Geometry- and QTAIM-Based Comparison of Intramolecular Charge

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Geometry- and QTAIM-Based Comparison of Intramolecular Charge-Inverted Hydrogen Bonds, M•••(H– Si) 'Agostic Bonds', and M•••(#-SiH) Sigma Interactions 2

Miros#aw Jab#o#ski J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b07013 • Publication Date (Web): 28 Oct 2015 Downloaded from http://pubs.acs.org on November 2, 2015

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The Journal of Physical Chemistry

Geometry- and QTAIM-Based Comparison of Intramolecular Charge-Inverted Hydrogen Bonds, M· · · (H–Si) ’Agostic Bonds’, and M· · · (η 2-SiH) Sigma Interactions MirosÃlaw JabÃloński∗ Department of Quantum Chemistry, Nicolaus Copernicus University in Toru´ n, 7-Gagarina St., PL–87 100 Toru´ n, Poland E-mail: [email protected] Phone: +48 (56) 6114695. Fax: +48 (56) 6542477

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Abstract Using large sets of systems having an intramolecular charge-inverted hydrogen bond (IMCIHB), M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction, we have compared both geometric and QTAIM-based topological parameters characterizing all these three types of interactions. It is shown that IMCIHBs can be distinguished from the other relevant interactions by the significantly less elongated Si–H bond. The other geometric parameters are not characteristic because they accept wide ranges of values in systems having either M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction. If QTAIM-based results are investigated then it is shown that IMCIHB can be characterized by the position of the BCPH···M that is closer to the metal atom, whereas, quite the contrary, this BCP has been found to be closer to the agostic hydrogen in complexes having either M· · · (Ha –Si) or M· · · (η 2 -SiH) interactions. Another difference is in the curvature of the M· · · H bond path. If the M· · · H bond path tracing the M· · · (H–E) (E = Si, C) interaction is curved then this curvature appears near the agostic hydrogen – a property particularly pronounced in M· · · (Ha –C) agostic bonds. Moreover, it has also been shown that IMCIHB can be characterized by lower curvatures and, in general, lesser values of the electron density computed at BCPH···Al than at BCPs of either M· · · (Ha –Si) or M· · · (η 2 -SiH) interactions. Importantly, IMCIHBs can be distinguished from the other two types of interactions on the basis of values of delocalization index, which are significantly lower for IMCIHBs. Other QTAIM-based parameters have occurred to be not characteristic for IMCIHBs due to wide ranges of their values obtained for M· · · (Ha –Si) and M· · · (η 2 -SiH) interactions. It has also been shown that PBE0 functional gives the best molecular structure in comparison with experimental data.

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Introduction By performing DFT-based calculations with several different exchange-correlation functionals and using quantum theory of atoms in molecules (QTAIM), 1–3 very recently 4 we have made a thorough comparative analysis of intramolecular charge-inverted hydrogen bonds (IMCIHBs) 4–11 and α-, β-, γ-, and δ-agostic bonds (ABs) of M· · · (Ha –C) (M = transition metal) type. 12–17 Our studies have shown 4 some substantial differences in positions of bond critical points (BCPs) of H· · · Al and M· · · Ha interactions as well as in curvatures of bond paths (BPs) tracing these interactions. Namely, the BCP of M· · · Ha is significantly closer to the agostic hydrogen (Ha ) than the metal atom, whereas, on the contrary, the BCP of H· · · Al in IMCIHB is somewhat closer to the metal atom. Considering curvatures of relevant bond paths, we have shown 4 that agostic bonds are characterized by M· · · Ha bond paths that are straight in the M· · · BCP section and highly curved near the agostic hydrogen. Any substantial curvature of BP in the proximity of hydrogen is not present in IMCIHBs. Quite the contrary, a considerable curvature of BP near the metal (aluminum) atom can be obtained instead. Further differences have also been obtained in values of some QTAIM parameters. Namely, in comparison to IMCIHBs, agostic bonds feature greater values of bond ellipticity computed at BCPM···Ha and of the electron density computed at ring critical point (RCP). As a consequence, we have shown 4 that the difference between IMCIHBs and M· · · (Ha –C) ABs is evident. Although the term agostic bond was originally coined by Brookhart and Green to refer to M· · · (Ha –C) interactions only, 12–14 nowadays one can see that other interactions of the M· · · (Ha –E) type are also treated as agostic bonds, those possessing E = Si or B being most common. 16–18 Moreover, some use the term agostic bond even if the Ha -acceptor is not a transition metal 16,19–21 or if the agostic hydrogen is replaced by another atom. 22 As a consequence, although on the basis of formal definitions of IMCIHB and AB the difference between both interactions seems to be clear, 4 some may treat the Si–H· · · Al IMCIHB as one of many types of agostic bonds if only “wider definitions” of an agostic bond, where neither 3



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E has to be necessarily carbon nor the Ha -acceptor atom has to be a transition metal, are in use. For this reason, to properly classify IMCIHBs and to show their autonomy, similarities and differences between IMCIHBs and ABs should be studied. Taking into account that IMCIHBs of the Si–H· · · Al type contain Hδ− -donating silicon atom instead of a carbon 6,7 we perform QTAIM-based comparison of Si–H· · · Al IMCIHBs and α-, β-, γ-, and δ-’agostic bonds’ (we will be using apostrophes to indicate that this interaction does not fulfill the original definition of an agostic bond where necessarily E = C) 12–14 of the M· · · (Ha –Si) type. To the latter set we also join intermolecular M· · · (Ha –Si) instances that are better referred to as M· · · (η 2 -SiH) sigma interactions. 23–30 The full characterization of our model systems having any of the three investigated interactions, i.e., IMCIHB, M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction is presented in the Systems section. It is commonly known 16,24 that due to higher polarizability of silicon in comparison to carbon and more hydridic hydrogen the Si–H bond is more prone to elongate than C–H. As a consequence, one should observe diverse Si–H bond distances, from a modest elongation only to a significantly advanced Si–H bond cleavage. The latter effect is characteristic for some systems having the M· · · (η 2 -SiH) sigma interaction. 24 In this way we will be able to compare the QTAIM-based characteristics of IMCIHB with those of the other M· · · H–Si interactions, being at different stages of the Si–H bond cleavage. At the same time our goal is to answer the question whether the previously found QTAIM-based features of IMCIHBs that allow to distinguish them from ABs, 4 will also remain in force when confronted with M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions.

Methodology Full geometry optimizations of molecules in their singlet spin-states and QTAIM-based calculations have been performed on the PBE0/aug-cc-pVTZ level of theory (aug-cc-pVDZ for transition metals). It will soon be shown that the PBE0 31–33 exchange-correlation functional

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gives the best geometry in comparison to experimental structure 23 of our MeCp(OC)2 Mn(H)SiCl3 test system (see Testing Exchange-Correlation Functionals subsection). Moreover, it has been shown 34 that PBE0 was one of the best performing for QTAIM calculations. On the other hand, we have shown recently 35,36 that the aug-cc-pVTZ basis set gives satisfactory values of QTAIM parameters similar to those obtained by the use of larger Dunning-type basis sets. Geometry optimizations and frequency calculations to analyse characters of obtained stationary points have been performed using Gaussian 09 suite of codes. 37 In order to improve the accuracy of calculations, the pruned (99,590) grid was requested (Integral(UltraFineGrid) command in Gaussian) and convergence criteria for geometry optimizations were additionally tightened (Opt = Tight option). No any imaginary frequency has been found confirming that obtained geometries correspond to local minima on the potential energy hypersurface. Detailed analysis of the topology of the electron density distribution has been made by means of QTAIM 1–3 using AIMAll package. 38

Systems Systems with IMCIHB Investigated systems having IMCIHBs are shown in Figure 1 and for the simplicity they are given labels as follows: (0) H3 Si–AlH2 , (1) H3 Si–CH2 –AlH2 , (2s) H3 Si–CH2 –CH2 – AlH2 , (2d) H3 Si–CH=CH–AlH2 , (3ss) H3 Si–CH2 –CH2 –CH2 –AlH2 , (3ds) H3 Si–CH=CH– CH2 –AlH2 , (3sd) H3 Si–CH2 –CH=CH–AlH2 , (4sss) H3 Si–CH2 –CH2 –CH2 –CH2 –AlH2 , (4dss) H3 Si–CH=CH–CH2 –CH2 –AlH2 , (4sds) H3 Si–CH2 –CH=CH–CH2 –AlH2 , (4ssd) H3 Si–CH2 – CH2 –CH=CH–AlH2 , (4dsd) H3 Si–CH=CH–CH=CH–AlH2 . The label is informative as the number indicates the number of carbon atoms in the molecular chain and the letter ’s’ or ’d’ indicates the formal type (single and double, respectively) of a bond joining two neighboring carbon atoms if the labeling is started from the silicon.

