Benchmark Study of the Structural and Thermochemical Properties of

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Benchmark Study of the Structural and Thermochemical Properties of a Dihydroazulene/Vinylheptafulvene Photoswitch Mads Koerstz, Jonas Elm, and Kurt V. Mikkelsen J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b01207 • Publication Date (Web): 28 Mar 2017 Downloaded from http://pubs.acs.org on April 3, 2017

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The Journal of Physical Chemistry

Benchmark Study of the Structural and Thermochemical Properties of a Dihydroazulene/Vinylheptafulvene Photoswitch Mads Koerstz,† Jonas Elm,‡ and Kurt V. Mikkelsen∗,† Department of Chemistry, H. C. Ørsted Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark., and Department of Physics, University of Helsinki, FI-00014 Helsinki, Finland. E-mail: [email protected]

∗

To whom correspondence should be addressed Department of Chemistry, H. C. Ørsted Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark. ‡ Department of Physics, University of Helsinki, FI-00014 Helsinki, Finland. †

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Abstract We investigate the performance of four different density functional theory (DFT) functionals (M06-2X, ωB97X-D, PBE0, and B3LYP-D3BJ) for calculating the structural and thermochemical properties of the dihydroazulene/vinylheptafulvene photoswitch (DHA/VHF). We find that all the tested DFT functionals yield equilibrium geometries in good agreement with higher level CCSD/cc-pVDZ calculations and that the basis set had little influence on the geometries of the photoswitch. We found a negligible difference in the thermal contribution to the Gibbs free energy between the tested functionals, indicating that the largest source of error when calculating storage free energies originates from errors in the calculated single point energies. It was found that ωB97X-D and M06-2X performed decently for predicting storage energies. While B3LYP-D3BJ and PBE0 generally underestimated the storage energy compared to CCSD(T)-F12a/VDZ-F12 results. Therefore, we tested if domain based local pair natural orbital coupled-cluster (DLPNO-CCSD(T)) provided an improvement over density functional theory methods for the single point energies. We observed that the DLPNO-CCSD(T) storage energies were in better agreement with CCSD(T)-F12a/VDZ-F12 results than the DFT results. The DLPNO-CCSD(T) results already converged at cc-pVTZ quality basis set, making it possible to perform accurate estimates of the thermochemical properties at a time scale that makes the DLPNO-CCSD(T) method feasible for routine calculations on the photoswitch. Using DLPNO-CCSD(T)/cc-pVTZ we calculate accurate storage energies for currently synthesised derivatives of the DHA/VHF photoswitch.

Introduction Photochromic molecules which undergo light-induced isomerization into higher energy, metastable isomers are promising candidates for closed-cycle systems of energy harvesting, storage, and release. For this purpose several molecular systems, such as azobenzene, 1 diarylethene 2,3 and spiropyranes 4,5 have been studied. A major challenge is to obtain as 2


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high an energy density as possible. An optimum value of 1 MJ/kg, corresponding to the energy density of the unsubstituted norbornadiene-quadricyclane (NB/QC) system, is desired. 6 However, the photoisomerization of unsubstituted norbornadiene does only have a quantum yield of 9%. Recent advances in the synthetic protocol for the NB/QC couple has lead to several derivatives, which have overcome this deficiency. 7 The improvements have been introduced by tuning the systems via various donor-acceptor substituents. 8,9 However, these compounds do typically also have a large molecular mass, leading to low storage densities. The photochromic dihydroazulene/vinylheptafulvene (DHA/VHF) photoswitch has, since the first derivates were introduced by Daub and co-workers in 1984, been of great interest due to its ability to store solar energy for longer periods of time. 10 The DHA molecule has an absorption maximum around 350 nm corresponding to high intensity of the solar flux and the VHF absorption is well separated from the DHA, with an absorption maximum around 470 nm. 11 This makes the DHA/VHF couple a viable candidate for applications as molecular solar thermal storage systems. The parent photoswitch is characterised by the photo-induced ring-opening of DHA, which forms the less stable s-cis-VHF that is in thermal equilibrium with the isomer s-trans-VHF. This process is reversible under standard conditions which implies that s-cis-VHF can only undergo a thermal induced ring-closure back to DHA. 12 The mechanism is illustrated for the parent system in Scheme 1. CN 7

