Quasi-relativistic study of nuclear electric quadrupole coupling constants in chiral molecules containing heavy elements

Figures & data

Figure 1. Choice of principal axes in CHBrClF (left) and CHClFI (right) in centre of mass coordinates. Equilibrium structures are shown as optimised in Ref. [37] at the level of CCSD(T) with small basis sets. The relative length chosen here for the principal axes corresponds to the relative size of the rotational constant. The a axis in CHClFI is scaled (shortened) by a factor of 2/3 relative to the b and c axes for a better representation. Atoms are labelled with mass numbers of used isotopes for ${}^{12}{\mathrm{C}}^1{\mathrm{H}}^{79}\mathrm{B}{\mathrm{r}}^{35}\mathrm{C}{\mathrm{l}}^{19}\mathrm{F}$ and ${}^{12}{\mathrm{C}}^1{\mathrm{H}}^{35}\mathrm{C}{\mathrm{l}}^{19}{\mathrm{F}}^{127}\mathrm{I}$.

Table A1. NEQM coupling tensor $\mathcal{X}$ of the ${}^{35}$Cl nucleus in CHBrClF calculated at level of Hartree–Fock (HF) and DFT with exchange-correlation functionals B3LYP, BLYP and LDA without inclusion of relativistic effects (NR) or relativistic effects included via the one-component (1cZORA) or two-component (2cZORA) ZORA approach. ZORA calculations of $\mathcal{X}$ are shown with (LL+SS) and without (LL) inclusion of picture change effects determined by consideration of small-component integrals and renormalisation. The NEQM of ${}^{35}$Cl was used as $Q^{35}\mathrm{Cl}=-8.11{\mathrm{fm}}^2$ as proposed in Ref. [2]. Non-relativistic HF values are compared to those calculated with the molecular structure reported in Ref. [58] (Hobi-G), or the 6-311+G(2df,2pd) basis set used in Ref. [58] (Hobi-B), or both (Hobi-B+G).

Method		$\frac{{\mathcal{X}}_{\mathrm{aa}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bb}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{cc}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ab}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ac}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bc}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$
NR	HF/Hobi-G	−22.6	−8.42	31.1	−54.7	24.2	19.9
	HF/Hobi-B+G	−21.0	−7.94	28.9	−51.1	22.6	18.6
	HF/Hobi-B	−23.3	−7.94	31.2	−53.7	23.1	19.1
	HF	−24.2	−8.23	32.4	−55.9	24.0	20.0
	B3LYP	−23.8	−7.68	31.5	−53.5	23.4	19.4
	BLYP	−23.4	−7.38	30.8	−52.2	22.9	19.0
	5LDA	−23.2	−7.32	30.5	−51.1	22.6	18.6
1cZORA (LL)	HF	−24.6	−8.32	32.9	−56.7	24.3	20.3
	B3LYP	−24.2	−7.75	32.0	−54.2	23.6	19.7
	BLYP	−23.8	−7.44	31.3	−52.9	23.1	19.2
	LDA	−23.6	−7.37	31.0	−51.7	22.8	18.9
1cZORA (LL+SS)	HF	−24.5	−8.31	32.8	−56.5	24.3	20.2
	B3LYP	−24.1	−7.73	31.9	−54.0	23.6	19.6
	BLYP	−23.8	−7.42	31.2	−52.7	23.0	19.2
	LDA	−23.5	−7.36	30.9	−51.6	22.7	18.8
2cZORA (LL)	HF	−24.6	−8.32	32.9	−56.7	24.3	20.3
	B3LYP	−24.2	−7.75	32.0	−54.2	23.6	19.7
	BLYP	−23.8	−7.44	31.3	−52.8	23.1	19.2
	LDA	−23.6	−7.38	31.0	−51.7	22.8	18.9
2cZORA (LL+SS)	HF	−24.5	−8.31	32.9	−56.5	24.3	20.2
	B3LYP	−24.1	−7.74	31.9	−54.0	23.6	19.6
	BLYP	−23.8	−7.43	31.2	−52.7	23.0	19.2
	LDA	−23.5	−7.37	30.9	−51.6	22.8	18.8
Experiment [26]		−20.60	−8.54	29.14	−51	23	19
NR-MP2 [58]${}^a$		−19.91	−7.41	27.31	47.92	21.87	−17.54

^aNon-relativistic second-order Møller–Plesset perturbation theory calculations (NR-MP2) performed with the 6-311+G(2df,2pd) basis in Ref. [58], scaled by a factor of $\frac{-8.11{\mathrm{fm}}^2}{-8.17{\mathrm{fm}}^2}\approx 0.994$ to account for the different value of $Q_{{}^{35}\mathrm{Cl}}$ employed in Ref. [58]

