Computational Evidence of Inversion of 1La and 1Lb-Derived Excited

Article pubs.acs.org/JCTC

Computational Evidence of Inversion of 1La and 1Lb‑Derived Excited States in Naphthalene Excimer Formation from ab Initio Multireference Theory with Large Active Space: DMRG-CASPT2 Study Soichi Shirai,*,† Yuki Kurashige,‡,§ and Takeshi Yanai*,‡ †

Toyota Central R&D Laboratories, Inc., Nagakute, Aichi 480-1192, Japan Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan § Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan ‡

S Supporting Information *

ABSTRACT: The naphthalene molecule has two important lowest-lying singlet excited states, denoted 1La and 1Lb. Association of the excited and ground state monomers yields a metastable excited dimer (excimer), which emits characteristic fluorescence. Here, we report a first computational result based on ab initio theory to corroborate that the naphthalene excimer fluorescence is 1La parentage, resulting from inversion of 1La and 1Lb-derived dimer states. This inversion was hypothesized by earlier experimental studies; however, it has not been confirmed rigorously. In this study, the advanced multireference (MR) theory based on the density matrix renormalization group that enables using unprecedented large-size active space for describing significant electron correlation effects is used to provide accurate potential energy curves (PECs) of the excited states. The results evidenced the inversion of the PECs and accurately predicted transition energies for excimer fluorescence and monomer absorption. Traditional MR calculations with smaller active spaces and single-reference theory calculations exhibit serious inconsistencies with experimental observations.

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INTRODUCTION Aromatic excimer (AE) is a short-lived dimeric complex in an electronically excited state.1 As schematized in Figure 1(a), it is

AEs has motivated several applications utilizing them, such as chemosensors,6,7 molecular beacons,8 and light-harvesting materials.9 The detailed physical-chemical understanding of the AE formation is thus an important subject; however, it has not been fully established. In the pioneering work of Förster, he first observed the AE fluorescence in pyrene and naphthalene10−12 and proposed that the lowest excited state of the excimer originates from the singlet La state (1La) of the excited monomer, which in fact is known to lie above the adjacent singlet Lb state (1Lb) as illustrated in Figure 1(a). Here, in the Platt’s notation,13 the electronic state is designated by A, B, C, ··· or K, L, M, ··· in accordance with its total momentum number Q (or total ring quantum number). The state symbol L is used when Q is given as Q = ±(2n + 1) where n refers to the number of rings; e.g., n = 2 for naphthalene. The subscriptions a and b indicate the location of the nodes of the wave function: with a and b, the nodes are indicated to be present on C−C bonds and on carbon atoms, respectively. Förster’s hypothesis above suggested that the energy levels of the 1La− and 1Lb− excited states of [R−R]*, which are the lower-energy components of the split 1La- and 1Lb-derived dimer states, respectively, should invert during the dimerization. This hypothetical mechanism based on the experimental evidence is widely accepted as a basic description. Note that aromatic

Figure 1. (a) Schematic diagram of the process of naphthalene excimer formation and the energy levels of the associated electronic states and (b) calculated model of the naphthalene dimer.

considered to be formed by the association of an excited molecule R* and a ground state counterpart R. This process is followed by a radiative deactivation of AE, emitting the socalled excimer fluorescence, which exhibits a broad structureless band and is substantially red-shifted relative to monomer emission.2,3 This conspicuous property of AE has attracted a great deal of interest for over half a century. Its importance has been recently revived because the formation of AE is closely related to a core process of energy transfer and electron transfer in condensed organic materials.4,5 In addition to fundamental research to dissect the mechanism, the potential usability of © 2016 American Chemical Society

