Supporting Information
An Improved Theoretical Approach to the Empirical Corrections of Density Functional Theory
Jenn-Huei Lii, Ching-Han Hu*
Department of Chemistry, National Changhua University of Education, Changhua 50058, Taiwan
15
Table 1S. List of the Training-set Alkanes for DHf calculationsLabel / Compound / Formulae / Exp DHf / POP / B3 / B3-CCAZD
Correction / MP / MP-CCAZD
Correction
alkh01 / Methane / C1H4 / -17.89 / 0.00 / -40.518383 / 0.0019928 / -40.479298 / -0.0010208
alkh02 / Ethane / C2H6 / -20.00 / 0.00 / -79.830419 / 0.0019903 / -79.766920 / 0.0015326
alkh03 / Propane / C3H8 / -24.82 / 0.00 / -119.144248 / -0.0000098 / -119.056665 / 0.0035279
alkh04 / Butane / C4H10 / -30.15 / 0.27 / -158.458046 / -0.0019150 / -158.346396 / 0.0054666
alkh05 / Pentane / C5H12 / -35.00 / 0.49 / -197.771781 / -0.0038681 / -197.636055 / 0.0073717
alkh06 / Hexane / C6H14 / -39.96 / 0.68 / -237.085500 / -0.0058286 / -236.925734 / 0.0092700
alkh07 / Heptane / C7H16 / -44.89 / 0.92 / -276.399229 / -0.0077949 / -276.215395 / 0.0111649
alkh08 / Octane / C8H18 / -49.82 / 1.16 / -315.712916 / -0.0097665 / -315.505030 / 0.0130579
alkh09 / Nonane / C9H20 / -54.75 / 1.41 / -355.026671 / -0.0117311 / -354.794731 / 0.0149508
alkh10 / Isobutane / C4H10 / -32.15 / 0.00 / -158.458807 / -0.0040166 / -158.347726 / 0.0047914
alkh11 / Isopentane / C5H12 / -36.92 / 0.06 / -197.771116 / -0.0064119 / -197.636445 / 0.0064612
alkh12 / Neopentane / C5H12 / -40.27 / 0.00 / -197.773001 / -0.0094936 / -197.639203 / 0.0052251
alkh13 / 2,3-Dimethylbutane / C6H14 / -42.49 / 0.15 / -237.082470 / -0.0109509 / -236.925129 / 0.0075329
alkh14 / 2,2,3-Trimethylbutane / C7H16 / -48.95 / 0.00 / -276.393195 / -0.0174242 / -276.214224 / 0.0074686
alkh15 / 2,2-Dimethylpentane / C7H16 / -49.20 / 0.00 / -276.397155 / -0.0144580 / -276.216322 / 0.0084336
alkh16 / 3,3-Dimethylpentane / C7H16 / -48.08 / 0.00 / -276.393917 / -0.0154500 / -276.214177 / 0.0081029
alkh17 / 3-Ethylpentane / C7H16 / -45.25 / 0.10 / -276.394564 / -0.0109694 / -276.212542 / 0.0097283
alkh18 / 2,4-Dimethylpentane / C7H16 / -48.21 / 0.16 / -276.397738 / -0.0132299 / -276.216592 / 0.0089514
alkh19 / 2,5-Dimethylhexane / C8H18 / -53.18 / 0.81 / -315.711505 / -0.0150897 / -315.505869 / 0.0109998
alkh20 / 2,2,3,3-Tetramethylbutane / C8H18 / -53.92 / 0.00 / -315.700916 / -0.0239121 / -315.500750 / 0.0076302
alkh21 / 2,2,3,3-Tetramethylpentane / C9H20 / -56.64 / 0.00 / -355.010389 / -0.0267915 / -354.788897 / 0.0086504
alkh22 / Di-t-butylmethane / C9H20 / -57.80 / 0.02 / -355.014205 / -0.0247893 / -354.789108 / 0.0089870
alkh23 / Tetraethylmethane / C9H20 / -55.67 / 0.00 / -355.014867 / -0.0224810 / -354.790773 / 0.0100367
