Interactions in coinage-metal/ligand complexes, CM–L, and their cations (CM = Cu, Ag, Au; L = CO, N₂ and H₂)

Figures & data

Table 1. Optimised geometries and vibrational wavenumbers of the T-Shaped cationic CM⁺–H₂ complexes (CM = Cu, Ag, Au)^a.

Method	Source^b	RCM–H / Å	rH–H / Å	σ / cm^–1	β / cm^–1	ωH-H / cm^–1
Cu^+–H2
HF	Ref. [40]			881	1146	3772
B3LYP	Present work	1.698	0.795 (0.743)	905	1217	3679 (4413)
B3LYP	Ref. [40]	1.75	0.79
CAM-B3LYP	Present work	1.638	0.796 (0.745)	939	1254	3697 (4407)
PW91	Present work	1.641	0.823 (0.749)	1033	1364	3342 (4330)
MP2	Present work	1.661	0.789 (0.737)	929	1333	3771 (4518)
MP2	Ref. [40]	1.74	0.78
CCSD(T)	Ref. [39]	1.746	0.780	818	1128	3882
CCSD(T)	Ref. [41]	1.76	0.78	775	1091	3909
CCSD(T)	Ref. [42]	1.712	0.786	866	1236	3805
Ag^+–H2
B3LYP	Present work	2.007	0.776 (0.743)	628	840	3932 (4413)
CAM-B3LYP	Present work	1.986	0.779 (0.745)	667	876	3929 (4407)
PW91	Present work	1.925	0.797 (0.749)	720	940	3677 (4330)
MPW1B95	Ref. [43]	2.003	0.775	624	867	^c
MP2	Present work	2.010	0.767 (0.737)	602	873	4070 (4518)
CCSD(T)	Ref. [44]	2.052	0.768	801	573	4048
Experiment	Ref. [43]	2.02^d				3751.0^e
Au^+–H2
B3LYP	Present work	1.754	0.858 (0.743)	932	1456	2979 (4413)
B3LYP	Ref. [46]	1.787	0.847	883	1329	3090
CAM-B3LYP	Present work	1.755	0.853 (0.745)	961	1477	3059 (4407)
PW91	Present work	1.683	0.934 (0.749)	921	1684	2454 (4330)
MP2	Present work	1.702	0.868 (0.737)	972	1641	2938 (4518)

^a Where R_CM–H represents the shortest CM–H distance; r_H–H represents the H–H bond length in the complex, with the value in parentheses that calculated for uncomplexed H₂ at the same level of theory (only for the present work); σ represents the intermolecular stretch vibration; β the intermolecular bend vibration; and ω_H-H represents the H-H stretch vibration in the complex, with the value in parentheses that calculated for uncomplexed H₂ at the same level of theory (only for the present work).

^b The values calculated in the present work were obtained employing the ECP + aug-cc-pwCVTZ basis sets, as described in the main text. Otherwise, results are given for selected previous results, usually selecting the highest levels of theory; please consult the original reference for details of basis sets employed.

^c Value not reported.

^d Experimental, R₀ value.

^e Experimental, fundamental, ω₀ value.

Table 2. Optimised geometries and vibrational wavenumbers of the cationic CM⁺–CO complexes (CM = Cu, Ag, Au)^a.

