Molecular Design of a Room-Temperature Maser

Supporting information for: Molecular Design of a Room-Temperature Maser

Stuart Bogatko,∗,†,‡,¶ Peter D. Haynes,†,§ Juna Sathian,† Jessica Wade,§,k Ji-Seon

Kim,§,k Ke-Jie Tan,† Jonathan Breeze,† Enrico Salvadori,⊥,# Andrew

Horseld,†,‡,¶ and Mark Oxborrow†

Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, UK, London Centre for Nanotechnology, Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, UK, Thomas Young Centre, Imperial College London, Exhibition Road, London SW7 2AZ, UK, Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, UK, Centre for Plastic Electronics, Imperial College London, Exhibition Road, London SW7 2AZ, UK, London Centre for Nanotechnology, University College London, 17-19 Gordon Street WC1H 0AH, London, UK, and School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road E1 4NS, London, UK

E-mail: [email protected]

S1 Experimental

Sample preparation

Crystals of pentacene and 6,13-diazapentacene in a p-terphenyl host lattice and phenazine in biphenyl were grown using an open system zone melting methodS1. The Pentacene and p-terphenyl were supplied by TCI Europe NV, Phenazine 98% (P13207-10G) and Biphenyl 99% (W312908-1KG) were obtained from Sigma Aldrich. The resulting concentrations of pentacene in p-terphenyl was 0.0045 mol/mol % pentacene. Concentrations of 6,13-diazapentacene and phenazine were not measured but can be constrained to less than 0.1 mol/mol % pentacene.

UV/Vis

Absorbance measurements were performed on samples of pentacene in p-terphenyl, 6,13-diazapentacene in p-terphenyl and phenazine in biphenyl (Figure 1, also appearing in Figure 3 of the manuscript). The absorbance measurements were performed using a Shimadzu UV-2550 spectrophotometer and an Agilent Cary 5000 UV-Vis-NIR Spectrophotometer which has an excellent photometric response in the 175-3300 nm range. The measurements were performed using the standard solid sample holder with a 1 mm aperture mask. The absorbance spectra of both pentacene and 6,13-diazapentacene solid samples were obtained using the Cary WinUV software of the spectrophotometer over the chosen wavelength 200-800 nm. Finally the concentration was calculated using Beer-Lambert law using the known value of

∗To whom correspondence should be addressed †Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, UK ‡London Centre for Nanotechnology, Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, UK ¶Thomas Young Centre, Imperial College London, Exhibition Road, London SW7 2AZ, UK §Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, UK kCentre for Plastic Electronics, Imperial College London, Exhibition Road, London SW7 2AZ, UK ⊥London Centre for Nanotechnology, University College London, 17-19 Gordon Street WC1H 0AH, Lon- don, UK #School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road E1 4NS, London, UK

S2 extinction coecient and the measured thickness of the sample.

Figure S1: UV/Vis spectra of Pentacene and 6,13-diazapentacene in p-terphenyl (top) and phenazine in biphenyl (bottom).

S3 From these spectra the peaks at 590 nm, 620 nm and 364 nm (corresponding to transition energies of 2.10 eV, 2.00 eV and 3.41 eV, respectively) are assigned to the S0 − S1 transition of pentacene, 6,13-diazapentacene and phenazine, respectively.

Time-resolved EPR

ZFS parameters (Table 1) of phenazine in biphenyl, pentacene and 6,13-diazapentacene (both in p-terphenyl) were obtained from simulation of X-band time resolved EPR spectra (Figure 2, also appearing in Figure 3 of the manuscript) of powder samples. The measurements were performed on a Bruker E580 pulsed EPR spectrometer equipped with a Bruker dielectric ring resonator (ER 4118X-MD5). The optical excitation was provided by a Surelite broadband OPO system (operating range 410 - 680 nm), pumped by a Surelite I-20 Q-switched Nd:YAG laser with 2nd and 3rd harmonic generators (20 Hz, pulse length: 5 ns). EPR spectra were simulated using the EasySpinS2 toolbox in MATLAB. Since the spin multiplicity n depends on S, the spin quantum number, (n = 2S + 1), the EPR spectrum of triplet states consists of two allowed EPR transitions for each molecular orientation with respect to the applied magnetic eld. In powder samples, as it is in the cases reported here, all orientations are present with the same probability and the resulting EPR spectrum is the sum of all contributions weighted over a sphere. Powder EPR spectra of organic triplet states are dominated by the ZFS interaction and electron spin polarization. For organic triplets, the ZFS interaction, which can be described with two independent parameters known as D and E, arises mostly from spinspin interaction between the magnetic dipoles and, to a lesser extent, from spinorbit interaction. For powder samples, the magnitudes of D and E can be estimated directly from the experimental EPR spectrum by measuring the distances between the characteristic turning points, as indicated in Figure 2 (top panel). These correspond to the canonical orientations of the zero-eld splitting tensor with respect to the applied magnetic eld and are denoted as X, Y, and Z in Figure 2; where the and + indexes refer to the mS = 1 → mS = 0 and mS = 0 → mS = +1 transitions,

S4 respectively. On the contrary, the sign of D and E cannot be readily determined from the EPR spectrum and therefore the modulus is often reported. The electron spin polarization results from the selective population of each triplet sublevel from the excited singlet state via the intersystem crossing (ISC) mechanism. Hence, the resulting sublevel populations dier considerably from those predicted by Boltzmann distribution. Particularly, population dierences, the physical quantity measured in a TREPR experiment, are larger than Boltzmann predictions and the corresponding EPR lines at early times after light excitation appear either in emission or in enhanced absorption.

