A hydrogen bond network in ammonia clusters plays a key role in understanding the properties of species embedded in ammonia. This network is dictated by the structures of neutral ammonia clusters. In this work, structures of neutral ammonia clusters (NH3)n(=2-10) have been studied at M06-2X/6-31++G(d,p) and MP2/6-31++g(d,p) levels of theory. The analysis of the relative stabilities of various hydrogen bond types has also been studied and vibrational spectroscopy of the ammonia pentamer and decamer is investigated. We noted that M06-2X provides lower electronic energies, greater binding energies and higher structural resolution than MP2. We also noted that at the M06-2X level of theory, the binding energy converges to the experimental vaporization enthalpy faster than that at the MP2 level of theory. As a result, it is found that the M06-2X functional could be more suitable than the MP2 ab initio method in the description of structures and energies of ammonia clusters. However, we found that the electronic energy differences obtained at both levels of computation follow a linear relation with n (number of ammonia molecules in a cluster). As far as the structures of ammonia clusters are concerned, we proposed new "significant" isomers that have not been reported previously. The most remarkable is the global minimum electronic energy structure of the ammonia hexamer, which has an inversion centre and confirms experimental observation. Moreover, we reported the relative stabilities of neutral ammonia clusters for temperatures ranging from 25 to 400 K. The stability of isomers changes with the increase of the temperature. As a result, the branched and less bonded isomers are the most favored at high temperatures and disfavored at low temperatures, while compact and symmetric isomers dominate the population of clusters at low temperatures. In fine, from this work, the global minimum energy structures of ammonia clusters are known for the first time at a given temperature (T ∼ 0-400 K) and at a reliable computational level of theory.

We have revised the structures of neutral water clusters, (H2O)n=2–30, with the affordable M06-2X functional, presenting up to 25 isomers for each cluster size.

The accurate determination of the solvation energies of a proton in ammonia is based on the precise knowledge of the structures of neutral and protonated ammonia clusters. In this work, we have investigated all the possible and stable structures of protonated ammonia clusters H(NH), along with their isomeric distribution at a specific temperature. New significant isomers are reported here for the first time and show that the structures of protonated ammonia clusters are not only branched linear as assumed by all previous authors. Branched linear structures are the only ones responsible for the population of protonated ammonia clusters for n = 4-6 at any temperature. However, for larger cluster sizes, these types of structures compete with branched cyclic, double cyclic, branched double cyclic and triple cyclic structures depending on the temperature. In addition, we have shown that protonated ammonia clusters are all Eigen structures and the first solvation shell of the related ammonium ion core is saturated by four ammonia molecules. We have also carried out a study of the hydrogen bond network of protonated ammonia clusters establishing the stability rule governing the various isomers of each cluster from estimated energies of the hydrogen bond types in H(NH). With all these results, a route for the accurate determination of the solvation energies of a proton in ammonia at a given temperature could be conceivable.

We provide in this work, the absolute solvation enthalpies and the absolute solvation free energies of the proton in ammonia explicitly versus temperature. As a result, the absolute solvation free energy of the proton remains quite constant for temperatures below 200 K. Above this temperature, it increases as a linear function of the temperature: ΔG(H,T)=-1265.832+0.210 T. This indicates that a temperature change of 100 K would induce a solvation free energy change of 21 kJ mol. Thus, ignoring this free energy change would lead to a bad description of hydrogen bonds and an unacceptable error higher than 3.7 pK units. However, the absolute solvation enthalpy of the proton in ammonia is not significantly affected by a temperature change and, the room temperature value is -1217 kJ mol. The change of the solvation enthalpy is only within 3 kJ mol for a temperature change up to 200 K.

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