Method	Source^b	RCM–C / Å	rC–O / Å	σ / cm^–1	β / cm^–1	ωC–O / cm^–1
Cu^+–CO
B3LYP	Present work	1.870	1.115 (1.125)	383	294	2303 (2204)
B3LYP^c	Ref. [9]	1.913	1.117	355	268	2313
CAM-B3LYP	Present work	1.932	1.135 (1.121)	309	195	2139 (2248)
BP86^c	Ref. [9]	1.854	1.131	415	283	2208
PW91	Present work	1.815	1.128 (1.135)	438	299	2208 (2126)
MP2	Present work	1.829	1.128 (1.137)	399	312	2181 (2110)
QCISD	Present work	1.909	1.117 (1.130)	350	292	2300 (2180)
UCCSD(T)	Ref. [16]	1.887	1.124	357^d	527^d	2250
Experiment	Ref. [9]					2234^e
Ag^+–CO
B3LYP	Present work	2.140	1.114 (1.125)	260	230	2304 (2204)
B3LYP	Ref. [19]	2.232	1.116	221	217	2315
CAM-B3LYP	Present work	2.138	1.109 (1.121)	267	236	2356 (2248)
BPW91	Ref. [19]	2.157	1.128	251	219	2222
PW91	Present work	2.059	1.125 (1.135)	304	231	2213 (2126)
MP2	Present work	2.131	1.128 (1.137)	262	237	2185 (2110)
UCCSD(T)	Ref. [16]	2.182	1.124	244^d	411^d	2245
Experiment	Ref. [19]					2233^e
Au^+–CO
B3LYP	Present work	1.940	1.116 (1.125)	393	315	2296 (2204)
B3LYP [19]	Ref. [19]	1.946	1.117	392	326	^g
CAM-B3LYP	Present work	1.948	1.110 (1.121)	387	318	2351 (2248)
BP86	Ref. [24]	^f	^f	418	^f	2211
PW91	Present work	1.896	1.129 (1.135)	439	321	2203 (2126)
PW91 [19]	Ref. [19]	1.903	1.130	439	331	2223
MP2	Present work	1.902	1.129 (1.137)	416	328	2188 (2110)
UCCSD(T)	Ref. [16]	1.950	1.124	377^d	567^d	2252
Experiment [19]	Ref. [19]					2237^e

^a Where r_C–O represents the C–O bond length in the complex, with the value in parentheses that calculated for uncomplexed CO at the same level of theory (only for the present work); σ represents the intermolecular stretch vibration; β the intermolecular bend vibration; and ω_C–O represents the C–O stretch vibration in the complex, with the value in parentheses that calculated for uncomplexed CO at the same level of theory (only for the present work).

^b The values calculated in the present work were obtained employing the ECP + aug-cc-pwCVTZ basis sets, as described in the main text. Otherwise, results are given for selected previous results, usually selecting the highest levels of theory; please consult the original reference for details of basis sets employed.

^c The explicit assignment of the two intermolecular vibrations was not given for Cu⁺–CO in Ref. [9]; however, based on the infrared intensities, and comparison with similar results for Ag⁺–CO and Au⁺–CO reported in Ref. [19], we have assigned those in the present work.

^d As commented on in the main text, in Ref. [16] the reported value of the bend is always of a higher wavenumber than the stretch for the CM⁺–CO complexes; however, our doubly-degenerate mode is always of the lower wavenumber, and this is also is the case in Ref. [19]. (The vibrational probability plots given in Ref. [16] suggest that the modes for low v are well-defined as bends and stretches.)

^e Experimental fundamental value.

^f Not reported in Ref. [24].

^g Reported value in Ref. [19] is incorrect and possibly had the leading ‘2’ omitted, which would correspond to a value of 2314 cm^–1.

Table 3. Optimised geometries and vibrational wavenumbers of the cationic CM⁺–N₂ complexes (CM = Cu, Ag, Au)^a.

Method^b	RCM-N / Å	rN–N / Å	σ/ cm^–1	β / cm^–1	ωL / cm^–1
Cu^+–N2
B3LYP	1.895	1.091 (1.091)	338	221	2440 (2445)
CAM-B3LYP	1.895	1.085 (1.086)	338	222	2505 (2497)
PW91	1.830	1.105 (1.101)	397	232	2318 (2352)
MP2	1.872	1.112 (1.112)	335	226	2201 (2194)
Ag^+–N2
B3LYP	2.245	1.090 (1.091)	207	159	2453 (2445)
CAM-B3LYP	2.229	1.085 (1.086)	219	167	2511 (2497)
PW91	2.163	1.101 (1.101)	235	158	2350 (2352)
MP2	2.239	1.111 (1.112)	210	159	2201 (2194)
Au^+–N2
B3LYP	2.059	1.091 (1.091)	283	211	2435 (2445)
CAM-B3LYP	2.065	1.085 (1.086)	286	215	2501 (2497)
PW91	1.986	1.104 (1.101)	337	224	2313 (2352)
MP2	2.033	1.112 (1.112)	293	211	2190 (2194)

^a Where R_CM–N represents the shortest CM–N distance; r_N–N represents the N–N bond length in the complex, with the value in parentheses that calculated for uncomplexed N₂ at the same level of theory (only for the present work); σ represents the intermolecular stretch vibration; β the intermolecular bend vibration; and ω_N–N represents the N–N stretch vibration in the complex, with the value in parentheses that calculated for uncomplexed N₂ at the same level of theory (only for the present work).

