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\newcommand\tabAE{
\begin{table*}[!htb]
\footnotesize
  \begin{center}
  \caption{\label{tab:AE55} Atomization energies (in kcal/mol) of the AE49 dataset (molecules of the G2-1 dataset except for the six molecules containing Li, Be, and Na) calculated by full-range HF+MP2, HF+dRPA-I, HF+RPAx-SO2 and range-separated RSH+MP2, RSH+dRPA-I, RSH+RPAx-SO2. The calculations were carried out using the cc-pVQZ basis set, MP2(full)/6-31G* geometries, and with the srPBE functional and $\mu=0.5$ in the case of the range-separated calculations. The reference values are the non-relativistic FC-CCSD(T)/cc-pVQZ-F12 values of Ref.~\onlinecite{Haunschild:12b}. For each method, the value with the largest absolute error is indicated in boldface.
}
  \begin{tabularx}{\textwidth}{lRRRcRRRR}\hline\hline
				& \multicolumn{3}{c}{\phantom{xxxxxx}HF+}      && \multicolumn{3}{c}{\phantom{xxxxxx}RSH+}      & \multicolumn{1}{R}{Reference}\\
                                  \cline{2-4}                                     \cline{6-8}
				& \multicolumn{1}{R}{MP2}
						& \multicolumn{1}{R}{dRPA-I}
								& \multicolumn{1}{R}{RPAx-SO2}
										&& \multicolumn{1}{R}{MP2}
												& \multicolumn{1}{R}{dRPA-I}
														& \multicolumn{1}{R}{RPAx-SO2}
																&		\\
\hline
CH$_2$ (singlet)		&	174.45	&	165.75	&	197.04	&&	171.39	&	170.64	&	172.69	&	180.62	\\
CH$_2$ (triplet)		&	188.70	&	181.63	&	201.41	&&	190.84	&	189.71	&	191.31	&	189.74	\\
CH$_3$Cl			&	394.58	&	370.34	&	417.42	&&	389.72	&	386.32	&	391.19	&	394.52	\\
CH$_3$				&	303.36	&	291.30	&	318.89	&&	303.79	&	302.23	&	304.71	&	306.59	\\
CH$_3$SH			&	469.94	&	442.53	&	495.56	&&	465.03	&	460.82	&	467.01	&	473.49	\\
CH$_4$				&	414.84	&	397.27	&	432.29	&&	411.74	&	409.65	&	413.14	&	418.87	\\
CH				&	 76.38	&	 74.13	&	 85.21	&&	 79.46	&	 79.19	&	 80.04	&	 83.87	\\
Cl$_2$				&	 60.43	&	 46.49	&	 79.13	&&	 55.73	&	 53.53	&	 56.71	&	 59.07	\\
ClF				&	 65.20	&	 45.91	&	 83.08	&&	 61.15	&	 60.68	&	 62.04	&	 62.57	\\
ClH				&	106.53	&	 98.52	&	119.27	&&	102.11	&	101.21	&	103.02	&	107.20	\\
ClO				&	 59.68	&	 42.55	&	 72.39	&&	 63.94	&	 62.60	&	 65.22 	&	 64.53	\\
CN				&	168.84	&	141.95	&	164.00	&&	176.12	&	173.99	&	177.86	&	180.06	\\
CO$_2$				&   {\bf409.33}	&	350.00	&	413.15	&&	395.12	&	392.37	&	396.91	&	388.59	\\
CO				&	269.30	&	234.43	&	276.58	&&	257.79	&	256.26	&	259.24	&	258.88	\\
F$_2$				&	 42.18	&	 15.59	&	 59.82	&&	 36.60	&	 36.99	&	 37.84 	&	 38.75	\\
FH				&	144.17	&	129.15	&	154.97	&&	138.23	&	137.89	&	138.65	&	141.51	\\
H$_2$CCH$_2$			&	561.39	&	528.59	&	582.70	&&	556.69	&	552.92	&	558.80	&	561.34	\\