NC CN

8

8a

1

6 2 5

4

DHA

NC

CN

hν CN

∆

3

s-cis-VHF

s-trans-VHF

Scheme 1: The structure and reaction scheme of the parent DHA/VHF photoswitch Quantum mechanical calculations are an important tool to shed light on the magnitude of the energy storage capacity of molecular photoswitches. Recent calculations at the M062X/6-311+G(d) level theory have shown that the Gibbs free energy difference of the parent 3



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DHA/VHF couple is 6.6 kcal/mol in vacuum. This corresponds to a Gibbs free energy density stored in the metastable VHF of only 0.11 MJ/kg. 13 In order to use the DHA/VHF system as efficient solar thermal storage systems, the energy density needs to be increased. More than a doubling of the energy density could be achieved by removing one of the two cyano groups in the compound, leading to a Gibbs free energy difference of 13.8 kcal/mol, corresponding to an energy density of 0.25 MJ/kg. Adding a phenyl group to position 3 of the parent system has been shown to increase the free energy storage to 12.3 kcal/mol at the M06-2X/6-311+G(d) level of theory in vacuum. 14 This will also increase the molecular weight of the compound, and thereby only correspond to an energy density of 0.15 MJ/kg. Simultaneously removing one cyano group and adding a phenyl group to position 3 has been shown to increase the Gibbs free energy difference to 17.2 kcal/mol in vacuum, corresponding to an energy density of 0.23 MJ/kg. 14 These findings indicate that the free energy storage capacity of the DHA/VHF photoswitch is still far from the optimal value of 1 MJ/kg, but the storage capacity is essentially additive for each modification. Further modifications, such as substituting one of the cyano groups with either a ketone, ester or amide 15 also effectively doubles the Gibbs free energy storage, but the increase in molecular weight, makes these derivatives less attractive than the corresponding mono-cyano system. Another approach to increase the storage energy is via benz-annulation. The DHA can either be destabilized or stabilized compared to the VHF depending on which position the aromatic ring is fused to the molecular framework. 16 We recently performed a large scale rational design analysis of the donor-acceptor properties of the DHA/VHF system. 17 Using NH2 and NO2 as the donor and acceptor substituents, we did not identify significant increases in the energy densities, except for the parent system with a NH2 group substituted at position 3, where the energy density was doubled to 0.22 MJ/kg. This indicates that geometrical effects by introducing conformational strain, 18 might be a more promising route to effectively increase the energy storage capacities of the DHA/VHF couple. With the ability to predict the properties of synthesised, and in particular unsynthesised

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derivatives of the molecular photoswitches, quantum chemical methods play a crucial role in the development of possible design strategies for future derivatives. Unfortunately, highly accurate ab initio methods such as MP2 and CCSD(T) have a steep computational scaling as the size of the molecular system increases. Therefore, the preferred choice for calculating molecular properties on the DHA/VHF photoswitch has previously been density functional theory (DFT), and benchmark studies have determined the best functionals for predicting the properties of the parent system compared to experimental results. 13 However, DFT accounts for electron correlation in an empirical and approximate fashion, and it is therefore difficult to systematically improve the DFT results. Previously, we have shown that DFT results yielded lower energy storage capacities compared to higher level DF-LCCSD(T)/VDZ-F12//MP2/631+G(d) calculations. 13 This indicates that there could be high uncertainties associated with DFT calculations. In this paper we compare the performance of four commonly utilized DFT functionals (B3LYP-D3BJ, PBE0, ωB97X-D, and M06-2X) with higher level ab initio methods such as MP2 and CCSD for obtaining the geometries and vibrational frequencies. We compare the DFT single point energies to highly accurate CCSD(T)-F12a/VDZ-F12 calculations. Furthermore, we assess the domain-based local pair natural orbital coupled cluster method (DLPNO-CCSD(T)), which due to the moderate computational scaling is an attractive alternative to the previously tested DFT methods.

