Preference of C_2v Symmetry in Low-Spin Hexacarbonyls of Rare-Earth and f Elements

Abstract

The structures and bonding of selected neutral M(CO)₆ complexes (M = Sc, Y, La, Lu, Ac and U) have been studied by density functional theory calculations. The calculations revealed the preference for C_2v symmetry and low-spin electronic state for most of these complexes. The relative stability of the low-symmetry species increases gradually with the size of the metal atom. While the characteristic O_h hexa-coordinated structure is favored in the high-spin electronic state of the smaller metals, for heavier metals, important advantages of the C_2v vs. O_h structures include larger charge transfer interactions in terms of transferred electrons as well as better steric conditions. Our joint experimental–theoretical analysis detected and confirmed the O_h structure of the Sc(CO)₆ complex in cryogenic CO/Ar matrices.

1. Introduction

Metal carbonyls are best known for their complexes with transition metals (TM), which have numerous applications like industrial catalysts or precursors for exotic compounds. They were extensively studied in the 1970s, using mostly matrix isolation trapping, spectroscopy and photochemical excitation [1,2,3,4,5,6,7], resulting in substantial amounts of experimental physicochemical data.

In the past two decades, numerous experimental studies were performed on gaseous ionic carbonyl complexes of f elements [8,9,10,11,12,13,14,15], heavy alkaline-earth (Ca, Sr, Ba) [16,17,18], rare-earth (Sc, Y) [19] and heavy transition metals (Zr, Hf) [20]. While the latter studies focused on the highest coordinated species (mostly eight, but in a few cases even nine, like Tm(CO)₉⁻, Lu(CO)₉⁻ [14] and La(CO)₉⁺, Ce(CO)₉⁺ [11]), lower coordinations were also documented in the mass spectra. A very recent study targeting the highest-coordination neutral carbonyl complexes of Sc, Y and La using gas-phase-size-specific infrared–vacuum ultraviolet spectroscopy reported Sc(CO)₇, Y(CO)₈ and La(CO)₈ as the highest-coordination species [21].

Quantum chemical calculations over the decades focused on the electronic structure, geometry and bonding interactions—revealing several interesting features [6,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37].

The best-characterized neutral TM hexacarbonyls are those of group VI (Cr, Mo, W). They are stable (crystalline) at room temperature and have a highly symmetric octahedral structure [24,38,39,40,41,42,43,44]. Their high stability has been attributed to their saturated valence shell following the so-called 18-electron rule [27,37,45,46,47]. However, the adjacent V(CO)₆ is also stable and octahedral [48,49], although it only has 17 valence electrons. The Ti(CO)₆ complex was found to be unstable; therefore it could only be detected and characterized under matrix isolation conditions [50].

Beyond neutral complexes, several ionic hexacarbonyl species stabilized by counterions have been synthesized in the solid phase [51,52,53,54,55]. The characteristic single absorption band of the CO stretching in the IR spectra provided strong evidence for the octahedral structure of these molecules [51,52,53,54,55].

Neutral lanthanide carbonyls were reported recently from a matrix isolation FT-IR study [56], where the interpretation of the spectra was facilitated by Density Functional Theory (DFT) calculations. The most abundant species in the cryogenic CO matrix proved to be Ln(CO)₈, but in a few cases, Ln(CO)₇ and Ln(CO)₆ could also be identified. Surprisingly, the DFT calculations indicated the preference of lower-symmetry C_2v structures (Figure 1) for those Ln(CO)₆ molecules—in contrast to the expected O_h symmetry based on the known TM(CO)₆ complexes [29,35,37].

The aim of the present study is to clarify how far the preference for lower symmetry goes in the rare-earth and f element groups of the periodic system and to uncover their bonding characteristics. This study is performed by means of DFT calculations extended with a Natural Bond Orbital (NBO) analysis [57,58,59,60,61] of the donor-acceptor interactions.

2. Computational and Experimental Details

2.1. Computational Details

The DFT computations were performed with the Gaussian09 suite of programs [62] using the hybrid B3LYP [63,64,65] exchange–correlation functional in conjunction with the correlation consistent cc-pVTZ basis sets for the light atoms C, O [66] and Sc [67]. For the heavy atoms, the quasi-relativistic small-core (4/5f-in-valence) pseudopotentials were applied: (i) for Y, La and Lu the one denoted as ECP28MWB [68,69] with contracted valence basis sets of (8s7p6d2f1g)/(6s5p3d2f1g) for Y [70] and (14s13p10d8f6g)/(10s8p5d4f3g) for La and Lu [71], and (ii) for Ac and U, the one named ECP60MWB [72,73] in conjunction with (14s13p10d8f6g)/(10s9p5d4f3g) valence bases [73,74].

