O-H stretch modes of dodecahedral water clusters: A statistical ab initio study

Infrared frequencies calculations were carried out for 20 (H2O)(20) water clusters obeying the 512 dodecahedral geometry, optimized at the B3LYP/6-311++G** level. Their combined spectra contained 800 O-H stretch modes, ranging from 2181 to 3867 cm(-1) (unscaled), which were treated and studied as a database. Of these, 752 modes (94%) could be assigned to a single dominant O*-H* stretch. These 752 were classified into five subdatabases depending on the local H-bond type of the dominant stretch. The frequency (v) was correlated with the O-H* distance (b(OH)), with H-bond length (R-OO) where applicable, and with other variables. The parameter bOH alone accounted for 96-99% of the variance in v for stretches in H-bonds. The correlation with R-OO is substantially weaker. Normal modes were classified as "high ratio" or "low ratio" depending upon the mode's distribution of kinetic energy among the O-H bonds. High-ratio modes (389 modes, or 49% of our sample) are modeled well as a single oscillator undergoing small perturbations by weak coupling from other oscillators. Low-ratio modes involve strong coupling with at least one other O-H stretch for which b(OH2) is close to b(OH). The IR intensities of modes vary widely but can be explained in terms of a single equation giving dipole moment derivatives as a function of boil. For the lowest-energy (H2O)(20) clusters, their IR stretch spectra contained eight distinguishable absorption bands. An explanation for eight bands in terms of the theory of polyhedral water clusters is offered.