Does metallophilicity increase or decrease down group 11? Computational investigations of [Cl–M–PH3]2 (M = Cu, Ag, Au, [111])

The electronic and geometric structures of Cl–M–PH3 and [Cl–M–PH3]2 (M = Cu, Ag, Au, [111]) have been studied computationally using post Hartree–Fock ab initio and density functional methods.

The trends in r(M–Cl) and r(M–P) in the monomers are discussed in the light of previous studies.

Previous MP2 data on the metallophilic interactions in [Cl–M–PH3]2 (M = Cu, Ag, Au) are reproduced (to within basis set differences), and new MP2 data for the transactinide element 111 are presented.

QCISD and coupled cluster calculations on the title systems are reported for the first time, and reveal that, contrary to the MP2 results, the strength of the metallophilic interaction essentially decreases as group 11 is descended.


“Metallophilic” interactions-the attractions between formally closed shell metal ions in compounds, archetypally a pair of Au(i) cations-are well established.1–14

Theoretical work in this area was pioneered by Pyykkö, who used Hartree–Fock (HF) and perturbation theory (MP2) methods to study the aurophilicity (metallophilicity between gold atoms) in [X–Au–PH3]2 dimers, where X is one from a range of groups such as the halogens, methyl and SCH3.4,5

The structure studied in most detail was the C2 symmetric arrangement shown in Fig. 1a, in which the P1–Au1–Au2–P2 dihedral angle is fixed at 90° in order to zero the leading dipole–dipole term between the two monomers, and hence to allow more unencumbered focus on the aurophilicity.

Pyykkö's calculations were extremely revealing.

At the HF level the monomer interaction energy curves are repulsive; an aurophilic attraction only manifests itself when electron correlation is introduced at the MP2 level.

It was therefore concluded that aurophilicity is due to electron correlation (or, put another way, van der Waals or dispersion forces), and also that the attraction is strengthened by relativistic effects.

The latter issue was revisited by Pyykkö in 1997,6 when it was concluded that relativistic effects are important but not dominant.

For example, a 27% increase in the interaction energy of two Cl–Au–PH3 monomers was found on going from a non-relativistic to a relativistic Au pseudopotential using monomer geometries optimised at the relativistic level.

If non-relativistic monomer geometries are used, the use of a relativistic pseudopotential in the interaction energy calculation produces only a 15% relativistic energy enhancement.

Further insight has more recently been gained from the work of Schütz, Werner et al.,7,10 which focuses on the use of the local MP2 (LMP2) approach.

The target systems were once again dimers of the form [X–M–PH3]2, where X = H, Cl and M = Cu, Ag and Au.

The LMP2 method has three advantages over more traditional MP2 implementations.

First, there is a substantial reduction in the computational cost, second, basis set superposition error (BSSE; a potentially very significant problem in theoretical studies of metallophilicity) is much reduced and, finally, LMP2 offers the possibility to decompose local correlation energies into different excitation classes.15

Magnko et al. confirmed what Pyykkö et al. had discovered previously, that the strength of the metallophilic interaction in [Cl–M–PH3]2 (M = Cu, Ag, Au) increases as the metal becomes heavier, by approximately 50% from Cu (ca. 22 kJ mol–1) to Au.

The LMP2 analysis revealed that the interaction between the monomers has several components, and that the relative magnitude of these changes quite significantly as group 11 is descended.

Electron correlation is not purely attractive; intramolecular correlation contributions (double excitations localized on one monomer) are repulsive, ca. 30–50% of the total LMP2 interaction energy.

Furthermore, the attractive intermolecular correlation contributions arise from both van der Waals and ionic excitations, with the latter being 60–100% of the former at reqm.

Perhaps most interestingly, the attractive part of the correlation does not arise solely from M(d10)–M(d10) interactions.

Pure Au(5d)–Au(5d) pair correlation amounts to no more than 35% of the total LMP2 attraction in [Cl–Au–PH3]2, and this decreases to only 13% in the analogous Cu compound.

Pair correlations involving only one or neither M(d10) centre make up the bulk of the attractive part of the correlation; for Cu, pair correlations involving neither Cu(3d10) centre are the leading term.

