Table 1 The Δ∠M‒A‒X angle, QTAIM atomic charges of M and A in MAX₃ systems, Q(M) and Q(A), the IQA interaction energy and its interatomic exchange-correlation and Coulombic energy components between metal and Al, B, or central C atoms in the studied systems, V_Int(M,A), V_XC(M, A) and V_C(M, A), and those of the metals with the substituents on the central atom, V_XC(M, X) and V_C(M, X), in kcal.mol⁻¹.

From: Collective interactions among organometallics are exotic bonds hidden on lab shelves

Molecules	ΔM‒A‒X	Q(M)	Q(A)	Q(X)	V_XC(M,A)	V_XC(M,X)	V_C(M,A)	V_C(M,X)	V_Int(M,A)	V_Int(M,X)
LiBH₃^−a	5.11	−0.010	1.326	−0.772	−20.8	−4.9	42.1	−27.8	21.3	−32.7
NaBH₃^−a	4.59	−0.195	1.524	−0.776	−18.7	−6.6	19.3	−9.5	0.6	−16.1
KBH₃^−a	3.11	−0.238	1.585	−0.781	−13.7	−6.0	13.8	−6.3	0.1	−12.3
MgBH₃	3.36	0.468	1.627	−0.698	−33.6	−11.9	133.9	−58.2	100.3	−70.1
CaBH₃^a	0.91	0.613	1.572	−0.729	−24.5	−11.1	163.7	−76.9	139.2	−88.0
LiAlH₃⁻	16.27	0.206	1.241	−0.816	−48.1	−2.8	23.6	−27.0	−24.5	−29.8
NaAlH₃^−a	14.86	−0.135	1.587	−0.817	−39.1	−3.4	3.5	−2.1	−35.6	−5.5
KAlH₃^−a	13.13	−0.204	1.681	−0.825	−24.1	−2.7	−0.9	0.4	−25.0	−2.3
MgAlH₃	2.83	0.172	2.112	−0.761	−17.9	−7.3	41.9	−13.7	23.9	−21.0
CaAlH₃	3.73	0.352	1.986	−0.779	−24.9	−6.5	80.2	−30.2	55.3	−36.7
i−CaAlH₃^a,b,d	−33.89	0.887	1.471	−0.786	−11.3	−24.1	239.5	−128.9	228.3	−153.0
LiCF₃	25.14	0.918	1.197	−0.705	−21.3	−0.7	93.8	−78.9	72.5	−79.6
NaCF₃	25.29	0.865	1.261	−0.709	−27.8	−1.1	98.8	−67.7	71.0	−68.8
BeCF₃⁺	19.12	1.625	1.303	−0.642	−61.6	−3.4	157.8	−151.3	96.2	−154.7
MgCF₃^+c	19.78	1.453	1.512	−0.655	−62.9	−4.5	227.0	−120.4	164.1	−124.9
i-LiCF₃^b,c,d	−31.33	0.932	1.203	−0.712	−0.6	−9.1	223.2	−122.8	222.6	−132.0
i-NaCF₃^b,c,d	−30.18	0.934	1.220	−0.718	−0.9	−10.1	188.8	−103.8	187.9	−113.9
i-KCF₃^b,d	−29.67^c	0.942	1.215	−0.719	−0.9	−11.6	168.0	−93.1	167.1	−104.7
i-MgCF₃^+b,d	−33.31	1.830	1.229	−0.686	−2.3	−19.2	403.1	−234.2	400.8	−253.4
i-CaCF₃^+b,d	−32.12	1.812	1.219	−0.677	−2.1	−24.5	351.1	−194.7	349.0	−219.1
i-SrCF₃^+b,d	−31.72	1.838	1.221	−0.686	−1.8	−23.6	338.3	−188.6	336.5	−212.2
i-MgC(CN)₃^+b	−26.32	1.776	0.243	−0.340	−3.3	−19.5	67.1	−122.5	63.8	−142.0
i-CaC(CN)₃^+b	−19.53	1.727	0.184	−0.304	−7.2	−23.5	41.5	−80.0	34.3	−103.5
i-SrC(CN)₃^+b	−17.83	1.756	0.172	−0.309	−7.2	−22.3	37.1	−75.1	29.9	−97.4
LiCH₃	22.64	0.899	−0.609	−0.097	−25.2	−0.5	−141.8	−7.9	−167.0	−8.4