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Systems with M· · · (Ha –Si) ’Agostic Bond’ The following set of molecules featuring M· · · (Ha –Si) ’agostic bond’ have been investigated: (T12A) [TiCl2 –SiH2 –CH3 ]+ , (T12B) [TiCl2 –CH2 –SiH3 ]+ , (T13B) [TiCl2 –CH2 – SiH2 –CH3 ]+ , (T13G) [TiCl2 –CH2 –CH2 –SiH3 ]+ , (T14G) [TiCl2 –CH2 –CH2 –SiH2 –CH3 ]+ , (T14D) [TiCl2 –CH2 –CH2 –CH2 –SiH3 ]+ , (T121 B) [TiCl2 –CH=SiH2 ]+ , (T131 G) [TiCl2 –CH=CH–SiH3 ]+ , (T141 D) [TiCl2 –CH=CH–CH2 –SiH3 ]+ , (T142 D) [TiCl2 –CH2 –CH=CH–SiH3 ]+ , (C13G) [CoCl2 – CH2 –CH2 –SiH3 ]2+ , (C14G) [CoCl2 –CH2 –CH2 –SiH2 –CH3 ]2+ , (C14D) [CoCl2 –CH2 –CH2 – CH2 –SiH3 ]2+ , (C131 G) [CoCl2 –CH=CH–SiH3 ]2+ , (C141 D) [CoCl2 –CH=CH–CH2 –SiH3 ]2+ , [CpCo(PH3 )(R)]+ , where Cp = η 5 -cyclopentadienyl and (C21A) R = -SiH3 , (C22A) R = -SiH2 –CH3 , (C22B) R = -CH2 –SiH3 , (C23B) R = -CH2 –SiH2 –CH3 , and (C23G) R = -CH2 –CH2 –SiH3 . Consecutive letters in the Xijk Y symbol are given the following meaning. X, which is either T or C, indicates the transition metal, Ti and Co, respectively. The number i indicates a ’class’ of a complex, 1 for that with chlorines, 2 for that having η 5 cyclopentadienyl ligand (denoted by Cp). The number j denotes the number of E atoms (E = C or Si) in the R group. The number k, which is present in labels of some few systems, points the position of a formally double bond in R, 1 if the double bond is placed between the first two E atoms, 2 if it is placed between the second two. Finally, Y indicates the type of the M· · · (Ha –Si) ’agostic bond’: A = α, B = β, G = γ, D = δ. Therefore, e.g., T142 D stands for a titanium complex of first class (i.e., having two chlorine atoms) possessing four E atoms in the R group (which itself contains a formally double bond between the second pair of E atoms, i.e., carbons) that forms δ-’agostic bond’ of the Ti· · · (Ha –Si) type. Notice that the position of the silicon atom in the R group is unambiguously definite by the type of the ’agostic bond’ (denoted by Y) it forms to metal. As a consequence, the introduced label is both informative (metal, class, alkyl chain (its length and type), ’AB’-type) and unique. Geometries of all these systems obtained by means of PBE0 are displayed in Figure 1.

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Systems with M· · · (η 2 -HSi) Sigma Interaction CpL2 Mn(H)SiR3 is the most systematically investigated type of complexes containing a metal-hydrogen-main group element 3-center bond. 23–30 At the same time these piano-stool complexes are unique with respect to studying oxidative addition in detail. By suitable choice of metal ligands (L) and substituents at the silane moiety (R) one can easily obtain a series of complexes corresponding to different points on the reaction coordinates of oxidative addition, from a position where the hydrogen is still strongly bonded to silicon (as in M· · · (Ha –Si) ’agostic’-bonded systems) to a fully oxidatively added silane with a considerable separation of H and Si atoms. Also transition metal can affect a stage of the oxidative addition and structure of the CpL2 M(H)SiR3 complex. It is known that the oxidative addition proceeds more readily with heavier transition metal. 24 Because our purpose is to compare IMCIHBs with M· · · (Ha –Si) interactions, where the Si–H bond is well preserved, and since our computations are of all-electron type, we have investigated CpL2 M(H)SiR3 , where M has been a transition metal from the first row: (1) CpL2 Mn(H)(SiH3 ) (where L = (a) OC, (b) Cl, and (c) PH3 ), (1a’) Cp(OC)2 Mn(H)(SiCl3 ), (1∗ a’) MeCp(OC)2 Mn(H)(SiCl3 ), (1c’) Cp(PH3 )2 Mn(H)(SiCl3 ), (2) [CpL2 Fe(H)(SiH3 )]+ (where L = (a) OC, (b) Cl, and (c) PH3 ). Also two (3) Bz(OC)2 Cr(H)(SiR3 ) (R = (a) H, (a’) Cl, and Bz = η 6 -C6 H6 ) complexes have been included. All these systems are shown in Figure 1. Considering the M-Hi -Si triangle, we have drawn a bond between a pair of relevant atoms if only this bond has been traced by a bond path on a molecular graph (see QTAIM-Based Analysis section). It is evident from Figure 1 that the lack of the M· · · Si bond path in some systems (1a, 1b, 2a, 2b, 2c, and 3a) entails that they should be considered as possessing an intermolecular M· · · Hi –Si interaction rather than the M· · · (η 2 -HSi) sigma interaction. This point of view makes them somewhat similar to systems with IMCIHB, however, with highly advanced transfer of H. Complex MeCp(OC)2 Mn(H)(SiCl3 ), i.e., 1∗ a’, is of particular importance in our studies because its experimentally determined structure 23 will be compared with structures obtained by means of our DFT calculations using seven exchange-correlation functionals. This is aimed 7



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to select one exchange-correlation functional only and then to use it in studies of the other systems. As a consequence, this approach will significantly reduce the amount of numerical data and will also greatly simplify the comparative analysis of relevant interactions.

Results and Discussion Testing Exchange-Correlation Functionals One of the smallest transition metal complexes, containing a Si–H bond pointing to a metal, with known experimentally determined 23 structure is MeCp(OC)2 Mn(H)(SiCl3 ), i.e., 1∗ a’ (see Figure 2). This structure has been compared with DFT-based geometries obtained by means of seven exchange-correlation functionals used also in our earlier studies on IMCIHB and M· · · (Ha –C) agostic bond: 4 BP86, 39,40 B3LYP, 41,42 B3PW91, 41,43,44 PBE0, 31–33 TPSSh, 45 M06-L, 46 and M06. 47 The reasoning of their use is given in ref. 4. Values of those geometrical parameters that had been earlier measured by Schubert et al. 23 are given in Table 1. We also have shown differences of individual geometrical parameters as compared to their experimental values. Finally, we have also computed root mean squares (RMS), separately for relevant bonds and angles. First of all it should be stressed that in fact all used exchange-correlation functionals give excellent accordance with the experimentally determined structure. In particular this conclusion applies to bond distances for which all ∆ values are lesser than 0.100 ˚ A. The greatest errors have been obtained for Mn–H, this may, however, result from a lesser precision in determining positions of hydrogen atoms. Larger disagreement with experimental values has been obtained in the case of bond angles, where |∆| up to 3.9◦ has been found for C2– Mn–H for M06L. Most |∆| values are, however, lesser than ca. 2◦ . Molecular structure is, however, determined by all geometrical parameters, and not just single, therefore it is much more important to take into account values of RMS (see the three lowest rows in Table 1). It is clear that PBE0 exchange-correlation functional gives the best values of bond distances 8


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when compared to the experimental data, whereas BP86 and B3LYP performs the worst. This conclusion is valid for all bonds as well as for bonds forming the Mn–Hi –Si triangle only (RMS amounts to 0.029 and 0.048˚ A for PBE0 and 0.048 and ca. 0.069˚ A for BP86 and B3LYP for all and chosen bonds, respectively). On the contrary, RMS for bond angles are close to each other (1.4 - 1.7◦ ) for all the exchange-correlation functionals, but M06L which gives RMS amounting to 2.1◦ . As a consequence of this analysis, PBE0 exchangecorrelation functional has been selected for the following presentation of all the other systems. Fortunately, PBE0 has also been one of the best performing for QTAIM calculations. 34 Therefore, we will use the same exchange-correlation functional for presentation of both the molecular structure and QTAIM-based parameters. It should be mentioned that despite the fact that our theoretically obtained geometries are in perfect accordance with the structure determined experimentally, 23 packing and other effects, which influence the structure of a molecular system in condensed phase, are not taken into account by gas-phase calculations.

