Theoretical investigation of structural, electronical, and optical properties of [18] DBA annulene and its derivatives

الموضوعات : Journal of Theoretical and Applied Physics

Mohammad Hossein Fekri ¹ (Department of Chemistry, Ayatollah Borujerdi University, Borujerd, Iran.)
Niko Karimpoor ² (Department of Chemistry, Ayatollah Borujerdi University, Borujerd, Iran.)
Motaleb Ghasemian ³ (Department of Chemistry, Ayatollah Borujerdi University, Borujerd, Iran.)
Samaneh Soleymani ⁴ (Department of Chemistry, Ayatollah Borujerdi University, Borujerd, Iran.)
Maryam Razavi Mehr ⁵ (Department of Chemistry, Ayatollah Borujerdi University, Borujerd, Iran.)

تاريخ الإرسال : 17 الخميس , ربيع الأول, 1444 تاريخ التأكيد : 05 الأحد , ربيع الثاني, 1444 تاريخ الإصدار : 09 الأربعاء , شعبان, 1444

الکلمات المفتاحية: Hyperpolarizability, Nonlinear optical property, annulene, Electronic property,

ملخص المقالة :

The structure geometry, vibrational frequencies, electronic and optical properties of a series of donor-acceptor substituted dodecadehydrotribenzo [18] annulenes ([18] DBA) were investigated using the B3LYP method at a 6-31+G (d, p) basis set. After optimization of the structures, HOMO and LUMO energies, gap energy (Eg), global hardness (η), chemical potential (μ), electrophilicity index (ω), maximum charge transfer (∆Nmax), electronegativity (χ), Fermi level (EFL), wavelength (λ), oscillator power (f0), and participation percentage (% Con) for [18] DBA derivatives. A significant increase in the first hyperpolarizability was observed by substitution on [18] DBA. The results of this study may be used to design and construct materials with adjustable electrical properties. The results indicate that the NLO response of [18] DBA could be enhanced by functionalizing different substitutions. In general, the NLO response and electronic properties of the S1-10 are more excellent than others.

نص كامل:



Theoretical investigation of Structural, Electronical, and Optical properties of [18] DBA annulene and its derivatives

Mohammad Hossein Fekri*, Niko Karimpoor, Motaleb Ghasemian, Samaneh Soleymani, Maryam Razavi Mehr

 

Department of Chemistry, Ayatollah Borujerdi University, Borujerd, Iran. 

[e-mail]

Abstract

The structure geometry, vibrational frequencies, electronic and optical properties of a series of donor-acceptor substituted dodecadehydrotribenzo [18] annulenes ([18] DBA) were investigated using the B3LYP method at a 6-31+G (d, p) basis set. After optimization of the structures, HOMO and LUMO energies, gap energy (Eg), global hardness (η), chemical potential (μ), electrophilicity index (ω), maximum charge transfer (∆Nmax), electronegativity (χ), Fermi level (EFL), wavelength (λ), oscillator power (f0), and participation percentage (% Con) for [18] DBA derivatives. A significant increase in the first hyperpolarizability was observed by substitution on [18] DBA. The results of this study may be used to design and construct materials with adjustable electrical properties. The results indicate that the NLO response of [18] DBA could be enhanced by functionalizing different substitutions. In general, the NLO response and electronic properties of the S1-10 are more excellent than others.

Keywords: annulene, nonlinear optical, electronic properties, hyperpolarizability.

 

1. Introduction

One of the important properties of annulene compounds is nonlinear optical properties (NLO). This property causes information storage, optical communications, optical switching devices, and the design of high-performance materials [1-5]. Since extra electrons play an essential role in increasing the first ultra-polarizability (β0), species such as the aromatic derivatives of annulene, which have excess electrons, can exhibit nonlinear optical properties [6-9].

