Two octahedral σ-borane metal (MnI and RuII) complexes containing a tripod κ3N,H,H-ligand: Synthesis, structural characterization, and theoretical topological study of the charge density

Article abstract of DOI:10.1016/j.molstruc.2019.127217

Theoretical electron density (QTAIM) studies in the gas-phase have shown that the attachment of the BH₃ group to the metal atom in complexes [Mn(κ³N,H,H-ⁱPr₂bzamBH₃)(CO)₃] (1) and [Ru(η⁵-C₅Me₅)(κ³N,H,H-ⁱPr₂bzamBH₃)] (2) (HⁱPr₂bzamBH₃ = N-trihydridoborane-N,N′-bis(isopropyl) benzamidine) is symmetric in the latter but asymmetric in the former, and involves two B–H–metal interactions that are intermediate between κ¹H (Shimoi type) and κ²H,B (agostic type). The herein reported results, coupled to previous ones on related complexes having a similar tripod κ³N,H,H-borane ligand, show that the bonding similarities and differences within each particular M(μ-H)₂B moiety are not related to the type of metal atom, nor even to its coordination geometry, but mainly to the molecular symmetry.

Full text of DOI:10.1016/j.molstruc.2019.127217

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II
Two octahedral σ-borane metal (Mn and Ru ) complexes containing a tripod
3
κ N,H,H-ligand: Synthesis, structural characterization, and theoretical topological
study of the charge density
Juan F. Van der Maelen, Javier Brugos, Pablo García-Álvarez, Javier A. Cabeza
PII:
S0022-2860(19)31326-2
DOI:
https://doi.org/10.1016/j.molstruc.2019.127217
MOLSTR 127217
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To appear in: Journal of Molecular Structure
Received Date: 10 June 2019
Revised Date: 9 October 2019
Accepted Date: 10 October 2019
Please cite this article as: J.F. Van der Maelen, J. Brugos, P. García-Álvarez, J.A. Cabeza, Two
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octahedral σ-borane metal (Mn and Ru ) complexes containing a tripod κ N,H,H-ligand: Synthesis,
structural characterization, and theoretical topological study of the charge density, Journal of Molecular
Structure (2019), doi: https://doi.org/10.1016/j.molstruc.2019.127217.
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Ms. for Journal of Molecular Structure (INVITED ARTICLE FOR THE SPECIAL ISSUE
ENTITLED “CHARGE-DENSITY STUDIES TOWARDS STRUCTURE-PROPERTY
CORRELATION”)
Two octahedral σ-borane metal (MnI and RuII) complexes containing a tripod
κ3N,H,H-ligand: Synthesis, structural characterization, and theoretical
topological study of the charge density
Juan F. Van der Maelena,b,*, Javier Brugosc, Pablo García-Álvarezc, Javier A. Cabezac
aDepartamento de Química Física y Analítica, Universidad de Oviedo, E-33006 Oviedo, Spain
bCentro de Investigación en Nanomateriales y Nanotecnología (CINN-CSIC), E-33940 El Entrego,
Spain
cDepartamento de Química Orgánica e Inorgánica and Centro de Innovación en Química Avanzada
(ORFEO-CINQA), Universidad de Oviedo, E-33006 Oviedo, Spain
*Corresponding author.
E-mail address: fvu@uniovi.es (J. F. Van der Maelen)
1

Abstract
Theoretical electron density (QTAIM) studies in the gas-phase have shown that the attachment of the
BH3 group to the metal atom in complexes [Mn(κ3N,H,H-iPr2bzamBH3)(CO)3] (1) and [Ru(η5-
C5Me5)(κ3N,H,H-iPr2bzamBH3)] (2) (HiPr2bzamBH3 = N-trihydridoborane-N,N’-bis(isopropyl)
benzamidine) is symmetric in the latter but asymmetric in the former, and involves two B–H–metal
interactions that are intermediate between κ1H (Shimoi type) and κ2H,B (agostic type). The herein
reported results, coupled to previous ones on related complexes having a similar tripod κ3N,H,H-borane
ligand, show that the bonding similarities and differences within each particular M(µ-H)2B moiety are
not related to the type of metal atom, nor even to its coordination geometry, but mainly to the
molecular symmetry.
Keywords: Quantum Theory of Atoms in Molecules (QTAIM), Electron Localization Function (ELF),
σ-Borane Complexes, Transition-Metal Carbonyl Complexes, Multicenter Bonding, Chemical
Bonding.
2

1. Introduction
In the last two decades, the analysis of the electron density’s topology under the perspective of the
Quantum Theory of Atoms in Molecules (QTAIM) [1] has been established as a powerful tool,
complementary to the Molecular Orbital (MO) theory, to analyze chemical bonds. QTAIM studies on
systems containing light atoms (periods 1–3 of the periodic table) have allowed the establishment of
useful links between bonding modes and topological properties of the electron density (both local and
integral) and its Laplacian, from both theoretically- and experimentally-determined electron densities
[2]. However, such links cannot be straightforwardly extended to compounds with transition-metal
atoms since the latter display a different and much narrower spectrum of topological indexes [3]. For
this reason, there is a general consensus among experts in the field about the urgent need for more work
in this area, in order to derive accurate correspondence rules that could unambiguously be applicable to
any kind of bonding interactions involving one or more transition-metal atoms, particularly when
regarding multiple bond orders and/or multicenter bonding [4].
The increasing interest in the use of amine−boranes (H2RNBH2R′; R, R′ = H, alkyl, aryl) as
molecular systems for hydrogen storage and transportation [5] and the discovery that transition-metal
complexes can promote their dehydrogenation to give H2 (or the transfer of H2 to other molecules)
[6,7] have recently boosted the study of their coordination chemistry [8,9], as well as that of
aminoboranes (HRNBHR′; R, R′ = H, alkyl, aryl) [10], which are intermediates in the dehydrogenation
of amine−boranes. In all these complexes, the ligand is attached to the metal atom almost exclusively
through one or two of the BH groups (σ-complexes) [11], involving either κ2H,B (agostic interaction:
both atoms of the BH group interact with the metal) or κ1H (Shimoi interaction: only the H atom of the
BH group is attached to the metal) interactions. In any of the two cases, borane−metal interactions are
usually weak [12].
In this context, we have recently described [13] the synthesis, experimental structural
characterization and QTAIM studies of the octahedral complexes [Mn(κ3N,H,H-mapyBH3)(CO)3] (3)
and [RuH(κ3N,H,H-mapyBH3)(CO)(PiPr3)] (4), and the pentacoordinated complexes [M(κ3N,H,H-
mapyBH3)(η4-cod)] (M = Rh (5), Ir (6); HmapyBH3 = N-trihydridoborane-2-(methylamino)pyridine;
cod = cycloocta-1,5-diene). In the four cases we found that: (a) all M–H interactions with the BH2
group show bond paths that are strongly inwardly curved, with greater deviations from a straight line
near the hydrogen atoms than near the metal centers; (b) no M–B bond paths were obtained, although
3

