Phosphorescent Modulation of Metallophilic Clusters and Recognition of Solvents through a Flexible Host-Guest Assembly: A Theoretical Investigation

MP2 (Second order approximation of Møller–Plesset perturbation theory) and DFT/TD-DFT (Density functional theory/Time-dependent_density_functional_theory) investigations have been performed on metallophilic nanomaterials of host clusters [Au(NHC)2]+⋅⋅⋅[M(CN)2]−⋅⋅⋅[Au(NHC)2]+ (NHC = N-heterocyclic carbene, M = Au, Ag) with high phosphorescence. The phosphorescence quantum yield order of clusters in the experiments was evidenced by their order of μS1/ΔES1−T1 values (μS1: S0 → S1 transition dipole, ∆ES1−T1: splitting energy between the lowest-lying singlet S1 and the triplet excited state T1 states). The systematic variation of the guest solvents (S1: CH3OH, S2: CH3CH2OH, S3: H2O) are employed not only to illuminate their effect on the metallophilic interaction and phosphorescence but also as the probes to investigate the recognized capacity of the hosts. The simulations revealed that the metallophilic interactions are mainly electrostatic and the guests can subtly modulate the geometries, especially metallophilic Au⋅⋅⋅M distances of the hosts through mutual hydrogen bond interactions. The phosphorescence spectra of hosts are predicted to be blue-shifted under polar solvent and the excitation from HOMO (highest occupied molecular orbital) to LUMO (lowest unoccupied molecular orbital) was found to be responsible for the 3MLCT (triplet metal-to-ligand charge transfer) characters in the hosts and host-guest complexes. The results of investigation can be introduced as the clues for the design of promising blue-emitting phosphorescent and functional materials.


Introduction
The relationship between the luminescent property and metallophilic Au(I)···M bond distance (M = Au I , Ag I , Cu I , Tl I , Hg II , Bi III , etc.) has attracted a great deal of attention in the last few years [1][2][3][4][5]. Many experimental and theoretical studies indicated that Au(I) complexes luminesce strongly, especially when the metallophilic interaction is present [6][7][8][9]. The organometallic complexes were applied extensively as emitters in organic light-emitting diodes (OLEDs) and phosphorescent OLEDs with green and red spectral range, which have already been demonstrated to be high efficiency and stability [10][11][12]. However, the blue-emitting OLEDs, which are essential for the commercial launch of devices for lighting, still lack stability and efficiency. Indeed, designing new materials to show higher energy, such as deep-blue emission, encounters more obstacles than the progress made for obtaining green and red colors.
progress made for obtaining green and red colors.
Considerable investigations have been carried out in developing blue OLEDs with high external quantum efficiency as well as a deeper blue color [13][14][15][16][17]. Recently, the highly phosphorescent organometallic nanomaterials of polymeric double salts [Au(NHC)2][M(CN)2] (NHC = N-heterocyclic carbene, M = Au or Ag) were prepared, which can provide a deep blue shifted phosphorescence spectrum with emission quantum yields of up to 90% [2]. It was found that the extended metallophilic d 10 d 10 interactions played significant role in the phosphorescence of quasi-2D polymeric nanostructures.
In the present paper, the metallophilic characters and the phosphorescent properties of the host clusters were investigated by density functional theory (DFT). Introducing the guest solvents CH3OH (S1), CH3CH2OH (S2), and H2O (S3), we mainly focus on: (a) the nature of homo/hetero-metallophilic interactions; (b) how the guest molecule affects the metallophilic distance, and (c) how the metallophilic distance affects the photophysical properties of the complexes. Our calculated results reported herein are predicted to provide blue-shift phosphorescence, which is helpful for the further synthesis of the organometallic compounds for blue-emitting OLEDs.
The geometries of all the structures were fully optimized using the GAUSSIAN09 program suite [76]. The orbital composition analysis is performed by the Multiwfn 3.3 suite of program [77]. The natural bond orbital (NBO) analysis is achieved by NBO 5.0 procedure [78].

