Study of ligand effects in aurophilic interactions using local correlation methods †

In this study, we present a series of calculations on Au(I) dimer complexes, investigating the interactions in play through the use of local correlation methods. The focus is placed on the impact of ligand effects in the interaction energy. Aurophilicity (the interaction between the closed shell Au(I) cationic centers) is commonly considered to be the major driving force for dimer formation. However, our calculations show that weak interactions between ligands can dominate even in relatively small complexes. This, in turn, can lead to an ambiguous ordering of the metallophilicity of Group 11 elements. We propose an unbiased separation of the metal–metal interaction through the use of local correlation and orbital population analysis. The latter reveals a constant energy profile for a variety of complexes which could in turn be used for the analysis of d–d interactions in more complex systems.


Introduction
It has been well established over the last few years that Au(I) d 10 complexes can interact strongly, resulting in the formation of dimers or even oligomers with relatively short Au-Au distances. 1,24][5] Similar complexes have also been observed or studied for Cu(I) and Ag(I) or even other ions with closed d 10 shells (e.g., Pt(0)), hence the term ''metallophilicity'' has been coined.
The nature of aurophilicity has been strongly debated ever since the pioneering theoretical study by Hoffmann and co-workers on Au(I)-Au(I) interacting complexes. 6Extended Hu ¨ckel calculations carried out at the time attributed the unusual interaction to the hybridization between the filled 5d and the empty 6s/6p shells of gold.Several years later, the first wave function calculations were performed. 7Pyykko ¨and Zhao studied a C 2 symmetric (ClAuPH 3 ) 2 model dimer, oriented so as to zero the leading dipole-dipole term and effectively single out the aurophilic interaction.Their study showed that at the Hartree-Fock level of theory no stable minimum could be found and only when including correlation effects could a favorable interaction be observed.This ruled out hybridization as the driving force behind aurophilicity.Relativity also plays a role, as it leads to a contraction of the electronic shells.In the same model system, it has been found to impact the well depth by about 20-30%. 8,9ne of the difficulties in addressing aurophilicity is the relatively high level of theory required to quantitatively describe the effect.][12] In the case of Møller-Plesset perturbation theory, the results tend to oscillate on going up the series from second-to fourthorder.Coupled cluster singles and doubles with perturbative triples (CCSD(T)) calculations have shown that MP2 tends to overestimate the interaction. 8The general profile, however, tends to be the same, revealing a R À6 dependence at large distances.This would fall in agreement with a dispersion-type interaction.
Theoretical studies of aurophilic systems have mainly focused on the total potential energy profile and on determining the Au-Au contact distances.3][14] Such studies have confirmed the decisive role of Au-Au dispersion interactions for the stability of such aggregates, while the ligand effect on the total interaction profile was deemed small.This is particularly clear in the study by Magnko et al., 13 where the interaction between X-M-PH 3 dimers (with X = H, Cl and M = Cu, Ag, Au) was investigated.The computed well depth of the Cl-Au-PH 3 dimer was À34.8 kJ mol À1 , with an Au-Au distance of 3.025 Å.At this distance, the main orbital contributions to the correlation energy (and, henceforth, dimer stabilization) are due to orbital pairs involving the gold d-shell.However, such conclusions have been mostly based on studies of small dimers.For larger complexes, the ligands could also contribute to the dimer formation as the two monomers approach and other interactions become significant.In the same study, it was shown that correlation contributions involving exclusively ligand orbitals can have a much more dominant role in Cu(I) and Ag(I) complexes.This is due not only to the weaker metal-metal interaction, but also to the smaller dimer distances, which allow for closer contacts between the ligands.
