1. Introduction {#sec1-molecules-22-00758}
===============

Phosphorescent transition metal materials such as Re(I), Ru(II), and Ir(III) complexes are of great interest \[[@B1-molecules-22-00758],[@B2-molecules-22-00758],[@B3-molecules-22-00758],[@B4-molecules-22-00758]\], because these materials have been extensively investigated for optoelectronic and microelectronic applications, such as dye-sensitized solar cells (DSSCs) and organic light-emitting diodes (OLEDs) \[[@B5-molecules-22-00758],[@B6-molecules-22-00758],[@B7-molecules-22-00758]\]. Among these emitters, Ir(4,6-dFppy)~2~(pic) (FIrpic) is one of the most well-known blue phosphorescent emitters, which is widely used as a dopant in the electroluminescent layers of OLEDs \[[@B8-molecules-22-00758],[@B9-molecules-22-00758],[@B10-molecules-22-00758]\]. However, the quantum yield and equilibrium between the hole and electron transportation of FIrpic are considered to be difficult for its further application. The development of high-performance blue-emitting materials is strongly required for the fabrication of OLEDs. Unfortunately, it is a challenging task to achieve stable and high-efficiency blue phosphorescent emitters because the blue phosphorescence complex has a high emission state compared with other color complexes. This enables thermal activation to triplet metal centered (^3^MC) d-d state, which is one of the main nonradiative processes from the emissive excited state for Ir(III) complexes \[[@B11-molecules-22-00758],[@B12-molecules-22-00758]\].

In OLEDs, researchers can control the emission color and photophysical properties of emitters by a modification of the chelating ligands \[[@B13-molecules-22-00758],[@B14-molecules-22-00758],[@B15-molecules-22-00758],[@B16-molecules-22-00758],[@B17-molecules-22-00758]\]. The common approach in tuning the photophysical properties of FIrpic is to modify the chemical structures of 2-(2,4-difluorophenyl) pyridine (C^∧^N) ligands. Baranoff et al. \[[@B18-molecules-22-00758]\] replaced the F atoms on FIrpic by H, Cl, and Br. They found that the large halogen substituent contributed to sizable distortions of specific (C^∧^N) ligands, which were likely to play a role in the emissive and nonradiative properties when coupled with the heavy-atom effect. Owing to the introduction of the strong electron withdrawing perfluoro carbonyl group on (C^∧^N) ligands of FIrpic, the newly designed Ir complexes displayed deepest blue emissions and considerably high external quantum efficiencies (EQEs) \[[@B19-molecules-22-00758]\]. Li et al. \[[@B20-molecules-22-00758]\] investigated a series of Ir(III) complexes by introducing tert-butyl, *n*-heptyl, 3-ethylheptyl, and 2,4,6-trimethylphenyl substituted groups into the (C^∧^N) ligands of FIrpic. They revealed that both the substituted group and position had an effect on tuning the emission energies and quantum yield. However, the important chelating picolinic acid (N^∧^O) ligand of FIrpic has not received as much attention, to the best our knowledge. Herein, we will theoretically design and investigate a type of Ir complexes *o*-FIr, *m*-FIr, *p*-FIr ([Figure 1](#molecules-22-00758-f001){ref-type="fig"}) by introducing the dimethylamine substituted at the picolinic acid (N^∧^O) ligand, because the dimethylamine is one of the most popular functional groups used as hole transfer materials. We perform detailed theoretical calculations on the electronic structure, absorption and emission properties, quantum efficiency, as well as charge transport properties, aiming at revealing the relationship between the structures and photophysical properties. This work is expected to give some insights into the design and synthesis of blue emitters with high quantum efficiency.

2. Results and Discussion {#sec2-molecules-22-00758}
=========================

2.1. The Optimized Geometries in the Ground and Lowest Lying Triplet Excited States {#sec2dot1-molecules-22-00758}
-----------------------------------------------------------------------------------

The schematic structures of FIrpic, *o*-FIr, *m*-FIr, and *p*-FIr are depicted in [Figure 1](#molecules-22-00758-f001){ref-type="fig"}. The ground-state (S~0~) geometry of FIrpic was optimized by B3LYP, CAMB3LYP, M06L, MPW1PW91 functionals with the same basis set. The detailed geometries and available crystal data of FIrpic \[[@B21-molecules-22-00758]\] are collected in [Table S1](#app1-molecules-22-00758){ref-type="app"} in supporting information. It is found that M06L functional predicts more satisfied geometrical structures by compared with the experimental data. Therefore, the S~0~ geometries of *o*-FIr, *m*-FIr, *p*-FIr are calculated by M06L functional, and the optimized geometries as well as the numbering of some key atoms are depicted in [Figure 2](#molecules-22-00758-f002){ref-type="fig"}. The optimized primary metal--ligand bond lengths of these designed complexes in the ground-state (S~0~) geometry are collected in [Table 1](#molecules-22-00758-t001){ref-type="table"}.

