An MS-CASPT2 Calculation of the Excited Electronic States of an Axial

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Spectroscopy and Excited States

An MS-CASPT2 Calculation of the Excited Electronic States of an Axial Difluoroborondipyrromethene (BODIPY) Dimer Jin Wen, Bowen Han, Zden#k Havlas, and Josef Michl J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00136 • Publication Date (Web): 06 Jun 2018 Downloaded from http://pubs.acs.org on June 7, 2018

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Journal of Chemical Theory and Computation

An MS-CASPT2 Calculation of the Excited Electronic States of an Axial Difluoroborondipyrromethene (BODIPY) Dimer Jin Wen,† Bowen Han,‡ Zdenìk Havlas,† and Josef Michl †‡* †

Institute of Organic Chemistry and Biochemistry AS CR, Flemingovo nám. 2, 16610 Prague 6, Czech Republic ‡

Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 803090215, U.S.A.

Abstract The previously reported (Duman et al., J. Org. Chem. 2012, 77, 4516) calculated state energies of monomeric difluoroborondipyrromethene (BODIPY) and its axial dimer would suggest that these dyes are promising candidates for singlet fission, and the dimer was computed to have an unusual low-lying doubly excited state. We find that these results were affected by the use of an imbalanced active space in multireference calculations and are not correct. Multistate complete-active-space second-order perturbation theory (MS-CASPT2/cc-pVDZ) calculations using an [8,8] (8 electrons in 8 orbitals) active space for the monomer and a [16,16] active space for the dimer reproduce quite well the observed excitation energies of the S1 states of both, and yield T1 excitation energies well in excess of half of the S1 excitation energies. We conclude that neither BODIPY monomer nor its axial dimer would permit exothermic singlet fission and are not worthy of investigation as potentially useful candidates, and that the unusual low-energy doubly excited states of the dimer were artifacts.

Introduction After the original synthesis in 1968,1 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene, known as BODIPY (a tetramethyl derivative 1 is shown in Chart 1), and its derivatives have been widely

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used in dye-sensitized solar cells,2,3,4 photodynamic therapy,5,6 cellular imaging,7,8,9,10 and photoinduced fluorescence switches,11 due to their interesting and tunable photophysical and chemical properties.12,13,14 In monomeric BODIPY, the S1 state is dominated by electron promotion from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).15 Some highly stable orthogonally twisted BODIPY dimers such as 2, with a sharp emission band and a high fluorescence quantum yield,16,17 were calculated to have an unusual low-lying "tetraradical" excited state involving double excitation from a pair of degenerate occupied orbitals.15 Excitation energies of the S1 state of BODIPY and its derivatives were initially calculated by time-dependent density functional theory (TD-DFT) methods with various functionals, including CAM-B3LYP and ùB97XD. These studies overestimated the S1 excitation energy by about 0.5 eV.18,19 Comparison with multireference calculations showed that the problem was due to inadequate treatment of electron correlation and to multireference character of the eletronic states of BODIPY. A mixed protocol was proposed, in which potential surfaces in ground and excited states were calculated by the TD-DFT method, while the vertical transition energies were calculated by CIS(D) and its scaled opposite spin counterpart method.20,21 In this procedure, a perturbative correction for double excitations was included to reduce the error to 0.1~0.2 eV.22 Using complete-active-space self-consistent field theory (CASSCF) with 6 electrons in 6 active orbitals for the axial BODIPY dimer 2 (Chart 1), S1 and T1 excitation energies of 3.69 and 1.79 eV, respectively, were reported.15 Since the computed T1 excitation energy is lower than half of S1 excitation energy, 2 appeared to represent a potential candidate for singlet fission, a process in which a singlet exciton splits into two triplet excitons.23 If correct, this could be a very significant result since new candidates for singlet fission are of considerable interest and are eagerly sought in many laboratories. The high stability of 1 and 2 would be very attractive for ultimate applications in solar cells. We wondered, however, whether a [6,6] active space was


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balanced and large enough to describe ðð* excitations in 2 correctly, and decided to verify the published results by a more extensive calculation. Our results are very different. The full ð space contains 24 electrons in 22 orbitals and is presently too large for a standard complete-active-space second-order perturbation theory (CASPT2) treatment. In this work, we first test different active spaces and basis sets in the monomer 1 and then adopt a compromise between computational feasibility and active space size by using 16 electrons in 16 orbitals to perform a CASPT2 calculation for the orthogonally twisted axial dimer 2. We find that the previous results were incorrect and that an experimental effort toward singlet fission in 2 is not warranted.

