The present paper aims at deriving classical expressions which permit calculation of the equilibrium constant for weakly interacting molecular pairs using a complete multidimensional potential energy surface. The latter is often available nowadays as a result of the more and more sophisticated and accurate ab initio calculations. The water dimer formation is considered as an example. It is shown that even in case of a rather strongly bound dimer the suggested expression permits obtaining quite reliable estimate for the equilibrium constant. The reliability of our obtained water dimer equilibrium constant is briefly discussed by comparison with the available data based on experimental observations, quantum calculations, and the use of RRHO approximation, provided the latter is restricted to formation of true bound states only.
We present new results for the water dimer equilibrium constant Kp(T) in the range 190−390 K, using a flexible potential energy surface fitted to spectroscopical data. The increased numerical complexity due to explicit consideration of the monomer vibrations is handled via an adiabatic (6 + 6)d decoupling between intra- and intermolecular modes. The convergence of the canonical partition function of the dimer is ensured by computing all energy levels up to dissociation for total angular momentum values J = 0−5 and using an extrapolation scheme to higher values. The newly calculated values for Kp(T) are in very good agreement with available experimental data at room temperature. At higher temperatures, an analysis of the convergence of the partition function reveals that quasi-bound states are likely to contribute to the equilibrium constant. Additional thermodynamical quantities (ΔG, ΔH, ΔS, and Cp) have also been determined and fit to quadratic expressions a + bT + cT2.
New experimental results on “warm” water dimer spectra under equilibrium conditions are presented. An almost equidistant series of six peaks corresponding to the merged individual lines of the bound dimer with consecutive rotational quantum numbers is studied in the 188-258 GHz frequency range in water vapour over a broad range of pressures and temperatures relevant to the Earth's atmosphere. The series is a continuation of the sequence detected earlier at lower frequencies at room temperature. The signal-to-noise ratio of the observed spectra allowed investigating their evolution, when water vapour was diluted by atmospheric air with partial pressure from 0 up to 540 Torr. Analysis of the obtained spectra permitted determining the dimerization constant as well as the hydrogen bond dissociation energy and the dimer spectral parameters, including the average coefficient of collisional broadening of individual lines by water vapour and air. The manifestation of metastable states of the dimer in the observed spectra is assessed. The contribution of three possible pair states of water molecules to the second virial coefficient is evaluated over the broad range of temperatures. The work supports the significant role for the water dimer in atmospheric absorption and related processes.
