Nureshan Mahamarakkalage and Kaidi Yang

High Precision Energy Calculations and Solvation Methods for Dissociation Reaction of Methyl-Diazonium

In assignment seven, we studied the dissociation of methyl diazonium ion in condensed phase, and later we calculated the energies corresponds dissociation of methyl diazonium at high theoretical levels to get the high precision energies. In the first part, we optimized the structures of each reactants and products namely methyl diazonium, methyl cation and nitrogen at MP2(full)/6-311G**[1],[2] level. Then we did a frequency calculation to see the structures are readily optimized in the gas phase. Then we repeated the above procedure at the condensed phase. We performed the optimization at SMD(MP2(full)/6-311G**)[3]level with water as solvent. To get more refined energy we did single point energy calculation for each reactant and product at SMD(MP2(full)/6-311G**) //MP2(full)/6-311G** level with water as solvent. In the final part, we used Gaussians - G4[4]method and CBS-4M[5] method to get high precision energies for reactants and products at gas phase.

The top two images of the Figure 1 depicts the structure of methyl diazonium and methyl cation at MP2(full)/6-311G** level in the gas phase whereas the bottom two images represent the structures of methyl diazonium and methyl cation at SMD(MP2(full)/6-311G**) level. The total energy of the molecules at bulk solvation is lower than the gas phase.In Table 1, we compare the total energy, thermal energy, and entropy for all the reactants and products at three different levels. It can be seen from the data that bulk solvation has decreased the energy of the reactants and products by about 0.2 Hartree. Solvent molecules, water in our case, can stabilize each substrate and product. The thermal energy has increased with the introduction of the solvents. With the introduction of solvent molecules are more degrees of freedom which cause this increment. The entropy values are almost equal in the different methods. Therefore we cannot exactly say the variation of enthalpy changes with the introduction of solvents such as water.

The reaction energies computed with bulk solvation are about 10 kcal/mol lower than the reaction energies computed without bulk solvation as shown in Table 3. That is because the positive charge on methyl diazonium can be delocalized while the positive charge on methyl cation is localized. The localized molecule gets more solvation effect, so it is more stable with the presence of solvent. With the product being lower in energy, this endothermic reaction has lower reaction energy. The reaction energies calculated at SMD(MP2(full)6311G**and at SMD(MP2(full)6311G**)//MP2(full)6-311G**are very similar, which means the geometry optimized at non-SMD-level can give the same result. Thus, the benefit of SMD-level geometry optimization is not much.

As shown in Table 1 and Table 2, in gas phase, the substances calculated at higher precision levels are more stable than the ones calculated at lower level. G4 and CBS - 4M method result in similar energies of the substances, and G4 is slightly better than CBS - 4M.The reaction energies are smaller at higher precision level as well according to Table 3.

In conclusion, solvation effect plays an important role in this reaction, and higher precision levels give lower reaction energies. Thus, it can be estimated that the dissociation energy in condensed phase should be the reaction energy calculated at the level of SMD(MP2(full)/6-311G**), which is E=37.92 kcal / mol, H298=34.18kcal / mol, and G298=24.64kcal / mol.

Nureshan Mahamarakkalage and Kaidi Yang

Figure 1.Optimized structure of H3C+ (top left) with H-C bond length 1.086 Angstrom, and H3C-N2+ (top right) with H-C-H angle 112.535 degrees, H-C bond length 1.088 Angstrom, N-C bond length 1.457 Angstrom, N-N bond length 1.112, at the MP2(full)/6-311G** level; Optimized structure of H3C+ (bottom left) with H-C bond length 1.081 Angstrom, and H3C-N2+ (bottom right) with H-C-H angle 112.797 degrees, H-C bond length 1.085 Angstrom, N-C bond length 1.443 Angstrom, and N-N bond length 1.110 Angstrom, at the SMD(MP2(full)/6-311G**) level. The total energy for the top molecules are -148.784934 and -39.374322while the bottom moleculeshas the energy values of-148.900577 and -39.505308 hartrees.

Nureshan Mahamarakkalage and Kaidi Yang

Table 1. The Total Energy, Thermal Energy and Entropy at MP2(full)/6-311G**, SMD(MP2(full)/6-311G**) and Single Point Energy Calculations at SMD(MP2(full)6311G**)//MP2(full)6-311G**

Method / Molecule / Total Energy/
Hartree / Thermal Energy
/ kcal/mol / Entropy/ cal /mol·K
MP2(full)/6-311G** / H3C-N2+ / -148.784934 / 30.81 / 60.67
H3C+ / -39.374322 / 21.90 / 45.96
N2 / -109.334062 / 4.61 / 45.84
SMD(MP2(full)/6-311G**) / H3C-N2+ / -148.900577 / 31.04 / 60.58
H3C+ / -39.505308 / 22.09 / 46.75
N2 / -109.334834 / 4.61 / 45.83
SMD(MP2(full)6311G**)//MP2(full)6-311G** / H3C-N2+ / -148.900401 / 30.81 / 60.67
H3C+ / -39.505262 / 21.90 / 45.96
N2 / -109.334833 / 4.61 / 45.84

Nureshan Mahamarakkalage and Kaidi Yang

Table 2. Energy Table at the Level of G4 and CBS-4M

Method / Molecules / Final Energy (Hartree) / Final Enthalpy (Hartree) / Free Energy (Hartree)
G4 / H3C-N2+ / -149.007199 / -149.006255 / -149.03395
H3C+ / -39.434821 / -39.433877 / -39.455734
N2 / -109.504146 / -109.503202 / -109.524945
CBS-4M / H3C-N2+ / -148.860072 / -148.859128 / -148.888056
H3C+ / -39.392641 / -39.391696 / -39.412852
N2 / -109.398926 / -109.397981 / -109.419697

Table 3. Reaction Energies at the Level of MP2(full)/6-311G**, SMD(MP2(full)/6-311G**), SMD(MP2(full)6311G**)//MP2(full)6-311G**, G4, and CBS-4M

Method / E
(kcal/mol) / H298 (kcal/mol) / G298(kcal/mol)
MP2(full)/6-311G** / 48.04 / 44.31 / 35.03
SMD(MP2(full)/6-311G**) / 37.92 / 34.18 / 24.64
SMD(MP2(full)6311G**)//MP2(full)6-311G** / 37.84 / 34.12 / 25.25
G4 / 42.82 / 43.41 / 33.43
CBS-4M / 42.99 / 43.58 / 34.83

Refferences

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