Complexes: Synthesis, Spectroscopy, Crystal Structure and Bonding Properties

: Complexes of trivalent lanthanides (Ln) with the hydridotris(1-pyrazolyl)borato (Tp) ligand Ln[ η 3 -HB(N 2 C 3 H 3 ) 3 ] 3 (LnTp 3 ) were subjected to a joint experimental–theoretical analysis. X-ray diffraction experiments have been performed on CeTp 3 , NdTp 3 , SmTp 3 , GdTp 3 , and TbTp 3 in the nine-fold coordination and on DyTp 3 , HoTp 3 , ErTp 3 , TmTp 3 , YbTp 3 , and LuTp 3 in the eight-fold coordination form. Density functional theory (DFT) calculations were carried out for all 15 LnTp 3 complexes. They extended the X-ray diffraction data available on the LnTp 3 compounds and facilitated a straightforward interpretation of trends in the structural parameters. As a result of the joint analysis, signiﬁcant steric strain in the equatorial coordination sites of the nine-coordinate structures was recognized. Trends in the bonding properties were elucidated by energy decomposition and quantum theory of atoms in molecules (QTAIM) analysis of the electron density distribution. These results revealed the major electrostatic character of the Ln . . . Tp bonding and ﬁne variation of charge transfer effects across the Ln row.


Introduction
The hydridotris(1-pyrazolyl)borato (Tp) molecule was first synthesized in 1966 [1]. Trofimenko named this ligand and its derivatives 'scorpionates' based on their characteristic shape: the pseudo-axial pyrazole rings resemble the stinger while the two equatorial pyrazole rings are like the claws of a scorpion [2]. Within the past two and a half decades, the Tp ligand and its derivatives have developed into popular ligands in the chemistry of transition metals [2][3][4][5]. They form a great variety of complexes in a tridentate fashion with most metals and metalloids.
The synthesis and structural data of Tp complexes of trivalent lanthanides (LnTp 3 ) have been previously reported by some of us. The complexes have been obtained by reaction of LnCl 3 with K[HB(N 2 C 3 H 3 ) 3 ] (KTp) [6]. Crystal structures have been reported for six complexes (Ln = La [7], Pr [6], Nd [6], Sm [8], Eu [7], and Yb [9]). In these studies, two structural isomers were identified: the light Ln (La, Pr, Nd, Sm, Eu) showed coordination numbers 9 in the complexes (in the following denoted by CN9), while in YbTp 3 , the Yb ion turned out to be eight-fold coordinated (denoted by CN8). In the CN9 isomers, the nine coordinating pyrazole rings form a tricapped prismatic coordination environment with high symmetry. In the CN8 isomers, the symmetry is reduced as one of the pyrazole rings is turned away from Ln, leaving only eight donor nitrogens for complex formation [9]. The two isomers also differ in morphology: CN9 crystallizes with high crystallographic symmetry in the hexagonal system while CN8 is orthorhombic. Additional structural information has been gained from IR spectra on the LnTp 3 complexes of the whole Ln row (except the radioactive Pm) [6]. Three spectral ranges have been identified (2440-2460, Inorganics 2021, 9,44 2 of 11 650-800, and 150-290 cm −1 ), where the two isomers show slight differences. On the basis of systematic IR spectral data, the CN9 isomers could unambiguously be assigned to light Ln (from La to Tb), while the CN8 isomers were assigned to the heavy Ln (Dy to Lu) complexes. DyTp 3 was found to be a borderline case: its dimorphic crystals contained both isomers.
Additional experimental studies included the measurement of absorption spectra and detailed analysis of the electronic transitions [7,8,[10][11][12]. The thermal behavior of some LnTp 3 compounds was also analyzed using TG/DTG and DSC methods [13]. Recently, we reported a joint experimental and theoretical study on the structural, bonding, and magnetic properties of AnTp 3 complexes, in which LaTp 3 and LuTp 3 were also included for comparison [14].