Table A2. NEQM coupling tensor $\mathcal{X}$ of the ${}^{79}$Br nucleus in CHBrClF calculated at level of Hartree–Fock (HF) and DFT with exchange-correlation functionals B3LYP, BLYP and LDA without inclusion of relativistic effects (NR) or relativistic effects included via the one-component (1cZORA) or two-component (2cZORA) ZORA approach. ZORA calculations of $\mathcal{X}$ are shown with (LL+SS) and without (LL) inclusion of picture change effects determined by consideration of small-component integrals and renormalisation. The NEQM of ${}^{79}$Br was used as $Q_{{}^{79}\mathrm{Br}}=30.87\mathrm{f}{\mathrm{m}}^2$ as proposed in Ref. [2]. Non-relativistic HF values are compared to those calculated with the molecular structure reported in Ref. [58] (Hobi-G), or the 6-311+G(2df,2pd) basis set used in Ref. [58] (Hobi-B), or both (Hobi-B+G).

Method		$\frac{{\mathcal{X}}_{\mathrm{aa}}({}^{79}\mathrm{Br})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bb}}({}^{79}\mathrm{Br})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{cc}}({}^{79}\mathrm{Br})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ab}}({}^{79}\mathrm{Br})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ac}}({}^{79}\mathrm{Br})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bc}}({}^{79}\mathrm{Br})}{h\mathrm{MHz}}$
NR	HF/Hobi-G	459	−213	−246	−250	191	−57.1
	HF/Hobi-B+G	459	−213	−246	−251	191	−57.6
	HF/Hobi-B	484	−225	−259	−253	190	−56.2
	HF	483	−225	−258	−252	189	−55.8
	B3LYP	471	−219	−253	−243	188	−54.1
	BLYP	461	−214	−247	−236	185	−52.5
	LDA	455	−210	−245	−233	184	−51.6
1cZORA (LL)	HF	522	−243	−279	−272	205	−60.5
	B3LYP	507	−235	−272	−261	203	−58.3
	BLYP	495	−230	−265	−254	199	−56.5
	LDA	489	−226	−263	−250	197	−55.6
cZORA (LL+SS)	HF	514	−239	−275	−268	202	−59.5
	B3LYP	499	−232	−267	−257	200	−57.4
	BLYP	487	−226	−261	−250	196	−55.7
	LDA	481	−222	−259	−246	194	−54.8
2cZORA (LL)	HF	522	−243	−279	−272	205	−60.5
	B3LYP	507	−235	−272	−261	203	−58.3
	BLYP	494	−230	−265	−254	199	−56.5
	LDA	489	−226	−263	−250	197	−55.6
2cZORA (LL+SS)	HF	516	−240	−276	−269	203	−59.8
	B3LYP	501	−233	−269	−258	200	−57.7
	BLYP	489	−227	−262	−251	196	−55.9
	LDA	483	−223	−260	−247	195	−55.0
Experiment [26]		456.07	−212.12	−243.94	−249.3	199	−59
NR-MP2 [58]${}^a$		431.19	−199.83	−231.38	234.39	184.51	53.25

^aNon-relativistic second-order Møller–Plesset perturbation theory calculations (NR-MP2) performed with the 6-311+G(2df,2pd) basis in Ref. [58], scaled by a factor of $\frac{30.87\mathrm{f}{\mathrm{m}}^2}{31.3\mathrm{f}{\mathrm{m}}^2}\approx 0.986$ to account for the different value of $Q_{{}^{79}\mathrm{Br}}$ employed in Ref. [58]

Table A3. NEQM coupling tensor $\mathcal{X}$ of the ${}^{35}$Cl nucleus in CHClFI calculated at level of Hartree–Fock (HF) and DFT with exchange-correlation functionals B3LYP, BLYP and LDA without inclusion of relativistic effects (NR) or relativistic effects included via the one-component (1cZORA) or two-component (2cZORA) ZORA approach. ZORA calculations of $\mathcal{X}$ are shown with (LL+SS) and without (LL) inclusion of picture change effects determined by consideration of small-component integrals and renormalisation. The NEQM of ${}^{35}$Cl was used as $Q_{{}^{35}\mathrm{Cl}}=-8.112\mathrm{f}{\mathrm{m}}^2$ as proposed in Ref. [2].