Table S1: Phenazine, pentacene and 6,13-diazapentacene ZFS parameters and relative zero-eld populations derived from simulation of the TR-EPR spectra recorded at 9GHz at room temperature. D and E were assumed to be both posi- tive resulting in the energy order Px > Py > Pz.TR-EPR (black lines) and relative simulations (red lines) of powder samples of phenazine in biphenyl and pentacene and 6,13-diazapentacene in p-terphenyl recorded at 9GHz at room temperature. Phenazine was excited at 355 nm, the pentacene and 6,13-diazapentacene were excited at 590 and 532 nm respectively. A = enhanced absorption, E = emission.

D (MHz) E (MHz) Px Py Pz Phenazine 2190 ± 10 326 ± 5 0.73 0.15 0.12 Pentacene 1400 ± 10 50 ± 5 0.76 0.16 0.08 6,13-diazapentacene 1370 ± 10 85 ± 5 0.60 0.21 0.19

S5 Figure S2: TR-EPR (black lines) and relative simulations (red lines) of powder samples of phenazine in biphenyl and pentacene and 6,13-diazapentacene in p-terphenyl recorded at 9GHz at room temperature. Phenazine was excited at 355 nm, the pentacene and 6,13-diazapentacene were excited at 590 and 532 nm respectively. A = enhanced absorption, E = emission. S6 Level of theory

In order to determine the optimal basis set, combining best accuracy with low computational expense, an initial study was performed using available experimental geometries for benzene, naphthalene, anthracene and pentaceneS3,S4. For the larger polyacenes, anthracene and pentacene, the cc-pvdz, cc-pvtz and cc-pvqz basis sets were used. The smaller sizes of naphthalene and benzene permitted the inclusion of the cc-pv5z and, in the case of benzene, the cc-pv6z basis set. TDDFT calculations were performed on these geometries in vacuum. The low lying singlet and triplet excited state energies (in eV) are plotted as a function of basis set size in Figure 3 and Figure 4. The singlet states presented (top row) are the lowest lying singlet states (Sn) with non-zero oscillator strength. Physically, this corresponds to the lowest excitation which may be stimulated by light absorption. The 2nd, 3rd and 4th rows correspond to the 1st, 2nd and 3rd lowest triplet excited states. Solid lines indicate TDDFT calculation results using the singlet ground state electronic conguration as a reference while dashed lines indicate a triplet ground state electron conguration (performed for naphthalene and pentacene triplet states only). Note that the T1 excitation energy is found by the dierence between the singlet and triplet ground state DFT energies. The excitation energies all appear to decrease with basis set size with the exception of the naphthalene T1 triplet state and pentacene T2 triplet state with the singlet ground state as reference. The T1 state of naphthalene and T2 state of pentacene show a slight increase in excitation energy with basis set size for the cc-pv5z and cc-pvqz basis sets, respectively. Performing a TDDFT calculation with a triplet ground state electronic conguration does decrease for increasing basis set size and suggests that explicit treatment of the triplet ground state electronic structure provides an important contribution that in turn aects the higher triplet excited states. As a result, we proceed below with two sets of TDDFT calculations wherein singlet and triplet excited states are computed relative to the singlet and triplet ground state, respectively.

S7 benzene naphthalene

T 1

T 2

T 3

Figure S3: Low lying excited states,Sn, T1, T2, T3 of benzene and naphthalene. Note that th benzene T2 and T3 states are degenerate and instead the T4 state is plotted on the 4 row. Solid lines indicate TDDFT calculation results using the singlet ground state electronic conguration as a reference while dashed lines indicate a triplet ground state electron conguration

S8 anthracene pentacene

T 1

T 2

T 3

Figure S4: Low lying excited states,Sn, T1, T2, T3 of anthracene, pentacene. Solid lines indicate TDDFT calculation results using the singlet ground state electronic conguration as a reference while dashed lines indicate a triplet ground state electron conguration

S9 Further to the discussion above, the excitation energies in Figure 3 and Figure 4 are expected to converge as basis set size increases. This conveniently permits a best choice for the basis set. To the extent that they were tested, the triplet excited states all appear to converge with basis set size. The convergence of the singlet states is less satisfactory. The benzene singlet excitation energy in particular appears to continually decrease with increasing basis set size, even when the basis set was increased to cc-pv6z. The naphthalene singlet excited state energy follows the same trend and continually decrease as basis set size increases. Anthracene and pentacene appear to converge nicely. However, the cc-pv5z basis set was not included due to computational constraints. In view of the data presented in Figure 3 and Figure 4, we have chosen to continue with the cc-pvqz basis set for the remaining TDDFT calculations.

Table S2: Spin-spin component of the D and E zero eld splitting parameters of pentacene.