Chart 1. Chemical Structures of 1 and 2.

Methods of Calculation Geometries of monomeric BODIPY (1) and its axial dimer (2, Chart 1) in their ground states were optimized in gas phase at the B3LYP/cc-pVDZ level using Gaussian 09, Revision D.01.24 Electronic structures of ground and excited states were calculated by MS-CASPT2 theory 25 at these geometries with the program Molcas 8.0.26 The basis sets cc-pVDZ27 and ccpVTZ28 were used to calculate vertical excitation energies and choose an optical active space. The IPEA shift29 was set to its default value of 0.25 a.u. For 1, we used [12,11], with 12 electrons in 11 active orbitals, and [8,8], with 8 electrons in 8 active orbitals. Subsequently, the



[16,16] space was used for the calculation of vertical excitation energies of low-energy excited singlet and triplet states of 2. The active space of 2 was derived from the active orbitals of 1, using canonical Hartree-Fock orbitals as initial guess. This was then followed by separate optimization of orbitals in singlet and triplet states in each symmetry. To save computer time, 36 core orbitals (20 of a1 and 16 of e symmetry) of 2 were frozen in the MS-CASPT2 calculations. We started the CAS procedure by comparing MS-CASPT2 excitation energies from a state-averaged CASSCF (SA-CASSCF) wave function for 5 singlet states (11A1, 21A1, 11E, 21E, 11A2) and 4 triplet states (13A1, 13E, 23E, 13A2). We then selected 3 low-lying excited singlets (21A1, 11E, 21E) and 3 triplets (13A1, 13E, and 23E) for further study with both SA-CASSCF and state-specific CASSCF (SS-CASSCF) wave functions. We also analyzed 3 singlet (21A1, 11B2, 21B2) and 3 triplet (13A1, 13B2, 23B2) excited states of 1 with SA-CASSCF wave function. Spin-orbit coupling was ignored in the calculation of oscillator strengths, which were obtained from the CASSCF transition dipole moment and MS-CASPT2 excitation energies.

Experimental Part To obtain the absorption and emission spectra of 2, we prepared a sample using a slightly modified published procedure.30 Argon-bubbled CH2Cl2 (40 mL), 2,4-dimethylpyrrole (2.05 mL, 20 mmol) and (COCl)2 (0.43 mL, 5 mmol) were stirred at room temperature overnight. Triethylamine (5 mL) and boron trifluoride diethyl etherate (6 mL, 48% BF3) were added and stirring was continued for 5 h. After solvent removal by evaporation under reduced pressure, column chromatography with 1:3 hexanes:CH2Cl2 yielded pure 2 in 5 % yield. 1H NMR and HRMS spectra agreed with those reported.

Results


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Excitation Energies of 1. As noted in the introduction, TD-DFT methods with approximate density functionals suggest that the T1 excitation energy is less than half of the S1 excitation energy. For instance, the vertical excitation energies of a BODIPY derivative were E(S1) = 2.69 and E(T1) = 1.15 eV at the CAM-B3LYP/TZVP31//ùB97XD/TZVP32 level. Excitation energies obtained with another functional, M06-2X, and with cc-pVDZ basis set, were 3.15 and 1.55 eV for S1 and T1 states, respectively,33 for 1 with -CH3 groups replaced by -H, and were corrected to 2.65 and 1.75 eV by Laplace-transform based local coupled-cluster singles and approximate doubles (LCC2*) method.34,35 Multireference methods reproduced the observed S1 excitation energy of 2.44 eV better: 2.42, 2.45, and 2.44 eV at CASPT2(8,8)36,37/cc-pVTZ, CASPT2(12,11)/cc-pVTZ, and CASPT2(12,11)/aug-cc-pVDZ levels, respectively.18

An

investigation of the effect of the size of the active space on the CASPT2 S1 excitation energy, starting with [2,2] and going up to [12,11], suggested that convergence to within 0.1 eV is reached at [8,8].16 The cc-pVTZ basis set appears to perform as well as the augmented one. To verify the adequacy of the [8,8] active space and the cc-pVDZ basis set, we first calculated the first few vertical excitation energies of 1 with the MS-CASPT2(12,11) method using cc-pVDZ and cc-pVTZ basis sets (Table 1; for the MS-CASPT2 wave functions, see Table S1). The resulting S1 excitation energies, 2.56 and 2.48 eV, were close to the previously reported values.18 We concluded that an [8,8] active space is a reasonable size for 1 and when doubled to [16,16], is likely to work for 2 as well. The T1 excitation energy for 1 was about 1.8 eV, which is 0.5 eV more than half of the S1 excitation energy.