non-negligible values were always calculated for the delocalization indexes of these interactions; (c) all
M–HB bonds are intermediate between those of the Shimoi type (κ1H coordination) and those of the
agostic type (κ2H,B coordination). On the other hand, while both M–HB bonds were found to be
equivalent for the Mn compound, they are not equivalent for the Ru, Rh, and Ir complexes, with one
bond more agostic (more curved, higher ellipticity) than the other (less curved, lower ellipticity).
In order to further explore the influence of the metal complex symmetry and that of the ligands
themselves in the bonding of this important class of borane derivatives, we decided to study two
additional complexes, that is, [Mn(κ3N,H,H-iPr2bzamBH3)(CO)3] (1) and [Ru(η5-C5Me5)(κ3N,H,H-
iPr2bzamBH3)] (2) (HiPr2bzamBH3 = N-trihydridoborane-N,N’-bis(isopropyl)benzamidine) (Scheme
1), which were selected not only because their ligands differ from those of the four complexes
previously reported (3-6) but also because they include the same metal atoms as two of them (Mn, Ru)
and have an a priori identical coordination geometry (octahedral). As a consequence, bonding
comparisons between 1 and 2 with the previously studied complexes could be made more
straightforwardly and mostly centered on the nature of the ligands. We report here the synthesis and
structural characterization of the borane adduct HiPr2bzamBH3 and its metal derivatives 1 and 2, as well
as a theoretical topological analysis of the bonding in the three compounds.
Scheme 1. Molecular diagrams of HiPr2bzamBH3, 1 and 2
4

2. Experimental and computational details
2.1. Synthetic procedures and spectroscopic data
General experimental data: Solvents were dried over appropriate desiccating reagents and were
distilled under argon before use. All reactions and manipulations were carried out under argon, using
dry box and/or Schlenk-vacuum line techniques. All reaction products were vacuum-dried for several
hours prior to being weighed and analysed. The metal complex [Ru2(η5-C5Me5)2Cl4] was prepared
following a published procedure [14]. All remaining reagents were purchased from commercial
suppliers. NMR spectra were obtained on Bruker DPX-300, NAV-400 and AV400 instruments and
1
were referenced using the residual protic solvent signal for H (7.16 ppm for d6-benzene), the solvent
signal for 13C (128.1 ppm for d6-benzene) and external F3B·OEt2 for 11B [δ = 0.00 ppm].
HiPr2bzamBH3: PhLi (1.1 mL, 2.0 mmol, 1.8 M in dibutyl ether) was added dropwise to a solution of
N,N'-bis(isopropyl)carbodiimide (0.3 mL, 2.0 mmol) in diethyl ether (3 mL) at 78º C. The resulting
white suspension was allowed to warm up to room temperature and then stirred for 3 h. Deoxygenated
water (0.08 mL, 4.4 mmol) was added to the previous suspension, which was then stirred for 30 min.
The solvent was removed under reduced pressure and the resulting whitish oily residue was extracted
into dichloromethane (2 x 5 mL), drying the resulting solution with Na2SO4, which was then filtered
with a cannula fitted with a small piece of filter paper wrapped around one of its ends. Solvent removal
under reduced pressure of the filtrate led to a yellowish oil, which was identified as N,N'-
bis(isopropyl)benzamidine (HiPr2bzam) by 1H-NMR analysis. The previous oil was dissolved in 2 mL
of toluene and subsequently was added dropwise to a solution of BH3·THF (2.4 mL, 2.4 mmol, 1.0 M
in THF) at 78º C. The resulting colourless solution was stirred at 78º C for 1h. Solvent removal allowed
the isolation of HiPr2bzamBH3 as a white solid that was washed with hexane (2 x 3 mL) and dried in
1
vacuo (314 mg, 72%). H NMR (C6D6, 400.54 MHz, 298 K): δ 7.10-6.90 (m, 3 H, 3 CH of Ph), 6.90-
6.80 (m, 2 H, 2 CH of Ph), 3.42 (sept, JH−H = 6.0 Hz, 1 H, 1 CH of iPr), 2.76 (m, 1 H, 1 CH of iPr), 2.64
(br q, JH−11B = 85.9 Hz, 3 H, BH3), 1.31 (d, JH−H = 6.0 Hz, 6 H, 2 CH3 of iPr), 0.70 (d, JH−H = 6.0 Hz, 6
i
11
H, 2 CH3 of Pr). B NMR (C6D6, 128.51 MHz, 298 K): δ −23.6 (br q, JH−11B = 85.9 Hz, BH3), this
signal collapses to a singlet in a 11B{1H} NMR spectrum. 13C{1H} NMR (C6D6, 75.5 MHz, 293 K): δ =
160.9 (NCN), 131.8 (Cipso of Ph), 130.0 (CH of Ph), 129.3 (2 CH of Ph), 127.1 (2 CH of Ph), 52.6 (1
CH of iPr), 46.1 (1 CH of iPr), 24.0 (2 CH3 of iPr), 21.8 (2 CH3 of iPr).
5