Computational Details Due to the steep computational scaling of the electron correlation methods the parent system (cf. Scheme 1) is reduced by interchanging the phenyl group with the smaller methyl group. By choosing the smaller system the number of electrons can be reduced from 134e to 102e and decrease the computational costs significantly. The structures for the benchmark system of interest are illustrated in Scheme 2.

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CN 7

NC CN

8

8a

1

6 2 5

4

NC

CN

hν CN

∆

3

DHA

s-cis-VHF

s-trans-VHF

Scheme 2: The structure and reaction scheme of the investigated derivate of the DHA/VHF photoswitch

Geometry Optimisations The geometry optimisations for the ground state structure of the DHA/VHF photoswitch were performed using both DFT, MP2 19 and CCSD. 19 The applied DFT functionals were: B3LYP 20 with damped empirical dispersion, 21 PBE0, 22 ωB97X-D, 23 and M06-2X 24 as implemented in Gaussian 09. 25 The MP2 structures were optimised using Gaussian 09, while the CCSD structures were computed using MOLPRO 2012.1. 26 The CCSD structures were optimised using the correlation consistent cc-pVDZ basis set, while the MP2 and DFT geometry optimisations were carried out utilizing the five different Pople style basis sets: 6-31+G(d), 6-31++G(d,p), 6-311G(d,p), 6-311+G(d), 6-311++G(d,p). The correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X=D,T) were also tested for MP2 and DFT. However, as previous studies have illustrated 13 the inclusion of diffuse functions yielded convergence issues and is therefore neglected in the current analysis.

Single-Point Energy Evaluations Single-point energies were computed with MP2 and the DFT functionals: B3LYP-D3BJ, PBE0, ωB97X-D and M06-2X. These DFT single-point calculations were performed utilising the 6-311+G(d) basis set, since it has been shown to be sufficiently accurate. 13 For MP2 calculations we also utilized the 6-311+G(d) basis set, however in order to investigate our MP2 results we also tested the cc-pVTZ basis set for computing single-point energies In order to improve the computation of single-point energies the DLPNO-CCSD(T) 6


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method is utilizied. 27 The DLPNO-CCSD(T) methods allow for the use of wave function theory for larger molecular systems at a reasonable computational cost. The DLPNOCCSD(T) energies were calculated using ORCA 3.0.3. 28 In this work two different settings for the DLPNO-CCSD(T) method were used: the "NormalPNO" (TCutPairs = 10−4 , TCutPNO = 3.33 × 10−7 , TCutMKN = 10−3 ) and the "TightPNO" (TCutPairs = 10−5 , TCutPNO = 10−7 , TCutMKN = 10−4 ). These methods were tested in conjugation with the correlation consistent basis set both with and without diffuse functions.

Results and discussion Geometry To accurately describe the thermochemical properties of the DHA/VHF photoswitch, it is important to start from an accurate structure. To get an indication of how accurate the geometries of DHA, s-cis-VHF, and s-trans-VHF are at MP2 and DFT level of theory the structures are compared to the structure obtained at the CCSD/cc-pVDZ level of theory. Table 1 presents the structures of DHA, s-cis-VHF, and s-trans-VHF calculated using DFT and MP2 in vacuum compared to the CCSD structure through the root mean square derivation (RMSD) computed with the Kabsch algorithm. 29,30 This gives an indication of how well each combination of basis set and functional performs in comparison to the CCSD structure. For each method it is observed that the structures have very little basis set dependence. For the DHA compound, we observe that there is almost no difference between the utilised basis sets, whereas the VHF structures show a slight basis set dependence. The ωB97X-D and M06-2X functionals are seen to be least dependent on the basis set used to obtain the geometry. It is observed that the structures strongly depend on the method used to compute the structures. The performance of the methods when compared to the structure predicted by CCSD/cc-pVDZ follow the order: M06-2X ≈ ωB97X-D > MP2 ≈ PBE0 > B3LYP-D3BJ. 7



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Table 1: RMSD in all bond lengths (Å) of DHA, s-cis- and s-trans-VHF in vacuum when compared to the CCSD/cc-pVDZ geometry Basis set

