MM Excited State Molecular Dynamics and Fluorescence

Article pubs.acs.org/JPCA

QM/MM Excited State Molecular Dynamics and Fluorescence Spectroscopy of BODIPY Edward A. Briggs, Nicholas A. Besley, and David Robinson* School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom ABSTRACT: Absorption and emission spectra arising from the lowest energy transition in BODIPY have been simulated in the gas phase and water using a quantum mechanics/ molecular mechanics (QM/MM) approach. Kohn−Sham density functional theory (DFT) is used to calculate both ground (So) and first excited (S1) states using the maximum overlap method to obtain the S1 state. This approach gives ground and excited state structures in good agreement with structures found using multiconfigurational perturbation theory (CASPT2). Application of a post-self-consistent field spin-purification relationship also yields transition energies in agreement with CASPT2 and available experimental data. Spectral bands were simulated using many structures taken from ab initio molecular dynamics simulations of the ground and first excited states. In these simulations, DFT is used for BODIPY, and in the condensed phase simulations the water molecules are treated classically. The resulting spectra show a blue shift of 0.3 eV in both absorption and emission bands in water compared to the gas phase. A Stokes shift of about 0.1 eV is predicted, and the width of the emission band in solution is significantly broader than the absorption band. These results are consistent with experimental data for BODIPY and closely related dyes, and demonstrate how both absorption and emission spectra in solution can be simulated using a quantum mechanical treatment of the electronic structure of the solute.

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diodes,10 energy transfer cassettes,11 dye-sensitized solar cells,12 and potential photosensitizers in photodynamic therapy.13 There are a number of features of BODIPY and its derivatives that make it well suited for such applications. It has a high molar absorption coefficient and quantum yields, with excitation energies in the visible range and fluorescent lifetimes on the nanosecond time scale. Furthermore, these properties can be modified by chemical substitutions around the BODIPY core.7 There is an extensive ongoing effort to synthesize BODIPYbased derivatives for new applications, for example, to detect the presence of Ca2+,14 Cu2+,15 and Zn2+ ions8 or nitric oxide16 in biological systems through changes in fluorescence. BODIPY is also utilized as a biological molecular probe and has been added to cholesterol to study membrane lipid domains17 and proteins to probe their activity.18−20 A key factor in the use of fluorescent probes is the response of the fluorescence to the molecular environment. Solvatochroism of the absorption and emission bands of a number of BODIPY-based molecules has been reported. Solvatochromic shifts of three BODIPY-based fluorescent dyes have been analyzed using a generalized solvent scale proposed by Catalán21 (considering dipolarity, polarizability, acidity, and basicity of the medium).22 Studies have shown that the observed spectral shifts are primarily dependent on solvent polarizability23 or solvent polarity,24 with hydrogen

INTRODUCTION Fluorescent imaging is widely used in biology and biomedical sciences, where it is an important technique that can further the understanding of the function of biological systems. Most natural biomolecules possess few optically active moieties that can be used in fluorescent measurements, and it is common to introduce external fluorescent labels. One commonly used class of fluorophore is that derived from 4,4-difluoro-4-bora-3a,4adiaza-s-indacene, also known as BODIPY (see Figure 1). BODIPY1 was discovered in 1968,2 but it is only relatively recently that BODIPY has become important in a wide range of applications,3 including as the lasing medium in a dye laser,4−6 biological imaging and sensing,7−9 organic light-emitting

Received: December 12, 2012 Revised: February 28, 2013 Published: March 5, 2013

Figure 1. Structure of BODIPY (a) and its deviation from planarity in the S1 state (b). HOMO (c) and LUMO (d) orbitals of BODIPY. © 2013 American Chemical Society

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dx.doi.org/10.1021/jp312229b | J. Phys. Chem. A 2013, 117, 2644−2650

