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. 2026 Apr 21;37(4):1703–1718. doi: 10.1007/s11224-026-02730-8

Table 6.

The A-A’ atomic energy (kJ/mol) terms of water in various environments. Grid is (15,15). The average value is given in the last row with the SD in brackets. Method: 2PDM-M/CCSD(T)/uncontracted 6–31 + G(d, p). Figure 1 displays the first and second solvating waters of protonated methylamine and the formate ion

Molecule O H1 H2 sum O H1 H2 sum
H2 O (reference molecule) 128.3 19.8 19.8 167.9 0.0 0.0 0.0 0.0
H2O.HOH (acceptor) 130.7 19.9 19.9 170.5 2.4 0.1 0.1 2.6
H2O.HOH (donor) 132.3 20.5 17.5 170.3 4.1 0.7 −2.3 7.1

H2O.H2O.H2Oa

Middle H2O

132.9 20.0 20.0 172.9 4.6 0.2 0.2 5.0

H2O.H2O.H2Oa

Terminal H2O (x2)

132.3 20.5 17.8 170.6 4.0 0.7 −2.0 6.8
NH3.H2O 134.1 21.0 17.3 172.4 5.8 1.2 −2.5 9.5
NH4+.H2O 130.3 19.0 19.0 168.4 2.1 −0.8 −0.8 3.7
CH3NH3+.H2O 130.6 19.4 19.4 169.3 2.3 −0.4 −0.4 3.2
CH3NH3+.(H2O)2 Fig. 1 (1) 130.4 19.5 19.5 169.5 2.2 −0.9 −0.9 3.9
CH3NH3+.(H2O)2 Fig. 1 (2) 130.4 19.5 19.5 169.5 2.2 −2.4 −0.3 4.9
HCO2−.H2O 145.1 19.0 19.5 183.5 16.8 0.1 −0.3 17.2
HCO2−.(H2O)2 Fig. 1 (1) 145.4 17.4 21.5 184.4 17.2 0.3 1.7 19.2
HCO2−.(H2O)2 Fig. 1 (2) 143.0 19.9 17.7 180.7 14.8 −2.1 −2.1 19.0
CH4.H2O 128.7 20.1 20.1 168.9 0.4 −1.0 0.3 1.7
H5O2+ 136.4 17.7 17.6 171.7 8.1 −0.8 −2.2 11.0
H7O3+ 132.6 18.8 18.7 170.0 4.3 −19.8 −1.1 25.2
H9O4+ 132.1 19.1 19.2 170.3 3.8 −19.8 −0.7 24.3

Average (SD)

include H2O

133.9 (5.3) 19.5 (0.9) 19.1 (1.1) 172.4 (5.1) 5.6 (5.3) −0.3 (0.9) −0.8 (1.1) 7.3 (6.1)

a The water trimer was forced to be a linear geometry (i.e open structure) rather than a cyclic one, as is found in the minimum energy form