Mediation of Electron Transfer by Quadrupolar Interactions: The Constitutional, Electronic, and Energetic Complementarities in Supramolecular Chemistry

Summary

Studies of intermolecular interactions enhance our knowledge of chemistry across molecular and supramolecular levels. Here, we show that host-guest quadrupolar interaction has a profound influence on the molecular system. With covalently bonded dimolybdenum complex units as the electron donor (D) and acceptor (A) and a thienylene group (C₄H₂S) as the bridge (B), the mixed-valence D-B-A complexes are shaped with clefts in the middle of the molecule. Interestingly, in aromatic solvents, the D-A electronic coupling constants (H_ab) and electron transfer rates (k_et) are dramatically reduced. Theoretical computations indicate that an aromatic molecule is encapsulated in the cleft of the D-B-A array; quadrupole-quadrupole interaction between the guest molecule and the C₄H₂S bridge evokes a charge redistribution, which increases the HOMO-LUMO energy gap, intervening in the through-bond electron transfer. These results demonstrate that a supramolecular system is unified underlying the characteristics of the assembled molecules through constitutional, electronic, and energetic complementarities.

Graphical Abstract

Highlights

• •Electron transfer in {[Mo₂]-C₄H₂S-[Mo₂]}⁺ is studied optically in aromatic solvents
• •Inclusion of a quadrupolar guest molecule gates the donor-acceptor electron transfer
• •Constitutional, electronic, and energetic complementarities in supramolecular system

Supramolecular Chemistry; Computational Molecular Modelling; Molecular Physics

Introduction

Electron transfer (ET) is one of the most fundamental chemical reactions, which is ubiquitous in chemical, biological, and physical systems (Balzani, 2001). Understanding and control of ET reactions has inspired intense theoretical and experimental studies for many decades (Creutz, 1983, Newton, 1991, Demadis et al., 2001), which have resulted in enormous achievements that benefit the developments of multiple disciplines as well as their intersection areas (Marcus, 1993, Migliore et al., 2014). The classical theoretic framework of ET was shaped in the 1960s, of which the core is the Marcus theory (Marcus, 1956, Marcus, 1964, Marcus, 1993). The Marcus ET theory is formulated with three independent energetic quantities, the free energy change (ΔG°), the reorganization energy (λ), and the electronic coupling (EC) matrix element (H_ab). In the condensed phase, reorganization energy for ET is determined by two factors, nuclear vibrations of the reactant and motions of the solvent molecules, which split λ into two terms λ_i (vibrational) and λ_o (solvent) (Marcus, 1964, Marcus, 1993, Marcus and Sutin, 1985), i.e., λ = λ_i + λ_o. In this context, for a given ET system, solvent effects play a critical role in governing the ET dynamics and kinetics (Rossky and Simon, 1994, Glover et al., 2010, Kubiak, 2013). However, not only do solvents affect an ET reaction through dipole solvation, which is modeled by the dielectric continuum theory (Marcus, 1956, Marcus, 1964, Marcus and Sutin, 1985, Chen and Meyer, 1998), but solvent molecule may also cause an intramolecular charge redistribution or alter the ET process by site-specific interactions with the solute molecules. For Ru²⁺(NH₃)₅-pyrazine in acidic solution, the red shift of metal (Ru) to ligand (pyrazine) charge transfer (MLCT) band from 21,000 to 19,000 cm⁻¹ was observed (Ford et al., 1968), which is attributed to the formation of hydrogen bonding derivative Ru²⁺(NH₃)₅-pyrazine-H⁺ from theoretical investigations (Zeng et al., 1996). Meyer and co-workers studied the solvent-induced intramolecular ET or change in the extent of electronic delocalization in the mixed-valence ions [(bpy)₂ClOs(L)Ru(NH₃)₅]⁴⁺ (bpy = 2,2′-bipyridine; L = 4,4′-bipyridine [4,4′-bpy] or pyrazine [pz]) (Hupp et al., 1986, Neyhart et al., 1996). Recent work showed that polar solvent molecules intervening between the electron donor and acceptor can facilitate electron tunneling through a space (Chakrabarti et al., 2009, Graff et al., 2016). Similarly, in biological systems, it is found that interfacial water molecules are able to enhance the EC and accelerate interprotein ET (Miyashita et al., 2005, Lin et al., 2005). In the study of U-shaped donor (D)-bridge (B)-acceptor (A) molecular systems, Zimmt (Han and Zimmt, 1998, Read et al., 1999) and Paddon-Row (Napper et al., 2002, Paddon-Row, 2003) have reported that the D-A electronic coupling is significantly enhanced in aromatic solvents. These unusual solvent effects are rationalized by inclusion of solvent molecule(s) in the cleft of the solute, which increases the electron tunneling efficiency; mechanistically, this EC phenomenon is referred to as “solvent-mediated superexchange coupling” (Han and Zimmt, 1998, Read et al., 1999, Napper et al., 2002, Paddon-Row, 2003, Kumar et al., 1996).

Aromatic solvents usually have zero or small dipole moments but large quadrupole moment. A quadrupole moment can be thought of as two dipole moments aligned in such a way that there is no net dipole (Dougherty, 1996). Benzene and hexafluorobenzene are the paradigms of quadrupolar molecules (Hunter et al., 2001, Williams, 2002). As shown in Figure 1, inverse charge distributions on the C₆ ring plane and edge are found for molecules C₆H₆ and C₆F₆ due to the opposite bond polarities for the C-H and C-F bonds, which endow the molecules with a large quadrupole moment with opposite signs, ca. −29.0 × 10⁻⁴⁰C m² for benzene and 31.7 × 10⁻⁴⁰C m² for hexafluorobenzene (Williams, 2002). Therefore, to maximize the Coulomb interactions, the C₆H₆-C₆H₆ dimer adopts a T-shaped (edge to face) (Figure 1A) geometry, whereas the C₆H₆-C₆F₆ adduct is formed with a sandwich (face to face) (Figure 1B) configuration (Williams, 2002, Lee et al., 2007). A survey of protein structures showed that T-shape or the close geometries are preferred for the aromatic-aromatic interactions in proteins (Burley and Petsko, 1985). In metalloproteinase (Finzel et al., 1998), a face-to-face interaction was found between Tyr155 and the pentafluorophenyl group of the 1,3,4-thiadiazole-2-thione inhibitor. Theoretical work predicts that the T-shaped benzene dimer (Lee et al., 2007) has a binding energy of 2.4–2.5 kcal mol⁻¹ and the C₆H₆-C₆F₆ pair (West et al., 1997) is stabilized by 3.7 kcal mol⁻¹. Quadrupole-quadrupole interaction, as a type of strong intermolecular interactions, has been employed to construct supramolecular arrays or ordered structures (Williams, 2002, Ponzini et al., 2000). Relating to the ET study of synthetic D-B-A systems, aromatic structural motifs are frequently used as bridges in the molecular architecture. For an ET system involving aromatic π moieties and operating in aromatic solvents, local quadrupole-quadrupole interactions may have significant impacts on solvation of the ET dynamics (Han and Zimmt, 1998, Read et al., 1999, Napper et al., 2002, Paddon-Row, 2003), which needs to be better understood.

Figure 1.

Quadrupole-Quadrupole Interactions between Aromatic Molecules

(A and B) Schematic representations of charge distribution and supramolecular conformations that maximize the electrostatic interaction energy between molecular electric quadrupole moments for an assemblage of benzene/benzene dimer (A) and benzene/hexafluorobenzene adduct (B).

