Agostic Bond

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List of participants[edit]

Carlos Martín Fernández, KU Leuven.[edit]


Ferran Feixas, Universitat de Girona[edit]


Henry Rzepa, Imperial College London[edit]

slides: DOI:b9r9

David L. Cooper, University of Liverpool[edit]


The term agostic interaction was proposed by Brookhart and Green [1] to "refer specifically to situations in which a hydrogen atom is covalently bonded simultaneously to both a carbon atom and to a transition metal atom." The word agostic is derived from the Greek word αγοστος which occurs in Homer and translates as to "clasp" or "hold to oneself".

The agostic interaction can be seen as an intermediate between a compound with a metal-alkyl bond and an alkylidene hydride, as shown in Fig. 1. This is one of the main reasons behind the fact that this kind of interaction appears numerous times in reaction mechanisms involving C-H bond activation.

Fig. 1 β-Agostic interaction as an intermediate between two structures

Some characteristics of the agostic interactions are:

  1. Low 1H-NMR field shifts.
  2. C-H bond lengthening.
  3. Reduced νC-H stretching frequencies.
  4. Short M-H distance.

Usually, agostic interactions are classified as α, β, γ... depending on the length of the chain of C atoms connecting the metal and the interacting CH group, as shown in Fig. 2.

Fig. 2 The common nomenclature of agostic interactions.

Some interesting reviews have been published in the past years, that deserve some careful reading. [2] [3] [4] [5]

Although there is a large amount of effort in trying to understand this kind of interaction/bond better, it is very challenging to do so. It is so weak that depending on the method you might or might not get a good geometry or wavefunction that will have the proper characteristics of an agostic interaction. And there has been some debate also on how to characterize different but similar CH→M interactions, such as agostic, anagostic, hydrogen bonds... Doing a careful review of the literature on this topic is, then, a challenge on its own.

Some calculations on a real system: (dmpe)Cl3TiEt[edit]

Carlos (talk): I have run some calculations on model complex (dmpe)Cl3TiEt (Fig. 3), which is a classic β-agostic complex. The structure was optimized at M06/def2TZVPP level of theory, and all calculations have been run with the same geometry/functional/basis set unless noted otherwise.

Fig. 3 The complex studied


From the structure it is clear that the agostic interaction causes a number of distortions. Firstly, the Ti-C-C angle is only 84.6°, which is very distorted from an expected angle of ∼109° of a tetrahedral C atom. Also the C-Hagost length is 1.123 Å, as compared to the 1.089 Å of the C-Hnon-agost. Finally, the distance between the Ti atom and the Hagost is 2.083 Å.


Another charateristic of the agostic interaction is that the C-Hagost stretching mode will be red shifted. And we can clearly see from our calculations that νC-Hagost is shifted to ∼2755 cm-1, while the other C-Hnon-agost show a symmetric and antisymmetric mode at 3072 and 3140 cm-1, respectively.

Agostic C-H stretching mode

Electron density shifts[edit]

I have also calculated the intramolecular electron density shift as proposed by Sánchez-Sanz and co-workers[6] (Fig. 4), and we can see the results in Fig. 5. It is clear from this figure that there is an increase in electronic density between the metal atom and the Hagost one. Also, we can see that the dmpe ligand does not seem to play an important role for the agostic interaction. Using this approach, we can also estimate the interaction energy, and we obtain an Eint ≈ 23 kJ/mol. This partition scheme is interesting because it can be used to compute interaction energies from the isodesmic reaction. One of the issues related to this partition, though, is that it is not feasible for α-agostic interactions.

Fig. 4 Partition scheme used for the calculation of intramolecular EDS.
Fig. 5 Intramolecular electron density shift (±0.001 a.u. isosurfaces). Blue and yellow colors correspond to negative and positive values of the electron density, respectively.