B3LYP-B3DJ

PBE0

ωB97X-D

M06-2X

MP2

0.09 0.09 0.09 0.09 0.09

0.05 0.05 0.05 0.05 0.05

0.05 0.05 0.04 0.05 0.05

0.03 0.03 0.03 0.03 0.03

0.12 0.12 0.14 0.13 0.14

0.27 0.22 0.21 0.22 0.19

0.20 0.17 0.17 0.18 0.16

0.12 0.12 0.12 0.11 0.11

0.12 0.12 0.12 0.12 0.12

0.19 0.18 0.16 0.20 0.18

0.18 0.19 0.18 0.15 0.17

0.16 0.17 0.17 0.14 0.16

0.05 0.05 0.05 0.04 0.05

0.07 0.07 0.06 0.06 0.05

0.07 0.06 0.04 0.07 0.05

DHA: 6-31+G(d) 6-31++G(d,p) 6-311G(d,p) 6-311+G(d) 6-311++G(d,p) s-cis-VHF: 6-31+G(d) 6-31++G(d,p) 6-311G(d,p) 6-311+G(d) 6-311++G(d,p) s-trans-VHF: 6-31+G(d) 6-31++G(d,p) 6-311G(d,p) 6-311+G(d) 6-311++G(d,p)

This indicates that the M06-2X and ωB97X-D functionals predict structures that have the most resemblance with the CCSD structure. Generally, the structures obtained from the small double zeta basis set 6-31+G(d) are almost identical to the structures obtained with the larger triple zeta basis set 6-311++G(d,p). In the following analysis we will utilise the structures obtained with the larger 6-311++G(d,p) basis set. However, for general purposes it is recommended to use the smaller sized 6311+G(d) basis set, which provides a good compromise between computational efficiency and basis set flexibility.

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Thermochemical properties Thermal contribution to the free energy When investigating the DHA/VHF photoswitch our primary interests is the energy storage capacity. The storage capacity is defined as the Gibbs free energy difference at 298.15 K between DHA and the most stable isomer (MSI) of VHF:

∆Gstorage = GDHA − GVHFMSI

(1)

The Gibbs free energy differences can be partitioned into two contributions: a purely electronic contribution and a thermal contribution to the free energy:

∆Gstorage = ∆E + ∆Gthermal

(2)

Table 2 presents the difference in thermal energy contribution (∆Gthermal ) to the free energy between DHA and the two VHF isomers. The thermal contribution to the Gibbs free energy is seen to correspond to 2.18 kcal/mol or less. The largest difference in thermal energy contribution is found between MP2/6-311++G(d,p) and B3LYP-D3BJ/6-311++G(d,p) and corresponds to 0.92 kcal/mol. All the tested DFT functionals agree relatively well on the magnitude of the thermal correction. This implies that the choice of DFT functional has little effect on the thermal contribution to the Gibbs free energy. If we compare the thermal energy difference to the electronic energy difference, which in section is found to be approximately 11 kcal/mol, it is a quite small contribution to the total free energy. Thus, in the following analysis of thermochemical properties we will approximate the storage capacity as the relative electronic energy difference between DHA and the MSI of VHF.

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Table 2: Thermal contribution to the free energy difference between DHA and the two VHF isomers.

DHA - s-trans-VHF DHA - s-cis-VHF a

B3LYP-D3BJ/ 6-311++G(d,p) 1.26 1.58

PBE0/ 6-311++G(d,p) 1.35 1.57

ωB97X-D/ 6-311++G(d,p) 1.21 1.37

M06-2X/ 6-311++G(d,p) 1.69 1.73

MP2/ 6-311++G(d,p) 2.18 2.01

All values are presented in kcal/mol.