In fact, the impact of site-specific solvation on ET dynamics raises important issues on fundamental chemistry: the constitutional, electromagnetic, energetic, and functional complementarities between the host and the guest molecules as well as the complementarities between these domains at the supramolecular molecular level. Supramolecular chemistry is aimed at providing general knowledge of host-guest molecular systems (Steed and Atwood, 2009) and now is moving forward to establish rules or regulations—adaptive chemistry toward the development of more complex, functional matters (Lehn, 2002). According to J. -M. Lehn, adaptive chemistry plays the role of bridging the chemical entities involving only covalent bonds (molecules) and those involving covalent and non-covalent bonds (supramolecules) (Lehn, 2007). Following this direction, the challenge would be how to unify a supramolecular system with discrete structural and electronic identities into one system through complementary chemistry to function differently or more efficiently. Complementary chemistry is well exemplified in nature by the unique double helix structures of DNA and its unreplaceable functionality, developed from the aromatic base pairs through non-covalent π-π interactions and hydrogen bonding (Calladine et al., 2004). The understandings on aromatic interactions can also be of particular importance in biological systems in which aromatic molecules and residues, such as tyrosine (Tyr), tryptophan (Trp), and phenylalanine (Phe) side chains, are widely spread (Burley and Petsko, 1985, Tatko and Waters, 2002). Strong local interactions between the aromatic side chains are the driving force for molecular recognition and self-organization, which controls the biochemical redox reactions or transport of electrons from one subunit to another (Meyer et al., 2003, Shih et al., 2008). Theoretical and experimental model systems have proven to be informative for interrogating the role of aromatic interactions (Waters, 2002, Thomas et al., 2002a, Thomas et al., 2002b, Chen et al., 2012).

In this study, a series of three symmetrical Mo₂ dimers bridged by a thienylene (C₄H₂S) group, [Mo₂(DAniF)₃]₂(μ-N(H)SC(C₄H₂S)CN(H)S) (DAniF = N,N′-di(p-anisyl)formamidinate), [Mo₂(DAniF)₃]₂(μ-OSC(C₄H₂S)COS), and [Mo₂(DAniF)₃]₂(μ-SSC(C₄H₂S)CSS), designated as, [thi-(NS)₂], [thi-(OS)₂], and [thi-(SS)₂], respectively, were synthesized and characterized crystallographically. Given a general formula [Mo₂]-C₄H₂S-[Mo₂], the three Mo₂ dimers share a common thienylene bridge –(2,5-C₄H₂S)– but differ in the complex units [Mo₂] by alternation of the ligating atoms of the bridging ligands from N to O and S, as shown in Figure 2, which modifies the electronic property of the [Mo₂] donor (or acceptor) in the mixed-valence (MV) complexes to tune the EC. In the preliminary communication (Wu et al., 2017), we have shown that the three MV complexes implement a systematic transition from Class II to Class III via Class II-III in the Robin-Day's scheme (Robin and Day, 1967), which has been a challenge in mixed-valence chemistry (Demadis et al., 2001, Brunschwig et al., 2002, Concepcion et al., 2007). This series also exhibits typical dipole solvation dynamics, as indicated by the variation of intervalence charge transfer (IVCT) characteristics (Wu et al., 2017). However, in this study, it is found that, in aromatic solvents with zero or small dipole moments, such as, toluene, benzene, and hexafluorobenzene, the EC strength and ET rates for the MV series are dramatically diminished. The electronic decoupling effects vary depending on the subtle differences of the [Mo₂]-C₄H₂S-[Mo₂] architectures and the magnitude of the effective quadrupolar moment ⟨Q⟩ of the solvents (Reynolds et al., 1996). These results are in sharp contrast to the solvent effects observed in the U-shaped organic D-B-A molecules in aromatic solvents, where inclusion of an aromatic molecule enhances the electronic coupling (Han and Zimmt, 1998, Read et al., 1999, Napper et al., 2002, Paddon-Row, 2003). Space filling models and density functional theory (DFT) calculations reveal that, in these systems, a solvent molecule (SM) is able to occupy the cleft between the two [Mo₂] units, forming an SM-included supramolecular entity, and mediate the ET process through quadrupole interactions between the SM and the thienylene (C₄H₂S) bridge. The quadrupole-quadrupole interaction results in mixing of the π orbitals of the bridging ligand and the guest molecule, consequently increasing the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gap and substantially attenuating or mediating the through-bond superexchange pathway.

Figure 2.

A Molecular Scaffold for the Mo₂ Dimeric Complexes under Investigation

By alternation of the chelating atoms of the thienyl dicarboxylate ligand from O to S, the electronic coupling between the donor and acceptor in the mixed-valence complexes can be significantly enhanced. The vertical aryl formamidinate ligands on the Mo₂ units, combining with the bridging ligand, create two inverse U-shaped clefts on the top and bottom in the middle of the molecule.

Results

Molecular Structures of the [Mo₂]-C₄H₂S-[Mo₂] Complexes

Three Mo₂ dimers, [Mo₂(DAniF)₃]₂(μ-N(H)SC(C₄H₂S)CN(H)S) (DAniF = N,N′-di(p-anisyl)formamidinate) ([thi-(NS)₂]), [Mo₂(DAniF)₃]₂(μ-OSC(C₄H₂S)COS) ([thi-(OS)₂]), and [Mo₂(DAniF)₃]₂(μ-SSC(C₄H₂S)CSS) ([thi-(SS)₂]), were synthesized by assembling two quadruply-bonded [Mo₂]⁺ complex units with a thiolated 2,5-thienylenedicarboxamidate and 2,5-thienylenedicarboxylate bridging ligand according to the published procedures (Wu et al., 2017). The molecular structures were determined by single-crystal X-ray diffraction, as shown in Figures 3A–3C; the crystallographic data and selected bond parameters are presented in Tables S1 and S2, respectively. The Mo−Mo bond distances of ∼2.10 Å are in agreement with those of the quadruply bonded Mo₂ cores in similar ligand environments (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017). The Mo−N, Mo−O, and Mo−S bond lengths in these complexes are comparable with those in the thiooxamidate (Cotton et al., 2007) and thiooxalate (Tan et al., 2017) bridged analogues. In [thi-(NS)₂] and [thi-(OS)₂], the chelating atoms N(O) and S on the bridging ligands are positioned in cis arrangement with respect to the thienylene bridge (Figures 3A–3C), unlike the phenylene bridged analogues, which have the different chelating atoms of the bridging ligands in trans positions (Xiao et al., 2013, Shu et al., 2014). It is worth noting that, in [thi-(OS)₂], the two S chelating atoms are situated away from the S atom of the C₄H₂S group, whereas in [thi-(NS)₂], the three S atoms are on the same side. The different arrangements of the S atoms in [thi-(OS)₂] and [thi-(NS)₂] are ascribable to the different sizes of the chelating atoms O, S, and the NH groups. Furthermore, in [thi-(OS)₂] and [thi-(SS)₂], the central thienylene group is almost coplanar with the Mo−Mo bond vectors, with torsion angles of <10°; however, in [thi-(NS)₂], the central C₄H₂S ring is deviated from the five-membered Mo₂ chelating rings by ∼27°. Apparently, the non-co-planarity of this molecule is caused by the steric hindrance of the amidate hydrogen (N-H). These compounds and the other reported Mo₂ dimers having DAniF auxiliary ligands (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017) share the same molecular scaffold, which may be described topologically by an architecture with two inverse U-shaped clefts on the top and bottom in the middle of the molecule (Figure 2). The U-shaped clefts are shaped with a width of ∼10 Å and a depth of ∼8 Å, about 1 Å narrower than those for the phenylene analogues (Shu et al., 2014), because of the reduced size of the bridge. Geometrically, the three [Mo₂]-C₄H₂S-[Mo₂] complexes are slightly different with respect to the size and shape of the clefts (Table 1). For example, the clefts in [thi-(OS)₂] may be described more precisely as a “V” shape with a wide open in the front and a narrow one in the back, different from those for the other two molecules (Figures 3A–3C) because of the atomic size difference between S and O atoms. However, the X-ray structure may not represent the range of structures or conformations available in fluid solution environment.

Figure 3.

X-ray Crystal Structures and Electronic Spectra of the Mo₂ Dimers

(A–C) Single-crystal XRD structures of [thi-(NS)₂] (A), [thi-(OS)₂] (B), and [thi-(SS)₂] (C). Displacement ellipsoids for the core structure are drawn at the 40% probability level. Hydrogen atoms are omitted for clarity.

(D–F) Electronic spectra of [thi-(NS)₂] (D), [thi-(OS)₂] (E), and [thi-(SS)₂] (F) in dichloromethane (black), toluene (red), benzene (blue), and hexaflurobenzene (green).

Table 1.