Usually a bond (even a weak one, such as a hydrogen bond) is associated with the existence of a bond path, and we can explain its nature by looking at certain properties at the bond critical point (BCP). However, the agostic interaction is tricky to study with this technique. The absence of a BCP in some agostic interactions has been explained before (look at the review by Scherer and McGrady[5], particularly Fig. 10) by the merging of the RCP and BCP, and they can be borderline systems of a bond catastrophe. In fact, if we compare the M06/def2TZVPP and B3LYP/def2TZVPP//M06/def2TZVPP we can see that in the M06 case we obtain no BCP, but we obtain it using B3LYP functional (Fig. 6). In any case, we can see a clear difference in densities with the C-H bonds for both cases. Using the M06 density, for C-Hagost we obtain ρBCP = 0.254 au, while for C-Hnon-agost we obtain ρBCP = 0.279 au. With the B3LYP density we also obtain a BCP between Ti and H, which presents ρBCP = 0.035 au. If we look at the electron density contours (Fig. 7), we can see that the overall description of the density is quite similar in both cases, with the exception of the appearance or not of a BCP. Are we again in a situation where Bond Critical Points are not really "critical" for agostic bonding?[7]

Fig. 6 Molecular graphs for the Ti complex using M06 or B3LYP functionals, with the M06 geometry. Note the RCP very close to the BCP (for the B3LYP case), which can cause the so-called bond catastrophe.
Fig. 7 Density isocontours using different functionals. Are BCPs really critical for agostic interactions?[7]


If we look at the NCI calculation, we can see clearly (Fig. 8) that the agostic interaction appears as a clear attractive interaction between the metal and H. However, it is also close to a repulsive area probably from the C atom. Note that this repulsive area only appears on the side of the alkyl chain, but if one rotates the molecule and looks at it from the metal "point of view", it looks attractive. Is this an artifact of the representation method? Also, it is noticeable (from the color scheme) that the agostic interaction looks as strong (blue) as the P-Ti bonds... All the connections with the Ti atom have been removed for the sake of clarity

  • --Henry (talk) 08:48, 12 August 2017 (CEST)The interactive NCI depiction looks great! I notice that it loads a cube density file and then produces an NCI iso-surface. The cube file is 4.3 Mbyte in size (1.6 Mbyte if gzipped, which I think JSmol supports?). One can select just the isosurface and express that as a .jvxl file, which I find is just 20 Kbyte in size. For those whose bandwidth is perhaps a bit slower, this latter file would load far faster than the cube file. And one can then use much higher resolution cube files to generate the .jvxl. Just a suggestion!
  • --CarlosMF (talk) 19:09, 16 August 2017 (CEST) I tried to do it using an .jvxl file, but I could not manage and that is why I used the .cube... If someone manages to work it out with the .jvxl (s)he is most welcome to edit the page!
  • --CarlosMF (talk) 11:19, 19 August 2017 (CEST) I have managed finally with the jvxl, but I have the feeling it still takes a bit of time to load, so I am not sure if something is wrong...

Fig. 8 3D plot of the NCI calculation


I have run some NBO calculations, in which the agostic interaction can be seen by looking at different parameters. Firstly, by looking at the occupation numbers of the NBOs it is clear that the σC-Hagost has a smaller occupation than the σC-Hnon-agost. And if we look at the perturbative treatment of the orbital interactions (that can account for processes like charge transfer), we can see the main transfers from the BD(C-Hagost) orbital are to the BD*(Ti-P) or LP*(Ti) orbitals.

  • CAUTION! By running calculations with different basis sets and different versions of the NBO program, one can get a similar result in terms of the different populations of the σC-H orbitals, but the E(2) analysis can be very different, particularly in determining the nature of the acceptor orbital. See table below.
  • Note that in their book "Valency and Bonding: A Natural Bonding Orbital Donor Acceptor Perspective", the NBO developers have a section devoted to agostic interactions (section 4.7.2, page 483), where in their calculation of YH2Et shows the agostic charge transfer as σC-H → n*Y. "The leading σCH→nY∗ NBO interaction associated with agostic distortions is shown in Fig. 4.56. As indicated, second-order perturbation theory suggests that this interaction stabilizes the structure by ∼9 kcal mol−1, easily surmounting the normal ∼3 kcal mol−1 barrier to eclipsing."
Comparison of NBO calculations with M06 functional NBOs
NBO version Basis set Donor (occupation) Acceptor (occupation) Agostic E(2) in kcal/mol BD (C-H) → LP* (Ti)
NBO 3.1 6-31G BD C-H (1.88301) LP* Ti (0.18384) 40.55
Tiagost nbo2.png
6-31+G(d,p) BD C-H (1.83360) LP* Ti (0.21532) 57.14
6-311G BD C-H (1.90861) BD* Ti-P (0.12239) 14.20
6-311+G(d,p) BD C-H (1.82713) LP* Ti (0.22099) 64.25
def2TZVPP BD C-H (1.82269) LP* Ti (0.21635) 59.34 BD (C-H) → BD* (Ti-P)
NBO 6.0 6-31G BD C-H (1.92007) BD* Ti-P (0.11394) 12.26
Tiagost nbo1.png
6-31+G(d,p) BD C-H (1.87547) BD* Ti-P (0.13104) 25.32
6-311G BD C-H (1.90962) BD* Ti-P (0.12639) 14.64
6-311+G(d,p) BD C-H (1.87877) BD* Ti-P (0.13149) 24.71
def2TZVPP BD C-H (1.90922) BD* Ti-P (0.12868) 15.05


