Water dimer equilibrium constant calculation: a quantum formulation including metastable states

We present a full quantum evaluation of the water second virial coefficient B(T) based on the Takahashi-Imada second order approximation. As the associated trace T r[e(-βH(AB)) - e(-βH(0)(AB))] is performed in the coordinate representation, it does also include contribution from the whole continuum, i.e., resonances and collision pairs of monomers. This approach is compared to a Path Integral Monte Carlo evaluation of this coefficient by Schenter [J. Chem. Phys. 117, 6573 (2002)] for the TIP4P potential and shown to give extremely close results in the low temperature range (250-450 K) reported. Using a recent ab initio flexible potential for the water dimer, this new formulation leads to very good agreement with experimental values over the whole range of temperatures available. The virial coefficient is then used in the well known relation Kp(T) = -(B(T) - bM)/RT where the excluded volume bM is assimilated to the second virial coefficient of pure water monomer vapor and approximated from the inner repulsive part of the interaction potential. This definition, which renders bM temperature dependent, allows us to retrieve the 38 cm(3) mol(-1) value commonly used, at room temperature. The resulting values for Kp(T) are in agreement with available experimental data obtained from infrared absorption spectra of water vapor.