DFT-D Investigation of the Interaction Between Ir(III) Based Photosensitizers and Small Silver Clusters Ag n ( n =2-20, 92)
DDFT-D Investigation of the Interaction Between Ir(III)Based Photosensitizers and Small Silver Clusters Ag n ( n =2–20, 92) Olga S. Bokareva a, ∗ , Oliver K¨uhn a a Institut f¨ur Physik, Universit¨at Rostock, D-18051 Rostock, Germany
Abstract
A dispersion-corrected density functional theory study of the photosensitizer[Ir(ppy) (bpy)] + and its derivatives bound to silver clusters Ag n ( n =2–20,92) is performed. The goal is to provide a new system-specific set of C interaction parameters for Ag and Ir atoms. To this end a QM:QM schemeis employed using the PBE functional and RPA as well as MP2 calculations asreference. The obtained C coefficients were applied to determine dissociationcurves of selected IrPS − Ag n complexes and binding energies of derivativescontaining oxygen and sulphur as heteroatoms in the ligands. Comparingdifferent C parameters it is concluded that RPA-based dispersion correctionproduces binding energies close to standard D2 and D3 models, whereasMP2-derived parameters overestimate these energies. Keywords: dispersion interaction, density functional theory,organic/inorganic hybrid systems, binding energies
1. Introduction
Inorganic/organic hybrid systems comprised of small metal nanoparticlesand different organic adsorbates like peptides and dyes represent a fascinatingtopic with prospective applications in, e.g., catalysis and bioelectronics (forreviews, see Refs. [1, 2, 3, 4]).Despite considerable progress, electronic structure calculations of such hy-brid systems with non-covalent interactions still pose a challenge for quantum ∗ Email: [email protected]
Preprint submitted to Chemical Physics February 19, 2014 a r X i v : . [ phy s i c s . a t m - c l u s ] F e b INTRODUCTION C atomic coefficients or the inclusion of non-localterms in the exchange-correlation (XC) kernel.The first approach includes dispersion-corrected atom-centered poten-tials (DCACP) [15, 16] as well as its local variants LAP [17] and CAP [18]and the recently proposed empirical force correcting atom-centred potentials(FCACP’s) [19]. It makes use of tuned effective core potentials placed ateach atom in the way that the dispersion energy is represented by a sum ofone-electron terms.The idea of representing the dispersion interaction by pairwise atomic − C n R − n potentials with proper damping functions was explored by manyauthors. In the exchange-hole dipole moment (XDM) approach [20, 21, 22,23, 24, 25, 26], the instantaneous dipole formed between an electron andits exchange hole is used to express the dispersion interaction between non-overlapping charge densities using the Casimir-Polder relation [27]. In most INTRODUCTION C , C and C coefficients). The impact of the chemical envi-ronment on the dispersion coefficients is taken into account through Hirshfeldpartitioning.In the DFT-D2 approach of Grimme, C parameters for the first part ofthe periodic table are derived from calculations of ionization potentials andstatic dipole polarizabilities for single atoms and proved to give an adequatedescription of non-covalent interactions. For heavy atoms, however, no re-liable parameters within the D2 model are available [28]. As proposed byGrimme, unknown coefficients could be deduced from atomic properties bythe London formula [29]. An alternative way to obtain dispersion correctionsis the so-called hybrid QM:QM approach [30, 31, 32]. In this method, the dis-persion energy is considered as the difference between the adsorption energiesfor adsorbate-substrate complex obtained with ab initio theory and DFT. Forabsorption of pyridine on gold clusters, it has been shown by Tonigold andGroß that QM:QM employing a MP2 (second order Møller-Plesset perturba-tion theory) reference gave substantially better agreement with experimentcompared to standard D2 [33].Later, Grimme has introduced the much advanced DFT-D3 method, tak-ing into account the surrounding of the atoms by means of coordinationnumbers in contrast to DFT-D2 where by construction the dispersion co-efficients are not system-dependent. In this approach, C coefficients werederived from averaged dipole polarizabilities at imaginary frequencies calcu-lated with time-dependent DFT (TD-DFT), while eighth order coefficients C follow from a simple recursion rules for the higher-multipole terms [34].DFT-D3 has been shown to provide higher accuracy and broader applicabil-ity for 94 elements of the periodic table than the earlier versions.Tkatchenko and Scheffler developed a method (TS or DFT-vdW) [35]of calculating dispersion coefficients and vdW radii from the ground-statemolecular or condensed