Theoretical investigation of steric effects on the S1 potential energy surface of o-carborane-anthracene derivatives

TDDFT scan calculations were performed for s-carborane-anthracene derivatives (o-CB-X-Ant where X=-H, -CH3, -C2H5 and tert-butyl or -tBu) in order to understand the interplay between the steric effects, S1 potential energy surface (PES) and photophysical properties. The results show that all systems exhibit three local minima on the S1 PES, which correspond to the emissive LE and TICT state, along with the nonemissive CT state respectively. In the case of the unsubstituted system (o-CB-H-Ant), and -CH3 and -C2H5 substituted cases, S1 PES is predicted to be quite flat for certain conformations indicating that it is possible for these systems to reach the nonemissive CT state without a large energy penalty. In comparison, conformational pathways for the nonemissive CT state are predicted to be energetically unfavorable for o-CB-tBu-Ant as a result of both steric and electronic effects. These results provide a mechanism for the enhanced emission of σ-CB-fluorophore molecules with bulky ligands.

fluorophore molecules. The results show that while the nonemissive CT state is energetically favorable for o-CB-H-Ant, emissive TICT state becomes significantly more favorable with -tBu substitution. It is also shown that energy barriers on S 1 PES for the conformations exhibiting parallel orientation of C 1 -C 2 bond and Ant are quite large with -tBu substitution compared to the cases in X =-H, -CH 3 and -C 2 H 5 . These findings provide a possible mechanism for the enhanced emission of σ-CB-fluorophore molecules with bulky ligands.

Materials and methods
All DFT and TDDFT computations were performed with Gaussian09 program package [40] using M06-2X [41] functional and 6-31g(d) basis set. In previous work, M06-2X functional is shown to provide better agreement with experiment for geometries and excited state properties compared to other functionals [22,42]. In addition, benchmark calculations on o-CB-H-Ant system with 6-311g(d) basis set were performed. It is seen that exited state energies differ only by 0.06-0.03 eV for LE, TICT, and CT states, indicating that 6-31g(d) provide sufficient accuracy for these systems. For TDDFT scan calculations, excited-state geometry optimizations were performed with constraints on C 1 -C 2 bond length, and the dihedral angle between C 1 -C 2 bond and the plane of Ant moiety, which are illustrated in Figure 1. Excited-state density differences and L values, which quantify the overlap between electron and hole wavefunctions for an excited state, were calculated using Multiwfn [43] program.
Solvent effects were considered with THF as solvent within the polarizable continuum formalism. In previous work, [44] solvent effects are shown to be small but noticeable for photophysical properties of σ-CB-fluorophore systems. In that aspect, benchmark calculations were performed for o-CB-H-Ant with toluene and acetonitrile as solvents in addition to THF. It is seen that while solvent effects are somewhat smaller (~0.05 eV) for the LE state, TICT and CT states become considerably stable (~0.2 eV) with acetonitrile as solvent compared to the case with toluene due to charge transfer nature of the excited states. Figure 2 shows the optimized ground state geometries, and the frontier energy levels which contribute significantly to the excited-state dynamics for o-CB-X-Ant. For ground state geometries, o-CB-H-Ant exhibits a -15° dihedral angle (φ), whereas the substituted systems (o-CB-CH 3 -Ant, o-CB-C 2 H 5 -Ant and o-CB-tBu-Ant) exhibit tilted φ ranging between -86° and -88°. This result originates from the fact that steric effects are quite substantial even with the -CH 3 substitution for small φ and unstretched C 1 -C 2 bond. It is seen that both HOMO and LUMO levels are mainly localized on the Ant moiety, while LUMO+2 level exhibits significant contribution from o-CB in all cases. It should also be noted that the LUMO+2 level exhibits large antibonding character on the C 1 -C 2 bond. As a result, this level is shown to undergo significant stabilization with increasing C 1 -C 2 bond length and ordering of LUMO and LUMO+2 can be altered upon excitation induced geometry change [22,27].