[Mn(κ3N,H,H-iPr2bzamBH3)(CO)3] (1): LiN(SiMe3)2 (0.1 mL, 0.1 mmol, 1 M in hexane) was added
dropwise to a solution of HiPr2bzamBH3 (22 mg, 0.1 mmol) in toluene (3 mL) at room temperature.
The resulting yellowish solution was then stirred for 1 h, which allowed the formation of the lithiated
salt LiiPr2bzamBH3. Then, this solution was added dropwise at room temperature to a yellow solution
of [MnBr(CO)3(NCMe)2] (0.1 mmol) in CH3CN (8 mL), which was previously prepared by refluxing
[MnBr(CO)5] (28 mg, 0.1 mmol) in CH3CN (8 mL) for 15 min. The resulting yellowish solution was
then stirred for 30 min. IR (ν(CO) analysis indicated no reaction completion. The solvents were
removed under reduced pressure and the resulting yellowish residue was dissolved in toluene (5 mL)
and the resulting solution was stirred at 50 ºC for 1 h. The colour changed from yellow to orange. An
IR analysis (ν(CO) region) indicated the consumption of all the starting materials. Complex 1, isolated
as an orange solid (14 mg, 40%), was purified by column chromatography in silica gel, using hexane as
1
eluant. IR (toluene): νCO 2031 (s), 1937 (vs, br) cm−1. H{11B} NMR (C6D6, 400.54 MHz, 298 K): δ
6.97 (br, 3 H, 3 CH of Ph), 6.62 (br, 2 H, 2 CH of Ph), 4.83 (s, br, 1 H, HBH2), 386 (s, br, 1 H, 1 CH of
iPr), 3.23 (s, br, 1 H, 1 CH of iPr), 1.23 (s, 6 H, 2 CH3 of iPr), 0.94 (s, 6 H, 2 CH3 of iPr), −9.88 (s, br, 2
H, MnH2B); the broad singlets at 4.83 and −9.88 ppm are transformed into two broad multiplets in a 1H
NMR spectrum. 11B{1H} NMR (C6D6, 128.51 MHz, 298 K): δ −19.6 (s, br, BH3), this signal becomes
11
13
broader in a B NMR spectrum. C{1H} NMR (C6D6, 100.6 MHz, 293 K): δ = 171.4 (NCN), 136.1
i
i
i
(Cipso of Ph), 129.1−127.0 (5 CHs of Ph), 56.4 (1 CH of Pr), 50.7 (1 CH of Pr), 26.3 (2 CH3 of Pr),
23.6 (2 CH3 of iPr). The resonances corresponding to the carbonyl ligands were not observed.
[Ru(η5-C5Me5)(κ3N,H,H-iPr2bzamBH3)] (2): LiN(SiMe3)2 (0.1 mL, 0.1 mmol, 1 M in hexane) was
added dropwise to a solution of HiPr2bzamBH3 (18 mg, 0.08 mmol) in toluene (5 mL) at room
temperature. The resulting yellowish solution was then stirred for 1 h, which allowed the formation of
LiiPr2bzamBH3. Then, this solution was added dropwise at room temperature to [Ru2(η5-C5Me5)2Cl4]
(25 mg, 0.04 mmol). The resulting brownish orange suspension was then stirred overnight and was then
filtered with a cannula fitted with a small piece of filter paper wrapped around one of its ends. The
solvents of the filtrate (red solution) were removed under reduced pressure and the resulting dark
brown residue was extracted into hexane (3 mL). Solvent removal allowed the isolation of 3 as a dark
orange solid that was dried in vacuo (18 mg, 41%). 1H NMR (C6D6, 400.54 MHz, 298 K): δ 7.05-6.90
(m, 3 H, 3 CH of Ph), 6.90-6.85 (m, 2 H, 2 CH of Ph), 4.81 (br q, JH−11B = 113.3 Hz, 2 H, HBH2), 3.81
(s, br, 1 H, 1 CH of iPr), 3.40 (m, 1 H, 1 CH of iPr), 1.95 (s, 15 H, 5 CH3 of C5Me5), 1.45 (s, br, 6 H, 2
6

CH3 of iPr), 1.20 (d, JH−H = 8.0 Hz, 6 H, 2 CH3 of iPr), −9.11 (m, br, 2 H, RuH2B); the broad signals at
1
11
4.81 and −9.11 ppm collapse to singlets in a H{11B} NMR spectrum. B NMR (C6D6, 128.51 MHz,
298 K): δ −16.4 (s, br, BH3), this signal does not change in a 11B{1H} NMR spectrum.
2.2. X-Ray diffraction analyses
Crystals of HiPr2bzamBH3·0.5(C7H8) (obtained by slow evaporation of a solution of the borane adduct
in toluene), 1 (obtained by slow evaporation of a solution of the complex in toluene) and 2 (obtained by
o
keeping at –20 C for 12 h a concentrated solution of the complex in toluene) were analysed by X-ray
diffraction. A selection of crystal, measurement and refinement data is given in Table S1 of the
Supplementary Material. Diffraction data were collected at 150(2) K on an Oxford Diffraction Xcalibur
Onyx Nova single crystal diffractometer. Empirical absorption corrections were applied using the
SCALE3 ABSPACK algorithm as implemented in CrysAlisPro RED [15]. The structures were solved
using SIR-97 [16]. Isotropic and full matrix anisotropic least square refinements were carried out using
SHELXL-2014 [17]. All non-H atoms were refined anisotropically. Hydrogen atoms of the BH3
moieties were located in their corresponding Fourier maps. The remaining hydrogen atoms were set in
calculated positions and refined riding on their parent atoms. The toluene molecules found in the
crystal of HiPr2bzamBH3·0.5(C7H8) were disordered about centres of symmetry and required restraints
on their geometrical and thermal parameters. The WINGX-2013 program system [18] was used
throughout structure determinations. Molecular plots were made with MERCURY [19]. CCDC
deposition numbers: 1921463 (HiPr2bzamBH3·0.5(C7H8)), 1921464 (1), and 1921465 (2).
2.3. DFT calculations and theoretical charge density studies
It has been previously shown that the use of relativistic hamiltonians is essential in order to obtain
accurate quantitative results from calculations on compounds containing third-row transition-metal
atoms [20], but the effect of using such hamiltonians on calculations involving second-row transition
metals is not yet clear. In order to compare our new results with the previously published ones [13], we
have used here exactly the same model chemistries (Hamiltonians, funcionals, and basis sets) than
before.
The X-ray diffraction (XRD) molecular structures of complexes 1 and 2 were used as starting points
to calculate the theoretically optimized geometries in gas phase. Density Functional Theory (DFT)
computations with non-relativistic wavefunctions were performed with the GAUSSIAN09 program
7