matter electron density. Here, the starting point isa high-level ground-state calculation of free-atom properties. In a secondstep the effect of the surroundings is taken into account by considering Hir-shfeld volumes and the electron density for the whole system. Further, theself-consistent screening is accounted for to reproduce the anisotropy of themolecular static polarizability [36]. In the DFT-vdWsurf variant the many-body collective response is analyzed for cases of adsorbates on a surface [37].In that respect, the DFT+vdW group is more akin to XDM, because it gives C coefficients that are dependent on the local environment, but not only on INTRODUCTION C coefficients. The similarity between vdW-DF and DFT-D can also be seenfrom the fact, that the non-local term of the former approach is typicallycomputed non-self-consistently, resulting in some additional contribution tothe DFT energy. Both routes describe the long-range vdW interaction and, atatomic overlap regions, link it to a standard exchange-correlation functional.The advantage of vdW-DF is that dispersion effects are calculated based onthe charge density, that is, in cases of charge transfer the effect of dispersionis naturally included. Recently, some progress in increasing their efficiencyhas been achieved making the computational costs comparable to those ofstandard DFT-GGA calculations what would enable their future applicationto large systems [43, 44, 45, 42]. For example, vdW-inclusive DFT methodsallow to reliably model adsorption of molecules on surfaces [46], for reviewsee [13].Although benchmarks for validation of new dispersion-corrected DFT ap-proaches have been reported (see, e.g., Refs. [25, 47, 48, 49, 50, 51] andreferences therein), mainly non-metal containing systems have been con-sidered such as the S22 standard set and nucleobase pairs. Exceptionsinclude the application of DFT-D to the adsorption of aliphatic and aro-matic molecules on metal surfaces like gold, silver, palladium, and copper[33, 34, 52, 53, 54, 55, 56, 57, 58], which gave a good agreement with ex-perimental adsorption energies, in contrast to conventional DFT. However, INTRODUCTION x -C n H m model systems, for instance, the DFT-D3 perfor-mance is comparable with that of conventional DFT [59]. An alternativefor improving the DFT-D performance is to use system-dependent C coef-ficients, rescaled on the basis of an embedding model; examples include theadsorption of small organic molecules on MgO and NaCl surfaces [60]. Inconclusion, the usage of dispersion-corrected DFT approaches for systemsincluding metal-containing surfaces or especially clusters clearly needs fur-ther investigation and comprehensive benchmarking in order to become astandard method comprising the modest computational costs of DFT withaccurate predictions.The present study aims at establishing an empirical dispersion correctionfor the system [Ir(ppy) (bpy)] + (IrPS) shown in Fig. 1 and its derivatives,bound to small silver clusters Ag n . In doing so we will contrast the con-ventional DFT-D technique, including D2, D3 corrections, with the hybridQM:QM approach for obtaining problem-specific C coefficients for the heavyatoms. Our choice of the system is motivated by the use of Ir(III) complexesas photosensitizers in photocatalytic water splitting. In Ref. [61], for in-stance, the homogeneous catalytic system consisting of IrPS combined withthe sacrificial reductant triethylamine and a water reduction iron catalysthas been demonstrated. Hybrid systems consisting of IrPS and small metalclusters hold the promise to obtain a heterogeneous catalytic system withimproved performance.The interaction of IrPS with small silver clusters (1–6 silver atoms) andin particular changes in absorption spectra upon binding have been studiedin Ref. [62] employing the long-range corrected DFT (LC-BLYP) approach.The obtained results demonstrated strong changes in the absorption spectraof the combined systems as compared with the pure constituents. To proceedwith larger metal clusters it is desirable to have a reliable method whichproperly describes binding interactions at low computational cost such asDFT-D.The paper is organized as follows: First, we briefly recall the main featuresof the DFT-D approach and outline the computational details in Section2. Second, in Section 3 we present the results of fitting C coefficients forIr and Ag atoms employing the QM:QM procedure. We proceed with theapplications of the new coefficient set to IrPS derivatives. Final conclusionsare given in Section 4. COMPUTATIONAL DETAILS
2. Computational Details
