Table 3 Deviations of equilibrium bond lengths r_e and harmonic frequencies ω_e of Sc₂ (X\({}^{5}{\Sigma }_{u}^{-}\)), Ti₂(X³Δ_g), V₂ (X\({}^{3}{\Sigma }_{g}^{-}\)), Ni₂ (X¹Γ_g), and Cu₂ (X\({}^{1}{\Sigma }_{g}^{+}\)) predicted by CASSCF, CASPT2, tBLYP, tB3LYP, and tB4LYP compared to the literature values

Molecule	Property	CASSCF	CASPT2	tBLYP	tB3LYP	tB4LYP	Lit.
Sc₂ (X\({}^{5}{\Sigma }_{u}^{-}\))	r_e	−8	5	−2	−3	0	261^a
CAS(6e, 12o)	ω_e	−19	-17	15	6	2	242^a
Ti₂(X³Δ_g)	r_e	−1	1	−3	−2	0	195^b
CAS(8e, 12o)	ω_e	−8	−2	32	18	−3	432^b
V₂ (X\({}^{3}{\Sigma }_{g}^{-}\))	r_e	2	−1	−3	−2	0	178^c
CAS(10e, 12o)	ω_e	−12	−3	24	9	−20	549^c
Cr₂(X\({}^{1}{\Sigma }_{g}^{+}\))	r_e	−123	1	−7	−7	−1	168^d
CAS(12e, 22o)	ω_e	388	−25	136	362	16	492^d
Ni₂ (X¹Γ_g)	r_e	−20	5	1	−1	0	226^e
CAS(20e, 12o)	ω_e	108	−3	18	32	25	276^e
Cu₂ (X\({}^{1}{\Sigma }_{g}^{+}\))	r_e	−26	0	−5	−8	−6	222^f
CAS(22e, 12o)	ω_e	89	−30	−6	10	2	267^f
MAE	r_e	29.9	2.2	3.5	3.8	1.1
	ω_e	104	13	38	73	11
MAE without Cr₂	r_e	11.4	2.4	2.8	3.2	1.2
	ω_e	47	11	19	15	10

The results are obtained with cc-pVQZ-DK sets using minimal active space denoted as CAS(Xe, 12o) for all dimers but Cr₂.The diatomic constants are obtained via a diatomic potential energy curve fit using a weighted least squares approach¹⁰³ followed by a second order vibrational perturbation theory treatment. The mean absolute errors (MAEs) with and without Cr₂ are calculated and shown at the bottom. The literature values are from high-level wavefunction methods as noted. The unit of the bond lengths is picometer(pm) and the unit of the harmonic frequencies ω_e is wavenumbers (cm⁻¹). Note that the r_e and ω_e for Cr₂(X\({}^{1}{\Sigma }_{g}^{+}\)) are calculated from the ZPE and first vibrational level energy in Table 2 using anharmonic oscillator energy level expression truncated at second order.
^aNEVPT2, NEVPT3 results from ref. ¹¹².
^bMRCI+Q results from ref. ¹¹³.
^cMRCI+Q results from ref. ¹¹⁴.
^dDerived from the composite method results from ref. ⁷³.
^eGVVPT2 results from ref. ¹¹⁵.
^fMRCI+Q results from ref. ¹¹⁶.

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