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ISSN : 1225-0112(Print)
ISSN : 2288-4505(Online)

Applied Chemistry for Engineering Vol.35 No.6 pp.565-571
DOI : https://doi.org/10.14478/ace.2024.1069

Experiments and Theoretical Prediction on the Photophysical Properties of Terphenyl- or Triphenylbenzene-Substituted Pyrenes

Kiho Lee, Changmin Lee, Hayoon Lee, Jongwook Park†

Integrated Engineering, Department of Chemical Engineering, Kyung Hee University, Yongin 17104, Korea

^† Corresponding Author: Kyung Hee University Integrated Engineering, Department of Chemical Engineering, Yongin 17104, Korea Tel: +82-31-201-3675 e-mail: jongpark@khu.ac.kr

Received October 2, 2024 ; Review October 10, 2024 ; Accepted October 10, 2024

Abstract

The structures of pyrene-based organic light-emitting diode materials were optimized, and their molecular orbitals, light absorption, and emission wavelength were predicted using density functional theory calculations with five different functionals: r²SCAN, B3LYP, M06-2X, cam-B3LYP, and wB97X. Additionally, the study examined trends in the results based on the different calculation methods and identified suitable functional-basis set combinations through comparison with experimental values. The four selected luminescent materials were substituted with bulky groups such as m-terphenyl and triphenylbenzene on the pyrene chromophore to prevent stacking of the pyrene, thereby suppressing the transition state caused by intermolecular interactions and preventing a reduction in luminescence efficiency. The qualitative trends from the calculations mostly matched the experimental results, with the B3LYP-D3/def2-QZVP method providing the closest agreement with experimental values, particularly in terms of absorption and emission wavelengths.

Key Words : Density functional theory , Excited state , HOMO-LUMO gap , Photoluminescence , Pyrene

Terphenyl 또는 Triphenylbenzene 기가 치환된 Pyrene 화합물의 발광특성에 관한 실험과 이론적 예측

이기호, 이창민, 이하윤, 박종욱†

경희대학교 융합공학전공 화학공학과

초록

파이렌 기반의 유기발광 다이오드 재료를 r²SCAN, B3LYP, M06-2X, cam-B3LYP, wB97X 다섯 가지 functionals들을 이용한 density functional theory 계산을 통해 최적화 구조, 분자궤도 함수, 흡수와 발광의 파장을 예측하였다. 또한, 계산 방법들에 따라 결과에 나타나는 변화의 경향을 알아보고, 실험값과 비교를 통해 적합한 functional-basis set 조합을 찾아내는 연구를 진행하였다. 선정된 4개의 발광재료들은 파이렌 발광체에 크기가 큰 치환기인 m-terphenyl, triphenylbenzene 기가 치환된 형태로 파이렌의 적층을 막음으로써 분자 간 인력에 의해 생기는 에너지 전이를 억제하고, 발광의 효율이 감소하는 것을 막고자 하였다. 계산에 의한 정성적 경향은 실험결과와 대부분 일치하였으며, 이 중 B3LYP-D3/def2-QZVP 방법의 결과들이 흡수와 발광파장 등에 대해서 실험결과에 가장 근접한 특성을 제시하였다.

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1. Introduction

Quantum mechanics-based electronic structure calculation methods have advanced to understand the physicochemical properties of materials. Among them, density functional theory (DFT), which uses the self-consistent field (SCF) method and the concept of electron density, has expanded its range of applications due to improvements in computational efficiency and the incorporation of additional theoretical approaches[1]. DFT calculations are performed by selecting a combination from hundreds of available functionals and basis sets. The levels of functionals and basis sets are categorized based on the type of additional functions and the number of parameters, which determine the accuracy and scalability of the calculations. The reason why so many functionals and basis sets have been proposed is that a universal combination capable of accurately calculating all molecules at the same level has yet to be discovered. Nevertheless, efforts to find the most appropriate functional or basis set for the desired calculations continue. Fundamentally, DFT is useful for determining optimized molecular structures through energy calculations and predicting the resulting properties of materials. It can also help classify molecular orbitals to understand electron levels and states. Although more sophisticated methods than DFT have been proposed, these methods are more accurate but require significantly more computational resources compared to DFT. DFT calculations are not only used for structure optimization but also for analyzing various material properties, such as thermodynamic analysis through vibrational frequency calculations, reaction energies, and excitation characteristics. In particular, excited states can be calculated using methods like time-dependent DFT (TDDFT)[2,3]. TDDFT calculations enable the analysis of the energy of wavelengths absorbed by light corresponding to specific singlet or triplet excitations, offering insights into oscillator strength, transition characteristics and spin-orbit coupling.

