The Blue–Violet Color of Pentamethylbismuth: A Visible Spin‐Orbit Effect

Abstract

Two‐component relativistic time‐dependent density functional theory calculations with spin‐orbit coupling predict yellow and orange–red absorption for BiPh₅ and BiMe₅, respectively, providing an excellent explanation for their respective violet and blue–violet colors. According to the calculations, the visible absorption is clearly attributable to a single transition from a ligand‐based HOMO to a low‐energy LUMO with a significant contribution from a relativistically stabilized Bi 6s orbital. Surprisingly, scalar releativistic calculations completely fail to reproduce the observed visible absorption and place it at the violet/near‐UV borderline instead.

Ever since their syntheses in the latter part of the 20^th century, the violet color of pentaphenylbismuth1, 2 and the blue–violet color of pentamethylbismuth3 have fascinated chemists.4 For comparison, it might be noted that PPh₅, AsPh₅, and SbPh₅ are all colorless.1, 5, 6 Surprisingly, despite the interest in the problem, the colors of BiPh₅ and BiMe₅ have not been investigated with modern quantum chemical methods. Early extended Hückel (EH)7 calculations on BiH₅ and subsequent spin‐orbit MS Xα 8 calculations on BiH₅ and Bi(CCH)₅ (CCH=ethynyl) correctly emphasized the key role of relativity on the lowest‐energy electronic transition: “non‐relativistic pentaphenylbismuth would not be violet.” Importantly, the authors also noted a much lower transition energy for the C _4v square‐pyramidal (SPy) form of BiH₅, relative to the D _3h trigonal‐bipyramidal form. These early corrections did not deploy any specialized excited‐state methodology and simply used a ΔSCF approach (the HOMO–LUMO gap) to predict transition energies. In the present reinvestigation of the problem, we studied BiMe₅, BiPh₅, and the as‐yet unknown Bi(CF₃)₅ with modern ground‐state density function theory (DFT) and time‐dependent density functional theory (TDDFT) calculations based on the zeroth order regular approximation (ZORA)9 to the two‐component Dirac equation, applied with both spin‐orbit coupling (SOC) and as a scalar correction.10

Scalar‐relativistic OLYP11 and/or B3LYP12 geometry optimizations with large STO‐TZ2P and QZ4P basis sets led to near‐equienergetic TBP and SPy minima, with the latter less than 0.1 eV higher in energy than the former for all three molecules. In the case of BiMe₅, the transition state for the Berry pseudorotation connecting the two conformations was also located and found to be <1 kcal mol⁻¹ higher in energy, relative to either conformer. The calculations thus appear to indicate a fluxional structure in solution for all three molecules.

These results are consistent with experimental studies on pentaarylbismuth derivatives, where the existence of both conformers in solution could be deduced from optical spectra; interestingly, their relative proportions were found to be independent of temperature, indicating near‐identical thermodynamic stabilities.7 Also, although the majority of pentaarylbismuth derivatives have exhibited SPy X‐ray structures,4 both BiMe₅ 3 and a substituted pentaarylbismuth derivative have been found to exhibit TBP geometries.7

For both conformers of all three compounds studied, regardless of the functional, basis set, and relativistic treatment, our calculations indicate simple HOMO→LUMO character for the lowest‐energy electronic transition (Figure 1 and Table 1). Furthermore, in each case, the HOMO was found to be an essentially ligand‐based MO and the LUMO was found to have substantial (ca. 20 %) Bi 6s character. These findings are qualitatively consistent with the notion that the color of BiMe₅ and BiPh₅ results from a low‐lying LUMO, whose low energy (in spite of the Bi−C antibonding interactions shown in Figure 2) owes significantly to the relativistic stabilization of the Bi 6s level.

Figure 1.

Gibbs free energies and geometries for the TBP, TS and SPy geometries of BiMe₅. ΔG ^≠=0.92 kcal mol⁻¹ (0.040 eV), ν_i=51.0i cm⁻¹.

Table 1.

ZORA TDDFT results for the lowest‐energy electronic transitions for BiMe₅, BiPh₅, and Bi(CF₃)₅.

