Dynamic and Static Nature of Br₄σ(4c–6e) and Se₂Br₅σ(7c–10e) in the Selenanthrene System and Related Species Elucidated by QTAIM Dual Functional Analysis with QC Calculations

Table 1

QTAIM functions and QTAIM-DFA parameters for ^BBr-∗-^ABr-∗-^A′Br-∗-^B′Br at BCPs in Br₄σ(4c–6e), together with ^ABr-∗-^ABr in Br₂, evaluated with MP2/BSS-A^a).

Species (symmetry)	Interaction X-∗-Y	ρb(rc) ()	c∇^2ρb(rc)^b) (au)	Hb(rc) (au)	kb(rc)^c)	R^d) (au)	θ^e) (°)	Cij (Å mdyn^−1)	θp:CIV^f) (°)	κp:CIV^g) (au^−1)	Predicted nature
Br2 (D∞h)^h)	Br-∗-Br	0.1130	−0.0001	−0.0497	−2.005	0.0497	180.1	0.4	191.8	1.8	SS/Cov-w^i)
(D∞h)^j)	^ABr-∗-^ABr	0.0922	0.0052	−0.0313	−1.751	0.0317	170.6	0.8	190.6	3.6	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0198	0.0058	0.0001	−0.995	0.0058	89.5	−19.6	118.2	146	p-CS/t-HBnc^l)
Br6 (C2)	^ABr-∗-^ABr	0.1099	0.0010	−0.0466	−1.960	0.0467	178.8	0.4	191.3	2.3	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0131	0.0049	0.0009	−0.899	0.0050	79.6	14.3	97.8	105	p-CS/t-HBnc^l)
Br6 (C2h)^m)	^ABr-∗-^ABr	0.1099	0.0010	−0.0466	−1.961	0.0467	178.8	0.4	191.7	1.7	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0131	0.0049	0.0009	−0.899	0.0050	79.6	14.3	97.6	97	p-CS/t-HBnc^l)
Br6 (C2h)obsd^n)	^ABr-∗-^ABr	0.0765	0.0053	−0.0200	−1.654	0.0207	165.2				r-CS
	^ABr-∗-^BBr	0.0156	0.0055	0.0007	−0.929	0.0055	82.5				p-CS
H2Br4 (C2h)	^ABr-∗-^ABr	0.1101	0.0008	−0.0468	−1.966	0.0468	179.0	0.4	191.7	2.0	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0118	0.0045	0.0010	−0.881	0.0046	78.0	15.5	94.7	100	p-CS/t-HBnc^l)
Me2Br4	^ABr-∗-^ABr	0.1076	0.0016	−0.0444	−1.932	0.0445	177.9	0.4	191.4	1.8	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0164	0.0057	0.0006	−0.945	0.0057	84.1	10.5	105.1	100	p-CS/t-HBnc^l)
H4Se2Br6 (Ci)	^ABr-∗-^ABr	0.1028	0.0031	-0.0400	−1.866	0.0401	175.6	0.5	191.5	2.5	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0220	0.0068	−0.0002	−1.016	0.0068	91.9	9.9	117.4	75	r-CS/t-HBwc^o)
Me4Se2Br6 (Ci)	^ABr-∗-^ABr	0.1028	0.0032	−0.0400	−1.862	0.0402	175.4	0.5	191.4	3.7	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0212	0.0067	−0.0001	−1.008	0.0067	90.9	9.9	116.4	101	r-CS/t-HBwc^o)
5 (Ci)^p)	^ABr-∗-^ABr	0.1016	0.0036	−0.0389	−1.844	0.0391	174.7	0.5	191.5	4.4	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0226	0.0070	−0.0003	−1.023	0.0070	92.7	6.8	118.0	557	r-CS/t-HBwc^o)
	^ABr-∗-^BBr^q)	0.0226	0.0070	−0.0003	−1.023	0.0070	92.7	6.8	118.0	551	r-CS/t-HBwc^o)
5 (Ci)^r)	^ABr-∗-^ABr	0.1047	0.0020	−0.0383	−1.905	0.0384	177.0	0.5	191.3	2.5	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0145	0.0048	0.0008	−0.904	0.0048	80.1	15.9	97.4	102	p-CS/t-HBnc^o)
6 (Ci)	^ABr-∗-^ABr	0.1014	0.0037	−0.0388	−1.841	0.0389	174.6	0.5	191.5	36	r-CS/CT-TBP^k)
	^ABr-∗-^ABr^q)	0.1014	0.0037	−0.0388	−1.841	0.0389	174.6	0.5	191.6	36	r-CS/CT-TBP^k)
	^ABr-∗-^BBr^q)	0.0227	0.0070	−0.0004	−1.024	0.0071	92.8	42.1	122.5	2474	r-CS/t-HBwc^o)
6 (Ci)^r)	^ABr-∗-^ABr	0.1044	0.0021	−0.0380	−1.901	0.0381	176.9	0.5	191.3	2.6	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0147	0.0048	0.0008	−0.907	0.0049	80.3	16.6	97.8	103	p-CS/t-HBnc^o)
1 (Ci)^r)	^ABr-∗-^ABr	0.1063	0.0013	−0.0398	−1.939	0.0398	178.1	0.5	191.7	2.3	r-CS/CT-TBP^k)
	^ABr-∗-^BBr	0.0123	0.0043	0.0010	−0.868	0.0044	76.9	18.3	91.8	100	p-CS/t-HBnc^l)
1 (Ci)obsd^s)	^ABr-∗-^ABr	0.1019	0.0032	−0.0393	−1.860	0.0394	175.3				r-CS
	^ABr-∗-^BBr	0.0200	0.0066	0.0003	−0.979	0.0066	87.7				p-CS

^a)See the text for BSS. ^b)c∇²ρ_b(r_c) = H_b(r_c) − V_b(r_c)/2, where c = ћ²/8m. ^c)k_b(r_c) = V_b(r_c)/G_b(r_c). ^d)R = (x² + y²)^1/2, where (x, y) = (H_b(r_c) − V_b()/2, H_b()). ^e)θ = 90° − tan⁻¹ (y/x).^f)θ_p = 90°– tan⁻¹(dy/dx). ^g)κ_p = |d²y/dx²|/[1 + (dy/dx)²]^3/2. ^h)The Br-Br distance in Br₂ was optimized to be 2.2756 Å with MP2/BSS-A, which was very close to the observed distance in the gas phase (2.287 Å) [63]. However, the values are shorter than those determined by the X-ray crystallographic analysis (2.491 Å) [40] by 0.210 Å. The noncovalent Br---Br distance is 3.251 Å in crystal, which is shorter than the sum of the van der Waals radii [64] by 0.45 Å. ⁱ⁾The SS interaction of the weak covalent nature. ^j)With one imaginary frequency for the vibration mode of the SGU symmetry. ^k)The regular-CS interaction of the CT-TBP nature. ^l)The pure-CS interaction of the HB nature with no covalency. ^m)With one imaginary frequency for the rotational mode around the linear Br₄ interaction. ⁿ⁾See ref. [40] ^o)The regular-CS interaction of the HB nature with covalency. ^p)With one imaginary frequency for the vibration mode of the AU symmetry. ^q) = (0), ±0.025, and ±0.05. ^r)At the CAM-B3LYP level. ^s)See ref. [39].