Crystal and Molecular Structures
The crystal and molecular structures of the nine-fold coordinated complexes CeTp 3 , NdTp 3 , SmTp 3 , and TbTp 3 were determined in the present study. Additional unpublished data from our archive on the nine-fold coordinated GdTp 3 plus the series of the eight-fold coordinated complexes DyTp 3 , HoTp 3 , ErTp 3 , TmTp 3 , YbTp 3 , and LuTp 3 are given in the Supplementary Materials (see Table S3). In the latter series, HoTp 3 is isostructural with its YbTp 3 analog reported in Ref. [9], whereas all the others are isostructural to each other. The single crystal structure determinations of NdTp 3 and SmTp 3 are re-investigations of older structures, as the present qualities are superior to the published ones from Refs. [6,8], respectively.
The high symmetry of the hexagonal space group is retained in the C 3h symmetry of the molecular complexes. In the crystal, only 1/6 of the molecule is found in the crystallographically independent unit of the elementary cell. The entire molecules are then generated by the crystallographic symmetry operations, leading to two entire molecules in the elementary cell separated by an inversion center ( Figure S2). The central Ln 3+ ion coordinates to the nine N atoms of the three Tp ligands in a tricapped trigonal prismatic geometry ( Figure 1). Each Tp ligand coordinates in a typical scorpionate-like way with two pyrazole rings forming the claws in the corners of the trigonal prism, whereas the third pyrazole ring takes over the role of the stinger capping the rectangular faces of the prism [2] ( Figure 1). The high symmetry is also reflected in the packing, where the views along the a-and b-axis are identical ( Figure S2) and always show the parallel orientation of one pyrazole ring to the axis. The view along the c-axis shows the perpendicular orientation of the third ring to this axis. All these together result in two distinct Ln-N bonds ( Table  2): the shorter one in the range from 2.659 Å (La) to 2.523 Å (Tb) covers the six N atoms forming the edges of the trigonal prism (apical positions) and nicely reflects the 'lanthanide contraction' with a shortening of ca 0.01 Å going from one element to the next. This effect is much less expressed in the longer Ln-N bonds to the capping (equatorial) N atoms in plane with the central metal ion (Figure 1) which cover a range from 2.80 Å to 2.75 Å (Gd, Tb, Table 2).       The theoretical data were obtained by ZORA-B3LYP-D3/TZP calculations. b From Ref. [7]. c From Ref. [6]. d From Ref. [8].
Our DFT calculations reproduced both the CN9 and CN8 structures of the LnTp 3 complexes as minima on the potential energy surfaces of the molecules. However, deviating somewhat from the crystal structure results, the calculations predicted the CN9 isomer as most stable for all the Ln in terms of electronic energies. Probing other DFT functionals did not change the trend in the relative stabilities of the two isomers. The effect of thermal corrections (in the Gibbs free energies) was a decrease in the relative energies by ca. 10 kJ/mol to the favor of CN8. It seems that theory is consistent for the energetic preference of the CN9 isomer even for the smallest LuTp 3 complex at the molecular level. These calculations, however, do not account for intermolecular steric forces from crystal packing, which may be a significant source for the deviation. Nevertheless, the gradually decreasing preference of the CN9 isomer over the CN8 one across the Ln row is predicted correctly by the calculations (see Figure S3 in the Supplementary Materials).
The computed apical and equatorial Ln-N distances of the two isomers are depicted together with available experimental crystal structure data in Figure 2. The computed geometrical parameters agree well with the literature [6,7,9] and new X-ray diffraction results. We note the considerable improvement in the NdTp 3 and SmTp 3 crystal structure data with respect to those in the literature [6,8].  Our DFT calculations reproduced both the CN9 and CN8 structures of the LnTp3 complexes as minima on the potential energy surfaces of the molecules. However, deviating somewhat from the crystal structure results, the calculations predicted the CN9 isomer as most stable for all the Ln in terms of electronic energies. Probing other DFT functionals did not change the trend in the relative stabilities of the two isomers. The effect of thermal corrections (in the Gibbs free energies) was a decrease in the relative energies by ca. 10 kJ/mol to the favor of CN8. It seems that theory is consistent for the energetic preference of the CN9 isomer even for the smallest LuTp3 complex at the molecular level. These calculations, however, do not account for intermolecular steric forces from crystal packing, which may be a significant source for the deviation. Nevertheless, the gradually decreasing preference of the CN9 isomer over the CN8 one across the Ln row is predicted correctly by the calculations (see Figure S3 in the Supplementary Materials).