Complex	Geometry	Functional	Relativistic	Basis	Excitation
			approximation	set	l [nm]	E [eV]	f	symmetry	% HOMO→LUMO
BiMe5	TBP (C 3v)	OLYP	scalar	TZ2P	382.6	3.24	1.39×10−14	A1	87.5
BiMe5	TBP (C 3v)	OLYP	spin‐orbit	TZ2P	592.0	2.09	2.41×10−6	E	99.6
BiMe5	TBP (C 3v)	OLYP	spin‐orbit	QZ4P	617.2	2.01	3.18×10−6	E	99.4
BiMe5	TBP (C 3v)	B3LYP	scalar	TZ2P	350.8	3.53	4.97×10−5	A1	97.4
BiMe5	TBP (C 3v)	B3LYP	spin‐orbit	TZ2P	611.7	2.03	7.44×10−8	E	97.9
BiMe5	TBP (C 3v)	B3LYP	spin‐orbit	QZ4P	634.9	1.95	1.17×10−7	E	97.1
BiMe5	SPy (C s)	OLYP	scalar	TZ2P	385.7	3.21	2.73×10−6	A′′	86.0
BiMe5	SPy (C s)	OLYP	spin‐orbit	TZ2P	637.8	1.94	1.18×10−9	A′	99.6
BiMe5	SPy (C s)	OLYP	spin‐orbit	TZ2P	637.1	1.95	8.68×10−5	A′	99.6
BiMe5	SPy (C s)	OLYP	spin‐orbit	TZ2P	637.1	1.95	8.74×10−5	A′′	99.6
BiMe5	SPy (C s)	OLYP	spin‐orbit	QZ4P	666.4	1.86	1.67×10−9	A′	99.4
BiMe5	SPy (C s)	OLYP	spin‐orbit	QZ4P	665.6	1.86	9.37×10−5	A′	99.4
BiMe5	SPy (C s)	OLYP	spin‐orbit	QZ4P	665.6	1.86	9.39×10−5	A′′	99.4
BiMe5	SPy (C s)	B3LYP	scalar	TZ2P	356.8	3.47	3.57×10−6	A′′	97.0
BiMe5	SPy (C s)	B3LYP	spin‐orbit	TZ2P	717.2	1.73	9.16×10−10	A′	98.1
BiMe5	SPy (C s)	B3LYP	spin‐orbit	TZ2P	714.1	1.74	7.69×10−5	A′	98.2
BiMe5	SPy (C s)	B3LYP	spin‐orbit	TZ2P	714.1	1.74	7.64×10−5	A′′	98.2
BiMe5	SPy (C s)	B3LYP	spin‐orbit	QZ4P	727.0	1.71	8.07×10−10	A′	97.2
BiMe5	SPy (C s)	B3LYP	spin‐orbit	QZ4P	723.7	1.71	8.37×10−5	A′	97.3
BiMe5	SPy (C s)	B3LYP	spin‐orbit	QZ4P	723.7	1.71	8.36×10−5	A′′	97.3
BiPh5	TBP (C 2)[a]	OLYP	scalar	TZ2P	391.7	3.17	3.03×10−5	A	90.6
BiPh5	TBP (C 2)[a]	OLYP	spin‐orbit	TZ2P	586.3	2.11	6.84×10−9	A	99.3
BiPh5	TBP (C 2)[a]	OLYP	spin‐orbit	TZ2P	586.3	2.11	4.50×10−8	B	99.3
BiPh5	TBP (C 2)[a]	OLYP	spin‐orbit	TZ2P	585.9	2.12	1.46×10−6	B	99.4
Bi(CF3)5	TBP (C 3v)	OLYP	scalar	TZ2P	425.5	2.91	1.29×10−6	A1	97.0
Bi(CF3)5	TBP (C 3v)	OLYP	spin‐orbit	TZ2P	825.9	1.50	1.44×10−6	E	99.7
Bi(CF3)5	SPy (C s)	OLYP	scalar	TZ2P	439.3	2.82	7.13×10−5	A′′	96.9
Bi(CF3)5	SPy (C s)	OLYP	spin‐orbit	TZ2P	993.1	1.25	6.27×10−7	A′	99.7
Bi(CF3)5	SPy (C s)	OLYP	spin‐orbit	TZ2P	989.9	1.25	5.57×10−5	A′	99.7
Bi(CF3)5	SPy (C s)	OLYP	spin‐orbit	TZ2P	989.9	1.25	5.64×10−5	A′′	99.7

[a] A “true” SPy structure could not be optimized; attempts at obtaining such a structure led to local minima intermediate between TBP and SPy geometries.

Figure 2.

OLYP‐ZORA‐SOC/QZ4P spinor‐MO overlays of the frontier orbitals for the two conformations of BiMe₅.

Quantitatively, the TDDFT calculations afforded a key surprise in that the scalar approximation completely fails to predict an absorption in the higher‐wavelength visible range that would account for the blue–violet or violet color of BiMe₅ and BiPh₅. The ZORA‐SOC calculations largely correct the problem, redshifting the transition energy by >200 nm to the orange and yellow parts of the spectrum, respectively (Table 1). By comparison, the choice of OLYP versus B3LYP has a relatively modest effect on the transition energy of BiMe₅, as does an STO‐QZ4P versus TZ2P basis set. Thus, B3LYP results in a redshift of approximately 20 nm relative to OLYP, as does QZ4P relative to TZ2P. For the as‐yet unknown Bi(CF₃)₅, ZORA‐SOC predicts a transition energy in the near‐IR, redshifted by 400 nm or more relative to the scalar relativistic value.

In qualitative agreement with EH and Xα calculations,^[7, 8] the SPy geometry results in a significant redshift in the transition energy, relative to the TBP geometry. Depending on the exact methodological details, the redshift at the ZORA‐SOC level is about 45–90 nm for BiMe₅ and 165 nm for the as‐yet unknown Bi(CF₃)₅. Unlike BiMe₅ and BiPh₅, Bi(CF₃)₅ is thus predicted to be colorless.

In summary, two‐component relativistic TDDFT calculations with spin‐orbit coupling provide an excellent explanation for the blue–violet color of BiMe₅ and the violet color of BiPh₅. In contrast, scalar relativistic calculations are completely inadequate, overestimating the transition energies by 200 nm or more. The present results may be viewed as a cautionary tale that, although scalar relativistic calculations may afford a reasonable description of many aspects of sixth‐row elements,13, 14 a correct description of spin‐orbit effects may be essential for an accurate description of the electronic absorption spectra of 6p compounds.

Experimental Section

All DFT calculations were carried out with the ADF (Amsterdam Density Functional) 2014 program system,15 employing the OLYP10 GGA (generalized gradient approximation) or the B3LYP11 hybrid functional, the ZORA8 Hamiltonian applied with spin‐orbit coupling or as a scalar correction, all‐electron Slater‐type TZ2P or QZ4P basis sets, a fine mesh for numerical integration, and full geometry optimizations with tight convergence criteria. Thermodynamic quantities were calculated as previously described16 through the standard implementations in ADF. All TDDFT calculations with a given functional and basis set also employed molecular geometries optimized with the same functional and basis set.

Supporting information

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

Supplementary

J. Conradie, A. Ghosh, ChemistryOpen 2017, 6, 15.