Schwerdtfeger and co-workers have recently examined metallophilicity using traditional MP.29,12

In 2001, they focused on cuprophilicity in [Me–Cu–X]2, where X is a range of σ and π (donor or acceptor) ligands.

They concluded that cuprophilicity is very sensitive to the choice of basis set, and that relativistic effects are important, even for Cu, for the accurate calculation of geometries and interaction energies.

As before, the Cu–Cu interaction curves were found to be repulsive at the HF level but attractive at MP2, the attraction being sensitive to the nature of X (σ donor/π acceptor ligands favour cuprophilicity).

In general, cuprophilic interactions were found to be weak; attractive by only up to 12 kJ mol–1.

It is clear that metallophilicity in group 11 has been extensively investigated over the past decade, and important progress has been made.

To the best of our knowledge, however, previous work has focused almost exclusively on the MP2 approach.

Pyykkö et al. used MP2, MP3 and MP4(SDQ) to study [H–Au–PH3]2 and [Cl–Au–PH3]2, extending their [H–Au–PH3]2 calculations to the CCSD and CCSD(T) levels.6

They found that the values of the interaction energy oscillated quite strongly as the higher level methods were introduced, and noted “this area will require further investigation”.

Magnko et al. acknowledge a potential problem with the MP2 approach, i.e. that it overestimates van der Waals attractions, and state “our MP2 results for the interaction energies….may well be too large by anything between 0 and 25%”.

We therefore felt that there was scope to explore metallophilicity in these group 11 dimers using methods beyond MP2.

To that end we report in this contribution the results of our studies into [Cl–M–PH3]2 (M = Cu, Ag, Au, [111]), using HF, MP2, QCISD and coupled cluster approaches.

We have also conducted density functional theory calculations.

While we acknowledge that, as Magnko et al. note, “van der Waals like attraction cannot be reliably described with current DFT schemes”, we were interested to see how DFT techniques fare in the metallophilicity arena.

DFT has a reputation for producing the correct answer for unreliable reasons.

As a final extension of previous work, we were keen to probe the metallophilicity in [Cl–[111]–PH3]2 ([111] = element 111), i.e. to study all four members of group 11.

It is now well established that there are four rows of the d-block, and we are currently embarking on an investigation of the chemistry of the transactinide (6d) elements.

The first results of this investigation are reported here.

Computational details

Codes employed

All calculations were performed using the Gaussian 9816 and MOLPRO 2002317. program suites.

The approach typically taken was to initially optimise the geometry of the [Cl–M–PH3] monomer using Gaussian 98 (gradients are not available in MOLPRO for pseudopotential basis sets).

For the higher level ab initio methods, we then encountered problems when performing calculations on the dimeric systems using Gaussian 98, as we frequently came up against the 16 GB limit on the scratch files (under 32-bit linux for Intel).

For the calculations of the metallophilic interaction (method described more fully in the main text) we therefore used the MOLPRO code.

This package seems to generate smaller scratch files for a given calculation, and we have also found that it is appreciably faster than Gaussian 98 for closed shell QCISD and couple cluster calculations (by up to a factor of 10).

In all post-Hartree–Fock calculations, the lowest 16 (monomer) and 32 (dimer) molecular orbitals were not included in the correlation window.

Basis set superposition errors have been accounted for using the counterpoise correction.

Basis sets

The choice of basis sets is important in all quantum chemistry, but particularly so when studying metallophilicity (a combination of the inherent weakness of the effect and the potential for BSSEs).

Pyykkö et al. found that, when studying [X–M–PH3]2 (X = H, Cl; M = Cu, Ag and Au) at the MP2 level, 19 valence electron pseudopotentials should be used for the metals.6

They also found that, for Au at least, diffuse s, p and d functions were not required in the valence basis set, but that two f polarisation functions were needed (one compact and one diffuse).

A DZP valence basis plus accompanying pseudopotential was employed for the non-metallic elements.

Not surprisingly, more recent studies have employed bigger basis sets.

The LMP2 work of Schütz, Werner et al. employed correlation consistent basis sets for the non-metallic elements, together with more extended metal basis sets than used by Pyykkö.

The Cu bases used by Schwerdtfeger et al. were also reasonably large.