The Journal of Physical Chemistry A

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bonding being of less importance.24 In particular, BODIPY derivatives have solvatochromic shifts dependent upon the polarizability of the solvent immediately surrounding the dye.21−23 Computational simulations are a potentially valuable tool to aid the interpretation of experimental measurements and can reveal in detail how intra- or intermolecular interactions affect the observed fluorescence. One challenge for theory is to simulate molecules such as BODIPY in complex environments, and for fluorescence emission spectroscopy, this is further complicated by the need to study fluorophores in electronically excited states. A number of groups have studied the absorption and emission spectroscopy of BODIPY and BODIPY-related molecules with a combination of density functional theory (DFT) and time-dependent density functional theory (TDDFT).6,23,25−28 This work has addressed the question of the choice of exchange-correlation functional28 and charge transport.27 TDDFT calculations with the B3LYP exchangecorrelation functional on the laser dye pyrromethane 567 (PM567), which comprises BODIPY with ethyl groups bonded at the C2 position in each of the rings, showed a smaller dipole moment in the S1 state. The computed transition energies were 0.4−0.5 eV larger than experiment.25 The ground and excited states of a range of BODIPY dyes have been studied using semiempirical methods.29−32 These studies have examined the radiative lifetimes of the various BODIPY derivatives and isolated different effects upon the spectral shifts including the dipolarity and polarizability of the solvent, extended π-systems, and other substituents with the theoretical predictions shown to be consistent with experimental evidence. In the majority of these studies the solvent is modeled using an implicit solvent model, such as the polarized continuum solvent model. It is preferable to have a more explicit treatment of solvent or biological environment. One approach to achieve this is to use a combination of classical molecular dynamics (MD) simulations and an electronic structure method such as TDDFT, wherein structures sampled from a MD simulation are used in TDDFT calculations. Examples of the calculation of emission spectra with this approach include the study of 5-hydroxytryptophan in solution33 and within proteins34 and molecular probes within a membrane bilayer environment.35,36 A limitation of this approach is that the derivation of force field parameters for the excited state simulations are often based on ad-hoc charges derived from quantum mechanical gasphase excited state calculations. A theoretically more robust approach is to use quantum chemical methods, such as DFT, directly in the molecular dynamics simulations. This involves a very large increase in computational expense. However, with modern computational resources, such simulations are possible and the extended environment, such as solvent, can be incorporated using a hybrid quantum mechanics/molecular mechanics (QM/MM) approach. Such an approach has been applied to study the excited state dynamics and emission spectrum of the first singlet excited state of acetone in water within restricted open-shell Kohn−Sham (ROKS) and TDDFT formalisms.37 It was shown that a purely classical description of the solvent was adequate through a comparison with results from simulations that also treated the first solvent shell of water at the quantum chemical level. A similar methodology has been applied to investigate the excited state dynamics and proton− electron transfer in guanine,38 and the excited state dynamics of pyrrole−water clusters has also been studied.39 In this paper, we report a QM/MM study of the excited state dynamics and

absorption and emission spectra of BODIPY in the gas phase and in water. In both the molecular dynamics and subsequent calculations of the spectroscopy, the electronic structure of the BODIPY molecule is described using DFT while the solvent is treated classically.

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COMPUTATIONAL DETAILS Geometry optimizations for the ground state and first excited singlet state of BODIPY were performed using the complete active space self-consistent field (CASSCF) with the multiconfigurational perturbation theory (CASPT2) approach40,41 using the 6-31G(d) basis set without any symmetry constraints. The active space of the CASSCF wave function consisted of the π-bond system, namely, 12 electrons in 12 orbitals, giving a total of 226 512 symmetry adapted configuration state functions. Using these geometries, additional calculations were performed to determine the absorption and emission energies using the larger ANO-L basis set42 (contracted to 4s3p2d for B, C, N and F; 2s1p for H). CASSCF/CASPT2 calculations were done using the MOLCAS software.43 Structures of the ground and first excited singlet state were also optimized using unrestricted DFT with the B3LYP functional and 6-311G** and 6-31G basis sets. In order to study the first excited singlet state within Kohn−Sham density functional theory, the maximum overlap method (MOM)44 was invoked to converge the SCF procedure to give an excited state solution. More specifically, an initial set of orbitals was generated using the orbitals for the ground state and moving a β electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) and then using the MOM procedure to prevent variational collapse to the ground state within the subsequent SCF calculation. An advantage of this approach is that the orbitals are directly optimized to describe the excited state of interest, and the transition energies can be determined using a ΔSCF approach, wherein the excitation energy is the difference between the excited state and the ground state energies. While this approach can give accurate excitation energies for a large number of states,44−47 excitation energies for open-shell singlet states involving excitation to valence orbitals are usually underestimated. The reason for this deficiency is associated with describing the open-shell singlet state with a single determinant to give a spin-mixed state. The computed excitation energies can be improved significantly by applying the post-SCF spin-purification correction of Ziegler48 E = 2ES − E T