^b All values were calculated in the present work employing the ECP + aug-cc-pwCVTZ basis sets, as described in the main text.

Table 4. Interaction energies (cm^–1) for the CM⁺–L complexes^a.

	Ligand
Metal	CO	N2	H2
Cu^+	12999	8203	6165
	[12400 ± 600] [26]	[7400 ± 2500] [31]	[5390 ± 350] [40]
Ag^+	8455	4880	3465
	[7400 ± 400] [26]
Au^+	16514	7943	7840
	[17500 ± 1750] [23]^b	[≥2400 ± 300] [34]

^a Values reported are our best D_e values that have been calculated using CCSD(T) single-point calculations at a geometry calculated at a lower level of theory, and have been corrected for basis set superposition error – see text for more details. Comments on previously-reported calculated values can be found in the text. Available experimental (D₀) values are given in square brackets.

^b Experimental value, but partially based on quantum chemical calculations.

Table 5. Calculated atomic charges and H(R_C) parameters for CM⁺–L using different methods^a.

			Complex^b
CM	Quantity	Method	CM–N1N2	CM–C1O2	CM–H1H2
Cu	QCu	Mulliken	0.948	1.064	0.770
		NPA	0.962	0.895	0.975
		AIM	0.910	0.842	0.867
	Q1	Mulliken	−0.142	0.333	0.115
		NPA	−0.218	0.379	0.013
		AIM	−0.204	1.188	0.067
	Q2	Mulliken	0.194	−0.397	0.115
		NPA	0.256	−0.274	0.013
		AIM	0.295	−1.031	0.067
	H(RC)		−0.038	−0.042	−0.035
Ag	QAg	Mulliken	0.827	0.789	0.765
		NPA	0.977	0.923	0.991
		AIM	0.927	0.849	0.891
	Q1	Mulliken	0.051	0.413	0.118
		NPA	−0.182	0.369	0.005
		AIM	−0.147	1.231	0.055
	Q2	Mulliken	0.123	−0.202	0.118
		NPA	0.205	−0.292	0.005
		AIM	0.220	−1.080	0.055
	H(RC)		−0.012	−0.026	-0.010
Au	QAu	Mulliken	0.716	0.731	0.705
		NPA	0.923	0.778	0.911
		AIM	0.854	0.699	0.758
	Q1	Mulliken	0.085	0.446	0.148
		NPA	−0.018	0.470	0.045
		AIM	−0.177	1.343	0.121
	Q2	Mulliken	0.199	−0.176	0.148
		NPA	0.258	−0.248	0.045
		AIM	0.323	−1.043	0.121
	H(RC)		−0.042	−0.086	−0.048

^a See text for details; charges calculated using the geometry obtained using CAM-B3LYP/aug-cc-pwCVTZ (see Tables 1–3).

^b For clarity, the ligand atom closest to CM⁺ is always labelled 1. For the homonuclear ligands, the charges on the two H atoms in the T–shaped CM⁺–H₂ complexes are expected to be equal; however, owing to convergence criteria, the optimisations yielded values that were very slightly different (< 0.004e), and in those cases the same averaged value is given.

Table 6. Electrostatic quantities for H₂, N₂ and CO^a.

	μ^b	α^//^c	α^⊥^c	Q^d
H2	0	6.35	4.91	0.47
N2	0	14.75	10.21	−1.1
CO	0.043	15.92	11.02	−1.4

^a Atomic units used throughout.

^b Dipole moment – Ref. [70].

^c Polarisabilities – the α^// value is that along the interatomic axis of the ligand, while the α^⊥ value is that perpendicular to this [71,72].