H$_2$CO				&	379.20	&	343.30	&	392.00	&&	370.88	&	368.85	&	372.48	&	373.21	\\
H$_2$NNH$_2$			&	432.47	&	394.47	&	431.32	&&	432.36	&	429.67	&	434.62	&	436.70	\\
H$_3$CCH$_3$			&	707.16	&	673.49	&   {\bf735.15}	&&	703.80	&	699.25	&	705.86	&	710.20	\\
H$_3$COH			&	513.32	&	477.43	&	534.34	&&	507.36	&	504.60	&	509.06	&	511.83	\\
HCCH				&	409.59	&	373.19	&	419.99	&&	401.10	&	397.40	&	403.34	&	402.76	\\
HCN				&	319.26	&	279.53	&	312.96	&&	308.30	&	305.60	&	310.48	&	311.52	\\
HCO				&	285.80	&	252.01	&	291.99	&&	280.35	&	278.63	&	281.90	&	278.28	\\
HOCl				&	168.50	&	141.01	&	184.05	&&	161.23	&	159.81	&	162.68	&	165.79	\\
HOOH				&	272.51	&	232.25	&	286.06	&&	263.66	&	262.62	&	265.56	&	268.65	\\
N$_2$				&	234.80	&	193.15	&	213.76	&&	222.17	&	220.46	&	224.27	&	227.44	\\
NH$_2$				&	176.66	&	165.16	&	179.49	&&	178.54	&	177.84	&	179.51	&	181.96	\\
NH$_3$				&	293.12	&	272.47	&	295.33	&&	290.20	&	288.89	&	291.65	&	297.07	\\
NH				&	 78.57	&	 74.39	&	 80.62	&&	 82.08	&	 81.82	&	 82.54 	&	 82.79	\\
NO				&	156.95	&	123.74	&	147.37	&&	155.31	&	154.30	&	156.90	&	152.19	\\
O$_2$				&	126.53	&	 92.04	&	113.98	&&	124.06	&	123.31	&	126.00	&	120.54	\\
OH$_2$				&	233.83	&	212.21	&	243.34	&&	226.55	&	225.77	&	227.54	&	232.56	\\
OH				&	105.78	&	 96.58	&	112.19	&&	105.25	&	104.93	&	105.73	&	106.96	\\
P$_2$				&	113.59	&	 88.61	&	105.38	&&	106.63	&	 99.52	&	107.19	&	115.95	\\
PH$_2$				&	144.95	&	141.41	&	152.46	&&	146.95	&	146.30	&	147.68	&	153.97	\\
PH$_3$				&	230.24	&	222.62	&	241.82	&&	229.63	&	228.31	&	230.84	&	241.47	\\
S$_2$				&	103.68	&	 85.63	&	109.74	&&	101.19	&	 96.76	&	102.13	&	103.11	\\
SC				&	175.16	&	146.58	&	186.41	&&	164.13	&	159.64	&	166.22	&	170.98	\\
SH$_2$				&	178.55	&	168.10	&	194.48	&&	174.35	&	172.84	&	175.82	&	183.30	\\
Si$_2$H$_6$			&	519.18	&	504.65	&	556.67	&&  {\bf517.31}	&   {\bf512.50}	&   {\bf520.68}	&	535.47	\\
Si$_2$				&	 59.29	&	 50.71	&	 67.94	&&	 72.31	&	 69.20	&	 75.82	&	 73.41	\\
SiH$_2$ (singlet)		&	145.90	&	141.61	&	165.21	&&	143.64	&	142.93	&	145.89	&	153.68	\\
SiH$_2$ (triplet)		&	128.93	&	126.44	&	141.38	&&	129.82	&	128.58	&	131.14	&	133.26	\\
SiH$_3$				&	220.51	&	216.07	&	237.96	&&	220.33	&	218.83	&	221.84	&	228.08	\\
SiH$_4$				&	314.28	&	307.46	&	336.62	&&	311.98	&	310.07	&	313.73	&	324.59	\\
SiO				&	200.09	&	165.92	&	203.39	&&	187.97	&	185.75	&	190.47	&	192.36	\\
SO$_2$				&	270.73	&   {\bf207.21}	&	269.30	&&	249.24	&	245.56	&	251.39	&	259.77	\\
SO				&	129.29	&	101.94	&	127.35	&&	125.02	&	123.21	&	126.41	&	125.80	\\[.5em]
MAD				&	  5.63	&	 23.23	&	 12.20	&&	  5.09	&	  6.80	&	  4.06	&		\\
  \hline\hline
  \end{tabularx}
  \end{center}
\normalsize
\end{table*}
}