package [21], using the B3P86 hybrid functional, which is known to give accurate results in medium-
sized transition-metal organometallic compounds [22]. All-electron 6-31G(d,p) and 6-
311++G(2df,2pd) standard basis sets were employed for Mn, C, H, N, and O atoms at different steps of
the procedure (the former basis set for the geometry optimizations and the latter for the single-point
electronic structure calculations at the optimized geometries), while the LanL2DZ effective core
potential and the large all-electron WTBS basis set (“Well-Tempered Basis Set” of Huzinaga and co-
workers [23]) were used for Ru atoms (again, the former for the geometry optimizations and the latter
for the electronic structure calculations).
Computations with relativistic wavefunctions were performed using the scalar ZORA hamiltonian,
the PW91 density functional, and the all-electron relativistic QZ4P basis set for all atoms [24], as
implemented in the ADF2012 program package [25], in order to obtain relativistically optimized
geometries, while the hybrid ZORA-B1PW91 model with relativistic QZ4P basis sets were then used
for single-point electronic structure calculations at the optimized geometries.
The obtained non-relativistic and relativistic ground-state electronic wavefunctions, which were
found to be stable, were then utilized for calculations on the topology of the electron density within the
framework of the QTAIM approach. These calculations included both local and integral properties and
were carried out with AIMAll [26], AIM2000 [27], and DGrid [28] programs from GTO- and STO-
based wavefunctions. The accuracy of local properties was 1.0×10–10 (from the gradient of the electron
density at the bond critical points), whereas that of integral properties was finally set at least at 1.0×10–
4
(from the Laplacian of the integrated electron density). Both all-electron non-relativistic B3P86/6-
311++G(2df,2pd)/WTBS(Ru) and relativistic ZORA-B1PW91/QZ4P models, applied to the
theoretically optimized geometries, were used in all cases to find critical points and calculate
topological parameters.
3. Results and discussion
The previously unknown borane adduct HiPr2bzamBH3 was straightforwardly prepared by treating
N,N'-bis(isopropyl)benzamidine (HiPr2bzam) with BH3·THF. Complexes 1 and 2 were synthesized by
reacting [MnBr(CO)3(NCMe)2] and [Ru2(η5-C5Me5)2Cl4] with LiiPr2bzamBH3. The latter was formed
in situ by treating HiPr2bzamBH3 with LiN(SiMe3)2 prior to its reaction with the corresponding metal
complex (see the previous “Experimental and computational details” section for synthetic details and
spectroscopic data). As may be seen in Figure 1, XRD analyses performed at 150(2) K confirm the
8

i
tripod κ3N,H,H coordination of the Pr2bzamBH3 ligand in 1 and 2, as well as the octahedral
environment of both Mn and Ru atoms (in 2, the C5Me5 ligand occupies three coordination sites).
Fig. 1 XRD molecular structures of HiPr2bzamBH3, 1 and 2 (ellipsoids drawn at 30% probability). Hydrogen atoms of
methyl, isopropyl and phenyl groups are omitted for clarity.
A close inspection of the experimental (XRD) metric data concerning the Mn atom and the atoms of
the BH3 group of complex 1 (Table 1) reveals that those involving H200 (Mn1–H200 1.49(6) Å, B1–
H200 1.34(6) Å, Mn1–H200–B1 98(3)°) exhibit significant differences from those involving H300
(Mn1–H300 1.59(6) Å, B1–H300 1.13(6) Å, Mn1–H300–B1 102(4)°). Regarding complex 2 (Table 2),
the data involving H200 (Ru1–H200 1.71(3) Å, B1–H200 1.29(3) Å, Ru1–H200–B1 92(1)°) are almost
identical to those involving H300 (Ru1–H300 1.72(3) Å, B1–H300 1.32(2) Å, Ru1–H300–B1 90(1)°).
As the XRD data involving the H200 and H300 atoms of 1 and 2 might be affected by packing effects
in the solid state as well as by experimental errors (some differences are within the estimated standard
deviations and it is well known that XRD is not the best method to locate hydrogen atoms accurately),
we decided to theoretically optimize the gas phase molecular structures of 1 and 2 without symmetry
restraints. The obtained results (Tables 1 and 2) show that only the relativistic method rendered a
perfectly symmetric CS structure for complex 2, while for 1 both methods (relativistic and non-
relativistic) deviate slightly from this symmetry, giving structures where, rather surprisingly, the two
NiPr ligands are not arranged in a fully eclipsed manner but twisted (tables of theoretical coordinates
are provided in the Supplementary Material).
9

