Comprehensive evaluation of the effect of various exchange correlation functionals on the optical properties of oligothiophenes

Journal Pre-proofs Comprehensive Evaluation of the Effect of Various Exchange Correlation Functionals on the Optical Properties of Oligothiophenes Vikramaditya Talapunur, Mukka Saisudhakar, Kanakamma Sumithra PII: DOI: Reference:

S2210-271X(19)30363-9 https://doi.org/10.1016/j.comptc.2019.112667 COMPTC 112667

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Please cite this article as: V. Talapunur, M. Saisudhakar, K. Sumithra, Comprehensive Evaluation of the Effect of Various Exchange Correlation Functionals on the Optical Properties of Oligothiophenes, Computational & Theoretical Chemistry (2019), doi: https://doi.org/10.1016/j.comptc.2019.112667

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Comprehensive Evaluation of the Effect of Various Exchange Correlation Functionals on the Optical Properties of Oligothiophenes Vikramaditya Talapunur1, Mukka Saisudhakar and Kanakamma Sumithra Correspondence to: Kanakamma Sumithra (E-mail: [email protected]) Department of Chemistry, Birla Institute of Technology and Science (BITS) Pilani, Hyderabad Campus, Hyderabad 500078, Telangana, India. Computational Molecular Engineering lab, Department of Chemical Engineering, National Taiwan University, Taipei, 10617, Taiwan.

Abstract Time-dependent density functional theory (TD-DFT) calculations are performed to systematically investigate the absorption and emission properties of α-oligothiophenes taking into account of various functionals, basis sets and bulk solvent effects. The effects of different functionals on the optical properties are investigated employing global and meta hybrid functionals B3LYP, M06 and also with range separated hybrid functionals like ωB97XD and CAM-B3LYP. The results are further assessed to test their validity against the available experimental data. The bulk solvent effects are introduced by the linear response (LR) and the state specific (SS) models in the framework of the polarizable continuum model (PCM).

Pople type of basis sets has been

employed and the role of inclusion of polarized and diffused functions in the basis sets in determining the optical properties is investigated. The long-range correction scheme in CAMB3LYP is found to produce accurate results for the excitation energies very much in agreement with the experimental data. Introduction Theoretical investigations of absorption and emission spectra by means of quantum mechanical calculations have become a very standard approach, widely used to help the assignment of the experimental spectra and to get insights of the underlying optical and electronic properties of technologically important molecules. The advantages of Density functional theory (DFT) and its time dependent formalism are combined in time- dependent DFT (TD-DFT) [1], [2], [3] to make it well suited for accurate description of structures, energies and electronic excitations over the past few years [4-9]. It is originally developed by Runge and Gross1 and can be easily applied to time-dependent quantum mechanical scenarios by establishing a relation between the time-dependent densities with the potentials. The accuracy of this theory is limited 1

because of the adiabatic approximation and requires the appropriate exchange correlation functional (XCF). Even though TD-DFT predicts molecular excited states correctly, long-range charge transfer effects are not accurately defined [10-13]. It is also known [10-15] that the use of conventional XCF drastically underestimates the charge transfer excitation energies and yields incorrect asymptotic potential energy surfaces. The selection of an appropriate XCF for modeling excited state properties has been a subject of several bench mark studies performed on different systems over the past few years [13-16]. It is now well established that the conventional functionals fail for long-range charge transfer states and also for the accurate prediction for optically excited states [17-23]. TD-DFT is already established as the most widely used, effective approach to investigate the optical spectra and excited state properties of organic molecules in gas phase, solution and also in complex environments [24-34]. Recent investigation by Wong et al.,[19] focus on the absorption and fluorescence properties of oligothiophene biomarkers employing long-range corrected TD-DFT. They have emphasized the importance of long-range corrected methods which significantly improve the description of the excitation energies, fluorescence energies, oscillator strength, excited state dipole moments etc. compared to the conventional hybrid functional with a constant fraction of Hartree-Fock exchange. The band shapes corresponding to both absorption and emission spectra of a set of conjugated molecules have been simulated with TD-DFT using various functionals and compared with experiment by Azzam and coworkers [20] concluding that the accuracy is significantly system-dependent. Recent interests in the field of TD-DFT excited states also focus on the effect of solvents using various approaches in the polarizable continuum model [33-35]. In a recent study, Pedone [33] have studied the role of solvent on charge transfer in 7-Aminocoumarin dyes using the state specific model in the PCM approach where the importance of CAM-B3LYP XCF in accurately predicting the excitation energy is highlighted. Using a corrected linear response approach, Jacquemin et al.,[31] have investigated medium induced structural changes, for example, the excited state geometries, of several chromophore representatives of key dye families. Another recent investigation [35] deals with a comparative study between state specific and linear response formalisms in calculating the vertical transition energies in solution, employing coupled cluster methods. It is evident from this study that the LR formalism can be used to study the solvent effect and to evaluate the transition probabilities while the SS approach is better for describing specific states and excited state potential energy surfaces 2