(1)

where E is the energy of the true or spin-purified singlet state, ES is the energy of the spin-mixed (single determinant) state, and ET is the energy of the corresponding triplet state. In this paper, we refer to calculations for the excited state with the B3LYP functional that have not been spin corrected (Es) as spin-mixed B3LYP (SM-B3LYP). Similarly, calculations that have been corrected according to eq 1 are referred to as spinpure B3LYP (SP-B3LYP). All DFT calculations were performed within a locally modified version of the Q-Chem software package49 in which DFT energies and analytical gradients modified according to eq 1 are available. Ab initio molecular dynamics simulations at 298 K for gasphase BODIPY were performed for the ground and first excited singlet state at the B3LYP/6-31G level. While a larger basis set could be used for gas-phase simulations, the 6-31G basis was chosen such that comparison could be made with the QM/MM 2645



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Table 1. Structural Parameters for the So and S1 States of BODIPY Computed at Different Levels of Theory and Taken from Experiment So CASPT2/ 6-31G* bonds (Å) B−F B−N N−C1 C1−C2 C2−C3 C3−C4 C4−C5 C4−N angles (deg) F−B−F N−B−N C4−C5−C6 N−C4−C5 B−N−C4−C5 a

1.388 1.561 1.352 1.406 1.390 1.425 1.385 1.389 111.8 104.9 121.7 121.3 0.0

B3LYP/ 6-311G** 1.387 1.572 1.338 1.411 1.386 1.418 1.389 1.393 111.3 105.5 121.9 120.6 0.0

S1 experiment

CASPT2/ 6-31G*

{1.378−1.405}a,b 1.545a 1.339a 1.400a 1.370a 1.410a 1.383a 1.391a

SM-B3LYP/ 6-311G**

1.390 1.555 1.343 1.418 1.406 1.408 1.418 1.420

108.6b 106.6b 123.3b 118.9b 4.3

SP-B3LYP/ 6-311G**

1.388 1.562 1.344 1.420 1.385 1.428 1.411 1.398

112.2 102.5 118.4 120.1 14.2

1.388 1.561 1.332 1.421 1.397 1.410 1.416 1.420

111.0 104.8 119.4 121.0 10.2

SM-B3LYP/ 6-31G 1.430 1.547 1.357 1.427 1.395 1.432 1.413 1.418

111.2 104.5 119.7 120.4 8.2

109.0 105.9 119.5 120.8 6.1

Taken from ref 52. bTaken from ref 54.

the only discrepancy is that the X-ray structure is nonplanar at the boron atomthis has been previously assigned to the packing forces present in the crystal structure, which are obviously lacking from the gas-phase isolated molecule. For the S1 state, all of the calculations find the rings to be nonplanar in the lowest energy structure, with the structure in which the rings are planar corresponding to a transition state. This nonplanar structure is shown in Figure 1. A nonplanar structure has also been reported in TDDFT calculations of the closely related pyrromethene laser dye PM597, although in the same study the S1 states of the two dyes PM567 and PM580 were reported to be planar.6 The extent to which the structure deviates from planarity is indicated by the B−N−C4−C5 dihedral angle, which is found to be 14.4° at the CASPT2 level with smaller values in the DFT calculations. Overall, for the excited state there is a small deviation between the structures predicted by CASPT2, SM-B3LYP, and SP-B3LYP, with the SP-B3LYP structure slightly closer to the CASPT2 one. For the MD simulations, it is desirable to reduce the cost of the calculations as much as possible. Also shown is the structure for SM-B3LYP with the 6-31G basis set. While the reduction in the basis set leads to some larger deviations in the structure compared to CASPT2, particularly the B−F bond length and F−B−F bond angle, the structure of the ring system, where the electronic excitation is localized, is predicted quite accurately. Calculated vertical absorption, emission, and 0−0 transition energies for BODIPY are given in Table 2. Excitation energies for singlet states computed with SM-B3LYP are expected to be too low, and the values for the S1 state of BODIPY are significantly lower than the corresponding values from