In Fig. 10 we can see the representation of the ELF calculation. There is a clear difference between the Hagost and the Hnon-agost. Actually, it has been reported[8] [9] that the ELF signature of agostic hydrogens is: 1. Metal QTAIM basin contribution to V(H,..)) population which ranges between 0.02 to 0.3 e. 2. The covariance matrix element of the V(H,..) and C(M) population < -0.02.

Fig. 10 ELF calculation
    • I would be happy if someone could run an ELF calculation on this complex, as it might help in giving a more complete picture of the interaction.
    • --Henry (talk) 09:36, 10 August 2017 (CEST) Re: ELF, do you have the .wfn file available for analysis?
    • --CarlosMF (talk) 14:34, 10 August 2017 (CEST) ELF calculations are being run by prof. B. Silvi, so hopefully he will post something about the results he obtains shortly.
    • --Henry (talk) 08:33, 11 August 2017 (CEST)The ELF does indeed show an interesting difference. Has the .wfn file been uploaded to the Wiki perchance? I ask because it would be good to have the volume and integrations of the basins as a quantitive measure of the difference.
    • --CarlosMF (talk) 14:13, 11 August 2017 (CEST) The wfn file at the M06/def2TZVPP level has been uploaded to in case anyone wants to run calculations on it
    • --CarlosMF (talk) 14:57, 11 August 2017 (CEST) The output from the ELF is in Since I do not know much about the interpretation of the ELF results, I very much appreciate all possible comments.
    • --Henry (talk) 07:21, 12 August 2017 (CEST)The ELF analysis of the wavefunction follows that of the NBO partition. Hagostic has a basin integration of 1.95e and a volume of 50.0 (the smaller volume is very apparent from the figure above). The non-agostic hydrogens have integrations of 2.00 and volumes of 76 - 77.5.
    • --Henry (talk) 07:21, 12 August 2017 (CEST)Bernard (Silvi): a question for you. The .wfn file provided for us was calculated using the Def2-TZVPP basis, which includes f-functions. I used TopMod09 for the analysis, which thinks this wavefunction has a pseudopotential. Might it be that the f-functions are confusing it? The results above used a WFN file recalculated using the 6-311G(d,p) basis instead[10], which does not use a pseudopotential for the Ti. The population file provided by Bernard (I think using a more recent version of Topmod?) returns values of 1.95 and 2.05 for the populations and 48/64-67 for the volumes, showing the results are mildly basis-set dependent.

CSD Search[edit]

--Henry (talk) 11:20, 10 August 2017 (CEST)

Fig. 11. Search of CSD for agostic interactions
Fig. 12. Search of CSD for agostic interactions
Here is a search of the CSD (Cambridge structure database) for agostic interactions as defined by this search query.[11] Here, the sub-structure is (any)metal-C(4-coordinate)-C(4-coordinate)-H. There is a distinct cluster revealed with metal-C-C angles < 90°, similar to the angle noted above, which shows how common the β-effect is (Figure 11).
Figure 13. Expansion of figure 12.
In Fig. 12, you can see that the lower angles tend to be associated with shorter metal-H distances, and signs of a separate cluster with M...H distances of about 2.0Å, as is the case for the system above. There are 23 hits when this distance is constrained to < 2.3Å and in close up some interesting strong interactions are revealed, ripe perhaps for further exploration (Fig. 13).
Fig. 14. Search of CSD for β and γ agostic interactions
Here is a plot (Figure 14) that include both β and γ interactions. The red circles are possible γ effects, whilst the green circle contains the β interactions.

