Exciplex Stabilization in Asymmetric Acene Dimers Rachel Ann Krueger, and Guillaume Blanquart J

Home , Acene

Subscriber access provided by Caltech Library A: Spectroscopy, Molecular Structure, and Quantum Chemistry Exciplex Stabilization in Asymmetric Acene Dimers Rachel Ann Krueger, and Guillaume Blanquart J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 11 Feb 2019 Downloaded from http://pubs.acs.org on February 11, 2019

Just Accepted

“Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties. Page 1 of 19 The Journal of Physical Chemistry

1 2 3 4 Exciplex Stabilization in Asymmetric Acene 5 6 Dimers 7 8 † ∗,‡ 9 Rachel A. Krueger and Guillaume Blanquart 10 11 Department of Chemistry, California Institute of Technology, Pasadena, California 91125, 12 United States, and Department of Mechanical Engineering, California Institute of 13 Technology, Pasadena, California 91125, United States. Phone: 1-626-395-4306. Email: 14 [email protected] 15 16 17 18 19 Abstract state is derived. Moderate exciplex stabiliza- 20 tion observed for the benzene-naphthalene and 21 Excimers play an important role in photochem- 22 naphthalene-anthracene exciplexes results from 23 ical processes ranging from singlet fission to a mixture of charge transfer and exciton delo- 24 DNA damage, and the characteristic red shift calization. 25 in fluorescence spectra associated with excimer 26 formation can provide information about ag- 27 gregate formation and the orientation of chro- 1. Introduction 28 mophores. When a mixture of chromophores is 29 Characterization of exciplexes represents an im- 30 present, exciplex formation may lead to spec- 31 tral characteristics distinct from those of ei- portant step in understanding the dynamic 32 ther monomer or the corresponding excimers. photophysical and photochemical processes of 33 To predict the effects of aggregation in a sys- multi-chromophore systems. Exciplex forma- 34 tion occurs when two or more molecules are 35 tem containing a mixture of small acenes, bind- involved in a photoabsorption event, often but 36 ing energies and minimum-energy geometries not necessarily beginning when the absorption 37 have been calculated for three mixed S1 exci- 38 plexes. Benchmark CASSCF/NEVPT2 mul- of one molecule perturbs the electronic state of 39 tireference binding energies of 18.2 kJ/mol, a neighbor. The resulting structure is called 40 an excimer—an excited dimer—in the case that 41 27.7 kJ/mol, and 49.3 kJ/mol are reported for 42 the benzene-naphthalene, benzene-anthracene, the molecules involved are identical, or as an 43 and naphthalene-anthracene exciplexes, respec- exciplex—an excited complex—in other cases. 44 tively. TDDFT calculations have been per- The wave function for an arbitrary exciplex con- 45 formed using a range of exchange-correlation taining molecules P and Q may be described as 46 a combination of Frenkel excitations, in which 47 functionals, showing that many functionals per- 48 form inconsistently, and the error in binding electrons are excited from donor orbitals into 49 energy often depends on the character of the acceptor orbitals located on the same molecule, ∗ ∗ 50 monomer excitation from which the exciplex P Q and PQ , and charge transfer states, in 51 which the donor and acceptor orbitals lie on 52 ∗To whom correspondence should be addressed different molecules, P ·−Q·+ and P ·+Q·−.1,2 Ex- 53 † Department of Chemistry, California Institute of ciplex formation often results in the stabiliza- 54 Technology, Pasadena, California 91125, United States 55 ‡Department of Mechanical Engineering, California tion of complexes at geometries that would be 56 Institute of Technology, Pasadena, California 91125, unfavorable or repulsive in the ground state.1,3 57 United States. Phone: 1-626-395-4306. Email: Recent interest in exciplex formation has 58 [email protected] been driven by efforts to determine singlet fis- 59 60 ACS Paragon Plus Environment 1 The Journal of Physical Chemistry Page 2 of 19

sion mechanisms, in which exciplexes repre- portant exciplexes represents a way forward, 1 2 sent intermediate or trap states in the conver- provided that computationally tractable meth- 3 sion of a singlet exciton into two lower-energy ods with acceptable accuracy are available. 4 triplet excitons.4–7 Long-lived charge-transfer- To date, most ab initio studies have focused 5 dominated exciplexes have been observed in on the smallest acene excimers. Binding en- 6 photoexcited DNA and RNA strands.8 ergies and singlet excitation energies for the 7 8 In laser-induced fluorescence (LIF) experi- benzene S1 excimer have been characterized us- 18,19 20 9 ments, excimer emission produces broad, struc- ing CASPT2, coupled cluster methods, 10 tureless peaks that are red-shifted with respect and equation-of-motion coupled cluster meth- 11 to the corresponding emissions from the parent ods.21 Binding energies have been evaluated 12 molecules due to excimer stabilization.9 In ex- at the global minimum potential energy con- 13 14 periments involving a single chromophore, ex- figuration for the excimer, corresponding to 15 cimer fluorescence is readily identified. When a an eclipsed configuration, with one monomer 16 wide range of chromophores are present, com- translated along the intermolecular coordinate 17 plexes containing two different chromophores with respect to the other. The results range 18 are likely to be more prevalent than dimers of from 33-48 kJ/mol19,20 when corrected for basis 19 10 20 a single chromophore, and it it not a pri- set superposition error (BSSE) by the counter- 22 21 ori apparent whether the emission from these poise (CP) method. Even the lowest binding 22 complexes will be distinguishable from the par- energy obtained is more than twice as large as 23 ent monomer emissions. This question is of the CP-corrected benchmark CCSD(T) binding 24 paramount importance for combustion systems, energies obtained for the ground state benzene 25 23 26 where LIF represents a promising technique for dimer in a parallel-displaced configuration. 11 27 characterizing soot precursors, which might Naphthalene and larger acenes are charac- 28 consist of PAH van der Waals dimers12 or even terized by two close-together, low-lying singlet 29 pairs of PAHs connected by aliphatic linkers13 π → π∗ excited states, polarized along the 30 capable of forming intramolecular exciplexes. two axes of the molecules. The B state, la- 31 2u 32 Accurately assigning fluorescence peaks, beled La, is described almost completely by a 33 though, will require a broad database of ex- HOMO→LUMO transition, while the B3u Lb 34 ciplex binding energies, the major contribu- state is the result of a mixed HOMO-1→LUMO 35 tor to the characteristic redshift.9,10 Exciplex and HOMO→LUMO+1 transition. In the 36 binding energy is defined here as the potential valence-bond theory framework, the La state is 37 24 38 energy difference between the minimum energy ionic and the Lb state covalent. 39 exciplex configuration and the two separated Time-dependent density functional theory 40 monomers, one of them excited. (TDDFT) calculations performed using hybrid 41 For ground state complexes, a roughly lin- exchange-correlation functionals tend to under- 42 ear scaling relationship between PAH molecu- estimate the energy of the La state, and this er- 43 25,26 44 lar weight and noncovalent dimer binding en- ror increases with increasing acene size. Al- 45 ergy has emerged for several homodimers,14,15 though the ionic description of the state hints at 16 46 the benzene-naphthalene heterodimer, and charge separation, the La state cannot be clas- 47 the naphthalene-anthracene heterodimer.17 For sified as a “true” charge transfer state,27,28 indi- 48 PAH exciplexes, though, the effects of monomer cating that the error is not directly attributable 49 50 substitution remain unclear—no binding ener- to the well-known failure of hybrid TDDFT 51 gies have yet been reported for mixed exciplexes to capture charge transfer behavior. Use of 52 containing small, unsubstituted PAHs. double-hybrid functionals improves La energies 53 Because of the large number of exciplexes that substantially.25,29 54 55 may be formed from even a moderate number The energy of the Lb state, on the other hand, 56 of small PAHs, characterizing each one exper- tends to be overestimated by TDDFT calcula- 57 imentally would represent a monumental task. tions using hybrid, double-hybrid, and range- 58 Obtaining accurate theoretical estimates of im- separated functionals. Errors remain roughly 59 60 ACS Paragon Plus Environment 2 Page 3 of 19 The Journal of Physical Chemistry

