Average Errors in ΔHf (Kcal.mol-1) and Bond-Lengths() (Home)

Expressing average errors in heats of formation and bond-lengths is difficult, in that the averages depend on the set of compounds involved.  So in order to provide meaningful values, average errors for various sets of elements are given here.

   Core elements: H, C, N, O, only

  Heats of Formation Bond-Lengths
Element PM6 PM3 AM1 No. in set   PM6 PM3 AM1 No. in set
Hydrogen 4.6 5.5 9.3 1,126

0.021

0.017

0.037

53

Carbon 4.7 5.5 9.3 1,123

0.012

0.012

0.016

157

Nitrogen 4.4 6.0 10.1 464

0.040

0.030

0.048

51

Oxygen 4.7 5.9 9.9 627

0.028

0.026

0.054

53

Average 4.6 5.7 9.5 3,340

0.021

0.018 0.031 314

"Organic" elements: H, C, N, O, F, P, S, Cl, Br, I, only

  Heats of Formation              Bond-Lengths
Element PM6 PM3 AM1 No. in set   PM6 PM3 AM1 No. in set
Hydrogen 4.7 6.4 9.6 1,513 0.029 0.019 0.031

93

Carbon 4.8 6.3 9.8 1,554 0.013 0.023 0.028

337

Nitrogen 4.8 6.5 10.7 542 0.035 0.032 0.046

73

Oxygen 5.2 7.9 13.3 820 0.025 0.034 0.054

130

Fluorine 6.7 12.2 26.4 176 0.034 0.028 0.043

69

Phosphorus 8.2 17.9 20.1 95 0.021 0.047 0.058

67

Sulfur 6.1 11.3 15.2 195 0.032 0.044 0.058

78

Chlorine 5.9 14.6 24.5 155 0.051 0.038 0.060

61

Bromine 5.7 9.7 18.2 58 0.034 0.111 0.077

33

Iodine 3.2 7.9 17.6 59 0.117 0.172 0.113

22

Average 5.0 7.5 12.0 5,167 0.027 0.036 0.044 963

Main-Group elements

  Heats of Formation Bond-Lengths
Element PM6 PM3 AM1 No. in set   PM6 PM3 AM1 No. in set