Initial geometry optimizations of IrPS − Ag n , bpy − Ag n , and ppyH − Ag n complexes as well as of pure organic and metal parts were carried out usingthe generalized gradient approximation (GGA) functional of Perdew, Burke,and Ernzerhof (PBE) [63] along with the def2-SV(P) basis set [64, 65]. Op-timizations were carried out without any symmetry constraints. Startinggeometries of small silver clusters Ag n , n =2–20 were taken from previousstudies [66, 67, 68, 69, 70]. On these optimized geometries, single point cal-culations with PBE, Random Phase Approximation (RPA), and MP2 weredone employing the def2-TZV(P) basis set [71, 72].The binding energy, E b , has been defined as E b = E tot − E Ag n − E IrPS (1)where E tot , E IrPS , and E Ag n are the total energies of the relaxed complex,dye molecule, and silver cluster, respectively.It goes without saying that at the moment for the present system, forexample, CCSD(T) reference calculations are out of reach. Higher orderperturbation theory (MP3, MP4) doesn’t improve the situation as shown inRef. [33]. An alternative is the RPA method, which is of slightly highercomputational cost as MP2, see [73]. Unlike MP2, the RPA method doesnot suffer from problems like infinite energies for small bandgap systems andit was shown to provide an adequate description for non-covalent interac-tions [74]. These authors also pointed out that sufficiently accurate bindingenergies of weakly bound systems can be obtained only by using completebasis set extrapolation or basis sets larger than quadruple- ζ . But, this level ishardly affordable for heavy elements like Ag or Ir, not to mention that besidesregular basis sets one would need auxiliary ones to perform RI-calculations[75, 73]. Therefore, we are forced to restrict our considerations to basis setsof triple- ζ quality. At least for the case of MP2 we have performed a con-vergence study and concluded that def2-TZVP binding energies are almostsaturated with respect to basis set; e.g. the corresponding binding energy inMP2 of IrPS − Ag were -0.887, -1.000, and -0.961 eV for def2-SV(P), def2-TZVP, and def2-QZVP, respectively.For the RPA calculations we have employed the resolution-of-the-identityapproximation (RI-RPA) for the two-electron integrals [76, 77, 78, 79, 80], thecorresponding auxiliary basis sets were taken from Refs. [65, 81, 72, 82]. TheRI-RPA calculations of the correlation energy were done non-self-consistently COMPUTATIONAL DETAILS E Hartree were frozen, i.e. 1sof nitrogen and carbon atoms, 4s of silver and 5s of iridium. All calculationswere done with the TURBOMOLE 6.3 program package [84].We introduced the dispersion term correcting DFT results according tothe Grimme DFT-D2 model [85, 28]. Here the total energy of system is givenby expression E DFT − D = E DFT + E disp , (2)where E DFT is the energy obtained from the DFT calculation and E disp is adispersion term including the C R − dependence. E disp has been determinedas introduced by Grimme for DFT-D2 [85, 28] E disp = − s (cid:88) i (cid:88) j C ij R ij f damp ( R ij ) (3) f damp ( R ij ) = 11 + exp[ − d ( R ij /R r − R r is the sum of van der Waals radii of the interacting atoms, d determines the steepness of the damping function, and C is obtained as C ij = (cid:113) C i C j . (5)The damping function f damp , the scaling factor s , and the atomic C i coefficients for non-metal atoms have been taken without changes from Ref.[28].Atomic coefficients for metal atoms (silver and iridium) have been ob-tained using the hybrid QM:QM method proposed in Ref. [30] and appliedto metal surfaces in Ref. [32]. In this approach, we assume the dispersionenergy to be the energy difference between binding energies calculated withthe reference (RPA or MP2) and DFT (for discussion see Section 3C). Theapplication of quite large basis sets allows one to neglect the BSSE correction RESULTS AND DISCUSSION n ) include two metalelements the task was divided into two steps. First, we considered structuresconsisting of the same small silver clusters and phenylpyridin (ppyH) or bi-pyridin (bpy) molecules. For these cases, we only needed to approximatethe dispersion coefficient for silver. This has been done using MP2 and RPAreferences. Second, we regarded the set of IrPS − Ag n structures and did thesame fitting procedure applying the coefficient for silver calculated at thefirst stage. However, for computational reasons this was possible for theMP2 reference only. Alternative to this two step procedure we approximatedthe two coefficients simultaneously using all dependencies. In this respect,the addition of sets of model structures, including separate ligands as organicpart, was reasonable because the interaction between IrPS and silver clustersis mainly due to the dispersion interaction with ligands, with the central Iratom being shielded.