In order to account for dispersion effects, the D3 version of Grimme’s empirical correction using the original damping [75] was utilized. Though somewhat old, the B3LYP exchange–correlation functional in conjunction with a triple-zeta basis set and proper dispersion correction belongs to the recommended methods for geometries and vibrational frequencies [76]. The predicted relative energies of the structural isomers were confirmed by calculations on selected complexes with the more robust PBE0 hybrid functional [77], in conjunction with the same basis set and other technical parameters as in the B3LYP jobs. (The PBE0 relative energies are given in Table S1 in the Supplementary Materials). Because of the weak character of coordination interactions, the integration accuracy was set to SuperFine grid. The ground states of the computed molecules were verified using the STABLE keyword. The spin-contaminations of the open-shell systems were checked in each calculation: the calculated <Ŝ²> eigenvalues proved to be consistent with the theoretical ones (cf. Table S1).

The single- vs. multireference character of the studied complexes was probed by populations of natural molecular orbitals, generated from the unrestricted B3LYP wavefunctions using the guess=(read, only, save, naturalorbitals) keyword. Significant deviations from double-, single- and/or unoccupation would point to a multireference character. For all the complexes, we obtained only negligible deviations from the reference values (2 or 1) of the occupied orbitals. Accordingly, the population of the virtual orbitals was also negligible, with the largest being 0.006 e in the case of quintet U(CO)₆.

Single-point relativistic complete active space self-consistent field (CASSCF) [78] calculations on the B3LYP reference geometries of the significant low- and high-spin structures were carried out by means of the MOLCAS 8.2 code [79,80], applying C₁ symmetry. The scalar relativistic effects were taken into account with the second-order Douglas–Kroll–Hess Hamiltonian [81,82]. The used atomic natural-orbital-type all-electron basis sets valence of the triple-zeta plus polarization quality developed for relativistic calculations (ANO-RCC) had the contraction schemes of [21s15p10d6f4g2h]/[6s5p3d2f1g] for Sc and [21s18p13d6f4g2h]/[7s6p4d2f1g] for Y [83], [24s21p15d5f3g2h]/[8s7p5d2f1g] for La and [25s22p15d11f4g2h]/[8s7p4d3f2g1h] for Lu [84], [27s24p18d14f6g3h]/[9s8p6d4f2g1h] for Ac and [26s23p17d13f5g3h]/[9s8p6d5f2g1h] for U [85] and [14s9p4d3f2g]/[4s3p2d1f] for C and O [86].

The active space consisted of the valence electrons and orbitals of the metals, viz. 3e/9o (electron/orbital) for Sc, Y and Lu and 3e/13o for La, Ac and U. The most stable electronic state was selected from the results of state-averaged 5-root calculations. Subsequent second-order perturbation theory calculations on the basis of the CASSCF wave functions (CASPT2) [87,88] accounted for dynamic electron correlation.

The CASSCF data confirmed a very slight multireference character of the studied complexes: the contribution of the main electron configuration was between 87–93%, and the populations of the 2- and 1-electron orbitals were between 1.83–1.88 and 0.93–0.98 e, respectively, while that of the most populated virtual orbital was 0.05 e.

An analysis of the intramolecular interactions was performed on the basis of the B3LYP calculations. The atomic charges and valence orbital populations of the metals were evaluated using the Natural Bond Orbital (NBO) model [57,58,59,60,61] by means of the NBO 6.0 code [89,90]. Due to the deficiency of NBO 6.0 for g functions, for this analysis, the g polarization functions were omitted from the metal basis sets. The DFT steric energy was estimated according to Shubin Liu’s energy decomposition analysis [91] using the Multiwfn code [92].