The development of blue-emitting materials with improved stability and efficiency has progressed through various experimental methods and electronic structure calculation techniques including DFT over the past few decades. In particular, DFT calculations offer the advantage of providing theoretically grounded development directions and reducing development costs. These calculations are helpful in predicting the physicochemical properties of materials and selecting suitable materials for initial applications when designing molecular structures for organic semiconductors or organic light-emitting diodes (OLEDs). Moreover, they assist in generating optimized devices and facilitating device analysis. In this study, we compared and analyzed the relationship between molecular structure changes and the optical properties of four luminescent materials, where bulky substituents such as m-terphenyl (TP) and triphenylbenzene (TPB) were substituted at the 1,6 and 4,9 positions of a pyrene core, using both experimental and computational methods. Additionally, in this process, various types of generalized gradient approximation (GGA) functionals were applied in an attempt to propose a functional-basis set combination that yields results closest to the experimental values.

2. Experiments and calculations

2.1. Materials

Figure 1 shows the four pyrene-based molecular structures used in this study: 1,6-di([1,1':3',1''-terphenyl]-5'-yl)pyrene (TP-(1,6)P-TP)[4], 4,9-Bis[1,1';3',1'']terphenyl-5'-yl-pyrene (TP-(4,9)P-TP)[5], 1,6-bis(5'-phenyl- [1,1':3',1''-terphenyl]-4-yl)pyrene (1,6-DTBP), and 4,9-bis(5'-phenyl-[1,1':3',1''- terphenyl]-4-yl)pyrene (4,9-DTBP)[6].

2.2. Density Functional Theory Calculations

The results of DFT calculations depend on the type of functional used and the selection of the basis set for the electronic wavefunction. The functionals used in this study fall into four main categories: (1) the composite electronic-structure method r²SCAN-3c (a meta-GGA r²SCAN functional with dispersion correction D4, geometrical counterpoise correction, and the meta-TZVPP basis set)[7]; (2) the dispersioncorrected global hybrid GGA density functional B3LYP-D3[8]; (3) the dispersion-corrected global hybrid meta-GGA functional M06-2X-D3(0) [9]; and (4) range-separated hybrid (RSH) GGA functionals wB97X-D3 [10] and cam-B3LYP[11]. In general, as the functionals listed above are applied in order, the chemical accuracy of the calculation results increases, but the complexity of the model also increases, which in turn requires more time and resources for the calculations. By applying various functionals and comparing the results in this way, we aim to determine whether this increase in accuracy also corresponds to or shows a similar trend with the accuracy in predicting photophysical properties.

The basis sets used were 6-311G(d,p) and def2-TZVP, which introduce three independent atomic functions per occupied valence orbital, and cc-pVQZ and def2-QZVPP, which introduce four functions per occupied orbital.

In this study, the 0-0 energy E_0-0 was calculated to predict photoluminescence[2]. As seen in Figure 2, the vertical absorption energy corresponding to the energy of the absorbed light's wavelength, is obtained from TDDFT calculations as show in equation (1), where R_S_0,opt represents the optimized geometry of the ground state, which can be obtained from standard DFT geometry optimization calculations.

E_{V A} = E_{S 1} (R_{S 0, o p t}) - E_{S 0} (R_{S 0, o p t})

(1)

On the other hand, R_S_1,opt is the optimized geometry in the lowest excited state S₁, which is obtained through TDDFT geometry optimization. If the emitted light's energy is produced without experiencing structural changes, then the energy for vertical fluorescent emission can be calculated using TDDFT.