Pentacene cc-pvdz cc-pvtz cc-pvqz cc-pv5z D (MHz) 859.547 855.651 852.953 852.654 E(MHz) 77.323 79.721 80.620 80.620

The test zero eld splitting parameters of pentacene in vacuum as shown in Table 2 demonstrate minimal basis set dependence when evaluated with cc-pvdz, cc-pvtz, cc-pvqz or cc-pv5z. Accordingly, we opted to evaluate all zero eld splitting parameters with the cc-pvdz basis set.

Correcting Energies

Singlet Excitation Energies

In Table 3 we present transition energies between the ground state and lowest lying photo- absorbing singlet state for the linear polyacenes and the diaza-substituted forms in this study. Our results include calculations in gas phase and in the presence of p-terphenyl like

S10 host crystal via a polarizable continuum model (PCM)S5 of the environment based on static and optical dielectric constants of 5760 and 2.86, respectively, of p-terphenylS6,S7. Literature values for experimental excitation energies of benzene, naphthalene, anthracene, tetracene and pentacene in gas phase are also provided. A comparison of calculated gas phase values to available experimental data is shown in Figure 5a where calculated and experimental values are plotted on the x and y axes, respectively. Values falling along the diagonal indicate calculated values in agreement with experimental data. Benzene and naphthalene are clearly in accord with experimental observations where deviations do not exceed 0.05 eV while anthracene, tetracene and pentacene are not. Anthracene, tetracene and pentacene fall along an o-diagonal line with slope 0.8432 and intercept -0.985 eV. We note that this is consistent with other observations that the errors in DFT appear to be length dependent for the linear polyacenesS17. Using this equation as a correction for our calculated excitation energies reduces the percent error (relative to experimental data) from 16%, 24% and 32% to 0.2%, 0.2% and 0.4% for anthracene, tetracene and pentacene, respectively. This corresponds to an average error of 0.04 eV in our gas phase estimates. This correction is applied to calculated absorption energies for anthracene, tetracene, pentacene and their associated nitrogen substituted derivatives whereas no correction is applied to those of benzene, naphthalene and their derivatives. This follows from calculated absorption energies for benzene and naphalene agreeing well with experimental observations (see table 2) and is supported by agreement between observed and calculated (with no correction) absorption energies for pyrazine and 1,5-naphthyridine, as shown in Figure 5b.

S11 Table S3: S1 excitation energies calculated in gas phase, obtained from published experimental data, calculated in the presence of p-terphenyl like medium and the relative dierence between gas phase and solvated excitation energies.

uncorrected excitation energy (eV) corrected excitation energy (eV) experimental excitation energy (eV)

gas phase (%err) p-terphenyl-like host ∆EPCM gas phase p-terphenyl gas phase benzene 6.94 6.60 -0.34 6.94 6.60 6.95S8,S9 (0.15%) (0.15%) pyrazine 3.54 3.60 0.07 3.54 3.60 3.83S10 (1.34%) (1.34%) naphthalene 4.05 4.01 -0.05 4.05 4.01 4.00S8,S11 (1.36%) (1.36%) 1,5-naphthyridine 4.08 4.25 0.17 4.08 4.25 4.02 S12 S12 2,6-naphthyridine 3.65 3.81 0.16 3.65 3.81 anthracene 2.88 2.83 -0.05 3.42 3.36 3.41S13 (15.67%) (0.19%) phenazine 2.48 2.62 0.15 3.08 3.22 pyrido[2,3-g]quinoline 2.95 2.94 -0.01 3.48 3.46 pyrido[3,4-g]isoquinoline 2.81 2.79 -0.02 3.36 3.33 tetracene 2.11 2.06 -0.05 2.77 2.72 2.78S14,S15 (24.01%) (0.24%) 5,11-diazatetracene 2.23 2.18 -0.05 2.87 2.82 1,7-diazatetracene 2.13 2.11 -0.03 2.79 2.76 2,8-diazatetracene 2.12 2.05 -0.07 2.78 2.70 pentacene 1.58 1.53 -0.05 2.31 2.27 2.31S15,S16 (31.80%) (0.35%) 6,13-diazapentacene 1.50 1.40 -0.09 2.25 2.15 5,12-diazapentacene 1.67 1.64 -0.03 2.39 2.36 1,8-diazapentacene 1.58 1.55 -0.03 2.32 2.29 2,9-diazapentacene 1.58 1.52 -0.06 2.32 2.26 Figure S5: Comparison of calculated and experimental singlet excitation energy data. Uncor- rected data (a) with linear t used used to correct gas phase anthracene, tetracene, pentacene and their diazasubstituted forms. Corrected gas phase data (b) along with experimental values for gas phase pyrazine and 1,5-naphthalene further justifying the use of uncorrected calculations for benzene, naphthalene and their diazasubstituted forms. Corrected values in a crystal host (c) showing qualitative agreement between predicted absorption energies of pentacene, 6,13-diazapentacene and phenazine in a p-terphenyl-like host and measured values in a p-terphenyl (for pentacene and 6,13-diazapentacene) and biphenyl (for phenazine) host crystal.

