The X1 family of methods that combines B3LYP with neural network
corrections for an accurate yet efficient prediction of thermochemistry
Jianming Wu, Yuwei Zhou, and Xin Xu
Correspondence to: Xin Xu (E-mail: xxchem@fudan.edu.cn)
Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of
Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical
Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
Table S1. The training set for the X1 family of methods. The core set includes the G2/97 set and
the border set.
G2/97
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
H2
HLi
HBe
CH
CH2
CH2
CH3
CH4
HN
H2N
H3N
HO
H2O
HF
H2Si
H2Si
H3Si
H4Si
H2P
H3P
H2S
HCl
Li2
LiF
C2H2
C2H4
C2H6
CN
CHN
CO
CHO
CH2O
CH4O
N2
H4N2
NO
O2
H2O2
F2
CO2
H2
LiH
BeH
CH
CH2 (3B1)
CH2 (1A1)
CH3
CH4
NH
NH2
NH3
HO
HOH
HF
SiH2 (1A1)
SiH2 (3B1)
SiH3
SiH4
PH2
PH3
H2S
HCl
Li2
LiF
C2H2
H2C=CH2
C2H6
CN
HCN
CO
HCO
H2C=O
CH3OH
N2
H2N-NH2
NO
O2
HOOH
F2
CO2
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
Na2
Si2
P2
S2
Cl2
NaCl
OSi
CS
OS
OCl
FCl
H6Si2
CH3Cl
CH4S
HOCl
O2S
BF3
BCl3
F3Al
AlCl3
CF4
CCl4
COS
CS2
COF2
F4Si
SiCl4
N2O
NOCl
NF3
F3P
O3
OF2
F3Cl
C2F4
C2Cl4
C2NF3
C3H4
C3H4
C3H4
C3H6
C3H6
C3H8
C4H6
Na2
Si2
P2
S2
Cl2
NaCl
SiO
CS
SO
ClO
ClF
H3Si-SiH3
CH3Cl
H3C-SH
HOCl
SO2
BF3
BCl3
AlF3
AlCl3
CF4
CCl4
O=C=S
CS2
COF2
SiF4
SiCl4
N2O
ClNO
NF3
PF3
O3
F2O
ClF3
C2F4
C2Cl4
CF3CN
propyne
allene
cyclopropene
propylene
cyclopropane
propane
butadiene
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
C4H6
C4H6
C4H6
C4H6
C4H8
C4H8
C4H10
C4H10
C5H8
C6H6
CH2F2
CHF3
CH2Cl2
CHCl3
CH5N
C2H3N
CH3NO2
CH3NO2
CH6Si
CH2O2
C2H4O2
C2H5NO
C2H5N
C2N2
C2H7N
C2H7N
C2H2O
C2H4O
C2H4O
C2H2O2
C2H6O
C2H6O
C2H4S
C2H6OS
C2H6S
C2H6S
C2H3F
C2H5Cl
C2H3Cl
C3H3N
C3H6O
C2H4O2
C2H3OF
C2H3OCl
2-butyne
methylene cyclopropane
bicyclobutane
cyclobutene
cyclobutane
isobutene
trans butane
isobutane
spiropentane
benzene
H2CF2
HCF3
H2CCl2
HCCl3
Methylamine
methyl cyanide
nitromethane
methyl nitrite
methyl silane
formic acid
methyl formate
acetamide
aziridine
cyanogen
Dimethylamine
trans ethylamine
H2C=C=O (ketene)
CH2-O-CH2 (oxirane)
CH3CHO (acetaldehyde)
O=CH-CH=O (glyoxal)
CH3CH2OH (ethanol)
CH3-O-CH3 (dimethylether)
CH2-S-CH2 (thiooxirane)
CH3CH3SO (dimethyl sulfoxide)
CH3-CH2-SH (ethanethiol)
CH3-S-CH3 (dimethyl sulphide)
H2C=CHF
CH3-CH2-Cl (ethyl chloride)
H2C=CHCl (vinyl chloride)
H2C=CHCN (acrylonitrile)
CH3-CO-CH3 (acetone)
CH3COOH (acetic acid)
