Substituent effects on the structure and properties of ( para -C 5 H 4 X)Ir(PH 3 ) 3 complexes in the ground state (S 0 ) and first singlet excited state (S 1 ): DFT and TD-DFT investigations

Abstract

The ground and lowest singlet excited state geometries of selected (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes (para-substituent = NH₂, OMe, Me, H, F, Cl, CCl₃, CF₃, NO₂) are optimized using the MPW1PW91 procedure employing the LanL2DZ(Ir) and 6-311G(d, p) (C, H, N, O, P, F, Cl, P) basis sets. The excited state is generated using the time-dependent density function method. The effects of electron-donating groups and electron-withdrawing groups on the energy, atomization energy, rotational constants, and frontier orbital energies in the first singlet excited state (S₁) of iridabenzene are investigated and compared to those of the ground state (S₀). The Ir–C and Ir–P bonds in the studied molecules are analyzed by electron localization function and localized-orbital locator methods. The correlations between the Ir-C and Ir–P bond distances, electron localization function, and localized-orbital locator values Hammett constants (σ_p) and dual parameters (σ_I and σ_R) are given for the two studied states. The para-delocalization index is used for investigation of the aromaticity of the studied complexes.

Introduction

Metallabenzenes are a type of metallacycle that consists of six-membered ring. Metallabenzenes are similar to benzene with one CH unit substituted by an isolobal transition-metal fragment.^1–5 Over the years, the preparation and characterization of various metallabenzenes have been reported.^6–13 The aromaticity of metallabenzenes compared to benzene and cyclic heteroaromatics has been investigated.^14–18

As an example, replacing a CH of benzene with isolobal fragments of iridium leads to the synthesis of different iridabenzenes.^19–22

Iridabenzene was the initial synthetic sample of a metallabenzene with a structure like that suggested by Thorn and Hoffmann. ²³ Crystal structures have been described for high oxidation state iridabenzenes. ²⁴ These 16-electron complexes have an open coordination site at iridium. In other studies, the nonlinear optical (NLO) properties of these complexes have been explored. ²⁵ The polarity effect of the solvent on the structure and electronic properties of these complexes have been reported using computational methods. ²⁶ Also, in the other theoretical studies, the structure, chemical reactivity, aromaticity, and ¹⁴N nuclear quadruple resonance (NQR) parameters of iridapyridine isomers have been investigated. ²⁷

It is well known that electron-withdrawing groups (EWGs) and electron-releasing groups (ERGs) influence molecular behavior. In other words, the presence of different substituents affects the physical, electronic, and spectroscopic features of molecules. This is why many theoretical studies have been conducted to show how various substituents influence the properties of organometallic complexes.^26,28–39 Moreover, it has been shown that quantitative substituent parameter scales can be used to explain how molecular properties are influenced by the polar or steric effects of the substituent. For example, the Hammett constant (σ_p) ⁴⁰ explains the electronic effects of substituents on the equilibrium and rate constants of a reacting molecule. The substituent effects in the structure and the properties of the para-substituted iridabenzene in the ground state have been studied. ²⁶

Investigation of variations in the structures and properties of molecules in the electronic excited states is possible by quantum chemical methods. The time-dependent density functional theory (TDDFT) approach ⁴¹ is one of the most commonly employed computational methods. Numerous computational studies on the excited states of molecules have been reported.^42–54

The absence of any theoretical or experimental investigations on the first singlet excited states of iridabenzene complexes encouraged us to study substitution effects on the structural, electronic properties, and aromaticity of para-substituted iridabenzenes at the first singlet excited state. We compare the obtained results with those of the ground states of the complexes.