Geometrical Data PBE0-based values of the most important geometric parameters relating to IMCIHBs in systems shown in Figure 1 are listed in Table 2. Results obtained for the other six exchangecorrelation functionals can be found in Table 1 in ref. 4. It is apparent that charge-inverted hydrogen bonds are characterized by the significantly longer Si–H bond interacting with Al (Si–Hi in Table 2). If only those IMCIHBs are considered that are traced by the presence of BPH···Al (thus, excluding H· · · Al contacts in 0 and 1) then the length of IMCIHB is 1.92 - 2.08˚ A, the greatest distances being for 2s (2.08˚ A) and 2d (2.03˚ A), both having a fivemembered quasi-ring. The H· · · Al distance increases to 2.28˚ A in the four-membered quasiringed 1, which, however, does not have BPH···Al . This shows that a strain of a molecular chain prevents formation of IMCIHB. 6 It was reported by Popelier and Logothetis 48 that the geometric trace of an interatomic interaction does not necessarily have to be supported by the presence of a bond path. This is, indeed, evident also from our results. Values of 9



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dSi···Al are in the range of 2.92˚ A (4dsd) to 3.11˚ A (3ds) and those of αSiHAl range from 114◦ (2s) to 126◦ (3ds), showing that αSiHAl for IMCIHBs is clearly larger than 90◦ . Values of some chosen geometrical parameters characterizing model systems having either M· · · (Ha –Si) (M = Ti, Co) α-, β-, γ-, and δ-’agostic bonds’ or M· · · (η 2 -SiH) (M = Mn, Fe, Cr) sigma interactions are listed in Table 3. These results show that values of presented geometrical parameters for both M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions may change in very wide ranges, much wider than those for IMCIHBs. Lengths of Si–Ha/i bond are from 1.541˚ A (T121 B) to 1.847˚ A (C14D) and from 1.555˚ A (1b) to 1.829˚ A (1c’) in M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions, respectively. It shows that Si–Ha/i is much more elongated in systems possessing either of these interactions than in systems with IMCIHB. This most likely results from both the ? stronger σSiHa/i →M interaction and the opportunity for M→ σSiH dπ back-donation. Both a/i

these interactions result in Si–Ha/i bond elongation. In general, calculated values of dM···Ha/i are in the range of 1.477˚ A (C14D) to 2.111˚ A (T121 B) or 1.543˚ A (1a’) to 1.654˚ A (1b) if neutral systems are considered only. Let us recall that the range of dH···Al values found for systems with IMCIHB was 1.92 - 2.08˚ A. Similarly, ranges of dM···Si values found for both M· · · (Ha –Si) ’AB’ and M· · · (η 2 -SiH) sigma interaction are very wide, from 2.113˚ A (C21A) to 3.162˚ A (T14D) and from 2.256˚ A (1c’) to 2.871˚ A (2b), respectively, as compared to 2.92˚ A - 3.11˚ A in systems with IMCIHBs. If values of αSiHa/i M are taken into account then, again, they extend wide ranges in systems with either M· · · (Ha –Si) ’AB’ (79.8◦ (C22A) 132.1◦ (C14D)) or M· · · (η 2 -SiH) sigma interaction (83.3◦ (1c’) - 127.2◦ (2b)) which comprise values of αSiHi M for IMCIHBs (114◦ - 126◦ ). Such wide ranges of analyzed geometrical parameters obtained for systems with either M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction show that one cannot distinguish IMCIHBs on the basis of values of geometrical parameters. Nevertheless, it appears that the only geometrical parameter that allows such a distinction is dSiHi , i.e., the length of the Si–Hi bond, which is smaller in systems having IMCIHB. As already explained, this results from both weaker σSiHi →M interaction and the

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? lack of Al→ σSiH dπ back-bonding, which would additionally weaken the Si–Hi bond, as Al i

has no d-electrons. It should be emphasized that such wide ranges of relevant geometrical parameters obtained for systems with M· · · (Ha –Si) ’agostic bonds’ as well as for systems with M· · · (η 2 -SiH) sigma interactions result from the fact that the structure of these systems can be easily tuned by many factors 16,24,28 such as, e.g., (i) the type and formal charge of the transition metal (ii) the type and size of metal ligands (iii) type of substituent(s) in the silyl group. This fact of course diversifies the bonding pattern of the M–Ha/i –Si triangle. We confine ourselves to provide just a few examples. On comparing 1a, 1b, and 1c first, one can see that the M· · · Si distance is the greatest in 1b (2.766˚ A), whereas it is the least in 1c (2.336˚ A). On the other hand, Si–Hi is the shortest (1.555˚ A) in 1b and the longest (1.822˚ A) in 1c. Exchange of metal ligand from -PH3 in 1c to -CO in 1a and then to -Cl in 1b causes the Si–Hi –M angle to open monotonically from 87.1◦ through 91.0◦ to 119.0◦ . These geometrical changes indicate that, in this triad, the oxidative addition is most advanced in 1c (i.e., Cp(PH3 )2 Mn(H)SiH3 ), whereas the least in 1b (i.e., Cp(Cl)2 Mn(H)SiH3 ). Similar effect takes place in the 2a, 2b, and 2c triad. This is in accord with Schubert that the PR3 (R = H in this case) ligand increases thermal stability of a complex and makes the elimination of the silane more difficult. 24 If, e.g., 1a and 1a’ or 3a and 3a’ pairs of systems are compared instead, then it is evident that the exchange of hydrogens in -SiR3 by chlorines leads to the strengthening of the sigma M· · · (η 2 -SiH) complex, i.e., to the more advanced oxidative addition of the silyl moiety. The M· · · Si and M· · · Hi distances become shorter, whereas Si–Hi gets longer. Also, the Si–Hi –M bond angle decreases from somewhat greater than the right angle (91.0◦ and 93.7◦ in 1a and 3a, respectively) to significantly lower that the right angle (86.3◦ and 87.9◦ in 1a’ and 3a’, respectively). It is seen that not only dSiHi , dM···Hi , and dM···Si , 24 but also the Si–Hi –M angle is a good indicator of the strength of the M· · · (η 2 -SiH) bond. It can be seen that CpL2 Mn(H)SiR3 complexes present particularly advanced stage on the oxidative addition reaction 24 as compared with their congeners possessing another transition

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metals. For example, dM···Si in 1a amounts to 2.375˚ A, whereas its values in 2a and 3a are 2.627˚ A and 2.446, respectively. Also the Si–Hi –M angle in 2a and 3a is greater (110.8◦ and 93.7◦ , respectively) than in 1a (91.0◦ ). It should be stressed that the gradual increase in the level of advancement of the addition process should alter the molecular graph in the M–Hi – Si triangle, from a situation where only two bond paths, of M· · · Hi and Hi –Si bonds, are present (similarly as in (IM)CIHBs) to the one, where all three bonds, i.e., M· · · Hi , Hi –Si, and M· · · Si are traced by corresponding bond paths. This issue will be addressed in next section. Our comparative analysis of M· · · Ha distances in M· · · (Ha –Si) and those found earlier 4 in M· · · (Ha -C) agostic bonds shows that the agostic hydrogen is much closer to a transition metal in M· · · (Ha –Si) ’agostic bonds’ than in M· · · (Ha –C) agostic bonds. This obviously results from more extensive elongation of Si–Ha as compared to C–Ha .