alkh24 / Tri-t-butylmethane / C13H28 / -56.40 / 0.00 / -512.210403 / -0.0447769 / -511.898990 / 0.0114687
alkh25 / Cyclopentane / C5H10 / -18.74 / 0.00 / -196.557078 / -0.0077175 / -196.437713 / 0.0115805
alkh26 / Cyclohexane / C6H12 / -29.43 / 0.00 / -235.880468 / -0.0104932 / -235.737090 / 0.0130643
alkh27 / Cycloheptane / C7H14 / -28.22 / 0.00 / -275.183549 / -0.0135142 / -275.016391 / 0.0142616
alkh28 / Cyclooctane / C8H16 / -29.73 / 0.00 / -314.490353 / -0.0172738 / -314.300143 / 0.0153145
alkh29 / Cyclononane / C9H18 / -31.73 / 0.77 / -353.798189 / -0.0203706 / -353.585582 / 0.0168521
alkh30 / Cyclodecane / C10H20 / -36.88 / 0.77 / -393.111392 / -0.0253497 / -392.874056 / 0.0175654
alkh31 / Cyclododecane / C12H24 / -54.59 / 0.92 / -471.746328 / -0.0303150 / -471.461268 / 0.0206648
alkh32 / 1,1-Dimethylcyclopentane / C7H14 / -33.04 / 0.24 / -275.185499 / -0.0174660 / -275.020514 / 0.0128832
alkh33 / Methylcyclopentane / C6H12 / -25.27 / 0.25 / -235.872577 / -0.0114948 / -235.729449 / 0.0127777
alkh34 / Ethylcyclopentane / C7H14 / -30.34 / 0.31 / -275.185470 / -0.0139631 / -275.018766 / 0.0143104
alkh35 / eq-Methylcyclohexane / C7H14 / -36.99 / 0.10 / -275.195630 / -0.0143390 / -275.028735 / 0.0141923
alkh36 / 1,1-Dimethylcyclohexane / C8H16 / -43.26 / 0.00 / -314.506740 / -0.0205841 / -314.318275 / 0.0141106
alkh37 / 1-ax-2-eq-Dimethylcyclohexane / C8H16 / -41.13 / 0.00 / -314.505347 / -0.0198389 / -314.316617 / 0.0145787
alkh38 / 1-eq-2-eq-Dimethylcyclohexane / C8H16 / -42.99 / 0.02 / -314.508531 / -0.0186670 / -314.318712 / 0.0150606
alkh39 / Bicyclo[3.3.1]nonane / C9H16 / -30.50 / 0.02 / -352.607987 / -0.0253067 / -352.410354 / 0.0206994
alkh40 / cis-Bicyclo[3.3.0]octane / C8H14 / -22.20 / 0.22 / -313.290440 / -0.0206616 / -313.116923 / 0.0195905
alkh41 / trans-Bicyclo[3.3.0]octane / C8H14 / -15.92 / 0.00 / -313.277645 / -0.0195610 / -313.103497 / 0.0202664
alkh42 / trans-Decalin / C10H18 / -43.54 / 0.00 / -391.933680 / -0.0264445 / -391.711531 / 0.0226254
alkh43 / cis-Decalin / C10H18 / -40.45 / 0.00 / -391.928523 / -0.0279408 / -391.708067 / 0.0219496
alkh44 / trans-Hydrindane / C9H16 / -31.45 / 0.00 / -352.609377 / -0.0232357 / -352.411169 / 0.0214114
alkh45 / cis-Hydrindane / C9H16 / -30.41 / 0.05 / -352.607125 / -0.0244610 / -352.410146 / 0.0208353
alkh46 / trans-syn-trans-Perhydroanthrancene / C14H24 / -58.12 / 0.00 / -547.986723 / -0.0425338 / -547.685849 / 0.0320438
alkh47 / trans-anti-trans-Perhydroanthrancene / C14H24 / -52.73 / 0.00 / -547.975693 / -0.0420801 / -547.675084 / 0.0322749
alkh48 / Norbornane / C7H12 / -13.12 / 0.00 / -273.968489 / -0.0175715 / -273.820952 / 0.0187075
alkh49 / 1,4-Dimethylnorbornane / C9H16 / -30.62 / 0.00 / -352.602147 / -0.0283508 / -352.407340 / 0.0193020