2.2. Matrix Isolation Spectroscopy

As described in detail previously [56,93], basically, a Displex closed-cycle helium refrigerator was used to cool a NaCl optical window to 10 K in a specialized vacuum system. Monoatomic scandium and yttrium vapors were generated by direct resistive heating of a metal filament (Goodfellow 0.25 mm, 99%) in a water-cooled oven, and high-purity gases were obtained from Messer-Griesheim (Ar 5.7, CO 4.7). Infrared spectra were recorded on Perkin-Elmer FT-IR spectrometers equipped with data collection computers and UV–visible spectra on computer-controlled double-beam Perkin-Elmer Hitachi 320 on the same sample within a few minutes. For narrow-band irradiations, the light of a 1000 W Hg/Xe lamp was selected by a monochromator system. The purpose of the UV–vis measurements was to check for impurities and to follow the progress of the Sc + CO reaction by the vanishing sharp peaks of the isolated Sc atoms. Representative IR and UV–vis spectra are given in Figures S2 and S3 of the Supplementary Materials.

3. Results and Discussion

3.1. Characteristic Structures

In the calculations on the M(CO)₆ complexes (M = Sc, Y, La, Lu, Ac, U), all the reasonable spin states were probed. The ground-state electron configurations of the studied group IIIB metals are ns¹(n−1)d² and ns²(n−1)d¹ for the high- and low-spin states, respectively. They correspond to spin multiplicities of 4 and 2, respectively, for Sc, Y, La, Lu and Ac. Due to the additional (n−2)f³ subshell of U, the possible spin multiplicities are 7, 5, 3 and 1. The obtained characteristic stationary points on the potential energy surfaces are given in

Table 1. Characteristic stationary points of the studied M(CO)₆ complexes from geometry optimizations.

M	Spin	Symmetry	Character 1	ΔE 2	ΔG10K	ΔG298K
Sc	4	Oh	min	0.0	0.0	0.0
	2	D4h	min	11.0	10.6	7.1
	2	C2v	min	8.5	10.9	9.0
Lu	4	Oh	min	2.8	0.2	0.0
	2	D4h	min	11.9	8.9	2.2
	2	C2v	min	0.0	0.0	1.7
Y	4	Oh	min	5.9	2.9	0.0
	2	D4h	i(2)	14.9
	2	C2v	min	0.0	0.0	0.8
U 3	7	Oh	i(3−)	36.6
	7	C2	min	22.3	17.0	1.4
	5	D4h	i(2−)	72.2
	5	C2v	min	0.0	0.0	0.0
	3	Cs	min	12.4	15.6	19.0
	1	C2h	min	93.6	91.2	86.9
La	4	Oh	min	21.8	17.6	6.6
	2	D4h	i(2−)	31.1
	2	C2v	min	0.0	0.0	0.0
Ac	4	Oh	min	25.1	20.3	4.5
	2	D4h	i(2−)	33.2
	2	C2h	min	25.4	22.6	15.4
	2	C2v	i(1−)	0.3
	2	Cs 4	min	0.0	0.0	0.0

¹ The abbreviations min and i(n−) mean minima and n-order saddle points on the potential energy surface, respectively. ² Difference (in kJ/mol) with respect to the electronic energy of the most stable form of the given complex. The electronic energies (in Hartree) are given in the Supplementary Materials at the Cartesian coordinates of the structures. ³ The C_s structure of triplet U(CO)₆ is a slightly deformed one from C_2v. The C₂ and C_2h species are shown in Figure S1 of the Supplementary Materials. ⁴ Slightly distorted from the C_2v saddle-point.

.

The data in Table 1 reveal that the preferred structure of the high-spin (quartet) M(CO)₆ complexes is the octahedral one. Interestingly, by contrast, the octahedral structure of the highest-spin septet U(CO)₆ is unstable—it is a third-order saddle point which, upon further optimization, converged to a C₂ minimum on the potential energy surface. The many unpaired U 5f electrons (partly participating in the bonding) result in a deformed electron density distribution influencing also the bonding directions.

The data in Table 1 show also that the octahedral symmetry is not stable for the low-spin M(CO)₆ complexes. Due to the Jahn–Teller effect, the O_h structures were distorted slightly in the geometry optimizations to D_4h—which proved to be local minima for M = Sc and Lu, whereas they are second-order saddle points in the case of the other M. Our calculations resulted in C_2v global minimum structures for most of the low-spin M(CO)₆ complexes. The exception is Ac with the largest radius, where the C_2v structure distorted slightly to a C_s minimum with a marginal (0.3 kJ/mol) energy difference.