DFT Calculated Frontier Molecular Orbital Energies for the Supramolecular Models in Comparison with the Spectral MLCT Data in CH₂Cl₂

Complex Model	DFT Calculation							Experiment
	Distance (Å)	HOMO−1 (eV)	HOMO (eV)	LUMO (eV)	ΔEH−H−1 (eV)	ΔEH−L (cm−1) (nm)	ΔΔEH−La (kcal mol−1)	λML (nm)	ΔEMLb (kcal mol−1)
[thi-(NS)2]′	–	−4.22	−3.88	−1.87	0.34	16,211 (617)		611
[thi-(NS)2]′⊂C6H5Me	6.9	−4.21	−3.87	−1.86	0.34	16,211 (617)	0	598	1.0
[thi-(NS)2]′⊂C6H6	6.1	−4.20	−3.86	−1.80	0.34	16,615 (602)	1.2	602	0.7
[thi-(NS)2]′⊂C6F6	5.3	−4.06	−3.76	−1.70	0.30	16,615 (602)	1.2	591	1.6
[thi-(OS)2]′	–	−4.35	−3.99	−2.22	0.36	14,276 (700)		680
[thi-(OS)2]′⊂C6H5Me	5.4	−4.28	−3.95	−2.08	0.33	15,082 (663)	2.3	662	1.1
[thi-(OS)2]′⊂C6H6	5.3	−4.26	−3.94	−2.04	0.32	15,324 (653)	3.0	655	1.6
[thi-(OS)2]′⊂C6F6	4.1	−4.14	−3.84	−1.83	0.30	16,211 (617)	5.5	625	3.7
[thi-(SS)2]′	–	−4.59	−4.11	−2.55	0.48	12,582 (795)		790
[thi-(SS)2]′⊂C6H5Me	5.3	−4.52	−4.10	−2.45	0.42	13,308 (751)	2.1	770	0.9
[thi-(SS)2]′⊂C6H6	5.3	−4.52	−4.11	−2.45	0.41	13,388 (747)	2.3	760	1.4
[thi-(SS)2]′⊂C6F6	4.0	−4.41	−4.01	−2.27	0.40	14,034 (713)	4.1	750	1.9

^aΔΔE_H−L refers to the difference of the HOMO-LUMO energy gap (ΔE_H−L) for the complex in the given aromatic solvent relative to the ΔE_H−L in DCM.

^bΔE_ML refers to the difference of the metal to ligand charge transfer energy (E_ML) measured in the spectra for the complex in the given aromatic solvent relative to the E_ML in DCM.

Electrochemistry and Spectroscopy of the Mo₂ Dimers in Dipole and Quadrupole Solvents

For the three Mo₂ dimers, electrochemical cyclic voltammograms (CVs) and differential pulse voltammograms (DPVs) were measured in dichloromethane (DCM) and toluene (C₆H₅Me); the CV diagrams are shown in Figure S1. In DCM, all three complexes display two reversible redox couples in the CVs, corresponding to the one-electron oxidations of the two Mo₂ centers from Mo₂(IV) to Mo₂(V). The redox potential separations (ΔE_1/2) were measured from the peak-to-peak values in the DPVs to be 118, 184, and 348 mV (Ag/AgCl) for [thi-(NS)₂], [thi-(OS)₂], and [thi-(SS)₂], respectively. In the series, the differences in ΔE_1/2 are extraordinary considering the very similar molecular and electronic structures between the complexes. Given the similar coordination environments for the Mo₂ centers and Mo₂⋅⋅⋅Mo₂ distances, which diminish the differences in electrostatic effects, the magnitude of ΔE_1/2 reflects the relative EC strength of the compound in the series. Therefore, the ΔE_1/2 values of this series in DCM confirm the conclusion that chelating atoms on the bridging ligand enhance the EC effect in the order of N < O < S (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017). The fully thiolated [thi-(SS)₂] exhibits an exceptionally large ΔE_1/2 (348 mV), signaling a very strong EC between the two [Mo₂] units in the MV state. Interestingly, for the series in toluene (Figure S2), the CV waves for the two one-electron redox processes are coalesced, giving ΔE_1/2 values 115 mV ([thi-(NS)₂]), 74 mV ([thi-(OS)₂]), and 78 mV ([thi-(SS)₂]). These results indicate that, in toluene, the EC of the complexes is greatly reduced. It is surprising that the weakly coupled [thi-(NS)₂] exhibits the largest ΔE_1/2, whereas similar and relatively small ΔE_1/2 values are found for the two analogues that exhibit strong coupling in DCM. There are two major factors, resonant and electrostatic effects, that account for the potential separation ΔE_1/2 in the MV complexes (Creutz, 1983, Crutchley, 1994). The diminished electronic decoupling in toluene should be attributed to a decrease of the resonant effect in that in a less polar solvent, the electrostatic effect is expected to increase.

Each of the Mo₂ dimers exhibits two absorption bands in the spectral region of 400–1,000 nm, as shown in Figures 3D–3F. The high energy (∼450 nm), weak absorbance arises from vertical transition of the valence electrons of the Mo₂ center from the bonding orbital (δ) to the antibonding orbital (δ∗) (Cotton et al., 2005). The intense, asymmetric, or overlapped absorptions can be assigned to metal (δ) to bridging ligand (π∗) charge transfer (MLCT) according to the literature work (Xiao et al., 2013, Cotton et al., 2003, Chisholm et al., 2005). In the spectra, the MLCT energies (E_ML) decrease and intensities increase when the chelating atoms change from N to O to S (Table 1), parallel to the phenylene bridged series (Xiao et al., 2013, Liu et al., 2013). Provided with the well-defined MLCT absorptions in the [Mo₂]-bridge-[Mo₂] systems, together with the bridging ligand to metal charge transfer (LMCT) bands for the MV complexes, we have verified the distant (Zhu et al., 2016), conformational (Kang et al., 2016, Chen et al., 2018), and conjugational (Gao et al., 2019) dependences of the superexchange (McConnell, 1961, Creutz et al., 1994) ET under the semi-classical theoretical framework. For [thi-(OS)₂] and [thi-(SS)₂] in the quadrupolar solvents, the MLCT band profiles are apparently changed and the intensity is lowered, in comparison with the spectra in DCM. Particularly, for [thi-(OS)₂] and [thi-(NS)₂], the asymmetrical MLCT bands in DCM split into two overlapped bands in the aromatic solvents, indicating considerable modification of the electronic structure. Dramatic spectral variation is found for complexes in hexafluorobenzene, whereas in benzene and toluene the spectra are similar. For instance, for [thi-(OS)₂], the MLCT band at 680 nm in DCM is shifted to 625 nm in C₆F₆ with a much lower molar extinction coefficient. For [thi-(NS)₂], however, the MLCT band profile is similar to that in DCM (Figure 3), showing weak solvent effects, which is consistent with the electrochemical results. Collectively, these results state that the aromatic solvent effects on the MLCT spectra are determined by the bilateral natures of the solvent and complex. Notably, the spectral differences in the aromatic solvents are even more pronounced than in strong dipole solvents, such as THF, acetone, and acetonitrile (Figure S3 and Table S3). Although the spectral variation in dipolar solvents is understood from the dielectric continuum theory (Marcus, 1956, Marcus, 1964, Marcus and Sutin, 1985, Chen and Meyer, 1998), the physical origin for the spectral variation in the nonpolar solvents needs to be rationalized.