Results and discussion

Atomization energies

Figure 1 displays the structures of the studied para-substituted iridabenzene molecules in our investigations. The atomization energy is the energy difference between a molecule and its constituent ground state atoms. To compute the atomization energies of the investigated iridabenzene molecules in the ground state (S₀) and first singlet excited state (S₁), molecules are considered as closed shell singlet and the multiplicities assumed for H, C, N, O, F, Cl, and P atoms are doublet, triplet, quartet, triplet, doublet, doublet, and quartet, respectively. The calculated atomization energies of the investigated molecules are listed in Table 1. Larger atomization energy values (E_atom) are observed for the S₀ state compared to the S₁ state.

Figure 1.

(a) Aromatic structure and (b) non-aromatic quinonoid structure of the (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes, where X represents an acceptor. For donors, the zwitterionic form has the opposite charge separation.

Table 1.

Total energy (E, a.u), excitation energy with respect to the ground state (ΔE, eV), atomization (E_atom, kcal/mol), dipole moment (µ, Debye), and para-delocalization index (PDI) values in the ground state (S₀) and first singlet excited state (S₁) of (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes.

	σp	σI	σR	E (GS)	E (ES)	ΔE	Eatom (S0)	Eatom (S1)	µ(S0)	µ (S1)	PDI (S0)	PDI (S1)
NH2	−0.66	0.17	−0.82	−1383.1736	−1383.1297	1.19	2237.76	2210.24	1.01	1.00	0.0715	0.0605
OMe	−0.27	0.3	−0.58	−1442.3342	−1442.2871	1.28	2461.72	2432.18	3.09	2.03	0.0757	0.0671
Me	−0.17	−0.01	−0.16	−1367.1242	−1367.0721	1.42	2357.23	2324.56	3.85	2.46	0.0871	0.0821
H	0.00	0.00	0.00	−1327.8050	−1327.7511	1.47	2053.80	2019.93	4.37	3.27	0.0929	0.0903
F	0.06	0.54	−0.48	−1427.0533	−1427.0021	1.39	2088.24	2056.14	5.72	4.39	0.0834	0.0771
Cl	0.23	0.30	−0.25	−1787.4407	−1787.3873	1.45	2051.84	2018.31	6.68	4.87	0.0851	0.0804
CCl3	0.46	0.36	0.08	−2745.9915	−2745.9331	1.59	2326.49	2289.83	8.50	6.47	0.0857	0.0807
CF3	0.54	0.40	0.11	−1664.8715	−1664.8121	1.62	2462.27	2424.99	8.11	6.66	0.0896	0.0903
NO2	0.78	0.67	0.10	−1532.3171	−1532.2542	1.71	2275.42	2235.91	10.79	8.54	0.0852	0.0889

PDI: para-delocalization index.

Hammett substituent constants (σ_p) and dual parameters (σ_I and σ_R) for substituents.

Since in atomization processes, we break all bonds in the molecule and form separated atoms; it seems plausible that the change in electronic energy for atomization can be estimated as the sum of the energies associated with each bond in the molecule. Therefore, the atomization energy is equivalent to the total binding energy.

Energetic aspects

The absolute energy values of the investigated complexes in the S₀ and S₁ states are collected in Table 1. The excitation energies with respect to the ground states (ΔE) are calculated (Table 1). The Hammett substituent constants (σ_p) ⁵⁵ and dual parameters (σ_I and σ_R) ⁵⁵ are also listed in Table 1. The σ_R and σ_I values are the resonance and inductive constants of the substituents, respectively.

The plot of ΔE values versus the Hammett constants (σ_p) values is shown in Figure 2. Surprisingly, the ΔE values demonstrate a linear relation with respect to the σ_p values

$$\mathrm{\Delta }\mathrm{E}=0.3555{\mathrm{\sigma }}_{\mathrm{p}}+1.4201;{\mathrm{R}}^2=0.9419$$

Figure 2.

Linear correlation between the ΔE = E(S₁) − E(S₀) values and Hammett constants (σ_p) in (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes.

It is found that these values are lower in the presence of electron-donating groups (EDG) compared to EWG.

Rotational constants

The calculated rotational constants for the investigated iridabenzene molecules in the S₀ and S₁ states are shown in Table 2.