^d Quadrupole moment – Ref. [62].

Figure 1. Molecular orbital diagram for Au⁺–H₂. See text for details. The contours are the same for all molecular orbitals shown. For H₂, the calculated orbital energy of the 1sσ_g orbital in the absence of the coulombic field arising from the metal atom is indicated in grey, while the solid line indicates its energy in the presence of the field. The position of the gold nucleus is indicated by a black dot, and that of the hydrogen nuclei by grey dots. Orbitals lie in the yz plane unless indicated by the presence of axes, where these axes are located on the Au⁺. In the latter cases, one or more of the hydrogen atoms may not be visible.

Figure 2. Molecular orbital diagram for Au⁺–CO. See text for details. The contours are the same for all molecular orbitals shown. For CO, the calculated orbital energies of the 2pσ and 2pπ orbitals in the absence of the coulombic field arising from the metal atom are indicated in grey, while the solid line indicates their energy in the presence of the field. The position of the gold nucleus is indicated by a black dot, and that of the carbon and oxygen nuclei by grey dots, with the carbon atom the one closest to the gold. Orbitals lie in the yz plane unless indicated by the presence of axes, where these axes are located on the Au⁺. In the latter cases, one or more of the CO atoms may not be visible.

Figure 3. Molecular orbital diagram for Au⁺–N₂. See text for details. The contours are the same for all molecular orbitals shown. For N₂, the calculated orbital energies of the 2pσ_g and 2pπ_u orbitals in the absence of the coulombic field arising from the metal atom are indicated in grey, while the solid line indicates their energy in the presence of the field. The position of the gold nucleus is indicated by a black dot, and that of the nitrogen nuclei by grey dots. Orbitals lie in the yz plane unless indicated by the presence of axes, where these axes are located on the Au⁺. In the latter cases, one or more of the nitrogen atoms may not be visible.

Figure 4. Contour plots for the HOMOs of the CM⁺–L complexes. See text for further comment and discussion. The position of the gold nucleus is indicated by a black dot, and that of the ligand nuclei by grey dots; in the case of CM⁺–CO, the carbon atom is closest to the gold. All orbitals lie in the yz plane.

Table 7. Optimised geometries and vibrational wavenumbers of the linear CM–H₂ complexes (CM = Cu, Ag, Au)^a.

Method	Source^b	RCM–H / Å	rH–H / Å	σ / cm^–1	β / cm^–1	ωH–H / cm^–1
Cu–H2
B3LYP^c	Present work					(4413)
CAM-B3LYP	Present work	3.691	0.746 (0.745)	31	75	4400 (4407)
PW91	Present work	1.989	0.773 (0.749)	257	300	3849 (4330)
PW91	Ref. [37]	2.188	0.766
MP2	Present work	3.535	0.738 (0.737)	38	83	4505 (4518)
Ag–H2
B3LYP^c						(4413)
CAM-B3LYP	Present work	3.805	0.746 (0.745)	51	70	4401 (4407)
PW91	Present work	2.595	0.757 (0.749)	98	258	4171 (4330)
MP2	Present work	3.515	0.738 (0.737)	55	107	4501 (4518)
Au–H2
B3LYP	Present work	3.010	0.745 (0.743)	37	161	4367 (4413)
CAM-B3LYP	Present work	2.751	0.749 (0.745)	70	179	4336 (4407)
PW91	Present work	2.037	0.779 (0.749)	347	319	3741 (4330)
MP2	Present work	3.000	0.739 (0.737)	93	181	4478 (4518)

^a Where R_CM–H represents the shortest CM–H distance; r_H–H represents the H–H bond length in the complex, with the value in parentheses that calculated for uncomplexed H₂ at the same level of theory (only for the present work); σ represents the intermolecular stretch vibration; β the intermolecular bend vibration; and ω_H-H represents the H-H stretch vibration in the complex, with the value in parentheses that calculated for uncomplexed H₂ at the same level of theory (only for the present work).

^b The values calculated in the present work were obtained employing the ECP + aug-cc-pwCVTZ basis sets, as described in the main text. Otherwise, results are given for selected previous results, usually selecting the highest levels of theory; please consult the original reference for details of basis sets employed.