E_{V F} = E_{S 1} (R_{S 1, o p t}) - E_{S 0} (R_{S 1, o p t})

(2)

The adiabatic excitation energy is the energy difference between the equilibrium structures of the ground state and the excited state, given by equation (3)

E_{A d} = E_{S 1} (R_{S 1, o p t}) - E_{S 0} (R_{S 0, o p t})

(3)

Meanwhile, the 0-0 energy is the energy difference between the ground and excited states, considering zero-point energy at the optimized geometries. This is expressed as equation (4), where the zero-point energy (ZPE) is the vibrational energy that remains even at absolute zero.

E_{0 - 0} = E_{A d} + Δ Z P E

(4)

ΔZPE is the difference in zero-point energies between the ground and excited states, as given by equation (5).

Δ Z P E = Z P E (R_{S 1, o p t}) - Z P E (R_{S 0, o p t})

(5)

3. Results and discussion

3.1. Experiments for molecular structures and photophysical properties

Pyrene has high luminescence efficiency and is easy to synthesize, making it a widely used chromophore in organic luminescent materials. However, due to its planar structure, pyrene chromophores easily form molecular stacking structures, which can lead to crystallization even in thin-film states. This facilitates the movement of excited electrons between molecules, reducing luminescence efficiency, making pyrene less suitable as a material for OLEDs. To address this issue, it is necessary to introduce substituents that can inhibit intermolecular interactions and maintain an appropriate distance between molecules. TP and TPB are well-known bulky side groups composed of phenyl rings, making them neutral. As such, they can effectively illustrate the characteristics of pyrene without any electron-donating or accepting effects based on the substitution position.

The ultraviolet–visible (UV-Vis) absorption of four pyrene-based materials showed a main absorption around 350-365 nm in the solution state and around 360~375 nm in the film state (Figure 3). This absorption is due to the π-π* transition of pyrene. When comparing the emission wavelengths of TP-substituted compounds at the 1,6 and 4,9 positions, i.e., TP-(1,6)P-TP and TP-(4,9)P-TP, the wavelengths in solution are 411 nm and 382 nm, respectively, showing a blue shift when substituted at the 4,9 positions (Table 1). Similarly, the emission wavelengths for TPB-substituted compounds 1,6-DTBP and 4,9-DTBP were 425 nm and 384 nm, following the same trend. This can be attributed to the dihedral angle of TP and TPB depending on the substitution position, as substitution at the 4,9 position not only induces a highly twisted structure but also helps prevent molecular packing. In the film state, the emission wavelengths of TP-(1,6)P-TP and 1,6-DTBP were similar, but the wavelengths of TP-(4,9)P-TP and 4,9-DTBP showed a significant difference, at 454 nm and 428 nm, respectively. This suggests that when bulky side groups are substituted at the 4,9 position, the effect of the torsion angle is pronounced, effectively suppressing intermolecular interactions.

3.2. Prediction of molecular geometry by calculations

According to the B3LYP-D3/def2-TZVP calculations, the dihedral angles between pyrene and the TP group in TP-(1,6)P-TP were 55.8° and 56.4°, whereas TP-(4,9)P-TP exhibited larger dihedral angles of 58.7° and 59.1° (Figure 4). Similarly, in 1,6-DTBP and 4,9-DTBP, the dihedral angles between pyrene and TPB in 4,9-DTBP were 58.9° and 58.8°, which were greater than the 54.7° and 54.8° observed in 1,6-DTBP. The difference in dihedral angles between TP-(1,6)P-TP and TP-(4,9)P-TP is not significant. The same trend is also observed in 1,6-DTBP and 4,9-DTBP. However, molecular calculations are predictions based on a single molecule in a vacuum, while the measured data reflect interactions influenced by the solvent polarity in solution samples or the proximity of surrounding molecules in film samples. Therefore, the effect of the dihedral angle is expected to differ. In fact, in the film state, where intermolecular forces are expected to be strongest, TP-(4,9)P-TP, which has a larger dihedral angle, exhibits emission in a blue-shifted region compared to TP-(1,6)P-TP. The same phenomenon is observed in 4,9-DTBP and 1,6-DTBP.

3.3. Molecular orbitals

The highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and the energy gap between these two values (HOMO-LUMO gap) significantly influence the properties of semiconductor materials, the design of OLED devices, and the determination of emission colors. As seen in Figure 5, the frontier molecular orbitals of the four molecules indicate that both HOMO and LUMO are formed on the pyrene moiety, while HOMO-1 and LUMO+1 are primarily located on the substituted phenyl groups. This suggests that the design for enhancing luminescence efficiency has been appropriately implemented. Additionally, the 1,6 positions of pyrene are shown as electron-rich lobes, while the 2,7 positions are electron- poor nodes. The 4,9 positions are also lobe positions on the pyrene molecule (Figure 5(e)).