Table 2.

Rotational constants (GHz) in the ground state (S₀) and first singlet excited state (S₁) of (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes.

X	Ne	S0			S1
		A	B	C	A	B	C
NH2	114	0.9550	0.4401	0.4056	0.8538	0.4221	0.3963
OMe	122	0.9287	0.3247	0.3035	0.8317	0.3169	0.2994
Me	114	0.9566	0.4404	0.4042	0.8549	0.4214	0.3944
H	106	0.9629	0.6276	0.5547	0.8621	0.5811	0.5287
F	114	0.9592	0.4282	0.3941	0.8518	0.4103	0.3856
Cl	122	0.9609	0.3133	0.2942	0.8520	0.3063	0.2922
CCl3	162	0.6190	0.1408	0.1368	0.5692	0.1421	0.1392
CF3	138	0.8259	0.2069	0.1980	0.7315	0.2051	0.2002
NO2	128	0.9018	0.2675	0.2478	0.7886	0.2635	0.2496

These values show that rotational constants in the excited state are less than those of the corresponding ground state rotational constants. Since the moment of inertia (and consequently the rotational constant) of a molecule is directly related to the nuclear coordinate, ⁵⁶ it is reasonable that the rotational constant changes in the S₀ and S₁ states.

By taking a closer look at the data in Table 2, it is revealed that the studied iridabenzenes are asymmetric top as expected (namely, A ≠ B ≠ C). With the electron number (N_e) of the molecule becoming larger, the rotational constants become smaller. It is interesting to note, however, that there are good linear correlations between the A values and number of electrons

$$\begin{array}{l}\mathrm{A}\left({\mathrm{S}}_{\mathrm{0}}\right)=-0.0064{\mathrm{N}}_{\mathrm{e}}+1.6976;{\mathrm{R}}^2=0.9233\\ \mathrm{A}\left({\mathrm{S}}_1\right)=-0.0055{\mathrm{N}}_{\mathrm{e}}+1.4887;{\mathrm{R}}^{\mathrm{2}}=0.9448\end{array}$$

Dipole moment

The dipole moment values of the studied para-substituted iridabenzene molecules in the S₀ and S₁ states are shown in Table 1. Larger dipole moment values are observed in the S₁ state compared to the S₀ state. Therefore, the electronic distributions of the first singlet excited state differ compared to the ground state because of the large charge transfer excitation. These electronic distributions are dependent on the substituent character.

However, the dipole moment values are larger in the presence of EWGs compared to EDGs in both the S₀ and S₁ states. It is interesting to note, however, that there are good linear correlations between the dipole moment values and the Hammett constants (Figure 3)

$$\begin{array}{l}\mathrm{\mu }\left({\mathrm{S}}_0\right)=6.7542{\mathrm{\sigma }}_{\mathrm{p}}+5.0631;{\mathrm{R}}^{\mathrm{2}}=0.9809\\ \mathrm{\mu }\left({\mathrm{S}}_1\right)=5.4409{\mathrm{\sigma }}_{\mathrm{p}}+3.8232;{\mathrm{R}}^{\mathrm{2}}=0.9686\end{array}$$

Figure 3.

Linear correlation between the dipole moment values and Hammett constants in (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes in the S₀ and S₁ states.

Bond distances

The C–C and Ir–C bond distances of the studied para-substituted iridabenzene molecules are listed in Table 3 for the S₀ and S₁ states.

Table 3.

Selected bond distances (in Å) in the ground state (S₀) and first singlet excited state (S₁) of (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes.