CH3COF (acetyl fluoride)
CH3COCl (acetyl chloride)
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
The border Set
211
305
306
382
671
687
690
698
715
737
740
755
769
789
797
833
838
839
C3H7Cl
C3H8O
C3H8O
C3H9N
C4H4O
C4H4S
C4H5N
C5H5N
HS
C2H
C2H3
C2H3O
CH3O
CH3O
C2H5O
CH3S
C2H5
C3H7
C4H9
NO2
CH3CH2CH2Cl (propyl chloride)
(CH3)2CH-OH (isopropanol)
C2H5-O-CH3 (methyl ethyl ether)
(CH3)3N (trimethylamine)
C4H4O (furan)
C4H4S (thiophene)
C4H4NH (pyrrole)
C5H5N (pyridine)
SH
CCH
C2H3 (2A')
CH3CO (2A')
H2COH (2A)
CH3O (2A')
CH3CH2O (2A")
CH3S (2A')
C2H5 (2A')
(CH3)2CH (2A')
(CH3)3C
NO2
P4
C7H16
C7H16
N3
Al2Cl6
Na2Cl2
Li3Cl3
H9B5
C6F10
C32H66
CN4O8
C7H5N3O6
S8
OF3P
H8Si3
Be2
CH3N5
Mg2
P4
3,3-dimethylpentane
2,2,3-trimethylbutane
azide radical
Aluminum trichloride dimer
Disodium dichloride
(LiCl)3
Pentaborane
Perfluorocyclohexene
n-C32H66
Tetranitromethane
2,4,6-trinitrotoluene
sulfur octamer (cyclic)
phosphorus oxyfluoride
Trisilane
Beryllium dimer
5-Aminotetrazole
Magnesium dimer
Other training molecules
149 C4H6
1,2-Butadiene
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
C5H8
C5H10
C5H12
C5H12
C6H8
C6H8
C6H12
C6H14
C6H14
C7H8
C7H16
C8H8
C8H18
C10H8
C10H8
C3H6O2
C4H10O
C6H7N
C6H6O
C4H6O
C4H8O
C5H8O
C6H4O2
C4H4N2
C2H6O2S
C6H5Cl
C4H4N2
C4H4N2
C4H4O
C4H6O
C4H6O3
C4H6S
C4H7N
C4H8O
C4H8O
C4H8O2
C4H8S
C4H9Cl
C4H9Cl
C4H9N
C4H9NO2
C4H10O
C4H10O2
C4H10S
Isoprene
Cyclopentane
n-pentane
Neopentane
1,3-cyclohexadiene
1,4-cyclohexadiene
Cyclohexane
n-Hexane
Pentane, 3-methylC6H5CH3 (toluene)
n-heptane
1,3,5,7-Cyclooctatetraene
n-octane
Naphthalene
Azulene
CH3COOCH3 (methyl acetate)
(CH3)3COH (t-butanol)
C6H5NH2 (aniline)
C6H5OH (phenol)
CH2=CH-O-CH=CH2 (divinyl ether)
Tetrahydrofuran
Cyclopentanone
[p-]benzoquinone
Pyrimidine
C2H6O2S (dimethyl sulphone)
chlorobenzene
1,2-dicyano ethane
pyrazine
CH3-CO-CCH (acetyl acetylene)
CH3-CH=CH-CHO (crotonaldehyde)
CH3-CO-O-CO-CH3 (acetic anhydride)
C4H6S (2,5-dihydrothiophene)
isobutane nitrile
methyl ethyl ketone
isobutanal
1,4-dioxane
tetrahydrothiophene
t-butyl chloride
n-butyl chloride
tetrahydropyrrole
nitro-s-butane
diethyl ether
1,1-dimethoxy ethane
t-butanethiol
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
212
213
214
215
216
217
218
219
220
221
222
223
227
230
235
236
237
242
250
252
255
258
259
274
286
287
292
C4H10S2
C4H11N
C4H12Si
C5H6S
C5H7N
C5H10O
C5H10O
C5H10O2
C5H10S
C5H11N
C5H12O
C6H4F2
C6H4F2
C6H5F
C6H14O