Thus, multireference calculations show that 1 does not meet the

requirement for exothermic singlet fission. The difference in excitation energies computed with the cc-pVDZ and cc-pVTZ basis sets is about 0.1 eV for S1 and close to zero for T1 (Table 1). With both active space choices, [8,8] and [12,11], the cc-pVDZ basis set overestimates the observed S1 excitation energy by about 0.1 eV but the cc-pVTZ basis set gives excellent ACS Paragon Plus Environment


Figure 1. Natural orbitals in the active space of 1 at (A) SA-CASSCF (8,8) and (B) SA-CASSCF (12,11) levels (the isosurface value is 0.03 a.u.). Dashed lines separate occupied and unoccupied orbitals. agreement. The experimentally unknownT1 excitation energy can be confidently predicted at ~1.8 eV from computations with both basis sets. Figure 1A shows the natural orbitals in the CASSCF(12,11) active space and dominant electron promotions that describe the MS-CASPT2/cc-pVDZ states (Table S1). The weight of the ground configuration in the perturbatively modified wave function of the S0 state is only about 84% and the biradicaloid character is about 10%, suggesting that single reference methods such as TD-DFT would not provide a good description of its excited states. Beyond the TD-DFT method, a multiconfiguration pair-density functional theory (MC-PDFT) provided accurate singlet-triplet gaps in the strongly correlated oligoacenes, which are biradicals and polyradicals in their ground state.38 Spin coupling could stabilize an electronic configuration with more unpaired electrons in an open-shell system.39 To give an accurate description of different spin


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states of the biradicaloid 1, selection of the active space is essential. Excitation energies of lowlying singlet and triplet states within both (8,8) and (12,11) active spaces are quite similar. The S1 and T1 states are both described by similar 6a2610b1 electron promotions, which contribute 68 and 82%, respectively. The S2 and T2 states are described by the 5a2610b1 electron promotion, with weights of 59 and 70%, respectively.

Table 1. Vertical Excitation Energiesa (eV) and Oscillator Strengthsb in 1 (C2v symmetry) from MS-CASPT2 Calculations Based on SA-CASSCF Wave Functions.

a

state

C2v

(8,8)/cc-pVDZ

(8,8)/cc-pVTZ

(12,11)/cc-pVDZ

(12,11)/cc-pVTZ

S1

B2

2.55 [1.16] (2.54)18

2.48 [1.12] (2.42)18

2.56 [1.34]

2.48 [1.30] (2.45)18

S2

B2

3.66 [0.02]

3.83 [0.08]

3.68 [0.06]

3.64 [0.06]

S3

A1

4.11 [0.01]

4.06 [0.02]

3.83 [0.08]

3.79 [0.06]

T1

B2

1.84 [0]

1.82

1.83

1.80

T2

B2

3.28 [0]

3.26

3.12

3.09

T3

A1

3.30 [0]

3.27

3.29

3.27

In parentheses, results of prior multi-reference computations.18 The value observed for E(S1)

is 2.44 eV (509 nm).15 b In square brackets, oscillator strength for transition from the ground state.

MS-CASPT2(16,16) Excitation Energies of the Axial Dimer 2. It seemed to us that the [6,6] active space chosen previously for 215 is unbalanced and that the reported S1 and T1 CASSCF(6,6)/CEP-31G excitation energies, 3.69 and 1.79 eV, respectively, are unreliable. The MOs of the orthogonally twisted dimer 2 occur in pairs that are exactly or nearly exactly degenerate. Since both a bonding MO and its antibonding counterpart need to be present in the active space, the number of MOs in the active space should be a multiple of four.



Figure 2. Natural orbitals in the active space of 2 at SA-CASSCF(16,16) level. Dashed lines separate occupied and unoccupied orbitals (the isosurface value is 0.03 a.u.).

We have now used a [16,16] active space, double of what appears to work for the monomer 1, and performed MS-CASPT2(16,16) calculations with cc-pVDZ basis set. The resulting vertical excitation energies and major electron promotions are collected in Table 2, and the natural orbitals in the active space are shown in Figure 2. The dominant excited state


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configurations are found in Table S3.