Received: February 25, 2016 Published: April 15, 2016 2366

DOI: 10.1021/acs.jctc.6b00210 J. Chem. Theory Comput. 2016, 12, 2366−2372

Article

Journal of Chemical Theory and Computation molecules which have the 1La state for their lowest excited state, such as 9-methyl anthracene and perylene, also emit excimer fluorescence.14−16 Theoretical approaches based on quantum chemical methods have played an important role in examining the details of the mechanism of the AE formation. Using semiempirical theory in combination with experimental data, a phenomenological model was formulated to deduce that 1La− is significantly stabilized by strong intermolecular interactions associated with exciton resonance (ER) and charge resonance (CR), resulting in the pronounced lowering of its energy level.12,15−18 High-accuracy prediction of the relative energy levels of the 1 La and 1Lb excited states using ab initio calculations is a challenging subject for modern quantum chemistry. The difficulties arise from that the prediction for the naphthalene excimer formation meets the following three requirements simultaneously to corroborate the experimental evidence: (i) the transition energies of the monomer absorptions for the 1La and 1Lb states and (ii) of the excimer fluorescence should be qualitatively computed with a small error relative to the experimental measurements and (iii) the energy levels of the 1 − La and 1Lb− dimer states invert in dimerization. The single reference electronic structure methods have been extensively used; however, none of them has been found satisfactory.19−21 This indicates that the multireference (MR) or multiconfigurational character of electron correlation is of great significance in the excited states.22 Indeed, it was demonstrated that the 1La and 1Lb excitation energies of the naphthalene monomer can be accurately predicted by the multireference perturbation theory (MRPT) methods,23,24 in which the central MR character is accounted for using the complete active space self-consistent field (CASSCF) theory.25 In the MRPT study, the full π valence CAS was used as an ideal MR treatment; for the naphthalene monomer, it is constructed by distributing all ten π electrons over ten π/π* orbitals and denoted CAS(10πe, 10πo). The extension of the MRPT treatment to the naphthalene dimer, however, raises fundamental difficulties, which are ascribed to the fact that the dimension of the full π valence CAS rises exponentially with increasing system size. The conventional MR methods are incapable of handling a double of the monomer CAS, namely CAS(20πe, 20πo), which corresponds to 3 × 1010-dimensional configuration space. In this study, we tackle this challenge using the density matrix renormalization group (DMRG) algorithm,26 which has recently been introduced as an exceedingly efficient MR electron correlation approach.27 The goal of this work is to provide the potential energy curves (PECs) of the excited states of the naphthalene dimer computed at the MRPT level of theory with the full π valence MR treatment. We shall show that our advanced MRPT method, referred to as DMRGCASPT2,28,29 offers the first accurate computational results that are based on ab initio calculations and essentially satisfy all of the aforementioned three requirements (i)−(iii). On the basis of our description, the mechanism of the excimer formation is analyzed in detail. For comparison, MRPT with truncated CAS references and several single-reference methods are benchmarked.

at the B3LYP/6-31G(d) level of theory. The optimized geometry was in good agreement with the experimental measurement.30 The errors in the bond length and bond angle relative to the experimental values are within 0.005 Å and 0.2°, respectively (Figure S1). The monomer geometry was kept fixed in dimer calculations. The eclipsed parallel conformer with D2h symmetry was chosen as a model of the dimer structure (Figure 1(b)). The normal line and long axis of the monomer plane were set as parallel to the z and x axes, respectively. The PECs of the 1La− and 1Lb− excited states and the ground state (1A1g) were computed as a function of the intermolecular distance r(R−R), ranging from 2.7 to 10.0 Å, using the DMRG-CASPT2 method. The reference MR wave functions were determined by the preceding DMRG-CASSCF calculations31,32 with the full π valence CAS(20πe, 20πo). Exact diagonalization with this large-size CAS was achieved using DMRG with 256 spin-adapted renormalized bases. In the DMRG step, the localized orbitals were used as a computationally suited basis; the orbital ordering for DMRG sites is shown in Figure S2. The dynamic correlation effects were accounted for by the CASPT2 treatment33 on top of DMRGCASSCF wave functions with an imaginary shift and an IPEA level shift set to i0.1 and 0.25 au, respectively. In DMRGCASPT2, the cumulant approximation was made to fourparticle-rank reduced density matrix.29 The basis sets used were Dunning’s cc-pVDZ and cc-pVTZ.34 The DMRG-CASSCF/ CASPT2 calculations were carried out using our in-house code. Conventional CASPT2 calculations with the truncated reference spaces, CAS(8πe, 8πo), CAS(10πe, 10πo), and CAS(12πe, 12πo), and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD)35,36 calculations were performed using the MOLPRO package.37 Time-dependent density functional theory (TDDFT) calculations were carried out with B3LYP, CAM-B3LYP,38 and ωB97XD39 functionals and the cc-pVTZ basis set. Geometry optimization, TDDFT calculations, and monomer EOM-CCSD calculations were performed using the Gaussian09 package.40 In the EOM-CCSD calculations, aug-cc-pVDZ and aug-cc-pVTZ basis sets34,41 were additionally used to examine the effect of diffuse functions. CIS(D) calculations42 with RI approximation were performed using the ORCA 3.0.3 program43 with cc-pVDZ, cc-pVTZ, augcc-pVDZ, and aug-cc-pVTZ basis sets. The sixth-order polynomial function was used for the fitting to PECs to obtain spectroscopic parameters. Let us briefly recapitulate the DMRG-CASSCF/CASPT2 methods. The DMRG-CASSCF provides the reference wave function |Ψ0⟩ that describes static correlation with active orbitals and electrons.31,32 The DMRG method plays a key role in computing the CASSCF wave function with the use of a large active space; in this study, it handled CAS(20πe, 20πo). On the top of the CASSCF reference, the dynamic correlation is additively accounted for with the perturbation treatment based on CASPT2 theory. In CASPT2, the correction to the reference wave function is obtained as the first-order perturbation |Ψ1⟩. The CASPT2 correction energy calculated as ΔCASPT2 = ⟨Ψ0|H|Ψ1⟩ is added to the CASSCF energy ECASSCF (= ⟨Ψ0|H|Ψ0⟩). Because the CASPT2 is built on the internal contraction MR scheme, it can be combined with the DMRG using the reduced density matrices of the DMRG wave function.28,29