Because of the potential of organic compounds to use as important nonlinear optical (NLO) responses due to fast nonlinear response times, better off-resonance susceptibilities, and small relative permittivity, in the past decade, many studies have focused on the properties of organic compounds for NLO applications [10-14]. Dehydrobenzo [n] annulenes (DBA) are important compounds among the comprehensive conjugated organic molecules. They have been recognized as an exciting class of carbon-rich materials, such as grapevines, which can be applied in various new electronic and optical materials [15]. Because of π-orbital overlap, intermolecular π-stacking, and highly tunable dipoles and symmetries found for several derivatives, the use of dehydrobenzo [n]annulenes has been explored in numerous applications [15-17]. The main focus of the present study is to analyze the simplest substructure of graphicness, dehydrobenzo [18] annulenes, for use in nonlinear optics due to the ease in placement of various groups on the benzene rings. Therefore, the series of one-dimensional molecules of dehydrobenzo [18] annulenes with systematic donor-acceptor substitutions have been investigated. The B3LYP /6-31+G (d, p) has been employed to determine the geometry optimization, vibrational frequencies, and electronic and optical properties of the considered structures.

 

2. Computational Details

Calculations were performed using the Gaussian 09 and Gauss Sum 03 package [18, 19]. The geometries of the pristine dodecadehydrotribenzo [18] annulene and their derivatives were fully optimized at the B3LYP/6-31+G (d, p) computational level [20-22]. In order to evaluate the [18] DBA and their derivatives reactivity, quantum descriptors such as HOMO and LUMO energies, gap energy (Eg), global hardness (η), chemical potential (μ), electrophilicity index (ω), maximum charge transfer (∆Nmax), electronegativity (χ) and Fermi level (EFL) were calculated. These indexes were estimated through the following equations [23-27]:

 (1)                      

(2)                                  

(3)                 

(4)                                                                                               

(5)                                                                             

(6)                                                                                                

(7)                                                                                   

In these equations, EHOMO and ELUMO refer to the energies of HOMO and LUMO, respectively. IP and EA show the ionization and electron affinity energies.

Harmonic vibrational frequency calculations at the same level confirmed the structures as minima and enabled the evaluation of zero-point vibrational energies (ZPVE). Time-dependent density functional theory has been employed here to calculate the absorption wavelength and oscillator strength on the ground-state optimized geometries at the 6-31+G (d, p) level. Also, we calculated the wavelength (λ), oscillator power (f0), participation percentage (% Con), polarizability (α), and first hyperpolarizability (β0) for [18] DBA derivatives.

The average polarizability (α) and first hyperpolarizability (β0) were estimated through the following equations [28-30]:

(8)                         

(9)                    

(10)                    

(11)                    

(12)                    

3. Results and Discussion

Results of geometry optimizations for the [18] DBA and its derivatives with different substations are classified into two categories. In the first type, denoted as M1-M7, we have one donor/acceptor substituent in predetermined positions, while the second type (S1-10) possesses two different donor and acceptor substituents on the phenyl rings. The optimized structures of these functionalized DBA are represented in Figures 1 and S1. The electronic and optical properties, as well as to incorporate easily polarizable functionalities of DBA have been shown to be strongly influenced by the nature of substituents. It would be interpretable in terms of charge transfer in conjugated π-systems with donor (D) and acceptor (A) moieties as terminal substituents. The electronic and optical responses of S1-10 construction, which are substituted at various positions with donor and acceptor groups, are often longer wavelengths. This corresponds to the transition of the excess electron. It has been proposed as a suitable approach to increase the NLO response. The selection bond lengths and bond angles of [18] DBA in optimized geometries indicate that all structure is planar conformation. 