As listed in [Table 1](#molecules-22-00758-t001){ref-type="table"}, the N~1~-Ir-N~2~ and O~1~-Ir-N~2~ of FIrpic are ca. 90°, and the dihedral angle of N~1~-O~1~-C~2~-C~1~ of FIrpic is 6.8°. Obviously, FIrpic has distorted octahedral geometry around the Ir(Ш) atom. [Table 1](#molecules-22-00758-t001){ref-type="table"} shows that the N~1~-Ir-N~2~, O~1~-Ir-N~2~, and N~1~-O~1~-C~2~-C~1~ of *o*-FIr, *m*-FIr, and *p*-FIr are similar to those of FIrpic. Clearly, the introduction of a dimethylamine moiety on the pyridine moiety of picolinic acid (N^∧^O) does not affect the distorted octahedral geometry of the Ir(Ш) complex. For *o*-FIr and *p*-FIr, because of the introduction of dimethylamine group on the pyridine, the Ir-N~1~ and Ir-O~1~ of *o*-FIr and *p*-FIr are shortened (0.005 Å and 0.01 Å for *o*-FIr, while 0.05 Å and 0.016 Å for *p*-FIr) in comparison to those of FIrpic. These calculated results indicate that there is a strong interaction between the Ir(Ш) and (N^∧^O) ligand. Furthermore, the Ir-N~1~ bond length of *o*-FIr, *m*-FIr, and *p*-FIr are significantly shortened compared with that of FIrpic; therefore, the possible of dissociation of Ir-N~1~ bond in the ^3^MC state is expected to be decreased by the incorporation of N(CH~3~)~2~ groups.

The lowest lying triplet excited states (T~1~) of studied complexes are also listed in [Table 1](#molecules-22-00758-t001){ref-type="table"}. As listed in [Table 1](#molecules-22-00758-t001){ref-type="table"}, the Ir-N~1~ bond length of these complexes is dramatically elongated in the T~1~ state in comparison with that in S~0~ state. This suggests that the interaction between the N^∧^O ligand and the metal is weakened in the T~1~ state. From the S~0~ to the T~1~ state, the Ir-C~1/2~ and Ir-N~2/3~ bond lengths of 2-(2,4-difluorophenyl)pyridine (C^∧^N) ligands in *o*-FIr, *m*-FIr, and *p*-FIr are contracted by the substitutions of the dimethylamine groups on the pyridine moiety. The strengthened metal--ligand bonds will strength the interaction between the metal and C^∧^N ligands and further benefit the charge transfer from the metal to ligand, which may improve the quantum efficiency.

2.2. Froniter Molecular Orbtials {#sec2dot2-molecules-22-00758}
--------------------------------

Considering that frontier molecular orbitals are useful to provide the nature of the charge transfer and photophysical properties in the excited state, the HOMO and LUMO energies, HOMO--LUMO energy gaps, and the contour plots of these orbitals of studied complexes are drawn in [Figure 3](#molecules-22-00758-f003){ref-type="fig"}. Detailed descriptions of the frontier molecular compositions are collected in [Table S2](#app1-molecules-22-00758){ref-type="app"} in the supporting information.