In the present study we were of course conscious of the desirability of using the biggest possible basis sets, but that this must be weighed against the feasibility of performing QCISD and coupled cluster calculations, particularly geometry optimisations.

For the bulk of our work we have therefore used the following combination of basis sets, designated basis α.

The 6-31G** basis sets have been used for Cl, P and H. For Cu, Ag and Au we followed Pyykkö’s procedure of supplementing the relativistic Stuttgart 19 valence electron pseudopotentials and accompanying valence basis sets (Cu;18 Ag and Au19) with two f polarisation functions.

The more diffuse f function was obtained by maximising the MP2 polarisability of the monocation, while the more compact f function was chosen so as to minimise the total CCSD(T) energy of the neutral atom.

The f exponents obtained in this manner are given in Table 1.

For [111] we used the relativistic pseudopotential and accompanying basis set devised by Seth et al.20

As this basis set already contains f polarisation functions, we did not alter it in any way.

Unless otherwise stated, all calculations have been performed with basis α.

In order to gauge the effect of basis set size on our results, we have conducted some MP2 and CCSD(T) single point calculations using bigger basis sets.

Basis β includes the same metal basis sets as basis α, except that the 2f functions for Cu, Ag and Au given in Table 1 were replaced with the 3f2g functions of .ref. 10

For P and Cl, the basis set was improved to 6-311G*, while that for H was unaltered.

Finally, basis γ is the same as β, but with the P and Cl basis sets improved to 6-311+G*.

For Au and [111] we have also performed some comparative non-relativistic calculations.

For Au, the non-relativistic pseudopotential and valence basis set of Schwerdtfeger et al21. was employed, supplemented by two f functions obtained as described above for the relativistic case (yielding α = 0.22 and 1.17).

For [111], the non-relativistic pseudopotential and basis set (including f polarisation functions) of Seth et al20. was employed.

Results and discussion

Cl–M–PH3 (M = Cu, Ag, Au, [111])

The geometry of the Cl–M–PH3 monomer was optimised for each of the methods employed, and the structural data are collected in Table 2, together with those from previous studies.

Although no symmetry constraints were applied, the Cl–M–P angle optimised to very close to 180° in all cases.

It may be seen that there is very little variation in the P–H distances and H–P–M angles, maximum differences being 3 pm and 2° across all of the molecules and methods.

By contrast, there is much greater variation in the M–Cl and M–P distances.

For Cu and Ag, the HF values are significantly larger than those obtained from the correlated methods, although this difference diminishes as the metal becomes heavier.

Among our data, MP2 gives the shortest M–Cl and M–P distances for all metals, the bond lengths increasing in the order MP2 < QCISD ≤ CCSD.

For Cu, Ag and Au at the CCSD(T) level, r(P–H) and ∠H–P–M are essentially identical to the CCSD values.

This is also the case for the metal–ligand bond lengths in Cl–Au–PH3, although slightly larger (0.01–0.02 Å) differences are found for the Ag and Cu systems.

We were unable to obtain a fully converged CCSD(T) geometry for Cl–[111]–PH3.

Some of the r(M–Cl) and r(M–P) data are plotted in Fig. 2.

The deviation between the non-relativistic QCISD and MP2 values of r(M–Cl) and r(M–P) and their relativistic counterparts increases very significantly as the metal becomes heavier, with the relativistic bond lengths being much shorter than the non-relativistic. For element 111, the difference between non-relativistic and relativistic r([111]–Cl) is ca. 30 pm, while that for r([111]–P) is as much as 60 pm.

The shortening of bond lengths upon the inclusion of relativistic effects is well established,22,23 though the differential effect of relativity on r(M–Cl) and r(M–P) in the present calculations deserves comment.

There is a striking difference between the trends in relativistic r(M–Cl) and r(M–P) for the heavier metals.

For both r(M–Cl) and r(M–P) there is a significant increase from Cu to Ag (c.

20 pm).

For r(M–Cl), changing from Ag to Au and [111] produces almost no difference.

By contrast, there is a marked contraction in r(M–P) from Ag to [111], by c.

10–15 pm, depending on the computational method.

This difference between the trends in r(M–Cl) and r(M–P) has been noted and studied previously by Bowmaker et al. for M = Ag and Au,24 and these workers put forward two possible explanations.