The computed apical and equatorial Ln-N distances of the two isomers are depicted together with available experimental crystal structure data in Figure 2. The computed geometrical parameters agree well with the literature [6,7,9] and new X-ray diffraction results. We note the considerable improvement in the NdTp3 and SmTp3 crystal structure data with respect to those in the literature [6,8].  In Figure 2, the following main features can be recognized: (i) The Ln-N bond distances in the CN8 structures are shorter than their analogs in the CN9 isomers. This is the result of the steric release upon turning one equatorial pyrazole ring away from Ln in the former isomers, facilitating more relaxed interaction for the remaining eight N donors. While the stronger (shorter) Ln-N ap bonds gain only slightly from the steric release, the weaker (longer) Ln-N eq bonds decrease by 0.1-0.2 Å.
(ii) In the CN9 structures, the Ln-N eq bond distances scatter around 2.78 Å without any definite trend. In contrast, in the CN8 isomers, a decreasing trend (obeying more-orless the contracting Ln 3+ radii) can be recognized in the Ln-N eq bonds. This significant change of character is the results of the reduced steric strain. Apparently, in the CN9 isomers the crowded surroundings of Ln do not allow for the weaker equatorial Ln-N bonds a relaxation with decreasing Ln 3+ radii.
(iii) The 'lanthanide contraction' is well reproduced in the Ln-N ap distances of both isomers. In fact, the decreasing trend is more pronounced in the Ln-N ap distances than in the above discussed Ln-N eq ones of the CN8 isomers. This suggests that the Ln-N eq interactions still suffer slightly from steric disadvantages in the latter structures as well.
In the ETS approach [15,18], the interaction energy between the selected fragments, ∆E int , is defined as where ∆V elst corresponds to the classical electrostatic interaction between the charge distributions of the isolated fragments upon complex formation, ∆E Pauli is the repulsion between occupied orbitals (practically the steric repulsion), and ∆E oi is the orbital interaction energy between the fragments in the complex, including electron pair bonding, charge transfer, and polarization [18]. We focus here on the total interaction energy as well as on the ratio of the ∆V elst and ∆E oi components. The ETS analysis could be performed in a straightforward manner for the La, Gd, and Lu complexes based on the distinguished ground electronic states of these three lanthanides (4f 0 , 4f 7 , and 4f 14 configurations, respectively). Their energy decomposition data are shown in Table 3. The main interaction in the title complexes is the electrostatic attraction between the charged Ln and Tp moieties. This amounts to ca. 70% of the total attraction (∆V elst + ∆E oi ) interactions. The trend in the attractive bonding interactions is a gradual increase from La to Lu as the contracting Ln radii strengthen both the electrostatic attraction and electron-sharing interactions. The repulsive Pauli interaction shows an opposite trend, but its magnitude is considerably smaller. Hence, the overall trend appearing in the total interaction energy is the increase from LaTp 3 to LuTp 3 as observed also in the computed dissociation energies of other Ln compounds [35][36][37][38]. The main metal-ligand bonding differences between the CN9 and CN8 isomers of LuTp 3 appear in the somewhat stronger orbital and Pauli interactions in the CN8 form as a result of the shortened Lu-ligand distances (vide supra). The marginal effect of the change from CN9 to CN8 on the global character of bonding can be seen in the marginal decrease of % ∆V elst /(∆V elst + ∆E oi ) in Table 3.
The covalent part of bonding corresponds to the Tp → Ln charge transfer, in which the N lone pairs donate electrons to the empty valence orbitals of the Ln 3+ ions. The charge transfer interactions in the CN9 structures of LaTp 3 and LuTp 3 complexes have recently been studied [14] by means of the natural bond orbital (NBO) model [39]. This analysis predicted an energetically somewhat stronger Tp → Ln charge transfer in the LuTp 3 complex, in agreement with the present ETS results. No Ln → Tp back-donation was found in the NBO analysis.