Normally, when the interfacial vacuum energy shift can be neglected, the hole (or electron) injection energy barrier from the electrode to semiconductor (Φ~h~) (or Φ~e~) can be calculated by Φ~h~ = \|HOMO\| − Φ~m~ (or Φ~e~ = Φ~m~ − \|LUMO\|), where Φ~m~ is the work function of the electrode \[[@B22-molecules-22-00758]\]. Consider that Au (Φ~m~ = 5.1 eV) is widely used as electrode in OLEDs; therefore, it is used as reference electrode \[[@B22-molecules-22-00758]\]. As depicted in [Figure 3](#molecules-22-00758-f003){ref-type="fig"}, the HOMO and LUMO energies of *o*-FIr, *p*-FIr, and *m*-FIr increase remarkably (−4.65 eV and −2.15 eV for *o*-FIr, −4.59 eV and −2.07 eV for *m*-FIr, −4.65 eV and −2.16 eV for *p*-FIr) compared with FIrpic (−4.80 eV and −2.30 eV). Therefore, the calculated Φ~h~ of these complexes are (in the region of 0.30--0.51 eV) much smaller than those of the calculated Φ~h~ values (in the region of 2.80--3.03 eV). It is obvious that these emitters are suitable for use as p-type organic semiconductors \[[@B23-molecules-22-00758]\]. Furthermore, the HOMO energy level of *o*-FIr (0.15 eV), *m*-FIr (0.21 eV), and *p*-FIr (0.15 eV) is significantly higher than that of FIrpic. The higher HOMO energies will benefit the hole injection abilities. Together with the increasing HOMO and LUMO energy, the HOMO--LUMO energy gaps of our designed molecules are similar to that of FIrpic, which means that absorption and phosphorescent spectra of these designed complexes might be similar to that of FIrpic when these spectra are predominantly contributed by the HOMO→LUMO transition.

For FIrpic, *o*-FIr, *p*-FIr, and *m*-FIr, the electron densities of HOMOs are mainly located on 50% d(Ir) orbital and 38% π(C^∧^N ligands) orbital, as shown in [Figure 3](#molecules-22-00758-f003){ref-type="fig"} and [Table S2](#app1-molecules-22-00758){ref-type="app"}. Owing to the introduction of N(CH~3~)~2~ groups, the LUMOs in *o*-FIr~,~ *m*-FIr~,~ and *p*-FIr are mainly focused on the C^∧^N ligands with about 90% compositions, while the LUMO in FIrpic is contributed by N^∧^O ligand. The HOMO-1 of these studied complexes is mainly focused on the ca. 50% d orbital the ca. 30% π orbitals of N^∧^O ligand, while theirs HOMO-2 are mainly contributed by N^∧^O ligand. The contributions of d(Ir) orbital on HOMO-3 of *o*-FIr (67.5%) and *m*-FIr (56.9%) are similar to that of FIrpic (67.1%). This means that the N(CH~3~)~2~ substitutions have a minor effect on the composition of the frontier molecular orbital. Therefore, the nature of electron transition upon excitations of *o*-FIr, *p*-FIr, and *m*-FIr might be similar with those of FIrpic, which will be further investigated in the following section.

2.3. Absorption Spectra {#sec2dot3-molecules-22-00758}
-----------------------

The calculated absorption spectra of studied complexes associated with oscillator strengths (f) and the corresponding compositions, as well as the experimental data \[[@B24-molecules-22-00758]\] are given in [Table 2](#molecules-22-00758-t002){ref-type="table"}. Simulated absorption spectra of these complexes with the data calculated at the TD-M06L method are drawn in [Figure 4](#molecules-22-00758-f004){ref-type="fig"}.

As listed in [Table 2](#molecules-22-00758-t002){ref-type="table"}, the main calculated values of these bands are localized at 453.00, 380.95, and 265.86 nm for FIrpic, respectively, which are in good agreement with the experimental results of 458, 379, and 256 nm, respectively \[[@B24-molecules-22-00758]\]. For the low-lying absorption spectra of FIrpic, the excitations of HOMO→LUMO + 1 and HOMO − 1→LUMO + 2 are dominantly responsible for the absorption peaks at 453.00 and 380.95 nm, respectively. As listed in [Table S2](#app1-molecules-22-00758){ref-type="app"}, the HOMO and HOMO − 1 are delocalized on the Ir(d), N^∧^O, and N^∧^C ligand, while the LUMO + 1 and LUMO + 2 are mainly contributed by the N^∧^C ligand. Therefore, from the analysis of FMOs, the absorption peaks at 453.00 and 380.95 nm can be characterized as metal-to-ligand charge transfer (MLCT), inter-ligand charge transfer (ILCT), and ligand--ligand charge transfer (LLCT). The absorption peak with largest oscillator strength (*f* = 0.2104) of FIrpic is located at 265.86 nm, which is arising from the HOMO − 8→LUMO + 2 and HOMO→LUMO + 7 transitions. Because of the large of amount of Ir(d) in HOMO (50.7%) and HOMO -- 8 (20.8%), the absorption peak at 265.86 nm can mainly be assigned to the MLCT/LLCT/ILCT character. From the analysis of frontier molecule orbital compositions, the mount of MLCT of the 453.00, 380.95, and 265.86 for FIrpic is 21.07%, 21.07%, and 7.16%, respectively. The significant MLCT contributions on the lower-lying absorptions of FIrpic are in good agreement with the experimental results \[[@B24-molecules-22-00758]\].