Table 2 summarizes the calculated LUMO, HOMO, and the gap between these two values for various functional-basis set combinations. The r²SCAN-3c calculations yielded a HOMO that is more than 0.7 eV lower than the experimentally measured HOMO, resulting in a predicted gap that is approximately 0.5 eV lower. When comparing dispersion- corrected global hybrid functionals with different basis sets, it was found that both HOMO and LUMO shift together, ultimately resulting in similar gaps. This indicates that changes in the basis set have a minimal impact on the calculation results. In contrast, as the functionals become more sophisticated—specifically, with global hybrid functionals, global meta-GGA, and RSH GGA—the HOMO-LUMO gap increasingly diverges from the measured values. This suggests that as the structure of the functional becomes more complex, the energy of the original orbitals is excessively corrected.

3.4. Excitation characteristics

Table 3 summarizes the wavelengths of light absorbed by each molecule, the oscillator strength, and the characteristics and contributions of the transitions. A notable result is that the dispersion-corrected hybrid meta-GGA and RSH GGA calculations, which were expected to best describe the excited states, predicted very short absorption wavelengths compared to other calculation results. The B3LYP functional provided the closest prediction for the absorption wavelengths, followed by r²SCAN-3c. While the oscillator strengths were generally similar across all calculation methods, the results from r²SCAN-3c exhibited relatively greater variation. Of particular interest is that the oscillator strengths for TP-(1,6)P-TP and 1,6-DTBP were significantly high, suggesting that these compounds are expected to have the strongest luminescence intensity. By examining the transition characteristics and contributions, it can generally be predicted that the absorption is primarily driven by the HOMO→LUMO transition of the π electrons localized on the pyrene.

3.5. Prediction on photoluminescence

Table 4 summarizes the E_0-0 calculation results for comparison with the PL_max values in Table 1. Since the calculations in this study were performed for gas-phase molecules, it is more appropriate to compare the results with those from solution states rather than film states. In the case of r²SCAN-3c, the predictions for TP-(1,6)P-TP were very close to the actual measurements, while the absorption wavelengths for the other molecules were longer. In contrast, the B3LYP-D3 functional provided predicted wavelengths that were generally close to the experimental values, particularly with the def2-QZVPP basis set yielding more accurate predictions. On the other hand, cam-B3LYP and M06-2X exhibited significant discrepancies.

4. Conclusion

We compared the experimentally measured optical properties with the predicted results from electronic structure calculations for four compounds such as TP-(1,6)P-TP, TP-(4,9)P-TP, 1,6-DTBP, and 4,9-DTBP. The four compounds introduced multi-phenyl groups, TP and TBP, at different positions on pyrene, either at the 1,6- or 4,9-positions. Analysis of the predicted molecular structures indicated that the introduced TP and TPB form different dihedral angles depending on the substitution position of the pyrene, effectively suppressing the π-π stacking of the pyrene chromophore. This effect was particularly pronounced as the bulky substituents were introduced at the 4,9 positions. Based on calculations using several functionals, a comparison of the maximum photoluminescence of the molecules with the E_0-0 values revealed that r²SCAN-3c and B3LYP-D3/def2-QZVPP predicted results closest to the experimental measurements.

Acknowledgments

This work was partly supported by the GRRC program of Gyeonggi province [(GRRCKYUNGHEE2023-B01), Development of ultra-fine process materials based on the sub-nanometer class for the next-generation semiconductors]. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1A6A 1A03048004)

Figures

Figure 1.The molecular structures of the pyrene-core molecules. (a) TP-(1,6)P-TP, (b) TP-(4,9)P-TP, (c) 1,6-DTBP, and (d) 4,9-DTBP.

Figure 2.A Franck–Condon principle energy diagram of ground and excited states for singlet transition.

Figure 3.UV-Vis and PL spectra (a) solution, (b) film state.