Table 1
Experimental (XRD) and theoretical (DFT) interatomic distances
(Å) and angles (°) in complex 1.
Atoms
Experimental ZORA-
(XRD) PW91/QZ4P 6-31G(d,p)
2.132(5)
B3P86/
Mn1–B1
2.128
1.678
1.703
2.065
1.784
1.791
1.787
1.195
1.321
1.315
75.7
2.115
1.673
1.698
2.047
1.780
1.782
1.782
1.195
1.312
1.308
75.6
Mn1–H200
Mn1–H300
Mn1–N2
Mn1–C101
Mn1–C102
Mn1–C103
B1–H100
1.49(6)
1.59(6)
2.071(3)
1.825(5)
1.817(5)
1.801(5)
1.08(6)
1.34(6)
1.13(6)
70(3)
B1–H200
B1–H300
H200–Mn1–H300
Mn1–H200–B1
Mn1–H300–B1
H200–B1–H300
N1–C4–N2
98(3)
89.6
89.4
102(4)
88.7
88.5
90(4)
118.5(3)
103.8
118.1
104.1
118.5
Table 2
Experimental (XRD) and theoretical (DFT) interatomic distances
(Å) and angles (°) in complex 2.
Atoms
Experimental ZORA-
B3P86/
(XRD)
PW91/QZ4P 6-31G(d,p)/
LanL2DZ(Ru)
Ru1–B1
2.173(3)
2.169
1.749
1.749
2.141
2.284
2.211
2.152
2.152
2.210
1.203
1.343
1.344
75.9
2.177
1.757
1.761
2.139
2.291
2.222
2.164
2.167
2.217
1.199
1.335
1.333
74.8
Ru1–H200
Ru1–H300
Ru1–N2
Ru1–C14
Ru1–C15
Ru1–C16
Ru1–C17
Ru1–C18
B1–H100
1.71(3)
1.72(3)
2.133(2)
2.250(2)
2.198(2)
2.143(2)
2.147(2)
2.189(2)
1.13(3)
1.29(3)
1.32(2)
73(1)
B1–H200
B1–H300
H200–Ru1–H300
Ru1–H200–B1
Ru1–H300–B1
H200–B1–H300
N1–C4–N2
92(1)
90(1)
103(2)
118.3(2)
88.0
88.0
106.4
118.1
88.4
88.3
106.4
118.7
10

Table 3
Experimental (XRD) and theoretical (DFT) interatomic distances
(Å) and angles (°) in the borane adduct HiPr2bzamBH3.
Atoms
Experimental ZORA-
B3P86/
(XRD) PW91/QZ4P 6-31G(d,p)
B1–H100
B1–H200
B1–H300
H100–B1–H200
H100–B1–H300
H200–B1–H300
N1–C4–N2
1.13(2)
1.13(2)
1.13(2)
112(1)
110(1)
108(1)
1.207
1.229
1.225
110.2
111.0
109.5
117.7
1.207
1.223
1.223
111.1
111.1
110.2
118.7
120.3(1)
The images depicted in Figure 2 were obtained by applying the QTAIM approach to the
theoretically optimized geometries of compounds 1 and 2. They show, along with the atoms
corresponding to each complex, the complete set of bond critical points (bcp’s), ring critical points
(rcp’s), and a cage critical point (ccp), together with bond paths (bp’s) connecting bonded atoms
through their corresponding bcp’s. As clearly seen in Figure 2, no bp has been found between metal
and boron atoms in any of the two complexes, while M
and H300 B1 bp’s, were found in each compound. Additionally, a rcp, located inside each M(µ-H)2B
ring, was obtained for each complex.
–H200 and M–H300 bp’s, as well as H200–B1
–
Fig. 2 Topological graphs (B3P86/6-311++G(2df,2pd)/WTBS(Ru) level) of compounds 1 and 2, showing bond paths (solid
lines) and bond (small red circles), ring (small yellow circles) and cage (small green circle) critical points. The graph of the
borane adduct HiPr2bzamBH3 is shown in the Supplementary Material.
11

A closer view of the M(µ-H)2B ring is depicted in Figure 3, where the gradient trajectory map of the
total electron density in the H200 H300 plane of both complexes is displayed, showing bp’s and
basins of the atoms contained in the chosen plane. As clearly seen in Figure 3, no M H bp is a straight
line, being strongly inwardly curved, with approximately the same curvature for the Ru1 H200 and
Ru1 H300 interactions, but slightly different for the Mn1 H200 and Mn1 H300 interactions. As a
consequence, the rcp for complex 2 is symmetrically located at the gravity center of the Ru1(µ-H)2B1
ring, while for 1 it is slightly displaced towards the Mn1 H300 bcp. Therefore, it is suggested that the
Ru1 H200 and Ru1 H300 interactions are equivalent to each other, as well as the B1 H200 and B1
–
M–
–
–
–
–
–
–
–
–
–
–
H300 interactions in 2, while for complex 1 they are not completely equivalent (see forthcoming tables
for a more quantitative comparison).
Fig. 3 Gradient trajectories (B3P86/6-311++G(2df,2pd)/WTBS(Ru) level) mapped on total electron density plots (contour
levels at 0.1 e Å–3) in H200–M–H300 planes containing the metal atoms of compounds 1 and 2, showing the atomic basins,
bp‘s (dashed red lines), bcp’s (red circles), and a rcp (green circle). Larger images are included in the Supplementary
Material file.
Integration of the electron density inside each atomic basin rendered the electric charge, Q, of each
atom. Table 4 compares relativistic QTAIM charges of selected atoms of 1 and 2 among them and also
with those previously published for the above mentioned complexes [Mn(κ3N,H,H-mapyBH3)(CO)3]
(3), [RuH(κ3N,H,H-mapyBH3)(CO)(PiPr3)] (4), [Rh(κ3N,H,H-mapyBH3)(η4-cod)] (5), and
12