The stability relations of the octahedral high-spin and lower symmetry low-spin species are important for the goal of the present study. In terms of the present B3LYP electronic energies, the high-spin O_h complex is preferred in the case of the small Sc—but in the case of the other metals, the lowest-energy forms are the low-spin states with C_2v/C_s structure. This trend is essentially confirmed by the PBE0 and CASPT2 results (given in Table S1), just the two forms of Sc(CO)₆ are energetically nearly identical at the latter theoretical levels.

The thermal effects increase the relative stabilities of the high-spin O_h/D_4h structures by a few kJ/mol. At low temperature (10 K), the calculated energy order of the different structures was preserved, but at room temperature, the energy order of Lu(CO)₆ and Y(CO)₆ changed in favor of the high-spin structures at the applied B3LYP level (see ΔG_10K and ΔG_298K in Table 1). In any case, the small energy differences in the Sc, Lu and Y hexacarbonyls indicate comparable stabilities of the high- and low-symmetry forms.

It should be noted that the relative energies of the studied open-shell complexes can be sensitive to the applied theoretical model. In an earlier CCSD(T) study of the Sc(CO)₆ complex using single-point calculations on BP86-optimized geometries, the preference for the low-spin C_2v structure was predicted [33]. Our matrix isolation IR results are discussed below in Section 3.4; however, they support our DFT predictions for the preference of the high-spin O_h structure, at least in the cryogenic Ar matrix. In view of the different order from CCSD(T)—though the energy differences are small—one could speculate whether the Ar matrix would stabilize the O_h structure, and in this way, turn over the stability relation of the two species. In order to estimate the effect of the matrix, we performed geometry optimizations using the polarized-continuum (PCM) solvation model [94,95] with Ar as a solvent on the low- and high-spin species of Sc(CO)₆. These calculations predicted a relative stabilization of the low-spin C_2v vs. the high-spin O_h structure by 3.4 kJ/mol and thus do not support a turn-over from C_2v to O_h in the Ar matrix. Altogether, it seems that for the slightly multiconfigurational open-shell Sc(CO)₆ complex, the less sophisticated DFT provided results closer to the experiment than the more sophisticated CCSD(T).

The computed B3LYP energies in Table 1 reveal a gradual increase in stability in the low-symmetry forms with increasing M size. This implies a definite role of steric effects for this property (which is elaborated in a later section of this paper).

Besides the symmetry, characteristic geometrical information is provided by the M-C bond distances of the M(CO)₆ complexes depicted in Figure 2. The first such information is the good correlation between the M³⁺ effective ionic radii [96] and the computed M-C bond distances. The only significant deviation can be observed for U, where the bonding interactions are more complex than in the cases of the other metals due to the involvement of 5f valence electrons. Because of the neutral character of the complexes, available empirical neutral M radii [97] were also considered in the above comparison. They have some deviations from the trend in the M³⁺ radii; thus, the agreement with the calculated M-C distances was worse (cf. Table S2).

The most important message of Figure 2 is, however, the characteristic differences in the M-C bond distances in the various structures. These bonds in the high-spin O_h and low-spin (from O_h slightly distorted) D_4h structures are nearly identical in the studied set of M(CO)₆ complexes. Also, the four equatorial M-C bonds in the C_2v structures (see Figure 1b) remain close to the six M-C bond distances of the symmetric O_h and D_4h isomers. In contrast, the two axial M-C bonds become gradually shorter with increasing M size. They correlate well with the above-mentioned increasing C_2v stability, implying the significant role of the axial ligands in the stability relations.

3.2. Steric Conditions

Steric interactions are closely related to the above-discussed structural properties and are determined by the particular structures and the size of M. Due to the fixed bond angles of 90/180 degrees in the O_h and D_4h structures, in these structures, steric relaxation can only occur by the elongation of the M-C bond distances. In contrast, in the C_2v structures, both the axial and equatorial C-M-C angles can vary, as presented in Figure 3.

The presented bond angles show a reasonable correlation with the M³⁺ radii (cf. Figure 2). The C₁-M-C₂ angles decrease gently with increasing axial M-C bond distances—as allowed by the decreasing steric repulsion of these adjacent groups. The similarly decreasing steric interaction between the axial and equatorial CO groups can be followed in the C₃-M-C₅ angles. In the case of the smaller Sc, Lu and Y metals, the equatorial CO groups are considerably bent away from the axial CO groups (downwards in Figure 1b). In the U, La and Ac complexes, however, the equatorial CO groups are slightly bent toward the axial ones (upwards in Figure 1b, indicated by the >180 deg. values for C₃-M-C₅), facilitated by the decreased steric repulsion. Accordingly, in these latter structures, there is more free place for the coordination of additional (hepta-, octa-) ligands at the bottom side of the structure.