constant with acene size. For several hybrid 2. Computational Methods 1 2 functionals, the combination of errors in both To avoid the pitfalls associated with the lowest- 3 state energies leads to the incorrect La–Lb state 4 ordering for the naphthalene monomer.25,26 energy electronic states of the small acenes, ∗ 5 For the naphthalene excimer (NN) , the La multireference complete active space self- 6 and Lb-derived states cross at an intermolecu- consistent field (CASSCF) calculations with 7 30,31 lar separation of 4.5 A,˚ and the La-derived a perturbative n-electron valence perturbation 8 34 9 state becomes the lowest-energy singlet excited theory second-order (NEVPT2) correction 10 state around the potential energy minimum have been performed to provide a reliable point 11 at an intermolecular separation of ≈ 3.08 A.˚ of comparison for TDDFT results. Benchmarks 12 CASPT2 calculations yielded non-CP-corrected have shown that the NEVPT2 method yields 13 binding energies of 128 kJ/mol and 60 kJ/mol perturbative dynamic correlation values simi- 14 35 15 for the La and Lb-derived states of the naph- lar to the popular CASPT2 method, but the 16 thalene excimer, respectively.30 Dyall Hamiltonian used in NEVPT2 prevents 17 The lowest singlet excited state of the intruder state mixing and eliminates the need 18 benzene-naphthalene exciplex is derived from for shift parameters.34 Perturbatively-corrected 19 CASSCF calculations have the capacity to cap- 20 the Lb state of the naphthalene monomer. An 21 approximate CP-corrected NEVPT2 complete ture both static and dynamic correlation, pro- 22 basis set binding energy of 19.2 kJ/mol has viding a balanced treatment of both the single 23 32 been reported for the complex in the S1 state, and double excitations observed among acenes. 24 indicating a much weaker interaction than the Standard EOM-CCSD potential energy curves 25 flip the order of the lowest-energy singlet ex- 26 ones observed for S1 benzene and naphthalene 27 excimers. cited states of the naphthalene excimer around 28 The first objective of this work is to evalu- the global minimum geometry, an error that 29 ate the effectiveness of TDDFT for calculat- CASSCF/CASPT2 calculations correct.30 For 30 ing exciplex binding and excitation energies the relative energy of the lowest-energy sin- 31 glet excited state of benzene, EOM-EE-CCSD 32 using several exchange-correlation functionals. 33 Three representative acene exciplexes have been and NEVPT2 calculations vary by less than 2 21,35 34 selected for study: the benzene-naphthalene kJ/mol. All CASSCF wave functions were 35 exciplex (BN)∗, the benzene-anthracene exci- further optimized in CASCI calculations to 36 plex (BA)∗, and the naphthalene-anthracene adjust orbital coefficients before NEVPT2 cor- 37 ∗ rections were calculated. 38 complex (NA) . TDDFT binding energies are 39 compared against CASSCF/NEVPT2 results. The CASSCF/CASCI/NEVPT2 techniques 40 Binding energies have also been calculated us- used here have been employed in previous 41 ing the second-order algebraic diagrammatic work,32 and only a brief review will be provided. 42 construction method, (ADC(2)),33 a comple- This multireference procedure is used here in 43 mentary single-reference approach. To the best order to calculate complete binding curves for 44 ∗ ∗ ∗ 45 of our knowledge, these binding energies are the (BN) , (BA) , and (NA) using the cc-pVDZ 46 first to be reported for (BA)∗ and (NA)∗. basis set,36 data that is reported here for the 47 To rationalize trends in exciplex binding en- first time. The use of a relatively small basis 48 ergies, the extent of the exciton delocaliza- set to describe noncovalent interactions might 49 rightly provoke skepticism. However, it has 50 tion and charge transfer in each complex has 51 been quantified using the one-electron transi- been shown that, for aromatic exciplexes, can- 52 tion density matrix. Developing a predictive cellation of BSSE and basis set incompleteness 53 model for spectroscopic parameters of arbitrary error yields cc-pVDZ binding energies very close 54 aromatic exciplexes will require a larger body of to the complete basis set limit, providing an ex- 55 cellent cost–accuracy trade-off.32 Energies cal- 56 data, but the benchmark results and systems 57 characterized in this work represent a first step culated according to this procedure will be de- 58 towards this goal. scribed simply as NEVPT2 energies. 59 60 ACS Paragon Plus Environment 3 The Journal of Physical Chemistry Page 4 of 19

The active spaces for multireference calcula- less than 1 kJ/mol, so the full binding curve 1 2 tions include one p orbital parallel to the inter- was generated using M = 500 for the CASSCF 3 molecular axis and one electron for each carbon step and RHF starting orbitals. 4 atom. Smaller active spaces yield the wrong For TDDFT calculations, representative func- 5 state ordering for naphthalene complexes.30 tionals from several major classes have been 6 The resulting active spaces range in size from chosen. The B3LYP functional45 has been 7 8 16 active orbitals and electrons to 24 active or- chosen from the hybrid GGAs, as well as the 9 bitals and electrons. BHandHLYP functional, with includes a larger 10 To make these large active spaces computa- amount of Hartree-Fock exchange than other 11 tionally tractable, the density matrix renor- hybrids.46 The B2PLYP functional47 with a 12 malization group (DMRG) approach37–39 was double excitation correction48 was chosen from 13 14 used in both CASSCF and NEVPT2 calcula- the double hybrids. Grimme’s D3 empirical dis- 15 tions. By employing an approximate wave func- persion correction with Becke-Johnson damp- 16 tion ansatz known as the matrix product state ing49 was applied to the B3LYP, B2PLYP, and 17 (MPS), the DMRG method offers a polynomial- BHandHLYP functional results. Though devel- 18 scaling alternative to exponentially-scaling oped for ground state DFT calculations, the 19 20 CAS methods. The accuracy of the wave func- D3 correction has also significantly improved 21 tion is determined by the dimension chosen for the TDDFT description of excimers, at least 22 the matrices, known as the bond dimension for dimers in valence excited states such as the 23 M. For a discussion of the errors associated ones considered in this work.50,51 To acceler- 24 with the DMRG approach and the conver- ate double hybrid calculations, the resolution 25 52 26 gence of DMRG results with increasing M, the of identity (RI) approximation was used in 27 reader is referred to recent discussions of the the evaluation of Coulomb integrals. 28 method.40,41 The number of variational param- Range-separated functionals have shown par- 29 eters scales as M 2. An approximate compressed ticular promise for describing the electronic 30 MPS perturber40 was used in NEVPT2 calcu- states of aromatic systems.27 Among these 31 53 32 lations, which were of the strongly contracted functionals, the ωB97 functional, which in- 33 type. DMRG calculations were performed us- cludes varying Hartree-Fock exchange for all 34 ing the Pyscf framework version 1.3b42 with long-range interactions, and the ωB97X-D3 35 an interface to the Block DMRG solver version functional,54 which includes a region of fixed 36 1.5.0.43 Hartree-Fock exchange, were used. 37 38 CASSCF starting orbitals were obtained from To control the transition between long-range 39 restricted Hartree Fock (RHF) calculations, exact exchange and short-range semilocal ex- 40 and active space p orbitals were selected using change, range separated functionals rely on the 41 the atomic valence active space (AVAS) tech- use of a range-split parameter γ. Tuning γ val- 42 nique.44 The choice of starting orbital type can ues for individual systems to enforce as closely 43 44 affect the convergence of DMRG energies with as possible the DFT version of Koopmans’ the- 45 increasing M, but aromatic exciplex binding orem has been shown to improve the accuracy 46 energies computed using canonical and local- of range-separated functionals.27,55 47 ized starting orbitals are both generally well- To examine the effectiveness of this tech- 48 converged with M = 500 for CASSCF calcula- nique for exciplex binding energy calculations, 49 50 tions and M = 1200 for CASCI and NEVPT2 the long-range corrected BLYP functional, LC- 51 calculations.32 For the larger (NA)∗ exciplex, BLYP,56 has been used, along with two variants 52 setting M = 1000 for the CASSCF step was of the LC-BLYP functional, each with γ tuned 53 necessary to obtain a converged binding energy, to minimize the difference between the energy 54 55 and localized B3LYP starting orbitals were used of the highest-occupied molecular orbital in the 56 because RHF orbitals generated were of poor ground state and the ground state ionization 57 quality. For (BA)∗, the binding energy calcu- energy. For one of the functionals, LC-BLYP- 58 lated using both sets of conditions differed by TM, the tuning is performed only for the larger 59 60 ACS Paragon Plus Environment 4 Page 5 of 19 The Journal of Physical Chemistry