3. Results and discussion
For each given combination of silver cluster and organic molecule, we havefirst optimized from 2 to 5 different structures starting from various initialrelative orientations. For brevity, in Fig. 2 only some examples of optimizedcomplexes are plotted, for the full list of structures and their notation seethe Supplementary Material [86]. In case of ppyH or bpy aromatic molecules,silver clusters are normally strongly bound to the N atoms of ppyH and bpy(Fig. 2a), which is impossible when interacting with IrPS where N atomsare oriented towards the central Iridium atom. Nevertheless, such structureshave been also taken into account because we do not want to exclude thepossibility of superposition of dispersion interactions. In structures wherethere is no direct interaction between Ag and N atoms, the silver cluster isbound to one of the rings (see Fig. 2b). For the ppyH molecule, in mostcases the cluster is attached to the heterocycle. Still another possibility isthat one of the silver cluster’s planes interacts with the π aromatic systemand is approximately parallel to the plane of one or both aromatic rings (seeFig. 2c, d). RESULTS AND DISCUSSION ° with severalexceptions where these changes achieve values in the range 26-33 ° . For ppyH,there are even more cases where changes are in the range of 23-35 ° . This couldbe due to the fact that the phenyl-ring of ppyH is repelled once the silvercluster comes close to bind with the N atom. The distances between theclosest atoms of the interacting subsystems are 2.3-4.0 ˚A.In our previous study on the IrPS bound to small ( n ≤
6) silver clusters[62], we found that configurations in which Ag n is situated in the cavitiesbetween ligands are the lowest in energy. Note that in all cases the inter-actions are ”weak” and no chemical bonds are formed. Here we extend thisstudy to IrPS − Ag n geometries up to 20 silver atoms, however, focussing onthose structures where the cluster is located in the ”ppy-ppy” cavity and n is even. Similar to the small systems [62], the geometry optimization wascarried out without symmetry constraints, except for some cases where theC point symmetry of the IrPS part [87] was retained. Some examples ofIrPS − Ag n complexes can be found in Fig. 3. Binding energies per silver atom of all structures (ppyH-Ag n , bpy − Ag n ,and IrPS − Ag n ) selected for further C coefficient fitting are plotted in Fig. 4(details are given in the Supplementary Material [86]). In general the range ofbinding energies (0.01-0.59 eV) is comparable for all sets of model structures.This corresponds to physisorption of the organic molecule on the silver clus-ters, with binding energies being about 10 times smaller compared to bindingenergies of silver atoms within large nanoparticles [88]. From Fig. 4 one canalso notice that E b decreases with increasing number of silver atoms in thesystem.Note that the RPA calculations were only computationally affordable forstructures containing up to 10 silver atoms and bpy or ppyH but not IrPS asan organic counterpart. Concerning the discrepancies between the PBE andMP2 calculations, it is observed that they are more pronounced for IrPS − Ag n systems, with MP2 results naturally being always larger than those of PBE.The RPA binding energies for bpy − Ag n and ppyH − Ag n lie in between PBEand MP2 ones, with RPA energies being in average 24% lower that MP2. RESULTS AND DISCUSSION
Using the QM:QM approach we obtained C coefficients for Ag and Irin two different ways as outlined in the Computational Details section. Thecoefficients obtained either in two-steps or by simultaneous fitting as wellas corresponding root mean squared deviations (RMSD) for binding energyfitting are collected in Table 1. For silver, the dispersion coefficient wasobtained using both RPA and MP2 as references. The C coefficients usedin the D2 model [28] are also given in Table 1. It should be noted that forAg and Ir only estimates of coefficients are available in D2. For example C Ag6 was assumed to be an average of preceding group VIII and followinggroup III element. The corresponding C coefficients of the D3 model arealso included in the Table 1 but two points should be highlighted beforethe comparison with the coefficients obtained in the current work. First,they are coordination number dependent; in the table only values whichwere applied for the systems