The steric interactions in the complexes are characterized by means of a steric analysis adapted from S. Liu [91,98]. In fact, the DFT steric energy of Liu corresponds to the Weizsäcker kinetic energy [99] representing spatial effects, but it lacks additional effects related to the Pauli exclusion. Nevertheless, this model has been successfully applied to study conformational changes [100], the anomeric effect [101] and chemical reactions [102].

The evaluated DFT steric energies (Table S4) were used to assess the relative order of repulsive steric effects in the characteristic O_h, D_4h and C_2v structures. Particularly interesting is the comparison of the D_4h and C_2v structures of the same (low) spin states. As discussed above, the C_2v structures proved to be more stable than D_4h in terms of electronic energy for all the studied M(CO)₆ complexes. The calculated DFT steric energies showed a significant steric preference of C_2v vs. D_4h (>600 kJ/mol, cf. Table S4). The spatial steric effect in the high-spin O_h structures is even larger. This steric strain supports the distortion of the low-spin D_4h structures to C_2v. Moreover, the steric preference of the low-spin C_2v structures can also be a significant factor for their higher stability compared with the high-spin O_h ones in the cases of the larger metals. A further important factor is the donor–acceptor interaction, discussed in the following subsection.

3.3. Donor–Acceptor Interactions

The metal–ligand interactions in carbonyl complexes involve very interesting bonding features and therefore have been investigated extensively [34,35,36,37,103,104,105,106]. They consist of CO→M σ donation and M→CO π backdonation, the σ and π notations representing the σ and π characters of the orbitals participating in these interactions.

Several studies have focused on the shifts in CO vibrational stretching frequencies, which are caused by the elongation or contraction of the CO bond depending on the nature of the donor–acceptor interaction. In neutral and most ionic M(CO)_x complexes, shifts to the lower wavenumbers (red shift) occur, originating from elongation of the CO bond upon backdonation from M to the π* orbitals of CO. This characteristic red shift has been used to characterize the strength of interaction [105], as well as to clarify coordination numbers [9,107,108,109,110,111,112].

The main bonding orbitals in the O_h and C_2v structures are demonstrated in Figure 4 by those of Y(CO)₆. In the high-spin O_h structure, the σ donation is manifested in two 2-electron orbitals: one involving an equatorial Y 4d acceptor orbital (upper row HOMO-4) and the other formed with the axial Y 4d acceptor orbital (upper row HOMO-3). The π backdonation interactions occur from three orthogonal singly occupied 4d orbitals of the Y atom (e.g., upper row SOMO). The low-spin C_2v isomer is formed by three 2-electron orbitals from which the σ donation from the equatorial and axial CO groups is distinguished (bottom row HOMO-5 and HOMO-1). The two π backdonation orbitals (bottom row HOMO and SOMO) are delocalized over the six CO groups.

Some quantitative information on the electrons participating in the donor–acceptor interactions can be provided by NBO analysis [57]. Selected NBO results on the studied complexes are compiled in

Table 2. NBO analysis results on the charge transfer (CT) interactions ¹ in selected M(CO)₆ complexes.

M	XAR 2	Spin	Sym	qM	CT		ΣCT	Pop
					(CO)6→M	M→(CO)6		s	d	f
Sc	1.20	4	Oh	−0.34	1.68	1.34	3.02	0.44	2.90	-
		2	D4h	−0.33	1.69	1.36	3.05	0.45	2.88	-
		2	C2v	−0.25	1.73	1.48	3.21	0.40	2.85	-
Lu	1.14	4	Oh	0.15	1.45	1.60	3.06	0.45	2.41	-
		2	C2v	0.23	1.51	1.74	3.25	0.41	2.37	-
Y	1.11	4	Oh	0.21	1.32	1.53	2.85	0.42	2.36	-
		2	C2v	0.33	1.36	1.68	3.04	0.37	2.29	-
U	1.22	7	C2	−0.10	1.80	1.70	3.50	0.41	2.61	3.04
		5	C2v	−0.16	2.07	1.91	3.98	0.33	2.63	3.15
La	1.08	4	Oh	0.08	1.28	1.36	2.64	0.33	2.54	0.04
		2	C2v	0.16	1.40	1.56	2.96	0.27	2.48	0.09
Ac	1.00	4	Oh	0.31	1.19	1.50	2.69	0.35	2.26	0.07
		2	Cs 3	0.41	1.31	1.72	3.03	0.30	2.16	0.11