Y	X	compound		Y	X	compound
R3	R4	S10		R1	NH2	S1
H	NH2	M1		R2	NH2	S2
H	OH	M2		R3	NH2	S3
H	Ph2N	M3		R1	OH	S4
H	R1	M4		R2	OH	S5
H	R2	M5		R3	OH	S6
H	R3	M6		R1	Ph2N	S7
H	R4	M7		R2	Ph2N	S8
H	H	M		R2	R4	S9

Fig. 1. Molecular structures of [18] DBA and their derivatives

3.1. Structure of dodecadehydrotribenzo39 [18] annulenes

The geometrical parameters, as well as vibrational spectra of the [18] DBA, are given in Figures 2, 3, and Table 1. The optimized geometry indicates that [18] DBA has planar conformation with D3h symmetry which is in favor of the intermolecular conjugated π-systems (Fig. 2). The symmetry MEP map indicates that the harmful potential sites are on the annulene ring, and the positive potential sites are around the hydrogen atoms.

Fig. 2. Contour maps and molecular electrostatic potential of [18] DBA compound.

Table 1. The optimized structural parameters, namely bond lengths, bond angles, and frequency of [18] DBA at B3LYP/6-31G + (d, p)

(Ao) bond length						(cm-1) frequency			(⁰)bond angle
r1-2	1.429		r5-6	1.222		vC-H	3218		q1-2-3	120.83
r2-3	1.416		r6-7	1.415		v3-4	2240		q2-3-4	179.96
r3-4	1.222		r7-8	1.429		v1-2	1520		q3-4-5	179.21
r4-5	1.356		ra-b	1.389		vring	990		q4-5-6	179.96

 

The nonlinear optical properties of the [18] DBA were evaluated. The reasonable first hyperpolarizability of DBA (1141.5 a.u.) implies a proper NLO response. The energy gap (Eg) value of DBA is 3.51 eV. Which is presented in the DOS spectrum (Fig. 3). The UV-Vis absorption spectra of [18] DBA display mainly three bands with proper oscillator strengths at 360, 419, and 439 nm.

 

 

Fig. 3. Vibrational spectra (a) and DOS spectra (b) of [18] DBA.

3.2. M1-M7 compounds (Derivatives of [18] DBA)

To investigate the effect of donor-acceptor substitutions on annulene molecule (M) from (H, NH2), (H, OH), (H, Ph2N), (H, R1), (H, R2), (H, R3) and (H, R4) are used with the letters M1, M2, M3, M4, M5, M6, and M7, respectively (Fig. 4). The parameters of stability energy (ES), bipolar moment (μ), polarizability (α), hyperpolarizability (β0), and anisotropy (IP) were investigated (Table 2). The results show that all substitutions lead to the stability of the annulene molecule. Among them, M3 has the highest stability (ES=-758.138 kcal/mol) and M6 has the lowest stability (ES=-746.1725 kcal/mol). Also, calculations show that the M4 has the highest and the M2 molecule has the lowest bipolar moment. Another parameter whose changes were evaluated by the mentioned substitutions is polarization (α). Polarity is the relative tendency of an electron charge distribution function to deviate from its standard shape by an external electric field. Accordingly, the M2 and M7 molecules have the lowest and highest polarizations, respectively. Also, based on the obtained results, it was observed that M1 and M4 molecules have the lowest and highest hyperpolarizability, respectively. Therefore, M1 with the electron donor group NH2 has more negligible effect on amplifying the properties of NLO, On the other hand, M4 with tetraciano electron acceptor (β0 ~ 19174) is the most suitable substitution to improve the nonlinear optical properties of annulene. Finally, the amount of anisotropy in M2 and M4 molecules has the lowest and highest values, respectively.

 

Fig. 4. Optimized structures of M1-M7 compounds at the level of B3LYP/6-31+G (d, p).

 

Table. 2.  Calculated values of stability energy (ES), bipolar moment (μ), polarizability (α), hyperpolarizability (β0), and anisotropy (IP) of M1-M7 compounds at B3LYP/6-31+G (d, p ) level.