[Ir(κ3N,H,H-mapyBH3)(η4-cod)] (6) [13]. Rather interestingly, the atomic charge of the Mn atom in 1
and 3 coincides with its formal charge (+1), while that of the corresponding M atom in 2, 4, 5, and 6 is
clearly smaller. Atomic charges of H200 and H300 are exactly equal in complex 2, reflecting that the
Cs symmetry of this complex is not only geometrical but topological as well. On the other hand, these
charges are clearly different in complex 1, while notably they are equal (within two significant digits)
in the similar octahedral Mn complex 3. It is also interesting to note that atomic charges of H200 and
H300 are clearly more negative in the borane adduct HiPr2bzamBH3 (last row in Table 4) than in any of
the six complexes, while H100 charges are very similar (even identical in the case of complex 2), as
expected.
Table 4
QTAIM (ZORA-B1PW91/QZ4P) atomic charges, Q (e), for selected atoms of complexes 1
and 2, and of borane adduct, compared to complexes 3 and 4 [13b], and to 5 and 6 [13a].
Complex
Ma
H100
H200
H300
B1
N1
N2
1.043
0.628
1.056
0.603
0.603
0.605
-----
–0.592
–0.621
–0.586
–0.587
–0.595
–0.591
–0.621
–0.496
–0.439
–0.504
–0.514
–0.514
–0.458
–0.601
–0.482
–0.439
–0.500
–0.491
–0.512
–0.467
–0.602
1.843
1.764
1.823
1.787
1.778
1.750
1.794
–1.401
–1.377
–1.436
–1.404
–1.372
–1.394
–1.306
–1.135
–1.050
–1.173
–1.121
–1.125
–1.128
–1.112
1
2
3
4
5
6
Bb
aM = Mn1 (1 and 3), Ru1 (2 and 4), Rh1 (5), Ir1 (6). bB = borane adduct HiPr2bzamBH3.
There are several local topological properties of the electron density (i.e., calculated at a bcp) that
have been successfully used to analyze the bonding in compounds containing transition metals. The
electron density (ρb), the ellipticity (εb), the Laplacian of the electron density ( 2ρb), the kinetic energy
density ratio (Gb/ρb) and the total energy density ratio (Hb/ρb, with Hb(r) = Gb(r) + Vb(r) and ¼ 2ρb(r) =
2Gb(r) + Vb(r), where Vb(r) is the potential energy density) are by far the most common [1–4]. Values
of these topological properties for selected bonds of complexes 1 and 2 are collected in Table 5, which
shows that bond path lengths (bpl’s) of M–H and B–H bonds are clearly longer in both compounds
than the corresponding interatomic distances (Tables 1 and 2) due to their curvature. For instance,
Ru1–H200 and Ru1–H300 bpl’s are both 0.052 Å longer than their corresponding interatomic
distances, while Mn1–H200 and Mn1–H300 bpl’s are, respectively, 0.095 Å and 0.125 Å longer,
showing a symmetric curvature in complex 2 but asymmetric in complex 1. In fact, all topological
parameters for Ru1-H200 and Ru1-H300 are nearly identical (Table 5), as well as those for B1-H200
13

and B1-H300 in complex 2, while this is not the case for the equivalent values in complex 1, where
significant differences are found. For instance, while the ellipticity of Ru1-H200 and Ru1-H300 bonds
is, respectively, 1.14 and 1.13, values for Mn1-H200 and Mn1-H300 are, respectively, 1.06 and 1.25.
Even greater differences are found in other local magnitudes, like the Laplacian of the electron density
(compare 6.63 e Å–5 for both Ru1–H bonds in 2 with 6.00 e Å–5 and 5.32 e Å–5 in 1 for, respectively,
Mn1–H200 and Mn1–H300).
The different nature of the interactions involving H-bridging atoms in 1 and 2 can be appreciated by
comparing, for instance, the local topological properties of the B1–H200 and B1–H300 bonds with
those of the B1–H100 bond in the same complexes and with the three B–H bonds in the borane adduct
HiPr2bzamBH3, since the latter is a good reference for borane compounds without attached transition-
metal atoms, where the BH3 moiety has three topologically equivalent B-H bonds. The large values of
the electron density (ρb > 1), the large and negative values of the Laplacian ( 2ρb << 0), the large and
negative values of the total energy density ratio (Hb/ρb< –1), the small values of the ellipticity, and the
straight bond paths for the latter are typical of well known open-shell bonds with cylindrical symmetry
between light atoms (covalent σ bonds in MO terminology). On the contrary, values for B1–H200 and
B1–H300 bonds in 1 and 2, in particular their curvature and the higher values for the ellipticity, are
characteristic of multicenter interactions (see below for a more detailed description involving also the
metal atoms) [3].
On the other hand, it is well known that integral topological properties (i.e., calculated over a whole
atomic basin, over an interatomic surface or along a bond path) are even more useful than local
topological properties for characterizing bonds in transition-metal compounds [1–4]. The delocalization
index, δ(A–B), which estimates the number of electron pairs delocalized between atoms A and B, is by
far the integral topological property that has been most frequently used in QTAIM studies. In the last
column of Table 5, values for the delocalization index of selected bonds for 1 and 2 are included. As
expected from our previous discussion, there is a clear asymmetry in the values for δ(M–H) (0.448 and
0.430 for H200 and H300, respectively) and δ(B–H) (0.364 and 0.374 for H200 and H300,
respectively) in complex 1, while for complex 2 there is a complete symmetry in this index too.
14

Table 5
Topological parameters (ZORA-B1PW91/QZ4P) of selected bonds of complexes 1 and 2, and of borane adduct.
Complexb
h
Bonda
d (Å)c
ρ
b (e Å–3)d
2ρb (e Å–5)e
Hb/
ρ
b (h e–1)f
Gb/
ρ
b (h e–1)g
εb
δ
(A–B)i
M–H200
1.773
1.801
1.830
1.801
1.195
1.192
1.207
1.338
1.364
1.229
1.329
1.365
1.225
2.081
2.152
1.483
1.491
1.580
1.795
1.801
2.160
0.589
0.656
0.571
0.656
1.229
1.198
1.143
0.875
0.868
1.074
0.888
0.866
1.087
0.535
0.584
1.204
1.173
0.894
1.007
1.007
0.635
5.997
6.634
–0.312
–0.340
–0.315
–0.340
–1.120
–1.091
–1.066
–0.909
–0.904
–1.031
–0.920
–0.903
–1.038
–0.164
–0.197
–0.988
–0.948
–0.804
–0.393
–0.393
1.025
1.048
0.967
1.047
0.601
0.683
0.750
0.645
0.590
0.758
0.644
0.588
0.757
1.222
1.264
1.406
1.468
1.536
1.406
1.400
0.988
1.065
1.136
1.253
1.130
0.009
0.004
0.103
0.271
0.351
0.139
0.256
0.353
0.128
0.084
0.175
0.009
0.013
0.015
0.119
0.073
0.839
0.449
0.575
0.431
0.575
0.550
0.540
0.521
0.364
0.366
0.506
0.374
0.366
0.509
0.517
0.641
0.451
0.451
0.375
1.138
1.133
0.539
1
2
1
2
1
2
B
1
2
B
1
2
B
1
2
1
2
B
1
1
2
M–H300
B1–H100
5.320
6.627
–9.115
–6.981
–6.482
–3.301
–3.892
–5.503
–3.495
–3.899
–5.707
8.089
B1–H200
B1–H300
M–N2
8.902
B1–N1
7.193
8.707
8.197
j
M–(CO)eq
M–(CO)ax
M–Cj
14.570
14.491
6.016
–0.323
d
aM = Mn1 (1), Ru1 (2). b B = borane adduct HiPr2bzamBH3. cBond path length. Electron density at the bcp. eLaplacian of the electron
density at the bcp. fTotal energy density ratio at the bcp. gKinetic energy density ratio at the bcp. hEllipticity at the bcp. iDelocalization
index. jAverage values.
Delocalization indexes of the non-bonding M···B1, M···N1, and M···H100 interactions in
complexes 1 and 2 (Table 6) also contribute to shed some light on the characteristics of these
interactions. Although δ(M···N1) and δ(M···H100) are indeed very small (they are included in the
15