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COMPUTATIONAL DETAILS The geometrical structure of the naphthalene monomer was optimized using density functional theory (DFT) calculations 2367


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Journal of Chemical Theory and Computation

Figure 2. DMRG-CASPT2 potential energy curves of the ground state (1Ag, ●), 1La− (1B3g, ▲), and 1Lb− (1B2g, △) excited states of the naphthalene dimer obtained by using (a) cc-pVDZ and (b) cc-pVTZ basis sets, respectively. The plotted energies are given relative to the ground state energy at r(R−R) = 10.0 Å.

Table 1. Equilibrium Intermolecular Distance (re), 11B3g−11B2g Inversion Distance (rinv), Dissociation Energies (De), and Transition Energies of the Naphthalene Dimer transition energy re (Å) method DMRG-CASPT2 CASPT2 (8πe, 8πo) (10πe, 10πo) (12πe, 12πo) CIS(D)

EOM-CCSD

TD-B3LYP TD-CAM-B3LYP TD-ωB97XD exptl

basis set

1

−

1

La ( B3g)

1

De

Lb−

1

( B2g)

cc-pVDZ cc-pVTZ

3.08 3.08

3.18 3.20

cc-pVDZ cc-pVDZ cc-pVDZ cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ cc-pVDZ aug-cc-pVDZ cc-pVTZd aug-cc-pVTZd cc-pVTZ cc-pVTZ cc-pVTZ

3.04 3.05 3.05 3.01 2.99 3.00 3.00 3.15 3.13

3.12 3.14 3.12 3.07 3.03 3.07 3.06 3.28 3.21

3.41 3.29 3.19 3.0−3.6e

3.44 3.40 3.25

rinv (Å) 3.26 3.62

4.70

4.55 4.36

1

−

1

La ( B3g)

1

−

1

Lb ( B2g)

1.23 1.33

0.54 0.62

1.16 1.03 1.02 1.49 1.97 1.58 1.76 0.83 1.19

0.67 0.54 0.72 0.92 1.19 1.04 1.10 0.36 0.79

0.56 0.47 1.01

0.22 0.16 0.67

r(R−R) = re −

La −

1

Lb−a

1

0.61 0.85

1.00

0.43 0.95 0.25f

La−c

r(R−R) = 10.0 Åb

1

1

−

1

3.43 3.18

3.72 3.63

4.92 4.74

4.31 4.26

3.02 3.17 3.17 3.62 3.32 3.45 3.35 4.02 3.74

2.51 2.71 3.44 3.53 3.27 3.42 3.33 3.92 3.70

3.31 3.63 3.48 3.13g

3.36 4.05 3.86

4.18 4.20 4.20 5.35 5.15 5.20 5.11 5.25 5.06 5.09 5.02 4.34 4.64 4.65 4.45,h 4.7i

3.18 3.26 4.17 4.53 4.46 4.46 4.43 4.46 4.46 4.42 4.39 4.44 4.59 4.60 3.97h

Lb

La−

Lb−

1

a

Calculated as the energy difference between 11B3g at r(R−R) = re and 11B2g at r(R−R) = 10.0 Å. Corresponding to the experimentally observed binding energy. bCorresponding to the monomer absorption energy. cCorresponding to the experimentally observed excimer fluorescence energy. d Values obtained by the calculations of the naphthalene monomer. eReference 2. fReference 44. Binding energy in solution. gReference 16. h Reference 45. The 0−0 transition in gas phase. iReference 46.