^c For Cu–H₂ and Ag–H₂, the optimisation using the B3LYP functional yielded a very long intermolecular bond length compared to the other methods, and the calculated parameters are not thought to be reliable, and hence are omitted. It is interesting that the same functional appeared to behave well for Au–H₂.

Table 8. Optimised geometries and vibrational wavenumbers of the neutral CM–CO complexes (CM = Cu, Ag, Au)^a.

Method	Source^b	RCM-C / Å	rC–O / Å	θCMCO / °	σ / cm^–1	β / cm^–1	ωC–O / cm^–1
Cu–CO
B3LYP	Present work	1.918	1.140 (1.125)	141.9	359	234	2045 (2204)
B3LYP	Ref. [9]	1.969	1.144	138.6	328	222	2037
CAM-B3LYP	Present work	1.916	1.126 (1.121)	163.5	304	67	2178 (2248)
BP86	Ref. [9]	1.891	1.160	141.3	415	237	1958
PW91	Present work	1.852	1.155 (1.135)	143.7	439	250	1967 (2126)
MP2	Present work	1.771	1.143 (1.137)	180.0	431	69	2053 (2110)
MP2	Ref. [12]	1.791	1.144	180.0	372	104	2067
MP2	Ref. [15]	1.810	1.149	180	399	115	2073
MP4	Ref. [15]	1.690	1.189	180	662	474	1740
MCPF	Ref. [13]	1.964	1.132	153.1	300	162	2117
QCISD	Present work	1.907	1.131 (1.130)	168.5			(2180)
UCCSD(T)	Ref. [16]	1.880	1.142	154.2	317	133	2065
UCCSD(T)	Ref. [13]	1.910	1.140	152.5	323	159	2086
CCSD	Ref. [15]	2.002	1.135	156.9	239	119	2205
CCSD(T)	Ref. [15]	1.934	1.144	157.0	288	144	2108
Experiment	Ref. [9]						2009.8/2029.7^c
Experiment	Ref. [8]				323	208	2010^d
Ag–CO
B3LYP	Present work	2.315	1.135 (1.125)	130.2	229	131	2082 (2204)
B3LYP	Ref. [19]	2.636	1.133	125.4	164	45	2130
CAM-B3LYP	Present work	2.349	1.126 (1.121)	131.5	198	111	2159 (2248)
PW91	Present work	2.131	1.152 (1.135)	132.6	317	199	1971 (2126)
PW91	Ref. [19]	2.273	1.153	128.9	261	149	1985
MP2	Present work	3.373	1.138 (1.137)	118.1	19	160	2101 (2110)
MP2	Ref. [12]	diss.
UCCSD(T)	Ref. [16]	3.665	1.136	120.2	14^e	21^e	2137
Experiment	Ref. [19]						^c
Au–CO
B3LYP	Present work	2.035	1.139 (1.125)	142.0	362	230	2067 (2204)
B3LYP	Ref. [19]	2.093	1.148	125.4	330	211	2066
CAM-B3LYP	Present work	2.031	1.129 (1.121)	147.0	331	199	2147 (2248)
PW91	Present work	1.974	1.154 (1.135)	142.2	439	255	1976 (2126)
PW91	Ref. [19]	2.016	1.157	138.8	400	243	1973
MP2	Present work	1.954	1.148 (1.137)	150.0	388	184	1992 (2110)
MP2	Ref. [12]	2.159	1.137	180	223	131	2137
UCCSD(T)	Ref. [16]	2.018	1.143	148.0	293	146	2058
Experiment	Ref. [19]						2053^c

^a Where r_C–O represents the C–O bond length in the complex, with the value in parentheses that calculated for uncomplexed CO at the same level of theory (only for the present work); σ represents the intermolecular stretch vibration; β the intermolecular bend vibration; and ω_C–O represents the C–O stretch vibration in the complex, with the value in parentheses that calculated for uncomplexed CO at the same level of theory (only for the present work).

^b The values calculated in the present work were obtained employing the ECP + aug-cc-pwCVTZ basis sets, as described in the main text. Otherwise, results are given for selected previous results, usually selecting the highest levels of theory; please consult the original reference for details of basis sets employed.