Supramolecular Space-Filling Models Developed Based on the Geometrical and Electrostatic Complementarities

Having the U-shaped clefts in the structures (Figures 3A–3C), the Mo₂ complex molecules are capable of accommodating two small guest molecules. Topologically, the sizes and shapes of the clefts are compatible with the aromatic solvent molecules. On the other hand, the thienylene bridging moiety of the Mo₂ dimers, like a C₆H₆ ring (Figure 1), has negative charge distributed over the C₄H₂S plane but is positive on the edge. The geometric and electrostatic complementarities of the complexes with the quadrupolar solvents lead us to propose a supramolecular system with a solvent molecule included in the cleft, similar to the reported U-shaped organic systems (Han and Zimmt, 1998, Read et al., 1999, Napper et al., 2002, Paddon-Row, 2003, Kumar et al., 1996). Presumably, the quadrupole-quadrupole interactions between the C₄H₂S moiety and the included aromatic molecule endow the complex system with unusual electrochemical and spectroscopic (Figures 3D–3F) properties. In light of this, host-guest models are built for the complexes in each of the solvents. In addition, it is assumed that, for each of these supramolecular entities, only one solvent molecule is included, although there are two clefts available, because inclusion of one solvent molecule reduces the affinity of the complex to the second solvent molecule. To maximize the host-guest electrostatic attractions, for benzene and toluene, the solvent molecule contacts the C₄H₂S group in a T-shaped geometry, whereas for hexafluorobenzene, a sandwich structure of C₆F₆/C₄H₂S is adopted (Hunter et al., 2001, Williams, 2002). Furthermore, to reduce the computational expense, in these models, the auxiliary ligands are changed to N,N′-diphenylformamidinate or DPhF from DAniF of the complexes. For the three Mo₂ dimers in the three different quadrupolar solvents, there are nine host-guest entities, namely, [thi-(NS)₂]⊂C₆H₆, [thi-(OS)₂]⊂C₆H₆, and [thi-(SS)₂]⊂C₆H₆ for the complexes in benzene; [thi-(NS)₂]⊂C₆H₅Me, [thi-(OS)₂]⊂C₆H₅Me, and [thi-(SS)₂]⊂C₆H₅Me in toluene; and [thi-(NS)₂]⊂C₆F₆, [thi-(OS)₂]⊂C₆F₆, and [thi-(SS)₂]⊂C₆F₆ in hexafluorobenzene.

These 1:1 models are optimized at the density functional level to reach the energy minimum of the supramolecular systems, by which the corresponding space-filling models are developed. As shown in Figures 4A–4C, for each of the space-filling models, the aromatic molecule is held in one of the clefts of the complex molecule in the expected orientation. The C₆H₅Me or C₆H₆ molecule in the cleft stands vertically on the C₄H₂S plane (edge to face) with a centroid distance of 5.3–6.9 Å (Figure S4), showing a typical CH⋅⋅⋅π quadrupolar interaction (Hunter et al., 2001, Nishio, 2004). The ring-ring distances between the host and guest molecules are in agreement with the computed interactions between the corresponding free arenes reported elsewhere (Singh et al., 2009) and fall in the range of 4.5–7.0 Å for aromatic-aromatic interactions in proteins (Burley and Petsko, 1985). The C₆F₆-C₄H₂S distances in [thi-(OS)₂]⊂C₆F₆ (4.1 Å) and [thi-(SS)₂]⊂C₆F₆ (4.0 Å) are comparable with 3.7 Å in the crystal structures of the C₆H₆-C₆F₆ adduct (Williams et al., 1992) and are in good agreement with the face-to-face interaction (3.8–4.0 Å) between Tyr155 and the pentafluorophenyl side chain of a metalloenzyme (Finzel et al., 1998). Owing to the large torsion angle (27°) of the C₄H₂S bridge, the guest molecule in [thi-(NS)₂] is more than 1 Å further away, in comparison with systems [thi-(OS)₂] and [thi-(SS)₂], and the C₆F₆ molecule is tilted in the cleft (Figures 4A–4C and Table S2). The host-guest distances in [thi-(OS)₂]⊂SM are slightly longer than those in [thi-(SS)₂]⊂SM because of the subtle geometric differences of the clefts (Figure S4). Therefore, these space-filling models show the molecular signature of a “lock and key” relationship in supramolecular chemistry (Lehn, 2007).

Figure 4.

Space-Filling Models and Frontier Molecular Orbitals Calculated on the Supramolecular Models

(A–C) Energy-optimized space-filling models for the host-guest entities. For each of the systems, a solvent molecule is encapsulated in the U-shaped cavity of the [Mo₂]-C₄H₂S-[Mo₂] molecule, where [Mo₂] = [Mo₂(DPhF)₃], in T-shaped and sandwich manners for benzene (or toluene) and hexafluorobenzene, respectively, in contact with the thienylene group of the bridging ligand. The centroid distances between the host moiety (C₄H₂S) and guest molecules are presented in Figure S4. Geometric optimizations starting with different host-guest geometries reached the configurations without quadrupole-quadrupole interaction between the guest molecule and the C₄H₂S group (Figure S5).

(D) Frontier molecular orbitals (isodensity value ±0.02) for the simplified models [thi-(OS)₂]′, [thi-(OS)₂]′⊂C₆H₅Me, [thi-(OS)₂]′⊂C₆H₆, and [thi-(OS)₂]′⊂C₆F₆, shown along with the relative orbital energies, the HOMO−LUMO energy gaps and density contributions of metal center (Mo₂), bridging ligand (thi) and solvent molecule (SM) to the MOs. For series [thi-(NS)₂]′ and [thi-(SS)₂]′, these theoretical results are presented in Figures S6 and S7, respectively.

DFT Calculations on the Supramolecular Models

DFT calculations were performed on the supramolecular models, in comparison with the complex models. The complex structures are simplified by replacing the bulky anisyl groups on the auxiliary ligands with hydrogen atoms, yielding the computational models, [thi-(NS)₂]′, [thi-(OS)₂]′, and [thi-(SS)₂]′. Previous work has proven that the calculated results from the simplified models are in excellent agreement with the experimental data (Xiao et al., 2013, Tan et al., 2017, Cotton et al., 2003). The computational models for the proposed supramolecular entities are constructed with a quadrupolar solvent molecule included in one of the clefts of the simplified complex models, corresponding to the space-filling models (Figures 4A–4C), which are [thi-(NS)₂]′⊂C₆H₆, [thi-(OS)₂]′⊂C₆H₆, and [thi-(SS)₂]′⊂C₆H₆ for the complexes in benzene; [thi-(NS)₂]′⊂C₆H₅Me, [thi-(OS)₂]′⊂C₆H₅Me, and [thi-(SS)₂]′⊂C₆H₅Me in toluene; and [thi-(NS)₂]′⊂C₆F₆, [thi-(OS)₂]′⊂C₆F₆, and [thi-(SS)₂]′⊂C₆F₆ in hexafluorobenzene.

The optimized geometries of the simplified supramolecular models are essentially the same as those of the space-filling models regarding to the host-guest contacts. For [thi-(OS)₂]′, the resultant frontier molecular orbitals HOMO, HOMO−1, and LUMO are shown in Figure 4D, as a representative of the three complex systems (see Figures S6 and S7 for the rest systems), and the MO energies are presented in Table 1, along with experimental results. As shown in Figure 4D, the HOMO results from the out-of-phase (δ − δ) combination of the δ orbitals with a filled π orbital of the bridging ligand, whereas the HOMO−1 is obtained by in-phase (δ + δ) combination of the δ orbitals with an empty π∗ orbital of the bridging ligand. These two metal orbitals are nondegenerate owing to d(δ)-p(π) orbital interactions between the Mo₂ centers and the bridging ligand (Xiao et al., 2013, Tan et al., 2017). The LUMO is contributed mainly by the π∗ orbital of the bridging ligand. Remarkably, for supramolecular systems [thi-(OS)₂]′⊂SM (Figure 4D) and [thi-(SS)₂]′⊂SM (Figure S7), the guest molecule is involved in the LUMO by contributing significant π electron density (∼6%), as a result, substantially raising the LUMO energy level, relative to that of the complex model. It is worth noting that, for both T-shaped and face-to-face interaction modes (Figure 4D), only the aromatic π orbital of the guest molecule is mixed with the π orbital of the bridging ligand. In the series, the LUMO energy increases as a function of the strength of the quadrupole-quadrupole interactions (Table 1 and Figures S6 and S7). For instance, small LUMO energy variation is found for [thi-(OS)₂]′⊂C₆H₅Me but large change for [thi-(OS)₂]′⊂C₆F₆ with strong quadrupole interactions. In contrast, Figure S6 shows that, for [thi-(NS)₂]′⊂SM, the included solvent molecule does not contribute electron density to the LUMO, although the MO energies are varied appreciably. The different solvation property of [thi-(NS)₂] should be attributed to the large host-guest distances and weak quadrupole effects, consistent with the experimental results. Calculations show clearly that the strong quadrupole-quadrupole interaction evokes charge redistribution, modifying the electronic structure of the bridging ligand. This means that intermolecular interaction is able to alter profoundly a chemical system.

