The following table is provided to show the user how well the free energies of solvation for various SMx models compare to experiment. All values in the tables are mean unsigned errors (MUEs), i.e., the average of the absolute values of the errors. The numbers in this table are taken from a variety of sources, as summarized next.
> The MUE provided in the table for the SM1, SM1a, SM2, SM2.1, SM3, and SM3.1 models are over the 147 neutrals in table 5 of reference 5 in the AMSOL bibliography or the 28 ions of table 6 in the same reference. No error is listed for the SM1a model under ions because that model is only valid for molecules in which atoms take on their standard hybridizations; this is a situation which is not realized for many of the ions in table 6 of reference 5 in the AMSOL bibliography
> The MUE provided in the table for the SM2.2 model are for the 139 molecules listed in reference 26 of the AMSOL bibliography
> The MUE provided in the table for the SM4 Alkane models are for the 506 solvent/solute pairs in references 15 and 18 of the AMSOL bibliography
> The MUE provided in the table for the SM5.0R model is derived from measurements on 235 neutral solutes as described in reference 32 of the AMSOL bibliography
> The MUE for the AM1-SM5.4/U, PM3-SM5.4/U, SM5.4/A, and SM5.4/P aqueous models are based on the 215 neutrals and 34 ions in the SM5.4 aqueous model neutral and ions training sets. See reference 24 in the AMSOL bibliography. An additional 4 neutral phosphorus molecules have been factored into the reported MUE for SM2.2PD/A, SM5.2PD/A, and SM5.2PD/P. See reference 26 in the AMSOL bibliography.
> The MUE for the SM5.4/A-organic and SM5.4/P-organic models are based on a total 1449 measurements of neutral molecules in a total of 78 different solvents. This excludes chloroform, benzene, and toluene. See reference 27 in the AMSOL bibliography.
> The MUE for the SM5.4/A-chloroform and SM5.4/P-chloroform models are based on free energies of solvation derived from measurements on 82 neutrals. See reference 28 in the AMSOL bibliography
> The MUE for the SM5.4-benzene models are based on free energies of solvation derived from measurements on 60 neutrals. See reference 34 in the AMSOL bibliography
> The MUE for the SM5.4-toluene models are based on free energies of solvation derived from measurements on 45 neutrals. See reference 34 in the AMSOL bibliography
> The MUE provided in the table for the AM1-SM4-SRP:Claisen model are for 39 alkanes, cycloalkanes, alkenes, conjugated polyenes, ethers, and aldehydes listed in table 2 of reference 13 in the AMSOL bibliography. The MUE provided in the table for the AM1-SM4-SRP:sugar model are for 47 compounds consisting of these 39 plus 8 alcohols as specified in reference 19 of the AMSOL bibliography
The user should note that since these MUE are not all based on the same set of solutes; thus even when they do refer to the same solvent, they are not strictly comparable. Nevertheless they are provided as a rough guide as to the reliability of the various methods.
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Algorithm Solvent(s) MUE MUE
neutrals ions
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AM1-SM1 water 1.1 2.9
AM1-SM1a water 0.6 -
AM1-SM2 water 0.7 4.1
AM1-SM2.1 water 0.7 3.2
AM1-SM2.2 water 1.2 -
AM1-SM2.2PD/A water 0.6 3.8
PM3-SM3 water 1.0 3.5
PM3-SM3.1 water 0.9 3.4
AM1-SM4 alkanes 0.3 -
PM3-SM4 alkanes 0.3 -
AM1-SM4-SRP:Claisen model water 1.0 -
AM1-SM4-SRP:sugar model water 0.9 -
SM5.0R water 0.6 -
AM1-SM5.2PD/A water 0.5 4.2
PM3-SM5.2PD/P water 0.5 3.6
AM1-SM5.4PD/A water 0.5 3.6
PM3-SM5.4PD/P water 0.4 3.7
AM1-SM5.4/U water 0.6 -
PM3-SM5.4/U water 0.5 -
SM5.4/AM1 water 0.5 4.3
SM5.4/PM3 water 0.4 4.4
SM5.4/AM1 organic, excl. chloroform, benzene, toluene 0.5 -
SM5.4/PM3 organic, excl. chloroform, benzene, toluene 0.4 -
SM5.4/AM1 chloroform 0.4 -
SM5.4/PM3 chloroform 0.4 -
SM5.4/AM1 benzene 0.5 -
SM5.4/PM3 benzene 0.4 -
SM5.4/AM1 toluene 0.3 -
SM5.4/PM3 toluene 0.3 -
SM5.2R/MNDO//HF/MIDI! water and organic solvents 0.4 3.8
SM5.2R/AM1//HF/MIDI! water and organic solvents 0.4 3.7
SM5.2R/PM3//HF/MIDI! water and organic solvents 0.4 3.6
SM5.42R/AM1//HF/MIDI! water and organic solvents 0.4 4.1
SM5.42R/PM3//HF/MIDI! water and organic solvents 0.4 4.2