The effect of electronic correlation and the interplay between Au-Au contacts and other weak interactions involving the ligands are the focus of this work.All structures included in our study are based upon bicoordinated complexes with the general formula Cl-Au-L.The ligands (L) used in this work are given in Fig. 1.We start with a benchmark of the electronic structure methods to be used by revisiting the potential energy profile of the Cl-Au-PH 3 dimer.We then proceed to look into Au(I) complexes with an N-heterocyclic carbene (NHC), namely imidazol-2-ylidene (NHC-H) and a phosphonium ylide with the formula C(PH 3 ) 2 .The (Cl-Au-L) 2 dimers with the aforementioned ligands are short-to long-ranged, which enables us to inspect the relative weights of the interactions for different interaction strengths and distances.The dimer orientations are shown in Fig. 2. The effect of varying ligands in aurophilic complexes has been recently studied in detail by Muniz et al., 15 but some aspects of the interaction were left unclear, particularly, the relative weight of d 10 -d 10 interactions and how it changes between different complexes and/or orientations.We find that this is a particularly important gap for our understanding of this class of complexes.
We also look in depth into another NHC complex, ClAu-[1-(benzyl)-3-(N-tert-butylacetamido)imidazole-2-ylidene], which will be referred to as Cl-Au-(NHC-B).The complex was synthesized by Ray et al. 16 and the crystal structure clearly identified strong dimer interactions.The silver complex was also synthesized.Somewhat surprisingly, the argentophilic interactions were deemed stronger than the aurophilic interactions.This is in line with the theoretical studies of O'Grady and Kaltsoyannis, 11 which on the basis of CCSD(T) calculations deemed Cl-Ag-PH 3 to be more strongly interacting than Cl-Au-PH 3 .One of our goals is also to clarify the observed trend, and thereby contribute to the ongoing debate around metallophilic d 10 -d 10 interactions.

Method
8][19] This class of methods allows for reduced computational costs, but also gives the possibility of analyzing molecular interactions at the correlated level.Since dispersion is a major feature of aurophilic complexes, and exclusively a result of electronic correlation, these stand as a useful tool for analyzing this particular type of systems.Given that we are interested in separating the effect of ligands from the Au-Au interactions, a further challenge is posed.Common intermolecular energy decomposition tools such as SAPT 20 only allow for a global monomer-monomer analysis.No distinction is made between the role of particular atoms within the monomers.In the case of local correlation methods such as LMP2 and LCCSD, it is possible to decompose the energy into pairs (or single orbitals) which are localized in a given region of the monomer.Therefore, it is possible to some extent to differentiate between different components of a dimer with the general formula (Cl A -Au A -L A )(Cl B -Au B -L B ).If the same ligands are used, the obvious choice would be to separate the dimer interaction into 6 classes, each computed as with X, Y = Au, Cl or L. Each DE refers to the correlation component of the interaction energy between two fragments  XÁ Á ÁY of the system.The problem remains on how to separate the different components, given that Au shares a covalent bond with both Cl and L. In the spirit of the Natural Population Analysis (NPA) criteria for orbital domains, 21,22 we make use of orbital NPA charges to split the interaction.Consider an orbital i shared between L and Au.Any interaction correlation energy term involving this orbital will be fractioned according to how the orbital charge is divided through the atoms in L and Au.The charge in a given atom A is determined according to where the matrix V is the transformation matrix from Natural Atomic Orbitals (NAOs) to the local occupied orbitals and D ˜rr is the occupation number for a given NAO r. 22 The sum over j only runs over occupied indices.The interaction energy obtained from a covalent bonding orbital i at the correlated level is then split, the fraction belonging to the Au atom is determined as The remaining fraction is attributed to the fragment L. In the most simple case where an orbital has a domain strictly located within a fragment the interaction energy does not need to be partitioned.
In the following calculations, extensive use was made of density-fitted local second order Møller-Plesset perturbation theory (DF-LMP2) 23 together with local coupled cluster singles and doubles with perturbative non-iterative triples (DF-LCCSD(T0)) calculations. 24When duly noted, spin component scaling was applied to the DF-LMP2 energies (DF-SCS-LMP2), as proposed by Grimme and co-workers. 25We have chosen the latter method since it allows for a straightforward correction of MP2 energies directly at the pair energy terms which are used in our decomposition.Since density fitting approximations were used throughout, we will from here on forward drop the prefix 'DF-'.In all local correlation calculations, the occupied orbitals were Pipek-Mezey localized. 26The orbital domains were determined according to the NPA criteria, 22 with T NPA = 0.03.In the case of local coupled cluster calculations, all intermolecular orbital pairs have been treated as strong pairs 19 and are, therefore, fully included in the coupled cluster treatment.
