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. Author manuscript; available in PMC: 2025 Dec 30.
Published in final edited form as: J Chem Theory Comput. 2024 Nov 26;20(23):10574–10587. doi: 10.1021/acs.jctc.4c01326

Table 1.

Mean Unsigned Errors (MUE) in Bond Length (A) and Bond Angle (deg) of Ethane Optimized Using the Projected Hybrid Orbital (PHO) Method with B3LYP Density Functional Theory (DFT) for One Methyl Group and the CHARMM36 Force Field for the Second Methyl Group in Comparison with DFT Calculations for the FULL Systema

def2-SVP
 def2-TZVP
 6–31G(d)
 6–311+G(d,p)
PHO Tet NR PHO Tet NR PHO Tet NR PHO Tet NR
CQ–HQ 0.012 0.010 0.010 0.009 0.008 0.008 0.012 0.010 0.011 0.009 0.008 0.008
CQ–CB 0.034 0.096 0.064 0.028 0.077 0.048 0.029 0.088 0.057 0.025 0.074 0.044
CB–HM 0.030 0.028 0.026 0.038 0.036 0.035 0.037 0.034 0.033 0.035 0.033 0.032
HQ–CQ–HQ 3.3 2.3 2.7 2.7 1.8 2.2 3.0 2.0 2.4 2.6 1.8 2.2
HQ–CQ–CB 2.9 2.0 2.4 2.4 1.7 2.0 2.7 1.8 2.2 2.3 1.6 2.0
CQ–CB–HM 2.9 2.7 11.9 3.1 3.0 12.4 3.0 2.9 12.2 3.1 2.9 12.4
HM–CB–HM 3.2 3.0 14.8 3.5 3.3 15.4 3.4 3.2 15.0 3.4 3.3 15.4
a

The carbon atom of the “MM” methyl group is designated as the boundary atom. Four basis sets are used, including def2-SVP, def2-TZVP, 6–31G(d), and 6–311+G(d,p), and the calculations were performed without local restraining terms (NR), with a tetrahedral restraint (Tet) and the full PHO model.