monomer in each complex. For the other, LC- acenes.14,66 Exciplex geometries considered in 1 2 BLYP-TD, tuning is performed for the com- this work (Fig. 1) resemble the minimum- 3 plete dimer at its minimum-energy geometry. energy structures for acene excimers, although 4 Values of γ used in each functional for each exci- the monomer size mismatch in the exciplex 5 plex are reported in Table S1. Optimal γ values structures means that the larger monomer is 6 do depend on the intermolecular separation of not perfectly eclipsed by the smaller one. For 7 ∗ 8 the complex, with γ for the dimer approaching (BA) , two eclipsed configurations are possible. 9 γ for the larger monomer at an intermolecular The configuration with the benzene centered 10 separation of 10 A.˚ To prioritize correct treat- over the middle ring of the anthracene was cho- 11 ment of the exciplexes near their energy min- sen because its binding energy is greater than 12 ima, we have chosen to set γ for the LC-BLYP- the binding energies of configurations with the 13 14 TD functional to the optimal value obtained for benzene centered over a side ring. 15 the minimum-energy dimer configuration. Binding curves were generated by translat- 16 The def2-TZVP57 basis set has been used for ing the monomers along the intermolecular co- 17 all TDDFT calculations, with the def2/JK aux- ordinate rz, with intramolecular coordinates 18 iliary basis58 used in RI calculations. TDDFT frozen at their ground state values. Ground 19 20 energies are generally less sensitive to basis set state monomer geometries were computed with 21 size than wave function methods. For elec- DFT using the B3LYP functional and the def2- 22 tronic transition energies in a range of organic TZVP basis set. Adiabatic absorption ener- 23 molecules, the def2-TZVP basis generally yields gies, the difference between the minima of the 24 small errors with respect to the much larger ground and S states, were computed for the 25 1 26 aug-cc-pVTZ basis, providing excellent accu- naphthalene and anthracene monomers using 59 27 racy relative to computational cost. Based each method for which excited-state gradients 28 on a benchmark study involving the ground were available. Relaxation of monomer and 29 state binding energies of the S66 noncovalent dimer structures in the S1 state performed using 30 dimer test set, BSSE is expected to repre- B3LYP TDDFT gradients has a minor impact 31 60 32 sent ≤ 12% of the total binding energy. The on intramolecular and intermolecular C–C dis- 33 Tamm-Dancoff approximation was applied in tances (≈ 0.02 A),˚ including a breaking of the 34 all TDDFT calculations. six-fold symmetry of the benzene in the (BN)∗ 35 As an alternative single-reference approach, complex (Tables S2-S5). Geometry changes are 36 the ADC(2) method33 was used together with small enough, though, that we expect relative 37 36 38 the smaller cc-pVDZ basis set because of trends in exciplex binding energy to apply to 39 the method’s high memory requirements.25,33 both relaxed and unrelaxed structures. 40 ADC(2) excitation energies were added to MP2 41 ground state energies, which are consistent with 42 the ADC(2) reference state.61 43 44 All TDDFT and ADC(2) calculations were 45 performed using the ORCA software package62 46 version 4.0.0 with integration grid size 5. Statis- 47 tical descriptors of exciton character were cal- 48 culated using the TheoDORE package version 49 1.0.63 Molecule graphics have been generated Figure 1: Eclipsed geometries from side and top 50 ∗ ∗ 51 using VMD version 1.9.1.64 perspectives for (BN) (left), (BA) (center), ∗ 52 Previous studies of aromatic excimers have and (NA) (right). The intermolecular coor- 53 shown that an eclipsed configuration is the dinate rz is marked with a dotted line. 54 55 most favorable geometry for complexes in 65–68 56 the lowest singlet excited state, while The binding energy EB is defined as 57 parallel-displaced configurations have larger 58 binding energies in the ground state for most EB = |E(rz = r0) − E(rz = 10 A)˚ |, (1) 59 60 ACS Paragon Plus Environment 5 The Journal of Physical Chemistry Page 6 of 19

where r is the minimum-energy intermolecu- relative energy is insensitive to γ outside the re- 1 0 2 lar separation. It is important to note that the gion of the global minimum, and the choice to 3 lowest-energy singlet excited state for the sep- tune γ based on the global minimum geometry 4 arated monomers (rz = 10 A)˚ has the larger is justified. 5 monomer in the first excited state (S1) and While another range-separated functional, 6 the smaller monomer in the ground state (S ) ωB97, matches the NEVPT2 potential energy 7 0 8 because the S0 → S1 transition energy de- surface extremely well around the minimum, it 9 creases with increasing acene size. This con- underbinds the complex in the 4-6 A˚ region, 10 figuration serves as the reference in EB cal- even slightly overshooting the rz = 10 A˚ value 11 culations. Excimers have degenerate reference around 5 A.˚ The ωB97X-D3 functional cor- 12 states. The excitation energies corresponding rects this error, but shows an extremely shifted 13 ˚ 14 to vertical monomer absorption, ∆EV , and adi- minimum. The r0 of 3.69 A would be more 15 abatic monomer absorption, ∆EA, refer to the characteristic of a ground-state aromatic com- 16 excitation energy of the larger monomer in the plex. The hybrid functionals both overbind 17 complex for the same reason. the complex, but the BHandHLYP functional, 18 with a significantly larger proportion of exact 19 20 exchange, performs much better. The B3LYP 21 3. Results and Discussion functional EB value is more than double the 22 NEVPT2 one, while the B2PLYP functional 23 Error in the TDDFT Description overbinds the complex by 80%. The disper- 24 sion contribution to E provided by the D3 25 of Exciplex Binding B correction is significant. Without this correc- 26 For (BN)∗, the potential energies computed for 27 tion, the B3LYP and BHandHLYP function- varying r (Fig. 2) at the NEVPT2/cc-pVDZ 28 z als do not show an attractive exciplex inter- 29 level yield an EB value of 18.16 kJ/mol (Ta- action (Fig. S2). The uncorrected B2PLYP 30 ble 1). The complex has an approximate com- functional still shows a stabilizing interaction, 31 plete basis set limit binding energy of 19.2 with the MP2 component of the double-hybrid 32 kJ/mol,32 more than 30% higher than the 33 functional likely capturing a portion of the dis- CCSD(T)-corrected DFT binding energy for 34 persion energy. The ADC(2) method is signif- 35 the ground state complex in an eclipsed config- icantly overbinding, yielding an EB more than 36 uration (≈ 14.5 kJ/mol).69 This difference sug- twice as high as the NEVPT2 result. The r0 37 gests that exciplex stabilization is an important ˚ 38 obtained is also more than 0.1 A smaller than contributor to the complex’s S1 binding energy. 39 the next-smallest r0. 40 Error due to the use of the DMRG approach is The (BA)∗ exciplex, not surprisingly, is bound 41 estimated at ≈ 1 kJ/mol based on EB conver- ∗ 32 more strongly than (BN) , with an NEVPT2 42 gence with M for this complex. binding energy of 27.69 kJ/mol. Similar E 43 B The shape and well depth of the inter- trends are observed in results from the LC- 44 molecular exciplex potential energy surface 45 BLYP and LC-BLYP-TM functionals (Fig. 3). 46 varies significantly between the TDDFT cal- For this complex, the LC-BLYP-TD improves 47 culations performed using different exchange- on the LC-BLYP-TM result by only ≈ 1.5 48 correlation functionals. The LC-BLYP func- kJ/mol. 49 tional has a binding energy 54% lower than E values for the ωB97X-D3 functional are 50 the NEVPT2/cc-pVDZ result. The tuned B 51 now too high, and both the ωB97 and ωB97X- 52 LC-BLYP functionals perform better—the LC- D3 functionals display an apparent instabil- 53 BLYP-TM functional yields a binding energy ity in the 3.1-3.2 A˚ region, resulting in lin- 54 28% too low, while the LC-BLYP-TD func- 55 ear regions in the potential energy curves to tional comes within 7% of the correct result. the left of r . Hybrid and double hybrid re- 56 For r ≥ 4.5 A,˚ all of the LC-BLYP function- 0 57 z sults match the NEVPT2 curve closely, with 58 als are in excellent agreement, suggesting that B2PLYP and B3LYP results almost identical 59 60 ACS Paragon Plus Environment 6 Page 7 of 19 The Journal of Physical Chemistry