simulations described below. Simulations were run for 120 fs, with a time step of 0.24 fs. Initial velocities were sampled from the Maxwell−Boltzmann distribution, and the system was equilibrated for the first 60 fs, with the velocities scaled to maintain a temperature of 298 K for the first 100 time steps. Structures for the last 250 time steps were used for subsequent calculations of the absorption and emission spectra. In order to extend the simulations to the condensed phase, a QM/MM approach was adopted where BODIPY is treated using DFT and the solvent (water) is treated classically using the TIP3P potential.50 These simulations were performed using the Q-CHEM/CHARMM interface.51 These simulations were carried out using the isothermal−isobaric ensemble, at atmospheric pressure and a temperature of 300 K. Truncated octahedral periodic boundary conditions were imposed, with a box of length 29.091 Å. BODIPY was treated in the QM region, employing the B3LYP functional with the 6-31G basis set. Within the framework of using excited state Kohn−Sham DFT to describe the excited state, a similar protocol can be applied to the S1 state. For the excited state simulation, ground state orbitals were initially generated to start the MOM procedure. Both simulations were initially heated and equilibrated for 10 ps, with production dynamics for the ground state simulation for 260 and 172 ps for the excited state simulations. A total of 129 structures were used from the ground state simulation, and 49 structures were used from the last 98 ps of the excited state simulation; these were taken at equal intervals of 2 ps. Spectra were generated by representing the computed transition energy and oscillator strength for each structural snapshot by a Gaussian function with a full width at half-maximum of 0.2 eV.

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RESULTS AND DISCUSSION Structural parameters for the So and S1 states of BODIPY from CASPT2 and DFT calculations are given in Table 1, along with experimental results obtained from X-ray crystallography.52−54 As expected, the ground state of BODIPY has C2v symmetry and there is a close agreement with the structures predicted by CASPT2 and B3LYP. The largest deviation in the bond lengths is 0.014 Å, and the bond angles agree within 1°. These computed results compare well with those from experiment;

Table 2. Computed Transition Energies for BODIPY

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method

vertical/eV

0−0/eV

emission/eV

CASPT2/6-31G* SM-B3LYP/6-311G** SP-B3LYP/6-311G** # SP-B3LYP/6-311G** † TD-B3LYP/6-311G**

2.62 2.06 2.41 2.36 3.15

2.58 2.01 2.33 2.35

2.37 1.97 2.23 2.26 1.43



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CASPT2. This error is partially corrected by spin purification, and the predicted transition energies for SP-B3LYP are closer to the CASPT2 values, although they remain about 0.3 eV lower. There is little change in the calculated SP-B3LYP/6311G** excitation energies when the structure was optimized at the SM-B3LYP/6-31G level, with the maximum change of 0.05 eV evident in the absorption energy. This is a consequence of the transition involving orbitals that are localized on the rings and the structure of the rings being reproduced accurately by the smaller basis set. This suggests that using the smaller basis set for the QM/MM dynamics will introduce only a small error. Vertical absorption and emission energies with TDDFT are further from the CASPT2 values, with the absorption and emission energies too high and too low, respectively. TDDFT excitation energies were also found to be too high in calculations on PM567.25 Comparison of the computed DFT emission energies with those from CASPT2 provides a test of their reliability. However, it is also insightful to compare with experiment. Unfortunately, absorption and emission spectra have not been reported for BODIPY in the gas phase, although solution-phase spectra are available.52−54 Absorption and emission energies have also been measured for three closely related pyrromethene laser dyes in methanol and ethanol solvents.6 The molecular structure of these dyes comprise BODIPY with alkyl substituents at the C2 position of both rings. Table 3 shows