The first, based on earlier work by Schwerdtfeger et al.,21 centres on the role of the metal’s valence ns atomic orbital.

The direct relativistic contraction of valence s and, to a lesser extent, p atomic orbitals is well documented (although its source is often misunderstood21,25,26).

The relativistic bond length contraction in Cl–M–PH3, the argument goes, will be larger when there is appreciable ns character to the bonding.

Thus for a completely ionic M+X bond, there will be no ns character and hence no relativistic contraction (indeed, there might be a slight increase in the bond length, on account of the indirect relativistic expansion of the valence d orbitals).

The contraction will progressively increase, for a given metal, from M+X through M–X to MX+, as the population of the M ns increases from formally 0 to 2.

As can be seen from the Mulliken charges given in Table 3, the M–Cl bond is certainly more ionic in the ClM+ sense than is the M–P (as expected given the relative electronegativity of Cl and P).

Thus the r(M–Cl) contraction should be less than that of r(M–P), as is indeed observed.

The problem with this argument, as indeed was noted by Bowmaker et al., is that the relativistic contraction of atomic orbitals and bond lengths have been shown to be two parallel but largely independent effects.

It is now more than 20 years since evidence was presented to suggest that relativistic bond length contractions are due to reduction of the kinetic repulsion between two atoms; the effect is seen even when non-relativistic atomic orbitals are employed in conjunction with a relativistic Hamiltonian.22,27

In the light of this argument, it is difficult to feel entirely comfortable with the ns explanation, notwithstanding that it accounts for the observed bond length variations.

A second explanation, also put forward by Bowmaker et al., involves changes in M–P backbonding.

Relativistic effects destabilise valence d orbitals, and thus should enhance π back-donation from the M nd orbitals to the PH3 group, strengthening (and presumably shortening) the M–P bond.

As shown in Table 4, the relativistic destabilisation of the [111] 6d atomic orbitals is larger than that of the 5d in Au, and hence it might be expected that π back-donation would be largest in Cl–[111]–PH3.

Table 4 also gives non-relativistic and relativistic metal ndπ populations in Cl–M–PH3.

The relativistic values for Cu and Ag, and the non-relativistic values for Au and [111], are very close to 4.0 for all methods, suggesting very little π back-donation in these cases.

By contrast, the relativistic values for Au, and particularly [111], are significantly smaller than the non-relativistic, by ca. 0.25 e in the [111] calculations.

This suggests that there may be well be some π back-donation in Cl–Au–PH3, with an increased effect in Cl–[111]–PH3.

As with the first explanation, the computational data lend weight to the π backbonding argument.

However, a significant relativistic bond length contraction has been found previously in [111]H,28 in which there cannot be any metal-ligand π effects.

This would suggest that enhanced π back-donation is unlikely to be the sole source of the relativistic M–P bond length contractions in Cl–Au–PH3 and Cl–[111]–PH3, although it may have a role.

Perhaps one needs to look no further than the original paper of Ziegler et al. These workers found that the relativistic bond length contraction decreased in the order Au2 > AuH > AuCl, and noted “the smallness of relativistic effects in AuCl compared to Au2 and AuH, is probably due to the fact that this compound is much more ionic than the other two, so that the valence orbitals are largely concentrated on the Cl centre, where relativistic effects are substantially smaller than on Au”27.

[Cl–M–PH3]2 (M = Cu, Ag, Au, [111])

Full optimisations: the role of structures 1b and 1c

When studying metallophilicity in [X–M–PR3]2, it has become traditional to adopt the following procedure.

The geometry of the monomer is first optimised using the favoured method (usually MP2 or B3LYP).

Subsequently, a series of single point calculations is performed on a dimeric system in which each monomer is held fixed at its previously optimised geometry.

The two monomers are oriented at a P1–M1–M2–P2 dihedral angle of 90°, as shown in Fig. 1a and discussed in the Introduction, and r(M–M) is varied.

At each value of r(M–M), a counterpoise corrected single point calculation is performed, and the results used to generate a metallophilic interaction energy curve.

We have also adopted this procedure, and the results are discussed below in section B(ii).