Results and discussion
In Table 1, the excited state energetics, oscillator strengths, and geometric parameters for vertical 0→1 transition (absorption), along with 1→0 transitions (emission) for LE, TICT, and CT states are tabulated. The geometries show only slight changes from the ground-state geometries for the 1→0 transitions of LE state. Regardless of this slight conformational change, both 0→1 transitions and 1→0 transitions in LE state originate from local π-π* transitions on the Ant moiety for all systems, while the contribution from o-CB is minimal. As a result, calculated oscillator strengths and energies (ƒ) show quite similar values due to similar nature of the transition for these systems.
For the case of TICT state, it is previously shown that o-CB-H-Ant undergoes to a rotation with respect to φ, along with C 1 -C 2 bond elongation compared to the LE or S 0 states [16]. For the substituted systems, the conformations for TICT state also exhibit a tilted φ and partially elongated C 1 -C 2 bonds. The elongation of C 1 -C 2 bond is slightly less for o-CB-CH 3 -Ant and o-CB-C 2 H 5 -Ant (2.11 and 2.14 Å respectively), while the same bond length becomes substantially larger for o-CB-tBu-Ant (2.35 Å). Furthermore, TICT state of o-CB-tBu-Ant shows significant stabilization (0.31 eV) for the adiabatic energy (E S1 ) compared to LE state. In comparison, calculated E S1 is quite comparable for LE and TICT states of other molecules. In all cases, TICT state exhibits an increase for the contribution of o-CB moiety to electron wavefunction along with an increase for the oscillator strengths showing hybridized local and charge transfer (HLCT) character.
In our recent work, it is seen that significant elongation of C 1 -C 2 bond and parallel orientation between two moieties (φ = 0°) result in a nonemissive CT state for o-CB-H-Ant. [22] Furthermore, this CT state is shown to be the global minimum for the S 1 PES, which suggests that it can be an important pathway for fluorescence quenching. A similar dark CT state is also found for all substituted systems as shown in Table 1. In the case of o-CB-CH 3 -Ant and o-CB-C 2 H 5 -Ant, C 1 -C 2 bond length becomes 2.59 Å for the dark CT state, while the same C 1 -C 2 bond becomes even more elongated for o-CB-tBu-Ant (2.68 Å), which most likely results from the steric hindrance of bulky -tBu group. Another important point is that while the E S1 of the CT state is ~0.2 eV lower compared to the E S1 of the TICT state of o-CB-H-Ant, the same CT state is energetically less favorable (~0.  To further understand the steric effects on the photophysical properties of o-CB-X-Ant systems, the PESs of the S 1 state are scanned with respect to C 1 -C 2 bond length and φ. In Figure 3a and 3b, the results are shown for conformations with varying C 1 -C 2 bond length, and fixed φ (-90° and 0°) respectively. For the tilted geometries (φ = -90°), elongation of C 1 -C 2 bond results in relatively flat PESs for the 1.7-2.4 Å range in the case of o-CB-H-Ant as shown in Figure 3a. Similar results are seen for the substituted systems when X = -CH 3 and -C 2 H 5 . For the latter, calculated E S1 shows an increase with further elongation of C 1 -C 2 bond beyond 2.4 Å. In comparison, the PES of o-CB-tBu-Ant shows a clear minimum between 2.3-2.4 Å, which roughly corresponds to the TICT (φ = -86°) state shown in Table 1. In this case, elongation of C 1 -C 2 bond results in a decrease for E S1 for the 1.7-2.4 Å range, which arises from the steric strain relaxation of bulky -tBu group.
For parallel geometries (φ = 0°), lowest energy points for the calculated E S1 are found with conformations showing fully elongated C 1 -C 2 bond lengths, which also correspond to the dark CT states of these systems as shown in Table 1. For o-CB-H-Ant, PES shows an energy barrier of ~0.4 eV, where the local maximum is located at 2.1 Å. This is also the case for o-CB-CH 3 -Ant and o-CB-C 2 H 5 -Ant, however, the calculated energy barriers are somewhat smaller (~ 0.1 eV) with respect to shorter C 1 -C 2 bonds. It should be noted that the steric effects are more pronounced for parallel conformations (φ = 0°) due to the alignment of -X group with anthracene moiety, and these steric effects mostly dominate the excited-state energetics for relatively short C 1 -C 2 bonds. In fact, the most drastic result is seen for X = -tBu case, for which the PES shows a large destabilization of E S1 as shown in Figure 3b. For this system, PES does not exhibit an energy barrier since calculated E S1 becomes continuously more stable with elongation of the C 1 -C 2 bond.