PF5
F6S
SO3
SCl2
OPCl3
PCl5
O2SCl2
PCl3
S2Cl2
SiCl2
CF3Cl
C2F6
CF3
C6H5
C2H2F2
C2H3Cl3
C2H5NO3
C2H8N2
C3H3NO
C3H6S
C3H8S
C3H8S
C3H10N2
C4H10O
C4H10O2
C5H11Cl
C6H4Cl2
C6H5NO2
C6H10
CH3CH2-S-S-CH2CH3 (diethyl disulfide)
(CH3)3C-NH2 (t-butylamine)
Si(CH3)4 (tetramethylsilane)
C5H6S (2-methyl thiophene)
C5H7N (N-methyl pyrrole)
C5H10O (tetrahydropyran)
CH3-CH2C(=O)-CH2CH3 (diethyl ketone)
CH3-C(=O)-O-CH(CH3)2 (isopropyl acetate)
C5H10S (tetrahydrothiopyran)
cyc-C5H10NH (piperidine)
(CH3)3-C-O-CH3 (t-butyl methyl ether)
C6H4F2 (1,3-difluorobenzene)
C6H4F2 (1,4-difluorobenzene)
C6H5F (fluorobenzene)
(CH3)2CH-O-CH(CH3)2 (di-isopropyl ether)
Phosphorus pentafluoride
Sulfur hexafluoride
Sulphur trioxide
Sulfur dichloride
Phosphorus oxychloride
Phosphorus pentachloride
Sulphuryl dichloride
Phosphorus trichloride
Sulfur monochloride
Dichlorosilylene (singlet)
Chlorotrifluoromethane
Ethane, hexafluoroTrifluoromethyl radical (*CF3)
Phenyl radical (*C6H5)
Ethene, 1,1-difluoro- (CH2=CF2)
1,1,1-trichloroethane
ethylnitrate
ethylenediamine (CRC#1,2-Ethanediamine)
oxazole
thiacyclobutane (CRC# Thietane)
1-propanthiol
Ethyl methyl sulfide
1,2-propanediamine
sec-butanol (CRC#2-Butanol)
1,4-butanediol
1-chloropentane
1,3-dichlorobenzene
nitrobenzene
Cyclopentene, 1-methyl-
293
301
305
307
314
318
323
324
330
336
344
357
363
364
377
378
379
380
381
383
384
385
395
398
399
403
404
412
437
460
473
479
504
518
523
525
527
530
534
536
537
538
540
544
C6H10
C7H6O
C7H16
C7H16S
C8H16
C8H18
C9H18O
C9H20
C12H10
C4H6
C5H8
C8H8
C14H10
C3O2
C3H8O2
C4H6O2
C4H10O2
C7H6O2
C4H2O3
H2N2
HN3
C4N2
C4H2N2
CH2N4
NO3
HNO2
HNO3
CH3NO3
NOF
C2H3Cl3
COCl
C7H5OCl
H2S5
C12H10S
C2H6S2
C3H8S2
C12H10S2
C3H4S3
H2SO4
C2H4OS
C4H8OS
C4H10OS
C3H8O2S
C2H6O3S
1,5-hexadiene
benzaldehyde
Pentane, 3,3-dimethyln-heptyl mercaptan
2,4,4-trimethyl-2-pentene
2,3,4-trimethylpentane
diisobutyl ketone (2,6-Dimethyl-4-heptanone)
Pentane, 3,3-diethylacenaphthene
ethylacetylene (CRC# 1-Butyne)
bicyclo[2.1.0]pentane (housane)
styrene
phenanthrene
carbon suboxide(O=C=C=C=O)
dimethoxymethane (CRC#methylal)
biacetyl(2,3-butanedione)
diethyl peroxide
benzoic acid
maleic anhydride
Z-diazene
hydrazoic acid
Dicyanoacetylene;2-Butynedinitrile
fumaronitrile;trans-2-Butenedinitrile
1H-tetrazole
nitrate radical(O=N(-O*)=O)
nitrous acid, trans
nitric acid
methyl nitrate
nitrosyl fluoride
1,1,2-trichloroethane
Carbonyl chloride
2-chlorobenzaldehyde