S13 After correcting the gas phase values as above, the solvation energies are added to obtain corrected estimates of the excitation energies in a p-terphenly like host. The solvation correction, 4EPCM , tabulated in table 3 were obtained by comparing excitation energies for the state of interest from calculations carried out in gas phase and in a PCM solvent as

4EPCM = EPCM − Egas. The nal equation describing our corrected excitation energies,

Ecorr, is Ecorr = (0.8432 × Egas + 0.985eV ) + 4EPCM . In Figure 5c, measured excitation energies of pentacene and 6,13-diazapentacene in a p-terphenyl host (2.10 eV and 2.00 eV, respectively) and of phenazine in biphenyl (3.4 eV) are compared to our calculated values demonstrating a good level of agreement between our predictions and observations. From this we also estimate that energies obtained via this approach carry an associated error of v0.2 eV.

Dark States

The lowest lying absorbing singlet state is not always the state of interest for the singlet- triplet intersystem crossing. If dark states exist between the ground and absorbing singlet state it is much more likely that the excited state will quickly decay to this lower singlet state via IC. Conceptually, this can be understood by noting that singlet-triplet transitions are spin forbidden while singlet-singlet (and triplet-triplet) transitions are not. In practice, this means ISC rates are typically much slower than IC rates. This is the case for the molecules presented in Table 4 below; these must relax to the lowest lying excited singlet in order for ISC to the triplet manifold to occur. Also provided are the excitation energies of the optically active and lowest lying excited singlet state. These molecules have the undesirable property of requiring a higher energy pump laser than the S0 − S1 energy dierence. Because the relaxation process to the lowest singlet state is via internal conversion, which transfers excess energy into vibrational modes dissipating into the crystal medium as heat, these molecules stand out as poor candidates for the room temperature maser. The corrected energies for the lowest lying singlet follow the same procedure as for the

S14 excitation energies discussed above, namely Ecorr = (0.8432 × Egas + 0.985eV ) + 4EPCM .

In this case, however, the solvation correction, 4EPCM = EPCM − Egas, is computed using the lowest lying singlet excitated state energies whereas above the state of interest was the lowest absorbing singlet excited state.

Table S4: Molecules which are optically excited to states above S0 (which is not optically active); maser action in these compounds would involve an additional internal conversion process.

molecule excitation energy (eV) lowest lying singlet (eV) Benzene 6.6 5.25 1,5-naphthyridine 4.25 3.19 2,6-naphthyridine 3.81 3.38

5,11-diazatetracene presents a special case where gas phase calculations reveal the lowest absorbing singlet lies, in uncorrected energies, at 2.23 eV , 0.04 eV above the lowest lying singlet excited state at 2.19 eV. In a PCM solvent, however, the lowest lying excited singlet state is the absorbing state with energy 2.18 eV. Thus a dark state exists below the absorbing singlet in gas phase only, and vanishes in the presence of the PCM environment. We have chosen to handle this case as follows: the excitation energy is computed using the lowest lying absorbing singlet energies of 2.23 eV in gas phase and 2.18 eV in the PCM environment.

This results in a solvation correction,4EPCM , of -0.05 eV. Applying the correcting procedure discussed above, Ecorr = (0.8432 × Egas + 0.985eV ) + 4EPCM , yields a value of 2.82 eV. Considering that the dierence in energy between the absorbing and lowest lying singlet excited states are 0.04 eV in gas phase, the potential errors arising from this switch are likely below the v0.2 eV error previously established.

Triplet Excitation Energies

S18,S19 In Table 5 we provide the calculated and experimentally observed T 1 energies for benzene, naphthalene, anthracene, tetracene and pentacene. The percent error relative to experimental data is shown in parenthesis for the PCM and corrected PCM (described below)

S15 data. These errors correspond to an average error of v0.03eV.

Table S5: T 1 energies in units of eV.

compound T 1 (gas phase) T 1(PCM) T 1 experiment corrected T 1(PCM) Benzene 3.37 3.40 (7.89% ) 3.66 3.69 (0.97% ) Naphthalene 2.30 2.32 (12.89% ) 2.65 2.61 (1.27% ) Anthracene 1.51 1.52 (18.85% ) 1.86 1.81 (2.86% ) Tetracene 0.98 0.98 (21.79% ) 1.25 1.27 (1.59% ) Pentacene 0.60 0.60 (29.80% ) 0.86 0.89 (3.69% )

The triplet excited state electronic structure was evaluated using the lowest lying triplet state as reference. Ample experimental data is available on the low-lying T 1 state. However, there are no experimental measurements on the energies of higher lying triplet states. In our calculations, the excitation energy corresponding to the lowest lying triplet is found by subtracting the ground state energies of the singlet and triple states, both evaluated using a molecular geometry optimized in the T 1 electronic conguration. The computed T 1 energies are compared to existing experimental data in Figure 5 below for benzene, naphthalene, anthracene, tetracene and pentacene. Excitation energies in gas phase and p-terphenyl-like PCM environment are also computed. Clearly there is no noticeable environmental eect, gas phase and PCM results being eectively identical. We therefore continued with the PCM results to generate the correcting function. All triplet excited state energies were computed with TDDFT using the complete expressions, with the exception of 2,6-naphthyridine and phenazine for which the Tamm Danco approximation (TDA) was used. For these two molecules, the triplet ground state wavefunction became unstable in gas phase using TDDFT resulting in an ill-dened 1st excitation energies. The lowest excitations for these molecules are shown in table 6 below. The Tamm Danco 1st excitation energies are very small, consistent with a 1st excitated state nearly degenerate to the true ground state. Other excitation energies show fair agreement between TDDFT and TDA. Furthermore, when the same excitations were computed in the presence of the PCM environment, all excitations

S16 including the 1st were in reasonable agreement with eachother. We chose to err on the side of caution in this case and used the TDA computed triplet excited state energies for 2,6-diazanaphthalene and phenazine.