Density functional theory (DFT) calculations were also carried out, with and without dispersion energy corrections, 27 by the use of the BP86, 28,29 B3LYP 30 and PBE 31 functionals.In the DFT energy calculations the def2-TZVPP basis set was used (including the ECP60MDF pseudopotential for Au). 32,33n wave function calculations, the Dunning aug-cc-pVTZ orbital basis set 34,35 was used in combination with the aug-cc-pVTZ-PP basis and ECP60MDF pseudopotential 36,37 for Au (this basis will be referred to as AVTZ).An alternative set without diffuse functions was also applied (cc-pVTZ and cc-pVTZ-PP for Au) and will be referred to as VTZ.The density fitting basis used were the corresponding defaults (for the aug-cc-pVTZ and aug-cc-pVTZ-PP basis) 38,39 except for SCF calculations with Au where the JKFIT def2-QZVPP 40 basis set was used.For the largest dimer in the study (Cl-Au-(NHC-B)), the corresponding non-augmented JKFIT and MP2FIT basis sets were used (with def2-QZVPP/JKFIT and cc-pVTZ-PP/MP2FIT for Au).All calculations were carried out with a development version of Molpro2010.2. 41Results and discussion We start with a well known benchmark system for aurophilic interactions, the Cl-Au-PH 3 dimer.The system has been thoroughly investigated in previous theoretical studies, so we will restrict our discussion.The dimer is oriented as in the previous studies, 13 in a non-planar orientation (with a 901 dihedral angle).
The monomer internal geometries were taken from ref. 13.We computed the energy profile of the dimer by calculating the energy with fixed monomer geometries at different r(Au-Au) distance values.Several different theory levels were used.These include canonical MP2 energies, counterpoise corrected MP2 (CP-MP2), 42 LMP2, SCS-LMP2 and LCCSD(T0).The results are shown in Fig. 3.
The energy curves show that MP2 severely overestimates the interaction, not only due to the lack of higher-order correlation effects, but also due to basis set superposition effects (BSSE).The counterpoise correction at the minimum amounts to 7.0 kJ mol À1 .The LMP2 results are strongly coincident with the latter series.Since in the local correlation case excitations are restricted to local orbital domains (domain approximation), BSSE is removed by construction from the correlation energy. 43In most cases, domain errors in the LMP2 energy are close to the error in the coupled cluster case. 44Given that the intermolecular terms are fully included in the coupled cluster treatment, our LCCSD(T0) results should be rather close to the CP corrected canonical CCSD(T) value.Lastly, the SCS-LMP2 potential curve is seen to be almost coincident with LCCSD(T0) (it is mostly overlapping and somewhat hard to distinguish in the figure).This agreement has been observed in all other dimer calculations and had This journal is c the Owner Societies 2013 already been noted in previous studies with SCS-MP2 and CCSD(T) calculations on other systems. 45,46he difference between (L)CCSD(T) and (L)MP2 in the treatment of aurophilic effects has been previously documented. 5,12The latter method tends to overestimate the well depth and converge to smaller Au-Au distances.This could be attributed to the AuÁ Á ÁAu interaction solely.To investigate whether this is the case, we have made use of the LMOMO approach, 47 treating the Au orbitals at the LCCSD(T0) level and all remaining orbitals with LMP2.The former also includes the Au-Cl and Au-P bond orbitals.The results are shown in Fig. 4. Comparing the potential curves, one can identify that the effect is not fully captured, and that the interaction curve is still halfway between the LMP2 and LCCSD(T0) result.This result shows that the errors are not restricted to the AuÁ Á ÁAu interaction solely.The dispersion interactions between the gold atoms and the ligands or even between the ligands are also not described at the MP2 level of theory and even for such a small system can lead to an overestimation of about 5 kJ mol À1 .