Electronic Energy Previous studies of the parent system and several derivatives suggest that s-trans-VHF is usually more stable than s-cis-VHF. 31 Table 3 presents the stability of s-trans-VHF relative to s-cis-VHF (∆Es-trans-VHF − ∆Es-cis-VHF i.e. a negative value indicates that s-trans-VHF is more stable than s-cis-VHF) in vacuum. We note that all MP2 energies are positive if the 6-311+G(d) basis set is utilised, while if the cc-pVTZ basis is utilised the energy difference between the two isomers of VHF is significantly smaller but still positive for DFT and MP2 structures. For the relative stability between the VHF isomers at the MP2/cc-pVTZ//CCSD/cc-pVDZ level of theory tips over and becomes negative. This indicates that the 6-311+G(d) basis set is insufficient to accurately describe the energy when utilised in connection with the MP2 method. The tendency of MP2 to generally predicting s-cis-VHF to be more stable than s-trans-VHF is in disagreement with the relative stability computed by the chosen DFT methods, which are all strictly negative. As a comparison we have performed an explicitly correlated coupled cluster single-point calculation (CCSD(T)-F12a/VDZ-F12) on the optimised structures. These single-point calculations unambiguously predict negative values, which indicates that s-trans-VHF is more stable than s-cis-VHF. Furthermore, the CCSD(T)-F12a/VDZ-F12 energies show very little variation depending on which functional was used for obtaining the geometry, with values between -0.59 and -0.94 kcal/mol. Thus, it seems that DFT methods predict relative energies between the two VHF isomers that are in better agreement with higher level ab initio calculations compared to MP2. Having defined the VHFMSI within each method we can compute the storage energies.

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Table 3: Electronic energy difference between the two isomers of VHF B3LYP-D3BJ/6-311+G(d) PBE0/6-311+G(d) ωB97X-D/6-311+G(d) M06-2X/6-311+G(d) MP2/6-311+G(d) MP2/cc-pVTZ

B3LYP-D3BJ/ 6-311++G(d,p) -0.54 -1.46 -0.31 -0.22 1.48 0.27

PBE0/ 6-311++G(d,p) -0.54 -1.47 -0.31 -0.22 1.55 0.01

ωB97X-D/ 6-311++G(d,p) -0.66 -1.48 -0.21 -0.17 1.24 0.35

M06-2X/ 6-311++G(d,p) -0.48 -1.33 -0.48 -0.39 1.06 0.41

MP2/ 6-311++G(d,p) -0.65 -1.59 -0.90 -0.71 1.46 0.69

CCSD/ cc-pVDZ -1.06 -1.76 -0.71 -0.77 0.40 -0.18

CCSD(T)-F12a/VDZ-F12

-0.94

-0.87

-0.87

-0.59

-0.96

-0.59

Energy/Structure

a


Table 4 contains the storage energy calculated as:

∆Estorage = EDHA − EVHFMSI

(3)

This implies that a negative value corresponds to DHA being more stable than the VHFMSI . We note that the storage energy in general depends slightly on the method used to compute the geometry. The largest discrepancy in storage energy between different structures is surprisingly between the two wave function theory (WFT) methods i.e. MP2 and CCSD. However, it is only approximately 1.5 kcal/mol depending on the method used to compute the energy. If we only consider the DFT methods, and compare the storage energies within each structure, it is illustrated that there is almost no differences. If we instead consider the storage energies within each geometry it is obvious that there are major differences depending on the method used to compute the energies. By comparing the computed storage energies to the energies obtained with CCSD(T)-F12a/VDZ-F12 method we note that B3LYP-D3BJ and PBE0 dramatically underestimates the storage energies while MP2 generally overestimates the storage energies. The remaining two DFT functionals (ωB97X-D and M06-2X) are seen to perform very similarly in predicting storage energies. However, there is a clear tendency for all the DFT functionals to predict storage energies that underestimate the storage energy when compared to the CCSD(T)-F12a/VDZF12//CCSD/cc-pVDZ method. We find that the method which predicts a storage energy that is in best agreement with the CCSD(T)-F12a/VDZ-F12//CCSD/cc-pVDZ method, is the MP2/cc-pVTZ//ωB97X11



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D/6-311++G(d,p) method with a discrepancy of 0.47 kcal/mol. However, due to the computational scaling of the MP2 method a more feasible method is the ωB97X-D/6-311+G(d)// ωB97X-D/6-311++G(d,p) method which predict a storage energy with a discrepancy of 0.92 kcal/mol. Table 4: Storage energy computed as the electronic energy difference between DHA and the MSI. B3LYP-D3BJ/ 6-311++G(d,p)

