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°.

By making use of known properties of orthogonal polynomials the discrete variable representation (DVR) method [J. C. Light, 1. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985)] has been rederived. Simple analytical formulas have been obtained for the matrix elements of DVRs of differential operators which may appear in the rovibrational Hamiltonian of a molecule. DVRs corresponding to Hermite, Laguerre, generalized Laguerre, Legendre, and Jacobi polynomial bases and to the Lanczos basis for Morse Qscillator, that is, to basis sets often used in calculating rovibrational energy levels, have been discussed.

High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory, explicitly correlated (linear R12) techniques, and full configuration interaction (FCI) benchmarks, with basis sets ranging from [O/H] [3s2p1d/2s1p] to [8s7p6d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best possible value for the barrier to linearity of water. Attention is given to the degree of accord among extrapolations of conventional MP2, CCSD, and CCSD(T) energies to the complete basis set (CBS) limit and corresponding linear R12 schemes for these correlation methods. Small corrections due to one- and two-particle relativistic terms, core correlation effects, and the diagonal Born–Oppenheimer correction (DBOC) have been incorporated. The final electronic (vibrationless) extrapolated barrier height of this study is 11 127±35 cm−1. Anharmonic force fields have been determined at the aug-cc-pCVTZ CCSD(T) level at equilibrium and at a linear reference geometry. These and previous sextic force fields are in general accord with the expansion terms of recent global potential energy hypersurfaces but also highlight some of their weaknesses.