Encouraged by the SCS-LMP2 results in Fig. 3, we proceeded to analyze the orbital interactions according to the interaction groups previously discussed.In the case of the present dimer, these will be DE(PH 3 Á Á ÁPH 3 ), DE(PH 3 Á Á ÁAu), DE(PH 3 Á Á ÁCl), DE(AuÁ Á ÁAu), DE(AuÁ Á ÁCl) and DE(ClÁ Á ÁCl).The energies were computed at the SCS-LMP2/AVTZ level and are shown in Fig. 5.As previously pointed out, gold-ligand interactions also have an important weight in the total energy.These were not corrected in the LCCSD(T0):LMP2 results and indeed explain the discrepancy between LCCSD(T0) and the LMOMO result.Already from these set of results, and for the smallest dimer considered in this study, it is apparent that the treatment of ligands in the context of aurophilicity should be carefully cared for.The correlation energy contributions from ClÁ Á ÁAu and LÁ Á ÁAu intermolecular contacts summed together are as significant as the AuÁ Á ÁAu direct contributions.
In another set of calculations, we have compared our LCCSD(T0)/ AVTZ reference values to DFT results.We have included results with and without dispersion corrections.We have included both D3 corrections with Becke-Jonhson damping 48 as well as non-local density dependent dispersion corrections (DFT-NL) as implemented in the Orca program package. 49,50Since D3 values in the latter package are not available for Au with double connectivity, the D3 corrections were computed with the dftd3 program, 27 using fitting coefficients for Au kindly provided by the authors. 51The latter were obtained by TDDFT calculations on the AuH 2 + system following the standard procedure of Grimme and co-workers. 27The results are shown in Fig. 6.As expected, bare DFT values strongly underestimate the interaction energy.The B3LYP curve is even almost purely repulsive.This is naturally linked to the lack of dispersion forces.Adding the above mentioned corrections, the DFT values come in very close agreement with the coupled cluster curve, even leading to an agreement between the two different functionals.The remaining discrepancies between the latter and the wave function values can be linked to the difference in the basis set convergence of the two methods as we have not included any corrections for basis set incompleteness.

Cl-Au-C(PH 3 ) 2 and Cl-Au-(NHC-H) dimers
We now consider the dimers with the C(PH 3 ) 2 and NHC-H ligands.We are interested in analyzing the effect of different ligands and   comparing the interactions for minima with varying Au-Au distances.The monomer geometries were optimized at the BP86/def2-TZVP level.The potential energy curves have also been plotted with the same set of methods as in the case of Cl-Au-PH 3 and are available in the ESI.† The conclusions are rather similar.We observe a good agreement between CP-MP2 values and LMP2, as well as between SCS-LMP2 and LCCSD(T0).Again, this confirms the previous observations that the effect of domain approximations mimics a BSSE correction, and that the SCS method effectively improves the LMP2 energy, providing the best agreement with our reference method (LCCSD(T0)/AVTZ).We start by discussing in detail the results for the NHC-H dimer.Two different orientations have been considered, faceto-face (ff) and edge-to-edge (ee), which are shown in Fig. 2. The ff dimer shows a minimum at 3.2 Å, the distance being 3.3 Å for the ee structure.The largest difference between the two can be observed in the well depth, which is more than doubled (À18.0 kJ mol À1 compared to À42.4 kJ mol À1 in the ee dimer).This result is in line with previous theoretical studies. 15The energy decomposition analysis for the ff dimer (Fig. 7) shows similar profiles to Cl-Au-PH 3 (Fig. 5), with the most significant contribution being linked to AuÁ Á ÁAu interactions, followed by AuÁ Á ÁCl and AuÁ Á ÁL.The minimum distances and total interaction energies are also very similar.