PBE0/ 6-311++G(d,p)

ωB97X-D/ 6-311++G(d,p)

M06-2X/ 6-311++G(d,p)

MP2/ 6-311++G(d,p)

CCSD/ cc-pVDZ

B3LYP-D3BJ/6-311+G(d) PBE0//6-311+G(d) ωB97X-D/6-311+G(d) M06-2X/6-311+G(d) MP2/6-311+G(d) MP2/cc-pVTZ

-1.27 -6.05 -10.15 -9.67 -14.74* -11.64*

-1.17 -6.10 -10.08 -9.68 -15.10 -11.95*

-1.28 -5.96 -10.22 -9.72 -14.96* -11.61*

-1.58 -6.49 -9.68 -9.31 -15.13* -12.03*

-0.47 -5.69 -8.65 -8.39 -15.42* -12.52*

-2.42 -7.32 -9.96 -9.61 -16.50* -13.56*


-11.00

-11.04

-10.94

-10.82

-10.40

-11.14

Energy/Structure

* Indicates a

that s-cis-VHF is more stable than s-trans-VHF. Hence, s-cis-VHF is the MSI. All values are presented in kcal/mol.

DLPNO-CCSD(T) WFT methods are rigorous and allow for an systematic way of achieving chemical accuracy. In particular the CCSD(T) method is often recognised as the "golden standard" within electronic structure theory. Unfortunately, due to the steep computational scaling of the CCSD(T) method it can only be applied systematically for relatively small systems. The DHA/VHF photoswitch is too big to routinely be handled with CCSD(T), therefore the only viable option has previously been DFT methods. However, in the following we will introduce an alternative way of predicting single-point energies for the DHA/VHF photoswitch i.e. the near linear scaling coupled cluster method: DLPNO-CCSD(T). The DLPNO-CCSD(T) is a promising method for achieving high accuracy for large scale chemical systems at a reasonable timescale. However, the DLPNO-CCSD(T) method has not yet been utilised in connection with the DHA/VHF photoswitch. The DLPNOCCSD(T) method is feasible to use in connection with the photoswitch and possible larger derivates since the NormalPNO DLPNO-CCSD(T) scales with system size almost identically to B3LYP. 32 12


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Table 5 contains the storage energies obtained from single-point DLPNO-CCSD(T) with varying basis set and PNO settings calculated from the structures obtained with: B3LYPD3BJ, PBE0, ωB97X-D, M06-2X, MP2, and CCSD. The storage energies are calculated analogously to Table 4 i.e. ∆EDHA − ∆EMSI . Here we see that the DLPNO-CCSD(T) method converges systematically with the increase in basis set size. The energy difference between results obtained with cc-pVTZ and cc-pVQZ quality basis set is observed to be quite small, hence the cc-pVTZ basis set can be utilised without any significant loss in accuracy. Using the DLPNO-CCSD(T) method to predict storage energies, we find that the method that is in best agreement with our best estimate of the storage energy (CCSD(T)-F12a/VDZF12//CCSD/cc-pVDZ) is the TightPNO/DLPNO-CCSD(T)/cc-pVTZ//M06-2X/6-311++ G(d,p) method with a discrepancy of only 0.07 kcal/mol. However, DLPNO-CCSD(T) with TightPNO are approximately twice as expensive as DLPNO-CCSD(T) with NormalPNO, therefore a more feasible method for larger derivatives of the photoswitch is the less expensive NormalPNO/DLPNO-CCSD(T)//M06-2X/6-311++G(d,p) which yielded results with an discrepancy of 0.74 kcal/mol. When we compare the best DFT result: ωB97X-D/6311+G(d)//ωB97X-D/6-311++G(d,p) (i.e. a discrepancy of 0.92 kcal/mol compared to CCSD(T)-F12a/VDZ-F12) to the DLPNO-CCSD(T) method, even with NormalPNO, the DLPNO-CCSD(T) method still yield slightly more accurate results compared to higher level ab initio methods. This implies that the DLPNO-CCSD(T) method for the DHA/VHF photoswitch is a more accurate alternative to the thoroughly tested DFT functionals.