alkh50 / Adamantane / C10H16 / -31.76 / 0.00 / -390.725211 / -0.0317952 / -390.522476 / 0.0265828
alkh51 / 1,3,5,7-Tetramethyladamantane / C14H24 / -67.15 / 0.00 / -547.990120 / -0.0528561 / -547.695532 / 0.0269838
alkh52 / Protoadamantane / C10H16 / -20.54 / 0.00 / -390.707855 / -0.0315831 / -390.506362 / 0.0262076
alkh53 / Congressane / C14H20 / -34.61 / 0.00 / -545.574077 / -0.0519872 / -545.310627 / 0.0395853
alkh54 / Bicyclo[2.2.2]octane / C8H14 / -22.58 / 0.00 / -313.289930 / -0.0215816 / -313.116727 / 0.0200099
alkh55 / Perhydroquinacene / C10H16 / -24.46 / 0.00 / -390.711036 / -0.0316759 / -390.507258 / 0.0257042
alkh56 / Dodecahedrane / C20H20 / 18.20 / 0.00 / -774.185418 / -0.0866005 / -773.863699 / 0.0681886
DHf: Experimental enthalpies of formation (in kcal/mol). Values are adopted from MM4 reports.[20].
POP: Conformational population terms (in kcal/mol) were used to add to the calculated DHf of the most stable conformations to compare to the experimental DHf. Values are adopted from MM4 reports.[20]
B3: B3LYP/6-31G* (in hartrees).
MP: MPWB1K/6-31G* (in hartrees).
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Table 2S. List of the Training-set Alcohols and Ethers for DHf calculationsLabel / Compound / Formulae / Exp DHf / POP / B3 / B3-CCAZD
Correction / MP / MP-CCAZD
Correction
alch01 / Methanol / C1H4O1 / -48.16 / 0.00 / -115.714407 / -0.0099535 / -115.648967 / -0.0161330
alch02 / Ethanol / C2H6O1 / -56.24 / 0.15 / -155.033805 / -0.0112786 / -154.944106 / -0.0137719
alch03 / 1-Propanol / C3H8O1 / -61.17 / 0.43 / -194.347719 / -0.0131783 / -194.234371 / -0.0119047
alch04 / 2-Propanol / C3H8O1 / -65.12 / 0.09 / -194.353318 / -0.0129862 / -194.239679 / -0.0113553
alch05 / Isobutanol / C4H10O1 / -67.84 / 0.34 / -233.662359 / -0.0169970 / -233.525614 / -0.0107292
alch06 / 1-Butanol / C4H10O1 / -65.79 / 0.78 / -233.661082 / -0.0150668 / -233.523265 / -0.0100433
alch07 / 2-Butanol / C4H10O1 / -69.98 / 0.25 / -233.667138 / -0.0148054 / -233.529889 / -0.0095194
alch08 / t-Butanol / C4H10O1 / -74.72 / 0.00 / -233.670958 / -0.0173440 / -233.534170 / -0.0107850
alch09 / 1-Pentanol / C5H12O1 / -70.66 / 1.13 / -272.974860 / -0.0170055 / -272.813012 / -0.0081489
alch10 / 2-Pentanol / C5H12O1 / -75.00 / 0.60 / -272.980859 / -0.0167405 / -272.819506 / -0.0077272
alch11 / 2-Methyl-2-Butanol / C5H12O1 / -79.06 / 0.09 / -272.983165 / -0.0196350 / -272.823355 / -0.0092327
alch12 / 1-Hexanol / C6H14O1 / -75.65 / 1.48 / -312.288597 / -0.0189671 / -312.102670 / -0.0062560
alch13 / 1-Heptanol / C7H16O1 / -79.09 / 1.83 / -351.602317 / -0.0209322 / -351.392342 / -0.0043634
alch14 / 1-Octanol / C8H18O1 / -85.30 / 2.18 / -390.916038 / -0.0228989 / -390.682012 / -0.0024710