[Table 2](#molecules-22-00758-t002){ref-type="table"} also shows the lowest-lying absorption peak of *o*-FIr, *m*-FIr, and *p*-FIr at 463.87, 462.95, and 463.29 nm, respectively, which is dominantly responsible for the excitation of HOMO→LUMO. [Table S2](#app1-molecules-22-00758){ref-type="app"} shows that the HOMO of *o*-FIr, *m*-FIr, and *p*-FIr is composed of 50.1% Ir(d) + 47.7% π(N^∧^O + N^∧^C), 50.3% Ir(d) + 47.9% π(N^∧^O + N^∧^C), 48.6% Ir(d) + 49.3% π(N^∧^O + N^∧^C), respectively, while their LUMOs are contributed by ca. 80% π\*(N^∧^C). Thus, the lowest-lying absorptions of these complexes originate from the \[Ir(d) + π(N^∧^O + N^∧^C)\]→π\*(N^∧^C) excited state with MLCT/ILCT/LLCT character. The mount of MLCT of the lowest-lying absorption of *o*-FIr, *m*-FIr, and *p*-FIr is ca.22%, which is similar to that of FIrpic. Furthermore, as shown in [Figure 4](#molecules-22-00758-f004){ref-type="fig"}, the absorption intensity of N(CH~3~)~2~-substituted Ir complexes (*m*-FIr, *o*-FIr, *p*-FIr) in the highest energy absorption spectra have been effectively enhanced, which may increase the intersystem crossing rates (ISC). For *o*-FIr, the highest energy absorption peak (262.33 nm) is contributed by the mixture excitations of HOMO − 9→LUMO + 2, HOMO − 5→LUMO + 5, HOMO − 4→LUMO + 5, HOMO − 2→LUMO + 5, HOMO − 1→ LUMO + 5. Since the Ir(d) in the HOMO − 9, HOMO − 4, HOMO is 22.7%, 67.5%, 50.1%, respectively, the MLCT contributed 8.9% to the 262.33 nm of *o*-FIr, which is slightly larger than that of FIrpic. For *m*-FIr and *p*-FIr, the absorption peak with large oscillator strength is located at 267.06 (attributed by HOMO − 8→LUMO + 2 and HOMO→LUMO + 7) and 271.08 nm (attributed by HOMO − 7→LUMO + 4, HOMO − 3→LUMO + 5, HOMO − 2→LUMO + 5, HOMO→LUMO + 7), respectively. Combining the transition configuration with the orbital composition, the mount of MLCT of the high energy absorption peaks for *m*-FIr and *p*-FIr are only 4.4% and 5.2%, respectively. Clearly, the contribution of MLCT in the whole absorption spectra of *o*-FIr are remarkably larger than those of FIrpic, *m*-FIr, and *p*-FIr. Normally, the participation of MLCT in the absorption spectra is a critical factor affecting the intensity of the singlet--triplet transitions, and thus improves the quantum efficiency. Thus, the calculated results indicate that the introduction of N(CH~3~)~2~ groups at the ortho-position of N^∧^O ligand is useful to enhance the intersystem crossing and singlet--triplet transitions, and therefore the possibility of the phosphorescent quantum yield might be enhanced.

2.4. Phosphorescence Emission Spectra {#sec2dot4-molecules-22-00758}
-------------------------------------

Based on the optimized lowest triplet excited state (T~1~) geometries, vertical T~1~--S~0~ transition energies (ΔE~vert~) and the emission wavelength (nm) obtained by CAMB3LYP functional are collected in [Table 3](#molecules-22-00758-t003){ref-type="table"}, together with available experimental values \[[@B24-molecules-22-00758]\]. Since the vertical T~1~--S~0~ transition energy (ΔE~vert~) is the electronic energy difference between the T~1~ and S~0~ state at the optimized T~1~ geometry, it is therefore strongly dependent on the functional. The molecular orbital compositions responsible for the emission spectra of the studied complex are given in [Table S3](#app1-molecules-22-00758){ref-type="app"}. The 0-0 T~1~→S~0~ transition energy (ΔE~0-0~) is calculated by the energy difference between the S~0~ and T~1~ states at their respective optimized geometries obtained by M06 functional.