Figure 4.Dihedral angles of the molecules geometrically optimized by B3LYP-D3/def2-TZVP DFT calculations. (a) TP-1,6-P-TP, (b) TP-4,9- P-TP, (c) 1,6-DTBP, and (d) 4,9-DTBP.

Figure 5.Molecular orbitals (a) TP-(1,6)P-TP, (b) TP-(4,9)P-TP, (c) 1,6-DTBP, (d) 4,9-DTBP, and (e) Pyrene.

Tables

Table 1.Experimentally Measured Wavelengths for Absorption and PL_max of the Pyrene Core Molecules

^aConcentration: 1 × 10^-5 M, ^bEvaported film on glass (thickness: 50 nm), ^cChloroform solution, ^dTetrahydrofuran (THF) solution

Materials	Solutiona	Filmb
TP-(1,6)P-TPc	365	411	372	460
TP-(4,9)P-TPd	349	382, 403	357	454
1,6-DTBPd	365	425	373	461
4,9-DTBPd	349	384, 405	358	428

Table 2.HOMO, LUMO Energy Levels, and Their Gaps for the Molecules in Experiments and Calculations

Molecule	Method	LUMO (eV)	HOMO (eV)	H-L gap (eV)
TP-(1,6)P-TP	Experiment	-2.900	-5.990	3.090
r2SCAN-3c	-2.439	-5.036	2.596
B3LYP-D3/6-311G(d,p)	-1.791	-5.350	3.559
B3LYP-D3/cc-pVQZ	-1.832	-5.389	3.558
B3LYP-D3/def2-QZVPP	-1.848	-5.403	3.555
M06-2X-D3(0)/def2-TZVP	-1.170	-6.602	5.432
wB97X-D3/def2-TZVP	-0.107	-7.372	7.265

TP-(4,9)P-TP	Experiment	-2.580	-5.810	3.230
r2SCAN-3c	-2.378	-5.101	2.723
B3LYP-D3/6-311G(d,p)	-1.717	-5.419	3.701
B3LYP-D3/cc-pVQZ	-1.762	-5.462	3.700
B3LYP-D3/def2-QZVPP	-1.790	-5.484	3.694
M06-2X-D3(0)/def2-TZVP	-1.079	-6.686	5.608
wB97X-D3/def2-TZVP	-0.005	-7.463	7.458

1,6-DTBP	Experiment	-2.760	-5.700	2.940
r2SCAN-3c	-2.458	-4.988	2.530
B3LYP-D3/6-311G(d,p)	-1.819	-5.307	3.488
B3LYP-D3/cc-pVQZ	-1.867	-5.352	3.485
B3LYP-D3/def2-QZVPP	-1.886	-5.366	3.480
M06-2X-D3(0)/def2-TZVP	-1.196	-6.552	5.356
wB97X-D3/def2-TZVP	-0.118	-7.337	7.219

4,9-DTBP	Experiment	-2.650	-5.780	3.130
r2SCAN-3c	-2.384	-5.072	2.688
B3LYP-D3/6-311G(d,p)	-1.729	-5.394	3.665
B3LYP-D3/cc-pVQZ	-1.782	-5.442	3.660
B3LYP-D3/def2-QZVPP	-1.802	-5.456	3.654
M06-2X-D3(0)/def2-TZVP	-1.099	-6.656	5.558
wB97X-D3/def2-TZVP	-0.015	-7.439	7.424

Table 3.Calculation Results for the Excitations of the Molecules: Absorption Wavelength, Oscillator Strength, the Characteristic of Transition, and Contribution

Molecule	Method	Absorption (nm)	Oscillator strength	Characteristic of transition	Contribution (%)
TP-(1,6)P-TP	r2SCAN-3c	386.9	0.620	H→L	55.7
373.5	0.236	H→L+2	58.8