NaCH₃	20.98	0.757	−0.536	−0.074	−40.1	−1.1	−86.3	−4.3	−126.4	−5.4
KCH₃	22.09	0.805	−0.516	−0.096	−35.3	−1.0	−77.8	−6.2	−113.1	−7.2
BeCH₃⁺	19.08	1.669	−0.971	0.101	−68.5	−1.5	−476.9	30.8	−545.4	29.3
MgCH₃⁺	16.63	1.397	−0.605	0.069	−78.9	−1.9	−196.6	16.4	−275.5	14.5
CaCH₃⁺	22.07	1.618	−0.621	0.001	−71.1	−1.9	−201.3	4.0	−272.4	2.1
SrCH₃⁺	22.03	1.616	−0.587	−0.010	−71.9	−1.9	−183.5	1.9	−255.4	0.0
LiC(Ph)₃	−6.73	0.894	−0.218	−0.225	−10.7	−5.5	−49.6	−31.0	−60.3	−36.5
NaC(Ph)₃	−5.35	0.907	−0.161	−0.249	−8.8	−6.8	−29.0	−29.4	−37.8	−36.2
KC(Ph)₃	−3.84	0.894	−0.142	−0.250	−10.8	−10.1	−22.7	−25.2	−33.5	−35.3
MgC(Ph)₃⁺	10.67	1.088	−0.391	0.101	−56.3	−10.0	−120.9	7.6	−177.2	−2.4
CaC(Ph)₃⁺	−6.42	1.554	−0.214	−0.113	−29.8	−26.0	−65.4	−47.4	−95.2	−73.4
SrC(Ph)₃⁺	−4.37	1.561	−0.214	−0.116	−32.8	−25.8	−64.5	−41.9	−97.3	−67.7
LiC(CH₃)₃^c	21.40	0.882	−0.470	−0.137	−24.8	−0.9	−125.9	−9.2	−150.7	−10.1
NaC(CH₃)₃^c	20.60	0.716	−0.329	−0.129	−38.8	−2.0	−65.8	−6.7	−104.6	−8.7
KC(CH₃)₃^c	21.18	0.799	−0.295	−0.168	−32.2	−1.6	−58.8	−10.2	−91.0	−11.8
BeC(CH₃)₃⁺	16.88	1.417	−0.772	0.119	−79.2	−3.8	−357.6	27.2	−436.8	23.4
MgC(CH₃)₃⁺	15.52	1.136	−0.428	0.097	−72.1	−5.0	−130.2	15.2	−202.3	10.2
CaC(CH₃)₃⁺	19.04	1.539	−0.412	−0.043	−71.5	−3.7	−153.6	−5.6	−225.3	−9.3
i-LiC(CH₃)₃^d	−12.92	0.799	−0.197	−0.201	−14.1	−11.6	−27.1	−32.3	41.2	−43.9
i-NaC(CH₃)₃^b,d	−11.21	0.754	−0.125	−0.210	−9.3	−12.8	−9.6	−26.1	−18.9	−38.9
i-KC(CH₃)₃^b,d	−7.01	0.783	−0.162	−0.207	−13.7	−14.2	−16.4	−21.7	−30.1	−36.0
i-BeC(CH₃)₃^+c,d	−16.98	1.520	−0.274	−0.082	−25.5	−31.0	−130.6	−81.3	−156.1	−112.3
i-MgC(CH₃)₃^+b,d	−5.76	0.300	0.033	0.222	−7.1	−10.9	1.1	4.9	−6.1	−6.0
i-CaC(CH₃)₃^+c,d	−3.55	1.460	−0.230	−0.077	−45.8	−24.9	−68.2	−25.1	−114	−50.0
i-SrC(CH₃)₃^+e,d	−0.32	1.466	−0.247	−0.073	−53.1	−23.0	−74.3	−20.2	−127.4	−43.2

The prefix i- denotes structures with an inverted geometry that have a negative M‒A‒X angle. The Δ∠M‒A‒X angle is defined as the difference between ∠M‒A‒X angle and a right angle as defined in ref. ⁹.
^aData obtained from BS-DFT calculations.
^bThe metal forms multiple (3,-1) CPs with the AX₃ fragment.
^cThe global minimum of the molecule.
^di- represents inverted structures, see Fig. 1.
^eThe global minimum of the molecule has a C_S point group, 1.6 kcal.mol⁻¹ lower in energy; therefore, it is not discussed here.

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