As listed in [Table 3](#molecules-22-00758-t003){ref-type="table"}, the calculated emission peak for FIrpic based on the calculated E~vert~ and E~0-0~ method is located at 490.49 and 480.86 nm, respectively. The slightly longer wavelength derived from E~vert~ is caused by only one single configuration, while real emission is composed of more than one configuration. The phosphorescence at 490.49 nm of FIrpic is contributed by the excitation of HOMO→LUMO. According to the orbital composition analyses, the HOMO is contributed by 42.8% Ir(d) + 54.3% π(C^∧^N + N^∧^O), while the LUMO is mainly focused on C^∧^N ligand. Accordingly, the emission of FIrpic can be attributed to ^3^MLCT/^3^LLCT/^3^ILCT character. The d(Ir) orbital contributes to 42.8% for HOMO, and thus the emission of FIrpic at 490.49 nm has ^3^MLCT (20.31%) transition character. For N(CH~3~)~2~-substituted Ir complexes, the phosphorescent emissions based on E~vert~ method are located at 492.78, 484.32, and 485.83 nm for *o*-FIr, *m*-FIr, and *p*-FIr, respectively, which is dominantly responsible for excitations of HOMO→LUMO and HOMO − 4→LUMO. This is because the HOMO and HOMO − 4 of *o*-FIr, *m*-FIr, and *p*-FIr are mainly contributed by d(Ir) and π(C^∧^N + N^∧^O) (besides the HOMO − 4 of *m*-FIr), while the LUMOs of *o*-FIr and *m*-FIr are located at π\*(C^∧^N). [Table 3](#molecules-22-00758-t003){ref-type="table"} shows that the calculated E~0--0~ for these designed complexes are ca. 480nm. Accordingly, these designed complexes have similar phosphorescent emissions and transition character with that of FIrpic, which might be a potential candidate for blue-emitting materials. Furthermore, the d(Ir) orbital contributions to HOMO and HOMO − 4 (42.8% and 0.97% for *m*-FIr, 30.68% and 36.68% for *p*-FIr) are much smaller than that of HOMO (41.35%) and HOMO − 4 (63.39%) for *o*-FIr. The larger d(Ir) orbital composition results in slightly larger ^3^MLCT% in its phosphorescence of *o*-FIr (18.78%) than *m*-FIr (9.11%) and *p*-FIr (11.56%). Therefore, the *o*-FIr may have improved Φ~p~ compared with *m*-FIr and *p*-FIr.

To give some insight into the nonradiative rate constant (k~nr~), the high lying metal-centered (^3^MC d-d) excited states of studied complexes---which is one of the most important deactivation pathways for the phosphoresce emission from T~1~ in transition-metal complexes---were optimized by unrestricted M06L method. The energy difference between ^3^MLCT/π-π\* and ^3^MC d-d excited states are drawn in [Figure 5](#molecules-22-00758-f005){ref-type="fig"}, along with the spin density distribution in the ^3^MC d--d state. As shown in [Figure 5](#molecules-22-00758-f005){ref-type="fig"}, the ^3^MC d-d state of studied complexes are lying at a relatively higher energy than that of ^3^MLCT/π-π\* state, which suggests that the possibility of a radiationless pathway is low. Furthermore, the energy difference between the ^3^MLCT/π-π\* and ^3^MC d-d excited states of *o*-FIr (0.30 eV) and *m*-FIr (0.30 eV) is larger than that of FIrpic (0.24 eV). Therefore, these calculation results show that ortho- and meta- substituted Ir complexes are useful to decrease the K~nr~. Based on the above viewpoint, it becomes clear that introducing the N(CH~3~)~2~ at the ortho-position of N^∧^O ligand in FIrpic led to larger ISC and k~r~ values, as well as the smaller k~nr~ value relative to others. Therefore, *o*-FIr is considered to be used as potential blue-emitting emits with high quantum efficiency.