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RESULTS AND DISCUSSION

Table S1−S3. In the labeling of the NOs, the dimer’s HOMO− 1 (2b1u), HOMO (1au), LUMO (2b3u), and LUMO+1 (2b2u) originate from the monomer’s counterparts. The NOONs indicate that the HOMO → LUMO singly excited configuration is dominant in 1La−, and the single-electron excitations in 1Lb− mainly take place within HOMO−1, HOMO, LUMO, and LUMO+1, as these reflect the excitation characters of the originating monomer states (see also ref 22). Let us first discuss the results obtained by DMRG-CASPT2 calculations with the CAS(20πe, 20πo) reference. The relative state energies are plotted as a function of the intermolecular distance, r(R−R), in Figure 2. The spectroscopic parameters from the PECs are shown in Table 1 along with the results obtained by various other methods and the experimental values. The DMRG-CASPT2 predicted that 1B3g is higher-lying than

The previous studies showed that the main configuration of the monomer 1La is HOMO → LUMO single electron excitation, whereas the monomer 1Lb is characterized by a superposition of HOMO → LUMO+1 and HOMO−1 → LUMO singly excited configurations;22−24 these monomer MOs and configurations are displayed in Figure S3. We characterized the excited dimer states by examining the natural orbitals (NOs) derived from the reference DMRG-CASSCF wave function. It was then found that 11B3g and 11B2g states are of 1La and 1Lb parentage, respectively, and thus correspond to 1La− and 1Lb−, respectively. The shapes of NOs for the ground state and the 1La− and 1Lb− excited states are shown in Figures S4, S5, and S6, respectively, and associated occupation numbers (NOONs) are given in 2368


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B2g at large intermolecular distances. This energetic ordering (1La− > 1Lb−) is consistent with the experimental observation for the monomer (1La > 1Lb).45 It was shown in Figure 2 that the PECs of 1La− and 1Lb− intercross during the association, and 1La− turns out to be the lowest excited state at the excimer structure r(R−R) = 3.08 Å (Table 1). The dissociation energies (De) for the PECs of 1La− and 1Lb− are 1.33 (1.23) and 0.62 (0.54) eV for cc-pVTZ (cc-pVDZ), respectively. Our approach thus confirmed that the excimer fluorescence is monomer 1La parentage and the PEC of 1La− is much deeper than that of 1 − Lb , as consistent with Förster’s hypothetical picture.12 This strong attractive potential of 1La− is a driving force of the excimer formation. The equilibrium intermolecular distances (re) and dissociation energies (De) of each state are less basis set dependent (Table 1), indicating that the PECs are similar in shape between cc-pVDZ and cc-pVTZ. In terms of the transition energies, 1La− is relatively sensitive to the basis set quality. Related to this, the inversion distance (rinv) with ccpVTZ (3.62 Å) is longer than that with cc-pVDZ (3.26 Å). The transition energies at the excimer and superdimer structures computed with cc-pVTZ are in good agreement with the experimental values. The excimer binding energy, defined by the energy difference between the minima of 1La− and the energy of 1Lb− at r(R−R) = 10.0 Å, was estimated to be seriously larger than the experimental value. In order to trace the origin of this overestimation, we examined basis set superposition errors (BSSE) and solvent effects22,47 at the second-order Møller−Plesset (MP2) level of theory. The BSSE for the naphthalene dimer with the near binding structure was estimated to be 0.33 and 0.17 eV for cc-pVDZ and cc-pVTZ, respectively, in the 1Ag state (Table S4); the account of these BSSE effects serves as appreciably reducing the overestimation. The solvent effect with n-heptane, which was used in the experiments in ref 44, seems to be negligibly small in the binding energy (Table S5). Note that the DMRG-CASSCF potential energy curves are repulsive or substantially shallow compared to DMRG-CASPT2 curves, and the intercross of the excited states was not predicted (Figure S7). The results indicate that the additive incorporation of dynamic electron correlation is absolutely necessary for reliable prediction of the intermolecular interactions in the excited states as well as the ground state. We analyzed the DMRG-CASSCF wave function in further detail. As indicated in the earlier semiempirical studies,15−18 the excimer formation is driven by the strong 1La’s attractive intermolecular interaction arising from a mixing of excition resonance (ER) and charge resonance (CR) configurations. ER is associated with the intramolecular excitation (R*R ↔ RR*) accompanied by the interaction between the transition dipole moments, |μ|, and the interaction energy EER is approximately written as EER ≈ |μ|2/{r(R−R)}3. CR is associated with the intermolecular charge-transfer excitation (R+R− ↔ R−R+). The interaction energy ECR is expressed as ECR ≈ IP − EA + C, where IP is the ionization potential of the monomer, EA is the electron affinity, and C is the Coulombic interaction between the positive and negative ions. The contributions of the ER and CR characters in the dimer wave function were estimated from a total of the weights of the corresponding configuration basis (Table 2). For this analysis, we exploited the structure of the DMRG wave function written as ΨDMRG = Σmωm|Lm⟩|Rm⟩, where |Lm ⟩ and |Rm⟩ each refer to the renormalized configuration of the basis of the monomer site, and ωm is the associated weight. At large distance r(R−R) = 5.2 Å, 1La− and