IP	β0	α	μ	ES (kcal/mol)
244.92	1141.508	448.638	0.000	-	M
294.629	3290.084	471.857	3.091	-752.373	M1
270.043	1012.682	459.444	1.535	-752.373	M2
409.018	7313.819	645.903	2.099	-758.138	M3
432.279	19174.243	635.705	11.068	-748.608	M4
385.673	10217.966	615.958	9.676	-753.628	M5
342.341	10201.764	650.394	7.781	-746.725	M6
430.068	12605.476	683.979	7.027	-752.373	M7

 

In Table 3, HOMO and LUMO energies, gap energy (Eg), wavelength (λ), global hardness (η), chemical potential (μ), electrophilicity index (ω), maximum charge transfer (∆Nmax), electronegativity (χ) and Fermi level (EFL) and in Table 4, oscillator power (f0), and participation percentage (% Con) for M1-M7 were shown. The results indicate that the M4 molecule with tetracyanone substitution and M7 molecule with diamine substitution have the lowest and highest energy boundary orbitals, respectively. Based on Eg, the electrical conductivity of the substations can be explained. As we know, a low value of Eg indicates a higher electrical conductivity. Accordingly to the data in Table 3, the M4 compound has the lowest Eg (2.06 eV) and the highest electrical conductivity compared to other substitutions. The process of increasing the electrical conductivity of other substations is as follows.

M4  M5  M7   M3 = M6  M1  M2

Physically, chemical potential (μ) describes the tendency of an electron to escape an equilibrium system. Negative values of chemical potential show that charge transfer between two particles is easy. In present work, the chemical potential electron (μ) for all compounds (M1-M7) is negative in the range of -3.23 to -4.98 eV. In a molecule, chemical hardness expresses resistance to changes in electron distribution or electron transfer or charge transfer. There is a direct relationship between chemical hardness and energy gap. Higher chemical hardness and energy gap means the reduced reactivity. Therefore, the M4 molecule with the highest chemical potential (-4.98 eV) and the lowest chemical hardness (1.03eV) and energy gap (2.06 eV) has the highest reactivity.

Electrophilicity (ω) is a parameter related to chemical potential and chemical hardness. In this research, ω for all of the molecules is high. Also, this parameter for M4 (12.04 eV) is higher than that for other moleculs.

Maximum charge transfer (ΔNmax) shows the charge capacity of the particle. According to the ΔNmax equation (Eq. 5), when the chemical potential increases, the chemical hardness decreases and the electrophilicity increases. The results showed that (Table 3) the level of this parameter in M4 is higher than that in other molecules.

 

Table 3. Molecular orbitals energy and quantum descriptors (eV) M1-M7 compounds.

	EHOMO	ELUMO	Eg	η	μ	ω	∆Nmax	χ	EFL
M	-5.60	-2.09	3.51	1.75	-3.84	4.21	2.19	3.84	-3.84
M1	-5.21	-1.99	3.22	1.61	-3.60	4.02	2.24	3.60	-3.60
M2	-5.43	-2.07	3.36	1.68	-3.75	4.19	2.23	3.75	-3.75
M3	-5.06	-2.01	3.05	1.52	-3.53	4.10	2.32	3.53	-3.53
M4	-6.01	-3.95	2.06	1.03	-4.98	12.04	4.83	4.98	-4.98
M5	-5.87	-3.45	2.42	1.21	-4.66	8.97	3.85	4.66	-4.66
M6	-5.39	-2.34	3.05	1.52	-3.86	4.90	2.54	3.86	-3.86
M7	-4.60	-1.87	2.73	1.36	-3.23	3.84	2.37	3.23	-3.23

 

Table 4. Wavelength (λ), oscillator power (f0), participation percentage (% Con) for M1-M7 compounds.