Before addressing these data, however, it is worth taking a moment to emphasise that this 90° orientation is not the most stable structure for these compounds.

The 90° orientation is chosen so as to minimise the dipolar interactions between the monomers, and if the restriction to P1–M1–M2–P2 = 90° is lifted, the molecules relax to an orientation in which this angle tends to 180°, as shown in Fig. 1b.

Table 5 contains the r(M–M), P1–M1–M2–P2 and interaction energy data for [Cl–M–PH3]2 (M = Cu, Ag, Au, [111]), optimised solely within the constraint of C2 symmetry.

Comparison of Table 5 with Table 6 (which contains analogous data for the systems restricted to 90°) reveals that in all cases the relaxation of the 90° restriction produces larger P1–M1–M2–P2, significantly bigger interaction energies and, in almost all cases, smaller r(M–M).

This illustrates the need for the 90° restriction when studying metallophilicity in these systems; without it, the dipolar interactions dominate.

It should also be noted that, for Cu and Ag, even the Fig. 1b structure is not the most stable.

For these metals the most stable structure is that shown schematically in Fig. 1c.

We calculate this Cl-bridged structure to be 69 (61) and 84 (50) kJ mol–1 more stable than 1b for Cu and Ag respectively at the MP2 (B3LYP) level.

By contrast, we could not locate an analogous structure using relativistic methods for Au and [111].

Structure 1c has been studied previously for the group 11 metals.12,29–31

El-Bahraoui et al. conducted a topological analysis of ρ(r) in [Cl–Cu–PH3]2, and concluded that there is no clear Cu⋯Cu interaction in this structure, on the basis of the absence of a bond critical point between the metal atoms.

Liu et al. noted that 1b is the favoured structure for [Cl–Cu–NH3]2 on account of significant intramolecular H-bonding, but that replacement of NH3 by PH3 reduces the H-bonding to the point at which 1c becomes the most stable geometry.

Very recently Schwerdtfeger et al. located structure 1c for non-relativistic gold, (relativistic gold optimised to structure 1b, as in our calculations).

These workers also report that structure 1c was located for Cu and Ag, and note that, for [X–M–PR3]2 (M = Cu, Ag, Au) “the gold compounds seem to polymerise with linear [X–M–PR3] chains at a P–Au–Au–P torsion angle of 90° thus maximising the aurophilic interaction, while the corresponding copper and silver compounds oligomerise with PR3 ligands attached to M2X2 units with bridging ligands X such as Cl or Br”.

In this context, the size of the R group in [X–Au–PR3]2 clearly influences the relative stabilities of structures 1a and 1b; large R favour 1a and optimum metallophilicity.

90° optimisations


We now turn to our calculations in which the P1–M1–M2–P2 dihedral angles are fixed to 90° (structure 1a).

The r(M–M) and interaction energies (Eint) are collected in Table 6, together with data from previous MP2 studies, and some of these data are also shown in Fig. 3.

In all cases bar [Cl–[111]–PH3]2 at the CCSD(T) level, our basis α (see Computational Details) results are obtained from calculations in which the method used to calculate Eint is the same as that used to optimise the geometry of the monomer.

As it proved impossible to fully converge the geometry of Cl–[111]–PH3 at the CCSD(T) level, we have used the CCSD monomer geometry to obtain the CCSD(T) r(M–M) and Eint data for [Cl–[111]–PH3]2.

We believe that very little error will be introduced by this approach, given the almost identical CCSD and CCSD(T) geometries of the Cu, Ag and Au monomers (Table 2).

Table 6 reveals that there is effectively no metallophilic interaction at the HF level.

This is well known, and was first pointed out by Pyykkö more than a decade ago.4,5

The inclusion of electron correlation through the use of post-HF techniques, however, changes the picture markedly, with very significant decreases in r(M–M) and concomitant increases in Eint.

As is best illustrated by Fig. 3a, there is a general trend to increasing r(M–M) as group 11 is descended.

Among the post-HF methods, the MP2 approach produces the shortest r(M–M) in all cases bar Cu (for which the CCSD(T) value is smallest).

The QCISD and CCSD data are very similar to one another, which is not surprising given the methodological similarities,32 with the CCSD(T) values being slightly shorter than the QCISD and CCSD for a given metal.