QTAIM-Based Analysis Before presenting the results based on QTAIM, it is worth mentioning that our earlier studies on IMCIHBs and M· · · (Ha –C) agostic bonds 4 have shown that exchange-correlation functionals have modest influence on values of electron density (ρb ) and electronic total energy density (Hb ) computed at BCPH···Al and BCPM···Ha . More significant effect of the functional has been found in the case of Laplacian (∇2 ρb ) and some its eigenvalues, namely λ3 in IMCIHBs or λ3 and λ2 in systems with ABs. As a consequence of the latter, also bond ellipticities (ε) can be influenced, particularly for M· · · (Ha –C) agostic bonds. Importantly, however, these possible discrepancy did not affect the general conclusions applying to reported differences between IMCIHBs and M· · · (Ha –C) agostic bonds. 4 To significantly reduce the amount of numerical data and greatly simplify the comparative analysis of interactions in question we have chosen one exchange-correlation functional only, namely PBE0, which has also been used to present molecular structures. Moreover, Tognetti and Joubert 34 have shown that PBE0 is one of the most reliable in calculations of values of 12


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QTAIM parameters and was also used by Tognetti et al. 49 in their studies on agostic bonds. Comparative Study of IMCIHBs, M· · · (Ha –Si) ’Agostic Bonds’, and M· · · (η 2 SiH) Sigma Interactions Values of some chosen QTAIM-based parameters characterizing model systems with IMCIHB, M· · · (Ha –Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions are presented in Tables 4 and 5. If electron density at relevant BCPs is taken into account then one can notice that its values are much lower in IMCIHBs (0.024–0.030 au) than in M· · · (Ha –Si) ’agostic bonds’ (0.038–0.136 au) and M· · · (η 2 -SiH) (0.082–0.121 au) in particular. Earlier reported values for M· · · (Ha –C) agostic bonds have also been greater (0.049–0.108 au). 4 This comparative analysis shows that IMCIHBs feature, in general, lesser values of ρb than the other relevant interactions, i.e., M· · · (Ha –E) (E = C or Si) and M· · · (η 2 -SiH). One should mention, however, that Tognetti et al. 49 have recently reported the range of 0.01–0.13 au for a set of 23 M· · · (Ha –C) agostic-bonded complexes. Some δ-agostic bonds considered by Tognetti et al. featured particularly low values of ρb (see Figure 5 in ref. 49). Nevertheless, taking even these few δ systems into account we conclude that, although lesser in the vast majority of cases, low values of ρb do not characterize IMCIHBs. On the contrary, the values of ∇2 ρb computed for IMCIHBs (0.045–0.089 au) are within the appropriate range for M· · · (Ha –Si) and M· · · (η 2 -SiH) together (0.043–0.259 au). The range of ∇2 ρb values is further extended to 0.03–0.29 au if M· · · (Ha –C) agostic bonds are included. 4,49 Although it prevents to distinguish IMCIHBs based on ∇2 ρb , in general, lower values of both ρb and ∇2 ρb found for IMCIHB shows that this interaction is significantly weaker than either M· · · (Ha –Si) or M· · · (η 2 -SiH). Importantly, all the interactions investigated in this study are characterized by positive values of ∇2 ρb and negative values of Hb , therefore they all should be considered as closedshell interactions, but with some covalent character. 50 The same conclusion has earlier been obtained for M· · · (Ha –C) agostic bonds, which seems to be independent on the exchange-

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correlation functional. 4 The partly covalent nature of investigated interactions can then be supported by values of −Gb /Vb ratio. If this ratio is lesser than 0.5 then an interaction is covalent (shared), if −Gb /Vb is between 0.5 and 1 the interaction is partly covalent in nature, whereas its value greater than 1 indicates noncovalent interactions. Values of this ratio has earlier been used to describe covalency of hydrogen-bonded molecules. 51 Although values of −Gb /Vb obtained for IMCIHBs (0.784–0.873) are slightly greater than for sigma interactions (0.625–0.755), they fall within the range of values for M· · · (Ha –Si) ’agostic bonds’ (0.529–0.931). Thus we conclude that IMCIHBs cannot be distinguished from M· · · (Ha –Si) ’agostic bonds’ solely on the basis of −Gb /Vb values. They can be, however, distinguished from both M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions if values of delocalization index 52,53 are considered. For IMCIHBs, values of δ(H,M) are 0.093–0.119, thus clearly lesser than those for Ti· · · (Ha –Si) (0.205–0.432) or Co· · · (Ha –Si) (0.604–0.773) ’agostic bonds’ and for M· · · (η 2 -SiH) sigma interactions (0.502–0.753). This result shows significantly lesser magnitude of electron charge shared between basins of H and Al atoms in IMCIHBs comparing to H and M in the other investigated interactions. In turn, this most likely results from the presence of an electron gap in the aluminum atom, which is reflected in a significantly positive atomic charge (see Table 5). Analysing results presented in Table 4 one can see that all curvatures characterizing IMCIHBs are lower than those for either M· · · (Ha –Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions. It is particularly evident for λ3 , i.e., the positive curvature in the direction of neighboring nuclei. Its range for IMCIHBs is 0.068–0.140, whereas 0.183–0.540 and 0.434– 0.544 for M· · · (Ha –Si) and M· · · (η 2 -SiH), respectively. Also, curvatures (λ2 and λ3 in particular) for M· · · (Ha –Si) are more diversified depending on the individual system. It is more interesting to look at values of bond ellipticities because it is often reported that they are large for agostic bonds. 48,49,54 Our recent studies, however, has not corroborated this opinion, showing that bond ellipticities of M· · · (Ha –C) agostic bonds were rather low, being in the range of 0.236–1.571. 4 The range of ε values for M· · · (Ha –Si) and M· · · (η 2 -SiH) interactions

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is even wider, 0.033–2.120; the greatest value obtained for T12A having an α-’agostic bond’. Corresponding range of ε for systems with IMCIHB is 0.048–2.481, but 0.048–0.584 only if 2s system, featuring particularly great bond ellipticity (2.481), is excluded. For this reason it may seem that charge-inverted hydrogen bonds can be characterized on the basis of lesser than in the case of either M· · · (Ha –Si) or M· · · (η 2 -SiH) values of ε. 4 This conclusion seems to be, however, doubtful if one takes into account both the general result and the fact that the value of ε can be significantly influenced by the exchange-correlation functional used in DFT calculations (in particular M06 has led to high values of ε of agostic bonds). 4 The other feature that is to be characteristic for agostic bonds is the close proximity of BCPM···Ha and RCP, i.e., low value of the dbr distance. 48,54 This distance can, however, be longer as, e.g., in a vanadium complex containing γ V· · · (Ha –C) agostic bond presented in Figure 6 of ref 34. Thus, it seems that dbr may significantly depend on the type of an agostic bond and on the size of a quasi-ring. Values of dbr are shown in Table 4. First of all, it can be seen that, indeed, values of dbr form a fairly broad ranges: 0.63–1.81˚ A for IMCIHBs, 0.49–1.35˚ A for M· · · (Ha –Si) ’agostic bonds’, and 0.43–1.32˚ A for M· · · (η 2 -SiH) sigma interactions. It should be emphasized that some M· · · (η 2 -SiH) systems analyzed in this study do not reveal RCPs – an evidence of poorly advanced oxidative addition of the silyl moiety. For this reason, in these cases the M· · · (η 2 -SiH) sigma interaction can be considered as an intermolecular M· · · Hi –Si interaction with significantly advanced transfer of H to M, more than in IMCIHB. It is interesting enough to compare dbr for complexes with the same formal order of a quasi-ring. Although it has been shown earlier 4 that dbr increases with the enlargement of the quasi-ring size in systems with either IMCIHB (the values of dbr for IMCIHBs forming 5-, 6-, and 7-membered quasi-ring are: 0.63–0.79˚ A, 1.22˚ A, and 1.43–1.81˚ A, respectively) or M· · · (Ha –C) agostic bonds (0.21–0.64˚ A, 0.87–1.11˚ A, and 1.12˚ A for β-, γ, and δ-agostic bonds, respectively), this effect is not observed for systems having ’agostic bonds’ of the M· · · (Ha –Si) type. This conclusion results from the fact that particularly low or high values

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of dbr can appear irrespectively of the formal order (type) of the quasi-ring. For example, although dbr in C21A, i.e., [CpCo(PH3 )(SiH3 )]+ , is 0.49˚ A only, it amounts to 1.21˚ A in T12A ([TiCl2 –SiH2 CH3 ]+ ). Similarly, dbr in T131 G ([TiCl2 –CH=CHSiH3 ]+ ) is 1.71˚ A, but only 0.54˚ A in T14G ([TiCl2 –CH2 CH2 SiH2 CH3 ]+ ). Also, for investigated systems having the M· · · (η 2 -SiH) interaction the range of dbr values is rather wide (0.43–1.32˚ A) with the lowest value for 3a’ (Bz(OC)2 Cr(H)(SiCl3 )) and the greatest for 1? a’ (MeCp(OC)2 Mn(H)(SiCl3 )). This shows that the BCPM···H · · · RCP distance is an individual topological feature of a system rather than necessarily results from the size of a quasi-ring. As a result of this analysis we conclude that systems with IMCIHB cannot be distinguished from other M· · · Ha –E (E = C, Si) interactions on the basis of dbr values due to, in general, their wide range. Although in many instances values of the electron density computed at relevant RCPs (ρr ) of systems possessing either M· · · (Ha –E) (E = C, Si) or M· · · (η 2 -SiH) interaction have been found to be greater than at RCPs formed by IMCIHBs (the ranges of ρr are 0.008–0.023 au, 0.029–0.080 au, 4 and 0.076-0.084 au for systems with IMCIHB, M· · · (Ha –C), and M· · · (η 2 SiH), respectively), the range of ρr values (0.014–0.093 au) for systems with M· · · (Ha –Si) overlaps with that for systems with IMCIHB. As a consequence, ρr is not characteristic for IMCIHBs. Nor is ∆ρbr , i.e., the difference of values of electron density at BCPM···H and RCP. The narrow range of ∆ρbr found for systems with IMCIHB (0.001–0.018 au) is enclosed in the very wide range for systems with either M· · · (H–Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions (0.001–0.122 au, see last column of Table 4). Curvatures of Bond Paths As already mentioned in Introduction, our recent studies have shown some substantial differences in positions of bond critical points of H· · · Al and M· · · Ha C interactions and curvatures of bond paths (BPs) tracing these interactions. 4 They have been demonstrated using three parameters describing the curvature of BP (see also Figure 3): ∆ld = (lH···BCP + lBCP···M ) − dH···M = lH···M − dH···M ≥ 0,