The QTAIM analysis provided descriptive integrated properties of the electron density distribution. The Ln atomic charges and non-localized electron densities around Ln are given in Figure 3. The latter quantity was obtained by subtracting the localized electron density (non-bonding electron density) from the total electron population assigned to Ln. Extended with the electron densities from the N bonding partners, it forms the Ln-N bonding densities. They, in terms of the number of electrons localized in the space between two interacting atoms, are manifested in the delocalization indices (DI). energy is the increase from LaTp3 to LuTp3 as observed also in the computed dissociation energies of other Ln compounds [35][36][37][38]. The main metal-ligand bonding differences between the CN9 and CN8 isomers of LuTp3 appear in the somewhat stronger orbital and Pauli interactions in the CN8 form as a result of the shortened Lu-ligand distances (vide supra). The marginal effect of the change from CN9 to CN8 on the global character of bonding can be seen in the marginal decrease of % ΔVelst/(ΔVelst + ΔEoi) in Table 3.
The covalent part of bonding corresponds to the Tp → Ln charge transfer, in which the N lone pairs donate electrons to the empty valence orbitals of the Ln 3+ ions. The charge transfer interactions in the CN9 structures of LaTp3 and LuTp3 complexes have recently been studied [14] by means of the natural bond orbital (NBO) model [39]. This analysis predicted an energetically somewhat stronger Tp → Ln charge transfer in the LuTp3 complex, in agreement with the present ETS results. No Ln → Tp back-donation was found in the NBO analysis.
The QTAIM analysis provided descriptive integrated properties of the electron density distribution. The Ln atomic charges and non-localized electron densities around Ln are given in Figure 3. The latter quantity was obtained by subtracting the localized electron density (non-bonding electron density) from the total electron population assigned to Ln. Extended with the electron densities from the N bonding partners, it forms the Ln-N bonding densities. They, in terms of the number of electrons localized in the space between two interacting atoms, are manifested in the delocalization indices (DI).
The presented QTAIM results provide insight into the charge transfer interactions (CT) in the complexes. They do not show a consistent gradual trend like the Ln 3+ ionic radii ('lanthanide contraction') and the Ln-N bond distances (vide supra) or the electron densities at the Ln-N bond critical points ( Figure S4 in the Supplementary Materials, cf. also Ref. [40] for other Ln complexes). In fact, such a trend is often absent in the physicochemical properties not strongly related to the structure of lanthanide compounds [41]. The Ln atomic charges in Figure 3 are between +2.1 and +2.3 due to the CT from Tp to Ln 3+ . The behavior of the Ln charge curve is different at the light and heavy lanthanides, the breaking point being Gd (with 4f 7 configuration). In the region of the light lanthanides a small minimum is formed, while for the heavy lanthanides the Ln charge slightly decreases. The minimum curve in the first half of the Ln row is associated with the maximum The presented QTAIM results provide insight into the charge transfer interactions (CT) in the complexes. They do not show a consistent gradual trend like the Ln 3+ ionic radii ('lanthanide contraction') and the Ln-N bond distances (vide supra) or the electron densities at the Ln-N bond critical points ( Figure S4 in the Supplementary Materials, cf. also Ref. [40] for other Ln complexes). In fact, such a trend is often absent in the physicochemical properties not strongly related to the structure of lanthanide compounds [41].
The Ln atomic charges in Figure 3 are between +2.1 and +2.3 due to the CT from Tp to Ln 3+ . The behavior of the Ln charge curve is different at the light and heavy lanthanides, the breaking point being Gd (with 4f 7 configuration). In the region of the light lanthanides a small minimum is formed, while for the heavy lanthanides the Ln charge slightly decreases. The minimum curve in the first half of the Ln row is associated with the maximum of the non-localized electron density, gained from the larger CT (cf. Figure 3). The decrease from Tb to Yb implies a slightly increasing CT from Tp. This slight increase, however, is accumulated in the non-bonding localized density around Ln as both the non-localized electron density ( Figure 3) and DI (Figure 4) are marginally decreasing in this region. The exceptional behavior of Lu may be attributed to its compact 4f 14 configuration.
tions, can be more clearly recognized in the Ln-Neq data. The Ln-Nap data are nearly constant with a weak maximum between La and Gd.