table only for comparison purposes), δ(M···B1) values are not negligible at all but comparable in
magnitude to, or even greater than, values found in many M–M interactions. For instance, δ(M–M)
values for [M2(CO)10] (M = Mn, Tc, Re) complexes, where a bp between metal atoms exists, are 0.281,
0.336, and 0.246, respectively, whereas δ(M···M) values for the H-bridged intermetallic interactions of
[M3(µ-H)3(CO)12], in which there is no bp between metal atoms, are 0.129, 0.134, and 0.134,
respectively [3s]. Analogously, in complex [Ru3(µ-H)2(µ3-MeImCH)(CO)9] (Me2Im = 1,3-
dimethylimidazol-2-ylidene), δ(Ru–Ru) is 0.458 for the metal-metal interaction where a bp does exist,
while δ(Ru···Ru) is 0.246 and 0.169 for the two H-bridged interactions where no bp exists [3j]. In fact,
by adding up δ(M–H200) and δ(B1–H200) values for the bonding interactions, with one half the value
of δ(M···B1) for the non-bonding M···B1 interaction in each M(µ-H)2B ring, a total of 0.896 (1) and
1.065 (2) electron pairs are obtained, which is approximately the same as if one single M–B1 bond,
without the bridging hydrogen, was present in each cluster. Similarly, by adding up δ(M–H300) and
δ(B1–H300) values with the other half of the δ(M···B1) value a total of 0.888 (1) and 1.065 (2)
electron pairs are obtained. For a comparison, in the previously studied borane complexes 3–6, values
between 0.9 and 1.1 are found for these additions [13]. In other words:
1
δ
δ
(M − H 200) +
(M − H300) +
δ
δ
(B1− H 200) +
(B1− H300) +
δ
δ
(M LB1) ≈ 1
(M LB1) ≈ 1
2
1
2
which clearly represents two 3c-2e bonding interactions in the M(µ-H)2B moiety of each complex.
Table 6
Delocalization indexes, δ(A···B), for
selected non-bonding A···B interactions of 1
and 2 (ZORA-B1PW91/QZ4P level).
Complexa M···B1 M···N1 M···H100
0.166
0.248
0.074
0.094
0.033
0.050
1
2
aM = Mn1 (1), Ru1 (2).
16

The integrated electron density over the whole interatomic surface,
∫ Bρ, which is also an integral
A∩
property, is an additional tool for characterizing bonding interactions since it is related to the bond
strength [1–4]. Table 7, which collects this magnitude for several bonding interactions in and
1
2,
shows that M–H200 and M–H300 bonds are slightly weaker than the B1-H200 and B1-H300 bonds,
while the B1–H100 bonds are clearly stronger than the former, with values similar to the ones found in
the borane adduct (last row in Table 7), which are typical of fully localized covalent bonds (note also
the differences in delocalization indexes between both kinds of B–H bonds in the last column of Table
5). Nevertheless, the values found for M–H200 and M–H300 are comparable to those obtained, for
instance, for the Zn–Zn bond of [Zn2(η5-C5Me5)2] (1.252 e Å–1) [3e] or even for the Mo–Mo of
[Mo2(µ-Ac)2(µ-Cl)2Cl4]2– (1.083 e Å–1), which has a formal bond order of three [3p], showing that they
are not particularly weak. Additionally, as clearly seen in Table 7, the asymmetry in complex 1
between Mn1-H200-B1 and Mn1-H300-B1 interactions is once again noteworthy, while for complex 2
both interactions are completely symmetrical.
Table 7
Integrated electron density over the whole interatomic surface, ∫A∩Bρ (e Å–1), for selected
bonding interactions of 1, 2, and the borane adduct (ZORA-B1PW91/QZ4P level).
Complexa M–H200
M–H300
1.140
1.347
-----
B1–H100
1.941
B1–H200
1.491
B1–H300
1.466
M–N2
1.306
1.557
-----
1.220
1.347
-----
1
2
1.968
1.500
1.500
Bb
1.793
1.898
1.891
aM = Mn1 (1), Ru1 (2). bB = borane adduct HiPr2bzamBH3.
Further insight into the multicenter character of the bonding in complexes
1
and
2 may be
obtained from the Electron Localization Function (ELF) [29]. ELF of complexes and
1
2 is depicted in
Figure 4, where two trisynaptic valence basins V(M,H,B) located on the H200 and H300 atoms are
shown for each complex, as previously observed for B2H6 and Al2H4(CH3)2, for instance, where two
V(B,H,B) and V(Al,C,Al) basins, respectively, are present [30]. They can be easily distinguished in
Figure 4 from more typical disynaptic valence basins, like V(M,C) or V(C,O), corresponding to M–CO
17

