Table 5.

WDUD values in the ablation study. Since the GNN-based vector-generation process has randomness, the results of all methods are shown by means and standard deviation over five trials.

	SUBMO w/o N	SUBMO w/ N	MS w/o N
mu (Debye)	$10.47\pm 0.10$	$10.65\pm 0.06$	$11.88\pm 0.06$
alpha (Bohr${}^3$)	$38.76\pm 0.47$	$37.03\pm 0.07$	$37.64\pm 0.49$
HOMO (Hartree)	$0.02931\pm 0.00194$	$0.02786\pm 0.00049$	$0.04135\pm 0.00115$
LUMO (Hartree)	$0.02243\pm 0.00212$	$0.02905\pm 0.00133$	$0.03360\pm 0.00058$
gap (Hartree)	$0.03542\pm 0.00181$	$0.03541\pm 0.00138$	$0.05428\pm 0.00086$
R2 (Bohr${}^2$)	$373.4\pm 18.6$	$359.0\pm 7.8$	$211.2\pm 4.2$
ZPVE (Hartree)	$0.02800\pm 0.00125$	$0.02320\pm 0.00118$	$0.01542\pm 0.00097$
U0 (Hartree)	$93.39\pm 2.08$	$85.09\pm 1.47$	$68.82\pm 0.62$
U (Hartree)	$93.39\pm 2.08$	$85.09\pm 1.47$	$68.82\pm 0.62$
H (Hartree)	$93.39\pm 2.08$	$85.09\pm 1.47$	$68.82\pm 0.62$
G (Hartree)	$93.40\pm 2.08$	$85.10\pm 1.47$	$68.83\pm 0.62$
Cv (cal/(mol K))	$5.788\pm 0.155$	$5.593\pm 0.129$	$4.893\pm 0.091$
ZPVE/$N_{\text{mode}}$ (Hartree)	$0.001572\pm 0.000008$	$0.001533\pm 0.000006$	$0.001547\pm 0.000004$
U0/$N_{\text{elec}}$ (Hartree)	$0.3956\pm 0.0293$	$0.3848\pm 0.0087$	$0.2163\pm 0.0139$
U/$N_{\text{elec}}$ (Hartree)	$0.3956\pm 0.0293$	$0.3848\pm 0.0087$	$0.2163\pm 0.0139$
H/$N_{\text{elec}}$ (Hartree)	$0.3956\pm 0.0293$	$0.3848\pm 0.0087$	$0.2163\pm 0.0139$
G/$N_{\text{elec}}$ (Hartree)	$0.3955\pm 0.0293$	$0.3848\pm 0.0087$	$0.2163\pm 0.0139$
Cv/$N_{\text{mode}}$ (cal/(mol K))	$0.4419\pm 0.0068$	$0.4681\pm 0.0031$	$0.4521\pm 0.0016$

	MS w/ N	MM w/o N	MM w/ N
mu (Debye)	$11.21\pm 0.21$	$11.15\pm 0.14$	$10.69\pm 0.18$
alpha (Bohr${}^3$)	$36.63\pm 0.36$	$38.86\pm 0.59$	$39.05\pm 0.73$
HOMO (Hartree)	$0.03101\pm 0.00128$	$0.03375\pm 0.00147$	$0.03067\pm 0.00100$
LUMO (Hartree)	$0.03385\pm 0.00228$	$0.02422\pm 0.00046$	$0.03140\pm 0.00151$
gap (Hartree)	$0.04084\pm 0.00300$	$0.04108\pm 0.00159$	$0.04061\pm 0.00267$
R2 (Bohr${}^2$)	$316.2\pm 20.9$	$342.0\pm 15.3$	$361.9\pm 12.6$
ZPVE (Hartree)	$0.01677\pm 0.00088$	$0.02501\pm 0.00176$	$0.02896\pm 0.00076$
U0 (Hartree)	$71.93\pm 2.06$	$89.49\pm 2.91$	$87.40\pm 2.20$
U (Hartree)	$71.93\pm 2.06$	$89.49\pm 2.91$	$87.40\pm 2.20$
H (Hartree)	$71.93\pm 2.06$	$89.49\pm 2.91$	$87.40\pm 2.20$
G (Hartree)	$71.94\pm 2.06$	$89.50\pm 2.91$	$87.40\pm 2.20$
Cv (cal/(mol K))	$5.299\pm 0.135$	$6.124\pm 0.110$	$5.877\pm 0.132$
ZPVE/$N_{\text{mode}}$ (Hartree)	$0.001497\pm 0.000006$	$0.001565\pm 0.000011$	$0.001553\pm 0.000006$
U0/$N_{\text{elec}}$ (Hartree)	$0.3487\pm 0.0407$	$0.3785\pm 0.0194$	$0.4525\pm 0.0141$
U/$N_{\text{elec}}$ (Hartree)	$0.3487\pm 0.0407$	$0.3785\pm 0.0194$	$0.4525\pm 0.0141$
H/$N_{\text{elec}}$ (Hartree)	$0.3487\pm 0.0407$	$0.3785\pm 0.0194$	$0.4525\pm 0.0141$
G/$N_{\text{elec}}$ (Hartree)	$0.3487\pm 0.0407$	$0.3784\pm 0.0194$	$0.4525\pm 0.0141$
Cv/$N_{\text{mode}}$ (cal/(mol K))	$0.4812\pm 0.0013$	$0.4632\pm 0.0051$	$0.4777\pm 0.0036$