hydrogen pentasulfide
diphenyl sulfide
2,3-dithiabutane
propane-1,3-dithiol
Disulfide, diphenyl
1,3-dithiolan-2-thione
sulfuric acid
thiolacetic acid
s-ethylthioacetate
diethyl sulfoxide
methylethyl sulfone
dimethyl sulfite
547
550
554
555
556
560
561
562
566
567
569
571
590
596
598
623
631
640
641
642
643
646
655
656
663
664
669
673
674
675
676
677
678
679
680
681
682
683
684
685
686
688
689
691
C2H6O4S
C3H4OS2
C2H5NS
C4H5NS
C7H5NS
CH4N2S
CH5N3S
CH6N4S
F4S
F5S
O2F2S
HO3FS
C18H15P
C3H9O3P
C6H15O4P
C2H8Si
C8H20Si
C3H10OSi
C5H14OSi
C6H16O2Si
C6H18OSi2
C5H15NSi
CH5SiCl
C2H7SiCl
H5SiP
Al2
OAl2
FAlCl2
BeO
LiNa
NaF
MgF
HLiO
NaOH
MgF2
Na2O
BeCl2
MgCl2
H3B
B2O2
Li2Cl2
Be2OF2
B2F4
B2Cl4
dimethyl sulfate
1,3-dithiolan-2-one
Ethanethioamide
4-methylthiazole
benzothiazole
thiourea
hydrazinecarbothioamide
carbonothioic dihydrazide
sulfur tetrafluoride
sulfur pentafluoride (*SF5)
sulfuryl fluoride
fluorosulfonic acid (HOSO2F)
triphenylphosphine
trimethyl phosphite
Triethyl phosphate
dimethylsilane
tetraethylsilane
trimethylsiliconhydroxide
Si(CH3)3OC2H5
Si(CH3)2(OC2H5)2
hexamethyldisiloxane
(CH3)3SiN(CH3)2
Methyl chlorosilane
chlorodimethylsilane
Silylphosphine
aluminum dimer
dialuminum oxide (:Al-O-Al:)
aluminum dichloridefluoride
BeO
LiNa
NaF
*Mg-F
LiOH
NaOH
MgF2
Sodium oxide (Na-O-Na)
Beryllium dichloride
Magnesium Chloride
Borane
Oxo(oxoboranyl)borane
Dilithium dichloride
O(BeF)2
Diboron Tetrafluoride
Diboron Tetrachloride
692
693
694
695
696
697
699
700
701
702
704
706
707
709
710
711
712
713
716
718
720
721
723
724
727
728
731
732
733
734
735
736
771
774
777
785
787
794
796
819
820
824
826
827
H6B2
C3H3N3
B3O3F3
B3O3Cl3
C3H6O3
CN4F8
C12H8
C12H10
C12H9N
C13H9N
C14H12
C16H10
C18H12
C20H12
C2H4N2O2
C3H2N2
C3H7NO2
C4H4O2
C8H18S
C10H22S
C11H24
C12H14O4
C12H24
C12H24O2
C13H26O2
C14H14
C16H22O4
C16H32O2
C16H34
C16H34O
C18H14
C18H38
H2S2
H2S4
C2H4N2S2
OP
FP
H4Si2
H5Si2
O2Al
O2Al2
FAl
F6Al2
AlCl
Boranylidyneborane
1,3,5-triazine
2,4,6-trifluoro-1,3,5,2,4,6-trioxatriborinane
2,4,6-trichloro-1,3,5,2,4,6-trioxatriborinane
trioxane (1,3,5-Trioxane)
Octafluoromethanetetramine
acenaphthylene
Biphenyl
Carbazole
acridine
(Z)-stilbene
Fluoranthene
Benz[a]anthracene
Perylene
Oxamide
malononitrile
Sarcosine
diketene
dibutyl sulfide
n-decyl mercaptan
n-undecane
diethyl phthalate
1-Dodecene
n-dodecanoic acid
methyl dodecanoate
1,2-diphenylethane
dibutyl phthalate
n-hexadecanoic acid
n-hexadecane