% Con	fo	λ(nm)	E(cm-1)∆
H-3->L (74%)	0.010	360.45	22746	M
H->L+ (50%)	0.010	419.08	22861
H->L (49%)	0.010	439.63	27743
H->L (56%)	0.760	380.19	26302	M1
H->L (82%)	0.060	443.45	22601
H-1->L (49%)	0.733	375.11	26659	M2
H-1->L (58%)	0.758	403.35	24792	M3
H->L+ (76%)	0.241	467.92	21371
H-2->L (97%)	0.043	500.20	19993	M4
H-1->L (87%)	0.153	667.12	14989
H-1->L+ (64%)	0.033	452.55	22097	M5
H-1->L (66%)	0.119	573.03	17360
H-1->L+1 (15%)	0.359	467.31	21398	M6
H-2->L+1 (30%)	0.287	418.51	23894	M7
H->L+1 (89%)	0.393	497.53	20099

 

The results show that M1 to M7 compounds have different UV-Vis spectra (S1). As expected, the M4 combination with the highest conductivity has the highest shift wavelength (667 nm), and the M2 showed the shortest shift wavelength (375 nm) relative to the annulene. Also, two different peaks appear for the M1 has a wavelength of 357.11 nm with an absorption intensity of 0.733, which is the highest peak. Similarly, for M3 in the region of 403.353 nm with an intensity of 0.758, M5 with a wavelength of 567.03 nm with an intensity of 0.119, M6 in the region of 467.31 nm with an intensity of 0.359, and the molecule M7 in the region of wavelength 497.53 nm with an intensity of 0.393 have the highest peak and the highest absorption intensity.

DOS analysis was performed based on B3LYP/6-31G+ (d, p) for compounds M1 to M7 similar to the annulene molecule. According to the results (S2), M2 and M4 molecules with values of 3.36 and 2.06 eV have the highest and lowest energy gap, respectively. The diversity and variety of electronic states in all forms is another reason for the optical properties of annulene derivatives.

Calculations of structural parameters were measured by determining the bond length, bond angle, and vibration spectroscopic properties to investigate the effect of substitution on annulene in compounds M1 to M7 compounds (S2). Observation of the values of lengths, angles, and bonding frequencies calculated for the M1 to M7 compounds in the range of 1.383-1.430 Ao, 179.06-179.91, and 3219-994 cm-1, respectively, and its comparison with annulene (M) indicate stabilization of annulene molecular skeleton has a flat structure. Also, Fig. 5 shows the infrared spectra of the M1 (electron donor) and M4 (electron acceptor) compounds. A comparison of these two spectra, in particular the observed absorption and displacement, clearly indicates the substitution effect.

 

Fig. 5. Comparison of infrared spectra of M1 and M4 compounds.

To compare the aromatic properties of the rings due to the presence of substitution, the NICS index was calculated at the level of B3LYP/6-31+G (d, p) (Fig. 6). NICS calculations were performed at distances of 0 and 1.5 from the centers of the rings to the M4 compound. The results in the 10.12-22.32 show that the ring scope has the highest value in the 0.5 Ao. The results also showed that the coverage of the ring involved with substitution is more than the ring without substitution.

 

Fig. 6. The image of the M4 compound from NICS calculations at B3LYP/6-31+G (d, p) level.

 

3.3. S1-S10 compounds (Derivatives of [18] DBA)

After examining the effect of one substitution on the properties of annulene, an important question that arises in mind is the effect of subsequent substitutions. For this purpose, the effect of two different substitutions on annulene was investigated (Fig. 7).

 

Fig. 7. Optimized structures of S1-S10 compounds at the level of B3LYP/6-31+G (d, p).

The results showed that annulene with two substitutions has a more stable structure than a single substitution. On the other hand, S8 has the most stability (Es~ -1509 eV). In this group, S3, S6, and S10 have the highest amount of energy and the least amount of stability. Calculations to determine the amount of dipole moment showed that S9 with the highest value of μ (16.418 D) had the lowest symmetry and S6 with the lowest value of μ (7.773 D) had the most symmetric state. The results showed that S3 and S7 compounds have the lowest and highest β0 values (1305.051 and 45547.212), respectively. As expected, the highest anisotropy was observed for the S7 molecule. Also, the results showed that (Tables 6 and 7) the effect of two-exchange electron donor and lethal groups (S7) on the single exchange (M4) shows the improvement of nonlinear optical properties of annulene.