Benchmark of Previous Computed Storage Energies A large amount of derivatives of the photoswitch have been investigated with DFT. In particularly the DFT method, M06-2X/6-311+G(d), has been the preferred tool when computing storage energies. In order to asses the accuracy and robustness of the DLPNO-CCSD(T) method in connection with the DHA/VHF photoswitch it is necessary to test the method against a wider selection of derivatives. Table 6 shows the DLPNO-CCSD(T) storage ener13



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Page 14 of 22

Table 5: Storage energy computed as the electronic energy difference between DHA and the MSI. B3LYP-D3BJ/ 6-311++G(d,p) -14.11 -12.15 -12.44

PBE0/ 6-311++G(d,p) -14.16 -12.15 -12.49

ωB97X-D/ 6-311++G(d,p) -14.07 -12.18 -12.35

M06-2X/ 6-311++G(d,p) -13.46* -11.88 -11.81

MP2/ 6-311++G(d,p) -13.57 -11.71 -11.67

CCSD/ cc-pVDZ -13.30 -12.03 -11.99

-13.28 -11.53 -11.59

-13.29 -11.57 -11.63

-13.25 -11.47

-12.88 -11.21 -11.22

-12.64 -10.94 -10.94

-12.78 -11.42 -11.46

-16.29* -13.39 -12.86

-16.17* -13.43 -

-16.16* -13.27 -12.79

-15.43* -12.78 -12.32

-15.63* -12.59 -

-15.22* -12.80* -12.50

TightPNO/aug-cc-pVDZ TightPNO/aug-cc-pVTZ

-15.41 -12.15

-15.39 -12.17

-15.39 -12.10

-15.01 -11.80

-14.73 -11.51

-15.00* -12.06


-11.00

- 11.04

-10.94

-10.82

-10.40

-11.14

Energy/Structure NormalPNO/cc-pVDZ NormalPNO/cc-pVTZ NormalPNO/cc-pVQZ TightPNO/cc-pVDZ TightPNO/cc-pVTZ TightPNO/cc-pVQZ NormalPNO/aug-cc-pVDZ NormalPNO/aug-cc-pVTZ NormalPNO/aug-cc-pVQZ

* Indicates a

that s-cis-VHF is more stable than s-trans-VHF. Hence, s-cis-VHF is the MSI. All values are presented in kcal/mol.

gies for a selection of previously published derivatives compared to the M06-2X/6-311+G(d) storage energies. For all the derivatives, there are only seen small differences between the TightPNO and NormalPNO settings. This implies that the NormalPNO setting can be applied, without causing significant errors. The system H is the only tested derivative for which the MSI of VHF is more stable than DHA, hence the energy is lost in the metastable VHF isomer, instead of being stored. Table 6 once again illustrates the tendency of M06-2X/6-311+G(d) to underestimate the storage energy compared to TightPNO/DLPNO-CCSD(T). The only exception is system D for which M06-2X/6-311+G(d) overestimates the storage energy compared to TightPNO/DLPNOCCSD(T). This suggests that our previously published storage energies are in fact too low due to inaccuracies in the M06-2X/6-311+G(d) energy. At the TightPNO/DLPNO-CCSD(T) level of theory the parent system A is found to have a storage energy of -10.3 kcal/mol. Each of the modifications such as adding a phenyl group at position 3 (system B) or removing a cyano group (system C) yield the same increase in energy storage compared to the parent system, with a value of -15.7 kcal/mol and -15.6 kcal/mol, respectively. Applying both these modifications yield a storage energy of -18.1 kcal/mol, hence confirming that each of the modifications does in fact additively give a

14


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Table 6: Storage energy computed as the electronic energy difference between DHA and the MSI of VHF NormalPNO/cc-pVTZ // M06-2X/6-311+G(d)

TightPNO/cc-pVTZ // M06-2X/6-311+G(d)

M06-2X/6-311+G(d)

