Article pubs.acs.org/JPCA
Structures and Binding Energies of the Naphthalene Dimer in Its Ground and Excited States N. O. Dubinets,†,‡ A. A. Safonov,† and A. A. Bagaturyants*,†,‡ †
Photochemistry Center, Russian Academy of Sciences, ul. Novatorov 7a, Moscow 119421, Russia National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoye shosse 31, Moscow 115409, Russia
‡
S Supporting Information *
ABSTRACT: Possible structures of the naphthalene dimer corresponding to local energy minima in the ground and excited (excimer) electronic states are comprehensively investigated using DFT-D and TDDFT-D methods with a special accent on the excimer structures. The corresponding binding and electronic transition energies are calculated, and the nature of the electronic states in different structures is analyzed. Several parallel (stacked) and T-shaped structures were found in both the ground and excited (excimer) states in a rather narrow energy range. The T-shaped structure with the lowest energy in the excited state exhibits a marked charge transfer from the upright molecule to the base one.
T
BHandHLYP functional19 for calculations of structures and binding energies of some excimers and exciplexes. Reasonable results obtained in ref 17 for the pyrene excimer encouraged us to use a similar approach for calculating naphthalene excimers. Therefore, in this work, all calculations for the ground electronic state of the naphthalene dimer, including geometry optimization, were performed by the DFT method with the empirical dispersion correction with Becke−Johnson damping (DFT-D3BJ),18 the BHandHLYP functional,19 and the TZVP basis set20 using the ORCA program.21 Similarly, the dimer in the first excited singlet electronic state was calculated by the TDDFT method using the same dispersion correction (TDDFT-D3BJ), the same BHandHLYP functional, and the SVP basis set22 for geometry optimization and the TZVP basis set for the final single-point calculations using the ORCA program. The Tamm−Dancoff approximation (TDA)23 was used in the TDDFT calculations, because only this version of TDDFT is implemented in the ORCA program for hybrid functionals. Population analysis for excited states is unavailable in the ORCA program; hence, the corresponding data were obtained by single-point TDDFT calculations using the GAMESS-US program.24,25 We constructed a set of structures of the naphthalene dimer with various mutual arrangements of the monomer molecules. All the structures corresponding to minima on the potential energy surfaces of the ground and excited states, both obtained in this work and reported previously,11−13 have either parallel (stacked) or T-shaped geometries.
he nature of intermolecular interactions of aromatic compounds in the first singlet excited state and the structure of their excimers are problems of great interest.1−5 Naphthalene is a classical example of aromatic compounds that form dimers in both the ground and excited states.1−4,6−8 From experimental data, the binding energy in the naphthalene dimer was estimated at 0.125 eV6 for the ground state and at 0.73− 0.73 eV9 for the excited state. The experimental transition energy to the first excited electronic state is 3.13 eV.10 In the most comprehensive theoretical study of the naphthalene dimer in its ground state, eight structures, six parallel-displaced and two T-shaped, were considered using the MP2/6-31G* approximation.11 The binding energy in the parallel structure of the naphthalene dimer was calculated by several high-level correlated methods: MP2, MP3, MP4(SDQ), MP4(SDTQ), CCSD, and CCSD(T).12 For the naphthalene dimer in the first excited state (excimer), only one face-to-face structure was considered using the TDDFT method with the aug-cc-pVDZ basis set and different functionals13 and the CASSCF/MCQDPT method with several basis sets.9 However, the entire variety of possible equilibrium structures of the naphthalene dimer in the excited state has not been investigated so far. As is known, reliable structures and binding energies of molecular structures including van der Waals complexes in the ground electronic state can be obtained using the DFT method with an empirical dispersion correction (DFT-D method).14−16 Although the dispersion correction was parametrized for the ground rather than excited state, Huenerbein and Grimme17 successfully applied the TDDFT technique in combination with an empirical dispersion correction (TDDFT-D) 18 and © XXXX American Chemical Society
Received: April 13, 2016
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DOI: 10.1021/acs.jpca.6b03761 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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molecule directed toward the base molecule. Structures with parallel arrangement of molecules are designated by symbol P followed by the sequential number of the structure and, analogously to T-shaped structures, supplied with index g or e. Parallel structures with different angles between the long axes of the molecules were taken as starting ones for geometry optimization. We optimized the geometries of the constructed structures and calculated their binding energies in the ground and excited electronic states. Optimized structures for the ground and excited states are schematically shown in Figure 2. Ground- and excited-state T-shaped structures are visually similar and, hence, are shown in common panels. For the ground electronic state, four parallel and two Tshaped structures were found: P1g with parallel long molecular axes, P2g with nearly perpendicular axes (97°), P3g with an angle between axes of 49°, and P4g with an angel of 123°, T12g, and T34g. No minima corresponding to the T23 geometry was found for the ground state. In all of the optimized parallel structures, the molecules in the dimer are shifted with respect to each other along both axes. Structures P1g, P2g, T12g, and T34g are similar to structures reported in ref 11 (PD-4, PD-6, T1, and T2, respectively). For the excimer, four parallel and three T-shaped structures were found: P5e, which is an exactly face-to-face structure with a zero angle between the axes of molecules and a zero shift, similar to that reported in ref 13; P6e with a zero shift and an angle of about 70° between the axes; P7e with an angle of about 100° and a significant shift of molecules with respect to each other; P8e with the zero angle and a large shift; and T-shaped
In the T-shaped structures, one of the monomer molecules lies in the basal plane and the other one occupies an upright position with respect to the base molecule and lies in the plane orthogonal to the basal plane. The upright molecule can be directed toward the base molecule by one of three possible pairs of hydrogen atoms (H1−H2, H2−H3, or H3−H4, Figure 1). The plane of the upright molecule is oriented along the
Figure 1. Naphthalene molecule.