The MP2 and LMP2 values of Magnko et al10. are smaller than our ab initio data, probably as a result of the use of bigger basis sets in these calculations.

Although the trend in the MP2 r(M–M) values from Cu → [111] is broadly similar to the QCISD and coupled cluster data, the increase in MP2 r(M–M) with increasing metal atomic number is not as pronounced.

Thus, while the r(Ag–Ag) values for MP2 and CCSD differ by 0.14 Å, the difference in the corresponding r([111]–[111]) data is 0.5 Å.

The difference between the MP2 and the other post-HF methods is even more noticeable in Eint (Fig. 3b).

Our basis α MP2 calculations predict an almost uniform increase in Eint from [Cl–Cu–PH3]2 to the transactinide system, from –13.5 to –32.0 kJ mol–1.

The trend in the MP2 and LMP2 data of Magnko et al. for Cu, Ag and Au is similar.

However, the trend in the QCISD and coupled cluster Eint values is quite different.

There is a small increase in Eint from Cu → Ag, but then there is a decrease from Ag → [111].

Eint for [Cl–Cu–PH3]2 at the MP2 and CCSD(T) levels is very similar (–13.5 vs. –15.3 kJ mol–1) but for the transactinide system the MP2 value is three times the CCSD(T).

The discrepancy between the MP2 and the other post-HF data is significant for two reasons.

First, as we are seeking information about the trend in metallophilicity as group 11 is descended, it is of concern that the conclusion from the MP2 data is exactly the opposite to that from the QCISD and coupled cluster approaches, at least as far as Eint is concerned.

QCISD and coupled cluster theory predict that Eint decreases from Ag → [111] whereas MP2 predicts the reverse.

Second, the vast majority of the previous work in this area has been done using variants of the MP2 approach, i.e. using the method which, using basis α at least, is inconsistent with the other post-HF techniques.

In order to determine the extent to which the discrepancy in the basis α Eint trend between MP2 and the other post-HF techniques is a consequence of the different geometries obtained by the different methods, we have calculated the MP2, CCSD and CCSD(T) Eint values at the QCISD minimum energy structures.

The results are shown in Fig. 4, together with the QCISD data for comparison.

It can be seen that there is little difference between the QCISD//QCISD and the CCSD//QCISD Eint data, which is not surprising given the similarities between the methods noted earlier.

The CCSD(T)//QCISD Eint values for Au and [111] are also quite similar to the CCSD(T)//CCSD(T) ones in Fig. 3b, the values being slightly less negative at the QCISD geometries, as expected.

The MP2//QCISD Eint value for [Cl–Cu–PH3]2 is very similar to the MP2//MP2.

For [Cl–M–PH3]2 (M = Ag, Au and [111]), the MP2//QCISD Eint values are less negative than the MP2//MP2 by several kJ mol–1, but the general trend in the MP2//QCISD data is the same as that for the MP2//MP2, i.e. the metallophilic interaction increases down group 11.

This is once again at odds with the other post-HF techniques.

In order to probe the extent to which our conclusions are dependent upon basis set size, we have conducted additional MP2 and CCSD(T) calculations using larger basis sets (β and γ, see Computational Details).

As geometry optimisations would be prohibitively costly using these bigger basis sets, we have confined ourselves to single point calculations at the basis α geometries.

For Cu, Ag and Au, the basis γ MP2 Eint values are 3–4 kJ mol–1 more negative than the basis α data, i.e. the trend to larger Eint with increasing atomic number persists at this level of theory.

Unlike our basis α data, however, the value of basis γ Eint for the [111] compound is essentially the same as for Au, i.e. the trend to increasing Eint as the metal becomes heavier is interrupted at [111] for the larger basis set.

By contrast to the MP2 data, the CCSD(T) single points using the larger basis sets do not change the trend in Eint as group 11 is descended.

There remains an increase in Eint from Cu → Ag for both bases β and γ, followed by a slight reduction to Au.

This reduction continues to [Cl–[111]–PH3]2 at basis β.

So does the metallophilic interaction energy increase or decrease down group 11?