alch15 / Cyclopentanol / C5H10O1 / -57.97 / 0.23 / -271.766511 / -0.0205686 / -271.621628 / -0.0035258
alch16 / Cyclohexanol / C6H12O1 / -69.31 / 0.26 / -311.090231 / -0.0232930 / -310.920895 / -0.0022256
alch17 / Dimethyl Ether / C2H6O1 / -43.99 / 0.00 / -155.025044 / -0.0002215 / -154.932862 / -0.0053292
alch18 / Methyl Ethyl Ether / C3H8O1 / -51.72 / 0.24 / -194.344306 / -0.0014472 / -194.227838 / -0.0030479
alch19 / Diethyl Ether / C4H10O1 / -60.26 / 0.30 / -233.663459 / -0.0027447 / -233.522679 / -0.0008160
alch20 / Methyl Propyl Ether / C4H10O1 / -56.88 / 0.39 / -233.657912 / -0.0033673 / -233.517404 / -0.0012424
alch21 / Methyl Isopropyl Ether / C4H10O1 / -60.24 / 0.04 / -233.660863 / -0.0041845 / -233.520948 / -0.0009745
alch22 / Methyl t-Butyl Ether / C5H12O1 / -67.68 / 0.00 / -272.974775 / -0.0097620 / -272.812506 / -0.0007583
alch23 / 1-Ethoxy Propane / C5H12O1 / -65.06 / 0.59 / -272.977074 / -0.0046836 / -272.812264 / 0.0009758
alch24 / Dipropyl Ether / C6H14O1 / -69.85 / 1.00 / -312.290709 / -0.0066241 / -312.101854 / 0.0027704
alch25 / Diisopropyl Ether / C6H14O1 / -76.20 / 0.00 / -312.296751 / -0.0081114 / -312.109105 / 0.0031153
alch26 / Isopropyl t-Butyl Ether / C7H16O1 / -85.50 / 0.00 / -351.609664 / -0.0142265 / -351.400166 / 0.0028510
alch27 / Di-n-butyl Ether / C8H18O1 / -79.82 / 1.70 / -390.917865 / -0.0104745 / -390.680844 / 0.0065033
alch28 / Di-t-butyl Ether / C8H18O1 / -87.10 / 0.00 / -390.916439 / -0.0200999 / -390.684879 / 0.0024247
alch29 / Tetrahydropyran (T.H.P.) / C5H10O1 / -53.39 / 0.00 / -271.770668 / -0.0097342 / -271.622413 / 0.0046491
alch30 / 3-Oxa-bicyclo[3.2.2]nonane / C8H14O1 / -53.18 / 0.00 / -388.493127 / -0.0234762 / -388.291261 / 0.0121893
alch31 / Tetrahydrofuran (T.H.F.) / C4H8O1 / -44.02 / 0.00 / -232.449443 / -0.0074916 / -232.325244 / 0.0030354
alch32 / 1-Me-cyclopentanol / C6H12O1 / -67.94 / 0.12 / -311.085205 / -0.0246653 / -310.916872 / -0.0029031
alch33 / 2-Me-1-butanol / C5H12O1 / -72.19 / 0.56 / -272.974059 / -0.0195148 / -272.814079 / -0.0091868
alch34 / i-Butyl t-Butyl Ether / C8H18O1 / -88.00 / 0.06 / -390.922265 / -0.0174388 / -390.688741 / 0.0037491
alch35 / 3-Me-2-butanol / C5H12O1 / -75.35 / 0.54 / -272.979478 / -0.0192051 / -272.819707 / -0.0086224
alch36 / 1,3-Propane Diol / C3H8O2 / -93.71 / 0.43 / -269.551494 / -0.0256631 / -269.411730 / -0.0268998
alch37 / Dimethoxymethane / C3H8O2 / -83.27 / 0.20 / -269.552251 / -0.0043904 / -269.408501 / -0.0099715
alch38 / 1,1-Dimethoxyethane / C4H10O2 / -93.26 / 0.34 / -308.871268 / -0.0069359 / -308.704452 / -0.0069834
alch39 / 1,3-Dioxane / C4H8O2 / -80.90 / 0.00 / -307.666287 / -0.0094015 / -307.514263 / -0.0030320
alch40 / 2-Methoxy T.H.P. / C6H12O2 / -95.50 / 0.20 / -386.299881 / -0.0140195 / -386.101250 / 0.0006424