In the work by Muniz et al., 15 the energy difference between the ee and ff conformations was considered in great detail.A variety of factors responsible for this difference were presented, including dispersion, induction, quadrupole-quadrupole interactions and also the difference in the onset of the repulsion curve.However, since in the SAPT analysis used each monomer is taken as a whole, the changes in the dispersion energy were not completely understood.Our results elucidate these earlier observations.The decomposition of the correlation energy shows that the added stability is not in the slightest linked to the AuÁ Á ÁAu interaction.The largest change is in the AuÁ Á Á(NHC-H) contact energy.The latter is even slightly larger than the AuÁ Á ÁAu contribution near the minimum.The ee dimer, by bringing the N-H groups closer to the Au centers, increases the interaction between the two monomers (Fig. 8).This effect accounts for a stabilization of À9.5 kJ mol À1 (at 3.2 Å intermonomer distance), close to half of the total difference.The remaining contributions will be linked to a change in the balance between the electrostatic and repulsion terms, which cannot be decomposed in a similar fashion.Nevertheless, the change in dispersion and higher-order induction effects are clearly linked to the AuÁ Á ÁL interaction.
We also considered the Cl-Au-(C(PH 3 ) 2 ) dimer, as an example of a complex in the weak interaction regime.The energy decomposition analysis for the respective dimer is shown in Fig. 9.In this case, the minimum is found at r > 4 Å (the largest in this study) which leads again to a new profile.In the case of the Cl-Au-(NHC-H) ff dimer, although the dimerization energy was small, the AuÁ Á ÁAu terms had a dominating role.In the case of Cl-Au-(C(PH 3 ) 2 ), the major contributions are from the C(PH 3 ) 2 ligand.Upon observing the AuÁ Á ÁAu curve it is clear that only at shorter distances will the aurophilic interaction truly impact the system.The results support the idea that simple distance criteria can be used to in fact characterize a compound as aurophilic.On the basis of the curve shown in Fig. 9, we would not include Cl-Au-C(PH 3 ) 2 in such a group.This journal is c the Owner Societies 2013

Cl-Au-(NHC-B) dimer
As a final application, we have chosen Cl-Au-(NHC-B), which is a more 'realistic' example of a Au(I)-Au(I) dimer.The full system amounts to 86 atoms.In order to obtain a suitable geometry for our calculations, and at an equal footing as in the other systems, the dimer was optimized at the BP86/def2-SVP level of theory, 32,52 starting from the crystal structure from ref. 16.The interaction energy curves were then obtained on the basis of this geometry by varying the Au-Au distance.We opted to optimize the dimer, instead of the monomer, to avoid changes in the conformation of the NHC-B ligand.The geometry obtained is shown in Fig. 10.Due to the size of the dimer, and since all intermolecular pairs have to be correlated at the LCCSD(T0) level (significantly increasing the computational cost) we have discarded functions.Although test calculations with added diffuse functions on the gold atoms showed no significant improvement, we do expect that these will be necessary to correctly quantify the total interaction.Nevertheless, the basis set should be suitable to give a semi-quantitative profile for the interactions taking place and, most of all, confirm the role of the ligands in the stabilization of the complex.As in the case of the previous dimers, we have performed an energy decomposition analysis (at the SCS-LMP2/VTZ level, see Fig. 11).In the case of AuÁ Á ÁAu interactions, the use of diffuse functions on gold led to no significant change in the profile.
In the case of the NHC-B dimer, the Hartree-Fock energies predict a minimum, indicating that electrostatic interactions (dipole and higher moments) already contribute to stabilize the structure.Nevertheless, the most significant interaction terms arise due to correlation effects.The interaction curves for different methods are given in the ESI.† From Fig. 11 it is clear that at a minimum distance of about 3.7 Å the direct interaction between the two gold centers provides a marginal contribution to the stabilization of the dimer.The correlation contributions are dominated by the DE(AuÁ Á ÁL) and DE(LÁ Á ÁL) terms (L = NHC-B) which result from the sheer size of the ligand.Again, one would be inclined to consider this system only slightly aurophilic, if at all.Even the interaction of a Au center with a ligand of a neighboring monomer outweights the d 10 -d 10 interaction which is usually the focus of the discussion for such compounds.
After examining the different interaction curves for the selected dimers, we were interested in discerning if the ligands could also impact the AuÁ Á ÁAu interaction itself.Although the aurophilic interaction is quite an odd case, one is often tempted to discuss it as other metal-metal interactions, where ligand effects can impact the electronic structure at these centers and consequently their affinity.In order to establish a clear comparison, we plotted the DE(AuÁ Á ÁAu) curves for all dimers as shown in Fig. 12.It should be noted that for (NHC-B) the VTZ basis was used, with AVTZ being applied in all other cases.However, as previously mentioned, the profile for NHC-B was found to be practically unchanged when adding diffuse functions at the Au centers.