¹ Natural charge of M (q_M) and populations (Pop) of its valence s/d/f orbitals (e); charge transfer between M and the (CO)₆ fragments (CT, e) derived from the populations of lone pair and—in the naked atom—empty valence orbitals of M. ² Allred-Rochow electronegativity [113] in Pauling units. ³ Slightly distorted from the C_2v saddle-point.

, together with the Allred–Rochow electronegativities [113].

The net natural charge of M (q_M) corresponds to the difference in CT to and from M. A negative q_M means that the number of donated electrons exceeds the backdonated ones—a case reported recently for several neutral and ionic metal carbonyls [37,56]. It can occur with a sufficiently large number of donor CO groups, while the surrounded M has only a limited number of electrons for backdonation.

Among the present complexes, a negative q_M was obtained for Sc and U. In the complexes of the other metals, the M→ (CO)₆ backdonation exceeded the (CO)₆→M donation. This feature is in accordance with the electronegativities of Sc and U being the largest in the present set (cf. Table 2). In general, there is a good correlation between the number of electrons transferred from (CO)₆ to M and the Allred–Rochow electronegativities (cf. Figure 5), suggesting a dominant role of electronegativity in this process. In contrast, no trend in the M→ (CO)₆ backdonation can be recognized (cf. Table 2), implying the comparable importance of electronegativity, spatial conditions and relative energies of the interacting orbitals.

The sum of the donated and backdonated electrons (Σ_CT) is around 3 e, which means covalent M-C bond orders of ca. 0.5 pro CO group. The somewhat larger value of U(CO)₆ is the result of the above-noted larger donation and backdonation interactions.

A very important observation in the presented CT data is that they are consistently larger in the low-spin C_2v structures than in the high-spin O_h ones (cf. Table 2 and Figure 5). Obviously, they are strongly related to the consistently shorter (both equatorial and axial) M-C bond distances in the former structures (cf. Figure 2).

The ground-state electron configurations of the studied metals are ns¹(n−1)d² and ns²(n−1)d¹ for the high- and low-spin states, respectively. In the case of U, it is extended with the (n−2)f³ subconfiguration. The metal valence orbital populations of the complexes in Table 2 are in agreement with extensive promotions of the valence s electrons to d orbitals as a prerequisite of complex formation. At the same time, the data confirm the dominant role of valence d orbitals, as is usual for d and f elements. The populations of valence f orbitals in the f elements are generally very small, indicating their small role in the bonding.

The excess of the 5f population with respect to the (n−2)f³ subconfiguration of U has a somewhat larger value for the C_2v isomer of U(CO)₆ (0.15 e), indicating enhanced contribution to bonding in the form of 6d/5f hybrid orbitals. An inspection of the molecular orbitals of U(CO)₆ also revealed a slight backdonation from the 1-electron 5f orbitals to the antibonding orbitals of the CO groups (Figure S4). The valence s populations are around 0.4 e in the complexes: they are manifested mainly in nonbonding lower-energy molecular orbitals, while a small bonding contribution was detected as d/s hybrid in M acceptor orbitals.

Looking back at Table 1, we can recognize slightly (but consistently) higher energies in the low-spin D_4h species with respect to the high-spin O_h ones. This seems to be in contradiction with the M-C bond distances being marginally smaller in the low-spin D_4h forms (cf. Figure 2). The smaller bond distance results in (marginally) larger CT data for the low-spin D_4h form with respect to those of the high-spin O_h one—as seen for the Sc(CO)₆ complex in Table 2. Altogether, the marginal differences between the CT properties of the D_4h and O_h species suggest that the change in spin state does not cause any significant difference in the electron transfer in these very similar structures. On the other hand, nonmarginal differences in the energies of the donor and acceptor orbitals in the two spin states cannot be excluded.

Visual inspection of the bonding molecular orbitals did not show any difference for the low-spin D_4h or high-spin O_h species (cf. Figure 4). The difference in the spin state, i.e., one of the 1-electron orbitals in the D_4h species has a spin opposite to the orthogonally oriented other two 1-electron orbitals, had no viewable effect on the shape of the molecular orbital. The very close atomic charges and visually identical molecular orbitals imply very similar charge distribution in the two complex forms. Accordingly, the change in spin state likely does not cause any significant difference in the electrostatic interactions.