Table S6: TDDFT and TDA results for 3 low-lying excited state energies (eV) of 2,6-diazanaphthyridine and phenazine in gas phase (GP) and a p-terphenyl like solvent (PCM).

molecule excitation TDDFT - TDA - GP TDDFT - TDA - GP (eV) (eV) PCM (eV) PCM (eV) 2,6-diazanaphthyridine 1 0.0168 0.2242 0.2312 2 0.3792 0.3902 0.665 0.6723 3 0.8865 0.9477 0.8988 0.9489 phenazine 1 0.0218 0.2026 0.216 2 0.9035 0.9477 0.8837 0.9261 3 1.2923 1.4119 1.2572 1.3814

In a similar fashion as with the singlet correction, the corrected energy, Ecorr, for the T 1 energies is found with the equation in Figure 6 describing the best t between calculated and experimental data.

Ecorr = (1.0027 × EPCM + 0.2885eV )

Figure S6: Triplet energies compared with experiment, geometry relaxed in the Triplet state.

S17 Pyrazine and Phenazine T 1 − S0 ISC

Figure S7: Reproduction of Figure 4B of the manuscript here with the addition of the observed ISC rates for two N-substituted polyacenes showing their proximity to our predicted curve (left) and on a log-log scale for clarity.

Deguchi observed a T 1 lifetime of 11 ms for phenazine which corresponds to an ISC rate of 90s−1 while Antheunis et al observed an ISC rate of 200s−1 S20,S21. Becker et al observed an ISC rate of 0.046s−1 for PyrazineS22. These rates are plotted, along with our predicted rates, in Figure 7 (left, and for clarity on a log-log scale in right panel). Compared to these experimental observations of the T 1-S0 ISC rates of pyrazine and phenazine our empirical predictor performs quite well at describing qualitative eects of length and nitrogen substitution.

Population model

The populations of the low lying states participating in masing (S0, S1 and T 1) were evaluated assuming steady state conditions in order to evaluate the feasibility of maser operation in continuous-wave mode. This task was facilitated by invoking a simplied model incorpo- rating the kST and kTS ISC rates as evaluated in the manuscript together with a parameter kex describing the maser excitation rate. The excitation rate incorporates physical and molecular properties such as laser power, photon absorption eciency and the rates of S1 − S0

uorescence and IC. Furthermore, the IC transition to T 1 from the higher lying triplet state,

T n, is assumed to be suciently fast such that the eective transition rate to T 1 can be

S18 approximated by the S1 − Tn ISC rate. A schematic diagram of this model is provided in Figure 5 of the manuscript. Based on the above simplifying assumptions we arrive at the following equations describing population dynamics of the S0, S1 and T 1 states

dNS0 dt = −NS0 kex + NT1 kTS

dNS1 dt = NS0 kex − NS1 kST

dNT 1 dt = NS1 kST − NT1 kTS assuming and setting the above derivatives to zero the steady state NS0 + NS1 + NT1 = N populations of the S0, S1 and T 1 states in terms of kex are

S0 = N/ (1 + kex/kST + kex/kTS)

S1 = N/ (1 + kST /kex + kST /kTS)

T 1 = N/ (1 + kTS/kex + kTS/kST ) Where N is set to 1 in the manuscript and fractional occupations are discussed.

Zero eld splitting

Table 7 below provides the D and E zero eld splitting parameters calculated for all molecules in this study along with published experimentalS23S27 values. The zero eld splitting parameters D and E, which describe the splitting between TZ and the midpoint between TX and T Y and between TX and TY , respectively, were computed using the method developed by Neese and co-workers and implemented in the ORCA packageS28,S29. Also shown are the corrected splitting terms Dcorr and Ecorr and the estimated error relative to experimental observations, which is notably reduced for the corrected values. The average error is 30 MHz for D and E.

S19 Table S7: Calculated Zero Field Splitting parameters D and E along with experimental values Dexp and Eexp and corrected theoretical values Dcorr and Ecorr. All values are in MHz.

D E Dexp Eexp Dcorr Ecorr Benzene 5524.88 28.78 4738 192 158 (16.61% ) (85.01% ) (17.63% ) Naphthalene 1614.38 80.64 3012 414 2992 378 (46.40% ) (80.52% ) (0.66% ) (8.70%) Anthracene 1205.47 60.86 2143 252 2170 294 (43.75% ) (75.85% ) (1.26% ) (16.71% ) Tetracene 963.83 31.18 1651 126 1684 168 (41.62% ) (75.26% ) (2.01% ) (33.58%) Pentacene 804.34 0.30 (99.42% 1404 52 1364 37 (42.71% ) ) (2.87% ) (28.03%)

Figure S8: Comparison of calculated and observed Zero Field Splitting D (7A) and E (7B) parameters for the linear polyacenes.