Ph

-9.9

-10.3

-8.2

Ph

-15.0

-15.7

-14.5

Ph

-15.0

-15.6

-15.1

Ph

-17.2

-18.1

-18.5

-14.3

-14.6

-12.9

-14.8

-15.9

-14.7

-14.7

-14.7

-13.1

9.7

9.1

11.8

Structure NC

CN

A: NC

CN

B: Ph CN

C: CN

D: Ph O NC

NH2

E:

Ph

O NC OCH3

F:

Ph

O NC

G: Ph

NC

H: a

CN Ph


15



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higher storage energy. As also pointed out in the introduction, we obtain no gain in the storage energy in exchanging one of the cyano group with either a ketone/ester or amide compared to the monocyano derivative. These findings indicate that in order to maximize the energy storage a monocyano derivative should be used, coupled with a phenyl group on position 3. As illustrated by system H, benzannulation has a high effect on the storage energy. To further increase the energy storage benzannulation at the 5-6 position should be performed in order to stabilize the DHA and destabilize the VHF. 33 These combined modifications can be seen in Figure 1. At the M06-2X level of theory the system shown in Figure 1 has a storage energy of -36.5 kcal/mol. Using TightPNO/DLPNO-CCSD(T)/cc-pVTZ we obtain a value of -36.6 kcal/mol, indicating that the M06-2X/6-311+G(d) slightly underestimates the storage energy. At the DLPNO level of theory this leads to a storage energy density of 0.43 MJ/kg. This value represents the potential maximum energy storage density, which can be achieved without drastically changing the DHA molecular framework. Currently, only the 7-8 benzannulated system (with additional ester functional groups) has successfully been synthesised. Given that the target molecule can be obtained, it represents an important starting point for further functionalization. For instance the two phenyl groups can be functionalized with either donor/acceptor groups to tune the properties of the system. CN Ph Ph

Figure 1: The molecular structure of the compound with potentially highest energy storage capacity.

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Conclusion We have investigated how four DFT functionals (B3LYP-D3BJ, PBE0, ωB97X-D, and M062X) performed in predicting geometries and thermochemical properties in vacuum when compared to MP2 and CCSD. It was illustrated, that the results for the DHA and both VHF structures were almost independent of the basis set used to compute the geometries. Furthermore, it was found that the M06-2X and ωB97X-D functionals predicted quite similar structures for DHA and both VHF isomers which are in good agreement with the CCSD/ccpVDZ structures. This implies that to run efficient calculations it is sufficient to compute DFT structures (M06-2X or ωB97X-D) with a small basis set i.e. 6-311+G(d). It was also tested, if the DLPNO-CCSD(T) method could be used as an alternative to DFT calculations for computing energies. It was found that DLPNO-CCSD(T) did produce storage energies that were in better agreement with higher level ab initio methods compared to DFT. It was illustrated that the DLPNO-CCSD(T) method converged already at ccpVTZ level of theory, which makes it possible to routinely apply this method to derivatives of the DHA/VHF photoswitch. Therefore, we can recommend that a DLPNO-CCSD(T)/ccpVTZ//M06-2X/6-311+G(d) or DLPNO-CCSD(T)/cc-pVTZ//ωB97X-D/6-311+G(d) level of theory should be applied for subsequent investigations of the DHA/VHF photoswitch.

Acknowledgement The authors thank University of Copenhagen and Danish e-Infrastructure Cooperation for financial support.

References (1) Hartley, G. S. The Cis-form of Azobenzene. Nature 1937, 140, 281–281. (2) Irie, M.; Mohri, M. Thermally Irreversible Photochromic Systems - Reversible Photocyclization of Diarylethene Derivatives. J. Org. Chem. 1988, 53, 803–808. 17



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Geometry

Single Point

The Journal of Physical Chemistry Page 22 of 22 Energy 1 2 DHA 3 4 5 6 7

?

CCSD

CCSD(T)

DLPNO-CCSD(T) DFT ΔE ACS Paragon Plus Environment MSI of VHF DFT DFT

Benchmark Study of the Structural and Thermochemical Properties of

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