B3LYP-D3/6-311G(d,p)	357.6	0.985	H→L	84.5

B3LYP-D3/ def2-QZVPP	360.1	0.962	H→L	84.4

M06-2X-D3(0)/def2-TZVP	292.3	1.024	H→L	75.2
230.3	0.418	H-2→L+2	24.6

cam-B3LYP/def2-TZVP	314.7	0.851	H→L	72.6
310.4	0.205	H-3→L, H→L+4	19.4, 24.2

TP-(4,9)P-TP	r2SCAN-3c	374.7	0.146	H→L+1	70.8

B3LYP-D3/6-311G(d,p)	338.9	0.335	H→L, H→L+1	47.5, 23.1
336.4	0.129	H-4→L, H→L	23.7, 30.8

B3LYP-D3/def2-QZVPP	341.9	0.374	H→L, H→L+1	53.4, 22.7

M06-2X-D3(0)/def2-TZVP	282.0	0.497	H→L	70.4
230.6	0.410	H-1→L+2	20.9

cam-B3LYP/def2-TZVP	300.5	0.497	H→L	82.4
255.7	0.131	H→L+1	24.3

1,6-DTBP	r2SCAN-3c	410.3	1.144	H→L	70.5

B3LYP-D3/6-311G(d,p)	371.2	1.484	H→L	86.5

B3LYP-D3/def2-QZVPP	374.1	1.476	H→L	87.0

M06-2X-D3(0)/def2-TZVP	295.7	1.434	H→L	74.0
235.2	0.521	H-1→L+1	21.7

cam-B3LYP/def2-TZVP	319.7	1.461	H→L	84.7

4,9-DTBP	r2SCAN-3c	386.7	0.399	H→L, H→L+2	45.0, 35.2

B3LYP-D3/6-311G(d,p)	344.4	0.734	H→L	77.7

B3LYP-D3/ def2-QZVPP	347.4	0.735	H→L	78.4

M06-2X-D3(0)/def2-TZVP	283.1	0.695	H→L	68.4
235.8	0.876	H-1→L+1	26.4

cam-B3LYP/def2-TZVP	301.9	0.705	H→L	82.0

Table 4.Calculated Energies for Vertical Absorption, Vertical Fluorescence, Adiabatic Transition and 0-0 Transition of the Pyrene-Core Molecules in the Research

Molecule	Functional/Basis set	EVA (eV)	EVF (eV)	EAd (eV)	E0-0 (eV, nm)
TP-(1,6)P-TP	r2SCAN-3c	3.205	2.729	2.996	2.983	415.8
B3LYP-D3/def2-TZVP	3.451	3.012	3.213	3.208	386.5
B3LYP-D3/def2-QZVP	3.443	3.010	3.205	3.176	390.4
cam-B3LYP/def2-TZVP	3.940	3.311	3.627	3.621	342.4
M06-2X-D3(0)/def2-TZVP	4.241	3.999	4.312	4.369	283.8

TP-(4,9)P-TP	TP-(1,6)P-TP	3.309	2.767	3.053	3.038	408.1
B3LYP-D3/def2-TZVP	3.634	3.239	3.452	3.438	360.7
B3LYP-D3/def2-QZVP	3.627	3.224	3.438	3.425	362.0
cam-B3LYP/def2-TZVP	4.031	3.667	3.908	3.897	318.2
M06-2X-D3(0)/def2-TZVP	4.396	3.741	4.099	4.148	298.9

1,6-DTBP	TP-(1,6)P-TP	3.022	2.620	2.798	2.801	442.7
TP-(4,9)P-TP	3.324	2.764	3.018	3.071	403.8
B3LYP-D3/def2-QZVP	3.314	2.761	3.012	3.013	411.6
cam-B3LYP/def2-TZVP	3.878	3.150	3.512	3.513	353.0
M06-2X-D3(0)/def2-TZVP	4.193	3.644	3.645	3.645	340.2

4,9-DTBP	TP-(1,6)P-TP	3.195	2.660	2.928	2.925	423.9
TP-(4,9)P-TP	3.585	3.006	3.305	3.304	375.3
B3LYP-D3/def2-QZVP	3.569	3.015	3.302	3.293	376.6
cam-B3LYP/def2-TZVP	4.028	3.533	3.858	3.853	321.9
M06-2X-D3(0)/def2-TZVP	4.380	4.002	4.002	4.002	309.9

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Materials	Solutiona		Filmb

	λabs (nm)	PLmax (nm)	λabs (nm)	PLmax (nm)

TP-(1,6)P-TPc	365	411	372	460
TP-(4,9)P-TPd	349	382, 403	357	454
1,6-DTBPd	365	425	373	461
4,9-DTBPd	349	384, 405	358	428