Table 2. Statistical Weights of Electron Configurations Ascribed to Exciton Resonance (ER) and Charge Resonance (CR) in the Expansion of the DMRG-CASSCF Wavefunction for 1La− (1B3g) and 1Lb− (1B2g) Excited States of the Naphthalene Dimer as a Function of the Monomer− Monomer Distance r(R−R) weight (%) excited state

r(R−R) (Å)

ER

CR

1

La− (1B3g)

1

Lb− (1B2g)

3.1 3.6 5.2 3.2 3.6 5.2

59.9 73.7 99.9 94.8 98.8 100.0

40.1 26.3 0.1 5.2 1.2 0.0

Lb− states are both characterized by near 100% ER. In 1La−, the CR character rises up to 40% for the excimer formation, while it remains negligible in 1Lb−. This near CR-free character in 1Lb− is an interesting finding; the previous semiempirical approaches were unable to unveil it. Since the transition dipole moment of the monomer 1Lb is much smaller than that of 1La, the attractive interaction in 1Lb− driven by ER alone should be far weaker than that in 1La−. In the presence of the transition dipole− transition dipole interaction, the attractive interaction in 1La− is further pronounced by the growth of its CR character, as modeled by the semiempirical approach. These imbalanced intermolecular interactions underlie the mechanism of the inversion of the two excitation levels. We now turn to the PECs obtained by conventional CASPT2 calculations with the truncated full π valence CAS (Figure 3). The relative energy level of the PEC of 1Lb− largely varies depending on the CAS size, while that of 1La− is almost unaltered by the CAS settings used. With CAS(8πe, 8πo) and CAS(10πe, 10πo), the excitation energies of 1Lb− are significantly underestimated relative to the DMRG-CASPT2 results and experimental observations, and the 1La−−1Lb− inversion is absent. Although the inversion is marginally observed with CAS(12πe, 12πo), the energy gap between 1 − La and 1Lb− in the dissociation region is extremely small (0.03 eV). Overall, the CASPT2 method with the truncation of the full π valence CAS poorly performed for describing excimer formation. It is of interest to illuminate the origin of the large dependence of MRPT results on CAS size. Here we focus on the NOONs of the CASSCF wave function, which are often used for elucidating MR character. Figure 4 shows ΔI (1La−) and ΔI (1Lb−) obtained with the NOONs resulting from the CASSCF calculations (Tables S1−S3) and the mean-field occupancies (Table S6), where the mathematical definitions of ΔI (1La−) and ΔI (1Lb−) are given in page S15. They represent the degree of the role of each active orbital in describing the electron correlation for the excited state (see page S15 for details). With 1La−, the pronounced correlation effects arise predominantly in HOMO and LUMO for all the CAS settings. This feature is in contrast with 1Lb−, in which a large part of the orbital set participates in describing electron correlation, and the roles of the active orbitals largely vary depending on the CAS size. This analysis clearly shows that for 1Lb−, the MR character is much stronger than that for 1La−, and the truncation of CAS has a great impact on the reference description. 1

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Figure 3. CASPT2/cc-pVDZ potential energy curves of the ground state (1Ag, ●), 1La− (1B3g, ▲), and 1Lb− (1B2g, △) excited states of the naphthalene dimer obtained by employing (a) CAS(8πe, 8πo), (b) CAS(10πe, 10πo), and (c) CAS(12πe, 12πo) as the reference spaces. The plotted energies are given relative to the ground state energy at r(R−R) = 10.0 Å.