Results and Discussion
We initially optimized the representative host cluster I which has seven oligomeric units ( Figure S1, see SI) and then calculated II and III with a similar procedure. The geometrical parameters of the ground state (S 0 ) for clusters I, II, and III at various calculated levels are in good agreement with their experimental X-ray structures, respectively. After further extensive testing, PBE0/BS1 was employed in the subsequent qualitative analysis as it was found to be time-economical and reliable to evaluate the geometrical, electronic, and spectral properties of weakly bound metal complexes (Table S1, see SI) [42][43][44]79,80].  15 and 3.06 Å for II and III, respectively. Therefore, the metallophilic interaction is decreased in II while it is strengthened in III, as compared with I. Both ∠CMC of anion [M(CN) 2 ] − and ∠AuMAu (M = Au, Ag) are 180.0 • in cluster X, which indicates that three metal atoms together with two CNions are in the same plane. The Au···M distances in X are shorter at least by 0.2 Å than that reported for the tetrameric CF 3 Au·CO [5,81], which suggests stronger metallophilic interactions in X than that in [CF 3 Au·CO] 4 .

Ground States Properties
The NBO results show that the metallophilic interactions between two adjacent metal atoms are all synergistically bidirectional (outward and inward), which is displayed using cluster I as an example ( Figure 2, Table S2 in SI). In outward aurophilic interactions, the electron is delocalized from the LP(5) orbital of central Au2 atom to the LP*(7) orbitals of two lateral Au1 and Au3 atoms E (2) ij :~30 kcal/mol respectively), whereas the electron is donated back from the LP(4) orbitals of Au1 and Au3 atoms to the LP*(6) orbital of central Au1 (E (2) ij :~28 kcal/mol respectively) in the inward aurophilic interactions. The E (2) ij of outward (62.83 kcal/mol) is 7 kcal/mol higher than that of inward (55.83 kcal/mol), and also, NBO results show that whether in inward or outward modes, the d orbits of Au atoms act as the electron donors and the electron acceptors originate from the p orbits of Au atoms.  Compared to free I, the structure of segment I in complex IS1 is changed. There are mutual HN and OH hydrogen bonds in complex IS1 and which leads NHC ligands of [Au(NHC)2] + to be torsional and the distances of Au1M2 and M2Au3 are not equal anymore. Figure 3 shows there are three complexation modes between X and two solvent molecules. The energy analysis revealed that mode 1 of X(S)2 is ~ 3 kcal/mol lower than those in modes 2 and 3. Therefore, the following discussions focus on the mode 1. In I(S1)2 ( Figure 4), two AuAu distances are elongated to 3.46 Å and the angles H1Au2H2 and Au1Au2Au3 both are 180. Besides the aurophilic interaction, two types of hydrogen bonds are also involved: two NH-O hydrogen bonds (1.87 Å ) and four OH-C bonds (2.42 Å ). The I(S1)2 is complexed together by hydrogen bond interactions.

Structures of X···(S) x Complexes
In this section, the solvents CH 3 OH (S1), CH 3 CH 2 OH (S2), and H 2 O (S3) are introduced to explore how they affect the metallophilic interactions and the phosphorescent properties of X. Figure 3 shows the formation model of complexes X···(S) x (X = I-III; x = 1-4). The skeletal diagram and key structural parameters are also listed in Figure S2 and Table S3, respectively.  Compared to free I, the structure of segment I in complex IS1 is changed. There are mutual HN and OH hydrogen bonds in complex IS1 and which leads NHC ligands of [Au(NHC)2] + to be torsional and the distances of Au1M2 and M2Au3 are not equal anymore. Figure 3 shows there are three complexation modes between X and two solvent molecules. The energy analysis revealed that mode 1 of X(S)2 is ~ 3 kcal/mol lower than those in modes 2 and 3. Therefore, the following discussions focus on the mode 1. In I(S1)2 (Figure 4), two AuAu distances are elongated to 3.46 Å and the angles H1Au2H2 and Au1Au2Au3 both are 180. Besides the aurophilic interaction, two types of hydrogen bonds are also involved: two NH-O hydrogen bonds (1.87 Å ) and four OH-C bonds (2.42 Å ). The I(S1)2 is complexed together by hydrogen bond interactions. Compared to free I, the structure of segment I in complex I···S1 is changed. There are mutual H···N and O···H hydrogen bonds in complex I···S1 and which leads NHC ligands of [Au(NHC) 2 ] + to be torsional and the distances of Au1···M2 and M2···Au3 are not equal anymore. Figure 3 shows there are three complexation modes between X and two solvent molecules. The energy analysis revealed that mode 1 of X···(S) 2 is~3 kcal/mol lower than those in modes 2 and 3. Therefore, the following discussions focus on the mode 1. In I···(S1) 2 (Figure 4), two Au···Au distances are elongated to 3.46 Å and the angles ∠H1Au2H2 and ∠Au1Au2Au3 both are 180 • . Besides the aurophilic interaction, two types of hydrogen bonds are also involved: two N···H-O hydrogen bonds (1.87 Å) and four O···H-C bonds (2.42 Å). The I···(S1) 2 is complexed together by hydrogen bond interactions.  For I(S1)3, both neighbor AuAu bond distances are 3.40 Å and there are three NH-O (~ 1.9 Å ) and six OH-C hydrogen bonds (2.3-2.5 Å ). Different from the I(S1)2, the angle Au1Au2Au3 of I(S1)3 is decreased to 158.5, which reflects that the three gold atoms are not in the same plane anymore.
Complex I···(S1)4 possesses D2h symmetry. The skeletons of [Au(CN)2] − and S1 lie in the same plane and they are encapsulated by two [Au(NHC)2] + segments. The fourth S1 for I(S1)3, the AuAu (3.25 Å) is decreased by 0.15 Å and the NH and OH bonds are 1.95 Å and 2.47 Å , respectively.
The structures for I(S2)x and I(S3)x are similar to those of corresponding I(S1)x with the same x. For example, the AuAu distances are 3.50, 3.45, 3.40, and 3.25Å for IS2, I(S2)2, I(S2)3, and I(S2)4, which are relatively close to those for I(S3)x. It can be seen from Table 3S, the other two metallophilic clusters II and III can be also adjusted by solvent and their structures are also similar to the those of I(S)x respectively. Therefore, the AuM (M = Au, Ag) distances are dramatically elongated with one S molecule inserted between two [Au(NHC)2] + . However, metallophilic AuM distance is decreased gradually as the number of S x increased. The phosphorescence character then can be predicted to be modulated with the AuM distance changed [1-5].