In studies of the Mo₂ dimers, it is well documented that the HOMO to LUMO electron transition gives rise to the metal to ligand charge transfer absorption (Xiao et al., 2013, Tan et al., 2017, Cotton et al., 2003, Chisholm et al., 2005); therefore, the HOMO to LUMO energy gap (ΔE_H-L) is transformed to the MLCT band energy (E_ML). Remarkably, for all the computational models, the calculated ΔE_H-L values (Table 1) are in good agreement with measured E_ML from the UV-visible spectra (Figures 3D–3F). For those without a guest molecule included, which model the spectra of the complexes in DCM, the ΔE_H-L values decrease with changing the chelating atoms from N to O to S, consistent with the variation trend of E_ML for the series. Importantly, for each of the three complex systems, the ΔE_H-L and E_ML values (eV) increase as a result of introducing a quadrupole molecule into the cleft. For the complex in different solvents, the magnitudes of ΔE_H-L vary depending on the nature of the included quadrupole molecule (Table 1) and thus correlating to the strength of quadrupole-quadrupole interaction. In general, toluene has the smallest influence on the electronic and spectroscopic properties and hexafluorobenzene the largest, as expected from the effective quadrupole moments of the solvents, that is, ⟨Q⟩ = 7.92 DÅ (C₆H₅Me) and 9.43 DÅ (C₆F₆) (Reynolds et al., 1996). The quadrupolar effect of benzene is generally larger than that in toluene, as measured from ΔE_H-L and E_ML (Table 1), because of the larger ⟨Q⟩ (8.35 DÅ). For [thi-(NS)₂], the MLCT energies in the aromatic solvents are higher than those in DCM, showing some quadrupolar effects. It is noted that the E_ML value in toluene (598 nm) is larger than that in benzene (602 nm), whereas the calculated electronic transition energy (ΔE_H-L) for the benzene-included system is larger (Table 1). This is because the toluene guest molecule exerts weak quadrupolar effects relative to benzene plus a significant dipole solvation effect that is not accounted for in the calculations. Therefore, the computational results are in excellent agreement with the experimental results, showing the strength of quadrupole effects exactly as predicated by the space-filling models.

The HOMO−HOMO−1 gap (ΔE_H-H-1) also measures the relative strength of EC between the two Mo₂ centers (Xiao et al., 2013, Tan et al., 2017, Cotton et al., 2007); large orbital splitting indicates a strong metal to metal interaction. In each complex system, the solvent-free model exhibits a ΔE_H-H-1 value larger than those of the supramolecular systems. Therefore, the decrease of ΔE_H-H-1 or ΔΔE_H-H-1 value (Table 1) in aromatic solvent accounts for the quadrupolar effect. System [thi-(NS)₂]′ has the smallest variation of ΔE_H-H-1 in aromatic solvents, thus experiencing the smallest impact from the aromatic guest. For [thi-(OS)₂]′ and [thi-(SS)₂]′, the changes in HOMO−HOMO−1 gap in the same solvent are similar, indicating similar solvent decoupling effects. The relatively weak quadrupolar effects for [thi-(OS)₂] is ascribable to the “V”-shaped geometry of the clefts in the molecular structure (Figure 3), which increases the host-guest centroid distances by 0.1 Å (Figure S4). Overall, DFT calculations on the complex models suggest that, in aromatic solvents, a solvent molecule included in the cleft of the [Mo₂]-C₄H₂S-[Mo₂] molecule impacts significantly the electronic configuration of the complex through quadrupole-quadrupole interactions with the C₄H₂S group.

Intervalence Charge Transfer Absorptions and the EC Parameters (H_ab) of the Mixed-Valence Complexes

The cationic mixed-valence complexes [thi-(NS)₂]⁺, [thi-(OS)₂]⁺, and [thi-(SS)₂]⁺ were produced by oxidation of the neutral compounds with one equivalent of ferrocenium hexafluorophosphate (in situ) and characterized by X-band EPR spectra with a g value of ∼1.95, as shown in Figure S8 (Wu et al., 2017, Xiao et al., 2013, Tan et al., 2017, Chisholm et al., 2005). The near-mid-IR spectra of the MV complexes in toluene, benzene, and hexafluorobenzene are shown in Figure 5 and the spectral parameters listed in Table 2, together with data in DCM for comparison, and the full spectra are presented in Figures S9–S18. Importantly, in the aromatic solvents, the MV complexes exhibit distinct spectra from those in DCM, especially for [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺, and the spectra in benzene and toluene are substantially different from those in hexafluorobenzene. For [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺, characteristic IVCT absorptions are detected with increased transition energies (E_IT) and decreased molar extinction coefficients (ε_IT) (Table 2), relative to the IVCT bands in DCM, whereas in hexafluorobenzene, a very weak and broad IVCT absorbance is observed for the three MV complexes. These optical behaviors show the electronic decoupling effects of the aromatic solvents according to the Hush formalism (Hush, 1967, Hush, 1968), in sharp contrast to the organic U-shaped donor-acceptor systems, in which inclusion of an aromatic solvent molecule improves the EC (Han and Zimmt, 1998, Read et al., 1999, Napper et al., 2002, Paddon-Row, 2003, Kumar et al., 1996). Notably, the spectral variations in aromatic solvents are quite different from the observations in dipole solvents THF, acetone, and acetonitrile (Figure S19), which show solvent independence of the IVCT energy for electron delocalized systems of Class III (Wu et al., 2017, Tan et al., 2017).

Figure 5.

Intervalence Charge Transfer Spectra of the Mixed-Valence Complexes in Various Solvents

(A–C) IVCT absorptions in the near-mid-IR region of the MV complexes [thi-(NS)₂]⁺ (A), [thi-(OS)₂]⁺ (B), and [thi-(SS)₂]⁺ (C) in dichloromethane (black), toluene (red), benzene (blue), and hexafluorobenzene (green). Shown in the inset are the y-expanded IVCT bands for the complex in the given solvents. [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ in hexafluorobenzene do not display characteristic IVCT bands.

Table 2.

Spectroscopic Data of the IVCT Bands and the Derived EC and ET Parameters for the MV Dimers [thi-(NS)₂]⁺, [thi-(OS)₂]⁺, and [thi-(SS)₂]⁺ in Different Solvents

System	EIT (cm−1)	ϵIT (M−1cm−1)	Δν1/2 (exp) (cm−1)	Δν1/2 (cal) (cm−1)	Hab (cm−1)	2Hab/λ	ΔG* (cm−1)	ket (s−1)
[thi-(NS)2]+a	2,630	7,933	2,480	2,464	892	0.68	68	3.6×1012
[thi-(NS)2]+⊂C6H5Me	2,062	7,760	1,845	2,176	668	0.65	64	3.7×1012
[thi-(NS)2]+⊂C6H6	2,365	5,085	2,242	2,337	638	0.54	125	2.7×1012
[thi-(NS)2]+⊂C6F6	5,745	913	4,255	3,632	580	0.20	915	6.0×1010
[thi-(OS)2]+a	2,254	11,398	2,009	2,281	1,127	1.00	0	5.0×1012
[thi-(OS)2]+⊂C6H5Me	4,570	1,512	2,564	3,240	517	0.23	684	1.8×1011
[thi-(OS)2]+⊂C6H6	4,886	1,017	2,936	3,350	469	0.19	797	1.1×1011
[thi-(OS)2]+⊂C6F6	/	/	/	/	/	/	/	/
[thi-(SS)2]+a	3,290	20,261	1,266	2,823	1,645	1.00	0	5.0×1012
[thi-(SS)2]+⊂C6H5Me	4,238	1,523	2,055	3,120	448	0.21	659	2.1×1011
[thi-(SS)2]+⊂C6H6	4,246	1,305	2,358	3,122	444	0.21	664	2.0×1011
[thi-(SS)2]+⊂C6F6	/	/	/	/	/	/	/	/

^aThe IVCT band parameters are reported by Wu et al., 2017.

