–H high frequency mode q, on the position coordinate Q of the low frequency υ_X–HY mode. One considers: ω=ω^o+bQ+cQ² and q_e=gQ+fQ². That leads to the anharmonic potential U: U=k₁q²+∑k_rQ^r+∑∑k_nmqⁿQ^m+k₁₅qQ⁵. Here k_r and k_mn (r=2–5, n=1,2 and m=1–4) are interrelated through b, c, g and f. By aid of the Hamiltonian involving U, we find the direct damped auto correlation function of υ_X–H, which, by Fourier transform, gives the IR spectral density (SD). When only b≠0, the SD is nothing but that given in a previous paper P. Blaise, O. Henri-Rousseau, Chem. Phys. 243 (1999) 229]. When the adiabatic approximation is performed, this SD becomes that of N. Rösch and M. Ratner J. Chem. Phys. 61 (1974) 3444] which reduces in turn to that of Maréchal and Witkowski in the absence of damping. With respect to b≠0, c produces a narrowing of the SD if c>0 and a subtle broadening if c<0. Besides, g induces the same narrowing for g>0 and g<0, while f gives subtle changes very sensitive to the sign of f and to the values of b, c and g. The situation b<0 and f>0 which is physically the most probable, leads to SDs which are the most evoking experimental profiles.