Table 4. Average Values of the Structural Parameters of the So and S1 States of BODIPY from Molecular Dynamics Simulations gas phase bonds (Å) B−F B−N N−C1 C1−C2 C2−C3 C3−C4 C4−C5 C4−N angles (deg) F−B−F N−B−N C4−C5−C6 N−C4−C5 B−N−C4−C5

molecule

Eabs (exp)

Eabs (calcd)

Eem (exp)

Eem (calcd)

2.46 2.40 2.39 2.37

2.36 2.22 2.23 2.19

2.41 2.32 2.31 2.20

2.26 2.12 2.12 2.01

So

S1

So

S1

1.426 1.576 1.360 1.419 1.396 1.427 1.397 1.413

1.439 1.562 1.370 1.428 1.397 1.434 1.407 1.418

1.481 1.516 1.373 1.405 1.410 1.417 1.397 1.423

1.479 1.511 1.376 1.419 1.401 1.430 1.411 1.432

110.8 105.3 122.1 120.4 6.2

110.5 105.0 120.3 120.8 9.5

102.4 109.0 120.5 120.4 7.6

101.7 109.2 119.3 120.7 7.0

phase simulations agree well with the experimental structural parameters presented in Table 1. Some structural differences are evident between the gas-phase and the condensed-phase simulations. These differences are largely focused on the B−F groups, where there is a significant increase in the B−F bond lengths and decrease in the B−N bond lengths in solution, with corresponding changes in the bond angles. Figure 2 shows the

Table 3. Calculated (SP-)B3LYP/6-311G**//B3LYP/6-31G and Experimental Absorption and Emission Energies for BODIPY and Three Derivativesa BODIPY PM567 PM580 PM597

solvated (water)

a

Experimental values4 are measured with methanol solvent, except for BODIPY,51 which is measured in cyclohexane.

the calculated absorption (S1 ← So) and emission (So ← S1) energies for BODIPY and the three laser dyes PM567, PM580, and PM597 determined using the (SP-)B3LYP/6-311G**// B3LYP/6-31G protocol, along with experimental values with methanol solvent.6 Calculated absorption energies are within 0.2 eV of experiment and do show a slightly lower absorption energy for PM597, which is evident in experiment, although we note that some difference with the experimental values would be expected because calculated gas-phase values are compared with experimental measurements with solvent. A similar level of agreement with experiment is found for the emission energies. A Stokes shift of about 0.1 eV is found for BODIPY, which agrees well with the experimental shift of 0.05 eV.52 A Stokes shift of 0.1 eV is also calculated for PM567 and PM580 with a larger value of 0.2 eV for PM597; a larger Stokes shift for PM597 is also evident in experiment. Overall, the results suggest that the (SP-)B3LYP/6-311G**//B3LYP/6-31G approach provides a relatively inexpensive but accurate description of the lowest absorption and emission transitions in BODIPY and related molecules that can be applied in QM/ MM simulations. Table 4 summarizes the average values for the structural parameters from the MD simulations for BODIPY. These show nonplanarity of the rings even for the ground state. The gas-

Figure 2. Simulated absorption (black line) and emission (red lines) bands for the lowest energy transition of BODIPY in the gas phase and water.

computed spectral bands for the lowest absorption band and emission band from the 250 structural snapshots taken from the gas-phase ab initio MD simulations using the SP-B3LYP/6311G**//B3LYP/6-31G approach for the ground state. For the emission spectrum a similar protocol is followed but with the SM-B3LYP/6-31G approach used for the excited state dynamics. The absorption band in the gas phase has a maximum at 2.32 eV, and the maximum of the emission band lies at 2.23 eV, giving a Stokes shift of 0.09 eV. These compare well with the experimentally determined absorption and emission maxima 2647