Figure 4. Natural orbital analysis based on the indices ΔI (1La−) (eq (S1a)) and ΔI (1Lb−) (eq (S1b)) to gauge the degree of the role of each natural orbital (I) in descrbing electron correlation for 1La− (1B3g) and 1Lb− (1B2g) states with the CASSCF(ne,no) wave function (n = 8, 10, 12, and 20). These indices were evaluated using the occupation numbers provided in Tables S1−S3 and S6, and the values are given in Table S7. The details of the definition of ΔI (1La−) and ΔI (1Lb−) are described on page S15.

Figure 5. Potential energy curves obtained by using single-reference methods: (a) EOM-CCSD/aug-cc-pVDZ, (b) CIS(D)/aug-cc-pVTZ, and (c) TD-B97XD/cc-pVTZ. See also Figures S8−S10 for other results.

The single-reference EOM-CCSD, CIS(D), and TDDFT potential energy curves are shown in Figures 5 and S8−S10. With EOM-CCSD, 1Lb− was predicted to be lower-lying than 1 − La across PEC where the inversion of these states did not occur (Figures 5(a) and S8). The augmentation of diffuse basis functions slightly decreased the transition energies and increased the binding energies; however, it did not make any

essential improvement on the PECs. The relative energies of CIS(D) accurately reproduced those of high-level EOM-CCSD at superdimer geometry, while they were underestimated at the excimer structure by an error of 0.4 eV relative to EOM-CCSD results (Figures 5(b) and S9). With TD-B3LYP, 1La− is lowerlying than 1Lb− in the entire PECs; this energy ordering is opposite to the experimental observation for the monomer 2370


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Journal of Chemical Theory and Computation (Figure S10(a)). The calculated 1La− transition energy at r(R− R) = re (3.31 eV) is close to the experimental excimer fluorescence energy (3.13 eV), while the ground state energy is overestimated. Although the 1La− and 1Lb− levels marginally cross in the PECs of TD-CAM-B3LYP and TD-ωB97XD based on the range-separation treatment, they converge to near degenerate energy levels at large intermolecular distance (Figures S10(b) and 5(c)). TD-B3LYP and TD-CAM-B3LYP gave longer re and smaller De than DMRG-CASPT2, indicating that the attractive interactions in 1La− and 1Lb− are underestimated compared to the DMRG-CASPT2 (Table 1). The re and De obtained by TD-ωB97XD are close to those by DMRGCASPT2, suggesting the importance of weak interactions driven by dispersion force. These functional dependences of transition energies are essentially similar to those reported in the calculation of the monomer.20,48,49 Overall, the singlereference electronic structure methods examined here were all inadequate to provide PECs consistent with experimental observation of the excimer formation. This indicates that the MR description is rather essential for characterizing the two excited states.

to Drs. Ryoji Asahi and Nobuko Ohba at Toyota Cental R&D Laboratories., Inc. for their suggestions, support, and encouragement. S.S. was supported by ACT-C, JST. Y.K. and T.Y. were supported by KAKENHI (Grant No. 25288013, 15H01097, 25410030, 26104538) from MEXT. Y.K. acknowledges a grant of Morino Foundation for Molecular Science. The Research Center of Computer Science at Institute for Molecular Science is acknowledged.

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CONCLUSION The excited states of the naphthalene dimer were investigated using DMRG-CASPT2 calculations with full π valence reference CAS(20πe, 20πo). To the best of our knowledge, our results serve as a first computational evidence to theoretically confirm that energy levels of 1La− and 1Lb− excited states invert during the excimer formation, and the excimer fluorescence is monomer La parentage. CASPT2 with truncated CAS references and EOM-CC and TDDFT calculations were inadequate for describing these excited states in a balanced manner and exhibited serious inconsistencies with the experimental observations. Appropriate ab initio descriptions were solely provided by our MR approach using a large reference space that can capture strong electron correlation in the exited states.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.6b00210. Monomer structure (Figure S1); localized orbitals used in DMRG (Figure S2); natural orbitals of naphthalene monomer and dimer (Figures S3−S6); occupation numbers (Tables S1−S3, S6); BSSE and solvent effect estimated by MP2 (Tables S4 and S5); PECs of CASSCF, EOM-CCSD, CIS(D), and TDDFT (Figures S7−S10); NOON analysis (Table S7); total energies (Tables S8−S14) (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. Shinji Inagaki and the members of his group; their experimental research on the light-harvesting materials9 strongly motivated us. The authors are also grateful 2371


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Computational Evidence of Inversion of 1La and 1Lb-Derived Excited

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