The calculated D and E parameters are compared with experimental measurements in Figure 8a and 8b, respectively, for benzene, naphthalene, anthracene, tetracene and pentacene. Clearly, with the exception of benzene's D splitting, one can see that the D and E parameters are consistently underestimated for the linear polyacenes. Linear ts of the D and E values indicate that D values are underestimated by roughly 1 while E values are un- 2

S20 derestimated by roughly 1 . One can also see, with the exception of the benzene D splitting, 4 a well behaved and systematic trend in the error arising from the this DFT based approach to estimated zero eld splitting parameters. As was done for the optical excitation energies and T 1 − S0 splittings, we use the equations in Figure 8A and 8B as empirical corrections for our DFT results.

Dcorr = 2.0103 × D − 253.33MHz

Ecorr = 4.2388 × E − 36.156MHz

The correction Dcorr is applied to all but benzene and pyrazine while the correction Ecorr is applied to all molecules. The D values calculated for Benzene (5525 MHz) and Pyrazine (5354 MHz) were found to be quite large relative to the other calculated values and did not fall along the line used for correcting calculated D values.

S21 Tabulated results

Table S8: Empirically corrected (for DFT errors; vide supra) excitation energies, energy gaps, ISC rates and ZFS parameters (D and E) for all molecules in a p-terphenyl-like host.

−7 −4 Compound Name excita- S1 − Tn (eV) kISC × 10 (s-1) T 1 − S0(eV) kISC × 10 (s-1) ZFS ZFS tion energies D E (MHz)

(eV) (MHz)

benzene 6.60 0.12 2.82 3.69 2.64E-06 5525 158

pyrazine 3.60 0.58 1.34 3.14 1.25E-05 5355 1780

naphthalene 4.01 0.20 1.88 2.61 7.36E-05 2992 378

1,5-naphthyridine 4.25 0.15 2.30 2.41 1.61E-04 8063 903

2,6-naphthyridine 3.81 0.26 1.61 2.43 1.45E-04 3209 426

anthracene 3.36 0.04 15.55 1.81 2.48E-03 2170 294

phenazine 3.22 0.27 1.60 1.85 1.99E-03 2268 360

pyrido[2,3-g]quinoline 3.46 0.38 1.43 1.87 1.86E-03 2289 395

pyrido[3,4-g]isoquinoline 3.33 0.33 1.49 1.73 3.93E-03 2253 220

tetracene 2.72 0.08 4.56 1.27 7.52E-02 1684 168

5,11-diazatetracene 2.82 0.06 7.45 1.43 2.35E-02 1732 161

1,7-diazatetracene 2.76 0.02 76.03 1.29 6.37E-02 1750 243

2,8-diazatetracene 2.70 0.01 307.09 1.23 1.05E-01 1725 130

pentacene 2.27 0.25 1.66 0.89 2.25E+00 1364 37

6,13-diazapentacene 2.15 0.29 1.55 0.87 2.85E+00 1415 117

5,12-diazapentacene 2.36 0.24 1.67 0.99 8.25E-01 1424 53

1,8-diazapentacene 2.29 0.20 1.84 0.90 1.97E+00 1400 84

2,9-diazapentacene 2.26 0.22 1.77 0.87 2.91E+00 1385 70

Energy Level Diagrams

The following energy level diagrams were produced to summarize the calculation results and outline the potential mechanism for maser action among these candidate molecules. The singlet and triplet manifolds appear on the left and right hand side of the gure, the energy scale is relative to the lowest lying singlet energy. The energies of relevant excited states are provided in eV and nm in normal type. The italic type, for T1, indicates an excitation energy computed using the relaxed geometry for the T1 triplet state. Key elements of the maser process pump, internal conversion (IC) and intersystem crossing (ISC) are clearly labelled.

S22 Benzene 8

(6.6, 187.98) IC

6 (5.13, 241.8) (5.25, 236.08) ISC IC (4.72, 262.94) ISC (4.39, 282.55) 4 (3.69, 335.78) ev 2

0 pump singlets triplets

S23 Pyrazine 5 4 (3.6, 344.05) ISC 3 IC ISC (3.03, 409.86) (3.14, 394.64) 2 ev 1 0 pump singlets triplets 1 2

S24 Naphthalene 6 5

(4.01, 309.43) ISC 4 IC (3.81, 325.44) 3 ISC (2.97, 417.2) (2.61, 474.8) 2 ev 1 0 pump singlets triplets 1 2

S25 1,5_diazanaphthalene 6 5 (4.25, 291.86) IC 4 (3.19, 389.13) ISC IC ISC (3.03, 408.59) 3 (2.41, 514.98)

ev 2 1 0 pump singlets triplets 1 2

S26 2,6_diazanaphthalene

4(3.81, 325.39) IC (3.38, 366.75) ISC (3.12, 397.63) IC 3 ISC (2.89, 429.48) (2.43, 509.33) 2 ev 1 0 pump singlets triplets 1 2