Based on the IVCT band parameters (E_IT, ε_IT, and Δν_1/2) (Table 2), we can quantitatively evaluate the quadrupolar effects on electronic coupling by calculation of the EC matrix elements H_ab using the Mulliken-Hush expression (Equation 1) (Creutz, 1983, Hush, 1967, Hush, 1968).

$$H_{\text{ab}}=2.06\times {10}^{-2}\frac{{\left(\Delta {\nu }_{1/2}{\epsilon }_{\max }{E}_{\text{IT}}\right)}^{1/2}}{r_{\text{ab}}}$$ (Equation 1)

For strongly coupled Class II-III and Class III, H_ab is determined directly from E_IT according to the semi-classical theory (Equation 2) (Creutz, 1983, Brunschwig et al., 2002),

$$H_{\text{ab}}=E_{\text{IT}}/2$$ (Equation 2)

In application of Equation 1, the effective ET distance r_ab is estimated to be 5.3 Å from the geometrical length of the “−CC₄H₂SC−” moiety, considering electron delocalization within the [Mo₂] unit (Wu et al., 2017, Xiao et al., 2013, Tan et al., 2017, Yu et al., 2016). In the previous communication (Wu et al., 2017), the H_ab parameters in DCM were determined to be 892 ([thi-(NS)₂]⁺), 1,127 ([thi-(OS)₂]⁺), and 1,645 cm⁻¹ ([thi-(SS)₂]⁺). For the series, the IVCT characteristics and the large H_ab values indicate that these MV complexes are moderately strongly or strongly coupled, thus being assigned to three different regimes, Class II, Class II-III, and Class III in Robin-Day's classification (Wu et al., 2017). In this study, for the MV complexes that exhibit well-defined IVCT bands in the aromatic solvents with the band parameters (E_IT, ε_IT, and Δν_1/2) determinable, we are able to derive the H_ab parameters from Equation 1 (Table 2). In DCM, by featuring an intense, low-energy (2,254 cm⁻¹) and half cutoff IVCT band in the spectra (Figure 5B), [thi-(OS)₂]⁺ is characterized as a species on the Class II-III borderline (Demadis et al., 2001, Wu et al., 2017, Brunschwig et al., 2002). For the fully thiolated [thi-(SS)₂]⁺, the IVCT band energy (E_IT) is increased to 3,290 cm⁻¹ and the band shape is more symmetric, which manifests the Class II-III crossover to Class III (Wu et al., 2017, Tan et al., 2017). Importantly, in the aromatic solvents, the differences in EC between [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ are blurred and the two complexes exhibit similar IVCT characteristics, which are completely different from the spectra in DCM (Figures 5B and 5C). For instance, for [thi-(SS)₂]⁺ in toluene and benzene, the IVCT band energy is no longer solvent independent as in polar solvents (Figure S19). For both, a very weak, Gaussian-shaped IVCT band is observed and the maximum absorption shifted toward high energy. The transition energies for [thi-(OS)₂]⁺, 4,570 cm⁻¹ in toluene and 4,886 cm⁻¹ in benzene, are significantly higher than those for [thi-(SS)₂]⁺ in these solvents (Table 2). The larger H_ab values for [thi-(OS)₂]⁺ as compared with [thi-(SS)₂]⁺ are in sharp contrast to observations that substitution of S atoms for the O chelating atoms greatly improves the EC between the two bridged Mo₂ centers (Xiao et al., 2013, Tan et al., 2017). Furthermore, in benzene and toluene, these two MV complexes exhibit the IVCT bands much narrower than those in dipole solvents (Table S4) (Wu et al., 2017) and those observed for other weakly coupled {[Mo₂]-bridge-[Mo₂]}⁺ complexes in DCM (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017, Kang et al., 2016). This implies that the nature of the bridge is somehow altered, in accordance with the computational results (Figure 4D). The significant change of the IVCT band features indicates the tremendous electronic decoupling effects of the aromatic solvents. Quantitatively, the H_ab values, ca. 450–520 cm⁻¹ (Table 2) are lowered to half or one-third of the values in DCM, indicating very weak EC, in comparison with the data for related Mo₂ D-B-A systems (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017, Kang et al., 2016). In hexafluorobenzene, the MV complexes experience very strong quadrupolar effects, displaying an extremely broad charge transfer absorption (Figure 5B), which does not characterize a classic double-well ET system (Creutz, 1983, Newton, 1991, Marcus, 1993, Marcus and Sutin, 1985).

Distinct optical properties are observed for [thi-(NS)₂]⁺ in the aromatic solvents. In benzene and toluene, it exhibits intense asymmetrical IVCT spectra, with band parameters similar to those in DCM (Figure 5 and Table 2). The H_ab values, 638 cm⁻¹ in benzene and 668 cm⁻¹ in toluene, are close to that in DCM (892 cm⁻¹) (Wu et al., 2017) and comparable with those for other moderately strongly coupled systems (Xiao et al., 2013). Of these two solvents, benzene gives the system a smaller H_ab, showing some quadrupolar effects, instead of dipole effect, whereas in toluene, the IVCT spectrum features lower transition energy (2,062 cm⁻¹), higher intensity (7,760 M⁻¹cm⁻¹), and smaller half-height bandwidth (1,845 cm⁻¹), indicating the stronger electronic coupling and typical dipole solvation behaviors. Obviously, the differences in mixed valency for the complexes in different solvents are caused by the subtle differences in the host-guest geometry and the magnitude of quadrupole moment between these two solvents. In hexafluorobenzene, there appear in the spectra typical absorption bands for MV Mo₂ dimers, δ→δ∗ at 440 nm, MLCT at 585 nm, LMCT at 790 nm, and IVCT at 5,745 cm⁻¹, although the absorbances are very weak (Figure S9), different from the charge transfer absorbances for [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ in the same solvent. Analysis of the IVCT band gives a H_ab of 580 cm⁻¹, indicating a significant electronic decoupling effect. It is clear that, for [thi-(NS)₂]⁺, the MV property is less affected by the aromatic solvents. As a result, this complex is even more strongly coupled than the other two analogues in the series. Collectively, the quadrupole effects on the mixed-valency and the IVCT spectra of the MV series are fully in accordance with host-guest geometries in the space-filling models. These results demonstrate an MV transition from strongly coupled Class III to weakly coupled Class II. Significantly, the system transition is realized by site-specific, single-molecule interactions, intrinsically different from dipole solvation (Creutz, 1983, Demadis et al., 2001, Chen and Meyer, 1998) and solvent dynamic effect (Rossky and Simon, 1994, Lear et al., 2007).

Impacts of the Quadrupolar Effects on the ET Rates (k_et)

According to the transition state theory, the through-bond ET rate for MV compounds is limited by the nuclear vibrational frequency, ca. 5 × 10¹² s⁻¹ (Creutz, 1983, Brunschwig et al., 2002, Brunschwig and Sutin, 1999). In DCM, [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ exhibit typical Class II-III and Class III spectral features and parameters (Figure 5 and Table 2), respectively, from which ET rates of 5 × 10¹² s⁻¹ are assigned arbitrarily. For those in Class II, the valence electrons are trapped to a varying extent with respect to the vibrational timescale (10⁻¹² s, or picoseconds). The thermal ET dynamics can be described adiabatically from the magnitude of H_ab under the semi-classical theoretic framework (Creutz, 1983, Demadis et al., 2001, Marcus and Sutin, 1985, Brunschwig and Sutin, 1999, Newton and Sutin, 1984). Combination of the Marcus theory of ET kinetics and Hush optical analysis of EC matrix element allows determination of ET dynamics (ΔG∗) and kinetics (k_et) at the level of the transition state from Equations 3 and 4.

$${\Delta G}^{\ast }=\frac{{\left(\lambda –2H_{\text{ab}}\right)}^2}{4\lambda }$$ (Equation 3)

$$k_{\text{et}}=A\exp \left(–\frac{{\Delta G}^{\ast }}{k_{\text{B}}T}\right)$$ (Equation 4)

In Equation 3, the reorganization energy λ = E_IT + ΔG⁰ and for symmetric systems (ΔG⁰ = 0), λ = E_IT (Creutz, 1983, Marcus, 1993, Marcus and Sutin, 1985). In Equation 4, the prefactor A is the product of electronic factor κ and electronic frequency ν_el or nuclear frequency ν_n, depending on the magnitudes of ν_el and ν_n (Brunschwig and Sutin, 1999, Sutin, 1983). For these Mo₂ dimers, A = 5.0 × 10¹² s⁻¹ by applying an averaged nuclear frequency (ν_n = 5.0 × 10¹² s⁻¹) because ν_el ≫ 2ν_n and the electronic factor κ ≈ 1 (Yu et al., 2016, Xiao et al., 2014, Chisholm and Patmore, 2007). Calculations yield the ET rate constants (k_et) in the range of 10¹⁰–10¹² s⁻¹ for the complex series in different solvents (Table 2). For [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ in C₆F₆, the strong quadrupole-quadrupole interactions preclude optical determination of k_et. In benzene and toluene, the k_et values are lowered by 1–2 orders of magnitude. For [thi-(NS)₂]⁺, similar ET rates (∼10¹² s⁻¹) are found in benzene, toluene, and DCM, as expected from the similar spectral features, whereas in hexafluorobenzene, the k_et is lowered to 6.0 × 10¹⁰ s⁻¹ (Table 2).