under investigation are collected. Second, tofit all the dispersion forces in DFT-D3 higher-order terms C and C arealso used. We also included in Table 1 the values of C obtained withinthe combination of dispersion-corrected density-functional theory (the DFT+van der Waals approach) [35], with the Lifshitz-Zaremba-Kohn theory for thenonlocal Coulomb screening within the bulk [37] . The average value of C deduced from CCSD(T) interaction energies between silver dimers at largedistances is also provided in Table 1 [89].Comparing new coefficients based on MP2 reference and standard (D2)coefficients, one notices that the present QM:QM C coefficients are substan-tially larger than those of the standard D2 model, with the differences forAg being more pronounced than for Ir (increase by 170-180% vs. 25-70 %).The two new C Ag6 coefficients are closer to each other than corresponding C Ir6 ones, hinting at the minor influence of Ir coefficient on the approximation of E MP2 − E PBE differences for the case of silver.Here, one should take into account the possible deficiencies of MP2 forpredicting binding energies. For example, for benzene molecule the C co-efficient evaluated by MP2 is overestimated by more than 40% [90]. Theseoverestimations could be even more pronounced for highly polarizable sys-tems such as metal clusters and for periodic systems should lead to infinite C coefficient because of vanishing bandgap. Indeed, if we compare highly RESULTS AND DISCUSSION C values from Table 1 of Ref. [37] for the bulk silver within DFT-vdWsurf approach which was obtained using the highly accurate experimen-tal dielectric function of the Ag bulk, our C is about one magnitude higher.The C value for free silver atoms from DFT-vdW [35] is about 3 times largerthan for the bulk phase [37]. However, all our systems have non-vanishingbandgap even up to Ag . For test cases (see the Supplementary Material),MP2 overestimates binding energies by only 10-40 % if compared to CCSD.The orbital shift in MP2 leads to almost linear scaling of energy [91] whichindirectly evidences the absence of problems with the bandgap. Neverthe-less, if one compares the present results with CCSD(T) for silver dimers, the C coefficients obtain by MP2 are three times larger. Summarizing, C co-efficients obtained by MP2 are likely to be overestimated, but one can statethat for small systems they are larger than for the bulk metal.Alternative to the MP2 reference we consider RI-RPA/def2-TZVP cal-culations. As noted before these have been performed for a smaller test setonly, which did not include IrPS − Ag n structures and cases with more than10 Ag atoms. Separate fitting leads to a substantially different C Ag6 coeffi-cient, which is even smaller (by 28%) than the corresponding standard D2value, see Table 1. In order to investigate this point further we performed atest calculation (Test1 in Tab. 1) where the MP2 reference is taken for thesame reduced set of structures. This yields a lowering of C Ag6 with respectto the full MP2 set, but still a notably higher value (13%) as compared withRPA.To scrutinize the large variability of C Ir6 further two additional fits havebeen performed. First, we fitted C Ag6 using all sets of test structures (MP2reference) and assuming C I r = 842 . A (D2 model), and second, weapplied the standard D2 C Ag6 = 255.69 and fitted C I r only for the IrPS − Ag n set of structures. The results are also shown in Table 1 (entries ”Test2”,”Test3”). Taking C I r = 842 . A leads to a slight increase of C A g ifcompared to the ”simultaneous” value, with the quality of fitting being prac-tically the same. Setting C Ag6 =255.69 led to an enormously increased C I r ,with the RMSD increasing dramatically as well. This finding can be rational-ized as follows: The Ir atom is situated in the center of photosensitizer andhence screened by the ligands what hinders a direct interaction with the sil-ver clusters. To cover the same amount of dispersion with the standard fixedvalue of C Ag6 is only possible with an extremely large coefficient for iridium.Hence, it can be argued that the actual coefficients are extremely sensitiveto the chemical environment, what in principle makes the simultaneous fit
RESULTS AND DISCUSSION s which is functional-dependent. In that way, the strength of dis-persion interaction is adjusted for different XC functionals. In case of PBE, s = 0 .