Table. 5.  Calculated values of stability energy (ES), bipolar moment (μ), polarizability (α), hyperpolarizability (β0), and anisotropy (IP) of S1-S10 compounds at B3LYP/6-31+G (d, p ) level.

IP	β0	α	μ	Es
523.509	28247.752	689.666	14.766	-1500.353	S1
460.661	18583.536	656.418	11.363	-1506.000	S2
592.155	1305.051	677.062	9.978	-1499.098	S3
473.765	19734.694	659.090	12.109	-1501.608	S4
420.656	13475.441	634.077	10.162	-1506.628	S5
564.804	3294.193	662.159	7.773	-1499.098	S6
662.638	45547.212	900.711	14.864	-1504.745	S7
591.754	28925.191	849.223	11.980	-1509.765	S8
633.592	43524.812	916.149	16.418	-1505.373	S9
728.512	15289.892	908.517	14.089	-1499.098	S10

 

The results of Table 6 show that molecules S4 and S10 have the lowest and highest amounts of HOMO and LUMO energy, respectively. Investigating electrical conductivity indicates that S6 and S7 molecules have the highest and lowest electrical conductivity, respectively. UV spectra show that the S7 compound has the highest wavelength. Other S compounds have different and, of course, different adsorptions from M compounds (S3).

Also, the chemical potential electron (μ) for all compounds (S1-S10) is negative in the range of -3.39 to -4.91 eV. The S4 molecule with the highest chemical potential (-4.91 eV) has the highest reactivity. In this research, ω for all of the molecules is high. Also, this parameter for S7 (13.57 eV) is higher than that for other moleculs. Also, the results showed that (Table 6) the amount of ΔNmax for S7 is higher than that in other molecules (5.86 eV).

 

Table 6. Molecular orbitals energy and quantum descriptors (eV) S1-S10 compounds.

	EHOMO	ELUMO	Eg	η	μ	ω	∆Nmax	χ	EFL
S1	-5.68	-3.83	1.85	0.92	-4.75	12.26	5.16	4.75	-4.75
S2	-5.52	-3.35	2.17	1.08	-4.43	9.09	4.10	4.43	-4.43
S3	-5.16	-2.19	2.97	1.48	-3.67	4.55	2.48	3.67	-3.67
S4	-5.93	-3.90	2.03	1.01	-4.91	11.93	4.86	4.91	-4.91
S5	-5.76	-3.41	2.35	1.17	-4.58	8.96	3.91	4.58	-4.58
S6	-5.30	-2.26	3.04	1.52	-3.78	4.70	2.49	3.78	-3.78
S7	-5.43	-3.84	1.59	0.79	-4.63	13.57	5.86	4.63	-4.63
S8	-5.32	-3.37	1.95	0.97	-4.34	9.77	4.51	4.33	-4.33
S9	-4.83	-3.26	1.57	0.78	-4.04	10.46	5.18	4.04	-4.04
S10	-4.68	-2.10	2.58	1.29	-3.39	4.45	2.63	3.39	-3.39

 

Table 7. Wavelength (λ), oscillator power (f0), and participation percentage (% Con) for S1-S10 compounds.