and slightly overbinding. puted for naphthalene (Table 2) overshoots the 1 2 Similar behavior is observed for the hybrids estimated experimental value by at least 30 ∗ 3 and double hybrid in the (NA) system (Fig. 4), kJ/mol. The trend among ∆EA values is sim- 4 although a few differences from the other ex- ilar. The difference between ∆EV and ∆EA 5 ciplexes are noticeable. In the absence of the results is related to the quality of the exited- 6 D3 correction, the three hybrid and double hy- state potential energy surface, and the differ- 7 8 brid functionals still show a stabilizing exci- ences obtained for naphthalene are noticeably 9 plex interaction (Fig. S2). Among the range- smaller than the estimated experimental differ- 10 separated functionals, the LC-BLYP-TM and ence. The NEVPT2 ∆EV reported here is ap- 11 LC-BLYP-TD binding energies are larger than proximately 27 kJ/mol higher than the ∆EV 12 the ωB97 and ωB97X-D3 ones. The ωB97 func- value reported for a similar CASPT2 calcula- 13 73 14 tional shows unusual behavior around r0, while tion. Based on additional NEVPT2 calcula- 15 the ωB97X-D3 functional r0 is again dramati- tions, we attribute ≈ 6 kJ/mol of this difference 16 cally shifted toward high rz values, a geometry to the difference in monomer geometries used 17 error accompanied by a binding energy more (B3LYP/def2-TZVP in this work vs. MP2/6- 18 than 50% too low. As in the case of (BN)∗, 31G∗), and a further ≈ 6 kJ/mol to the dif- 19 20 tuning the LC-BLYP functional for the com- ferent NEVPT2 basis sets (cc-pVDZ in this 21 plex rather than the larger monomer alone im- work vs. TZVP). The additional 15 kJ/mol 22 proves the binding energy—by approximately difference may be attributed to the different 23 10 kJ/mol for this complex. This LC-BLYP-TD perturbative correction approach (NEVPT2 vs 24 E value falls within 1 kJ/mol of the NEVPT2 CASPT2). For anthracene, though, values of 25 B 26 reference, though the r0 obtained is more than ∆EA and ∆EV are generally in better agree- 27 0.15 A˚ too low, consistent with most of the ment with experiment, and the agreement be- 28 other functionals. tween computed and experimental ∆EV −∆EA 29 values is excellent. 30 Table 1: Binding Energies EB and Opti- When E values for the exciplexes are consid- 31 B mal S1 Intermolecular Separations r0 for ered, though, the pattern becomes more com- 32 (BN)∗, (BA)∗, and (NA)∗ 33 plex. To provide more examples of each type, 34 ∗ (BN)∗ (BA)∗ (NA)∗ the La- and Lb-derived states of (NN) in the 35 eclipsed configuration are also considered. It Excitation Type L L L 36 b a a is immediately apparent that the B2PLYP and 37 EB r0 EB r0 EB r0 38 Method (kJ/mol) (A)˚ (kJ/mol) (A)˚ (kJ/mol) (A)˚ B3LYP functionals perform much better for La- 39 NEVPT2 18.16 3.34 27.69 3.28 49.30 3.34 derived states than for Lb-derived states, with 40 ADC(2) 38.60 3.00 46.58 3.16 92.10 3.05 LC-BLYP 8.37 3.41 10.78 3.49 25.04 3.25 no meaningful difference between the two func- 41 LC-BLYP-TM 13.06 3.25 15.93 3.40 40.26 3.21 tionals for La-derived states. Both function- 42 LC-BLYP-TD 16.97 3.17 17.47 3.35 48.90 3.19 als predict L vertical excitation energies for 43 ωB97 17.13 3.48 21.39 3.44 37.28 3.40 b ωB97X-D3 15.46 3.69 29.34 3.47 27.04 3.71 the naphthalene monomer that are in excel- 44 BHandHLYP 24.79 3.25 25.94 3.42 53.63 3.25 45 B2PLYP 32.67 3.15 34.40 3.33 73.97 3.19 lent agreement with the NEVPT2 excitation 46 B3LYP 42.08 3.13 32.69 3.33 76.90 3.23 energy (Table 2), so the error stems from prob- 47 lems with the description of the exciplex in its 48 Separating the exciplexes into those derived minimum-energy conformation. 49 50 from La states of the larger monomer and those The ωB97 and ωB97X-D3 functionals per- 51 derived from Lb states (Fig. 5) is a useful form well for Lb-derived states, despite the fact 52 first step in analyzing trends in TDDFT er- that their ∆EV values are 20-30 kJ/mol higher 53 ror. ∆EV and ∆EA values suggest that, be- than the NEVPT2 ones. The fact that this 54 tween the anthracene and naphthalene parent 55 destabilization of the excited monomer does not 56 monomers, the Lb naphthalene excitation rep- lead to overbinding indicates that the exciplex 57 resents a greater challenge than the La an- with rz = r0 is destabilized to a similar degree. 58 thracene excitation. Every ∆EV value com- For La-derived states more strongly bound than 59 60 ACS Paragon Plus Environment 7 The Journal of Physical Chemistry Page 8 of 19

Table 2: Monomer S1 Absorption Energies ∆EV and ∆EA. 1 2 3 Naphthalene (Lb) Anthracene (La) 4 Method ∆EV ∆EA ∆EV -∆EA ∆EV ∆EA ∆EV -∆EA 5 (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) 6 7 LC-BLYP 453.8 448.3 5.5 383.0 366.4 16.6 8 9 LC-BLYP-TM 444.6 437.2 7.4 365.0 347.6 17.4 10 ωB97 466.6 456.2 10.4 391.8 373.3 18.5 11 ωB97X-D3 457.1 448.9 8.2 378.1 360.6 17.5 12 13 BHandHLYP 463.2 458.7 4.5 363.2 347.2 16.0 14 B3LYP 433.3 422.8 10.5 330.6 313.5 17.1 15 NEVPT2 436.4 – – 366.3 – – 16 17 ADC(2) 440.9 – – 368.5 – – 18 B2PLYP 431.0 – – 346.7 – – 19 Exptl. 398.8a 383.1b 15.7 347.7a 331.0c 16.7 20 a 26 21 Estimated vertical excitation energies with solvent correction derived from experimental 0–0 excita- 70 b 71 c 72 22 tion energies. Ref. Ref . 23 24 25 0 0 0 26 27 10 10 10 28

29 20 20 20 30 NEVPT2 31 E (kJ/mol) LC-BLYP BHandHLYP 30 30 B97X-D3 30 32 LC-BLYP-TM B2PLYP LC-BLYP-TD B97 B3LYP 33 40 NEVPT2 40 NEVPT2 40 ADC(2) 34 35 3 4 5 6 3 4 5 6 3 4 5 6 36 r (Å) r (Å) r (Å) 37 z z z 38 39 ∗ 40 Figure 2: S1 potential energies for (BN) relative to rz = 10 A.˚ Lines have been added to guide the 41 eye. 42 43 44 (BA)∗, both functionals are underbinding, al- kJ/mol, when experimental reports range from 45 though the ordering of the two E values varies 45-70 kJ/mol.30 This depressed L energy likely 46 B a 47 between complexes. contributes to the most notable BHandHLYP 48 A diﬀerence between EB results for La- EB error, observed for the La-derived naphtha- 49 and Lb-derived states is also apparent for the lene excimer. 50 BHandHLYP functional. For Lb-derived states, Perhaps the most consistent TDDFT errors 51 the functional is uniformly overbinding, a re- are observed from the LC-BLYP and tuned 52 53 sult consistent with a good description of the LC-BLYP functionals. The tuned functionals 54 exciplex but a high Lb excitation energy for in particular yield reasonable ∆EV values, al- 55 the naphthalene monomer. The La excita- though absolute error does increase with in- 56 tion energy for naphthalene is not correspond- creasing interaction strength. A similar La–Lb 57 ingly high, resulting in an L –L gap of only 8 energy diﬀerence for the naphthalene monomer 58 b a 59 60 ACS Paragon Plus Environment 8 Page 9 of 19 The Journal of Physical Chemistry

1 2 0 0 0 3 10 10 10 4 5 20 20 20 6 NEVPT2

E (kJ/mol) LC-BLYP BHandHLYP 7 30 30 30 8 LC-BLYP-TM B97 B2PLYP LC-BLYP-TD NEVPT2 B3LYP 9 40 40 40 10 NEVPT2 B97X-D3 ADC(2) 11 12 3 4 5 6 3 4 5 6 3 4 5 6 13 rz (Å) rz (Å) rz (Å) 14 15 16 Figure 3: S potential energies for (BA)∗ relative to r = 10 A.˚ 17 1 z 18 19 20 0 0 0 21 20 20 20 22 23 40 40 40 24 60 60 60 NEVPT2 25 (kJ/mol) B LC-BLYP BHandHLYP 26 E 80 LC-BLYP-TM 80 B97 80 B2PLYP 27 LC-BLYP-TD NEVPT2 B3LYP 28 100 NEVPT2 100 B97X-D3 100 ADC(2) 29 30 3 4 5 6 3 4 5 6 3 4 5 6

31 rz (Å) rz (Å) rz (Å) 32 33 34 ∗ 35 Figure 4: S1 potential energies for (NA) relative to rz = 10 A.˚ 36 37 100 150 B3LYP 38 39 ADC(2) 80 125 B2PLYP 40 (NA) * 41 100 60 BHandHLYP 42 (BN) * (kJ/mol) 75 B97 43 * 40 (BA) (NN) * B97X-D3

44 TDDFT 50

45 B , * LC-BLYP-TD E 20 (NN) 46 25 LC-BLYP-TM Lb La 47 0 0 LC-BLYP 48 0 25 50 75 100 0 50 100 150

49 EB, NEVPT2 (kJ/mol) EB, NEVPT2 (kJ/mol) 50 51 52 53 Figure 5: TDDFT binding energies EB as a function of NEVPT2 binding energies for exciplexes 54 in the Lb state (left) and the La state (right). For the naphthalene excimers, CASPT2/cc-pVDZ 55 binding energies30 are substituted for NEVPT2 values. 56 57 58 59 60 ACS Paragon Plus Environment 9 The Journal of Physical Chemistry Page 10 of 19

1 B3LYP 2 ADC(2) 3.6 3.6 * 3 (BA) B2PLYP 4 BHandHLYP 5 (Å) 3.4 3.4 (NN) * 6 (NN) * B97

7 TDDFT B97X-D3

0, 3.2 3.2 8 r LC-BLYP-TD 9 (BN) * 3.0 3.0 * LC-BLYP-TM 10 Lb (NA) La 11 LC-BLYP 12 3.00 3.25 3.50 3.75 3.00 3.25 3.50 3.75