75 is used. Such an ad hoc treatment is justified at short distanceswhere it provides a correction to the overestimated dispersion forces, but ithas no direct meaning at long distances. The Fermi-type damping functionincludes an additional empirical parameter d , the steepness of the dampingfunction which is universal for all functionals. As it was already pointed outin Sec. 1, the damping function is needed to smoothly switch-off the dis-persion term at short distances. The choice of a particular type of dampingfunction has no crucial impact on the results (for a discussion see Ref. [34]).In more advanced DFT-D variants such as DFT-D3, TS, and XDM, thereis no direct scaling of C coefficients, but damping functions include moreempirical parameters, like (order-dependent-) coefficients which scale vdW(or cutoff) radii for each density functional applied. Furthermore, the cutoffradius itself is also an arbitrary parameter that is not universal for differentDFT-D approaches and should be chosen separately. In DFT-D3, the s parameter is used to scale the contribution of triple-dipole interactions and s -scaling is applied for double-hybrid density functionals. Summarizing, allDFT-D schemes include empirical corrections justified by physical meaningand by fitting to experimental or more precise computational results. In the RESULTS AND DISCUSSION
Table 1: Values of C Ag6 and C Ir6 (in eV˚A ) fitted separately and simultaneously with theQM:QM method (RMSD of E r ef − E PBE − D ∗ in eV are given in parenthesis) and fromliterature. For D3 value, the coefficients are only given for coordination numbers (CN)in parenthesis. *The unscreened (free) value from [35] is given for comparison. For themeaning of Tests see text. present treatment we do not aim at refitting the scaling factor and take theDFT-D2 model as developed previously.In the following applications we continue to consider two sets of coeffi-cients: First the MP2 result obtained from simultaneous fitting (PBE-D2*).This includes the complete set of test structures which is not available forthe most likely more accurate RPA. Note, however, since no exact referenceis available the judgement concerning accuracy of the two methods is solelybased on results reported for other systems in literature. Therefore MP2derived results will be contrasted to RPA ones which are supplemented bythe C Ir6 coefficient taken from the D2 model (PBE-D2**).
First, the obtained coefficients for Ag and Ir were verified for dissociationof two complexes: IrPS − Ag and IrPS − Ag . The optimized (PBE/def2-SV(P)) geometries were frozen and distances between Ir and closest Ag atomswere changed. Single point calculations of obtained structures were doneusing PBE (pure and in different dispersion-included variants) and MP2 withthe def2-SV(P) basis set.The dependencies of calculated binding energies on the Ir-Ag distanceare plotted in Fig. 5. Naturally, a very good agreement between MP2 and RESULTS AND DISCUSSION coefficients. RPA based results as well as coefficientsthemselves are lying between corresponding PBE-D2 and PBE-D3 curves,demonstrating slightly slower binding energies closer to dissociation limit.As a second application, we evaluated the binding energy of the largenearly spherical silver cluster Ag . The initial geometry of this cluster wascut from the fcc bulk silver and optimized with PBE/def2-SV(P) separately.Then the silver cluster was placed in the ppy-ppy cavity of the photosensitizeranalogous to the smaller systems. The constructed complex was partiallyoptimized using PBE-D2*, i.e. only those silver atoms nearest to the IrPSand all atoms of IrPS were allowed to relax upon optimization. (Note for thepurposes of comparison, we also performed an optimization with PBE-D2 andPBE-D3; the changes in geometries are only minor (up to 0.06 ˚A and 0.2 ° )and can be neglected.) The resulting geometry is shown in Fig. 6 togetherwith the corresponding binding energies per one silver atom calculated withindifferent PBE-D models. The IrPS − Ag complex has no symmetry and thedistance between central Ir atom and nearest silver atom is 5.2 ˚A which isslightly higher than in the case of small silver clusters. Due to steric reasonsthe large silver cluster can not come closer without significant distortionsin its shape. The binding energy of the largest investigated system per onesilver atom is very small and in the region of 0.004–0.021 eV for all PBE-D variants. Similar to the small systems, the account for dispersion forcesincreases the binding energy E b : from 0.004 (PBE) to 0.012 (both PBE-D2and PBE-D3, PBE-D2**) and to 0.021 eV (for PBE-D2*). The obtainedvalue also confirms the decrease of E b per 1 silver atom with increasingsystem size. The trend can be clearly seen in Fig. 6 where binding energiesfor selected examples of IrPS − Ag n calculated with MP2 and all the PBE-Dvariants (within def2-TZVP basis set) are plotted. For clarity, only caseswith the largest binding energies within MP2 are selected.Finally, we apply the new coefficients to derivatives of IrPS. Although ourcoefficients are by construction suited for the particular photosensitizer withppy and bpy ligands (isolated or located around Ir central atom) we wantedto scrutinise the sensitivity with respect to the type of heteroatom. For thisreason we investigated the binding between and Ag cluster an a photosen-sitizers containing oxygen ([Ir(op) (bpy)] + ) and sulphur ([Ir(bt) (bpy)] + ) inthe ligands. The structures of optimized complexes are depicted in Fig. 7 and CONCLUSIONS − Ag and corresponds againto a weak interaction (physisorption).