The Tp → Ln CT is mainly governed by a balance of Ln-N distances, donor and acceptor orbital energies, and repulsion from the electron density distribution around Ln 3+ . The Ln-N distances cover the steric factor due to the 'lanthanide contraction'. The decreasing Ln-N distances (forced by the decreasing Ln 3+ ionic radii) generate increasing steric interactions between the Tp ligands. This effect was shown above for the Ln-Neq bond distances (cf. Figure 2) and is also reflected in the DI values of these bonds in Figure  4. In the LnTp3 complexes, the above conditions for CT in terms of transferred electrons appear to be most favorable in the Ce 3+ -Sm 3+ region. Less favorable is the CT to Ln 3+ ions with 4f 0 , 4f 7 , 4f 14 configurations as well as in the second half of the Ln row.

Materials
The complexes LnTp3 were prepared by various routes following published procedures [6][7][8]. The lanthanide salts were dissolved in water and added to a solution of KTp in water under formation of the LnTp3 precipitates. These were washed with water, EtOH, The single-bond DI data demonstrate the expected stronger character of the Ln-N ap bonds in agreement with their shorter bond distances. On the other hand, the character of the Σ(Ln-N) curve, i.e., the maximum in the early Ln and the decrease in the late Ln sections, can be more clearly recognized in the Ln-N eq data. The Ln-N ap data are nearly constant with a weak maximum between La and Gd.
The Tp → Ln CT is mainly governed by a balance of Ln-N distances, donor and acceptor orbital energies, and repulsion from the electron density distribution around Ln 3+ . The Ln-N distances cover the steric factor due to the 'lanthanide contraction'. The decreasing Ln-N distances (forced by the decreasing Ln 3+ ionic radii) generate increasing steric interactions between the Tp ligands. This effect was shown above for the Ln-N eq bond distances (cf. Figure 2) and is also reflected in the DI values of these bonds in Figure  4. In the LnTp 3 complexes, the above conditions for CT in terms of transferred electrons appear to be most favorable in the Ce 3+ -Sm 3+ region. Less favorable is the CT to Ln 3+ ions with 4f 0 , 4f 7 , 4f 14 configurations as well as in the second half of the Ln row.

Materials
The complexes LnTp 3 were prepared by various routes following published procedures [6][7][8]. The lanthanide salts were dissolved in water and added to a solution of KTp in water under formation of the LnTp 3 precipitates. These were washed with water, EtOH, Et 2 O, and dried in vacuum. Single crystals of the CN9 isomers of LnTp 3 were obtained by extraction with benzene, whereas single crystals of the CN8 isomers were the product of vacuum sublimation at 200 • C and 0.014 mbar. Potassium tri(1-pyrazolyl)borohydride was purchased from Sigma-Aldrich (St. Louis, MO, USA) and used directly. The salts of the lanthanides, chlorides, or nitrates contain water and were used without further purification.

X-Ray Diffraction
Single crystal XRD measurements were performed at 100 K on a Bruker APEX II Quazar (Ce, Nd, Sm) or at 200 K on a Bruker SMART CCD 1K (Tb) diffractometer with monochromated Mo Kα irradiation collecting at least one sphere of data in the range θ ≤ 28.5 • [42,43]. Frames were collected with an appropriate irradiation time between 1 and 10 s per frame using ωscan technique (SMART CCD 1K, ∆ω = 0.45 • ) or combined ωand ϕscan technique (Bruker APEX II Quazar, ∆ω = ∆ϕ = 0.5 • ). Data were integrated with SAINT and corrected to Lorentz and polarization effects, and an experimental adsorption correction with SADABS was applied [42,43]. The structures were solved by direct methods and refined to an optimum R 1 value with SHELX-2013 [44]. Visualization for evaluation was performed with winray-32 [45]. For more details see Table 1.