X	S0					S1
	Ir–C2	C2–C3	C3–C4	Ir–Pax	Ir–Peq	Ir–C2	C2–C3	C3–C4	Ir–Pax	Ir–Peq
NH2	1.994	1.373	1.406	2.279	2.331	2.028	1.361	1.419	2.912	2.326
OMe	2.001	1.368	1.406	2.276	2.337	2.028	1.363	1.412	2.926	2.336
Me	1.987	1.381	1.397	2.263	2.341	2.019	1.373	1.406	2.934	2.342
H	1.988	1.383	1.392	2.259	2.343	2.020	1.374	1.401	2.944	2.346
F	1.989	1.381	1.386	2.268	2.340	2.024	1.372	1.394	2.942	2.341
Cl	1.986	1.382	1.390	2.264	2.344	2.017	1.369	1.402	2.959	2.343
CCl3	1.973	1.389	1.388	2.257	2.348	2.004	1.377	1.400	2.984	2.354
CF3	1.984	1.382	1.393	2.255	2.349	2.010	1.372	1.403	3.017	2.355
NO2	1.987	1.380	1.390	2.250	2.352	2.010	1.367	1.403	3.038	2.358

These values show that the Ir–C2, C3–C4, and Ir–P_ax bond distances are longer in the S₁ state than in the S₀ state. In contrast, the C2–C3 and Ir–P_eq bond distances are shorter in S₁ state than S₀ state.

The study of changes in bond distances in S₁ state compared to S₀ state shows that the most changes occurs in Ir–P_ax bond distance. These changes are larger in the presence of EWGs.

As shown, the Ir–P_ax bond lengths are longer in the presence of EDGs than in the EWGs in the S₀ state. In contrast, the Ir–P_ax bond lengths are longer in the presence of EWGs compared with EDGs in the S₁ state.

The Ir–C and C–C bond lengths in the ground state are compatible with the experimental data of similar compounds. ⁵⁷ The shorter C2–C3 bond in the S₁ state compared to that in the S₀ state indicates a larger contribution of the zwitterionic resonance structure to the S1 state (Figure 1(b)).

The plots of the Ir–C and Ir–P bond distances versus Hammett constants give the following equations:

S ₀ state

$$\begin{array}{l}\mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=-0.0196{\mathrm{\sigma }}_{\mathrm{p}}+2.2658;{\mathrm{R}}^2=0.8286\\ \mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=0.0144{\mathrm{\sigma }}_{\mathrm{p}}+2.3411;{\mathrm{R}}^2=0.9611\end{array}$$

S ₁ state

$$\begin{array}{l}\mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=0.0904{\mathrm{\sigma }}_{\mathrm{p}}+2.952;{\mathrm{R}}^2=0.8978\\ \mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=0.022{\mathrm{\sigma }}_{\mathrm{p}}+2.342;{\mathrm{R}}^2=0.9160\end{array}$$

It can be found that there are better Hammett correlations for the Ir–P_eq bonds compared to Ir–P_ax bonds.

Next, we studied the multiple linear regression which considers the inductive (σ_I) and resonance (σ_R) dual parameters. The results of these correlations are as follows:

S ₀ state

$$\begin{array}{l}\mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=-7.50\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{I}}-2.70\\ \times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}+2.26;{\mathrm{R}}^2=0.9679\\ \mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=1.02\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{I}}+1.70\\ \times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}+2.34;{\mathrm{R}}^2=0.9902\end{array}$$

S ₁ state

$$\begin{array}{l}\mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=0.10{\mathrm{\sigma }}_{\mathrm{I}}+0.09{\mathrm{\sigma }}_{\mathrm{R}}\\ +2.95;{\mathrm{R}}^2=0.9143\\ \mathrm{r}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=1.35\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{I}}+2.76\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +2.35;{\mathrm{R}}^2=0.9966\end{array}$$

These equation show good correlations for r(Ir–P) bonds in the S₀ and S₁ states. In these equations, the major contribution of the σ_R parameter is demonstrated in the Ir–P_eq bonds.

Frontier orbital energies and HOMO-LUMO gap

The computed frontier orbitals energies and highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap energies of the studied para-substituted iridabenzene complexes in the S₀ and S₁ states are shown in Table 4.

Table 4.