S27 Anthracene 5 4 (3.36, 368.58) ISC IC (3.32, 373.12) 3 2 ISC (1.98, 625.98) (1.81, 684.57) ev 1 0 pump singlets triplets 1 2

S28 Phenazine 5 4 (3.22, 385.0) ISC (2.95, 419.98) 3 IC (2.24, 552.98) 2 ISC (2.03, 611.93) (1.85, 669.18) ev 1 0 pump singlets triplets 1 2

S29 Pyrido[2,3-g]quinoline 5 4 (3.27, 378.91) (3.46, 358.05) ISC IC (3.08, 402.11) 3 (3.08, 403.17) ISC (2.17, 571.62) 2 (1.87, 664.5) ev 1 0 pump singlets triplets 1 2

S30 Pyrido[3,4-g]isoquinoline 5 4 (3.33, 372.2) ISC (3.0, 412.9) 3 IC (2.85, 435.19)

2 ISC (1.96, 633.77) (1.73, 718.27) ev 1 0 pump singlets triplets 1 2

S31 Tetracene

3 (2.72, 456.62) ISC IC (2.63, 471.36) 2 ISC (1.32, 937.18) ev 1 (1.27, 976.51)

0 pump singlets triplets 1

S32 5,11-diazatetracene

(2.75, 450.37) 3(2.82, 440.45) ISC IC (2.65, 468.76) (2.23, 555.3) 2 ISC (1.5, 829.4) ev 1 (1.43, 865.17)

0 pump singlets triplets 1

S33 1-7,diazatetracene

4 (2.74, 452.03) (2.74, 452.62) 3(2.76, 449.68) ISC IC (2.74, 452.95) 2 ISC (1.38, 895.67) ev 1 (1.29, 959.72)

0 pump singlets triplets 1

S34 2,8-diazatetracene

4 (2.69, 460.32) 3 (2.65, 467.22) (2.7, 458.81) ISC IC (2.63, 471.48) 2 ISC (1.32, 942.16) ev 1 (1.23, 1010.52)

0 pump singlets triplets 1

S35 Pentacene 4

3 (2.27, 546.89) ISC 2 IC (2.02, 613.42)

ev 1 ISC (0.87, 1419.44) (0.89, 1390.7) 0 pump singlets triplets 1

S36 6-13,diazapentacene 4

(2.15, 575.67) ISC (1.87, 664.82) 2 IC (1.81, 685.09)

ev 1 ISC (0.84, 1468.5) (0.87, 1425.64) 0 pump singlets triplets 1

S37 5,12_diazapentacene 4

3 (2.36, 524.85) ISC 2 IC (2.12, 584.84)

(1.0, 1243.3) ev 1 ISC (0.99, 1252.87) 0 pump singlets triplets 1

S38 1,8_diazapentacene 4

3 (2.29, 542.4) ISC 2 IC (2.08, 595.28)

ev 1 ISC (0.9, 1372.07) (0.9, 1371.63) 0 pump singlets triplets 1

S39 2-9,diazapentacene 4

3 (2.26, 549.28) ISC 2 IC (2.04, 608.11)

ev 1 ISC (0.87, 1429.6) (0.87, 1428.6) 0 pump singlets triplets 1

References

(S1) Breeze, J.; Tan, K. J.; Richards, B.; Sathian, J.; Oxborrow, M.; Alford, N. M. En- hanced Magnetic Purcell Eect in Room-Temperature Masers. Nat. Commun. 2015, 6, 6215.

(S2) Stoll, S.; Schweiger, A. EasySpin, a Comprehensive Software Package for Spectral Simulation and Analysis in EPR. J. Magn. Reson. 2006, 178, 4255.

(S3) The Cambridge Crystallographic Data Centre. www.ccdc.cam.ac.uk.

(S4) NIST Chemistry WebBook, NIST Standard Reference Database Number 69 ; Na-

S40 tional Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov , (retrieved March 31, 2015).

(S5) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 29993093.

(S6) Selvakumar, S.; Murugaraj, R.; Viswanathan, E.; Sankar, S.; Sivaji, K. Dielectric Properties and Relaxation Mechanism of Organic Trans-Stilbene and p-Terphenyl Molecular Crystals Using Impedance Spectroscopy. J. Mol. Struct. 2014, 1056, 152156.

(S7) Tarasenko, O. Features of Charge Pairs Recombination in the Track Regions of Organic Solid Scintillators. Funct. Mater. 2012, 19, 421428.

(S8) Hashimoto, T.; Nakano, H.; Hirao, K. Theoretical Study of the Valence Pi->Pi* Ex- cited States of Polyacenes: Benzene and Naphthalene. J. Chem. Phys. 1996, 104, 62446258.

(S9) Hiraya, A.; Shobatake, K. Direct Absorption-Spectra of Jet-Cooled Benzene in 130-260-nm. J. Chem. Phys. 1991, 94, 77007706.