4. Conclusions
The interaction of Ir(III) photosensitizers containing ppy and bpy ligandswith small silver clusters Ag n ( n =2–20) is studied using dispersion-correcteddensity functional theory together with the RPA and MP2 methods. Thegoal has been to develop a system-specific set of C parameters for Ir andAg atoms in the spirit of the D2 correction. To this end the QM:QM schemewas employed for a set of model structures. An important aspect for thisparticular type of system is that the Ir atom is shielded by the ligands. As aconsequence the Ir parameters turn out to be rather sensitive to the actualmethod of fitting, whereas the Ag coefficients are more robust.In general binding of silver clusters to IrPS is weak and in the physisorp-tion range. The binding energy per silver atom decreases with the size ofthe cluster to become as small as 0.01–0.02 eV for the largest cluster studied( n = 92).Although our new coefficients are by construction suited for the partic-ular example of interaction of silver clusters with organic or metalorganicmolecules containing ppy and bpy ligands, the transferability of new C co-efficients for similar systems was shown using the exemplary cases of IrPScontaining O and S heteroatoms.In order to derive C two references have been considered, i.e. MP2 andRPA. It was found that MP2 did not give convergence and bandgap-relatedproblems, most likely since the considered metal clusters still have molecularcharacter and can be described with respective orbitals. However, based onreports in literature one would expect that RPA is more reliable for the de-scription of binding in these weakly bound organic/inorganic hybrid systems.Therefore, the C Ag6 value obtained on the RPA level should be considered asbeing more accurate compared to MP2. This value turns out to be closeto the ones of the Grimme D2/D3 sets. However, this similarity should betaken with care. In view of the fact that the polarizability is determined by anon-local response kernel, the reduction to a single coefficient for an arbitrary
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Acknowledgements
This work has been financially supported by the ESF project ”Nanos-tructured Materials for Hydrogen Production (Nano4-Hydrogen)” and theBMBF project ”Light2Hydrogen” (”Spitzenforschung und Innovation in denNeuen L¨andern”).
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EFERENCES .[85] S. Grimme, J. Comp. Chem. 25 (2004) 1463.[86] See Supplementary Material Document No. for binding energies of allinvestigated structures (Table S1), the full list of optimized geometriesand corresponding names for bpy–Ag n (Fig. S1), ppyH–Ag n (Fig. S2),and IrPS–Ag n (Fig.S3).[87] K. King, R. Watts, J. Amer. Chem. Soc. 109 (1987) 1589.[88] E. Fern´andez, J. Soler, I. Garz´on, L. Balb´as, Phys. Rev. B 70 (2004)165403.[89] R. Hatz, M. Korpinen, V. H¨anninen, L. Halonen, J. Phys. Chem. A 116(2012) 11685–11693.[90] A. Tkatchenko, R. A. DiStasio, M. Head-Gordon, M. Scheffler, J. Chem.Phys. 131 (2009) 094106.[91] B. O. Roos, K. Andersson, Chem. Phys. Let. 245 (1995) 215–223.[92] T. Buˇcko, S. Leb`egue, J. Hafner, J. G. ´Angy´an, Phys. Rev. B 87 (2013)064110. EFERENCES Ir ppy bpy + N NN2
Figure 1: Chemical formula of [Ir(ppy) (bpy)] + . EFERENCES b bpy-Ag4b-4 a bpy-Ag6a-1 c bpy-Ag6b-3 d bpy-Ag20a-3 Figure 2: Some representative examples of bpy − Ag n optimized geometries (for a full listincluding the nomenclature see Supplementary Material). EFERENCES IrPS-Ag2-1 IrPS-Ag6c-2IrPS-Ag14a-1 IrPS-Ag20a-1
Figure 3: Some examples of optimized IrPS − Ag n structures (for a full list see Supple-mentary Material [86]). EFERENCES E b , e V E b , e V E b , e V n (Ag) n (Ag) n (Ag) a)b)c) Figure 4: Binding energies per silver atom of all model structures under study: a)ppyH − Ag n , b) bpy − Ag n , c) IrPS − Ag n . Black squares: PBE, blue hollow triangles:RPA, red circles: MP2. For illustration some examples for Ag are shown. Noticethat for simplicity, we do not mark the corresponding points (PBE, RPA, MP2) for eachstructure. EFERENCES PBEPBE-D2PBE-D3PBE-D2*PBE-D2**MP2 RR R(Ir-Ag) , Å