alch41 / 1,3-Dioxacycloheptane / C5H10O2 / -82.84 / 0.51 / -346.979482 / -0.0116599 / -346.803927 / -0.0024573
alch42 / 2,2-Dimethoxypropane / C5H12O2 / -102.15 / 0.25 / -348.187862 / -0.0108992 / -347.998814 / -0.0054402
alch43 / 1,3-Dioxolan / C3H6O2 / -72.10 / 0.00 / -268.343846 / -0.0079479 / -268.215567 / -0.0052537
alch44 / 1,3,5-Trioxane / C3H6O3 / -111.35 / 0.00 / -343.565415 / -0.0096903 / -343.410748 / -0.0113923
alch45 / 1,3,5,7-Tetraoxocane / C4H8O4 / -148.24 / 0.30 / -458.090920 / -0.0105559 / -457.881836 / -0.0154902
alch46 / 3,5-Dioxahepntane / C5H12O2 / -99.16 / 0.53 / -348.190480 / -0.0070622 / -347.998132 / -0.0058890
alch47 / 3,5,7-Trioxanonane / C6H14O3 / -138.92 / 0.60 / -462.717402 / -0.0097988 / -462.473124 / -0.0096977
alch48 / 1,1,1-Trimethoxyethane / C5H12O3 / -136.44 / 0.25 / -423.399495 / -0.0121003 / -423.181880 / -0.0149156
alch49 / Ethylene Glycol / C2H6O2 / -92.64 / 0.21 / -230.240962 / -0.0215602 / -230.125818 / -0.0262613
alch50 / 1,2-Propane Diol / C3H8O2 / -102.70 / 0.07 / -269.560754 / -0.0237077 / -269.421856 / -0.0241977
alch51 / 1,2-Dimethoxyethane / C4H10O2 / -81.93 / 0.45 / -308.855968 / -0.0036549 / -308.686751 / -0.0066525
alch52 / 1,2-Diethoxyethane / C6H14O2 / -97.59 / 0.46 / -387.494396 / -0.0062461 / -387.276551 / -0.0022353
alch53 / 1,4-Dioxane / C4H8O2 / -75.36 / 0.00 / -307.658240 / -0.0078102 / -307.504787 / -0.0025302
alch54 / Water / H2O1 / -57.80 / 0.00 / -76.408953 / -0.0212576 / -76.370902 / -0.0271630
DHf: Experimental enthalpies of formation (in kcal/mol). Values are adopted from MM4 reports.[42-44].
POP: Conformational population terms (in kcal/mol) were used to add to the calculated DHf of the most stable conformations to compare to the experimental DHf. Values are adopted from MM4 reports.[42-44].
B3: B3LYP/6-31G* (in hartrees).
MP: MPWB1K/6-31G* (in hartrees).
Table 3S. Enthalpies of Formation for Training-set Alkanes, Shown as Difference from the Experimental Values (kcal/mol)aAZ (Atomization) / ISOD (Isodesmic)
Label / Exp
DHf / D MM4c / D G3 / D CBS-
QB3 / D B3 / D MP / D B3
-AEc / D MP
-AEc / D B3-
CCAZDc / D MP-
CCAZDc / D G3 / D CBS-
QB3 / D B2P
LYP-D / D B3 / D MP / D B3-
GEc / D MP-
GEc
Sign Avgb / 0.08 / -0.07 / 2.42 / 10.92 / -8.88 / -0.01 / 0.10 / 0.14 / 0.16 / 0.32 / 0.27 / -2.27 / 10.55 / 1.42 / 0.04 / 0.11
AADb / 0.34 / 0.54 / 2.42 / 11.04 / 8.90 / 1.67 / 1.03 / 0.45 / 0.50 / 0.63 / 0.61 / 2.39 / 10.55 / 5.20 / 1.46 / 0.70
alkh01 / -17.89 / 0.00 / -0.16 / 0.16 / -1.25 / 0.64 / -0.06 / -0.42 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 4.09 / 2.09
alkh02 / -20.00 / 0.49 / 0.02 / 0.64 / -1.28 / -1.49 / -1.56 / -1.37 / -0.27 / -0.76 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 1.76 / 0.64