Hydrogen

5.7 16.3 20.1 2,246   0.034 0.033 0.029 213

Helium

0.0     1   0.411     5

Lithium

7.3 18.1 17.2 83   0.149 0.163 0.157 111

Beryllium

5.9 29.6 18.5 34   0.065 0.066 0.089 42

Boron

8.2 12.7   118   0.033 0.067   122

Carbon

5.6 14.4 17.9 2,038   0.031 0.049 0.060 608

Nitrogen

6.0 18.3 23.0 714   0.084 0.120 0.153 245

Oxygen

6.2 19.6 26.4 1,218   0.091 0.090 0.097 576

Fluorine

7.1 19.9 35.3 344   0.065 0.067 0.092 247

Neon

0.0     1   0.378     5

Sodium

11.7 8.6 10.4 39   0.369 0.189 0.123 33

Magnesium

7.9 20.0 18.7 66   0.075 0.159 0.061 106

Aluminium

7.3 19.1 19.2 75   0.040 0.098 0.138 70

Silicon

5.7 13.0 16.6 93   0.033 0.074 0.073 95

Phosphorus

8.2 17.4 19.4 98   0.034 0.075 0.074 90

Sulfur

7.4 19.1 27.0 308   0.070 0.088 0.135 184

Chlorine

6.8 18.3 25.5 368   0.065 0.088 0.130 256

Argon

0.0     1   0.253     4

Potassium

6.6 9.8 42.5 42   0.125 0.142 0.239 47

Calcium

8.9 41.9 53.3 43   0.080 0.158 0.100 72

Gallium

7.6 47.5 46.5 47   0.048 0.195 0.144 80

Germanium

9.7 15.8 19.1 67   0.037 0.056 0.066 133

Arsenic

7.0 16.8 17.4 49   0.067 0.085 0.102 70

Selenium

4.9 41.1 32.4 24   0.042 0.075 0.060 49

Bromine

5.9 24.6 25.4 185   0.093 0.130 0.120 169

Krypton

0.0     1   0.128     6

Rubidium

11.0 21.6 28.1 24   0.416 0.176 0.197 36

Strontium

7.4 76.6 57.6 38   0.085 0.085 0.200 56
Cadmium 3.4     38   0.150     57

Indium

7.4 29.7 32.2 54   0.040 0.154 0.106 77

Tin

6.7 16.9 21.0 78   0.072 0.077 0.082 98

Antimony

5.4 34.7 35.1 58   0.060 0.084 0.131 90

Tellurium

8.1 46.9 22.1 45   0.065 0.115 0.116 81

Iodine

5.8 27.5 32.5 163   0.127 0.145 0.177 132

Xenon

0.0     1   0.626     8

Cesium

8.1 54.4 55.3 40   0.313 0.200 0.324 44

Barium

11.8 129.6 145.4 37   0.146 0.183 0.202 52

Thallium

11.3 70.8 114.7 45   0.203 0.137 0.214 60

Lead

8.3 14.6 16.7 44   0.123 0.095 0.103 53

Bismuth

7.8 28.9 119.7 53   0.139 0.220 0.635 81

Average

6.2 19.1 24.1 8,983   0.080 0.097 0.116 4,506

 

All elements, except Ce, Pr, Nd, Pm Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and the elements with Z > 83,  PM6 only,

Element ΔHf No. in set   Bond-Length No. in set
Hydrogen

7.4

3,044

 

0.05

240
Helium 0.0 1   0.41 5
Lithium 7.3 83   0.15 111
Beryllium 5.9 34   0.07 42
Boron 7.7 121   0.04 122
Carbon 7.5 2,806   0.05 1,193
Nitrogen 8.6 1,068   0.09 664
Oxygen 8.3 1,765   0.10 1,187
Fluorine 8.1 497   0.07 406
Neon 0.0 1   0.38 5
Sodium 11.5 40   0.37 33
Magnesium 7.9 66   0.08 106
Aluminium 7.0 75   0.05 77
Silicon 5.5 98   0.04 102
Phosphorus 8.2 110   0.04 146
Sulfur 9.0 428   0.09 365
Chlorine 8.7 671   0.08 674
Argon 0.0 1   0.25 4
Potassium 6.7 43   0.13 47
Calcium 8.9 43   0.08 72
Scandium 10.2 52   0.06 92
Titanium 10.3 85   0.08 140
Vanadium 15.0 59   0.08 169
Chromium 12.5 60   0.09 89
Manganese 12.3 45   0.09 108
Iron 18.0 76   0.10 118
Cobalt 11.1 42   0.09 101
Nickel 15.2 51   0.06 135
Copper 17.0 49   0.19 132
Zinc 6.7 54   0.08 74
Gallium 7.6 47   0.05 80
Germanium 9.7 67   0.04 134
Arsenic 7.0 49   0.07 72
Selenium 4.7 25   0.04 56
Bromine 7.8 330   0.10 359
Krypton 0.0 1   0.13 6
Rubidium 11.0 24   0.42 36
Strontium 7.4 38   0.09 56
Yttrium 13.1 51   0.14 71
Zirconium 11.8 48   0.06 68
Niobium 9.1 51   0.06 88
Molybdenum 13.8 70   0.10 89
Technetium 15.3 50   0.08 84
Ruthenium 16.1 57   0.08 115
Rhodium 21.7 32   0.15 71
Palladium 12.5 47   0.08 121
Silver 5.7 14   0.16 41
Cadmium 3.4 38   0.15 54
Indium 7.2 54   0.04 77
Tin 6.7 78   0.07 98
Antimony 5.5 58   0.06 91
Tellurium 7.9 46   0.06 82
Iodine 7.6 279   0.14 287
Xenon 0.0 1   0.63 8
Cesium 8.1 40   0.31 44
Barium 11.8 37   0.15 52
Lanthanum 11.2 38   0.30 44
Lutetium 7.9 24   0.05 60
Hafnium 9.1 37   0.07 42
Tantalum 15.8 36   0.07 59
Tungsten 8.1 28   0.13 58
Rhenium 9.8 57   0.07 108
Osmium 6.6 19   0.07 54
Iridium 10.2 25   0.19 72
Platinum 11.5 77   0.06 141
Gold 16.3 32   0.22 87
Mercury 6.0 51   0.14 64
Thallium 11.3 45   0.20 60
Lead 8.3 44   0.12 53
Bismuth 7.8 53   0.14 81
Average 8.3 13,766   0.09 10,082