13 r0, NEVPT2 (Å) r0, NEVPT2 (Å) 14 15 16 17 Figure 6: TDDFT optimal intermolecular separations r0 as a function of NEVPT2 r0 values for 18 exciplexes in the Lb state (left) and the La state (right). For the naphthalene excimers, CASPT2/cc- 19 30 pVDZ r0 values are substituted for NEVPT2 results. 20 21 22 of approximately 30 kJ/mol is obtained from 23 100 all three LC-BLYP functionals. Although ADC(2) 24 B3LYP 25 smaller than the reported NEVPT2 energy dif- B2PLYP 80 BHandHLYP 26 ference, this result is at least on the same LC-BLYP LC-BLYP-TM 27 order of magnitude. EB errors of 20-40% LC-BLYP-TD 28 are observed for all exciplexes, suggesting that 60 B97 29 B97X-D3 the under-stabilization of minimum-energy ex- NEVPT2 30 (kJ/mol) B 40 31 ciplexes might have a uniform cause for both E 32 La- and Lb-derived states. 33 Errors in r0, illustrated in Fig. 6, do not 20 34 show a uniform dependence on the exciplex 35 state. For the more tightly-bound exciplexes 36 15 18 21 24 37 (NEVPT2 r0 < 3.25 A),˚ all results agree N 38 within ≈ 0.1 A.˚ Error increases signiﬁcantly C 39 for the more loosely-bound complexes. The 40 B2PLYP and B3LYP functionals give r val- 41 0 ˚ Figure 7: Binding energy EB as a function of 42 ues approximately 0.2 A too small for the Lb- ∗ the number of carbons N in each exciplex. 43 derived (BN) , but perform very well for the C ∗ 44 La-derived (BA) . The r0 values obtained from 45 the ωB97X-D3 functional vary unpredictably— be due in part to the commonly-observed ten- 46 for (NA)∗, the r obtained is 0.37 A˚ too high. 47 0 dency of the MP2 method—which supplies the 48 The most consistent errors overall in both ground state energy in ADC(2) calculations— 49 EB and r0 values are observed for the ADC(2) to overbind van der Waals complexes. Using a 50 method. ADC(2) ∆EV results for both naph- larger basis set seems unlikely to alleviate the 51 thalene and anthracene monomers are in ex- issue, as recalculation of the binding energy of 52 cellent agreement with the NEVPT2 values. ∗ 53 (BN) using the cc-pVTZ basis at the cc-pVDZ 54 However, the complexes are uniformly over- minimum geometry and reference conﬁguration 55 bound, with absolute EB errors in the 20-40 yields an even higher binding energy of 45.5 56 kJ/mol range, and the r0 values obtained are kJ/mol, and repeating the procedure for (BA)∗ 57 all 0.05-0.1 A˚ too low. This overbinding may results in E = 46.89, a value virtually identi- 58 B 59 60 ACS Paragon Plus Environment 10 Page 11 of 19 The Journal of Physical Chemistry

cal to the cc-pVDZ result. yielding a larger area of enriched electron den- 1 2 Beyond reproducing individual binding ener- sity between the molecules. 3 gies, it is desirable for functionals to capture To quantify the degree of exciton delocaliza- 4 the relationships between the EB values ob- tion and the charge transfer contribution, sta- 5 tained for each complex. The ωB97X-D3 and tistical descriptors based on the one-electron 6 B3LYP functionals fail to capture the mono- transition density matrix formulated by Plasser 7 31,76 8 tonic increase in EB values with respect to com- and coworkers. These descriptors have been 9 plex mass (Fig. 7). The remaining functionals calculated for the B2PLYP functional and the 10 severely underestimate difference in EB values LC-BLYP-TM functional (Table 3). Charge 11 ∗ ∗ for (BN) and (BA) . The NEVPT2 EB re- transfer number CT ranges from zero for a com- 12 sults for the two differ by more than 50% (9.5 pletely localized Frenkel excitation to unity for 13 14 kJ/mol), while the maximum obtained is 29% complete charge transfer. For the La-derived 15 (2.4 kJ/mol) from the LC-BLYP functional. state of the naphthalene excimer, CT = 0.5, 16 indicating equal charge transfer and localized 17 31 Physical Origins of Exciplex Sta- excitation character. 18 The participation ratio PR of each monomer 19 bilization 20 in the excitation represents a second measure 21 It remains, then, to rationalize both TDDFT of excitation delocalization, with PR = 2 in 22 errors and the observed NEVPT2 trends in ex- the case of a symmetric excimer like (NN)∗, 23 ciplex binding energy. The binding energies of where the two indistinguishable monomers par- 24 ticipate equally. The average exciton position, 25 ground-state noncovalent aromatic complexes 26 scale approximately linearly with the number POS, ranges from 1-2, POS = 1, 2 corresponds 14–16,74,75 27 of carbon atoms in the complex NC . to exciton localization on a single monomer, 28 This is not the case for the exciplexes consid- and maximally delocalized excited states have 29 ered here (Fig. 7). For (BN)∗ and (BA)∗, the POS = 1.5. For the mixed exciplexes, POS = 1 30 indicates exciton localization on the smaller 31 ratios of EB,NEV P T 2 to NC are 1.16 kJ/mol and 32 1.15 kJ/mol, respectively. For (NA)∗, the ratio monomer and POS = 2 indicates localization 33 is 2.05 kJ/mol. on the larger monomer. Population analysis for 34 Considering the form of the natural orbitals the electron and hole created by the excitation 35 involved in the electronic transitions can help has also been performed to locate the charge 36 shed light on their varying character. Natural carriers on specific monomers. 37 ∗ 38 transition orbitals (NTOs) have been calculated For (BN) , the picture that emerges from 39 for each exciplex using one generally overbind- both functionals is one in which the excita- 40 ing functional, B2PLYP, and one underbinding tion is primarily localized on the naphtha- 41 functional, LC-BLYP-TM. For (BN)∗, the dif- lene monomer, but not exclusively—it is spa- 42 tially shifted in the direction of the benzene 43 ference between the EB values obtained from 44 each is high—the B2PLYP EB is 80% too high, monomer, which has nonzero electron and hole 45 and the LC-BLYP-TM EB is 28% too low. In populations. However, the degree of delocal- 46 both sets of NTOs (Fig. 8), the electron density ization varies noticeably between the two func- 47 is shifted toward the naphthalene monomer, tionals, with the overbinding B2PLYP func- 48 tional producing additional exciton delocaliza- 49 suggesting that the exciplex excitation is prin- 50 cipally a naphthalene excitation. However, this tion. The difference in CT values is particu- 51 shift is more dramatic for the LC-BLYP-TM larly apparent, with the B2PLYP CT almost 52 NTOs. The LC-BLYP-TM bonding orbitals 80% higher than the LC-BLYP-TM CT. 53 In the case of (BA)∗, the exciton descriptors 54 show significantly less electron density in the 55 intermolecular region. Differences in electron obtained using each functional are much more 56 density between the ground and excited states similar, and considering the NTOs for the ex- 57 (Fig. S3) show a similar contrast between the ciplex (Fig. 9) suggests why this might be the 58 two functionals, with the B2PLYP functional case—the electron density is located almost en- 59 60 ACS Paragon Plus Environment 11 The Journal of Physical Chemistry Page 12 of 19

1 2 3 4 5 6 7 LC-BLYP-TM LC-BLYP-TM 8 B2PLYP LUMO B2PLYP LUMO+1 LUMO LUMO+1 9 10 11 12 13 14 15 LC-BLYP-TM LC-BLYP-TM 16 B2PLYP HOMO-1 B2PLYP HOMO HOMO-1 HOMO 17 18 Figure 8: Frontier natural transition orbital isosurfaces for (BN)∗. 19 20 21 tirely on the anthracene monomer, particularly 22 23 for the bonding LUMO orbitals. With CT < 24 0.1 and PR < 1.1, it is clear that (BA)∗ would 25 be better described as BA∗. 26 If so, why is the per-carbon binding energy 27 B2PLYP LUMO LC-BLYP-TM LUMO so similar to the one obtained for (BN)∗, where 28 29 moderate exciplex stabilization is present? The 30 larger size of the BA compared to BN suggests 31 enhanced noncovalent interactions regardless of 32 electronic state, and electronic excitation can 33 77 34 B2PLYP HOMO LC-BLYP-TM HOMO increase the polarizability of aromatics. Thus, 35 the excitation of the anthracene monomer may 36 Figure 9: Frontier natural transition orbital iso- increase the interaction strength even with- ∗ 37 surfaces for (BA) . out notable exciton delocalization. The fact 38 that the excitation is largely localized on the 39 40 anthracene monomer likely also explains why 41 the performance of the LC-BLYP-TM and LC- 42 BLYP-TD functionals was so similar for (BA)∗; 43 the electronic state of the benzene molecule re- 44 mains nearly unchanged, so including it in the 45 B2PLYP LUMO LC-BLYP-TM LUMO 46 structure used for tuning does not signiﬁcantly 47 improve the description of the excited complex. 48 Although the NEVPT2 binding energy for 49 (BA)∗ falls between the LC-BLYP-TM and 50 B2PLYP ones, it is signiﬁcantly larger than 51 ∗ 52 B2PLYP HOMO LC-BLYP-TM HOMO the calculated (BN) NEVPT2 binding energy. 53 Examination of the canonical HOMO orbitals 54 Figure 10: Frontier natural transition orbital obtained in the NEVPT2 calculation reveals a 55 isosurfaces for (NA)∗. small amount of electron density on the benzene 56 monomer (Fig. S4). Orbitals plotted with the 57 58 same isovalue obtained from the LC-BLYP-TM 59 60 ACS Paragon Plus Environment 12 Page 13 of 19 The Journal of Physical Chemistry