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(1)

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%HM = 100 µ ∆%HM = 100

dBCP···M , dH···M

¶ dH···BCP + dBCP···M −1 . dH···M

(2) (3)

Successively their meaning is as follows: ∆ld is the difference between the length of the H· · · M bond path and the H· · · M distance, %HM measures the BCP· · · M distance relative to the H· · · M distance, and ∆%HM describes the displacement of BCP relative to the line connecting H and M atoms. Values of ∆ld , %HM , ∆%HM , together with lengths of H· · · BCP and BCP· · · M parts of BPH···M (lH···BCP and lBCP···M , respectively) are listed in Table 5. Of course lH···BCP ≥ dH···BCP and lBCP···M ≥ dBCP···M , and, as a consequence, lH···M ≥ dH···M (i.e., ∆ld ≥ 0) since bond path is in general curved (see Figure 3). One can see that lH···BCP > lBCP···M for IMCIHBs, whereas the opposite relation, i.e., lH···BCP < lBCP···M , holds for both M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions. It has been shown earlier that the latter relation is also valid for M· · · (Ha –C) agostic bonds. 4,48,49,54 This result shows that BCP is somewhat closer to the metal atom (Al) in systems having IMCIHB, whereas this BCP is, instead, significantly closer to the agostic hydrogen is complexes with M· · · (Ha –C) agostic bonds, M· · · (Ha –Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions. This conclusion can be further supported by values of %HM . They are somewhat lower than 50 (47-48) for IMCIHBs, whereas they are clearly greater than 50 (55-64) in systems having M· · · (Ha –C) agostic bonds, 4 M· · · (Ha –Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions. The latter range of %HM values is even widened to 55-69 if results obtained by Tognetti et al. 49 are also taken into account. It is interesting to analyse values of ∆ld . The range found for IMCIHBs (0.008–0.063˚ A) overlaps with the range of ∆ld for M· · · (Ha –Si) and M· · · (η 2 -SiH) interactions (0.002– 0.049˚ A), therefore ∆ld does not characterize IMCIHB. It is worth mentioning, however, that the range of ∆ld found earlier for agostic bonds was significantly wider and shifted upward (0.031–0.118˚ A). 4 It shows that bond paths for M· · · (Ha –C) agostic bonds are considerably more curved than bond paths tracing IMCIHBs, M· · · (Ha –Si) ’agostic bonds’ or 17



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M· · · (η 2 -SiH) sigma interactions. Values of ∆%HM found for M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions together (0.0–1.0) are similar to those for IMCIHBs if only the 2s system is excluded (0.0–0.7). High value of ∆%HM obtained for 2s (2.1) causes that the range of ∆%HM for IMCIHBs significantly widens and becomes similar to that for M· · · (Ha –C) agostic bonds (0.1–2.2), 4 which is even wider if values of ∆%HM obtained by Tognetti et al. 49 are also taken into account (0–6). As a result we conclude that the ∆%HM parameter is not characteristic for IMCIHBs. Although the parameters shown in Table 5 describe both the position of BCP relative to the M· · · Ha/i direction and the length of BPM···Ha/i relative to the M· · · Ha/i distance, they, however, do not give a detail information on how the M· · · Ha/i bond path really looks like. Detailed insight into the route of the M· · · Ha/i bond path can, however, be made by drawing molecular graphs. They are displayed in Figure 4. Molecules having IMCIHB feature Hi · · · Al bond paths that are rather straight; however, concavity of BPHi ···Al towards RCP can easily be noticed in systems 2s, 2d, and 3ss. Curvatures of M· · · Ha/i bond paths in systems with either M· · · (Ha –Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions are quite similar, i.e., they are either rather straight (this particularly holds for systems having M· · · (η 2 -SiH) sigma interactions) or somewhat curved. Importantly, in the latter case, the curvature is, however, observed near the agostic hydrogen (see molecular graphs of T121 B and T131 G), whereas the M· · · Ha/i bond path is straight in the M· · · BCP section. Similar effect has also been observed for M· · · (Ha –C) agostic bonds, however, it has been much more pronounced. 4,48,49,54 This exemplary situation is shown in Figure 5 for 2s, T121 B, and [Co(Cl2 )C3 H7 ]2+ systems; the last one possessing γ-agostic bond. As a consequence of this analysis we conclude that IMCIHBs can be distinguished from M· · · (Ha –E) (E = C, Si) interactions on the basis of differences in curvatures of their Ha/i · · · M bond paths. It has been shown earlier 4 that in systems with IMCIHB some exchange-correlation

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functionals (e.g., B3LYP) can lead to Hi · · · Al bond path being significantly curved near the metal (aluminum) atom (see Figure 4 in ref 4). This curvature has not, however, been obtained if PBE0 was used. Instead, another topological dissimilarity has revealed. It is seen that, in the case of IMCIHB, the Si–Hi bond path is straight, whereas the Si–Ha/i bond path is significantly inwardly curved in some systems possessing the M· · · (Ha –Si) ’agostic bond’ (see, e.g., T12A, C21A or C22A) or the M· · · (η 2 -SiH) sigma interaction. Since this significant curvature of the Si–Ha/i bond path has not, however, been observed for all investigated systems possessing either the M· · · (Ha –Si) ’agostic bond’ or the M· · · (η 2 -SiH) sigma interaction (see, e.g., T12B, T13G, C141 D or 1b), its lack in systems with IMCIHB cannot characterize them. Electron Density Distribution in the M-Ha/i -Si Ring At present we briefly refer to fragments of a molecular graphs describing the M-Ha/i -Si ring in C21A, C22A, 1c, 1a’, 1? a’, 1c’, and 3a’ systems. As already mentioned, for example, systems C21A and C22A feature significantly inwardly curved BPSi−Ha . Moreover, the BCP of this bond path is close to the RCP of the M-Ha -Si ring (Figure 4). Similar situation occurs in systems 1c, 1a’, 1? a’, and 3a’, however, in all these systems the RCP of the M-Hi -Si ring is even closer to the BCP of the M· · · Si interaction. In their article devoted to a thorough examination of the electron density distribution in 1a’ (i.e., Cp(OC)2 Mn(H)(SiCl3 )) Bader and Matta 27 proclaimed that the close proximity of these three topological elements of the electron density distribution in the M-Hi -Si ring is a harbinger of the susceptibility to ring opening by rupture of either of these bond paths. Such a rupture of the M· · · Si bond really happens in 1a, 1b, 2a, 2b, 2c, and 3a as neither the M· · · Si bond path nor the RCP of the M-Hi -Si ring is present in all these systems. As already mentioned, these systems can thus be considered as having an intermolecular M· · · Hi –Si interaction rather that the M· · · (η 2 -SiH) sigma interaction; the former being somewhat similar to IMCIHB, although revealing much more advanced stage of the Hi transfer toward M.

