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This paper by Xinchuan Huang et al. gives a calculation for the dissociation energy of a water dimer. The electronic dissociation energy (what they call $D_e$) is around 21 kJ/mol, and this is combined with the zero-point energy of the dimer and monomers to give a true dissociation energy ($D_0$) of 13.5 kJ/mol.

The CCSD(T)-PES and MP2-DMS dissociate correctly (and symmetrically) to two H2O monomers, with $D_e$) 1665.7 cm-1 (19.93 kJ/mol). Accurate quantum calculations of the zero-point energy of the dimer (using diffusion Monte Carlo) and the monomers (using a vibrational configuration interaction approach) are reported, and these together with De give a value of $D_0$ of 1042 cm-1 (12.44 kJ/mol). A best estimated value is 1130 cm-1 (13.5 kJ/mol).

How does the zero point energy affect the dissociation energy of the dimer? Is it essentially that the zero point energy of the dimer is different from the sum of zero point energies of the monomers, because the vibrations are coupled and/or the force constants are different?

The paper gives the zero point energy of the water monomer as 4686.5 cm^-1 and dimer as 10088 cm^-1 (harmonic, based on the PES). Converting these gives 56.1 kJ/mol and 120.7 kJ/mol, so dimer - 2*monomer = 8.5 kJ/mol. All of these values seem quite large compared to the electronic dissociation energy. Is the zero point energy really this large?

This seems like a huge effect in the case of the water dimer, reducing the dissociation energy by 35%. Back of the envelope, how can we understand such a massive reduction? If we think of this as a simplified model of two coupled harmonic oscillators, it seems the only way this would work is if the coupling results in a large reduction of the frequency. But identical coupled harmonic oscillators actually have a symmetric mode which is the same frequency as a single non-coupled oscillator.

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    $\begingroup$ The dimer has more vibrational degrees of freedom than the two separate monomers. These extra vibrational modes will be weak, but do contribute to the total ZPE. $\endgroup$ Dec 19, 2023 at 9:56
  • $\begingroup$ +1. I've sent this question to Xinchuan. $\endgroup$ Dec 19, 2023 at 15:23

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