of solvated systems. Through all the above studies, it is established that the performance of the long range corrected functionals, especially CAM-B3LYP is superior than the other DFT varieties. Of recent, there are a lot of interest for tuning of the parameters for range separated functionals [36-38].

These studies suggest that tuned long-range corrected functionals/range separated

functionals further improve their performance in predicting accurate absorption, fluorescence, singlet-triplet energy gaps and frontier molecular orbital energies. However in the current study, default parameters are used. There is also a recent interesting attempt to extrapolate the oligomeric results for larger polymeric systems employing simple models [39]. Their results show that among the functionals used, M06-2X , reproduces the experimental results for oligothiophenes in choloroform, closely. However, any extrapolation to polymeric system with trivial models should be taken with care, for predicting the properties of excited states of large polymers. In the current study, we investigate the absorption and emission of α-oligothiophenes employing TDDFT using various functionals together with the solvent effect on the electronic spectra, estimated with polarized continuum model. Thiophene based compounds are widely used to extend the π-conjugation in dye sensitized solar cells, OLEDs etc [40,41] because of their effective conjugation through the greater tendency to be coplanar with other thiophene groups, compared to benzene and methylene bearing groups [42,43]. Although the effect of various functionals in determining the properties of different systems are studied in the literature [17,19,31,42], the combined effect of functionals, both hybrid and long-range corrected, together with basis sets and solvent formalism, in determining the optical properties of π-conjugated systems is rarely discussed and therefore, a systematic computational work is necessary. A proper choice of exchange correlation functional, solvent formalism and basis set determine the accuracy in the calculation of optical properties of π-conjugated compounds. Many of the computational studies done so far [17,19,31,35,42,44] concentrate on one of these aspects, whereas the accuracy can depend on various parameters. In this article, we have considered all these factors, calculated absorption and emission properties of thiophene oligomers and compared the results with the existing experimental results [45]. The main aim of the current work is to guide the reader to choose a proper TD-DFT formalism in order to calculate accurate optical properties especially for molecules with extended π-conjugation which are widely used in the field of organic electronics. We investigate the absorption and emission of oligothiophenes of chain 3

length (2-7) with different functionals and basis sets. The most popular hybrid functionals B3LYP, M06 and range-separated hybrid functionals (RSH),

CAM-B3LYP and ωB97XD

employing different basis sets are considered in order to assess the effect of functionals together with the inclusion of polarization and diffusion functions in basis sets, in predicting the absorption and emission properties. Optical spectra of industrially meaningful compounds are often measured in condensed phase thus accurately including environmental effects. Therefore, to better understand the solvent effects on the photophysical properties, the electronic spectra are estimated with the polarizable continuum model [46-48] in 1,4-Dioxane, in which the experimental results are available.

The current study validates the importance of long-range, distance-dependent

contribution of exchange in TD-DFT in accurate description of the optical properties of oligothiophenes. Computational Methodology All quantum mechanical calculations are performed with Gaussian 09 [49] employing various functionals namely, global hybrid functional B3LYP [50,51], meta hybrid functional M06 [52], range-separated hybrid functionals ωB97XD [53] and CAM-B3LYP [54] with basis sets 6-31G(d), 6-31G(d,p) and 6-31+G(d,p). (In few cases Hartree-Fock methods employing correlation consistent basis sets have been used for comparison). Oligothiophenes of chain length (2-7) are considered and the ground state geometry optimizations are carried out employing DFT. The absorption and emission studies are carried out employing TD-DFT, using the above mentioned functionals and basis sets. It is clearly noted in the literature that by using hybrid exchange-correlation functionals for the systems containing extended π-conjugation can result in large errors in the charge-transfer (CT) excitation energies. This is because of the incorrect description of the distance coordinate matrix due to the non-local nature of the interactions involved in the CT state [55,56]. We have used the well-known polarizable continuum model [46-48] to investigate the bulk solvent effects. It allows one to consider the solvent effect by considering the solute inside a cavity that is surrounded by structureless media that has the macroscopic characteristics of the solvent. Two formalisms available to compute transition energies within the PCM framework are 4

State-Specific [57,58] and Linear-Response [46] approaches.

The former provides a more

complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient and transition properties are well defined. Absorption studies (TDD-FT) are evaluated from the optimized ground state geometries of DFT, Fluorescence studies are calculated from the corresponding optimized first excited geometries employing TDDFT. For strong time-dependent potentials, the full Kohn-Sham density must be obtained as a function of position and time and since the time-dependent potential is weak in an optical absorption, one can use the LR theory to obtain the excitation energies [57]. Thus the LR-TD-DFT has become a suitable method for the computation of excited state energies and properties of large molecular systems [58]. The absorption and emission energies have been computed with both LR and SS-PCM in our study. Proper choice of basis set is also essential in order to well approximate the excited state energy by optimizing the Lagrangian on the corresponding subspace [59]. In this paper, we have used split valence basis sets which are better in describing the changes associated with molecular bond formation. Results and Discussion Recent theoretical studies are focusing on calculating 0-0 transition energies rather than calculating wavelength of maximum absorption and emission (λmax) employing vertical approximation methods [31]. The λmax values of absorption and emission of various compounds are widely available in literature, but accurate 0-0 transition energies are quite uncommon. For example, experimental 0-0 transition wavelength of oligothiophene of chain length of three monomeric units is found to be 720 nm [60], 788 nm and predicted even more up to 826nm [45]. Therefore, depending upon the experimental procedures 0-0 transition energies varies, which makes difficult to compare the obtained theoretical results. Hence vertical approximation methods although not accurate, are still a better approximation to evaluate λmax values of absorption and emission. Since the functionals discussed here are comprised of many empirical fitted parameters, there is no guarantee that the performance would be improved with increase in basis sets levels. The main idea of the current work is to evaluate the accuracy of various functionals with respect to various basis sets against the experimental values and also to understand their in determining the optical properties. 5

Absorption and Emission studies The percentage deviation of absorption and emission energies of oligothiophenes of chain length (2-7) (with respect to experimental values) employing various functionals and basis sets with both SS and LR approaches in PCM solvent formalism are shown in Fig. 1 and 2 respectively. From the figures it is clear that Hybrid functional B3LYP and Meta hybrid functional M06 yielded poor results in comparison with range-separated hybrid (RSH) functionals with both SS and LR PCM solvent formalisms. With increase in chain length hybrid functional B3LYP has shown an increase in deviation of absorption and emission energies. The lowest deviation is found to be 2.93% for dimer and highest for 7-mer with 24.11% in state-specific approach.

Fig.1. The percentage deviation of absorption energies with respect to experimental energies employing various functionals and basis sets.

6

Fig. 2. The percentage deviation of emission energies with respect to experimental energies employing various functionals and basis sets. 6-31G(d) is one of the most widely used basis set in the literature. Inclusion of higher angular momentum functions in basis sets enables the molecular density to distort from the usual spherical symmetry of the atoms at the levels of DFT and HF and also serves in describing the electron correlation cusp for correlated calculations [60]. The percentage deviation of absorption is found to be in the range of 1.95-20.57%, 4.63-23.76% with SS and LR approaches. Deviation in emission energies is found to be in the range -0.87-14.41% (SS-approach) and 3.5-19.82% (LR approach). Inclusion of additional “p” functions produced absolutely no effect on the absorption and emission properties employing 6-31G(d,p) basis sets. Absorption and emission values remained the same as that of 6-31G(d) basis sets. (λmax values are given in additional information). Employing 6-31+G(d,p) basis set with B3LYP functional with diffused functions resulted in varied results with lower and higher chain lengths. For example, with dimer, the deviation in absorption and emission energies is found to be more in comparison with 6-31G(d) basis sets. Deviation in 7

absorption energies with 6-31G(d) and 6-31+G(d,p) for a dimer are 1.95%, 6.1% respectively with SS approach and 4.63%, 8.78% with LR approach. With higher chain lengths the deviation observed is found to be not as appreciable as in the case of lower chain lengths. Deviation in absorption energies for 7-mer is found to be 14.41%, 16.67% with SS approach and 19.82%, 21.21% with LR approach with 6-31G(d) and 6-31+G(d,p) respectively. Emission energies are found to follow a similar trend as that of absorption. Meta hybrid functional M06 exhibited a similar trend with respect to both absorption and emission in comparison with global hybrid functional B3LYP. But from Fig. 1 and 2 we conclude that, M06 functional predicts absorption and emission energies better than with B3LYP, with lesser magnitude of deviation.

RSH functionals predicted absorption and emission values of

oligothiophenes better in comparison with hybrid functionals which is evident from Fig.1 and 2. ωB97XD functional although predicts optical properties better than hybrid functionals, we observe that it constantly underestimates absorption energies with various basis sets. With 6-31G(d) and 6-31+G(d,p), the maximum deviation is found to be for 6-mer around -15.79%, -12.98% (SS and LR approaches) and -15.09% and -12.28% (SS and LR approaches) respectively. In contrast to absorption energies, this underestimation is not observed in emission in most of the cases with the ωB97XD functional employing various basis sets and it is evident from Fig. 2. We do not observe any specific trend of increase or decrease in accuracies with respect to increase in chain lengths or increasing the hierarchy of basis sets. Emission energies of 6-31+G(d,p) basis set with SS approach and 6-31G (d) basis set with LR approach employing ωB97XD functional are found to predict emission energies closer to the experiments. Among all the functionals tested, CAM-B3LYP results are found to be closer to the experimental values. We observe a slight underestimation in the absorption and emission energies in most of the cases with SS approach employing 6-31G(d) basis sets. 6-31+G(d,p) basis set is found to give most accurate results with respect to absorption and emission energies in SS approach employing CAMB3LYP. Absorption and emission energies deviations are found to be in the range of -1.46% to 1.77%, 0.45 to 2.05% respectively. These results are presented in Table 1 and Table 2. With LR approach 6-31(d) basis set is found to give better results in comparison with the other basis sets. The deviations in absorption and emission energies with CAM-B3LYP employing 6-31G(d) basis set is found to be in the range of -0.7% -3.66% and 0.0% - 3.90% respectively. 8

Chain length

B3LYP

M06

wB97XD

CAMB3LYP

Exp

2

3.94410

3.91975

4.55197

4.27609

4.19142

3

3.20707

3.22335

3.98119

3.60795

3.58757

4

2.79736

2.84753

3.70262

3.2732

3.23980

5

2.53493

2.61317

3.46995

3.06763

3.04556

6

2.36059

2.45174

3.35979

2.93303

2.91284

7

2.22807

2.33886

3.2732

2.84116

2.87982

Table 1. Absorption energy values for various chain lengths with 6-31+g(d,p) basis set employing state specific approach in electron volts (eV). Chain length

B3LYP

M06

wB97XD

CAMB3LYP

Exp

2

3.3687

3.32461

3.51801

3.48901

3.50829

3

2.76688

2.74298

2.97424

2.92627

2.98122

4

2.41905

2.41905

2.68499

2.6294

2.6569

5

2.18589

2.2087

2.51485

2.44701

2.47082

6

2.01908

2.06169

2.41445

2.33456

2.36499

7

1.89836

1.95988

2.36059

2.26381

2.26786

Table 2. Emission with 6-31+g(d,p) basis set employing state specific approach in electron volts (eV). The raw data of computed λmax values (absorption and emission) together with the experimental values are plotted in Fig. 3 and 4 respectively which gives a clear idea as to how the values differ with the use of each functional and basis set.

9

Fig. 3. Absorption λmax of Oligothiophenes of chain length (2-7), with SS and LR approaches with various functionals and basis sets.

10

Fig. 4. Emission λmax of Oligothiophenes of chain length (2-7), with SS and LR approaches with various functionals and basis sets. It is observed that the RSH functionals show a marked improvement over the Global and Meta hybrid functionals. Better calculation of absorption properties allows us to look at the importance of the Hatree-Fock exchange contribution for the long-range region and the DFT counterpart for the short-range region for RSH functionals. From the calculated values of absorption and emission it is clear that no definite trend of increase or decrease in accuracy is followed with increasing basis sets level which is the major drawback of Pople type of basis sets. This can be analyzed by the fact that, different primitive GTOs are employed in the basis sets which are lacking sufficient higher angular momentum basis functions. So, we have calculated the absorption and emission energies employing a very large basis set 6-31+G(3df,3pd) using CAM-B3LYP, the best functional among the functionals studied in the current work, for a dimer.

11

Fig. 5. The percentage deviation of absorption and emission energies of dimer employing CAMB3LYP functional with various basis sets. From Fig. 5, it is clear that no specific trend of increase or decrease in accuracy is obtained even with very large basis Pople basis sets. A similar study of absorption and emission are carried out employing Hartree-Fock method employing correlation- consistent polarized (ccp) valence double zeta (VDZ) and valence triple zeta (VTZ) basis sets shown in Table 1. Table 3. The absorption and emission energies of dimer and trimer oligothiophenes with ccp basis sets with HF method along with the experimental values. Chain

CCP-

CCP-

Experimental

length

VDZ

VTZ

(eV)

(eV)

(eV)

12

2 (A) 3 (A) 2 (E) 3 (E)

4.65

4.60

(4.55)

(4.50)

4.05

4.02

(3.95)

(3.93)

3.51

3.41

(3.35)

(3.27)

2.97

2.90

(2.81)

(2.74)

4.10 3.51 3.43 2.92

(A) and (E) indicates absorption and emission. Values outside the parenthesis indicates SS approach and inside the parenthesis indicates LR approach. We observe from Table 3 that there is a trend of increase in accuracy with the increase in the level of basis sets employing HF method. But CAM-B3LYP results with Pople basis sets are very much closer to the experimental values, making DFT formalism attractive. Unlike correlation consistent basis sets which converges towards the basis set limit by increasing the level of basis set in a systematic fashion, the same do not hold true with Pople basis sets with DFT functionals. Exchange-correlation functionals used in DFT are developed adopting two strategies, either the functional should be self-interaction free, density should become constant in the case of uniform electron gas, and few other constrains [61] or by fitting the parameters to reproduce the experimental results. Empirical functionals which are tested here contain a large number of parameters which are fitted to a training set to produce accurate experimental data and they give accurate results for the systems and properties contained in the training set [62]. The same is evident from examining the optical properties with various basis sets. When we increase the hierarchy of basis sets, we do not observe any specific trend being followed w.r.t various exchangecorrelation functionals, unlike non-empirical functionals which contain few or no fitted parameters which usually exhibit a trend. The inaccuracies in DFT formalisms arise basically due to lack of functional which exactly gives accurate exchange correlation energy and also due to insufficient basis set. A proper combination of functional and basis set which probably cancels out the error arising due to each other would give values closer to the experiments. Among the functionals 13

tested, CAM-B3LYP is found to give values closer to the experiments with various basis sets and solvent formalisms chosen. Conclusions The role of functional, solvent formalisms and basis set effects in determining optical properties is investigated for oligothiophenes. Among the various functionals tested, range separated hybrid functional, CAM-B3LYP gave the results closer to the experiment when compared to the Global and Meta hybrid functionals. The accuracy of hybrid and meta-hybrid functionals decreased with increase in chain length and addition of diffusion functions whereas the inclusion of “d” functions in the basis set improved results. On the other hand inclusion of “p” functions in the basis set with all the functionals and solvent formalisms had no effect in varying the optical properties. Among the four functionals studied, the long-range corrected CAM-B3LYP produced accurate results and ωB97XD functional consistently underestimated the wavelength maxima values. State specific approach in combination with CAM-B3LYP functional employing 631+G(d,p) provided better results, which can be attributed to proper description of short and long range effects in the functional, proper description of molecular orbitals through the basis set and a better description of solute-solvent effects. The most significant aspect which is often not highlighted in literature is the fact that the accuracy of DFT methodologies with proper choice of basis set can also be due to the cancellation of errors. DFT methodologies employ empirical parameters based on comparison with experimental data using a specified basis set where DFT parameters absorbing the errors arise due to the incompleteness of basis sets [62]. The important aspect which we can notice is that with the increase in the level of basis set with various functionals we do not observe any regular trend of increase or decrease in accuracies of the optical properties. Hence it need not be assumed that employing a very large basis set assures the accuracy in DFT formalism with functionals fitted with various empirical parameters. Thus we have shown how the accuracy of different functionals varies depending upon the basis set chosen and solvent formalism employed in determining the optical absorption and emission of an important π-conjugated system. Range separated hybrid functionals out-perform global hybrid functionals. The effect of tuning of the parameters may further improve the performance of these functionals in predicting accurate absorption and emission properties. 14

Acknowledgments K. Sumithra gratefully acknowledges the Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi for financial support in the form of a project grant (01 (2748/13/EMR-II). M. Saisudhakar acknowledges support from Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi for funding in the form of fellowship. T. Vikramaditya thanks Ministry of Science and Technology (MOST 104-2221-E002-186-MY3 and 106-2811-E-002-020) and National Taiwan University (NTU -CDP106L7827) for financial support. Keywords: Oligothiophenes, TD-DFT, Basis sets, Functionals, Polarized Continuum Model, Linear response approach, State-specific approach

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Graphical abstract

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Highlights   

Optical properties of oligothiophenes. The role of long-range functionals in determining the optical properties of oligothiophenes. Emphasizes the importance of using a proper functional in the TD-DFT formalism.

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