1-hexadecanol
p-terphenyl
n-Octadecane
Disulfides
Hydrogen tetrasulfide
Ethane dithioamide
Phosphorus oxide(*P=O)
Phosphorus monofluoride (triplet)
Silylidenesilane
Disilanyl radical
Aluminum dioxide (radical)
Dialuminum dioxide
Aluminum fluoride (singlet)
Aluminumtrifluoride dimer
Aluminum chloride (singlet)
829
830
831
832
834
835
836
837
840
Only for X1se
911
930
931
972
973
974
975
976
977
978
979
980
981
FAlCl
C16H26
C8H23N5
C6H18N4
C2H4N4
C2H4N4
C2H6N2O
C3H8N2O
OS2
Aluminum chloride fluoride (radical)
n-decylbenzene
tetraethylenepentamine
triethylene tetramine
1H-Tetrazole, 5-methyl1H-Tetrazole, 1-methylUrea, methylUrea, ethylDisulfur monoxide
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
Butane, 2,2,3,3-tetramethylHexane, 3,4-dimethylHexane, 2,4-dimethylHeptane, 2-methylHeptane, 3-methylHexane, 2,2-dimethylHexane, 2,5-dimethylHexane, 3,3-dimethylPentane, 3-ethyl-2-methylPentane, 3-ethyl-3-methylPentane, 2,2,3-trimethylPentane, 2,2,4-trimethylPentane, 2,3,3-trimethyl-
The general rule to calculate ECB can be found on the Web (http://www.xdft.org/dft , 2015). Here
are some examples.
1. For n-C5H12, the ECB value equals to 6. The number assigned on the bond indicates the
quantity of single bonds connected to it. This number happened to be exactly double of the
number of protobranching of alkanes.
1
2
2
1
2. In 2,2,4-trimethylhexane (C9H20), there are 1 single C-C bond (C6-C8) connected to the C8-C9
bond. The ECB value for this bond is 1. And there are 3 bond connected to the bond (C6-C8),
then its ECB value is 3. The total ECB value for this molecule is to sum up all the values. So
ECB= 1+2+3*5+4 = 22. Here the subscripts of the carbon atom are the labels of the atoms.
3. For (1R,2R,4S,5S)-tricyclo[3.2.1.02,4]oct-6-ene (C8H10), ECB=18. The bonds on the
cyclopropane do not contribute to the ECB value.
3
2
4
3
2
4
4. For (CH3)3C-OCH3, the ECB value is composed of 3 similar parts. One is ECB(C1-C4)=3,
which indicates that there are 3 single bonds connected to it. They are C2-C4, C3-C4, and C4-O.
The SC descriptor was defined as the difference between the numbers of singly-occupied electrons
(SE) in the constituent atoms and in the molecule (∑𝑎𝑡𝑜𝑚 𝑆𝐸 − 𝑆𝐸𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑒 ).
For example, H2O has no singly-occupied electron, SEH2O=0, H has one singly-occupied electron
and O has two. Therefore SC for H2O is (2*1 + 2 -0) = 4.