% Con	λ(nm)	E(cm-1)∆
H->L (99%)	771.14	12967	S1
H-1->L+2 (14%)	476.64	20980	S2
H->L (98%)	657.85	15201
H->L (78%)	479.29	20863	S3
H-2->L (97%)	511.15	19563	S4
H-1->L (15%)	704.69	14190
H-1->L+2 (20%)	460.24	21727	S5
H-1->L (10%)	608.42	16435
H-1->L+1 (10%)	469.73	21289	S6
H-2->L (95%)	596.13	16774	S7
H->L (99%)	893.32	11194
H-2-> (94%)	518.15	19299	S8
H->L (99%)	731.95	13662
H-2->L (65%)	576.75	17338	S9
H->L (99%)	905.06	11048
H->L (18%)	527.82	18945	S10

 

DOS analysis based on B3LYP/6-31G+ (d, p) was performed for S1-S10 compounds similar to the annulene molecule (S4). According to the results, molecules S6 and S7, with values of 3.04 eV and 1.59 eV, respectively, have the highest and lowest energy gap, and as a result, the optical properties are desirable. Calculations were performed for S1-S10 compounds to determine the amount of bond length in the range of 1.431-1.382 Ao. The measured frequency values are in the range of 993-3233 cm-1. Also, the bonding angle for S1-S10 compounds was observed in the range of 121.13-179.30o, which all indicates that the structure of the all compounds are flat (S5).

3.4. Effect of heterocyclic rings on the structure of [18] DBA (structures H1-H8)

To investigate the effect of heterocyclic rings on the properties of annulene, symmetric heterocyclic in [18] annulene were designed and optimized (Fig. 8 and 9).

Y	X	molecule 2		Y	X	molecule 1
O	CH	H6		CH	N	H1
CH	S	H7		N	CH	H2
S	CH	H8				molecule 2
CH	CH2	H9		CH	N	H3
CH2	CH	H10		N	CH	H4
				CH	O	H5

Fig. 8. Structure of heterocyclic [18] annulene

 

 

 

 

 

 

 

 

 

 

 

Fig. 9. Optimized structures of H1-H10 compounds at the level of B3LYP/6-31+G (d, p).

The effect of heterocyclic rings on the properties of [18] DBA shows the following results (Table 8). The effect of dipole moment showed that the H2 molecule has the highest polarity (2.590 D), and other molecules have the lowest polarity and are similar to annulene (M). Also, the highest hyperpolarizability was observed for H9 (361.699) due to the lower transfer energy, but, generally it is much lower than M and S molecules.

 

 

 

 

Table. 8.  Calculated values of stability energy (ES), bipolar moment (μ), polarizability (α), hyperpolarizability (β0) and anisotropy (IP) of H1-H10 compounds at B3LYP/6-31+G (d, p ) level.

IP	β0	α	μ	E
231.903	337.258	429.713	0.001	-1198.225	H1
245.269	335.808	424.672	2.590	-1198.229	H2
210.494	233.781	387.817	0.001	-1083.911	H3
192.378	78.478	357.521	0.004	-1083.899	H4
200.618	251.335	372.303	0.004	-1143.451	H5
175.153	120.328	329.475	0.003	-1143.439	H6
237.124	178.733	446.450	0.002	-2112.395	H7
215.586	298.569	409.895	0.001	-2112.385	H8
229.163	361.699	437.432	0.001	-1035.726	H9
194.683	80.087	380.991	0.001	-1035.702	H10

 

The results in table 9 show that the H9 molecule and H6 molecule have the lowest and highest energy levels in HOMO and LUMO, respectively. Hence, H9 has the highest wavelength at 559 nm. Of course, it is emphasized that the Eg values of H compounds are insignificant compared to S and M. Investigation of the DOS diagram for H1 to H10 compounds showed that they are similar to the annulene molecule (S6). Also, calculations were performed for M1-M10 compounds to determine the amount of bond length, frequency values, and bonding angle (S8). The results showed that the flatness of annulene is similar to the previous cases.

According to the values of chemical potential, chemical hardness and energy gap, it can be concluded that molecule A has the highest reactivity.

 

 

 

 

 

Table 9. Molecular orbitals energy and quantum descriptors (eV) H1-H10 compounds.

