The potential energy surface for the electronic ground state of $H_{2}{^{16}} O$ determined with a new level of accuracy

Author Institution: Physikalisch-Chemisches Institut, Justus Liebig-Universit\""{a}t Giessen; Department of Physics and Astronomy, University College LondonThe potential energy function for the electronic ground state of the water molecule has been obtained by fitting rotation-vibration terms value involving $J \leq 14$ for 24 vibrational states of $H_{2}^{16}O$ together with 25 additional vibrational term values belonging to higher excited states. The fitting was carried out by means of an exact kinetic energy Hamiltonian. It was found that the differences between the exact kinetic energy calculations and calculations with MORBID program (i.e., calculations with approximate kinetic energy operator) depend only very slightly on the particular parameters of the potential. This fact allowed us to make an inexpensive fitting using the MORBID approach and still get the accuracy obtainable with the exact kinetic energy Hamiltonian. The standard deviation for 1600 term values was $0.36 cm^{-1}$. For 220 ground state energy levels the standard deviation was $0.03 cm^{-1}$. With the fitted potential, calculations of term value with $J \leq 35$ were carried out. This showed the excellent predictive power of this potential. For instance the discrepancy for the highest observed $K_{a} = 20$ level of the ground state, $20_{200}$, is only $0.001 cm^{-1}$. The discrepency for the observed level with the highest {J}, $35_{035}$ was $0.1 cm^{-1}$. Because of the level of accuracy achieved in these calculations, we can for the first time demonstrate the breakdown of the Born Oppenheimer approximation for the water molecule. The high $K_{a}$ level calculations allow us to show that the rotational energy level structure in water is at least of a very different nature than the four-fold cluster structure observed for $H_{2}Se$ and calculated for $H_{2}S, H_{2}Se$ and $H_{2}Te$