2.5. Performance in OLEDs {#sec2dot5-molecules-22-00758}
-------------------------

To evaluate the performance of OLED devices, it is highly important to investigate the charge injection and transfer ability. The ionization potential (IP) and electron affinity (EA) are usually employed to evaluate the energy barrier for the hole and electron injections. Normally, the lower IP (larger EA) value suggests that it is easier to inject hole (electron). According to the Marcus theory \[[@B25-molecules-22-00758]\], the electron transfer rate constants can be expressed by the following formula:$$k = \left( \frac{\pi}{\lambda k_{B}T} \right)^{1/2}\frac{V^{2}}{\hslash}\exp( - \frac{\lambda}{4k_{B}T})$$ where T and k~B~ is the temperature and Boltzmann constant, respectively. The λ is the reorganization energy, and V is the coupling matrix element. According to Equation (1), the intermolecular charge transfer rate k is determined by two factors, λ and V. Due to the limited intermolecular charge transfer range in the solid state, the mobility of charges has been demonstrated to be primarily associated with the reorganization energy λ for OLED materials \[[@B26-molecules-22-00758]\]. The detailed description of the calculations of vertical ionization potential (IP(v)), vertical electron affinity (EA(v)), hole extraction potential, (HEP), electron extraction potential (EEP) and electron reorganization energy (λ~electron~), as well as hole reorganization energy (λ~hole~) are listed in our previous report \[[@B16-molecules-22-00758]\]. According to the previous report \[[@B16-molecules-22-00758]\], the IP, EA, and λ of studied complexes are calculated and listed in [Table 4](#molecules-22-00758-t004){ref-type="table"}.

Compared with FIrpic, all these designed complexes have smaller IP(v) and HEP, which is consistent with their higher HOMO energy levels. Thus, the hole injection ability of these designed complexes are improved by introduction of dimethylamine substitutions at the C^∧^O ligand. However, *o*-FIr, *m*-FIr, and *p*-FIr have smaller EA values than FIrpic, which will lead to worse electron injection ability compared with FIrpic. According to Equation (1), the λ is required to be small for efficient charge transport. As listed in [Table 4](#molecules-22-00758-t004){ref-type="table"}, the λ~electron~ of studied complexes are slightly smaller than that of FIrpic, indicating that these complexes have excellent electron transfer ability. The difference between the λ~hole~ and λ~electron~ of FIrpic, *o*-FIr, and *p*-FIr is less than 0.05 eV. Hence, it is expected that the FIrpic, *o*-FIr, and *p*-FIr might have excellent charge transfer balance, which is one of the key factors affecting the performance of OLEDs.

3. Computational Details {#sec3-molecules-22-00758}
========================

The geometrical structures of the ground state (S~0~) of FIrpic were fully optimized by B3LYP \[[@B27-molecules-22-00758],[@B28-molecules-22-00758]\], CAMB3LYP \[[@B29-molecules-22-00758]\], M06L \[[@B30-molecules-22-00758]\], and mPW1PW91 \[[@B31-molecules-22-00758]\] methods, respectively, combined with 6-31G(d) basis set for the non-metal atoms (H, C, N, O, and F) and a "double-j" quality basis set LANL2DZ for Ir atom. The calculated vibrational frequencies with no imaginary frequencies based on the optimized geometries verify that each of the optimized structures was a true minimum on the potential energy surface. The calculated results are collected in [Table S1](#app1-molecules-22-00758){ref-type="app"} in the supporting information, together with the crystal data \[[@B21-molecules-22-00758]\]. As depicted in [Table S1](#app1-molecules-22-00758){ref-type="app"}, the bond lengths obtained for B3LYP and CAMBLYP overestimated the bond lengths, especially Ir-N~1~ (0.024 Å for CAMB3LYP and 0.031 Å for B3LYP) and Ir-N~3~ (0.049 Å for CAMB3LYP and 0.073 Å for B3LYP), while the bond length differences between the calculated results obtained by M06L and crystal data were small. Therefore, the ground-state geometries of the studied complexes were calculated by M06L method. Based on the ground-optimized structure, the vertical excitation energies were calculated by TD-M06L method with continuum polarizable continuum model (CPCM). The lowest-lying triplet excited state geometries (T~1~) and triplet-centered (^3^MC) d-d states were optimized by unrestricted M06L method. Based on the T~1~ equilibrium geometries, four different functionals---PBE0, B3LYP, CAMB3LYP, and M06L---were performed on the emission spectra calculations (as listed in [Table S4](#app1-molecules-22-00758){ref-type="app"}). The CAMB3LYP functional was adopted to predict the emission spectra of these complexes, because the calculated results obtained by CAMB3LYP were consistent with the experimental results. All calculations were performed with the Gaussian 09 software package \[[@B32-molecules-22-00758]\].