Frontier orbital energies and HOMO-LUMO gap energies (eV) in the ground state (S₀) and first singlet excited state (S₁) of (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes.

X	S0			S1
	HOMO	LUMO	ΔE	HOMO	LUMO	ΔE
NH2	−4.46	−0.84	3.62	−4.21	−2.01	2.20
OMe	−4.75	−1.03	3.72	−4.42	−2.23	2.19
Me	−4.90	−1.23	3.68	−4.56	−2.46	2.10
H	−5.01	−1.31	3.70	−4.68	−2.58	2.10
F	−5.07	−1.33	3.74	−4.75	−2.61	2.14
Cl	−5.17	−1.54	3.63	−4.84	−2.78	2.07
CCl3	−5.41	−1.92	3.49	−5.06	−3.11	1.95
CF3	−5.39	−1.78	3.61	−5.02	−3.01	2.01
NO2	−5.59	−2.35	3.24	−5.31	−3.51	1.80

HOMO: highest occupied molecular orbital; LUMO: lowest unoccupied molecular orbital.

These values show that the energy of stability of the frontier orbitals increases in the presence of EWGs in both the S₀ and S₁ states. In comparison, the stability of the frontier orbitals decreased in the presence of EDGs in both the S₀ and S₁ states.

Good linear correlations can be observed between the frontier orbital energy values and Hammett constants in both the S₀ and S₁ states:

S ₀ state

$$\begin{array}{l}\mathrm{E}\left(\mathrm{HOMO}\right)=-0.029{\mathrm{\sigma }}_{\mathrm{p}}-0.1837;{\mathrm{R}}^2=0.9917\\ \mathrm{E}\left(\mathrm{LUMO}\right)=-0.0375{\mathrm{\sigma }}_{\mathrm{p}}-0.0503;{\mathrm{R}}^2=0.9400\end{array}$$

S ₁ state

$$\begin{array}{l}\mathrm{E}\left(\mathrm{HOMO}\right)=-0.0278{\mathrm{\sigma }}_{\mathrm{p}}-0.172;{\mathrm{R}}^2=0.9865\\ \mathrm{E}\left(\mathrm{LUMO}\right)=-0.0373{\mathrm{\sigma }}_{\mathrm{p}}-0.0952;{\mathrm{R}}^2=0.9656\end{array}$$

However, there are larger HOMO-LUMO gap values in the presence of EDGs compared with EWGs in both the S₀ and S₁ states. This trend is due to an electron-withdrawing inductive effect which concentrates the electronic density over the substituted region of the complex. The HOMO-LUMO gap values are larger in the S₀ state compared to the S₁ state.

Electron localization function analysis

We analyzed the nature of the chemical bonding in the Ir–C and Ir–P bonds on the basis of the electron localization function (ELF) ⁵⁸ distribution, which is indicative for concentrations of valence electron density in regions of chemical bonds.

A large ELF value corresponds to largely localized electrons which indicates that a covalent bond, a lone pair, or inner shells of the atom are involved. Table 5 reveals larger ELF values for the Ir–C bond compared to Ir–P bonds. There are larger ELF values for the Ir–C bond in the presence of EWGs. However, the ELF values of the Ir–C bond are larger in the S₀ state than the S₁ state. There are larger ELF values for the Ir–P_ax bond compared to the Ir–P_eq bond in the S₀ state. The plots of ELF values of the Ir–C and Ir–P bonds versus the Hammett constants give the following equations:

Table 5.

ELF and LOL values of selected bonds in the ground state (S₀) and first singlet excited state (S₁) of (para-C₅H₄X)Ir(PH₃)₃ iridabenzene complexes.

