Letter | Published:

Zero Point Energy and Physical Properties of H2O and D2O

Nature volume 135, pages 229230 (09 February 1935) | Download Citation



THE marked differences between the physical properties of H2O and D2O (and of all polar compounds of H and D) cannot be due to intramolecular differences, which are far too small, but must be connected with differences of effective intermolecular forces. It is possible to account for these differences in a quantitative way by taking into consideration the differences in the frequency of angular vibration or libration of a molecule in the field of its neighbours. The mean frequency in ice can be calculated from the model of the water molecule already put forward1. The frequency found, B = 14·3 × 1012 sec.1, is large enough to have a zero point energy of 17 per cent of the total energy of ice. As in such a libration only the hydrogens are effectively in motion, it is decreased by the factor 2 on substituting D for H. Apart from less important changes due to symmetry conditions and the differences in the nuclear spins, this change of frequency accounts for the greater part of the difference of energy content and specific heats of H2O and D2O. Thus the differences of the heats of evaporation of D2O and H2O ices at the melting points is calculated 0·35, as against the observed value2 of 0·32 k. cal. per mol. This may be regarded as the best check of the essential correctness of the theory. The difference of the specific heats of ice are calculated as 0·7 and observed3 c. 1 cal. per mol. degree.


  1. 1.

    , and , J. Chem. Phys., 1, 515; 1933; and Proc. Roy. Soc., A, 114, 1; 1934.

  2. 2.

    , J. Amer. Chem. Soc., 55, 3057; 1933. and , ibid., 56, 2641; 1934; and , (private communication).

  3. 3.

    (private communication).

  4. 4.

    , J. de Phys., 5, 347; 1934.

Download references

Author information


  1. Crystallographic Laboratory, Cambridge.

    • J. D. BERNAL
  2. Physical Institute of the Academy of Sciences, Moscow.

    • G. TAMM


  1. Search for J. D. BERNAL in:

  2. Search for G. TAMM in:

About this article

Publication history





By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.