The structures have been deposited at The Cambridge Crystallographic Data Centre with the reference CCDC numbers 2,074,868 (Ce), 2,074,869 (Nd), 2,074,870 (Sm), 2,074,871 (Tb), they contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from the CCDC via www.ccdc.cam.ac.uk/data_request/cif (accessed on 19 March 2021).
In addition, we report here unpublished X-ray diffraction data from our archive on all the eight-fold coordinated LnTp 3 complexes plus the nine-fold coordinated GdTp 3 . These measurements were performed in the late 1980s and early 1990s on an ENRAF-NONIUS CAD4 diffractometer at room temperature. Structure determination and refinement was carried out with the Enraf-Nonius SDP-Plus software [46]. The intensity data do not exist anymore, but for completeness we deposited the coordinates at The Cambridge Crystallographic Data Centre with the reference CCDC numbers 2078671-2078677; the crystallographic details of these complexes are presented in Table S3 of the Supplementary Materials.

Computational Details
Our previous DFT calculations on AnTp 3 , LaTp 3 , and LuTp 3 were performed with the Gaussian09 code utilizing small-core relativistic pseudopotentials [14]. Unfortunately, this 4f-in-valence approach failed for most LnTp 3 complexes because of severe self-consistent field (SCF) convergence problems. Therefore, in the present study, we chose another code and theoretical level. The geometry optimizations and bonding analyses were performed with the Amsterdam Density Functional (ADF2017) software [47,48]. Scalar (SF) relativistic effects were accounted for by utilizing the zeroth-order regular approximation (ZORA) [49]. The theoretical level of the calculations consisted of the B3LYP exchange-correlation functional [50,51] in conjunction with an uncontracted set of Slater-type orbitals (STOs) of triple-zeta-plus-polarization quality optimized for use with ZORA [52]. The small-core frozen-core option and an auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately in each SCF cycle. For the sake of consistency, both the closed-(La, Lu) and open-shell systems were treated using the spin-unrestricted formalism. Only the high-spin electron configurations of the Ln 3+ ions were considered. The minimum characters of the obtained structures were confirmed by frequency analyses. The dispersion effects were taken into account using the empirical D3 parameters of Grimme et al. [53].

Conclusions
We reported a joint experimental-theoretical analysis of the complexes of trivalent lanthanides with the hydridotris(1-pyrazolyl)borato (scorpionate) ligand focusing on the structural and bonding properties. The experimental part included advanced X-ray diffraction experiments on CeTp 3 , NdTp 3 , SmTp 3 , TbTp 3 while the theoretical analysis covered the whole lanthanide row. The structural studies confirmed the CN = 9 character of the complexes in the first two-third section of the Ln row. The DFT computations predicted that there is an increasing steric strain in the equatorial coordination sites of the CN9 structures upon decreasing Ln 3+ radii, which leads to a destabilization of these structures towards a CN = 8 coordination. The above steric strain is well manifested in the nearly constant Ln-N eq distances in the CN9 structures in contrast to the Ln-N ap ones which follow consistently the decreasing trend in the Ln 3+ radii.
Energy decomposition analysis of the electron density distribution revealed the major electrostatic character of the Ln . . . Tp bonding. Together with the steric effects it determines the metric parameters of the complexes at the first place. The minor contributor CT obeys to the metric conditions but can also influence them in some extent through back-coupling. The QTAIM data indicate characteristic differences in the CT in the first and second half of the Ln row. The largest CT (in terms of transferred electrons) occurs to the lanthanides from Ce 3+ to Sm 3+ , facilitated by an optimal balance of the orbital energies, Ln-N distances and repulsion from filled 4f orbitals. Less favorable is the CT to the Ln 3+ ions with 4f 0 , 4f 7 , 4f 14 configurations as well as in the second half of the Ln row.