In addition to the excited-state energetics, it is important to assess the nature of S 1 →S 0 transitions on the PESs to fully understand the photophysical processes and the origin of energy barriers. In Figure 4a and 4b, calculated Λ values, which quantify the overlap degree (0 ≤ Λ ≤ 1) between electron and hole wave functions [45], are illustrated for the S 1 →S 0 transitions of tilted (φ = -90°) and parallel conformations (φ = 0°) with respect to C 1 -C 2 bond lengths. For both φ, S 1 →S 0 transitions mainly originate from local π-π* transition on the anthracene moiety, and show LE character for shorter C 1 - C 2 bond lengths with Λ larger than 0.8. In the case of tilted geometries, calculated Λ values become continuously smaller with increasing C 1 -C 2 bond lengths, indicating more HLCT character for the S 1 →S 0 transitions of all systems. This result originates from the larger o-CB character for the electron wave function with elongated C 1 -C 2 bond lengths. This effect is also illustrated with excited-state density differences shown in Figure 4c for o-CB-tBu-Ant. As the C 1 -C 2 bond length elongates from 2.0 Å to 2.2 Å, electron density (shown as red) on o-CB gradually increases showing CT from Ant to o-CB  upon excitation. Meanwhile, there is also considerable hole (shown as blue) and electron density on Ant, which indicates the presence of local π-π* character for the overall excited state nature. For parallel conformations (φ = 0°), calculated Λ values (0.8-0.9) also exhibit LE character for the S 1 →S 0 transitions when the C 1 -C 2 bond length is within 1.7-2.1 Å. At 2.1 Å, however, the nature of S 1 →S 0 transitions drastically transform to CT character as indicated from the sharp decrease of Λ values. This effect is also evident from excited-state density differences shown in Figure 4d. While electron and hole densities are mainly localized on Ant moiety when the C 1 -C 2 bond length is 2.0 Å, they show a strong charge separation when C 1 -C 2 bond length is 2.2 Å. It should also be noted that PESs (Figure 2b) show a significant decreasing trend for the calculated E S1 of all systems at 2.1 Å bond length, which is initiated with the LE→CT transformation of S 1 →S 0 transitions.
Similar to the C 1 -C 2 bond elongation, the PESs of the S 1 states are also scanned with respect to j for selected bond lengths (1.7 or 2.6 Å). The results are illustrated in Figure 5a and 5b, respectively. For the unsubstituted system, calculated PES shows two local minima with respect to j (φ ≈ -90° and φ ≈ -13°) when the C 1 -C 2 bond length is 1.7 Å. In comparison, PESs of substituted systems exhibit only one local minimum at φ » -90°, whereas φ ≈ 0° corresponds to the maxima for these cases. This energy penalty for the S 1 stated at φ ≈ 0° results from steric effects, which is significantly larger for the bulky -tBu group as shown in Figure 5a. For these conformations, S 1 →S 0 transitions show LE character (π-π* transition on the anthracene moiety) for all systems regardless of φ in all cases as indicated by calculated Λ values and excited state density differences as shown in Figure 6a and 6c. As a result, excited state energetics are governed mainly by the steric hindrance of the bulky group rather than electronic effects for these conformations.
For conformations with fully elongated C 1 →C 2 bond (2.6 Å), S 1 PESs show quite similar trends for both substituted and unsubstituted systems (Figure 5b) unlike the PESs with unstretched C 1 →C 2 . This is related to the reduction of steric hindrance on the molecular geometries with C 1 -C 2 bond elongation. As shown in Figure 5b, two local minima (φ ≈ -90° and φ ≈ 0°) exist in the PESs for all systems, which correspond S 1 ®S 0 transitions with HLCT and CT characters (Figures 6b and  6d) respectively. With -CH 3 and -C 2 H 5 substitution as well as with the unsubstituted system, parallel conformation (φ = 0°) is predicted to be energetically more favorable compared to the tilted conformation (φ = 90°), whereas tilted conformation is still energetically more favorable with -tBu substitution. In addition, the rotational energy barrier is significantly larger with -tBu substitution (~0.7 eV)), indicating a less probable path for the formation of dark CT state for this case.