^c Experimental fundamental values. For Cu–CO, the lower value was obtained by IR spectroscopy in an Ar matrix, while the higher value was in a Ne matrix. No absorption for Ag–CO was seen in Ref. [19]. The value for Au–CO was obtained in an Ar matrix.

^d Experimental fundamental value for the Cu–¹²C¹⁶O isotopologue using IR spectroscopy; values for other isotopologues were also reported in Ref. [8].

^e ω₀ value, as it was not possible to extract an ω_e value as there were too few bound levels.

Table 9. Optimised geometries and vibrational wavenumbers of the neutral CM–N₂ complexes (CM = Cu, Ag Au)^a.

Method	Source^b	RCM-N / Å	rN–N / Å	θCMNN / °	σ / cm^–1	β / cm^–1	ωN–N / cm^–1
Cu–N2
B3LYP	Present work	2.102	1.100 (1.091)	138.6	186	125	2295 (2445)
CAM-B3LYP	Present work	2.195	1.090 (1.086)	141.6	136	45	2422 (2497)
PW91	Present work	1.903	1.120 (1.101)	142.3	327	205	2132 (2352)
MP2	Present work	3.775	1.112 (1.112)	122.0	40	21	2189 (2194)
Ag–N2
B3LYP^c	Present work
CAM-B3LYP	Present work	4.809	1.086 (1.086)	127.5	11	6	2497 (2497)
PW91	Present work	3.675	1.101 (1.101)	126.8	53	23	2345 (2352)
MP2	Present work	3.768	1.112 (1.112)	121.8	45	24	2188 (2194)
UCCSD(T)	Ref. [32]	3.95	1.277^d	119.9
Au–N2
B3LYP^c	Present work
B3LYP	Ref. [33]	3.956	1.091	180^e			2352
CAM-B3LYP	Present work	3.945	1.086 (1.086)	128.0	29	14	2496 (2497)
PW91	Present work	2.214	1.113 (1.101)	136.1	207	144	2200 (2352)
PW91	Ref. [33]	3.463	1.102	180^e			2355
MP2	Present work	3.363	1.113 (1.112)	116.4	57	33	2184 (2194)

^a Where r_N–N represents the N–N bond length in the complex, with the value in parentheses that calculated for uncomplexed N₂ at the same level of theory (only for the present work); σ represents the intermolecular stretch vibration; β the intermolecular bend vibration; and ω_N–N represents the N–N stretch vibration in the complex, with the value in parentheses that calculated for uncomplexed N₂ at the same level of theory (only for the present work).

^b The values calculated in the present work were obtained employing the ECP + aug-cc-pwCVTZ basis sets, as described in the main text. Otherwise, results are given for selected previous results, usually selecting the highest levels of theory; please consult the original reference for details of basis sets employed.

^c For Ag–N₂ and Au–N₂, the optimisation using the B3LYP functional yielded a very long intermolecular bond length compared to the other methods, and the calculated parameters are not thought to be reliable, and so are omitted. The bending vibrational wavenumber was calculated to be imaginary, likely due to the flat potential and the use of numerical second derivatives; we did not pursue this further. It is interesting that the same functional appeared to behave well for Cu–N₂ (cf. the CM–H₂ complexes where again the B3LYP functional did not perform well, but apparently was fine for Au–H₂).

^d This was fixed at this value in Ref. [32].

^e In contrast to the our results, the geometry was calculated to be linear in Ref. [33] using the same functionals, but Pople-style basis sets.

Figure 5. Molecular orbital diagram for Au–H₂. See text for details. The contours are the same for all molecular orbitals shown. The position of the gold nucleus is indicated by a black dot, and that of the hydrogen nuclei by grey dots. Orbitals lie in the yz plane unless indicated by the presence of axes, where these axes are located on the Au. In the latter cases, one or more of the hydrogen atoms may not be visible.