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recorded in ethanol of 2.49 and 2.32 eV, respectively.52 While the fwhm values given in Figure 2 are much larger than experiment (0.35 and 0.4 eV for the absorption and emission bands, respectively), this is an artifact of the method used to produce the plots. The width of the emission band is larger than that for the absorption band, which is reflected in standard deviations of 0.06 and 0.10 eV for the absorption and emission energies, respectively. Again, this compares well with experimentally observed spectra of BODIPY.53 Overall, there is a relatively modest difference in the structure of the molecule between the So and the S1 states. There is a small decrease in the B−N bond length and a small increase in the other bond lengths of the ring and the degree of nonplanarity of the rings. The average dipole moment of the ground state is calculated to be 4.6 D, while the dipole moment of the excited state is found to be lower at 3.8 D. A lower value for the dipole moment in the S1 state is consistent with calculations on PM567.25 Radial distribution functions for the distance between the boron atom of BODIPY and the oxygen atoms of the water molecules are shown in Figure 3. The radial distribution

maxima in more polar solvents. Another feature of the simulations is that the emission band is significantly broader than the absorption band. Experimental spectra show a ratio in the full width at half-maximum for the absorption and emission bands of approximately 1.1 for a BODIPY-based dye in methanol23 and 1.7 for PM546 in methanol.55 The ratio in the widths of the simulated bands is 1.5, which is consistent with the experimental values. However, the actual widths of the bands are larger than those observed in experiment (0.75 and 0.5 eV for the calculated emission and absorption, respectively, compared with ∼0.11 and 0.09 eV for the experimental values23). This is likely to be partly associated with treating the water molecules that are very close to BODIPY as point charges in the DFT calculations to determine the transition energies. This could be addressed by treating these water molecules fully within the DFT calculations.

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CONCLUSIONS

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AUTHOR INFORMATION

The structure, dynamics, and associated absorption and emission spectra have been simulated for the So and S1 states of BODIPY in the gas phase and water. In the simulations, the excited state has been calculated using Kohn−Sham DFT, exploiting methods to converge the SCF calculation to give an excited state. Using this approach, it is necessary to apply a post-SCF spin-purification correction to give accurate transition energies. The optimized structure of the S1 state is calculated to be nonplanar using both CASPT2 and DFT methods, and it is found that accurate absorption and emission energies can be computed using structures optimized using DFT with a relatively small basis set and then evaluating the absorption and emission energies using a larger basis set. Molecular dynamics simulations have been performed for both So and S1 states, and for the simulation in the condensed phase the solvent is incorporated within a QM/MM framework. The resulting computed absorption and emission bands are consistent with available experimental data. A Stokes shift of about 0.1 eV is predicted, and both absorption and emission bands are blue shifted by about 0.3 eV in water compared to the gas phase. Furthermore, simulations show the width of the emission band in solution to be significantly broader than the absorption band by a similar amount observed in experimental spectra of a closely related molecule.

Figure 3. Radial distribution functions of the BODIPY boron to water oxygen distance for the ground state (black line) and excited state (red line).

functions for the So and S1 states are similar with the first solvent shell at about 3.6 Å, with a second solvent shell at about double the distance of the first shell at 6.4 Å. This second shell is less ordered than the first, as the peak observed at the second solvent shell is not as distinct as for the first solvent shell. The simulated absorption and emission bands for BODIPY in water are also shown in Figure 2. With the solvent, simulations predict an absorption band centered at 2.62 eV and an emission band centered at 2.53 eV. Both bands show a significant blue shift of approximately 0.3 eV compared to the gas-phase simulations. This is consistent with the dipole moment of the excited state being smaller than the ground state, which would lead to a blue shift in the transition energies in a polar solvent. Furthermore, the computed gas-phase absorption and emission energies for the PM laser dyes (Table 3) were lower than the experimental values measured in methanol. On the basis of the results for water, a blue shift in the transition energies is also expected for these closely related molecules in methanol, which would bring the computed values in close agreement with experiment. Boens et al. reported absorption and emission spectra for BODIPY-based dyes for a range of solvents.23 These spectra also show a small shift to higher energies of the band

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the University of Nottingham for a studentship for E.A.B. and access to its High Performance Computing facility. D.R. is also thankful to the Leverhulme Trust for the award of an Early Career Fellowship.

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REFERENCES

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