Interaction Energies
Interaction energies of AuM in clusters X The BSSE-corrected interaction energy (obtained from the electronic energy) computations using the GAUSSIAN09 program will be denoted with the superscript CP. The CP add E (added) and CP tot E (total) interaction energies defined in Equations 1 and 2 [5] are investigated.
The calculated level test showed that the PBE0-D3/BS3 method is the most reliable and financial in time to estimate E CP .  For I···(S1) 3 , both neighbor Au···Au bond distances are 3.40 Å and there are three N···H-O (~1.9 Å) and six O···H-C hydrogen bonds (2.3-2.5 Å). Different from the I···(S1) 2 , the angle ∠Au1Au2Au3 of I···(S1) 3 is decreased to 158.5 • , which reflects that the three gold atoms are not in the same plane anymore.
The structures for I···(S2) x and I···(S3) x are similar to those of corresponding I···(S1) x with the same x. For example, the Au···Au distances are 3.50, 3.45, 3.40, and 3.25Å for I···S2, I···(S2) 2 , I···(S2) 3 , and I···(S2) 4 , which are relatively close to those for I···(S3) x . It can be seen from Table S3, the other two metallophilic clusters II and III can be also adjusted by solvent and their structures are also similar to the those of I···(S) x respectively. Therefore, the Au···M (M = Au, Ag) distances are dramatically elongated with one S molecule inserted between two [Au(NHC) 2 ] + . However, metallophilic Au···M distance is decreased gradually as the number of S x increased. The phosphorescence character then can be predicted to be modulated with the Au···M distance changed [1-5].

Interaction energies of Au···M in clusters X
The BSSE-corrected interaction energy (obtained from the electronic energy) computations using the GAUSSIAN09 program will be denoted with the superscript CP. The E CP add (added) and E CP tot (total) interaction energies defined in Equations (1) and (2) [5] are investigated. The calculated level test showed that the PBE0-D3/BS3 method is the most reliable and financial in time to estimate E CP . Table 1 shows that the interaction energies are very close for the isolated I, II, and III, in which E CP add and E CP tot are~−30 and~−102 kcal/mol, respectively. The clusters X E CP tot values for two metallophilic bonds are 3-4 times of those of E CP add of X, suggesting a degree of cooperativity [5,[82][83][84]. The EDA interaction energies of clusters I-III are reported in Table 2, where the contributors E es , E ex , E pol , E disp , and E corr are attractive and E rep is repulsive. It should be noted that E add and E tot values are very close to their corresponding electrostatic energy (E es ) term, indicating that the clusters are mainly stabilized by the electrostatic interactions [5,84].