Another significant contribution to the energetics of bonding is the Pauli repulsion, i.e., the repulsion of the electrons with the same spin. This can result in the lower stability of the high-spin O_h form, where there are three orthogonal 1-electron orbitals of the same spin (e.g., SOMO in Figure 4 upper row).

Finally, the promotion process should be mentioned, i.e., the energy needed to promote the M atoms from their ground states to the excited states with the right orbital populations for the donor–acceptor interactions. In the above arguments, we showed that most metal–ligand interactions seem to be more favorable for the low-spin C_2v structure than for the high-spin O_h one. Yet, among the studied complexes, Sc(CO)₆ prefers the high-spin O_h form in terms of electronic energy (cf. Table 1). In view of the above considerations, a lower promotion energy of the quartet (4s¹3d²) Sc atom with respect to the doublet (4s²3d¹) one may be the key factor for that.

3.4. Matrix Isolation IR

We analyzed earlier recorded unpublished matrix isolation IR spectra of Sc carbonyl complexes in order to find experimental evidence on the Sc(CO)₆ complex and its structure. The spectra revealed a mixture of various coordinations. Annealing and irradiation experiments clarified the relation of the bands, and these data are compiled in Table S5 of the Supplementary Materials. The assignments are based on the computed vibrational frequencies and IR intensities, as presented in Figure 6. In order to facilitate an easier visual overview, the overestimated B3LYP frequencies were corrected by the scale factor 0.96 from ref. [56].

The bands of Sc(CO)_x complexes at 1984, 1965, 1955, 1930, 1980 and 1866 cm⁻¹ observed in the CO/Ar matrix can be attributed to the complexes with coordination numbers of 8, 7, 6, 5, 4 and 3, respectively (cf. Figure 6 and Table S5). The observed bands of the octa- and heptacarbonyl species complement a previous report on the [Sc(CO)₈]⁻ [13] and [Sc(CO)₈]⁺ ions [19] observed in the gaseous phase by mass spectrometry and confirm the possibility of octa-coordination as the highest one for neutral scandium atoms too.

The main message from this section is the assignment of the strong 1955 cm⁻¹ absorption to Sc(CO)₆ on the basis of the present B3LYP vibrational data. In the annealing and irradiation experiments, its intensity changed independently (cf. Table S5), confirming the single-band character of this absorption. According to the B3LYP calculations, the less symmetric C_2v form can be expected to give four bands of comparable intensity within a range of ca. 30 cm⁻¹; thus, the single absorption band confirms the high-spin O_h structure of the Sc(CO)₆ complex.

The IR spectra of low-coordinated Sc(CO)_x complexes trapped in solid Ar and Ne have been reported by Zhou and Andrews [6]. From their crowded spectrum (due to the formation of numerous excited-state byproducts upon high-energy laser evaporation), the absorptions at 1865.4 and around 1890 cm⁻¹ are in good agreement with our weak bands at 1866 and 1890 cm⁻¹ (cf. Table S5). Here, we revised the literature assignments of the former bands based on unscaled BP86 frequencies with rather poor agreements [33].

4. Conclusions

The main question of this study was the preference of the (low-spin) low-symmetry C_2v structure vs. the (high-spin) high-symmetry O_h one. The computed electronic energies supported this stability for most M in the present study, the exception being the smallest Sc. The O_h structure of Sc(CO)₆ was confirmed by the here-reported matrix isolation IR results.

The computations clarified several advantages of the C_2v species vs. the O_h/D_4h ones:

(i)

Closer M-C distances, implying stronger bonding interactions;

(ii)

Weaker steric effects, particularly in the cases of larger M-s;

(iii)

Generally stronger CT interactions in terms of transferred electrons,

(iv)

Less Pauli repulsion because of the low-spin character.

On the other hand, orbital overlaps seem to be less advantageous in the C_2v structures of small M, where the equatorial {C₃,C₄,C₅,C₆,M} moieties are considerably distorted from planarity in contrast to the planar features in the O_h and D_4h structures.

An unknown but important factor is the promotion energy getting the electronic structure of M optimal for donor–acceptor interactions—this can be considerably different for the high- and low-spin states.