Figure 6. Molecular orbital diagram for Au–CO. See text for details. The contours are the same for all molecular orbitals shown. The position of the gold nucleus is indicated by a black dot, and that of the carbon and oxygen nuclei by grey dots, with the carbon atom the one closest to the gold. Orbitals lie in the yz plane unless indicated by the presence of axes, where these axes are located on the Au. In the latter cases, one or more of the CO atoms may not be visible.

Figure 7. Molecular orbital diagram for Au–N₂. See text for details. The contours are the same for all molecular orbitals shown. The position of the gold nucleus is indicated by a black dot, and that of the nitrogen nuclei by grey dots. Orbitals lie in the yz plane unless indicated by the presence of axes, where these axes are located on the Au. In the latter cases, one or more of the nitrogen atoms may not be visible.

Figure 8. Contour plots for the HOMOs of the CM–L complexes. See text for further comment and discussion. The position of the gold nucleus is indicated by a black dot, and that of the ligand nuclei by grey dots; in the case of CM–CO, the carbon atom is closest to the gold. All orbitals lie in the yz plane.

Figure 9. Contour plots of the HOMOs of the indicated CM–L complex, at the indicated geometry. The Au–L//Au–L′ notation employed indicates that the contours of Au–L are shown, calculated at the optimised geometry of Au–L′, with the latter calculated at the MP2 level of theory using the triple–ζ quality basis sets described in the main text. The position of the gold nucleus is indicated by a black dot, and that of the ligand nuclei by grey dots; in the case of Au–CO, the carbon atom is closest to the gold. All orbitals lie in the yz plane. See text for further discussion.

Table 10. Interaction energies (cm^–1) for the CM–L complexes^a.

	CO	N2	H2
Cu	2740 [2100 ±400] [11]	66	44
Ag	140	114	50
Au	3282	130	97

^a Values reported are our best D_e values that have been calculated using RCCSD(T) single-point calculations at a geometry calculated at a lower level of theory, and have been corrected for basis set superposition error – see text for more details. The only available experimental (D₀) value is given in square brackets. Comments on other calculated values can be found in the text.

Table 11. Calculated atomic charges (Q), spin densities (ρ), and H(R_C) parameters for CM–L using different methods^a.

