Vibration-rotation wavefunctions and energies for the ground electronic state of the water molecule by a variational method

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Abstract
In the previous paper [1], the vibration-rotation wavefunctions of polyatomic systems were approximated by a linear combination of suitable expansion functions, the coefficients of which were found by solving the secular equations. Here the practicability of the method is examined by some calculations on the water molecule. Three potential surfaces are used: The energies for (i) are in excellent agreement. A comparison of the results from (ii) and (iii) with observed frequencies indicates that the self-consistent-field surface gives values which are in error by at least 100 cm-1, while the experimentally determined surface gives values which are in error by 40 cm-1. For example, the computed band origins for transitions from the ground vibrational state to the first-excited vibrational state are 1728·21 cm-1, 1559·97 cm-1 and 1594·78 cm-1 for the S.C.F. surface, experimental surface and from experiment, respectively. The S.C.F.-surface result is not surprising, but the results for the experimentally determined surface indicate that the methods used for obtaining this surface are unsatisfactory. This new variational method appears to be capable of finding the vibrational-rotational energies for any potential surface, and the results are most encouraging for its further application.