4. Conclusions {#sec4-molecules-22-00758}
==============

In this work, the geometrical and electronic structures, absorption and emission spectra, as well as phosphorescence efficiencies for a series of dimethylamine-substituted iridium(Ш) complexes FIrpic have been investigated by density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods. The results indicate that the introduction of dimethylamine is useful to extend the π-electron delocalization, increase HOMO energy levels, and enhance hole injection and transfer ability. Furthermore, the absorption intensity and participation of MLCT of these dimethylamine substitutions are significantly stronger than that of FIrpic, suggesting the possibility of singlet-to-triplet transitions are enhanced, and therefore the phosphorescent quantum yield might be increased by introducing dimethylamine. Importantly, through the analyses of triplet energy (E~T1~), participation of ^3^MLCT in phosphorescent spectra, as well as the energy difference between the ^3^MLCT/π-π and ^3^MC d-d state, it can be inferred that *o*-FIr has larger k~r~ values and smaller k~nr~ values compared with other molecules. So, the strategy of introducing the dimethylamine in N^∧^O ligand of FIrpic should be useful in the design of more-efficient blue emitters.

Financial supports from the Fundamental Research Funds for the Central Universities (No. 2015XKMS042). We are grateful to the High Performance Computing Center of China University of Mining and Technology for the award of CPU hours to accomplish this work.

*Sample Availability:* Not available.

Supplementary materials are available on line.

###### 

Click here for additional data file.

Hong-Qu Tang performed the calculation work; Guo-Jun Kang and Xue-Feng Ren analyzed the data and wrote the manuscript.

The authors declare no conflict of interest.

![Schematic structures of the studied complexes.](molecules-22-00758-g001){#molecules-22-00758-f001}

![Optimized structures of *o*-FIr, *m*-FIr, and *p*-FIr in the ground state, together with the number of some key atoms.](molecules-22-00758-g002){#molecules-22-00758-f002}

![The orbital energies and contour plot of the HOMO and LUMO of studied complexes.](molecules-22-00758-g003){#molecules-22-00758-f003}

![Simulated absorption spectra of studied complexes with the data calculated at the TD-M06L level.](molecules-22-00758-g004){#molecules-22-00758-f004}

![Energy level diagram of the studied complexes in the T~1~ and triplet metal centered (^3^MC) excited states, together with the contour plots of the spin density distribution in the ^3^MC state.](molecules-22-00758-g005){#molecules-22-00758-f005}

molecules-22-00758-t001_Table 1

###### 

Calculated metal--ligand bond lengths (Å), bond angles (°), and dihedral angles (°) for studied complexes in the ground state (S~0~) and first excited triplet state(T~1~).

  Molecule   State   Ir-N~1~   Ir-O~1~   Ir-N~2~   Ir-C~1~   Ir-N~3~   Ir-C~2~   N~1~-Ir-N~2~   O~1~-Ir-N~2~   N~1~-O~1~-C~2~-C~1~
  ---------- ------- --------- --------- --------- --------- --------- --------- -------------- -------------- ---------------------
  FIrpic     S~0~    2.215     2.190     2.066     2.001     2.058     1.997     88.4           93.5           6.8
  T~1~       2.313   2.172     2.069     1.979     2.060     1.975     97.1      88.7           −3.4           
  *o*-FIr    S~0~    2.210     2.180     2.066     2.002     2.054     1.997     87.3           94.0           5.0
  T~1~       2.316   2.154     2.057     1.981     2.067     1.977     84.4      93.7           3.1            
  *m*-FIr    S~0~    2.206     2.193     2.064     2.002     2.056     1.995     88.6           93.0           7.2
  T~1~       2.285   2.171     2.069     1.979     2.057     1.978     95.9      89.0           −4.6           
  *p*-FIr    S~0~    2.165     2.177     2.055     2.010     2.045     2.001     87.6           92.9           6.3
  T~1~       2.305   2.160     2.068     1.982     2.058     1.977     97.4      88.7           −3.0           

molecules-22-00758-t002_Table 2

###### 

The calculated maximum absorption wavelength (nm), oscillator strengths (*f*), and major contribution transition composition for studied complexes obtained by TD-M06L method. FIrpic: Ir(4,6-dFppy)~2~(pic).