Interaction energies of complexes X···(S) x
In this section, the total interaction energies E CP and the E CPn (n = 1, 2, 3, and 4) are considered. The E CP1 , E CP2 , E CP3 , and E CP4 respectively correspond to the interaction energies between one, two, three, and four S molecules and the remainder parts in X···(S) x (Table 3). For I···(S1) x , the E CP1 value is decreased from −16.6 to −11.8 kcal/mol as the number of S1 increasing from one to four. The E CPn value for I···(S2) x is very similar with the case in I···(S1) x , indicating that the solvents S1 and S2 behave similar in controlling the interaction energies for I···(S) x . Furthermore, the solvents S1 and S2 also act very similarly to adjust the interaction energy for II···(S) x or III···(S) x . Therefore, the interaction energy might not be adjusted by the carbon chain growth. All E CPn values for X···(S) x are negative, which shows S can stabilize the X···(S) x complexes.
The GKS-EDA results ( Figure S3a-c) of complexes X···(S2) x [85] further reveal that the solvents S1 and S2 contribute very similar behavior to change the interaction energy for II···(S) x or III···(S) x . In other words, the EDA values have small differences between X···(S1) x and X···(S2) x at the same x with the same X. The EDA results showed that E ex is the most important energy component for all complexes except X···S2, in which electrostatic force is most important (Table S4).   Interestingly, the energy contributors of E ex , E rep , E pol , E disp , and E corr are summed close to zero and an excellent correlation R = 1.00 between the E tot and the E es values was found for I···(S2) x , II···(S2) x , and III···(S2) x with the linear equation (Figure S3a -c ). These results further reinforce our finding that the investigated interaction is governed by the electrostatic term ( Figure S4).

Excited State's Properties
The M-related bond lengths, bond angles, and the major geometrical changes between the ground state S 0 and lowest lying triplet excited state T 1 are summarized in Table 4. The parameters reveal that the Au1···M2 and Au3···M2 bonds are shorter maximally by~0.40 Å for T 1 than those for the corresponding S 0 of the cluster X. The metallophilic Au···M distance in S 0 can be increased by introducing S into cluster X. However, the Au···M distances are shortened by 0.35 Å for triplet III···(S1) 4 and even by 0.80 Å for triplet III···S1 as compared with the corresponding S 0 of III···(S) x , respectively. a the atom numbering scheme is given in Figure 1. b Cplx = Complex. ∆ = the different between bond length/bond angle in T 1 and S 0 state. Table 5 shows the calculated emission energies, the electron transition assignments, and the experimental values of complexes I-III. The calculated emission wavelengths of 457, 483, and 417 nm are in good agreement with the experimental emission values of 448, 465, and 446 nm, which respectively correspond to the clusters I, II, and III. The electron transition from HOMO to LUMO is responsible for the emission at 457 nm for I. The HOMO of cluster I mainly consist of natural atomic orbital (NAO) of Au (77.23%, d: 45.29%), while LUMO has less NAO of Au (35.71%) and more significant NAO of the ligands (64.29%), which is MLCT character from the metal-centred to ligands excited states (Table S5). II and III also display similar MLCT phosphorescence nature to I (Table S6). The phosphorescent emission wavelengths can be tuned as the Au-M distances change with the solvent effect (Table S3). The Au···M distances in S 0 of X···(S) x are lengthened compared to those in free X. However, the Au···M distances in X···(S) x are dramatically shorter in the T 1 state than those in S 0 . Actually, Au···M distances in X···(S) x are changed little compared with those in free X no matter with the type and the number of S in the triplet state, which is significantly different from the case in S 0 . Therefore, the Au···M distance change in S 0 as x increases can reflect the photoluminescence change since the phosphorescent emission involves electron transition from T 1 to S 0 .
It can be seen obviously that the photoluminescence of X can be tuned (∆λ) by Au···M distance change (∆d) through introducing S to X, and photoluminescence of the X···(S) x complexes shows blue shift compared with free X (Table S3 and Figure S5). Especially, X···(S) 4 (X = I, III) provide the largest blue-shifted photoluminescence, while II···(S) 4 has the smallest blue-shifted emission wavelengths. The photoluminescent emission wavelength for II···S is significantly different from those for II···(S) x (x = 2, 3, 4) because I is distorted in I···S. However, similar to the photoluminescence of X, the excitations from HOMO to LUMO of X···(S) x are still responsible for their emission at their maximum wavelength which mainly originates from MLCT character between metal-centred and ligands (Tables  S5 and S6). The MLCT character becomes most obvious at x = 4 because of the charge transfer capacity from metal-centred to ligands of~38%,~44%, and~31% for I···(S) 4 , II···(S) 4 , and III···(S) 4 , respectively. Moreover, different solvents, S1 and S2, have little effect on MLCT character of X at specific x. For example, the charge transfer capacity for I···(S1) 4 and I···(S2) 4 are respectively 37.63% and 37.60% (Table S5) so that the maximum photoluminescent wavelengths of them are also the same with 412 nm.
The radiative (k r ) and the non-radiative (k nr ) rate constants are linked to the phosphorescence quantum yield (Φ PL ) from an emissive excited state to the ground state by Equation (3).
Theoretically, k r is related to the mixing between S 1 and T 1 , which is proportional to the spin-orbit coupling (SOC) rate constants. SOC rate constants are linked to the phosphorescence quantum efficiency between the two states, according to Equation (4).
In general, smaller ∆E S 1 −T 1 and larger µ S 1 or µ S 1 ∆E S 1 −T 1 for the system could induce a higher Φ PL [86].
The µ S1 /∆E S1−T1 values for complexes X are in the order: 0.99 (I) > 0.91 (II) > 0.83 (III), which is rationalized by the Φ PL in experimental order: 90% (I) > 67% (II) > 11% (III). An excellent correlation (R = 0.943) was observed between the theoretical for free X ( Figure S6). We further employ this equation to predict the Φ PL values of X···(S) x , which reveal that fourteen complexes have high phosphorescence efficiency with Φ PL larger than 50% (Table S7, see SI).