	EHOMO	ELUMO	Eg	η	μ	ω	∆Nmax	χ	EFL
H1	-5.98	-2.45	3.53	1.76	-4.21	5.04	2.39	4.21	-4.21
H2	-6.12	-2.83	3.29	1.64	-4.47	6.09	2.73	4.47	-4.47
H3	-4.89	-1.44	3.45	1.72	-3.16	2.90	1.84	3.16	-3.16
H4	-4.90	-0.88	4.02	2.01	-2.89	2.08	1.44	2.89	-2.89
H5	-5.49	-2.15	3.34	1.67	-3.82	4.37	2.29	3.82	-3.82
H6	-5.77	-1.60	4.17	2.08	-3.68	3.26	1.77	3.68	-3.68
H7	-5.49	-2.30	3.19	1.59	-3.89	4.76	2.45	3.89	-3.89
H8	-5.67	-1.71	3.96	1.98	-3.69	3.44	1.86	3.69	-3.69
H9	-5.17	-2.30	2.87	1.43	-3.73	2.42	2.61	3.73	-3.73
H10	-5.39	-1.91	3.48	1.74	-3.65	3.83	2.48	3.65	-3.65

 

Table 10. Wavelength (λ), oscillator power (f0), and participation percentage (% Con) for H1-H10 compounds.

% Con	λ(nm)	E(cm-1)∆
H-1->L (22%)	439.45	22755	H1
H->L (41%)	418.47	23896
H-2->L (71%)	379.88	26323
H >L+1 (22%)	443.34	22556	H2
H->L (79%)	432.60	23116
H-2->L (56%)	381.44	26216
H->L (49%)	450.34	22205	H3
H >L+1 (49%)	431.21	23190
H >L+3 (39%)	365.31	27374
H >L+1 (48%)	381.49	26212	H4
H->L (50%)	354.73	28190
H -1>L+3 (37%)	333.21	30011
H-1 >L+1 (47%)	461.76	21656	H5
H >L+1 (47%)	453.59	22046
H >L+1 (52%)	359.31	27831
H-1 >L+1 (38%)	360.67	27726	H6
H-1->L (41%)	340.80	29342
H-1>L+1 (31%)	330.48	30258
H->L (31%)	483.99	20661	H7
H-1->L (31%)	473.58	21115
H-1>L+2 (55%)	356.77	28028
H-1->L (42%)	380.74	26264	H8
H-1>L+1 (44%)	360.69	27724
H >L (14%)	347.32	28791
H-1>L+1 (50%)	556.35	17974	H9
H ->L (49%)	526.27	19001
H-3>L (46%)	390.77	25590
H>L (99%)	398.63	25085	H10
H-2>L (60%)	371.06	26949

 

Comparing the value of first hyperpolarizability (β0) which is an important parameter in nonlinear optical compounds shows that in single substitution and double substitution, the highest amount belongs to M4 (β0=19174.243) and S7 (β0=45547.212). Figure 10 shows the spectra of DOS and UV-Vis of M4 and S7 compounds.

 

Fig. 10. DOS and UV-Vis spectra of M4 and S7 compounds.

Conclusion

We have investigated the effect of functionalizing on the static first hyperpolarizability of dodecadehydrotribenzo132 [18] annulene ([18] DBA). The NBO analysis shows a meaningful charge transfer between functional groups and [18] DBA, leading to a considerable variation in the dipole moments and a notable decrease in the Eg value. The results showed that the [18] DBA has unique electrical and optical properties. Substitution on [18] DBA improved these properties. Comparing the stability energy values of M4 and S8 derivatives (each of which had the highest stability compared to the compounds in the same group), it was observed that the S8 compound is more stable than the M4, which confirms that S- derivatives are more stable than M- derivatives. Finally, the effect of substitution on the nonlinear optical properties of [18] DBA was Investigated, and it was found that the S7 compound (β0=45547.212) has the best optical properties.

Acknowledgment

The authors express their appreciation to the post-graduate office of Ayatollah Alozma Borujerdi University for the financial support of this work.

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