In previous experimental and theoretical studies, it is shown that o-CB-H-Ant exhibits dual emission in solution from energetically close LE and TICT conformations on S 1 PES [16]. However, experimentally obtained quantum yield of the florescence is quite low in solution (ФPL = 0.02), which is associated with quenching through low-energy dark CT state [22,27], along with the vibrational motion of C 1 -C 2 bond on o-CB. [32] Correspondingly, a single emission band with low quantum yield (ФPL < 0.01) is found previously for o-CB--CH 3 -Ant in solution state. In the case of bulky substituents such as -TMS (trimethylsilyl) or -tBu, however, a significant increase for the quantum yield is observed for o-CB-Ant or other o-CB-fluorophore systems [12,17,38]. The increase in the emission quantum yield is often associated to the suppression of C 1 -C 2 vibrational motion as a result of steric effects induced by bulky groups. In this investigation, it is shown that the S 1 PESs of o-CB-tBu-Ant exhibit distinct features compared to the unsubstituted or -CH 3 and -C 2 H 5 substituted systems. One main difference is that the excited-state energies of parallel conformations (φ ≈ 0°) with relatively short C 1 -C 2 bonds are significantly higher for o-CB-tBu-Ant compared to other systems. For these geometries, calculated E S1 also surpasses the initial excitation energy (E 0®1 ) for o-CB-tBu-Ant, indicating energetically inaccessible conformations on S 1 PES.
Another important feature is that the twisted conformations (φ ≈ -90°) are energetically more favorable for -tBu substituted system, especially for 2.2-2.6 Å C 1 -C 2 bond range. As a result, twisted conformation is predicted to be the minima for o-CB-tBu-Ant even at 2.6 Å C 1 -C 2 bond length, meanwhile parallel conformations (dark CT state) are predicted to be the minima for the other systems with the same C 1 -C 2 bond length. It should also be noted that the CT state of the o-CB-H-Ant is predicted to be the global minimum on the S 1 PES, while CT state of o-CB-CH 3 -Ant and o-CB-C 2 H 5 -Ant are within 0.05 eV with the TICT state of the same systems. Meanwhile, the difference between TICT and CT states of o-CB-tBu-Ant is 0.22 eV, where the TICT conformation is predicted to be the global minimum on the S 1 PES. These results show that there is a substantial energy penalty for o-CB-tBu-Ant to reach the parallel conformations and resulting dark CT state, which most likely constrain the molecule in the emissive twisted conformations.

Conclusion
In this contribution, TDDFT calculations were performed for the S 1 PES of o-CB-H-Ant, o-CB-CH 3 -Ant, o-CB-C 2 H 5 -Ant, and o-CB-tBu-Ant to understand the steric effects on the photophysical properties of o-CB-fluorophore systems. It is shown that a nonemissive CT state exists for all systems as a result of C 1 -C 2 bond elongation (2.53-2.68 Å) and parallel orientation (φ ≈ 0°) between two moieties. In the case of unsubstituted system (o-CB-H-Ant), the adiabatic energy of this CT state is lowest on the S 1 PES, whereas the CT state shows similar energetics with the emissive TICT state (φ ≈ -90°) for -CH 3 and -C 2 H 5 substituted cases. For these systems, it is seen that S 1 PES is predicted to be quite flat for conformations especially for tilted conformations, indicating that it is possible for these systems to reach the nonemissive CT state without a large energy penalty. In comparison, S 1 PES of o-CB-tBu-Ant clearly shows a global minimum for the conformations with φ ≈ -90° (TICT state), and the energy difference between the TICT and CT states are quite large (0.22 eV) with former being energetically favorable. In addition, adiabatic energies are significantly higher for parallel conformations (φ ≈ 0°) of o-CB-tBu-Ant compared to the initial vertical excitation energy (absorption), especially for shorter C 1 -C 2 bonds. These results show that both pathways for the nonemissive CT state are energetically unfavorable for o-CB-tBu-Ant as a result of the interplay between steric and electronic effects, which results in higher emission yields even in solution state.