X	S0			S1
	Ir–C2	Ir–Pax	Ir–Peq	Ir–C2	Ir–Pax	Ir–Peq
(a) ELF
NH2	0.47753	0.43373	0.33439	0.43003	0.22769	0.32469
OMe	0.48374	0.43756	0.33803	0.43720	0.22274	0.32038
Me	0.49132	0.45144	0.33019	0.44521	0.22048	0.31739
H	0.49208	0.45639	0.32921	0.44778	0.21745	0.31650
F	0.48083	0.44818	0.33169	0.43275	0.21742	0.31941
Cl	0.48596	0.45418	0.32997	0.43932	0.21225	0.32478
CCl3	0.49445	0.46380	0.32628	0.45414	0.20535	0.31485
CF3	0.49457	0.46516	0.32768	0.45101	0.18394	0.31973
NO2	0.49709	0.47423	0.32682	0.45209	0.18951	0.32763
(b) LOL
NH2	0.48877	0.46675	0.41482	0.46485	0.35200	0.40950
OMe	0.49188	0.46868	0.41680	0.46848	0.34878	0.40712
Me	0.49567	0.47569	0.41252	0.47253	0.34729	0.40546
H	0.49605	0.47818	0.41199	0.47383	0.34529	0.40496
F	0.49042	0.47405	0.41335	0.46623	0.34527	0.40658
Cl	0.49299	0.47707	0.41240	0.46956	0.34182	0.40955
CCl3	0.49723	0.48191	0.41038	0.47703	0.33714	0.40404
CF3	0.49729	0.48259	0.41115	0.47546	0.32204	0.40676
NO2	0.49855	0.48713	0.41067	0.47600	0.32607	0.41112

ELF: electron localization function; LOL: localized-orbital locator.

S ₀ state

$$\begin{array}{l}\mathrm{ELF}\left(\mathrm{Ir}-\mathrm{C}\right)=0.0122{\mathrm{\sigma }}_{\mathrm{p}}+0.4873;{\mathrm{R}}^2=0.6401\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=0.0277{\mathrm{\sigma }}_{\mathrm{p}}+0.4509;{\mathrm{R}}^2=0.9074\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=-0.0068{\mathrm{\sigma }}_{\mathrm{p}}+0.3312;{\mathrm{R}}^2=0.6486\end{array}$$

S₁ state

$$\begin{array}{l}\mathrm{ELF}\left(\mathrm{Ir}-\mathrm{C}\right)=0.0153{\mathrm{\sigma }}_{\mathrm{p}}+0.4416;{\mathrm{R}}^2=0.6091\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=-0.0305{\mathrm{\sigma }}_{\mathrm{p}}+0.214;{\mathrm{R}}^2=0.8212\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=0.0007{\mathrm{\sigma }}_{\mathrm{p}}+0.3205;{\mathrm{R}}^2=0.0059\end{array}$$

It can be seen that there are poor Hammett correlations for these equations.

We also studied the multiple linear regression which considers the inductive (σ_I) and resonance (σ_R) dual parameters. The results of these correlations are:

S₀ state

$$\begin{array}{l}\mathrm{ELF}\left(\mathrm{Ir}-\mathrm{C}\right)=-4.8\times {10}^{-4}{\mathrm{\sigma }}_{\mathrm{I}}+1.96\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4930;{\mathrm{R}}^2=0.9340\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=1.72\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{I}}+3.44\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4562;{\mathrm{R}}^2=0.9730\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=-1.60\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{I}}-9.72\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.3288;{\mathrm{R}}^2=0.7874\end{array}$$

S₁ state

$$\begin{array}{l}\mathrm{ELF}\left(\mathrm{Ir}-\mathrm{C}\right)=-1.43\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{I}}+2.51\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4492;{\mathrm{R}}^2=0.9180\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=-3.26\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{I}}-3.10\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.2138;{\mathrm{R}}^2=0.8317\\ \mathrm{ELF}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=9.79\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{I}}-4.42\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.3167;{\mathrm{R}}^2=0.3322\end{array}$$

These equations show good correlations of ELF(Ir–C) for the S₀ and S₁ states and ELF(Ir–P_ax) for the S₀ state. In these equations, the major contribution of the σ_R parameter is demonstrated.