and B2PLYP calculations do not show this den- difference in the energies of each monomer’s 1 2 sity, suggesting that both functionals may un- frontier orbitals inhibit their mixing and thus ∗ 3 derestimate the (BA) PR value—an error that the formation of bonding orbitals. In every 4 would not be uncovered by considering each case, though, the degree of stabilization makes 5 binding energy in isolation. Shorter intermolec- the electronic structure of the mixed exciplexes 6 ular distances are generally associated with in- distinct from both the parent monomers and 7 8 creased orbital overlap and thus increased pos- excimers of the parent monomers, an experi- 9 sibility for exciton delocalization. Differences mentally observable effect that should be ac- 10 in the observed levels of exciton delocalization, counted for in interpretation of fluorescence 11 then, are consistent with differences in r0, which spectra. 12 is overestimated by every DFT functional rel- The difficulties involved with calculating ac- 13 14 ative to the NEVPT2 result, regardless of the curate valence excitation energies for acenes 15 absolute binding energies obtained. using TDDFT are well known, but this work 16 Finally, the binding energies obtained from also demonstrates that the accuracy of exciplex 17 the two functionals for (NA)∗ are in better binding energies depends on the character of the 18 agreement, each falling within 30% of the monomer excited state from which the exciplex 19 20 NEVPT2 result. The geometric agreement is is derived. Binding energy errors are not easily 21 striking; r0 values differ by less than 0.02 A,˚ predictable from the magnitude of the monomer 22 and the NTOs are virtually identical (Fig. 10). excitation energy error. Double-hybrid func- 23 With CT ≈ 0.35 and PR > 1.5, the charge tionals offer advantages over hybrid GGAs in 24 transfer and exciton delocalization contribu- providing a balanced description of both states, 25 ∗ 26 tions to stabilization of (NA) are the largest but strong overbinding is still observed for Lb- 27 obtained for any of the exciplexes. The sim- derived states. Significant variation is observed 28 ilarity of the exciton delocalization descrip- among the range-separated functionals consid- 29 tors obtained using both functionals reflects the ered, with functionals in the ωB97 family yield- 30 smaller relative error of each as well as the ge- ing inconsistent results. While the LC-BLYP 31 32 ometric similarity. functional is extremely underbinding for all 33 complexes, tuning the range-separation param- 34 eter for each complex, or even for the larger 35 4. Conclusions monomer in each complex, improves binding 36 energies significantly. The performance of each 37 In this work, we have reported the binding ener- functional considered is summarized in Table 38 gies, geometries, and exciton properties of three 39 S6. Despite many promising results, it is clear acene exciplexes. These represents the first the- 40 that noncovalent excited-state interactions re- oretical investigation of the benzene-anthracene 41 main a significant challenge for TDDFT meth- 42 and naphthalene-anthracene exciplexes, and ods. 43 the first TDDFT investigation of the benzene- 44 naphthalene exciplex. CASSCF/NEVPT2 45 46 benchmark calculations have been performed Supporting information 47 to account for multireference character. We 48 have shown that the benzene-naphthalene and Values of γ for tuned LC-BLYP functionals, 49 naphthalene-anthracene exciplexes are stabi- bond lengths for structures optimized in the ex- 50 lized by a moderate degree of exciton de- cited state, binding curves calculated without 51 52 localization over both monomers and charge the D3 correction, difference densities for S1 ex- 53 transfer that is revealed by analysis of TDDFT citations, NEVPT2 orbitals for BA, qualitative 54 one-electron transition density matrices. The functional quality table. 55 exciton in the benzene-anthracene complex is 56 shown to be localized almost entirely on the an- 57 58 thracene monomer, perhaps because the large 59 60 ACS Paragon Plus Environment 13 The Journal of Physical Chemistry Page 14 of 19

∗ ∗ ∗ Table 3: Statistical descriptors for (BN) , (BA) , and (NA) computed using the S1 1 TDDFT one-electron transition density matrices at r . 2 0 3 4 5 Large Monomer Small Monomer 6 Complex Functional CT PR POS h+ pop. e- pop. h+ pop. e- pop. 7 8 B2PLYP 0.254 1.415 1.821 0.778 0.824 0.197 0.151 (BN)∗ 9 LC-BLYP-TM 0.142 1.272 1.879 0.846 0.874 0.133 0.105 10 11 B2PLYP 0.060 1.063 1.969 0.945 0.936 0.025 0.034 (BA)∗ 12 LC-BLYP-TM 0.053 1.058 1.972 0.926 0.928 0.027 0.026 13 14 B2PLYP 0.354 1.560 1.765 0.712 0.768 0.255 0.199 (NA)∗ 15 LC-BLYP-TM 0.349 1.546 1.771 0.713 0.766 0.246 0.193 16 17 18 19 Acknowledgement (6) Casanova, D. Bright Fission: Singlet Fis- 20 sion into a Pair of Emitting States. J. R. A. K. acknowledges funding from the 21 Chem. Theory Comput. 2015, 11, 2642– NSF Division of Graduate Education (DGE- 22 2650. 23 1745301). The authors thank Qiming Sun for 24 helpful discussions. (7) Bardeen, C. J. The Structure and Dy- 25 26 namics of Molecular Excitons. Annu. Rev. 27 References Phys. Chem. 2013, 65, 127–148. 28 29 (1) Scholes, G. D.; Ghiggino, K. P. Electronic (8) Takaya, T.; Su, C.; de La Harpe, K.; 30 Interactions and Interchromophore Exci- Crespo-Hernandez, C. E.; Kohler, B. 31 tation Transfer. J. Phys. Chem. 1994, 98, UV Excitation of Single DNA and RNA 32 Strands Produces High Yields of Exciplex 33 4580–4590. 34 States Between Two Stacked Bases. Proc. 35 (2) East, A. L. L.; Lim, E. C. Naphthalene Natl. Acad. Sci. 2008, 105, 10285–10290. 36 Dimer: Electronic States, Excimers, and 37 Triplet Decay. J. Chem. Phys. 2000, 113, (9) Miller, J. H. Aromatic Excimers : Evi- 38 8981–8994. dence for Polynuclear Aromatic Hydrocar- 39 bon Condensation in Flames. Proc. Com- 40 (3) Birks, J. B. Photophysics of Aromatic bust. Inst. 2005, 30, 1381–1388. 41 Molecules; Wiley – Interscience: New 42 43 York, 1970. (10) Adkins, E. M.; Giaccai, J. A.; Miller, J. H. 44 Computed Electronic Structure of Polynu- 45 (4) Xia, J.; Sanders, S. N.; Cheng, W.; clear Aromatic Hydrocarbon Agglomer- 46 Low, J. Z.; Liu, J.; Campos, L. M.; Sun, T. ates. Proc. Combust. Inst. 2017, 36, 957– 47 Singlet Fission : Progress and Prospects 964. 48 in Solar Cells. Adv. Mater. 2017, 29, 49 1601652. (11) Michelsen, H. A. Probing Soot Formation, 50 51 Chemical and Physical Evolution, and Ox- 52 (5) Feng, X.; Krylov, A. I. On Couplings and idation: A Review of in Situ Diagnos- 53 Excimers: Lessons from Studies of Singlet tic Techniques and Needs. Proc. Combust. 54 Fission in Covalently Linked Tetracene Inst. 2017, 36, 717–735. 55 Dimers. Phys. Chem. Chem. Phys. 2016, 56 18, 7751–61. (12) Wang, H. Formation of Nascent Soot 57 and Other Condensed-Phase Materials in 58 59 60 ACS Paragon Plus Environment 14 Page 15 of 19 The Journal of Physical Chemistry

