A nonperturbative theory of zero-phonon transitions in impurity centers in crystals is proposed in the case of arbitrary linear and quadratic vibronic interaction with a phonon continuum. Formulas for the temperature dependence of frequency, width, Huang-Rhys facto and asymmetry parameter are obtained. It was found that linear and quadratic vibronic interactions jointly contribute to the frequency, the Huang-Rice factor and the asymmetry parameter of these transitions. However, the width is completely determined by the purely quadratic part of this interaction. The obtained formulas can be used to verify the simulation of tunneling by the quantum Monte Carlo method.