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Conclusions and Future Perspectives Using large sets of systems possessing an intramolecular charge-inverted hydrogen bond (IMCIHB), M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction, we have compared both geometrical and QTAIM-based topological parameters characterizing all these three types of interactions. The main purpose of this comparative analysis was to see whether the previously found differences between IMCIHBs and M· · · (Ha –C) agostic bonds 4 are further applicable in the case of the other interactions involving the Si–H bond interacting with a transition metal atom. In particular, by utilizing various systems with the latter interaction, we could study diverse stages of oxidative addition of the silyl group to the metal moiety. At the beginning, we have used MeCp(OC)2 Mn(H)SiCl3 complex to compare our theoretical structures with experimental data. 23 We have shown that, although all used exchangecorrelation functionals have given excellent accordance with the experimentally determined structure, 23 PBE0 has performed the best (also for QTAIM calculations 34 ), whereas BP86 and B3LYP have performed the worst. As a consequence, PBE0 exchange-correlation functional has been used to present results for the other systems. It has been shown that for M· · · (Ha –Si) ’agostic bonds’ and M· · · (η 2 -SiH) sigma interactions values of geometrical parameters may change in very wide ranges, being much wider than for IMCIHBs. Hence, one cannot, in general, distinguish IMCIHBs on the basis of values of geometrical parameters only. It appears, however, that one can make such a distinction on the basis of the length of the Si–H bond, which is significantly less elongated in IMCIHBs than in either M· · · (Ha –Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions. We have shown that not only dSiHi , dM···Hi , and dM···Si , but also the Si-Hi -M angle is a good indicator of the strength of the M· · · (η 2 -SiH) bond. By comparison of M· · · (Ha –Si) with M· · · (Ha –C) agostic bonds we have shown that the former interaction leads to shorter M· · · Ha distances that results from more extensive elongation of the Si–Ha bond. Wide ranges of values of QTAIM-based parameters obtained for diverse M· · · (Ha –Si) and M· · · (η 2 -SiH) interactions (as well as for M· · · (Ha –C) agostic bonds) have brought about that 20


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some of those obtained earlier for IMCIHB are, in general, no longer characteristic. It has happened, for example, in cases of values of bond ellipticity at BCP and the electron density at the RCP. Also values of the BCP· · · RCP distance (dbr ) can change widely depending on the molecular system. Moreover, they do not necessarily increase with enlargement of a quasi-ring. On the contrary, IMCIHBs feature lesser values of the electron density at BCP than M· · · (Ha –Si) or M· · · (η 2 -SiH) interactions. Moreover, all curvatures (λ3 in particular) characterizing IMCIHBs are lower than those for either M· · · (Ha –Si) or M· · · (η 2 -SiH). It has also been shown that IMCIHBs can be distinguished from the other two types of interactions on the basis of values of delocalization index, which are significantly lower for IMCIHBs. Most importantly, even after the extension of our collection of investigated systems by those having either M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction, different positions of BCPs of these interactions relating to IMCIHB have been found to be still evident. Namely, the BCPHi ···M in IMCIHB is closer to the metal (aluminum) atom, whereas it is closer to the agostic/interacting hydrogen in the case of M· · · (Ha –E) (E = Si, C) and M· · · (η 2 -SiH) interactions. Moreover, if the bond path tracing M· · · (Ha –E) (E = Si, C) is curved, then this curvature appears near the agostic hydrogen – a property particularly pronounced in M· · · (Ha –C) agostic bonds. The results show that IMCIHBs feature several individual characteristics and should therefore be classified as a new type of interaction. It is likely that the differences in the positions of relevant BCPs result from different radii of aluminum and transition metal atoms as well as the lack of d-electrons in the former. As a consequence it would be interesting to compare both molecular structures and topological properties of electron density distributions of systems having either M· · · (Ha –Si) ’agostic bond’ or M· · · (η 2 -SiH) sigma interaction with those featuring IMCIHB of Si–H· · · Ga type.

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Acknowledgment Calculations have been carried out at the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM) at the University of Warsaw thanks to the G50-10 grant.

References (1) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: New York, 1990. (2) Popelier, P. L. A. Atoms in Molecules. An Introduction; Longman: Singapore, 2000. (3) Matta, C. F.; Boyd, R. J. The Quantum Theory of Atoms in Molecules; Wiley-VCH: Weinheim, 2007. (4) JabÃlo´ nski, M. QTAIM-Based Comparison of Agostic Bonds and Intramolecular ChargeInverted Hydrogen Bonds. J. Phys. Chem. A 2015, 119, 4993–5008. (5) JabÃlo´ nski, M. Binding of X–H to the Lone-Pair Vacancy: Charge-Inverted Hydrogen Bond. Chem. Phys. Lett. 2009, 477, 374–376. (6) JabÃlo´ nski, M. Intramolecular Charge-Inverted Hydrogen Bond. J. Mol. Struct: THEOCHEM 2010, 948, 21–24. (7) JabÃlo´ nski, M. Full vs. Constrain Geometry Optimization in the Open-Closed Method in Estimating the Energy of Intramolecular Charge-Inverted Hydrogen Bonds. Chem. Phys. 2010, 376, 76–83. (8) JabÃlo´ nski, M. Theoretical Insight into the Nature of the Intermolecular Charge-Inverted Hydrogen Bond. Comput. Theor. Chem. 2012, 998, 39–45. (9) JabÃlo´ nski, M.; Sokalski, W. A. Physical Nature of Interactions in Charge-Inverted Hydrogen Bonds. Chem. Phys. Lett. 2012, 552, 156–161. 22


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28


29


a

exp.a 1.79(4) 2.254(1) 1.47(3) 1.798(7) 1.790(6) 2.115(6) 2.140(6) 2.064(2) 2.053(2) 2.070(2) 41(1) 87.6(3) 113.3(2) 81.1(2) 75(2) 114(2) 117.46(8) 117.22(8) 113.95(8) 102.50(8) 100.87(8) 102.47(8) 92(1) 96(1) 154(1) – – – BP86 1.845 2.324 1.555 1.790 1.788 2.144 2.174 2.111 2.090 2.116 41.8 86.6 111.1 80.4 73.6 113.4 115.2 115.6 113.3 104.9 102.1 104.2 88.7 94.9 154.5 0.048 0.071 1.6

∆ 55 70 85 -8 -2 29 34 47 37 46 0.8 -1.0 -2.3 -0.7 -1.4 -0.6 -2.3 -1.7 -0.6 2.4 1.2 1.8 -3.3 -1.1 0.5 – – –

B3LYP 1.776 2.334 1.552 1.812 1.803 2.158 2.189 2.100 2.085 2.110 41.7 88.1 111.4 81.2 75.3 113.0 115.9 115.5 112.4 105.6 102.0 103.9 89.8 95.3 153.6 0.047 0.067 1.4

∆ -14 80 82 14 13 43 49 36 32 40 0.7 0.5 -1.9 0.1 0.3 -1.0 -1.6 -1.7 -1.5 3.1 1.1 1.4 -2.2 -0.7 -0.4 – – –

Experimentally determined values by Schubert et al. 23

Parameter Si–H Mn–Si Mn–H Mn–C1 Mn–C2 Mn–Cmin Mn–Cmax Si–Cl1 Si–Cl2 Si–Cl3 Mn–Si–H C1–Mn–C2 C1–Mn–Si C2–Mn–Si C1–Mn–H C2–Mn–H Mn–Si–Cl1 Mn–Si–Cl2 Mn–Si–Cl3 C11–Si–Cl2 C11–Si–Cl3 C12–Si–Cl3 H–Si–Cl1 H–Si–Cl2 H–Si–Cl3 RMS(bonds) RMS(bondsb ) RMS(angles) b

∆ PBE0 ∆ 10 1.798 8 50 2.291 37 74 1.544 74 -6 1.790 -8 -5 1.782 -8 12 2.117 2 16 2.142 2 27 2.085 21 22 2.070 17 28 2.093 23 1.0 42.2 1.2 -0.2 87.6 0.0 -1.8 112.0 -1.3 -0.6 80.1 -1.0 -0.8 74.2 -0.8 -1.2 112.5 -1.5 -1.8 115.6 -1.8 -1.7 115.7 -1.6 -0.9 113.0 -1.0 2.7 105.4 2.9 1.1 102.0 1.1 1.3 103.7 1.2 -2.5 89.6 -2.4 -1.3 94.5 -1.5 0.6 154.8 0.8 – 0.029 – – 0.048 – – 1.5 –

TPSSh 1.786 2.302 1.557 1.802 1.793 2.122 2.148 2.094 2.077 2.103 42.5 87.5 112.4 80.2 75.4 112.4 115.5 115.7 113.0 105.4 101.8 103.7 89.4 94.4 155.0 0.035 0.057 1.5

∆ -4 48 87 4 3 7 8 30 24 33 1.5 -0.1 -0.9 -0.9 0.4 -1.6 -1.9 -1.5 -1.0 2.9 1.0 1.3 -2.6 -1.6 1.0 – – –

M06L 1.776 2.293 1.569 1.803 1.788 2.110 2.132 2.080 2.060 2.090 43.1 87.1 112.5 78.4 75.7 110.1 115.2 116.1 112.1 106.1 101.9 104.0 89.4 94.2 154.7 0.035 0.062 2.1

∆ -14 39 99 5 -2 -5 -8 16 7 20 2.1 -0.5 -0.8 -2.7 0.7 -3.9 -2.3 -1.1 -1.9 3.6 1.0 1.6 -2.6 -1.8 0.7 – – –

M06 1.813 2.295 1.557 1.809 1.796 2.114 2.138 2.086 2.070 2.096 42.5 87.6 111.9 78.9 74.8 112.5 115.9 115.3 112.5 105.8 102.0 103.9 89.2 94.8 154.4 0.034 0.057 1.7 RMS for bonds forming the Mn–Hi –Si ring, i.e., Si–Hi , Mn–Si, and Mn–Hi .