Figure 4 presents shaded surface maps with projections of the ELF in the (para-C₅H₅)Ir(PH₃)₃ iridabenzene complex for S₀ and S₁ states.

Figure 4.

Shaded surface maps with projection of (a) the electron localization function (ELF) and (b) the localized-orbital locator (LOL) in the (para-C₅H₅)Ir(PH₃)₃ iridabenzene complex in the S₀ and S₁ states.

Localized-orbital locator analysis

A developed descriptor for electron localization is the localized-orbital locator (LOL).^59,60 The LOL gives simple, recognizable patterns in classic chemical bonds and proves useful in interpreting the structures of unusual materials. LOL analysis focuses on the topological properties of kinetic energy density. ⁶¹

A large LOL value corresponds to largely localized electrons which indicates that a covalent bond, a lone pair, or inner shells of the atom are involved. Table 5 reveals larger ELF values for Ir–C bonds compared to Ir–P bonds. There are larger LOL values for Ir–C bonds in the presence of EWGs. However, the LOL values of Ir–C bonds are larger in the S₀ state than in the S₁ state. There are larger LOL values for the Ir–P_ax bond compared to the Ir–P_eq bond in the S₀ state. In contrast, there are larger LOL values for the Ir–P_eq bond compared to the Ir–P_ax bond in the S₁ state.

The plots of the LOL values of the Ir–C and Ir–P bonds versus Hammett constants give the following equations:

S₀ state

$$\begin{array}{l}\mathrm{LoL}\left(\mathrm{Ir}-\mathrm{C}\right)=0.0061{\mathrm{\sigma }}_{\mathrm{p}}+0.4937;{\mathrm{R}}^2=0.6397\\ \mathrm{LOL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=0.014{\mathrm{\sigma }}_{\mathrm{p}}+0.4754;{\mathrm{R}}^2=0.9074\\ \mathrm{LoL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=-0.0037{\mathrm{\sigma }}_{\mathrm{p}}+0.4131;{\mathrm{R}}^2=0.6498\end{array}$$

S₁ state

$$\begin{array}{l}\mathrm{LoL}\left(\mathrm{Ir}-\mathrm{C}\right)=0.0078{\mathrm{\sigma }}_{\mathrm{p}}+0.4707;{\mathrm{R}}^2=0.6092\\ \mathrm{LOL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=-0.0208{\mathrm{\sigma }}_{\mathrm{p}}+0.3429;{\mathrm{R}}^2=0.8101\\ \mathrm{LoL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=0.0004{\mathrm{\sigma }}_{\mathrm{p}}+0.4072;{\mathrm{R}}^2=0.0057\end{array}$$

It is observed that there are poor Hammett correlations for these equations.

Studying the multiple linear regression, which considers the inductive (σ_I) and resonance (σ_R) dual parameters, gave the following correlations:

S₀ state

$$\begin{array}{l}\mathrm{LOL}\left(\mathrm{Ir}-\mathrm{C}\right)=-2.5\times {10}^{-4}{\mathrm{\sigma }}_{\mathrm{I}}+9.83\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4966;{\mathrm{R}}^2=0.9340\\ \mathrm{LOL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=8.62\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{I}}+1.73\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4781;{\mathrm{R}}^2=0.9705\\ \mathrm{LOL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=-8.8\times {10}^{-4}{\mathrm{\sigma }}_{\mathrm{I}}-5.3\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4118;{\mathrm{R}}^2=0.7884\end{array}$$

S₁ state

$$\begin{array}{l}\mathrm{LOL}\left(\mathrm{Ir}-\mathrm{C}\right)=-7.30\times {10}^{-4}{\mathrm{\sigma }}_{\mathrm{I}}+1.27\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4746;{\mathrm{R}}^2=0.9185\\ \mathrm{LOL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{ax}}\right)=-2.23\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{I}}-2.10\times {10}^{-2}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.3427;{\mathrm{R}}^2=0.8218\\ \mathrm{LOL}\left(\mathrm{Ir}-{\mathrm{P}}_{\mathrm{eq}}\right)=5.42\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{I}}-2.50\times {10}^{-3}{\mathrm{\sigma }}_{\mathrm{R}}\\ +0.4050;{\mathrm{R}}^2=0.3325\end{array}$$

These equations show good correlations for LOL(Ir–C) in the S₀ and S₁ states and for LOL(Ir–P_ax) in the S₀ state. In these equations, the major contribution from the σ_R parameter is demonstrated.