Discussion

This study shows that perturbation of the bridge by interaction with an associated guest molecule is able to shift an MV system from the delocalized to the localized regime and gate the D-A ET by directly intervening with the bridge π orbital that serves as the charge transfer platform. Therefore, the quadrupolar effects on EC and ET are best described as solvent-mediated superexchange decoupling, in contrast to the reported solvent-mediated superexchange coupling (Han and Zimmt, 1998, Read et al., 1999, Napper et al., 2002, Paddon-Row, 2003, Kumar et al., 1996). The contrary behaviors of aromatic solvents are due to the different bonding characters of the bridge in the D-B-A systems. Unlike the present complexes, in the U-shaped organic D-B-A molecules, the bridges are built by covalent σ bonds, which do not function well for through-bond superexchange; thus, inserting an aromatic molecule improves the donor-acceptor electronic communication. In this study, the 2H_ab/λ values for [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ decrease from 1.0 to ∼0.2 (Table 2) with changing the solvent from DCM to benzene (or toluene), showing the efficient mediation of quadrupolar effects on the EC (Brunschwig et al., 2002). In chemical D-B-A systems, a general strategy to control EC and ET is to modify the geometric and electronic properties of the bridge. Remarkably, here, dramatic electronic decoupling occurs in mixed-valent state in the quadrupole solvents, whereas the {[Mo₂]-C₄H₂S-[Mo₂]}⁺ structure remains intact. This means that taking advantage of geometric and electronic complementarities between the host and guest molecules, one can tune the electronic coupling through non-covalent interactions, which is controllable and reversible.

Moreover, calculations show that inclusion of an aromatic molecule increases the low-lying π∗ orbital energy and stabilizes the ground state by decreasing the high-lying π orbital energy. Thus, we can estimate the stabilizing energy (−ΔG°) or free energy of association (ΔG°) from the decrease of the occupied π orbital energy, which equals approximately the change of HOMO-LUMO energy gap or ΔΔE_H-L in the aromatic solvents relative to the ΔE_H-L in DCM. The calculated ΔΔE_H-L data are compared with the experimental results (ΔE_ML), as shown in Table 1. In hexafluorobenzene, [thi-(OS)₂] and [thi-(SS)₂] present the ΔΔE_H-L (≈−ΔG°) values of 4.1 and 5.5 kcal mol⁻¹, respectively, close to the calculated stabilizing energy of 3.7 kcal mol⁻¹ for the C₆H₆-C₆F₆ adduct (West et al., 1997). This stabilization energy, gained by C₆F₆-C₄H₂S quadrupolar interaction, is reasonably smaller than the association energy (7.1 kcal mol⁻¹) for C₆F₆ parallel stacked on the top of Zn porphyrin with a short separation (2.93 Å) (Morisue et al., 2017). In benzene (toluene), the ΔΔE_H-L values fall in the range of 2.1–3.0 kcal mol⁻¹ (Table 1), in excellent agreement with the calculated stabilizing energy (Hobza et al., 1996) of 2.3 kcal mol⁻¹ and the association energy (Tsuzuki and Uchimaru, 2006) of 2.46 kcal mol⁻¹ for the T-shaped benzene dimers.

Shown in Figures 6A–6C are the plots of ΔΔE_H-L against the effective quadrupole moments ⟨Q⟩ (Reynolds et al., 1996), in comparison with the spectroscopic data, ΔE_ML versus ⟨Q⟩. For [thi-(OS)₂] and [thi-(SS)₂], a good linear relationship between ΔΔE_H-L and ⟨Q⟩ is found. For [thi-(OS)₂] (Figure 6B), the linear plot of ΔΔE_H-L versus ⟨Q⟩ has a larger slope than that for [thi-(SS)₂] (Figure 6C), indicating the larger decoupling effects, which is in contrast to its larger coupling constants H_ab. The stronger quadrupolar effects for [thi-(OS)₂] from calculations can be rationalized by the electronegative O chelating atoms of the bridging ligand, which then enhances the host-guest electrostatic interactions, as indicated by the larger density contribution of the guest molecule to the LUMO (Figures 4 and S7). On the other hand, the relatively small decoupling effects (relatively large H_ab) in solution is likely due to the V-shaped cleft of the molecular structure (Figure 3B) that prevents the guest molecule getting close to the C₄H₂S bridge as much as in [thi-(SS)₂]. Remarkably, linear correlations of ΔE_ML versus ⟨Q⟩ are also obtained in both systems (Figures 6B and 6C and Table 1), which are nearly parallel to the theoretical results. The deviations between the experimental and theoretical results can be rationalized by the dipole solvation and molecular dynamics in solution. In benzene and toluene, the changes of the MLCT energies or ΔE_ML, ca. 0.7–1.6 kcal mol⁻¹ (Table 1), which may be considered to be the experimental values of stabilizing energy (−ΔG°) of the supramolecular systems, are in excellent agreement with the free energies (ΔG° = −0.6 to −1.3 kcal mol⁻¹) contributed by aromatic pairs in protein (Burley and Petsko, 1985). In contrast to [thi-(OS)₂] and [thi-(SS)₂], [thi-(NS)₂] does not exhibit the linear relationship between the ΔΔE_H-L (or ΔE_ML) and the solvent ⟨Q⟩ values (Figure 6A and Table 1). These results are understandable from the simultaneous presence of weak site-specific quadrupole interactions and significant dipole solvation, as expected from the space-filling models and the calculated results. Therefore, for this Mo₂ D-B-A system, the increase of the HOMO-LUMO energy gap is a good estimate of the stabilizing energy of including an aromatic molecule through quadrupole-quadrupole interaction, which provides a vital interpretation on the supramolecular complementarity in constitution, electronic state, and energetics.

Figure 6.

Correlations of ΔΔE_H-L and ΔE_ML with Quadrupole Moments of the Aromatic Solvents in Use and Electrostatic Potential Maps of the Free Aromatic Solvent and Complex Molecules and the Supramolecular Entities

(A–C) Plots of changes of the HOMO−LUMO energy gaps (ΔΔE_H-L) of complex models in aromatic solvents, relative to that in DCM, against the effective quadrupole moments ⟨Q⟩ of the solvent molecules (SM), along with the experimental data ΔE_ML versus ⟨Q⟩, showing the quadrupole effects for supramolecular systems [thi-(NS)₂]⊂SM (A), [thi-(OS)₂]⊂SM (B), and [thi-(SS)₂]⊂SM (C) (SM = C₆H₅Me, C₆H₆ and C₆F₆).

(D and E) The DFT calculated electrostatic potential surface maps for the complexes and free aromatic solvent molecules (D) and the complex systems with a solvent molecule encapsulated (E). For both of the molecular and supramolecular systems, the electrostatic potential maps refer to the same color codes as shown.

