Hydrogen peroxide is said to be unstable, for it undergoes auto-oxidation on standing/heating:

$$\ce{2H_2O_2 -> 2H_2O + O_2}$$

where $\Delta S=\pu{70.5 J {mol}^{-1}K^{-1}}$ and $\Delta H^{\Theta} = \pu{-98.2 kJ {mol}^{-1}}$.

I speculate if the decomposition can be reversed in some way under suitable conditions, particularly at infinite pressure and near absolute zero temperature. At once this seems to be a problem of entropy reversal. But I seek a more rigorous treatment of the problem with the help of quantum theory. Consider the molecular wavefunctions $\Psi_{1A}$ , $\Psi_{1B}$ of water (2 molecules) and $\Psi_2$ of dioxygen respectively. By studying the interaction potentials of these three wavefunctions as a function of different thermodynamic coordinates, it can be possible to find the desired suitable conditions.

However, the problem begins here – this is not a case of just two molecules where we have a number of methods of analysing the system, I am talking about three molecules, so the calculation is not simple. Moreover, I doubt if I need to study the wavefunction of hydrogen peroxide too in some respect. Overall, I am lacking some theoretical and computational knowledge. Any help is greatly appreciated.

  • 2
    $\begingroup$ You could make a start by looking up information about a related reaction such as OH+OH studied via what are called LEPS potentials. $\endgroup$
    – porphyrin
    Dec 6, 2018 at 9:36
  • $\begingroup$ @porphyrin, the LEPS potentials talk about spatial coordinates of the molecules, on the other hand I am interested in thermodynamic coordinates i.e. $P$ and $T$. $\endgroup$ Dec 6, 2018 at 10:22

1 Answer 1


Yes, if you use some quantum chemistry tool like density functional theory to find the enthalpy of the compounds at many different conditions then you can determine where hydrogen peroxide is the ground state.

You would probably find this at low temperatures and high pressures since it is denser than the other two phases and oxygen is condensed as a liquid or solid so the entropic contribution is smaller.

  • 2
    $\begingroup$ I guess hydrogen peroxide is never the ground state. True, I didn't run the calculations at wide range of conditions, so it is just a guess. But then again, it is a somewhat educated guess. $\endgroup$ Dec 6, 2018 at 6:36
  • $\begingroup$ @Ivan Neretin, in that case it must be possible to prove that hydrogen peroxide is not the ground state. $\endgroup$ Dec 6, 2018 at 7:03
  • $\begingroup$ Of course it must be possible, but it is a great deal harder than you seem to think, and even harder than that. $\endgroup$ Dec 6, 2018 at 7:16
  • $\begingroup$ Density functional approximations are not nearly accurate enough to predict any of these values with any confidence. And then there is the problem of treating a condensed phase the same as a 'gas'... and other problems. $\endgroup$ Dec 7, 2018 at 20:02
  • $\begingroup$ The scenario in question would probably occur when all three phases are at low temperature and high pressure, and all three crystallized. DFT would be fine in that case. $\endgroup$ Dec 8, 2018 at 4:32

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