\newcommand\tabBH{
\begin{table*}[!htb]
\footnotesize
  \begin{center}
  \caption{\label{tab:BH24} Forward (F) and reverse (R) reaction barrier heights (in kcal/mol) of the DBH24/08 dataset calculated by full-range HF+MP2, HF+dRPA-I, HF+RPAx-SO2 and range-separated RSH+MP2, RSH+dRPA-I, RSH+RPAx-SO2. The calculations were carried out using the aug-cc-pVQZ basis set, QCISD/MG3 geometries, and with the srPBE functional and $\mu=0.5$ in the case of the range-separated calculations. The reference values are taken from Ref.~\onlinecite{Zheng:09}. For each method, the value with the largest absolute error is indicated in boldface.
}
  \begin{tabularx}{\textwidth}{lCCCcCCCC}\hline\hline
								& \multicolumn{3}{c}{\phantom{xxxxxx}HF+}				&& \multicolumn{3}{c}{\phantom{xxxxxx}RSH+}				& \multicolumn{1}{C}{Reference}\\
								  \cline{2-4}								   \cline{6-8}
								& \multicolumn{1}{C}{MP2}
											& \multicolumn{1}{C}{dRPA-I}
														& \multicolumn{1}{C}{RPAx-SO2}
																	&& \multicolumn{1}{C}{MP2}
																				& \multicolumn{1}{C}{dRPA-I}
																							& \multicolumn{1}{C}{RPAx-SO2}
																										&			\\
\hline
								&	\multicolumn{1}{C}{F/R}
											&	\multicolumn{1}{C}{F/R}
														&	\multicolumn{1}{C}{F/R}
																	&&	\multicolumn{1}{C}{F/R}
																				&	\multicolumn{1}{C}{F/R}
																							&	\multicolumn{1}{C}{F/R}
																										&\multicolumn{1}{C}{F/R}\\
Heavy-atom transfer						&			&			&			&&			&			&			&			\\
H+N$_2$O $\rightarrow$ OH+N$_2$					&	35.94/89.26	&     28.20/{\bf100.80}	&     32.74/{\bf100.57}	&&	18.11/74.67	&	18.00/76.40	&	17.92/74.43	&	17.13/82.47	\\
H+ClH $\rightarrow$ HCl+H					&	22.79/22.79	&	24.07/24.07	&	23.33/23.33	&&	19.07/19.07	&	19.36/19.36	&	18.44/18.44	&	18.00/18.00	\\
CH$_3$+FCl $\rightarrow$ CH$_3$F+Cl				&	19.74/74.29	&	17.63/75.16	&	21.67/66.18	&&	 7.19/61.68	&	 7.38/61.98	&	 7.40/61.25	&	 6.75/60.00	\\[.5em]
Nucleophilic substitution					&			&			&			&&			&			&			&			\\
Cl$^-$$\cdots$CH$_3$Cl $\rightarrow$ ClCH$_3$$\cdots$Cl$^-$	&	14.64/14.64	&	15.92/15.92	&	15.05/15.05	&&	15.12/15.12	&	15.85/15.85	&	14.76/14.76	&	13.41/13.41	\\
F$^-$$\cdots$CH$_3$Cl $\rightarrow$ FCH$_3$$\cdots$Cl$^-$	&	 4.59/28.88	&	 4.78/33.98	&	 4.35/33.29	&&	 4.43/30.70	&	 4.62/31.50	&	 4.09/30.43	&	 3.44/29.42	\\
OH$^-$+CH$_3$F $\rightarrow$ HOCH$_3$+F$^-$			&	-1.75/17.86	&	 1.23/22.00	&	 0.52/20.92	&&	-2.33/20.59	&	-1.43/21.22	&	-2.60/19.81	&	-2.44/17.66	\\[.5em]
Unimolecular and association					&			&			&			&&			&			&			&			\\
H+N$_2$ $\rightarrow$ HN$_2$					&	27.60/8.06	&	22.54/12.53	&	23.36/12.59	&&	13.23/12.66	&	13.34/12.59	&	12.81/12.47	&	14.36/10.61	\\
H+C$_2$H$_4$ $\rightarrow$ CH$_3$CH$_2$				&	 9.32/46.54	&	 6.67/48.13	&	 7.80/49.83	&&	 2.38/45.29	&	 2.62/45.24	&	 2.20/44.74	&	 1.72/41.75	\\
HCN $\rightarrow$ HNC						&      34.46/{\bf52.09}	&	36.14/49.49	&	34.73/47.08	&&     34.36/{\bf47.93}	&      34.85/{\bf48.15}	&      34.03/{\bf47.70}	&	48.07/32.82	\\[.5em]
Hydrogen transfer						&	     		&			&			&&			&			&			&			\\
OH+CH$_4$ $\rightarrow$ CH$_3$+H$_2$O				&	 7.66/25.01	&	13.65/24.16	&	 9.28/25.55	&&	 4.63/18.62	&	 4.77/18.82	&	 4.14/18.16	&	 6.70/19.60	\\
H+OH $\rightarrow$ O+H$_2$					&	17.56/15.58	&	15.42/20.08	&	16.13/15.90	&&	12.44/8.22	&	12.07/8.03	&	11.88/7.64	&	10.70/13.10	\\
H+H$_2$S $\rightarrow$ H$_2$+HS					&	 6.42/16.36	&	 7.18/20.71	&	 6.32/15.59	&&	 4.28/15.00	&	 4.42/15.89	&	 3.84/14.29	&	 3.60/17.30	\\[.5em]
MAD								&	 6.17		&	 6.95		&	 6.40		&&	 2.94		&	 3.01		&	 2.83		&			\\
  \hline\hline
  \end{tabularx}
  \end{center}
\normalsize
\end{table*}
}
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\begin{document}

