Knowledge Bank

We consider water dimer energy levels using a moderately high-barrier tunneling assumption. This permits us to divide the problem into two parts: one relating to determination of feasible tunneling paths and corresponding tunneling frequencies, the other to determination of how rotational motions modify the tunneling splittings as a function of J and K. For the first part, based on numerical diagonalizations of one-dimensional multipleminima vibrational problems, using potential surfaces given by Coker and $Watts1$, we find that for the most symmetric isotopic species $(H2O)2$ and $(D2O)2$, two large amplitude motions seem especially feasible. One of these is the $(HF)2$-like motion extensively studied in the pioneering work of Dyke $etal.2$, with tunneling splittings of approximatly 19527 and 1172 MHz, respectively. The other apparently quite feasible motion consists of a $180\circ$ internal rotation of the H-donating momomer about the O{\ldots}H---O bond, accompanied by a simultaneous inversion of the H-accepting monomer's $-OH2$ group. Our calculations estimate this splitting for the fully protonated dimer to be of the order of 70000 MHz. The $method3$ we use to calculate the J and K dependence of the splittings involves $DKK\prime J(Xp,\prime \theta p,\prime \varphi p)$ factors which appear in the tunneling matrix elements between two frameworks, and which reflect the mismatch of the rotational wavefunctions. The three angles $Xp,\theta p,\varphi p$ were computed for 6 tunneling paths, using a computer program to solve the required coupled ordinary differential equations. In an attempt to gain further information about tunneling paths not extensively discussed by Dyke et al., we have made new measurements on $1\leftarrow 0$ and $2\leftarrow 1$ transitions with $K=0$ for several partially deuterated species of the water dimer. Small splittings, ranging from 4 to 75 MHz were observed. (Because of the nature of the tunneling motions involved, these new data yield only differences in tunneling splittings between the upper and lower state arising from the difference in B values.) Work is in progress and we hope to find the $K=1$ transitions.