The quadrupole-quadrupole interactions in these supramolecular complex systems are visualized by the electrostatic potential maps generated from DFT calculations on the simplified models. The electrostatic potential maps (Figure 6D) show that the free benzene (toluene) and hexafluorobenzene molecules display opposite charge distributions surrounding the C₆ rings, as depicted in Figure 1. Of the three complex models, the electrostatic potentials vary in the order of [thi-(NS)₂]′ > [thi-(SS)₂]′ > [thi-(OS)₂]′. This order is consistent with that of the electrochemical potentials E_1/2(1) of the complexes in DCM, that is, 0.41 V ([thi-(NS)₂]), 0.42 V([thi-(SS)₂]), and 0.48 V ([thi-(OS)₂]) (versus Ag/AgCl) (Wu et al., 2017). The relatively low electrostatic potential for [thi-(OS)₂]′ is likely due to the presence of more electronegative O chelating atoms of the bridging ligand. For the three supramolecular entities, as shown in Figure 6E, the electrostatic potential surfaces for the guest molecules vary substantially, but not apparently for the host complexes, because the charge redistribution is averaged or “diluted” by the large number of atoms on the complex molecule. Importantly, in the systems of [thi-(OS)₂]′ and [thi-(SS)₂]′ (Figure 6E), the overall electrostatic potentials for the included C₆H₅Me and C₆H₆ molecules increase, in comparison with the free solvent molecules (Figure 6D); in contrast, the included C₆F₆ molecule exhibits lower electrostatic potentials compared with free C₆F₆. Therefore, the electrostatic potential maps of the guest molecules demonstrate that benzene and toluene molecules, as electron donors, contribute π electron density to the host molecule through quadrupole-quadrupole interaction, whereas the hexafluorobenzene molecule is the electron acceptor because of the electron deficiency of the ring center (Figure 6D). The electrostatic potential maps for the supramolecular systems are in accordance with the IVCT spectra of the complexes in the aromatic solvents. For [thi-(NS)₂], the variation of electrostatic potential maps is less pronounced; similarly, the spectral changes of the MV complex in the aromatic solvents are minor, except for the case of hexafluorobenzene.

On the basis of the experimental observations and the computational results, the perturbation of the guest molecule on the ET dynamics and mechanism can be described by Figure 7. Pictorially, in the supramolecular ET systems, typically, for [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺, the guest molecule C₆H₆ or C₆H₅Me vertically standing in the middle of the D-B-A molecule builds a “wall” that blocks the electrons transferring from the donor to the acceptor (Figure 7B). Electronically, the intervening molecule donates π electron density to the anti-bonding bridge π∗ orbital, diminishing the d(δ)-p(π) orbital interaction between the Mo₂ centers and the bridge. In the two-state model, the ET energetics are characterized by the higher reorganization energy (λ) and activation energy (ΔG∗). The single, Gaussian-shaped IVCT band in the spectra (Figure 5) implies that the system retains its original ET reaction coordinate, with increased λ and decreased H_ab. Correspondingly, the single-well potential energy surfaces (PES) for ET (Figure 7A) are altered to a double-well PES diagram (Figure 7B). The ET process is dominated by the through-bond superexchange mechanism (McConnell, 1961), as evidenced by the presence of MLCT and LMCT in the spectra for the MV complexes (Figures S10 and S11) (Creutz et al., 1994). However, for systems in hexafluorobenzene, there is no characteristic IVCT band observed. The broad, weak absorbances in the near-mid-IR region dictate that the system undergoes a different ET process via a distinct mechanism. In this scenario, considering that the C₆ ring center is electron deficient, we propose that the C₆F₆ molecule lying on the top of the C₄H₂S group plays a role of electron relay for the D-A ET, which is schematically represented in Figure 7C. In the ET course, the C₆F₆ molecule serves as an acceptor with respect to the Mo₂ donor, but a donor for the Mo₂ acceptor for completion of the two electron hopping steps. This hypothesis is further supported by the absence of an LMCT band in the spectra of the MV complexes (Figures S10 and S11), indicating that the electron-hole superexchange pathway is not in operation (Liu et al., 2013, Creutz et al., 1994). Accordingly, the two-state model for the ET reaction is constructed with two asymmetrical potential energy surfaces crossing over the transition state of the reaction, as described in Figure 7C. Continuous electron hopping from the Mo₂ donor to acceptor generates the broad, featureless, weak charge transfer absorptions as observed (Figures 5B and 5C). As a result of intervening of the C₆F₆ molecule, the ET system is transformed from the adiabatic to the non-adiabatic regimes. However, in [thi-(NS)₂]⁺⊂C₆F₆, in which the C₆F₆ molecule stays further from the C₄H₂S bridge, the perturbation on the ET reaction is not as strong as in [thi-(OS)₂]⁺⊂C₆F₆ and [thi-(SS)₂]⁺⊂C₆F₆, as evidenced by the MLCT, LMCT, and IVCT bands in the spectra (Creutz et al., 1994), although the ET rate is significantly reduced (Table 2). Therefore, in this system, electron transfer proceeds via the through-bridge superexchange pathway as shown in Figure 7D.

Figure 7.

Schematic Illustration of Quadrupole Effects on Thermal Electron Transfer in the Mixed-Valence Mo₂ Dimers

(A–D) Donor-bridge-acceptor models (top) and the corresponding ET potential energy surface diagrams (bottom) for [thi-(OS)₂]⁺ and [thi-(SS)₂]⁺ in DCM (A), benzene (B), and hexafluorobenzene (C) and for [thi-(NS)₂]⁺ in hexafluorobenzene (D).

Collectively, three MV [Mo₂]-C₄H₂S-[Mo₂] complexes in DCM belong to three different mixed-valent regimes, Classes II, II-III, and III in the Robin-Day's classification, by changing the chelating atoms from N to O and S. Surprisingly, in the aromatic solvents, such as, benzene, toluene, and hexafluorobenzene, the IVCT characteristics are significantly altered; the electronic coupling matrix elements (H_ab) and electron transfer rate constants (k_et), determined by optical analysis under the Marcus-Hush theory, are dramatically reduced, in contrast to the predications from the dielectric continuum model. Space-filling models developed by DFT calculations show that an aromatic molecule is encapsulated in the cleft of the D-B-A molecule, contacting with the C₄H₂S ring in T-shaped (for benzene and toluene) or face-to-face (for hexafluorobenzene) geometries with varying distances (4.0–6.9 Å). Remarkably, it is found that, in the aromatic solvents, the magnitudes of H_ab and k_et are correlated to the strength of quadrupole-quadrupole interactions between the guest molecule and the C₄H₂S bridge. Theoretical results reveal that the quadrupole effect evokes a charge redistribution of the bridging ligand and increases the HOMO-LUMO gap, consequently gating the electron transfer from one Mo₂ center to the other. From the increase of the low-lying π∗ orbital energy the stabilizing energies for the supramolecular systems are estimated to be 2.2–5.5 kcal mol⁻¹. Evidently, intervening of the guest molecule to the bridge modifies the electronic structure and alters the ET pathway; thus, the D-B-A system undergoes a chemical transformation without bond breakage and formation. Therefore, this work, with the rare examples, demonstrates that a supramolecular system is unified underlying the characteristics of the assembled molecules through constitutional, electronic, and energetic complementarities. With the molecular signature on “the chemistry beyond the molecule” provided in this study, it is substantiated that the general principles developed in molecular chemistry are universal, which govern supramolecular systems as well.

Limitations of the Study

In this study, the stabilization energies of the supramolecular systems through quadrupole-quadrupole interaction were estimated based on the measured MLCT energies or calculated HOMO-LUMO gaps. No strict theoretic calculations of the potential energy for the system were performed, although reasonable results were obtained in comparison with the literature data. As the investigation goes deep, the issues of energetic complementary of the supramolecular system can be further addressed using well-developed theoretic methods. In the Mo₂-Mo₂ mixed-valance system with a saturated bridge, enhancement of electronic coupling through solute-solvent interactions, as seen in the organic U-shaped systems in photoinduced ET, was not observed.

Methods

All methods can be found in the accompanying Transparent Methods supplemental file.

Published: December 20, 2019

Data and Code Availability

The X-ray crystallographic data ([thi-(NS)₂], [thi-(OS)₂] and [thi-(SS)₂]) reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition number CCDC 1935628-1935630.