bonds, and from monosynaptic basins, likes those located at carbonyl O atoms, V(O), corresponding to
lone pairs.
Fig. 4 Electron Localization Function (ELF) isosurface (ZORA-B1PW91/QZ4P level), at η = 0.8 e Å–3, for complexes 1
and 2. Additional and larger images are included in the Supplementary Material file.
Figure 5 is a representation of the Laplacian of the electron density in the H200–M–H300 plane
of both complexes, which is also very useful to analyze M–H and M–CO interactions, among others.
This figure shows that the valence shell of each M atom has a nearly perfect cubic shape due to its
octahedral coordination. Valence shell charge concentrations (VSCC’s) of H atoms are distorted
toward the midpoint of each M’s valence shell edge, where it is located its valence shell charge
depletion (VSCD), showing clearly the curvature of each M–H interaction. This behavior, typical of
multicenter bonds, has been previously observed in many other H-bridged systems, like in the
previously mentioned Mn, Ru, Rh, and Ir borane complexes [13], and also in metal cluster complexes,
such as [M3(
ꢀ
-H)3(CO)12] (M = Mn, Tc, Re) [3s], [Ru3(
ꢀ
-H)2(ꢀ3-MeImCH)(CO)9] [3j,3r], [Os3(
-Cl)(CO)10] [3n], among others, some
ꢀ-
H)2(CO)10] [3n], [Os3(
ꢀ
-H)( -OH)(CO)10] [3n] and [Os3( -H)(ꢀ
ꢀ
ꢀ
of them studied from both theoretical and experimental electron densities. On the other hand, the key-
lock mechanism prototypical of the Dewar-Chatt-Duncanson (DCD) donor-acceptor model for
18

interactions between a transition-metal atom and a non-metal atom is clearly appreciated here in Mn1–
CO bonds. Each C atom points its VSCC directly toward a VSCD of the metal atom along a straight
line, with no curvature at all in this case.
Fig. 5 Laplacian of the electron density in relevant planes (B3P86/6-311++G(2df,2pd)/WTBS(Ru) level) containing the
metal atoms of complexes 1 and 2 (contour levels at 0.0 and ± (1,2,4,8) × 10n e Å–5, with n ranging from +3 to –3). Blue and
red lines represent negative and positive values, respectively. Larger images are included in the Supplementary Material
file.
4. Conclusions
Several local and integral topological properties of the electron density associated to the different
interatomic interactions present in the transition-metal borane complexes [Mn(κ3N,H,H-
iPr2bzamBH3)(CO)3] ( ) and [Ru(η5-C5Me5)(κ3N,H,H-iPr2bzamBH3)] ( ) (HiPr2bzamBH3 = N-
1 2
trihydridoborane-N,N’-bis(isopropyl)benzamidinate) have been obtained using non-relativistic and
relativistic QTAIM calculations. A comparative analysis of these results has allowed the establishment
of the following main conclusions:
19

(a) Most M–L interactions (L = CO, iPr2bzam) in both complexes follow the classical Dewar-Chatt-
Duncanson (DCD) donor-acceptor model, as revealed by the key-lock mechanism showed in Laplacian
representations as well as by the straight bond paths obtained, among other features. They can be
considered classical polar covalent bonds.
(b) No M–B bond paths have been obtained for any of the two complexes, although non-negligible
delocalization indexes have been calculated for these interactions.
(c) All M–H interactions with the BH2 group in both complexes show bond paths that are strongly
inwardly curved, with greater curvature near hydrogen atoms than near metal centers. These bonds can
be considered intermediate between those of the Shimoi or σ-terminal type (κ1H coordination of the B–
H bond, no M–B interaction) and those of the agostic type (κ2B,H coordination of the B–H bond, M–B
and M–H interactions).
(d) The two M–H interactions in the Ru complex
2
are equivalent to each other, as well as the two
are
B–H interactions within the Ru(µ-H)2B moiety. On the contrary, Mn–H interactions in complex
1
not completely equivalent, one of them being more agostic than the other, i.e. Mn1–H300 (more curved
and higher ellipticity).
(e) Two 3c-2e bonding interactions may be postulated for the M(µ-H)2B moiety in both complexes.
(f) A comparison of the results described in this work with those previously reported for σ-borane
complexes (M = Mn (3), Ru (4), Rh (5), and Ir (6
)), containing a similar tripod κ3N,H,H borane ligand
but different additional ligands, shows that the bonding similarities and differences within each
particular M(µ-H)2B moiety are not related to the type of metal atom, nor even to its coordination
geometry, but mainly to the molecular symmetry, since a plane of symmetry that contains atoms M, B,
H100, N1 and N2 is present in complexes with equivalent interactions (2 and 3) but it is absent in those
with non-equivalent interactions (1, 4, 5, and 6).
Acknowledgements
This work has been supported by Spanish MINECO projects (MAT2016-78155-C2-1-R and CTQ2016-
75218-P) and Principality of Asturias grants (GRUPIN14-060 and GRUPIN14-009).
Supplementary material
CCDC1921463, CCDC1921464, and CCDC1921465 contain the supplementary crystallographic data
for this paper. These data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/.
20

Selected X-ray diffraction data, atomic coordinates for the theoretically optimized geometries and
additional figures are available at https://doi.org/10.1016/j.molstruc.20xx.xx.xxx. Checkpoint files of
geometry optimizations and electronic structure calculations for the borane adduct, and for complexes
and are available from the authors upon request.
1
2
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25

Highlights
(1) No Metal-Boron bond paths have been found in any of the two complexes.
(2) All Metal-Hydrogen bonds are intermediate between agostic and σ-terminal types.
(3) Two 3c-2e bonding interactions are present within each MH2B moiety.
(4) Other Metal-Ligand interactions follow the Dewar-Chatt-Duncanson model.
(5) The presence of a plane of symmetry is essential for obtaining equivalent M-H-B
bonds.

Declaration of interests
⊠ The authors declare that they have no known competing financial interests or personal relationships
that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered
as potential competing interests: