In the Quest for a Stable Triplet State in Small Polyaromatic Hydrocarbons : an In-Silico Tool for Rational Design and Prediction

doi.org/10.26434/chemrxiv.8143274.v1

In the Quest for a Stable Triplet State in Small Polyaromatic Hydrocarbons : An In-Silico Tool for Rational Design and Prediction

Madhumita Rano, Sumanta K Ghosh, Debashree Ghosh

Submitted date: 17/05/2019 • Posted date: 17/05/2019 Licence: CC BY-NC-ND 4.0 Citation information: Rano, Madhumita; Ghosh, Sumanta K; Ghosh, Debashree (2019): In the Quest for a Stable Triplet State in Small Polyaromatic Hydrocarbons : An In-Silico Tool for Rational Design and Prediction. ChemRxiv. Preprint.

Combining the roles of spin frustration and geometry of odd and even numbered rings in polyaromatic hydrocarbons (PAHs), we design small molecules that show exceedingly small singlet-triplet gaps and stable triplet ground states. Furthermore, a computationally efficient protocol with a model spin Hamiltonian is shown to be capable of qualitative agreement with respect to high level multireference calculations and therefore, can be used for fast molecular discovery and screening.

File list (1) chem_arXiv.pdf (2.17 MiB) view on ChemRxiv download file In the Quest for a Stable Triplet State in Small Polyaromatic Hydrocarbons : An in-silico tool for Rational Design and Prediction

Madhumita Rano, Sumanta K Ghosh, and Debashree Ghosh∗

School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032

E-mail: [email protected] Phone: (033) 2473 4971 (Ext 1103)

Abstract

Combining the roles of spin frustration and geometry of odd and even numbered

rings in polyaromatic hydrocarbons (PAHs), we design small molecules that show ex-

ceedingly small singlet-triplet gaps and stable triplet ground states. Furthermore, a

computationally ecient protocol with a model spin Hamiltonian is shown to be capa-

ble of qualitative agreement with respect to high level multireference calculations and

therefore, can be used for fast molecular discovery and screening.

Introduction

Oligoacenes,17 have formed the basis of intense research for a few decades due to their tunable optical gaps. Oligoacenes, up to undecacene,810 have been synthesized. Due to

1 their fascinating properties, the theoretical aspects related to their π-bonding topology have been studied extensively,2,4,5,1113 and their possible usage in singlet ssion phenomenon1418 have been investigated. From a theoretical perspective, the electronic structure of oligoacenes have been the subject of intense debate. Stable triplet states in longer polyacenes have been predicted.2 Multi-reference calculations,11,19,20 however, did not observe triplet ground states, which have been corroborated by experiment.8 However, the exact nature of decay of the singlet triplet (ST) gap was extremely relevant to the synthesis of materials with functionalities important for organic electronics.2127 Theoretical studies till recently showed that the optical gap decreases monotonically for long polyacenes.28,29 However, a recent study reports a non- monotonicity of the decay in the optical gap with the size of polyacenes.30 Therefore, our understanding of the electronic structure of polyacenes is incomplete to this day. Azulene, consisting of a fused ve and seven membered ring, have been much less dis- cussed.31 It is known that azulene has a signicantly lower ST gap as compared to its acene isomer, naphthalene. Since the ve and seven membered rings do not satisfy the (4n+2) rule, the singlet state of azulene is signicantly less stable, thereby reducing the ST gap. In fact, the dipole moment of the singlet state of azulene points towards a charge (or electron) trans- fer from the seven to ve membered rings, to attain a stable electronic situation. Repeated fused azulene moieties show low ST gaps and a crossover of the triplet state as the ground state (as opposed to singlet state).32 This observation is fundamentally dierent from that of the acenes and was also predicted from UB3LYP level of theory.33 In our work, we will show that UB3LYP method gives rise to certain artifacts which might lead to such conclusions and multireference calculations can change the quantitative ndings quite signicantly. We have designed a class of fused acene-azulenes (Fig. 1) that can reduce the ST gap much more eectively than only repeated azulene units. What is even more signicant is that this class of fused acene-azulenes are as stable as the polyazulenes, and yet shows a much lower ST gap. We also show that the determining factor behind this large ST gap

2 reduction is multiple spin frustrated pairs or bonds. Thus, the number of spin frustrated bonds can form a simple design principle to eectively tune the ST gap. We have developed a simple protocol for parametrizing a model Hamiltonian that is capable of fast molecular screening and discovery.

Figure 1: (a) Polyacenes, (b) Fused acene-azulenes and (c) Polyazulenes

Computational details

The geometries of polyacenes are taken from earlier work by Hachmann et al.11 and Bendikov et al..2 Geometries of the fused acene-azulenes and polyazulenes are optimized at the (2e,2o) CASCI/RB3LYP/6-31G(d), (10e,10o) CASSCF/6-31G(d) and UB3LYP/6-31G(d) levels of theory. All the optimized geometries for both singlet and triplet states are given in the SI. It was noticed that UB3LYP optimizations gave rise to qualitatively dierent geometries (dierent bond length alternation(BLA) pattern) as compared to full valence CASSCF optimizations for small PAHs (2 and 3 fused rings)(shown in Fig. 2(a)-Fig. 2(e). On the other hand, the scheme of obtaining RB3LYP orbitals followed by a minimal CASCI(2e,2o) optimization (refered to as (2e,2o)CASCI/RB3LYP/6-31G(d)) gives the correct BLA pattern (shown in Fig. 2(c) and Fig. 2(f)). Therefore, this computationally aordable scheme of optimization have been used for larger PAHs. In case of polyacenes, Yang and co-workers34 have also noticed that dierent levels of theory can give rise to dierent patterns of BLA and subsequent symmetries. With

3 (a) (2e,2o)DFT-CASCI (b) (10e,10o)CASSCF (c) UB3LYP/6-31G(d)

(d) (2e,2o)DFT-CASCI (e) (10e,10o)CASSCF (f) UB3LYP/6-31G(d)

Figure 2: Comparison of geometries (BLA) of small PAHs at dierent levels of theory.

the minimal active space DFT-CASCI optimized geometries, DMRG(full valence 2pz active space),3941,43,44 CASSCF(14e,14o)35 and CASPT2(14e,14o)36 calculations have been performed using cc-pVDZ basis set.37 CASSCF and CASPT2 calculations have been performed using quantum chemistry software package Molpro 2018.2.38 We have used Block-1.5.342 for DMRG calculations and Q-Chem 5.145 for DFT optimizations.

Tuning the J parameter

For the calculations of the model Hamiltonian, we have considered each C atom as a spin- 1 2 site which are antiferromagnetically coupled (favorable interaction between opposite spins) with nearest neighboring sites with equal coupling parameter J. This essentially corresponds to bonding interactions between nearest neighbor bonded C atoms. J parameters in the Heisenberg spin Hamiltonian of the polyacenes have been tuned to reproduce the adiabatic DMRG/cc-pVDZ ST gap of the molecular Hamiltonian. These tuned J values are used for isomeric polyazulenes and fused acene-azulenes.

4 Results and Discussions

Adiabatic ST gap

Three types of structures (shown in Fig. 1) are considered and compared - (a) polyacenes, (b) fused acene-azulenes and (c) polyazulenes. The adiabatic ST gaps, calculated at the DMRG/cc-pVDZ level of theory, for the fused rings of size 2-7 are shown in Fig. 3(a). The complete 2pz valence space is chosen as the active space. As expected, the azulene ST gap is signicantly lower than its isomer, naphthalene. However, we notice that the rate of decay of adiabatic ST gap for polyazulene is much lower than the polyacenes. Therefore, contrary to what has been observed at the model Hamiltonian32 and UDFT level of theory,33 accurate multireference calculations show that the polyazulenes do not form stable triplet states within 6 fused rings. Surprisingly a combined acene-azulene fused system(Fig. 1(b)) shows the lowest adiabatic ST gaps. Within 5 fused rings the ST gap of the fused system is close to the computational accuracy of the method (∼ 0.05 eV). The ST gaps with various levels of multireference theory (CASSCF and CASPT2) show the same qualitative trend (given in SI). It is important to note that when the acenes and azulenes are fused in dierent order,46 i.e., structures with fused 7-5-6 or 7-5-6-6 rings, they show much higher (1.58 and 1.40 eV respectively) adiabatic ST gaps than 7-6-5 or 7-6-6-5 motifs (0.97 and 0.46 eV respectively) calculated at DMRG/cc- pVDG level of theory. Furthermore, a comparison of the stabilization energies per C atom of the isomeric systems of PAHs show that the fused acene-azulenes (8-9 kcal/mol) are comparable in stability with the polyazulenes (8-9 kcal/mol). But both of these systems are somewhat less stable than the acene-azulene systems that have already been synthesized (10-11 kcal/mol), such as 7-5-6 and 7-5-6-6 moieties.46 These stabilization energies were calculated with the help of isodesmic reactions of the form,

PAH + n1CH4 → n2C2H4 + n3C2H6, (1)

5 (a) (b)

(c)

Figure 3: Variation of ST gap for the acene, azulene and fused acene-azulene system with (a) the DMRG/cc-pVDZ level of theory and (b) Spin-Hamiltonian model calculations. (c) Correlation between the ST gaps with model and molecular Hamiltonians. The black circles refer to the acenes (used for tuning) and red circles are for other PAHs. The tness measure or correlation coecient is 0.96 for all the PAHs. and the extra stabilization energy with respect to equal number of C-C single and double bonds and C-H bonds computed. The details of the stabilization energies of all the systems are included in the SI. The single reference UDFT calculations when compared to the multireference calculations shows that for most of these systems UDFT level of theory gives rise to quantitatively wrong results (preferential stabilization of triplet states). On the other hand, the multireference calculations are computationally expensive and cannot be routinely used for molecular design and screening. Therefore, we try to develop a model Hamiltonian based protocol to predict the ST gaps in a computationally aordable way.

6 The ST gaps are calculated with a model Heisenberg Hamiltonian, given by,

ˆ X ~ ~ Hmodel = −J Si.Si+1, (2) i

th where Si denotes the spin at the i site (C atom), and J is the coupling constant between neighboring spins (on C atoms), which signies the eective bonding interaction. J is parametrized with respect to ST gaps of acenes.47 Since, here the eective Hamiltonian thus formed is dependent only on the nearest neighbor interactions between bonded pz orbitals, the computational cost is signicantly reduced. The ST gaps calculated with this model Hamiltonian (Fig. 3(b)) show the same qualitative trends as the ab initio calculations (Fig. 3(a)). The correlation between these calculations (Fig. 3(c)) shows that the ST gaps estimated with the model Hamiltonians are in excellent agreement with that of the molecular Hamiltonian and can therefore, be used as an eective screening and prediction tool.

(a)

(b)

Figure 4: (a) Example congurations of spins on the polyazulene and fused acene-azulene systems. (b) Probabilities of same spins across bonds.

7 Spin frustration

The model Hamiltonian wavefunction gives us a simple paradigm to understand the physics behind ST gaps in these molecules. It is important to note that the spins in adjacent sites (bonded C atoms) are antiferromagnetically coupled, so as to model the bonding interactions between them. Thus, opposite spins on adjacent sites refer to bonding and therefore, stabilization, while same spins on adjacent sites destabilize the congurations. The even- membered rings can contain congurations with all anti-parallel adjacent spins (i.e. stable congurations), while this is not possible in case of odd-membered rings. This leads to spin frustration,48 in the odd-membered rings. Examples of such congurations are shown in Fig. 4(a) for polyazulene and fused acene-azulene. There are eectively one frustrated pair for each azulene unit (2 fused rings). In case of fused acene-azulene, this situation may be exacerbated. It should be noted that in fused acene-azulene system, congurations with at least 2 spin frustrations are possible. The probability of nding same spins in adjacent sites can, therefore, form a measure of destabilization and are shown in Fig. 4(b) . Since the acenes are made of even-membered rings only, there is low probability of encountering same spins on adjacent sites. However, in case of both polyazulene and fused acene-azulene there are regions of high probabilities, especially across certain common bonds (bonds shared by two fused rings). To measure the instability in each system, the probabilities of same spins across any bonds are computed. It is 0.22 for tetracene, 0.24 for 4-azulene and 0.24 for 4-fused acene-azulene system. We notice that in case of polyazulenes, each azulene (7-5 membered fused ring) forms a unit and the common bond between the 7 and 5 membered rings show a higher probability of same spin conguration. In case of fused acene-azulene, this trend is spread across all common bonds and sometimes even across the rings. These observations point towards the presence of spin frustration in polyazulenes and fused acene-azulenes, as opposed to acenes. From the comparison of the probabilities it is expected that the polyazulenes and fused acene-azulenes would be of comparable stability in its singlet state and both these compounds

8 would be less stable than acenes. This is indeed noticed from the ab initio calculations. Furthermore, one would expect that the regions of high same-spin probability would try to reduce the instability by introducing lattice degrees of freedom, i.e., change in molecular geometry. In line with our expectations, the geometries of the fused acene-azulene and polyazulene systems (shown in Fig. 5) show elongated bond lengths across the common bonds with high same-spin probability (Fig. 4(b)). This is akin to Peierls distortion in polyenes and polyacenes.

Figure 5: Optimized geometries of singlet states of (a) fused acene-azulene, and (b) polyazulene.

In the polyacenes we notice the expected BLA, where the fused bonds also participate in the BLA pattern.49 In case of polyazulene (Fig. 5a), we notice that each azulene moiety forms a unit and the common bond in this unit is elongated. This common bond is almost single bond in nature (1.48Å ), i.e., only minimally participates in conjugation. Thus, each azulene forms a pseudo ten membered conjugated ring pattern. However, the common bond between the two azulene moieties are shorter than a single bond (1.39Å ) and takes part in conjugation. The situation is quite dierent when we notice the bond lengths of the fused acene-azulene system (Fig. 5b). Here, all the common bonds are elongated to almost single bond lengths (1.47-1.48Å ) and all of these bonds are minimally present in conjugation. These observations are in accordance with that of the spin probabilities calculated in the model system.

9 Stability of triplet state

The discussion till now considered only the relative stability of the singlet states and showed that both polyazulenes and fused acene-azulenes are expected to have low ST gaps. How- ever, in case of polyazulenes, triplet state is destabilized with respect to that of fused acene- azulene(Fig. 6). This can be explained from the spin probabilities in the same line of ar- gument as for singlets. The probabilities of nding same spins in adjacent sites for the triplet states are 0.255 in polyazulene and 0.24 in fused acene-azulene. Thus, the ST gap of polyazulenes are not as low as expected from its unstable singlet state. Polyazulenes do not show a ST crossover within 6 fused rings.

Figure 6: Molecular and model Hamiltonian energies for the singlet and triplet states are compared for 4-fused ring systems, i.e., tetracene, polyazulene and fused acene-azulene.

Symmetry of the molecule also plays a minor role in the ST gaps. The dierence in ST gaps of straight and kinked acenes have been reported before.50 The same is noticed here. The bent PAHs, i.e., polyazulenes have higher ST gaps than the straight isomers, fused acene-azulene. It was further noticed that fused acene-azulenes that were arranged so as to attain a bent topology also shows relatively higher ST gaps. Therefore, if one were to design a low ST gap molecule, there are three considerations - (i) maximize spin frustrations in singlet, (ii) minimize spin frustrations in triplet and (iii) more symmetric molecules. With these considerations in mind, a large number of dierently fused acene-azulene systems have been designed and screened. We notice that the lowest ST gap moiety consists of fused ring motif 7-6...6-5 membered rings.

10 Conclusions

In conclusion, we have developed a novel model Hamiltonian based approach for design of PAHs with tunable ST gaps. We have noticed that the ST gaps predicted by the model Hamiltonian approach are well correlated with the ab initio calculations. Therefore,this approach have been used to predict the smallest PAH with negative ST gap. The stability of these species were tested with the help of isodesmic reactions and were shown to be reasonably stable with respect to their acene analogues. We have further been able to propose a few succinct design principles which can be used to engineer low ST gap species. In this study, we have tested only the systems that are isomeric with polyacenes, however, we believe that this method can be used for other PAH systems as well.

Acknowledgements

The authors thank Dr. Manoranjan Kumar and Ms. Debasmita Maiti, SNBNCBS for help- ful discussions, IACS for computational resources and DST-SERB (EMR/2017/001054) for funding. M.R. and S.K.G. thank CSIR and UGC for fellowships.

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