Expressions are derived within the relativistic regular approximation (ZORA) for the evaluation of the magnetic hyperfine interactions in paramagnetic molecules. For hydrogen-like atoms exact first order relations between the ZORA and Dirac formalism are given for the calculation of g- and A-tensors. Density functional calculations are performed on the neutral atoms Cu, Ag and Au, on some small test molecules NO2, HCO, and TiF3, and on some paramagnetic clusters consisting of 5 or 7 atoms of the group IB metals: Cu7, Cu2Ag5, CuAg6, Ag5, Ag7, and Au7. It is shown that the calculated ESR parameters of the heptamers are in good agreement with results of experiments, which originally were assigned to pentamers.

A method has been developed for the calculation of the g-tensor of Kramers doublet open shell molecules, which uses the spinor of the unpaired electron of the paramagnetic molecule, obtained from a density functional calculation. Spin–orbit coupling is taken into account variationally using the zeroth-order regular approximation (ZORA) to the Dirac equation. The problem of gauge dependence is solved by using gauge including atomic orbitals (GIAO’s). The method gives fair agreement with experimental values for the g values of some small test molecules NO2, HCO, and TiF3.

A new ab initio pair potential for water was generated by fitting 2510 interaction energies computed by the use of symmetry-adapted perturbation theory ͑SAPT͒. The new site-site functional form, named SAPT-5s, is simple enough to be applied in molecular simulations of condensed phases and at the same time reproduces the computed points with accuracy exceeding that of the elaborate SAPT-pp functional form used earlier ͓J. Chem. Phys. 107, 4207 ͑1997͔͒. SAPT-5s has been shown to quantitatively predict the water dimer spectra, see the following paper ͑paper II͒. It also gives the second virial coefficient in excellent agreement with experiment. Features of the water dimer potential energy surface have been analyzed using SAPT-5s. Average values of powers of the intermolecular separation-obtained from the ground-state rovibrational wave function computed in the SAPT-5s potential-have been combined with measured values to obtain a new empirical estimate of the equilibrium O-O separation equal to 5.50Ϯ0.01 bohr, significantly shorter than the previously accepted value. The residual errors in the SAPT-5s potential have been estimated by comparison to recent large-scale extrapolated ab initio calculations for water dimer. This estimatetogether with the dissociation energy D 0 computed from SAPT-5s-leads to a new prediction of the limit value of D 0 equal to 1165Ϯ54 cm Ϫ1 , close to but significantly more accurate than the best empirical value.

Nearly exact six-dimensional quantum calculations of the vibration-rotation-tunneling ͑VRT͒ levels of the water dimer for values of the rotational quantum numbers J and K р2 show that the SAPT-5s water pair potential presented in the preceding paper ͑paper I͒ gives a good representation of the experimental high-resolution far-infrared spectrum of the water dimer. After analyzing the sensitivity of the transition frequencies with respect to the linear parameters in the potential we could further improve this potential by using only one of the experimentally determined tunneling splittings of the ground state in (H 2 O) 2 . The accuracy of the resulting water pair potential, SAPT-5st, is established by comparison with the spectroscopic data of both (H 2 O) 2 and (D 2 O) 2 : ground and excited state tunneling splittings and rotational constants, as well as the frequencies of the intermolecular vibrations.

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