The interaction curves in Fig. 12 show that the direct interaction between the two Au centers is independent of the choice of ligand L.Although three of the systems studied do include the same gold coordination (Cl-Au-C), there are still reasonable differences between the use of PH 3 , C(PH 3 ) 2 or the N-heterocyclic carbenes.Such a result emphasizes that aurophilic interactions will in fact only kick in when the distance between the centers is below 4 Å (this will certainly depend on what one considers   a sizeable interaction, the value of 10 kJ mol À1 is first reached at r = 3.7 Å, for example).Furthermore, it supports the concept of approaches such as the D3 correction in DFT, as the interaction remains constant for a similar connectivity pattern.
In addition, we computed the same interaction term for the dimers Cl-Cu-PH 3 and Cl-Ag-PH 3 using the same procedure as described for the Au complex.These values are also plotted in Fig. 12.The curves show that the direct metal-metal interactions increase when going down the period, as one would expect.However, the differences are surprisingly large.The CuÁ Á ÁCu interaction, for example, only becomes relevant at r o 3 Å.This, in turn, means that ligand interactions will become even more relevant for Ag and Cu (as already hinted in the study by Magnko et al. 13 ).With a later onset of the repulsive regime in the latter metals, the ligands can be brought into closer contact, increasing the overall interaction energy.This leads to a not so clear relationship between the metallophilic interaction and the total dimerization or oligomerization energy.

Conclusions
We have presented an analysis of the interaction between different gold complexes with the general formula Cl-Au-L.Through the decomposition of the correlation energy, it was possible to identify the relative weight of ligands and metal centers and general trends in their energy profiles.It has been shown that the direct AuÁ Á ÁAu interaction at the correlated level is, for most purposes, independent of the ligand chosen.Given that for the simplest dimer species Hartree-Fock theory leads to a repulsive profile (forces such as Pauli repulsion and induction cancel out), 5 this implies that the aurophilic interaction potential is transferable from simple model systems to more complex aggregates.We also briefly discuss its implications in the metallophilicity along Period 11.Given that for larger dimer structures, such as Cl-Au-(NHC-B), the interaction energy will be dominated by the ligands, a simple measure of the total dimerization energy or the metal-metal distance will not be directly related to the strength of the d 10 -d 10 interaction.The conclusion will depend on the concept of metallophilicity one adopts.If one understands it as the direct interaction between the two metal centers, then Au will be the most metallophilic when compared to Cu and Ag.If metallophilicity is interpreted as the potential for two different metals to form aggregates, the answer will depend on the system under study.
The analysis presented here could also explain some unexpected results for other Cl-Au-L dimers.One example would be the complex with the Me 2 -bimy, bimy = benzimidazol-2-ylidene ligand. 53Although the structure is closely related to the Cl-Au-(NHC-H) dimer, the observed dimer adopts a face-toface orientation (instead of the edge-to-edge orientation, which was largely favored in the case of NHC-H).In larger complexes, the weak interactions between ligands can add up and become the determining factor in dimer formation.In the case of Me 2bimy, a face-to-face orientation leads to closer contacts between the ligands.

Fig. 3
Fig. 3 Potential energy curve of the Cl-Au-(PH 3 ) dimer at different theory levels.All results have been computed with the AVTZ basis.

Fig. 4
Fig. 4 LCCSD(T0), LMP2 and LCCSD(T0):LMP2 results for the Cl-Au-(PH 3 ) dimer.In the latter calculation, only the Au orbitals are treated at the CC level.All results have been computed with the AVTZ basis.

Fig. 12
Fig. 12 Au-Au SCS-LMP2 correlation energy decomposition for all complexes featured in this study, including a comparison of the AgÁ Á ÁAg and CuÁ Á ÁCu interactions in Cl-M-PH 3 .