Supporting information for:

Molecular Design of a Room-Temperature

Maser

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

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

Hors�eld,†,‡,¶ 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: s.bogatko@ic.ac.uk

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 % pen-

tacene.

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 per-

formed 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‖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, Lon-

don, UK#School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road E1 4NS,

London, UK

S2

extinction coe�cient and the measured thickness of the sample.

Figure S1: UV/Vis spectra of Pentacene and 6,13-diazapentacene in p-terphenyl (top) andphenazine 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 spin�spin interaction between the mag-

netic dipoles and, to a lesser extent, from spin�orbit 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

di�er considerably from those predicted by Boltzmann distribution. Particularly, popula-

tion di�erences, 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 andrelative zero-�eld populations derived from simulation of the TR-EPR spectrarecorded 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 relativesimulations (red lines) of powder samples of phenazine in biphenyl and pentaceneand 6,13-diazapentacene in p-terphenyl recorded at 9GHz at room temperature.Phenazine was excited at 355 nm, the pentacene and 6,13-diazapentacene wereexcited 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 0.12Pentacene 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 samplesof phenazine in biphenyl and pentacene and 6,13-diazapentacene in p-terphenyl recordedat 9GHz at room temperature. Phenazine was excited at 355 nm, the pentacene and6,13-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 con�guration as a reference while

dashed lines indicate a triplet ground state electron con�guration (performed for naphthalene

and pentacene triplet states only). Note that the T1 excitation energy is found by the

di�erence 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 con�guration 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 a�ects 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

Sn

T 1

T 2

T 3

Figure S3: Low lying excited states,Sn, T1, T2, T3 of benzene and naphthalene. Note thatbenzene T2 and T3 states are degenerate and instead the T4 state is plotted on the 4th

row. Solid lines indicate TDDFT calculation results using the singlet ground state elec-tronic con�guration as a reference while dashed lines indicate a triplet ground state electroncon�guration

S8

anthracene pentacene

Sn

T 1

T 2

T 3

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

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 ofpentacene.

Pentacene cc-pvdz cc-pvtz cc-pvqz cc-pv5z

D (MHz) 859.547 855.651 852.953 852.654E(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, re-

spectively. Values falling along the diagonal indicate calculated values in agreement with

experimental data. Benzene and naphthalene are clearly in accord with experimental obser-

vations 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 (rel-

ative 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

TableS3:S1excitationenergiescalculatedin

gasphase,obtainedfrom

publishedexperimentaldata,calculated

inthepresence

ofp-terphenyllikemedium

andtherelativedi�erence

betweengasphase

andsolvatedexcitation

energies.

uncorrectedexcitationenergy(eV)

correctedexcitationenergy(eV)

experi-

mental

excitation

energy

(eV)

gasphase

(%err)

p-terp

henyl-likehost

∆E

PCM

gasphase

p-terp

henyl

gasphase

benzene

6.94

(0.15%)

6.60

-0.34

6.94

(0.15%)

6.60

6.95S8,S9

pyrazine

3.54

(1.34%)

3.60

0.07

3.54

(1.34%)

3.60

3.83S10

naphthalene

4.05

(1.36%)

4.01

-0.05

4.05

(1.36%)

4.01

4.00S8,S11

1,5-naphthyridine

4.08

4.25

0.17

4.08

4.25

4.02S12

2,6-naphthyridine

3.65

3.81

0.16

3.65

3.81

anthracene

2.88

(15.67%)

2.83

-0.05

3.42

(0.19%)

3.36

3.41S13

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

(24.01%)

2.06

-0.05

2.77

(0.24%)

2.72

2.78S14,S15

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

(31.80%)

1.53

-0.05

2.31

(0.35%)