Figure 4 reveals shaded surface maps with projection of the LOL in the (para-C₅H₅)Ir(PH₃)₃ iridabenzene complex for the S₀ and S₁ states.

Aromaticity

The para-delocalization index (PDI) is a quantity for measuring the aromaticity of six-membered rings.^62,63 PDI is fundamentally the averaged para-delocalization index (para-DI) in six-membered rings. In the studied systems, this parameter is calculated as

$$PDI=\frac{DI\left(1,4\right)+DI\left(2,5\right)+DI\left(3,6\right)}{3}$$

The foundation of PDI was laid according to a study by Bader et al., who believed that the DI in benzene is greater for para-related than for meta-related carbon atoms. It is obvious that the PDI would mean a larger delocalization and stronger aromaticity. The main limitation of the definition of PDI is its applicability for studying the aromaticity of six-membered rings only; it was reported that the PDI is unsuitable for cases in which the ring plane has an out-of-plane distortion.

The PDI values of the studied molecules are listed in Table 1. These values show larger PDI values for EWGs compared to EDGs. This result is consistent with nucleus-independent chemical shift (NICS) values in previous studies on para-substituted iridabenzenes. ³⁴

Conclusion

Computational investigations of the substitution effects on the structures and properties of para-substituted iridabenzenes in the ground state and first singlet excited state showed the following:

1. Atomization energy values (E_atom) for the S₁ state were larger compared to the S₀ state.

2. The energy difference values of the ground state and first singlet excited state were lower in the presence of EDGs compared to EWGs.

3. The rotational constants in the excited state were less than those of the corresponding ground state rotational constants.

4. The dipole moment values were larger in the presence of EWGs compared to EDGs in both the S₀ and S₁ states. There were good linear correlations between the dipole moment values and the Hammett constants.

5. The Ir–P_ax bond lengths were longer in the presence of EDGs compared with EWGs in the S₀ state. In contrast, the Ir–P_ax bond lengths were longer in the presence of EWGs compared with EDGs in the S₁ state.

6. The ELF and LOL values for the Ir–C bond are larger compared to the Ir–P bonds. There are larger ELF and LOL values for the Ir–C bond in the presence of EWGs. However, the ELF and LOL values of Ir–C bond are larger in the S₀ state than the S₁ state.

7. The larger PDI values for EWGs compared to EDGs indicate their enhanced aromatic properties in the presence of EWGs.

Computational methods

All calculations were carried out with the Gaussian (Version 09) software package ⁶⁴ using the standard 6-311G (d, p) basis set computations for systems involving the main group elements.^65,66 For Ir, the standard LANL2DZ basis set^67–69 is applied and Ir is explained by the effective core potential (ECP) ⁷⁰ with a double-ξ valance using the LANL2DZ basis set.

The ground state and first singlet state geometry optimizations were carried out by applying the parameter hybrid functional with adapted Perdew–Wang exchange and correlation (MPW1PW91). ⁷¹ According to the results of computations for transition-metal complexes, the MPW1PW91 functional outperformed B3LYP.^72–75 A vibrational analysis at each stationary point verified its identity as an energy minimum. The first singlet excited states of the target compounds were determined by the TD-DFT method. ⁴¹

The Multiwfn 3.5 program was used for topological analysis of the ELF, the LOL, and for calculation of the PDI. ⁷⁶