B3PW91 1.800 2.304 1.544 1.792 1.785 2.127 2.156 2.091 2.075 2.098 42.0 87.4 111.5 80.5 74.2 112.8 115.6 115.6 113.1 105.2 102.0 103.8 89.5 94.7 154.6 0.033 0.052 1.5

∆ 23 41 87 11 6 -1 -2 22 17 26 1.5 0.0 -1.4 -2.2 -0.2 -1.5 -1.6 -1.9 -1.5 3.3 1.1 1.4 -2.8 -1.2 0.4 – – –

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1: Values of Geometrical Parameters for Cp(OC)2 Mn(H)(SiCl3 ) Shown in Figure 2. Bond Distances in ˚ A, Bond Angles in Degrees, Differences with Respect to the Experimental Values (∆) are Given in m˚ A and Degrees for Bond Distances and Bond Angles, Respectively

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Table 2: Values of the Most Important Geometric Parameters Relating to Intramolecular Charge-Inverted Hydrogen Bonds in Systems Shown in Figure 1 system 0 1a 2s 2d 3ss 3ds 3sd 4sss 4dss 4sds 4ssd 4dsd a

dSiH dSiHi 2 x 1.493 1.496 2 x 1.486 1.537 1.488; 1.487 1.532 2 x 1.488 1.532 1.487; 1.486 1.529 1.485; 1.489 1.535 1.488; 1.484 1.524 1.484; 1.490 1.527 1.484; 1.488 1.530 1.484; 1.489 1.518 1.487; 1.485 1.525 1.488; 1.483 1.533

dHi ···Al 3.28 2.28 2.08 2.03 2.00 1.96 1.99 1.98 1.92 1.98 1.95 1.93

dSi···Al 2.46 2.73 3.04 3.05 3.04 3.11 3.10 3.07 2.98 3.32 2.99 2.92

αSiHi Al 45 89 114 117 118 126 123 122 119 144 119 115

Somewhat more stable form with two Si–Hi · · · Al contacts (no bond paths) has also been obtained.

30


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

dSiH 1.483 2 x 1.475 1.478 1.473; 1.475 1.478 1.478; 1.481 1.473 2 x 1.474 1.475; 1.476 1.473; 1,478

1.472; 1.478 1.472 1.477; 1.479 2 x 1.477 1.473; 1.480

2 x 1.486 1.490 1.477; 1.481 1.481 1.480; 1.485 1.491; 1.496; 1.498 1.470; 2 x 1.487 1.501; 1.504; 1.511 — — —

1.477; 1.478; 1.483 1.468; 2 x 1.480 1.485; 1.488; 1.490

1.490; 2 x 1.501 —

system T12A T12B T13B T13G T14G T14D T121 B T131 G T141 D T142 D

C13G C14G C14D C131 G C141 D

C21A C22A C22B C23B C23G 1a 1b 1c 1a’ 1∗ a’ 1c’

2a 2b 2c

31


3a 3a’

1.737 1.774

1.623 1.604 1.708

1.696 1.721 1.673 1.686 1.608 1.773 1.555 1.822 1.801 1.798 1.829

1.725 1.735 1.847 1.739 1.739

dSiHa/i 1.640 1.614 1.632 1.571 1.580 1.585 1.541 1.563 1.551 1.595

1.614 1.601

1.569 1.600 1.528

1.593 1.575 1.575 1.569 1.581 1.549 1.654 1.557 1.543 1.544 1.551

1.512 1.500 1.477 1.519 1.486

dM···Ha/i 1.895 1.935 1.905 1.927 1.901 1.907 2.111 1.950 2.001 1.944

2.446 2.346

2.627 2.871 2.428

2.113 2.118 2.395 2.414 2.591 2.375 2.766 2.336 2.294 2.291 2.256

2.370 2.390 3.042 2.665 2.884

dM···Si 2.417 2.710 2.712 2.634 2.633 3.162 2.619 2.646 2.894 2.740

93.7 87.9

110.8 127.2 97.1

79.9 79.8 95.0 95.7 108.7 91.0 119.0 87.1 86.3 86.2 83.3

93.9 95.0 132.1 109.6 126.6

αSiHa/i M 86.0 99.2 99.9 97.2 97.9 129.5 90.3 97.1 108.4 101.0

-

-

133.0 77.0 77.6 108.5 -

78.6 78.3 107.6 104.7 123.3

αMEα Eβ 127.2 88.8 88.9 83.2 82.5 116.0 91.5 84.4 93.9 78.7

-

-

122.8 97.5 -

126.0 127.4 117.3 117.6 126.6

αEα Eβ Eγ 119.7 129.2 129.6 113.0 137.9 125.9 122.1

-

-

-

115.9 113.3 107.7

αEβ Eγ Eδ 111.5 113.0 113.5 134.1

-

-

95.8 94.2 105.3 -

99.9 98.0 98.5 97.3 94.0

αCSiHa 92.6 91.2 105.3 103.8 104.8 101.4 103.4 101.1 95.9

41.2 43.0

34.0 26.3 38.6

40.7 31.5 41.7 42.2 42.2 43.1

-

αMSiHi -

Table 3: Values of Some Chosen Geometric Parameters Characterizing Model Systems Shown in Figure 1 and Having Either M· · · (Ha –Si) (M = Ti, Co) ’Agostic Bonds’ or M· · · (η 2 -SiH) (M = Cr, Mn, Fe) Sigma Interactions

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Table 4: Values of Some Chosen QTAIM Parameters Characterizing Model Systems with IMCIHB, M· · · (H–Si) ’Agostic Bonds’ or M· · · (η 2 -SiH) Sigma Interactions System 2s 2d 3ss 3ds 3sd 4sss 4dss 4sds 4ssd 4dsd T12A T12B T13B T13G T14G T14D T121 B T131 G T141 D T142 D

ρb 0.024 0.025 0.026 0.028 0.026 0.027 0.030 0.025 0.029 0.030 0.062 0.057 0.062 0.053 0.057 0.054 0.038 0.051 0.043 0.052

∇2 ρ b 0.045 0.058 0.066 0.072 0.067 0.069 0.089 0.063 0.080 0.088 0.177 0.110 0.110 0.160 0.163 0.109 0.115 0.151 0.122 0.130

Hb -0.004 -0.004 -0.004 -0.004 -0.004 -0.004 -0.004 -0.003 -0.004 -0.004 -0.010 -0.010 -0.012 -0.006 -0.007 -0.009 -0.002 -0.005 -0.003 -0.007

−Gb /Vb 0.784 0.826 0.845 0.842 0.853 0.853 0.873 0.849 0.865 0.871 0.843 0.790 0.767 0.887 0.869 0.797 0.931 0.896 0.907 0.852

δ(H,M) 0.093 0.101 0.104 0.114 0.104 0.107 0.119 0.104 0.112 0.117 0.432 0.319 0.342 0.304 0.323 0.285 0.205 0.280 0.233 0.302

λ1 -0.018 -0.021 -0.021 -0.025 -0.020 -0.021 -0.027 -0.020 -0.024 -0.028 -0.089 -0.082 -0.091 -0.077 -0.084 -0.089 -0.038 -0.071 -0.055 -0.074

λ2 -0.005 -0.013 -0.016 -0.021 -0.018 -0.018 -0.024 -0.019 -0.022 -0.024 -0.029 -0.075 -0.085 -0.033 -0.040 -0.079 -0.029 -0.034 -0.043 -0.051

λ3 0.068 0.092 0.103 0.118 0.105 0.109 0.140 0.102 0.127 0.140 0.294 0.268 0.287 0.270 0.287 0.278 0.183 0.256 0.219 0.254

ε 2.481 0.584 0.307 0.181 0.125 0.190 0.138 0.048 0.101 0.169 2.120 0.091 0.076 1.309 1.092 0.133 0.318 1.098 0.266 0.462

dbr 0.63 0.79 1.22 1.22 1.22 1.74 1.81 1.43 1.63 1.69 1.21 0.70 0.76 0.95 0.54 1.15 1.01 1.71 0.92 1.22