MP2 is generally regarded as the least accurate of the post-HF techniques we have used.32

Indeed, for a system which is well defined by a single reference wavefunction, the CCSD(T) approach should be close to the full CI limit for the basis set employed.

The T1 diagnostic values for the CCSD(T)/basis α calculations at the maximum Eint structures are 0.030, 0.017, 0.017 and 0.014 respectively for the Cu, Ag, Au and [111] dimers.

The limit above which there may be appreciable multi-reference character to the wavefunction is generally taken to be 0.02, so we can see that with the exception of the Cu dimer, all of our systems are below this limit (perhaps the Cu dimer breaks the Eint trend from [111] → Au → Ag because it may not be as well-defined by a single reference).

This suggests that the Ag, Au and [111] coupled cluster data should be reliable, and we are therefore inclined to conclude that the strength of the metallophilic interaction decreases from [Cl–Ag–PH3]2 to [Cl–[111]–PH3]2.


As noted in the introduction, van der Waals-like interactions cannot reliably be described by current density functional approaches;10 indeed, Pyykkö writes that “the dispersion-type, R–6 terms resulting from the dipole-dipole Hamiltonian in second order, are not explicitly included in the derivation of DFT”.3

Nevertheless, out of curiosity we have studied structure 1a using two of the most common DFT approaches, the pure DFT BP86 method and the hybrid B3LYP variant.

The calculation of r(M–M) and Eint was done in the same way as for the ab initio calculations described above, and the results are given in Table 6 and Fig. 3.

We do not wish to dwell overly on these data, but note that the DFT values are not significantly out of step with the ab initio results.

The BP86 calculations produce a negative interaction energy between the two [Cl–M–PH3] monomers in all cases, the value of which decreases down group 11, as is the case for all of the post-HF methods bar MP2.

B3LYP produces smaller Eint values than any of the other methods, but the lack of a converged structure for the transactinide dimer precludes any conclusions as to the trend in Eint down group 11.

It would therefore appear that DFT can reproduce metallophilic interactions, at least in the present systems, although the reasons why are not clear.

Summary and conclusions

In this contribution we have reported the results of ab initio and density functional calculations of Cl–M–PH3 (M = Cu, Ag, Au, [111]) monomers and dimers.

The key conclusions may be summarised as follows.

For the monomers there is an increase in r(M–Cl) and r(M–P) between M = Cu and Ag.

As M changes to Au and [111], r(M–Cl) remains essentially constant while r(M–P) decreases significantly.

Evidence is found to support previous explanations based on (a) metal ns populations and (b) M → P π backdonation, but we cannot state categorically which, if either, explanation is correct.

The effects of relativity on r(M–Cl) and r(M–P) for the heavier group 11 elements are very significant, 30 and 60 pm respectively for M = [111] (the relativistic bonds being the shorter).

For the dimers, the most stable structure for M = Cu and Ag is that shown schematically in Fig. 1c.

For M = Au and [111], structure 1b is the most stable.

Notwithstanding these observations we, like many previous workers, have analysed the metallophilic interactions between the two monomers oriented as in structure 1a.

In agreement with previous results, we find that there is essentially no metallophilic interaction at the Hartree–Fock level.

The inclusion of electron correlation at the MP2 level generates significant metallophilicity, which increases steadily down group 11 from –13.5 kJ mol–1 for [Cl–Cu–PH3]2 to –32 kJ mol–1 for [Cl–[111]–PH3]2 at the basis α level.

This trend has also been found previously from MP2 calculations.

By contrast, including electron correlation through the QCISD and coupled cluster approaches changes the trend in metallophilic interaction down group 11.

QCISD, CCSD and CCSD(T) calculations all suggest that [Cl–Ag–PH3]2 has the strongest metallophilic attraction, and that the interaction weakens from Ag → Au → [111] (e.g. from –16.7 kJ mol–1 in [Cl–Ag–PH3]2 to –11.2 kJ mol–1 in [Cl–[111]–PH3]2 at the CCSD(T)/basis α level).

Increasing the size of the basis set does not qualitatively change the CCSD(T) results.

We conclude that metallophilicity is weaker in [Cl–[111]–PH3]2 than in any of the lighter group 11 analogues, and suggest that MP2 may not be the most appropriate technique for the study of this effect.