\title{Supplementary material for ``Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights''}

\author{Bastien Mussard}\email{bastien.mussard@upmc.fr}
\affiliation{Sorbonne Universit\'es, UPMC Univ Paris 06, Institut du Calcul et de la Simulation, F-75005, Paris, France}
\affiliation{Sorbonne Universit\'es, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Th\'eorique, F-75005 Paris, France}
\affiliation{CNRS, UMR 7616, Laboratoire de Chimie Th\'eorique, F-75005 Paris, France}
\author{Peter Reinhardt}
\affiliation{Sorbonne Universit\'es, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Th\'eorique, F-75005 Paris, France}
\affiliation{CNRS, UMR 7616, Laboratoire de Chimie Th\'eorique, F-75005 Paris, France}
\author{J\'anos G. \'Angy\'an}
\affiliation{CRM2, Institut Jean Barriol, Universit\'e de Lorraine, F-54506 Vand{\oe}uvre-l\'es-Nancy, France}
\affiliation{CRM2, Institut Jean Barriol, CNRS, F-54506 Vand{\oe}vre-l\'es-Nancy, France}
\author{Julien Toulouse}\email{julien.toulouse@upmc.fr}
\affiliation{Sorbonne Universit\'es, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Th\'eorique, F-75005 Paris, France}
\affiliation{CNRS, UMR 7616, Laboratoire de Chimie Th\'eorique, F-75005 Paris, France}

\maketitle

The detailed results of the calculations on the AE49 and DBH24/08 datasets for the full-range and range-separated MP2, dRPA-I, and RPAx-SO2 methods at $\mu=0.5$ are reported in Tables~\FloatRef{tab:AE55} and~\FloatRef{tab:BH24}.


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\bibliographystyle{jchemphys}

\begin{thebibliography}{1}

\bibitem{Haunschild:12b}
R.~Haunschild and W.~Klopper, J. Chem. Phys. {\bf 136}, 164102 (2012).

\bibitem{Zheng:09}
J.~Zheng, Y.~Zhao and D.~G. Truhlar, J. Chem. Theory Comput. {\bf 5}, 808
  (2009).

\end{thebibliography}


\end{document}