2.27

2.31S15,S16

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

S12

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, pentaceneand their diazasubstituted forms. Corrected gas phase data (b) along with experimental val-ues for gas phase pyrazine and 1,5-naphthalene further justifying the use of uncorrectedcalculations for benzene, naphthalene and their diazasubstituted forms. Corrected values ina crystal host (c) showing qualitative agreement between predicted absorption energies ofpentacene, 6,13-diazapentacene and phenazine in a p-terphenyl-like host and measured val-ues 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 di�erence. 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 notoptically active); maser action in these compounds would involve an additionalinternal conversion process.

molecule excitation energy (eV) lowest lying singlet (eV)

Benzene 6.6 5.251,5-naphthyridine 4.25 3.192,6-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 di�erence 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

In Table 5 we provide the calculated and experimentally observed T 1 energiesS18,S19 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 con�guration. 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 e�ect,

gas phase and PCM results being e�ectively 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-de�ned 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-terphenyllike solvent (PCM).

molecule excitation TDDFT -GP (eV)

TDA - GP(eV)

TDDFT -PCM (eV)

TDA -PCM (eV)

2,6-diazanaphthyridine 1 � 0.0168 0.2242 0.23122 0.3792 0.3902 0.665 0.67233 0.8865 0.9477 0.8988 0.9489

phenazine 1 � 0.0218 0.2026 0.2162 0.9035 0.9477 0.8837 0.92613 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 theobserved ISC rates for two N-substituted polyacenes showing their proximity to our predictedcurve (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 experi-

mental observations of the T 1-S0 ISC rates of pyrazine and phenazine our empirical predictor

performs quite well at describing qualitative e�ects of length and nitrogen substitution.

Population model

The populations of the low lying states participating in masing (S0, S1 and T 1) were evalu-

ated assuming steady state conditions in order to evaluate the feasibility of maser operation

in continuous-wave mode. This task was facilitated by invoking a simpli�ed 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 molec-

ular properties such as laser power, photon absorption e�ciency 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 su�ciently fast such that the e�ective 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= −NS0kex +NT1kTS

dNS1

dt= NS0kex −NS1kST

dNT1

dt= NS1kST −NT1kTS

assuming NS0 + NS1 + NT1 = N and setting the above derivatives to zero the steady state

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 experimentalS23�S27 values. The zero �eld splitting pa-

rameters 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 ex-perimental 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(16.61% )

28.78(85.01% )

4738 192 � 158(17.63%

)Naphthalene 1614.38

(46.40% )80.64

(80.52% )3012 414 2992

(0.66% )378

(8.70%)Anthracene 1205.47

(43.75% )60.86

(75.85% )2143 252 2170

(1.26% )294

(16.71%)

Tetracene 963.83(41.62% )

31.18(75.26% )

1651 126 1684(2.01% )

168(33.58%)

Pentacene 804.34(42.71% )

0.30 (99.42%)

1404 52 1364(2.87% )

37(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 pen-

tacene. 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 12while E values are un-

S20

derestimated by roughly 14. One can also see, with the exception of the benzene D splitting,

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 ap-terphenyl-like host.

Compound Name excita-tion

energies

(eV)

S1 − Tn (eV) kISC × 10−7(s-1) T1 − S0(eV) kISC × 10−4 (s-1) ZFS

D

(MHz)

ZFS

E (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

2

0

2

4

6

8

ev

(5.25, 236.08)

(6.6, 187.98)

pump

IC

(4.39, 282.55)(3.69, 335.78)

(4.72, 262.94)(5.13, 241.8)ISC IC

ISC

singlets triplets

Benzene

S23

21012345

ev

(3.6, 344.05)(3.6, 344.05)

pump

(3.03, 409.86)(3.14, 394.64)

ISCIC ISC

singlets triplets

Pyrazine

S24

210123456

ev

(4.01, 309.43)(4.01, 309.43)

pump

(2.97, 417.2)(2.61, 474.8)

(3.81, 325.44)ISC ICISC

singlets triplets

Naphthalene

S25

210123456

ev

(3.19, 389.13)

(4.25, 291.86)

pump

IC

(3.03, 408.59)(2.41, 514.98)

