On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born–Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [Polyansky et al.Science 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born–Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about $3×10−5Å$ and 0.02° for water. The mass-independent [Born–Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is $reBO=0.95782Å$ and $θeBO=104.485°$⁠, respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of $H2O16$ is $read=0.95785Å$ and $θead=104.500°$⁠, respectively, while those of $D2O16$ are $read=0.95783Å$ and $θead=104.490°$⁠. Pure ab initio prediction of $J=1$ and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than $0.002cm−1$ for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than $0.05cm−1$ (or the lower ones to better than $0.0035cm−1$⁠) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for $A0$ and $B0$⁠. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born–Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of $H2O16$⁠, obtained from experimentally determined $A0′$ and $B0′$ rotational constants corrected empirically to obtain equilibrium rotational constants, are $resp=0.95777Å$ and $θesp=104.48°$⁠.