ρr 0.023 0.022 0.016 0.015 0.015 0.011 0.012 0.008 0.012 0.014 0.061 0.042 0.043 0.044 0.045 0.014 0.036 0.043 0.025 0.040

∆ρbr 0.001 0.003 0.010 0.013 0.011 0.016 0.018 0.017 0.017 0.016 0.001 0.015 0.018 0.009 0.011 0.041 0.002 0.008 0.018 0.012

C13G C14G C14D C131 G C141 D

0.128 0.131 0.136 0.124 0.130

0.096 0.084 0.044 0.088 0.090

-0.076 -0.081 -0.089 -0.073 -0.080

0.568 0.557 0.529 0.565 0.562

0.742 0.752 0.773 0.718 0.729

-0.219 -0.230 -0.248 -0.208 -0.231

-0.189 -0.202 -0.240 -0.199 -0.219

0.504 0.516 0.532 0.495 0.540

0.164 0.142 0.033 0.046 0.051

1.29 1.21 1.35 1.11 1.30

0.060 0.059 0.015 0.037 0.019

0.068 0.072 0.122 0.087 0.111

C21A C22A C22B C23B C23G 1a 1b 1c 1a’ 1∗ a’ 1c’ 2a 2b 2c 3a 3a’

0.102 0.105 0.105 0.106 0.097 0.117 0.082 0.115 0.121 0.120 0.118 0.103 0.096 0.119 0.100 0.105

0.259 0.255 0.214 0.214 0.238 0.180 0.233 0.186 0.168 0.170 0.178 0.217 0.190 0.199 0.214 0.201

-0.044 -0.048 -0.050 -0.051 -0.044 -0.059 -0.028 -0.057 -0.063 -0.063 -0.060 -0.048 -0.043 -0.063 -0.040 -0.044

0.713 0.699 0.675 0.673 0.703 0.637 0.755 0.645 0.625 0.626 0.635 0.680 0.679 0.641 0.700 0.682

0.679 0.703 0.641 0.651 0.604 0.700 0.502 0.692 0.665 0.661 0.673 0.636 0.545 0.753 0.621 0.598

-0.122 -0.133 -0.144 -0.147 -0.134 -0.186 -0.116 -0.175 -0.194 -0.193 -0.186 -0.155 -0.144 -0.182 -0.140 -0.150

-0.069 -0.086 -0.125 -0.128 -0.121 -0.157 -0.086 -0.153 -0.164 -0.162 -0.158 -0.134 -0.133 -0.163 -0.123 -0.132

0.451 0.474 0.483 0.489 0.493 0.523 0.436 0.515 0.526 0.525 0.522 0.506 0.468 0.544 0.477 0.483

0.755 0.537 0.157 0.152 0.103 0.188 0.353 0.144 0.183 0.189 0.172 0.158 0.078 0.117 0.134 0.135

0.49 0.56 0.85 0.85 1.21

0.093 0.091 0.065 0.064 0.038 no RCP no RCP 0.077 0.083 0.084 0.083 no RCP no RCP no RCP no RCP 0.076

0.008 0.015 0.040 0.042 0.060

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1.29 0.77 1.32 0.71

0.43

0.038 0.037 0.037 0.036

0.029

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Table 5: Atomic Charges of H and M and Curvature of H· · · Al and H· · · M Bond Paths Tracing IMCIHBs, M· · · (H–Si) ’Agostic Bonds’ or M· · · (η 2 -SiH) Sigma Interactions system 2s 2d 3ss 3ds 3sd 4sss 4dss 4sds 4ssd 4dsd T12A T12B T13B T13G T14G T14D T121 B T131 G T141 D T142 D

q(H) -0.725 -0.724 -0.741 -0.739 -0.738 -0.743 -0.758 -0.738 -0.754 -0.762 -0.608 -0.623 -0.619 -0.653 -0.657 -0.669 -0.681 -0.655 -0.675 -0.624

q(M) 2.262 2.278 2.266 2.267 2.277 2.265 2.272 2.261 2.284 2.284 1.704 1.968 1.967 1.884 1.883 1.949 1.950 1.912 1.937 1.915

lH···BCP 1.147 1.093 1.073 1.034 1.056 1.052 1.020 1.029 1.037 1.030 0.818 0.822 0.796 0.854 0.823 0.792 0.994 0.876 0.888 0.836

lBCP···M 0.998 0.961 0.949 0.936 0.947 0.945 0.915 0.954 0.929 0.918 1.095 1.121 1.114 1.103 1.097 1.119 1.166 1.110 1.136 1.121

∆ld 0.063 0.027 0.024 0.014 0.017 0.017 0.014 0.008 0.018 0.017 0.016 0.009 0.005 0.031 0.020 0.005 0.049 0.036 0.024 0.014

%HM 48 47 47 48 48 48 48 48 48 48 57 58 58 57 58 59 55 57 57 58

∆%HM 2.1 0.7 0.5 0.3 0.3 0.3 0.3 0.0 0.3 0.3 0.3 0.2 0.1 0.8 0.5 0.1 0.9 1.0 0.5 0.2

C13G C14G C14D C131 G C141 D

-0.336 -0.327 -0.250 -0.326 -0.310

0.939 0.930 1.009 1.011 1.010

0.556 0.547 0.561 0.576 0.557

0.960 0.958 0.920 0.963 0.958

0.005 0.005 0.004 0.006 0.010

63 64 64 63 64

0.2 0.2 0.0 0.1 0.0

C21A C22A C22B C23B C23G 1a 1b 1c 1a’ 1∗ a’ 1c’ 2a 2b 2c 3a 3a’

-0.446 -0.429 -0.505 -0.502 -0.579 -0.397 -0.621 -0.368 -0.290 -0.292 -0.314 -0.553 -0.520 -0.510 -0.478 -0.351

0.287 0.264 0.624 0.623 0.623 0.801 1.216 0.551 0.796 0.795 0.584 0.804 1.123 0.520 0.984 0.980

0.646 0.624 0.611 0.608 0.615 0.570 0.652 0.576 0.576 0.564 0.581 0.595 0.614 0.563 0.615 0.620 33

0.966 0.959 0.973 0.970 0.979 0.983 1.015 0.986 0.981 0.981 0.983 0.986 0.993 0.972 1.006 0.988

0.019 0.009 0.010 0.009 0.014 0.005 0.014 0.006 0.002 0.002 0.003 0.012 0.008 0.008 0.008 0.007

60 61 61 61 61 63 61 63 63 63 63 62 62 63 62 62

1.0 0.5 0.1 0.1 0.0 0.1 0.1 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.1



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Figure 1: Geometries of investigated model systems with intramolecular charge-inverted hydrogen bonds of the Si–H· · · Al type, M· · · (H–Si) ’agostic bonds’ (M = Ti, Co) or M· · · (η 2 SiH) sigma interactions (M = Cr, Mn, Fe). Colours of atoms are as follows: H, gray; C, black; Si, blue; Al, magenta; Cl, green; P, orange, O, dark blue; Ti, dark red; Co, light red; Mn, brown; Fe, golden; Cr, greenish. 34


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Figure 2: Atom labeling in MeCp(OC)2 Mn(H)(SiCl3 ) used for the test of exchangecorrelation functionals presented in Table 1.

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Figure 3: Parameters describing the curvature of the H· · · Al/M bond path and the position of BCP.

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Figure 4: Molecular graphs of investigated model systems with intramolecular chargeinverted hydrogen bonds, M· · · (H–Si) ’agostic bonds’ or M· · · (η 2 -SiH) sigma interactions. Colours of atoms are as follows: H, gray; C, black; Si, blue; Al, magenta; Cl, green; P, orange; O, dark blue; Ti, dark red; Co, light red; Mn, brown; Fe, golden; Cr, greenish. Bond critical points are shown by red small balls,37 ring critical points by yellow small balls, and cage critical points by green small balls.



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Figure 5: Comparison of curvatures of Hi/a · · · M bond paths in 2s having IMCIHB, T121 B having Ti· · · (Ha –Si) ’agostic bond’, and [Co(Cl2 )C3 H7 ]2+ having Co· · · (Ha –C) agostic bond. Length of Hi/a · · · BCP bond path is in red, length of Hi/a · · · BCP distance in black, difference of both in blue.

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Graphical TOC Entry

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Geometry- and QTAIM-Based Comparison of Intramolecular Charge

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