			CAM-B3LYP^b,c,d			MP2^b,c,e
CM	Quantity	Method	CM–N1N2	CM–C1O2	CM–H1H2	CM–N1N2	CM–C1O2	CM–H1H2
Cu	QCu	Mulliken	−0.010	−0.093	−0.004	−0.010	−0.082	−0.009
		NPA	−0.002	−0.068	0.000	−0.005	−0.077	0.001
		AIM	0.025	0.015	0.005	0.010	−0.003	0.006
	Q1	Mulliken	0.044	0.353	0.044	0.010	0.439	0.024
		NPA	−0.071	0.583	−0.002	−0.002	0.591	−0.003
		AIM	−0.094	1.280	−0.004	−0.011	1.283	−0.005
	Q2	Mulliken	−0.034	−0.260	−0.041	0.000	−0.357	−0.015
		NPA	0.073	−0.515	0.001	0.007	−0.514	0.002
		AIM	0.069	−1.294	−0.001	0.001	−1.280	−0.002
	ρCu	Mulliken	0.975	0.987	1.000	1.006	1.034	1.004
		NPA	0.948	0.939	1.000	0.997	0.949	1.000
		AIM	0.941	0.998	1.000	0.985	0.997	1.001
	ρ1	Mulliken	−0.002	−0.001	−0.002	−0.007	−0.037	−0.005
		NPA	0.036	0.055	0.000	−0.001	0.049	0.000
		AIM	0.043	0.002	0.000	0.010	0.003	0.000
	ρ2	Mulliken	0.027	0.014	0.002	0.001	0.004	0.001
		NPA	0.016	0.006	0.000	0.004	0.002	0.000
		AIM	0.016	0.000	0.000	0.004	0.000	0.000
	H(RC)		−0.009	−0.034	0.000	0.000	−0.068	0.000
Ag	QAg	Mulliken	−0.021	0.008	−0.005	−0.018	−0.013	−0.010
		NPA	−0.005	0.016	0.001	−0.005	−0.001	0.003
		AIM	0.014	0.018	0.006	0.013	0.020	0.008
	Q1	Mulliken	0.015	0.287	0.020	0.012	0.397	−0.026
		NPA	−0.004	0.423	−0.003	−0.003	0.479	−0.005
		AIM	−0.016	1.169	−0.005	−0.015	1.177	−0.008
	Q2	Mulliken	0.006	−0.295	−0.015	0.006	−0.383	0.035
		NPA	0.009	−0.439	0.002	0.008	−0.478	0.003
		AIM	0.003	−1.187	0.000	0.002	−1.198	0.000
	ρAg	Mulliken	1.016	0.910	1.001	1.013	1.016	1.004
		NPA	0.995	0.893	0.998	0.996	0.981	0.996
		AIM	0.979	0.890	0.991	0.981	0.962	0.987
	ρ1	Mulliken	−0.014	0.063	−0.003	−0.012	−0.018	−0.005
		NPA	0.001	0.076	0.000	−0.002	0.010	0.001
		AIM	0.016	0.073	0.007	0.013	0.027	0.010
	ρ2	Mulliken	−0.002	0.027	0.003	−0.002	0.002	0.001
		NPA	0.004	0.031	0.002	0.006	0.009	0.003
		AIM	0.005	0.036	0.002	0.007	0.012	0.003
	H(RC)		0.000	−0.011	0.000	0.000	0.001	0.000
Au	QAu	Mulliken	−0.001	−0.028	−0.007	−0.008	−0.097	−0.009
		NPA	−0.006	−0.042	0.015	−0.006	−0.026	0.008
		AIM	0.005	−0.051	0.012	0.008	−0.044	0.009
	Q1	Mulliken	0.034	0.348	−0.037	0.009	0.530	−0.080
		NPA	0.000	0.445	−0.018	−0.006	0.433	−0.009
		AIM	−0.006	1.214	−0.001	−0.012	1.190	−0.002
	Q2	Mulliken	−0.032	−0.321	0.044	−0.001	−0.433	0.089
		NPA	0.006	−0.403	0.003	0.012	−0.407	0.001
		AIM	0.001	−1.163	−0.011	0.004	−1.146	−0.007
	ρAu	Mulliken	1.001	0.827	0.993	1.007	0.943	1.004
		NPA	0.999	0.791	1.001	0.994	0.777	1.000
		AIM	0.992	0.815	1.001	0.982	0.807	1.001
	ρ1	Mulliken	−0.001	0.145	−0.008	−0.008	0.046	−0.006
		NPA	0.001	0.193	0.000	0.045	0.207	0.000
		AIM	0.007	0.153	−0.001	0.052	0.161	−0.001
	ρ2	Mulliken	0.000	0.027	0.016	0.001	0.011	0.002
		NPA	0.001	0.017	−0.001	−0.039	0.016	0.000
		AIM	0.001	0.032	0.000	−0.034	0.032	0.000
	H(RC)		0.000	−0.059	0.001	0.001	−0.082	0.001

^a See text for details; charges calculated using the geometry obtained using CAM-B3LYP/aug-cc-pwCVTZ or MP2/aug-cc-pwCVTZ (see Tables 7–9).

^b For clarity, the ligand atom closest to CM is always labelled 1.

^c For Cu–CO, the NPA and AIM charges were calculated using the ROHF density, owing to technical issues with the NPA program with the UQCISD density; in all other cases the UQCISD density was employed.

^d For Ag–N₂, the PW91 geometry was employed, as the CAM-B3LYP geometry is not thought to be reliable.

^e For Cu–CO, the MP2 geometry is not thought to be reliable, but the charges are included here for completeness.

Table 12. Calculated interaction energies (cm^–1) for the CM⁽⁺⁾–RG complexes^a.

	Cu		Ag		Au
RG	Neutral	Cation	Neutral	Cation	Neutral	Cation
He	6	790	8	396	15	385
Ne	22	842	28	575	47	565
Ar	91	4212	114	2607	185	3745
Kr	144	5890	169	3878	300	6155
Xe	224	8301	2534	5864	590	10063
Rn	334	9264	356	6822	819	11754

^a Values taken from Refs. [73,74].

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Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.