Flames. Proc. Combust. Inst. 2011, 33, (21) Diri, K.; Krylov, A. I. Electronic States 1 2 41–67. of the Benzene Dimer: A Simple Case of 3 Complexity. J. Phys. Chem. A 2012, 116, 4 (13) Adamson, B. D.; Skeen, S. A.; Ahmed, M.; 653–662. 5 Hansen, N. Detection of Aliphatically 6 Bridged Multi-Core Polycyclic Aromatic (22) van Duijneveldt, F. B.; van Duijneveldt- 7 Hydrocarbons in Sooting Flames with van de Rijdt, J. G. C. M.; van 8 Atmospheric-Sampling High-Resolution Lenthe, J. H. State of the Art in Counter- 9 10 Tandem Mass Spectrometry. J. Phys. poise Theory. Chem. Rev. 1994, 94, 1873– 11 Chem. A 2018, acs.jpca.8b08947. 1885. 12 13 (14) Podeszwa, R.; Szalewicz, K. Physical Ori- (23) Miliordos, E.; Aprà,E.; Xantheas, S. S. 14 gins of Interactions in Dimers of Polycyclic Benchmark Theoretical Study of the π-π 15 Aromatic Hydrocarbons. Phys. Chem. Binding Energy in the Benzene Dimer. J. 16 Chem. Phys. 2008, 10, 2735–2746. Phys. Chem. A 2014, 118, 7568–7578. 17 18 (15) Ehrlich, S.; Moellmann, J.; Grimme, S. (24) Orchin, M.; Jaffè,H. H. Symmetry, Or- 19 20 Dispersion-Corrected Density Functional bitals, and Spectra; Wiley: New York, 21 Theory for Aromatic Interactions in Com- 1971. 22 plex Systems. Acc. Chem. Res. 2013, 46, 23 916–926. (25) Prlj, A.; Sandoval-Salinas, M. E.; 24 Casanova, D.; Jacquemin, D.; Cormin- 25 (16) Lee, N. K.; Park, S.; Kim, S. K. Ab Initio boeuf, C. Low-Lying pi-pi* States of 26 Studies on the van der Waals Complexes 27 Heteroaromatic Molecules: A Challenge 28 of Polycyclic Aromatic Hydrocarbons. I. for Excited State Methods. J. Chem. 29 Benzene-Naphthalene Complex. J. Chem. Theory Comput. 2016, 12, 2652–2660. 30 Phys. 2002, 116, 7910–7917. 31 (26) Grimme, S.; Parac, M. Substantial Errors 32 (17) Lee, N. K.; Park, S.; Kim, S. K. Ab Initio from Time-Dependent Density Functional 33 Studies on the van der Waals Complexes Theory for the Calculation of Excited 34 of Polycyclic Aromatic Hydrocarbons. 35 States of Large π Systems. Chemphyschem 36 II. Naphthalene Dimer and Naphthalene- 2003, 4, 292–295. 37 Anthracene Complex. J. Chem. Phys. 38 2002, 116, 7910–7917. (27) Kuritz, N.; Stein, T.; Baer, R.; Kronik, L. 39 Charge-Transfer-Like ππ* Excitations in 40 (18) Jara-Cortés, J.; Rocha-Rinza, T.; Time-Dependent Density Functional The- 41 Hernández-Trujillo, J. Electron Den- ory: A Conundrum and its Solution. J. 42 sity Analysis of Aromatic Complexes in 43 Chem. Theory Comput. 2011, 7, 2408– 44 Excited Electronic States: The Benzene 2415. 45 and Naphthalene Excimers. Comput. 46 Theor. Chem. 2015, 1053, 220–228. (28) Richard, R. M.; Herbert, J. M. Time- 47 Dependent Density-Functional Descrip- 48 (19) Rocha-Rinza, T.; Vico, L. D.; Verya- tion of the 1La State in Polycyclic Aro- 49 zov, V.; Roos, O. A Theoretical Study of matic Hydrocarbons: Charge-Transfer 50 Singlet Low-Energy Excited States of the 51 Character in Disguise? J. Chem. Theory 52 Benzene Dimer. Chem. Phys. Lett. 2006, Comput. 2011, 7, 1296–1306. 53 426, 268–272. 54 (29) Goerigk, L.; Grimme, S. Double-Hybrid 55 (20) Rocha-Rinza, T.; Christiansen, O. Lin- Density Functionals Provide a Balanced 56 ear Response Coupled Cluster Study of Description of Excited 1L and 1L States 57 a b the Benzene Excimer. Chem. Phys. Lett. in Polycyclic Aromatic Hydrocarbons. J. 58 2009, 482, 44–49. 59 60 ACS Paragon Plus Environment 15 The Journal of Physical Chemistry Page 16 of 19

Chem. Theory Comput. 2011, 7, 3272– (38) Chan, G. K.-L.; Dorando, J. J.; 1 2 3277. Ghosh, D.; Hachmann, J.; Neuscam- 3 man, E.; Wang, H.; Yanai, T. In Frontiers 4 (30) Shirai, S.; Kurashige, Y.; Yanai, T. Com- in Quantum Systems in Chemistry and 1 5 putational Evidence of Inversion of La Physics; Wilson, S., Grout, P. J., Maru- 1 6 and Lb-Derived Excited States in Naph- ani, J., Delgado-Barrio, G., Piecuch, P., 7 thalene Excimer Formation from ab Initio Eds.; Springer Netherlands: Dordrecht, 8 Multireference Theory with Large Active 9 2008; pp 49–65. 10 Space: DMRG-CASPT2 Study. J. Chem. 11 Theory Comput. 2016, 12, 2366–2372. (39) Chan, G. K. L.; Head-Gordon, M. Highly 12 Correlated Calculations with a Polyno- 13 (31) Plasser, F.; Lischka, H. Analysis of Ex- mial Cost Algorithm: A Study of the 14 citonic and Charge Transfer Interactions Density Matrix Renormalization Group. 15 from Quantum Chemical Calculations. J. J. Chem. Phys. 2002, 116, 4462–4476. 16 Chem. Theory Comput. 2012, 8, 2777– 17 (40) Guo, S.; Watson, M. A.; Hu, W.; Sun, Q.; 18 2789. 19 Chan, G. K. L. N-Electron Valence State 20 (32) Krueger, R. A.; Blanquart, G. Multirefer- Perturbation Theory Based on a Den- 21 ence Exciplex Binding Energies: Basis Set sity Matrix Renormalization Group Ref- 22 Convergence and Error. Int. J. Quantum erence Function, with Applications to the 23 Chem. 2019, 119, e25819. Chromium Dimer and a Trimer Model 24 25 (33) Troﬁmov, A. B.; Schirmer, J. An Eﬃ- of Poly(p-Phenylenevinylene). J. Chem. 26 cient Polarization Propagator Approach Theory Comput. 2016, 12, 1583–1591. 27 28 to Valence Electron Excitation Spectra. J. (41) Olivares-Amaya, R.; Hu, W.; 29 Phys. B: At. Mol. Opt. Phys. 1995, 28, Nakatani, N.; Sharma, S.; Yang, J.; 30 2299–2324. Chan, G. K.-L. The Ab-Initio Den- 31 sity Matrix Renormalization Group in 32 (34) Angeli, C.; Cimiraglia, R.; Evangelisti, S.; Practice. J. Chem. Phys. 2015, 142, 33 Leininger, T.; Malrieu, J. P. Introduc- 34102. 34 tion of n-Electron Valence States for Mul- 35 36 tireference Perturbation Theory. J. Chem. (42) Sun, Q.; Berkelbach, T. C.; Blunt, N. S.; 37 Phys. 2001, 114, 10252. Booth, G. H.; Guo, S.; Li, Z.; Liu, J.; Mc- 38 Clain, J.; Sayfutyarova, E. R.; Sharma, S. (35) Schapiro, I.; Sivalingam, K.; Neese, F. As- 39 et al. The Python-based Simulations of 40 sessment of n-Electron Valence State Per- Chemistry Framework (PySCF). Wiley 41 turbation Theory for Vertical Excitation Interdiscip. Rev. Comput. Mol. Sci. 2017, 42 Energies. J. Chem. Theory Comput. 2013, 43 e1340 . 44 9, 3567–3580. 45 (43) Sharma, S.; Chan, G. K.-L. Spin-Adapted (36) Dunning, T. H. Gaussian Basis Sets for 46 Density Matrix Renormalization Group Use in Correlated Molecular Calculations. 47 Algorithms for Quantum Chemistry. J. 48 I. The Atoms Boron Through Neon and Chem. Phys. 2012, 136, 124121. 49 Hydrogen. J. Chem. Phys. 1989, 90, 50 1007–1023. (44) Sayfutyarova, E. R.; Sun, Q.; Chan, G. 51 K. L.; Knizia, G. Automated Construction 52 (37) Chan, G. K.-L.; Keselman, A.; 53 of Molecular Active Spaces from Atomic Nakatani, N.; Li, Z.; White, S. R. 54 Valence Orbitals. J. Chem. Theory Com- 55 Matrix Product Operators, Matrix Prod- put. 2017, 13, 4063–4078. 56 uct States, and Ab Initio Density Matrix 57 Renormalization Group Algorithms. J. (45) Stephens, P. J.; Devlin, F. J.; Cha- 58 Chem. Phys. 2016, 014102, 014102. balowski, C. F.; Frisch, M. J. Ab Initio 59 60 ACS Paragon Plus Environment 16 Page 17 of 19 The Journal of Physical Chemistry