Comparison with the observed absorption and

fluorescence spectra (Table 2) shows that the calculated S1 excitation energy of 2.64 eV is 0.2 eV too high. This result provides a substantially better agreement with experiment (2.42 eV16) than the previously reported15 3.69 eV obtained with the [6,6] active space. The results for the excitation energies of the S2 and S3 states agree with observation quite well. The doubly excited "tetraradical" states reported previously15 appear as S4 and T4 (Table S3), with excitation energies of 3.90 and 3.77 eV, respectively, but we do not find any indication of them among the lower excited states. We attempted to reduce the 0.2 eV error in the MS-CASPT2/cc-pVDZ result, and Tables S4 and S5 compare the excitation energies calculated with both cc-pVDZ and cc-pVTZ basis sets at several levels: CASSCF, CASPT2, and MS-CASPT2 with SA-CASSCF and SS-CASSCF wave functions. Based on the difference between CASSCF and CASPT2, the correction for dynamic correlation is about 1.0 eV and changes the order of wave functions of S2 and S3 states. With the larger basis set, cc-pVTZ, the mixing between S1 and S2 states is increased significantly, reducing the S1 energy by 0.3 eV and increasing the S2 energy by 0.5 eV upon going from CASPT2 to MS-CASPT2 (Table S5). We do not find any significant difference between CASPT2 and MS-CASPT2 results with SS-CASSCF wave function and this is reasonable, since the S1 and S2 states are not mixed in SS calculations. From Table 3 we find that the excitation energy of the S1 state at the CASPT2/cc-pVTZ level (2.46 eV) from SA-CASSCF wave function agrees better with the experimental spectrum, and use these results in Figure 3.



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Figure 3. Absorption (black) and fluorescence (red) spectra of 1.5×10-5 M 2 in CH2Cl2 and CASPT2(16,16)/cc-pVTZ excitation energies and oscillator strengths (blue bars).

Table 2. MS-CASPT2(16,16)/cc-pVDZ Vertical Excitation Energies from SA-CASSCF Wave Functions and Oscillator Strengthsa of 2 (D2d symmetry).

a

state

sym

E/eVa

S0

A1

0

S1

E

2.64 [1.28]

12a2 6 32e

S2

E

3.35 [0.02]

10a2 6 32e

S3

A1

3.83 [0.04]

31e 6 32e

T1

E

1.73

12a2 6 32e

T2

E

2.87

10a2 6 32e

T3

A1

3.24

31e 6 32e

electron promotions

In square brackets, oscillator strength for transition from the ground state.

Table 3. CASPT2(16,16)/cc-pVTZ Vertical Excitation Energies and Oscillator Strengthsa of 2 (D2d symmetry) from SA-CASSCF Wave Functions.


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state

sym

E/eVa

electron

weight

promotions

a

S0

A1

0

S1

E

2.46 [1.06 ]

12a2 6 32e

0.74

S2

E

3.23 [ 0.01]

10a2 6 32e

0.56

S3

A1

3.99 [0.02 ]

31e 6 32e

0.33

T1

E

1.82

12a2 6 32e

0.76

T2

E

2.89

10a2 6 32e

0.64

T3

A1

3.30

31e 6 32e

0.59

0.77

In square brackets, oscillator strength for transition from the ground state.

At the CASPT2/cc-pVTZ level (Table 3), the weight of the ground configuration in the perturbatively modified wave function of S0 state is about 77%, demonstrating that a multireference method is needed for the interpretation of excited states of 2. Both the S1 state calculated at 2.46 eV and the T1 state calculated at 1.82 eV are degenerate and the dominant electron promotion is 12a2632e. The S2 and T2 states with excitation energies of 3.23 and 2.89 eV, respectively, are also both doubly degenerate, and the dominant promotion is 10a2632e. The non-degenerate S3 and T3 states located at 3.99 and 3.30 eV, respectively, result from the electron promotion 31e632e. The calculated S2 and S3 excitation energies agree well with the observed absorption spectrum. The T1 excitation energy of a supramolecular assembly containing Pt(II)-terpyridine acetylide and BODIPY was measured as 1.6 eV from emission spectrum at 77 K,40 close to our prediction of 1.7~1.8 eV in 2. We believe that there is no doubt that the excitation energy of the T1 state in 2 is about 0.5 eV above half the excitation energy of the S1 state. Like the monomer 1, 2 does not promise efficient singlet fission. Since 2 is a nonpolar molecule, solvation is not expected to affect its excitation energies significantly.