Other C-H→M interactions[edit]

Over the last years, some differences have been noted for certain C-H→M contacts, prompting new (improved?) definitions of the agostic interaction nad/or the other interactions. For instance, in their 2007 review[4], Brookhart, Green and Parkin make a difference between "agostic" and "anagostic" interactions:

CH→M interactions
Agostic Anagostic
3c2e interaction largely electrostatic interaction
d(M-H) ≈ 1.8 - 2.3 Å d(M-H) ≈ 2.3 - 2.9 Å
M-C-H ≈ 90 - 140° M-C-H ≈ 110 - 170°
δH upfield of uncoordinated CH δH downfield of uncoordinated CH

But in a rather recent paper[8] it has been argued that there are two kinds of anagostic interactions (H-anagostic and C-anagostic), and also it is argued that the traditional agostic (what they call η2(C,H) form) can be "regarded as a balanced symmetrical hybrid of the basic H- and C-anagostic forms".

--Henry (talk) 11:35, 11 August 2017 (CEST)[edit]

I have calculated the NMR shieldings for the complex, using the same method as you do, but adding CDCl3 as solvent to make it more realistic. The chemical shift of the agostic proton is ~4.73 ppm, whilst the other two protons attached to this carbon come at 1.15 and 1.47 ppm[12]. Thus the agostic proton is downfield with respect to the non-agostic protons. According to the classification above (which I think is too simplistic), this is an anagostic interaction?

--CarlosMF (talk) 18:48, 18 August 2017 (CEST) Crabtree's "Organometallic Chemistry" book (2005, 4th edition, page 58) states that "These agostic alkyls can be detected by X-ray or neutron crystal structural work and by the high-field shift of the agostic H in the proton NMR. The lowering of the J (C,H) and ν(CH) in the NMR and IR spectra, respectively, on binding is symptomatic of the reduced C−H bond order in the agostic system." I guess high-field and upfield should mean the same?

Possible questions for discussion[edit]

  1. Agostic "bond" vs. agostic "interaction"
  2. Should only CH→M interactions be considered agostic? Or also for other cases with different σ bonds (BH, CC, SiH...)?
  3. Should (and how) agostic interactions be taken into account for "electron counting" in organometallic complexes?
  4. How to quantify the strength of an agostic interaction?

--Henry (talk) 09:03, 12 August 2017 (CEST)[edit]

Figure 15. Crystal structure search for β-agostic interactions from B-H bonds
Here is a possible insight into M-C-B-H β-agostic interactions (Figure 15) obtained from a crystal structure search. It shows two interesting clusters at low angles at the α-C, the second with very short M...H distances. This suggests that the B-H...M agostic interaction might be stronger than for C-H bonds.

--Henry (talk) 09:13, 12 August 2017 (CEST)[edit]

Figure 16. Crystal structure search for β-agostic interactions from Si-H bonds
Figure 16 shows the results for M-C-Si-H systems. The red hot-spot occurs at an angle at C of ~90°, but there is a smaller cluster at angles of almost 70° with shorter M...H distances which suggest these examples are well worth exploring!

--Henry (talk) 11:10, 13 August 2017 (CEST)[edit]

Figure 17. B-H...metal β-agostic interaction
Here are some wavefunctions for S-H[13] and B-H systems[14] (Fig 17.)

Comment on using signs of 3-centre indices[edit]

David L. Cooper:

Ferran Feixas demonstrated the use of 3-centre electron sharing indices (3c-ESI) to distinguish between agostic, anagostic and hydrogen bonding. Given that a simple 3-centre 3-orbital Hückel-like model predicts positive bond indices for 3c-2e and negative values for 3c-4e bonding motifs [15], it does indeed follow that we could expect positive 3c-ESI for 3c-2e agostic bonding and negative 3c-ESI for 3c-4e hydrogen bonds (with 3c-ESI values close to zero for anagostic interactions).

Without wishing to detract in any way from this work, it could be useful to add a word of caution about the use of the signs of 3-centre bond indices to distinguish between 3c-2e and 3c-4e bonding: there are certainly situations for which the predictions of the simple 3-centre 3-orbital Hückel-like model can prove misleading. One such example is a recent study [16] of the bonding in a recently synthesized neutral complex of so-called zero-valent beryllium that features a central C-Be-C unit [17]. A combination of domain-averaged Fermi hole analysis and various multicentre bond indices confirms the anticipated dominance of 3c-2e π bonding in the central C-Be-C fragment, reinforced by two donor-acceptor Be-C σ bonds, but it also reveals the presence of 3c-4e σ bonding [16]. It is important in the present context to point out that the contributions from the 3c-2e π and 3c-4e σ bonding to the total 3-centre bond index are both positive in this particular system [16], contrary to the expectations of the simple 3-centre 3-orbital Hückel-like model [15]. Closer inspection shows that a more appropriate model for the 3c-4e σ bonding should in fact involve four orbitals, rather than three, with the central atom contributing to the multicentre bonding not just by one orbital but by two. It does indeed turn out that a simple 3-centre 4-orbital Hückel-like model can rationalize the observation of a positive contribution from the 3c-4e σ bonding to the overall 3-centre bonding index.