Calculation of Vibrational Absorption and sion Corrections. J. Chem. Theory Com- 1 2 Circular Dichroism Spectra Using Density put. 2013, 9, 263–272. 3 Functional Force Fields. J. Phys. Chem. 4 1994, 98, 11623–11627. (55) Stein, T.; Kronik, L.; Baer, R. Reli- 5 able Prediction of Charge Transfer Excita- 6 (46) Becke, A. D. A New Mixing of Hartree- tions in Molecular Complexes Using Time- 7 Fock and Local Density-Functional Theo- Dependent Density Functional Theory. J. 8 ries. J. Chem. Phys. 1993, 98, 1372–1377. Am. Chem. Soc. 2009, 131, 2818–2820. 9 10 (47) Grimme, S. Semiempirical Hybrid Den- (56) Leininger, T.; Stoll, H.; Werner, H.-J.; 11 12 sity Functional with Perturbative Second- Savin, A. Combining Long-Range Con- 13 Order Correlation. J. Chem. Phys. 2006, figuration Interaction with Short-Range 14 124, 034108. Density Functionals. Chem. Phys. Lett. 15 1997, 275, 151–160. 16 (48) Head-Gordon, M.; Rico, R. J.; Oumi, M.; 17 Lee, T. J. A Doubles Correction to Elec- (57) Weigend, F.; Ahlrichs, R. Balanced Basis 18 tronic Excited States from Configuration Sets of Split Valence, Triple Zeta Valence 19 20 Interaction in the Space of Single Substi- and Quadruple Zeta Valence Quality for 21 tutions. Chem. Phys. Lett. 1994, 219, 21– H to RN: Design and Assessment of Accu- 22 29. racy. Phys. Chem. Chem. Phys. 2005, 7, 23 3297–3305. 24 (49) Grimme, S.; Ehrlich, S.; Goerigk, L. Ef- 25 fect of the Damping Function in Disper- (58) Weigend, F. Hartree-Fock Exchange Fit- 26 27 sion Corrected Density Functional Theory. ting Basis Sets for H to RN. J. Comput. 28 J. Comput. Chem. 2010, 31, 2967–2970. Chem. 2008, 29, 167–175. 29 30 (50) Huenerbein, R.; Grimme, S. Time- (59) Laurent, A. D.; Blondel, A.; 31 Dependent Density Functional Study of Jacquemin, D. Choosing an Atomic 32 Excimers and Exciplexes of Organic Basis Set for TD-DFT, SOPPA, ADC(2), 33 Molecules. Chem. Phys. 2008, 343, 362– CIS(D), CC2 and EOM-CCSD Calcu- 34 35 371. lations of Low-Lying Excited States of 36 Organic Dyes. Theor. Chem. Acc. 2015, 37 (51) Briggs, E. A.; Besley, N. A. Modelling Ex- 134, 1–11. 38 cited States of Weakly Bound Complexes 39 with Density Functional Theory. Phys. (60) Sure, R.; Brandenburg, J. G.; Grimme, S. 40 Chem. Chem. Phys. 2014, 16, 14455– Small Atomic Orbital Basis Set First- 41 14462. Principles Quantum Chemical Methods 42 for Large Molecular and Periodic Systems: 43 (52) Weigend, F.; Hser, M.; Patzelt, H.; 44 A Critical Analysis of Error Sources. 45 Ahlrichs, R. RI-MP2: Optimized Auxil- ChemistryOpen 2016, 5, 94–109. 46 iary Basis Sets and Demonstration of Effi- 47 ciency. Chem. Phys. Lett. 1998, 294, 143– (61) Dreuw, A.; Wormit, M. The Algebraic Di- 48 152. agrammatic Construction Scheme for the 49 Polarization Propagator for the Calcula- 50 (53) Chai, J. D.; Head-Gordon, M. Systematic 51 tion of Excited States. Wiley Interdiscip. 52 Optimization of Long-Range Corrected Rev. Comput. Mol. Sci. 2015, 5, 82–95. 53 Hybrid Density Functionals. J. Chem. 54 Phys. 2008, 128, 084106. (62) Neese, F. The ORCA Program System. 55 Wiley Inderdiscip. Rev. Comput. Mol. Sci. 56 (54) Lin, Y.-S.; Li, G.-D.; Mao, S.-P.; Chai, J.- 2012, 2, 73–78. 57 D. Long-Range Corrected Hybrid Den- 58 sity Functionals with Improved Disper- 59 60 ACS Paragon Plus Environment 17 The Journal of Physical Chemistry Page 18 of 19

(63) Plasser, F. TheoDORE 1.0: A Package for (73) Schreiber, M.; Silva-Junior, M. R.; 1 2 Theoretical Density, Orbital Relaxation, Sauer, S. P.; Thiel, W. Benchmarks for 3 and Exciton Analysis. http://theodore- Electronically Excited States: CASPT2, 4 qc.sourceforge.net. CC2, CCSD, and CC3. J. Chem. Phys. 5 2008, 128 . 6 (64) Humphrey, W.; Dalke, A.; Schulten, K. 7 VMD – Visual Molecular Dynamics. J. (74) Wang, W.; Sun, T.; Zhang, Y.; 8 Molec. Graphics 1996, 14, 33–38. Wang, Y. B. The Benzene - - - Naph- 9 thalene Complex: A More Challenging 10 (65) Iyer, E. S. S.; Sadybekov, A.; Liouba- 11 System than the Benzene Dimer for Newly 12 shevski, O.; Krylov, A. I.; Ruhman, S. Developed Computational Methods. J. 13 Rewriting the Story of Excimer Forma- Chem. Phys. 2015, 143, 0–6. 14 tion in Liquid Benzene. J. Phys. Chem. 15 A 2017, 121, 1962–1975. (75) Fedorov, I. A.; Zhuravlev, Y. N.; 16 Berveno, V. P. Structural and Electronic 17 (66) Dubinets, N. O.; Safonov, A. A.; Bagatu- Properties of Perylene from First Princi- 18 ryants, A. A. Structures and Binding 19 ples Calculations. J. Chem. Phys. 2013, 20 Energies of the Naphthalene Dimer in 138, 1–6. 21 Its Ground and Excited States. J. Phys. 22 Chem. A 2016, 120, 2779–2782. (76) Plasser, F.; Bäppler,S. A.; Wormit, M.; 23 Dreuw, A. New Tools for the Systematic 24 (67) Casanova, D. Theoretical Investigations Analysis and Visualization of Electronic 25 of the Perylene Electronic Structure: 26 Excitations. II. Applications. J. Chem. 27 Monomer, Dimers, and Excimers. Int. J. Phys. 2014, 141, 024107. 28 Quantum Chem. 2015, 115, 442–452. 29 (77) Benchea, A. C.; Babusca, D.; Mo- 30 (68) Amicangelo, J. C. Theoretical Study rosanu, A. C.; Dimitriu, D. G.; Doro- 31 of the Benzene Excimer Using Time- hoi, D. O. Excited State Molecular Po- 32 Dependent Density Functional Theory. J. larizability Estimated by Solvatochromic 33 Phys. Chem. A 2005, 109, 9174–9182. 34 Means. AIP Conf. Proc. 2017, 1796, 35 (69) Bludský, O.; Rubeˇs, M.; Soldán, P.; 030013. 36 37 Nachtigall, P. Investigation of the 38 Benzene-Dimer Potential Energy Surface: 39 DFT/CCSD(T) Correction Scheme. J. 40 Chem. Phys. 2008, 128 . 41 42 (70) Biermann, D.; Schmidt, W. Diels-Alder 43 Reactivity of Polycyclic Aromatic Hydro- 44 45 carbons. 1. Acenes and Benzologs. J. Am. 46 Chem. Soc. 1980, 102, 3163–3173. 47 48 (71) Reylè,C.; Brèchignac, P. Fluorescence of 49 Jet-Cooled Naphthalene: Emission Spec- 50 tra, Lifetimes and Quantum Yields. Eur. 51 52 Phys. J. D 2000, 8, 205–210. 53 54 (72) Staicu, A.; Rouillè,G.; Sukhorukov, O.; 55 Henning, T.; Huisken, F. Cavity Ring- 56 Down Laser Absorption Spectroscopy of 57 Jet-Cooled Anthracene. Mol. Phys. 2004, 58 102, 1777–1783. 59 60 ACS Paragon Plus Environment 18 Page 19 of 19 The Journal of Physical Chemistry TOC image 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment 19