Conclusions
In summary, a detailed study of metallophilic Au···M bonding in host clusters from self-assembled [Au(NHC) 2 ] + and [M(CN) 2 ] − (M = Au, Ag) and the characters of their host-guest complexes are presented by the second-order Møller−Plesset (MP2) method, density functional theory, and qualitative analysis via GKS-EDA and NBO methods with a series of basis sets.
The largest and smallest µ S1 /∆E S1−T1 values for cluster I and III, respectively, were the highest and lowest Φ PL among three experimental clusters I-III. Based on host-guest complexation, the phosphorescence of hosts can be modulated and the guest solvents can be recognized. The metallophilic interactions are mainly derived from electrostatic interaction. The solvents methanol, ethanol, and water can adjust the geometries of Au(I)···Au(I)/Ag(I) clusters with H-bond interaction between the cluster and the solvents, especially changing the distance between two neighbor metal centres, leading to blue-shift phosphorescence of the clusters. These results highlight that the metal···metal interaction and the photoluminescence characters of the clusters can be functionally controlled by solvent molecules. The linear relationship between ∆λ and ∆d and the binding energies of host-guest complexes suggest that the phosphorescence wavelength shift can be predicted through the M···M distances in T 1 states, and the interactions in clusters can offer potential applications in solvent and catalysis transport and recognition using synthetic functional materials in the future. This work will be expanded upon by employing related binuclear complexes under systematic variation of the metal ions and solvents.
Supplementary Materials: The following are available online at http://www.mdpi.com/2079-4991/8/9/685/s1, Figure S1: Structure diagrams of clusters, Figure S2: Top view (a) and face view (b) of the representative cluster X···(S) x (X = I-III; x = 1-4), Figure S3: Trends of interaction energies (a, b, c) and the relationships between the E es and E tot (a , b , c ), Figure S4, The relationships between the E es and E tot (a) I···(S2) x , (b) II···(S1) x , (c) II···(S2) x and (d) III···(S2) x for the E CP1 of clusters, Figure S5: The relationship between ∆d and ∆λ for complexes X···(S) x in T1 states, Figure S6: The relationship between µ S1 /∆E S1−T1 values in theory and the Φ PL values in experiment, Table S1: Comparing the calculated and experimental parameters for the different oligomeric I (bond length: Å, wavelength: nm), Table S2: The NBO results of the clusters, Table S3: The key parameters and the phosphorescent character of complexes X···(S) x , Table S4: Selected GKS-EDA results of X···(Sn) x , Table S5: Molecular Orbitals and their main consist of natural atomic orbital and the characters, Table S6: Calculated phosphorescent emission (in nm) of the studied complexes with the TDDFT method, along with experimental values, Table S7: The singlet-triplet splitting energy (∆E S1−T1 , in eV), transition electric dipole moment (µ S1 , in atomics units), the µ S1 /∆E S1−T1 , and the predicted Φ PL (> 50%) for complexes X···(S) x , Table S8: The E CP of cluster I at different calculated levels (kcal/mol), Table S9: The EDA results of cluster I at different calculated levels (kcal/mol).