The M06-2X/cc-pVDZ method estimated the T1 excitation energy (1.43 eV) as slightly higher than half of S1 excitation energy of 2 (2.77 eV) and the LCC2 method corrected these numbers to 2.29 and 1.44 eV for the S1 and T1 states, respectively, when -CH3 was replaced by -H.33 Although LCC2 method underestimates S1 and T1 excitation energies by 0.2~0.3 eV, it supports our conclusion that T1 excitation energy is higher than half the S1 excitation energy. Following a benchmark publication on the IPEA correction to the excitation energies of organic molecules,41 we also used an IPEA shift of 0.0 a.u. for comparison with the default value of 0.25 a.u. To avoid intruder states, we set the imaginary shift42 to 0.1 a.u., and the excitation energies for 2 at the state-average MS-CASPT2(16,16)/cc-pVDZ level are listed in Table S6. Compared with experimental excitation energies, the resulting energies for the S1 and T1 states are about 0.2 eV too low. To include all ð and ð* orbitals of 2, an [24,22] active space would be required, and this is beyond the practical [18,18] limit of the CASSCF method. Methods that could be used to perform calculations with a [24,22] active space are restricted active space SCF (RASSCF)43 and generalized active space SCF (CASSCF).44 Excitation energies are quite sensitive to the partition in CASSCF, and we performed RASSCF(24,22) calculations with quadruple excitations to improve the accuracy. The RASPT2(24,22)/cc-pVDZ excitation energies are listed in Table S7, but they do not provide a better agreement with experiment.

Discussion For 1, already the smaller [8,8] active space is sufficient for the MS-CASPT2 method to reproduce the observed S1 energy well, both with cc-pVDZ and cc-pVTZ basis sets. The lowlying singlet and triplet excited states are all of singly excited character (Tables S1 and S2). For 2, the calculated S1 excitation energy is 2.46 eV with the cc-pVTZ basis set at the CASPT2 level, just 0.04 eV above the observed value.16 The excitation energies of the S2 and


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S3 states both agree well with the observed spectrum, and it appears that the CASPT2(16,16)/ccpVTZ method offers a reliable quantitative description of ðð* electronic excitations in 2. It is fortunate that the [16,16] active space appears sufficient, since we do not have the computational resources needed to go beyond this limit. All the low-lying singlets and triplets are singly excited, and we detect no evidence for the previously claimed low lying doubly excited singlet state in 2. The MOs and the excited state wave functions of 2 can be built from those of 1 in a straightforward way. The result for the T1 excitation energy indicates that the value is about 1.7 - 1.8 eV, about 0.5 eV higher than half the observed S1 excitation energy. We believe that there is no hope for efficient singlet fission in solid 2.

Conclusion The MS-CASPT2(8,8) and MS-CASPT2(12,11) methods account for the electronic excited states of the monomer 1 nicely and the cc-pVDZ and cc-pVTZ basis sets yield comparable results. Also for the singlet states of the axial dimer 2, the MS-CASPT2(16,16)/ccpVDZ and CASPT2(16,16)/cc-pVTZ methods reproduce the observed absorption spectrum well, with errors of 0.22 and 0.04 eV in the energy of the S1 state, respectively. The results are significantly better than those of the previously reported CASSCF(6,6)/CEP-31G calculations, which overestimated the S1 excitation energy by ~1.1 eV and provided misleading conclusions concerning a low-lying doubly excited state. The presently calculated T1 excitation energy of 2 is 0.5 eV higher than half of the observed S1 excitation energy and there is no reason to expect singlet fission in 2 to be exothermic.

ORCID Jin Wen: 0000-0001-6136-8771



Zdenìk Havlas: 0000-0002-8369-7303 Josef Michl: 0000-0002-4707-8230

Acknowledgement. Work in Prague was supported by the Institute of Organic Chemistry and Biochemistry (RVO: 61388963) and GAÈR (15-19143S). Work in Boulder was supported by the U.S. Department of Energy, Office of Science, Office of Chemical Sciences, Biosciences, and Geosciences (DE-SC0007004). We thank Dr. Nadia Korovina for a stimulating discussion.

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For Table of Contents use only An MS-CASPT2 Calculation of the Excited Electronic States of an Axial Difluoroborondipyrromethene (BODIPY) Dimer Jin Wen, Bowen Han, Zdenìk Havlas, and Josef Michl


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An MS-CASPT2 Calculation of the Excited Electronic States of an Axial

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