  Molecule            Transition   λ(nm)    *f*                 Composition     CI        Exp. \[[@B24-molecules-22-00758]\] (nm)
  ------------------- ------------ -------- ------------------- --------------- --------- -----------------------------------------
  FIrpic              S~0~→S~2~    453.00   0.0250              HOMO→LUMO + 1   0.68971   455
  S~0~→S~7~           380.95       0.0614   HOMO − 1→LUMO + 2   0.55936         379       
  S~0~→S~50~          265.86       0.2104   HOMO − 8→LUMO + 2   0.38300         256       
  HOMO→LUMO + 7       0.24359                                                             
  *o*-FIr             S~0~→S~1~    463.87   0.0258              HOMO→LUMO       0.70168   
  S~0~→S~7~           395.15       0.0266   HOMO − 2→LUMO + 2   0.56244                   
  HOMO − 1→LUMO + 2   −0.40890                                                            
  S~0~→S~52~          269.04       0.1135   HOMO − 9→LUMO + 1   0.25480                   
  HOMO − 5→LUMO + 5   0.42176                                                             
  HOMO − 1→LUMO + 7   0.23321                                                             
  S~0~→S~53~          268.66       0.1642   HOMO − 7→LUMO + 4   −0.35667                  
  HOMO − 1→LUMO + 7   0.36355                                                             
  S~0~→S~54~          266.76       0.1318   HOMO − 9→LUMO + 2   0.21920                   
  HOMO − 2→LUMO + 7   0.26962                                                             
  HOMO − 1→LUMO + 7   −0.21838                                                            
  HOMO→LUMO + 7       0.41903                                                             
  S~0~→S~55~          266.32       0.0836   HOMO − 5→LUMO + 5   0.42068                   
  S~0~→S~56~          264.54       0.1094   HOMO − 9→LUMO + 2   0.48856                   
  HOMO − 8→LUMO + 2   −0.19242                                                            
  HOMO − 1→LUMO + 5   0.27865                                                             
  S~0~→S~57~          262.33       0.1716   HOMO − 9→LUMO + 2   −0.24371                  
  HOMO − 5→LUMO + 5   −0.24091                                                            
  HOMO − 4→LUMO + 5   −0.25407                                                            
  HOMO − 2→LUMO + 5   0.20626                                                             
  HOMO − 2→LUMO + 7   0.30782                                                             
  HOMO − 1→LUMO + 5   0.32002                                                             
  *m*-FIr             S~0~→S~1~    462.95   0.0263              HOMO→LUMO       0.70166   
  S~0~→S~6~           393.55       0.0423   HOMO − 2→LUMO       −0.41398                  
  HOMO − 2→LUMO + 1   0.42182                                                             
  HOMO − 1→LUMO + 1   0.31148                                                             
  S~0~→S~53~          267.06       0.3060   HOMO − 8→LUMO + 2   −0.24031                  
  HOMO→LUMO+7         0.25154                                                             
  *p*-FIr             S~0~→S~1~    463.29   0.0286              HOMO→LUMO       0.70148   
  S~0~→S~8~           388.02       0.0581   HOMO − 1→LUMO + 1   −0.43685                  
  HOMO→LUMO + 3       0.47613                                                             
  S~0~→S~52~          271.08       0.2512   HOMO − 7→LUMO + 4   −0.27219                  
  HOMO − 3→LUMO + 5   0.21898                                                             
  HOMO − 2→LUMO + 5   0.29024                                                             
  HOMO→LUMO + 7       −0.21723                                                            

molecules-22-00758-t003_Table 3

###### 

The calculated phosphorescence emission wavelength (nm), along with metal--ligand charge transfer character (^3^MLCT, %) and available experimental values.

  Molecule   E~vert~   E~0-0~   Exp \[[@B24-molecules-22-00758]\]                                
  ---------- --------- -------- ---------------------------------------- ------- -------- ------ -----
  FIrpic     490.49    2.53     0.49 (HOMO→LUMO)                         20.31   480.86   2.58   468
  *o*-FIr    492.78    2.52     0.45 (HOMO − 4→LUMO) 0.43 (HOMO→LUMO)    18.78   482.58   2.60   
  *m*-FIr    484.32    2.56     −0.36 (HOMO − 4→LUMO) 0.40 (HOMO→LUMO)   9.11    481.78   2.57   
  *p*-FIr    485.83    2.55     −0.36 (HOMO − 4→LUMO) 0.49 (HOMO→LUMO)   11.56   481.76   2.57   

molecules-22-00758-t004_Table 4

###### 

The calculated ionization potential (IP, eV), electron affinities (EA, eV), hole extraction potential, (HEP, eV), electron extraction potential (EEP, eV) hole/electron reorganization energy (λ~hole~/λ~electron~, eV).

  Molecule   IP(v)   HEP    EA(v)   EEP    λ~hole~   λ~electron~
  ---------- ------- ------ ------- ------ --------- -------------
  FIrpic     6.56    6.29   0.72    0.98   0.27      0.26
  *o*-FIr    6.32    6.06   0.48    0.69   0.26      0.21
  *m*-FIr    6.39    6.09   0.56    0.75   0.30      0.19
  *p*-FIr    6.34    6.11   0.53    0.73   0.23      0.20