(S10) Yamazaki, I.; Murao, T.; Yamanaka, T.; Yoshihara, K. Intramolecular Electronic Relaxation and Photoisomerization Processes in the Isolated Azabenzene Molecules Pyridine, Pyrazine and Pyrimidine. Farad. Discuss. 1983, 75, 395405.

(S11) George, G. A.; Morris, G. C. The Intensity of Absorption of Naphthalene from 30 000 cm1 to 53 000 cm1. J. Mol. Spectrosc 1968, 26, 6771.

(S12) Chappell, P. J.; Fischer, G.; Reimers, J. R.; Ross, I. G. Electronic-Spectrum of 1,5-Naphthyridine - Theoretical Treatment of Vibronic Coupling. J. Mol. Spectrosc. 1981, 87, 316330.

S41 (S13) Ferguson, J.; Reeves, L. W.; Schneider, W. G. Vapor Absorption Spectra and Oscil- lator Strengths of Naphthalene, Anthracene, and Pyrene. Can. J. Chem. 1957, 35, 11171136.

(S14) Dick, B.; Zinghar, E.; Haas, Y. Spectral Hole-Burning of Tetracene and Tetracene Argon Complexes in a Supersonic Jet. Chem. Phys. Lett. 1991, 187, 571578.

(S15) Hartmann, M.; Lindinger, A.; Toennies, J. P.; Vilesov, A. F. The Phonon Wings in the (S-1 <- S-0) Spectra of Tetracene, Pentacene, Porphin and Phthalocyanine in Liquid Helium Droplets. Phys. Chem. Chem. Phys. 2002, 4, 48394844.

(S16) Heinecke, E.; Hartmann, D.; Muller, R.; Hese, A. Laser Spectroscopy of Free Pentacene Molecules (I): The Rotational Structure of the Vibrationless S-1 <- S-0 Transition. J. Chem. Phys. 1998, 109, 906911.

(S17) Grimme, S.; Parac, M. Substantial Errors from Time-Dependent Density Functional Theory for the Calculation of Excited States of Large Pi Systems. Chemphyschem 2003, 4, 292295.

(S18) Thompson, N. J.; Wilson, M. W. B.; Congreve, D. N.; Brown, P. R.; Scherer, J. M.; Bischof, T. S.; Wu, M. F.; Geva, N.; Welborn, M.; Van Voorhis, T. et al. Energy Har- vesting of Non-Emissive Triplet Excitons in Tetracene by Emissive PbS Nanocrystals. Nat. Mater. 2014, 13, 10391043.

(S19) Hajgato, B.; Szieberth, D.; Geerlings, P.; De Proft, F.; Deleuze, M. S. A Benchmark Theoretical Study of the Electronic Ground State and of the Singlet-Triplet Split of Benzene and Linear Acenes. J. Chem. Phys. 2009, 131, 224321.

(S20) Antheunis, D. A.; Schmidt, J.; van der Waals, J. H. Spin-Forbidden Radiationless Processes in Isoelectronic Molecules: Anthracene, Acridine and Phenazine. Mol. Phys. 1974, 27, 15211541.

S42 (S21) Deguchi, M.; Suzuki, D.; Ito, R.; Matsumoto, M.; Yagi, M. Time-resolved Electron Paramagnetic Resonance of the Lowest Excited Triplet State of Phenazinium Cation. Spectrochim. Acta Mol. Biomol. Spectrosc. 2005, 61, 11471151.

(S22) Becker, I.; Cheshnovsky, O. The Decay of Triplet Pyrazine and Pyrazine-D-4, in Su- personic Jets - Isotope Eects. J. Chem. Phys. 1994, 101, 36493655.

(S23) Vergragt, P. J.; Vanderwaals, J. H. Lowest Triplet-State of Benzene - Dierences in Electronic-Structure in 2 Crystalline Modications of a Cyclohexane Host. Chem. Phys. Lett. 1975, 36, 283289.

(S24) Hutchison, C. A.; Mangum, B. W. Paramagnetic Resonance Absorption in Naphtha- lene in Its Phosphorescent State. J. Chem. Phys. 1961, 34, 908922.

(S25) Grivet, J. P. Electron Spin Resonance of Phosphorescent Anthracene. Chem. Phys. Lett. 1969, 4, 104106.

(S26) Yu, H. L.; Lin, T. S.; Sloop, D. J. An Electron-Spin Echo Study of the Photo- Excited Triplet-State of Tetracene in Para-Terphenyl Crystals at Room-Temperature. J. Chem. Phys. 1983, 78, 21842188.

(S27) Lang, J.; Sloop, D. J.; Lin, T. S. Dynamics of p-Terphenyl Crystals at the Phase Transition Temperature: A Zero-Field EPR Study of the Photoexcited Triplet State of Pentacene in p-Terphenyl Crystals. J. Phys. Chem. A 2007, 111, 47314736.

(S28) Neese, F. Calculation of The Zero-Field Splitting Tensor on the Basis of Hybrid Den- sity Functional and Hartree-Fock Theory. J. Chem. Phys. 2007, 127, 164112.

(S29) Neese, F. The ORCA Program System. WIREs-Comput. Mol. Sci. 2012, 2, 7378.

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