When using the signs of 3c-ESI values to distinguish between different bonding patterns it could be important to bear in mind that the predicted sign of the 3c-4e bond index can change if a simple 3-centre 4-orbital Hückel-like model is more appropriate than the usual one that is based on just 3 orbitals.

Relevant references[edit]

  1. Brookhart, M.; Green, M. L. H. Carbon-hydrogen-transition metal bonds. J. Organomet. Chem., 1983, 250, 395-408. DOI:10.1016/0022-328X(83)85065-7
  2. Clot E.; Eisenstein O. (2004) Agostic Interactions from a Computational Perspective: One Name, Many Interpretations. In: Principles and Applications of Density Functional Theory in Inorganic Chemistry II. Structure and Bonding, vol 113. Springer, Berlin, Heidelberg. DOI:10.1007/b97940
  3. Lein, M. Characterization of agostic interactions in theory and computation. Coord. Chem. Rev., 2009, 253, 625-634. DOI:10.1016/j.ccr.2008.07.007
  4. 4.0 4.1 Brookhart, M.; Green, M. L. H.; Parkin, G. Agostic interactions in transition metal compounds. PNAS, 2007, 104 (17), 6908-6914. DOI:10.1073/pnas.0610747104
  5. 5.0 5.1 Scherer, W.; McGrady, G. S. Agostic interactions in d0 Metal Alkyl Complexes. Angew. Chem. Int. Ed., 2004, 43, 1782-1806. DOI:10.1002/anie.200200548
  6. Sánchez-Sanz, G.; Trujillo, C.; Alkorta, I.; Elguero, J. Electron density shift description of non-bonding intramolecular interactions. Comp. and Theor. Chem., 2012, 991 (1), 124-133. DOI:10.1016/j.comptc.2012.04.007
  7. 7.0 7.1 Lane, J. R.; Contreras-García, J.; Piquemal, J-P.; Miller, B. J.; Kjaergaard, H. G. Are Bond Critical Points Really Critical for Hydrogen Bonding?. J. Chem. Theory Comput., 2013, 9 (8), 3263–3266.DOI:10.1021/ct400420r
  8. 8.0 8.1 Lepetit, C.; Poater, J.; Esmail Alikhani, M.; Silvi, B.; Canac, Y.; Contreras-García, J.; Solà, M.; Chauvin, R. The Missing Entry in the Agostic-Anagostic Series: Rh(I)-η1-C Interactions in P(CH)P Pincer Complexes. Inorg. Chem., 2015, 54(6), 2960-2969. DOI:10.1021/acs.inorgchem.5b00069
  9. E-L. Zins, B. Silvi, M.E. Alikhani, Phys. Chem. Chem. Phys, 2015, 17, 9258-9281, DOI:10.1039/c4cp05728g
  10. For wavefunction and ELF analysis, see DOI:10.14469/hpc/2889
  11. H. S. Rzepa, 2017, DOI:cbp3
  12. H. S. Rzepa, 2017, DOI:cbqz
  13. H. S. Rzepa, DOI:cbr6
  14. H. S. Rzepa, DOI:cbr5
  15. 15.0 15.1 Ponec, R.; Mayer, I. Investigation of some properties of multicenter bond indices. J. Phys. Chem. A, 1997, 101, 1738-1741. DOI:10.1021/jp962510e
  16. 16.0 16.1 16.2 Ponec, R.; Cooper, D. L. Insights from domain-averaged Fermi hole (DAFH) analysis and multicenter bond indices into the nature of Be(0) bonding. Struct. Chem., 2017, 28, 1033-1043. DOI:10.1007/s11224-017-0914-2
  17. Arrowsmith, M.; Braunschweig, H.; Ali Celik, M.; Dellermann, T.; Dewhurst, R. D.; Ewing, W. C.; Hammond, K.; Kramer, T.; Krummenacher, I.; Mies, J.; Radacki, K.; Schuster, J. K. Neutral zero-valent s-block complexes with strong multiple bonding. Nature Chem., 2016, 8, 890-894. DOI:10.1038/nchem.2542