Method		$\frac{{\mathcal{X}}_{\mathrm{aa}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bb}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{cc}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ab}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ac}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bc}}({}^{35}\mathrm{Cl})}{h\mathrm{MHz}}$
NR	HF	−17.3	−14.8	32.1	−56.0	−23.2	−21.2
	B3LYP	−17.4	−13.9	31.3	−53.8	−22.6	−20.5
	BLYP	−17.2	−13.5	30.7	−52.5	−22.1	−20.0
	LDA	−17.3	−13.2	30.5	−51.6	−21.9	−19.6
1cZORA (LL)	HF	−17.8	−14.9	32.7	−56.8	−23.3	−21.4
	B3LYP	−17.8	−14.0	31.8	−54.4	−22.7	−20.8
	BLYP	−17.7	−13.5	31.2	−53.1	−22.2	−20.3
	LDA	−17.7	−13.3	31.0	−52.1	−21.9	−19.9
1cZORA (LL+SS)	HF	−17.7	−14.9	32.5	−56.6	−23.2	−21.4
	B3LYP	−17.8	−13.9	31.7	−54.3	−22.6	−20.7
	BLYP	−17.6	−13.5	31.1	−53.0	−22.1	−20.2
	LDA	−17.6	−13.2	30.9	−52.0	−21.8	−19.9
2cZORA (LL)	HF	−17.7	−14.9	32.6	−56.6	−23.3	−21.4
	B3LYP	−17.7	−14.0	31.7	−54.3	−22.6	−20.7
	BLYP	−17.6	−13.5	31.1	−53.0	−22.1	−20.3
	LDA	−17.6	−13.3	30.9	−52.0	−21.9	−19.9
2cZORA (LL+SS)	HF	−17.6	−14.9	32.5	−56.5	−23.2	−21.4
	B3LYP	−17.7	−14.0	31.6	−54.2	−22.6	−20.7
	BLYP	−17.5	−13.5	31.0	−52.9	−22.1	−20.2
	LDA	−17.5	−13.3	30.8	−51.9	−21.9	−19.9
Experiment [27]		−13.40	−15.45	28.85	−51.4	−22.7	−21.1

Table A4. NEQM coupling tensor $\mathcal{X}$ of the ${}^{127}$I nucleus in CHClFI calculated at level of Hartree–Fock (HF) and DFT with exchange-correlation functionals B3LYP, BLYP and LDA without inclusion of relativistic effects (NR) or relativistic effects included via the one-component (1cZORA) or two-component (2cZORA) ZORA approach. ZORA calculations of $\mathcal{X}$ are shown with (LL+SS) and without (LL) inclusion of picture change effects determined by consideration of small-component integrals and renormalisation. The NEQM of ${}^{127}$I was used as $Q_{{}^{127}\mathrm{I}}=-68.822\mathrm{f}{\mathrm{m}}^2$ as proposed in Ref. [2].

Method		$\frac{{\mathcal{X}}_{\mathrm{aa}}({}^{127}\mathrm{I})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bb}}({}^{127}\mathrm{I})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{cc}}({}^{127}\mathrm{I})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ab}}({}^{127}\mathrm{I})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{ac}}({}^{127}\mathrm{I})}{h\mathrm{MHz}}$	$\frac{{\mathcal{X}}_{\mathrm{bc}}({}^{127}\mathrm{I})}{h\mathrm{MHz}}$
NR	HF	−1620	792	827	633	524	−118
	B3LYP	−1560	763	797	602	517	−112
	BLYP	−1520	742	775	583	506	−108
	LDA	−1500	732	771	576	505	−106
1cZORA (LL)	HF	−1950	956	998	764	634	−144
	B3LYP	−1860	908	949	718	617	−135
	BLYP	−1800	879	918	691	600	−129
	LDA	−1780	868	914	684	600	−127
1cZORA (LL+SS)	HF	−1880	920	961	736	611	−139
	B3LYP	−1790	875	915	692	594	−130
	BLYP	−1730	848	885	667	579	−124
	LDA	−1720	837	882	659	578	−123
2cZORA (LL)	HF	−1960	957	1000	766	636	−144
	B3LYP	−1850	903	944	715	614	−134
	BLYP	−1790	874	912	687	597	−128
	LDA	−1770	862	908	679	596	−126
2cZORA (LL+SS)	HF	−1900	932	973	745	618	−141
	B3LYP	−1800	881	920	696	598	−131
	BLYP	−1740	852	889	670	582	−125
	LDA	−1730	841	886	662	581	−123
Experiment [27]		−1704.58	838.58	866.0	699.77	622.7	−140.4

R. Berger and J.L. Stuber, Mol. Phys. 105, 41–49 (2007).

 Web of Science ®Google Scholar

P. Pyykkö, Mol. Phys. 116 (10), 1328–1338 (2018).

 Web of Science ®Google Scholar

F. Hobi, R. Berger and J. Stohner, Mol. Phys. 111 (14–15, SI), 2345–2362 (2013).

 Web of Science ®Google Scholar

A. Bauder, A. Beil, D. Luckhaus, F. Müller, and M. Quack, J. Chem. Phys. 106, 7558–7570 (1997).

 Web of Science ®Google Scholar

P. Soulard, P. Asselin, A. Cuisset, J.R.A. Moreno, T.R. Huet, D. Petitprez, J. Demaison, T.B. Freedman, X.L. Cao, L.A. Nafie, and J. Crassous, Phys. Chem. Chem. Phys. 8, 79–92 (2006).

 PubMed Web of Science ®Google Scholar