ISC IC ISC

singlets triplets

1,5_diazanaphthalene

S26

21012345

ev

(3.38, 366.75)(3.81, 325.39)

pump

IC

(2.89, 429.48)(2.43, 509.33)

(3.12, 397.63)ISC IC ISC

singlets triplets

2,6_diazanaphthalene

S27

21012345

ev

(3.36, 368.58)(3.36, 368.58)

pump

(1.98, 625.98)(1.81, 684.57)

(3.32, 373.12)ISC IC

ISC

singlets triplets

Anthracene

S28

21012345

ev

(3.22, 385.0)(3.22, 385.0)

pump

(2.03, 611.93)(1.85, 669.18)

(2.24, 552.98)

(2.95, 419.98)ISC IC

ISC

singlets triplets

Phenazine

S29

21012345

ev

(3.46, 358.05)(3.46, 358.05)

pump

(2.17, 571.62)(1.87, 664.5)

(3.08, 403.17)(3.08, 402.11)(3.27, 378.91)

ISC IC

ISC

singlets triplets

Pyrido[2,3-g]quinoline

S30

21012345

ev

(3.33, 372.2)(3.33, 372.2)

pump

(1.96, 633.77)(1.73, 718.27)

(2.85, 435.19)(3.0, 412.9)ISC IC

ISC

singlets triplets

Pyrido[3,4-g]isoquinoline

S31

2

1

0

1

2

3

4

ev

(2.72, 456.62)(2.72, 456.62)

pump

(1.32, 937.18)(1.27, 976.51)

(2.63, 471.36)ISC IC

ISC

singlets triplets

Tetracene

S32

2

1

0

1

2

3

4

ev

(2.82, 440.45)(2.82, 440.45)

pump

(1.5, 829.4)(1.43, 865.17)

(2.23, 555.3)(2.65, 468.76)(2.75, 450.37)

ISC IC

ISC

singlets triplets

5,11-diazatetracene

S33

2

1

0

1

2

3

4

ev

(2.76, 449.68)(2.76, 449.68)

pump

(1.38, 895.67)(1.29, 959.72)

(2.74, 452.95)(2.74, 452.62)(2.74, 452.03)

ISC IC

ISC

singlets triplets

1-7,diazatetracene

S34

2

1

0

1

2

3

4

ev

(2.7, 458.81)(2.7, 458.81)

pump

(1.32, 942.16)(1.23, 1010.52)

(2.63, 471.48)(2.65, 467.22)(2.69, 460.32)

ISC IC

ISC

singlets triplets

2,8-diazatetracene

S35

2

1

0

1

2

3

4ev

(2.27, 546.89)(2.27, 546.89)

pump

(0.87, 1419.44)(0.89, 1390.7)

(2.02, 613.42)ISC IC

ISC

singlets triplets

Pentacene

S36

2

1

0

1

2

3

4ev

(2.15, 575.67)(2.15, 575.67)

pump

(0.84, 1468.5)(0.87, 1425.64)

(1.81, 685.09)(1.87, 664.82)ISC

IC

ISC

singlets triplets

6-13,diazapentacene

S37

2

1

0

1

2

3

4

ev

(2.36, 524.85)(2.36, 524.85)

pump

(1.0, 1243.3)(0.99, 1252.87)

(2.12, 584.84)ISC IC

ISC

singlets triplets

5,12_diazapentacene

S38

2

1

0

1

2

3

4

ev

(2.29, 542.4)(2.29, 542.4)

pump

(0.9, 1372.07)(0.9, 1371.63)

(2.08, 595.28)ISC IC

ISC

singlets triplets

1,8_diazapentacene

S39

2

1

0

1

2

3

4ev

(2.26, 549.28)(2.26, 549.28)

pump

(0.87, 1429.6)(0.87, 1428.6)

(2.04, 608.11)ISC IC

ISC

singlets triplets

2-9,diazapentacene

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