The behavior of the hydrogen bond vibration, nu(sigma), of substituted phenol-trimethylamine N-oxide systems was investigated with quantum chemical molecule simulations (PM3 Hamiltonian) and compared with the experimental results. The semiempirically found shift of nu(sigma) as a function of the pK(a) value of the phenol is in good agreement with experimental results for complexes in which the nonpolar structure OH ... N predominates, but the absolute values are always too high. On the basis of the obtained geometry, harmonic force constants of the hydrogen bond vibrations are calculated (3-21G basis set) for the nonpolar (k(sigma)(n)) and polar (k(sigma)(p)) limiting structures, respectively. The k(sigma) values are first-order functions of the pK(a) values, k(sigma)(p) with positive slope and k(sigma)(n) with negative. The influence of the environment was taken into account by the term mu F (mu is the dipole moment of the complex; F is the electric field of the environment). The fast fluctuation between the nonpolar and polar proton limiting structures is treated with the Kubo theory, and an effective force constant as a function of the pK(a), of the phenol is obtained. The pK(a) dependence agrees very well with the experiment.