longer (x) axis of the base molecule; no structures with the orientation of the upright molecule along the shorter (y) plane of the base molecule were found. T-shaped structures are designated by symbol T followed by a pair of numbers denoting the pair of hydrogen atoms in contact with the base molecule and index g or e denoting that the structure is optimized for either the ground or the excited state. For example, symbol T12g relates to a T-shaped structure optimized for the ground electronic state with the H1 and H2 atoms of the upright
Figure 2. Structures of the naphthalene dimers in the ground (T12g, T34g, P1g, P2g, P3g, and P4g) and excited (T12e, T23e, T34e, P5e, P6e, P7e, and P8e) states. B
DOI: 10.1021/acs.jpca.6b03761 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A structures T12e, T23e, and T34e. The parallel structures of the excimer Pe largely differ from the parallel structures of the ground-state dimer Pg, whereas T-shaped structures Tg and Te are rather similar; however, an additional T-shaped structure T23e was found for the excimer. The distance between the molecules in the dimer was defined as the distance between the planes of the two molecules for the parallel structures and as the distance between the plane of the base molecule and the nearest H atoms of the upright molecule for the T-shaped structures. In the ground-state dimer, the distance between molecules was found to be 3.3−3.5 Å for the parallel structures, which is in agreement with values reported in ref 11 (3.5−3.6 Å) and 2.5 Å for T-shaped structures. The T-shaped structures can be compared with those from ref 6 using the distance between the plane of the base molecule and the center of the upright molecule; this distance was 5.9 and 5.0 Å for our structures T12g and T34g and 6.1 and 5.1 Å for analogous structures T1 and T2 from ref 11. In the excimer, the distance between molecules is 2.9−3.1 Å for parallel structures (decreases by ∼0.4 Å in comparison with the ground-state dimers), 2.5 Å for T12e and T23e (remains unchanged in comparison with T12g), and 2.1 Å for T34e (decreases by 0.4 Å in comparison with T34g). The calculated binding energies of the naphthalene dimer in the ground electronic state are presented in Table 1. The binding energy for the ground state was calculated as the difference between the total energy of the dimer and twice the total energy of a single molecule.
Table 2. Calculated Characteristics of Naphthalene Dimer Structures in the Excited State at the Equilibrium ExcitedState Geometries: Binding Energies De, Transition Energies T(S1→S0), and Values of Charge Transfer
De, this work
De, ref 11
P1g P2g P3g P4g T12g T34g
−5.98 −5.93 −6.19 −5.52 −4.59 −5.00
−6.36 −6.14
De, kcal/mol
T(S1→S0), eV
charge transfer
P5e P6e P7e P8e T12e T23e T34e
−24.1 −23.6 −13.0 −14.2 −6.3 −5.0 −8.2
3.01 3.18 3.60 3.86 4.36 4.56 4.17
0.000 0.000 0.045 0.001 0.006 0.011 0.349
The experimental estimate of the binding energy of the naphthalene exciplex is −0.73 to −0.76 eV (about −17 kcal/ mol).9 It is seen in the table that the minimum binding energy for naphthalene dimers in the excited state corresponds to the P5e structure. For the parallel structures, the obtained binding energies of the naphthalene dimer in the excited-state are much larger in magnitude than those in the ground state, which is typical of excimers.1−5 For the T-shaped structures, the difference between the binding energies in the excited and ground states is rather small (1−3 kcal/mol). The calculated S1 → S0 transition energies can be compared with the experimental emission energy of the naphthalene excimer, 3.13 eV10 and with the results of CASSCF/MCQDPT calculations with different basis sets for a structure similar to P5e: from 3.17 eV (6-31G*) to 2.58 eV (aug-cc-pVDZ).13 Note that only partial geometry optimization (along the distance between molecular planes) was performed in the latter work.13 In most structures of the naphthalene excimer, charge transfer is insignificant except for the T34e structure. Note that it is the only T-shaped structure in which the distance between molecules in the excited state is significantly shorter than that in the ground state. In Figure 3, charge transfer for the S1 → S0
Table 1. Calculated Binding Energies (De, kcal/mol) of Naphthalene Dimer Structures in the Ground State structure
structure
−3.75 −4.25
It is seen in the table that the minimum binding energy corresponds to the P3g structure; however, the difference between the calculated energies of P1g, P2g, and P3g structures is less than 0.3 kcal/mol. The parallel structures are slightly more favorable than the T-shaped structures. However, the scatter in the values for all the studied structures is less than 1.2 kcal/mol. For P1g, P2g, T12g, and T34g structures, our DFT-D binding energies are in reasonable agreement with the results of MP2 calculations11 and even in better agreement with the binding energy −5.69 kcal/mol calculated by high-level correlated method CCSD(T) for the parallel structure.12 The experimental binding energy is D0 = 125 meV (−2.9 kcal/mol). Table 2 presents the calculated characteristics of naphthalene dimer structures in the first excited singlet electronic state: binding energies De, transition energies T(S1→S0) at geometries optimized for the excited state, and values of charge transfer. The binding energy for the excited state was calculated as the difference between the total energy of the dimer in the excited state and a sum of the total energy of a single molecule in the ground state and the total energy of a single molecule in the excited state. Charge transfer was calculated as a sum of Mulliken charges over the monomer fragments in the excited states.
Figure 3. Natural transition orbitals for the S1 → S0 transition in the T34e structure of the naphthalene excimer.
transition in the T34e structure of the naphthalene excimer is visualized using natural transition orbitals (NTOs) involved in the transition. The transition almost totally proceeds within a single NTO pair.
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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.jpca.6b03761. C
DOI: 10.1021/acs.jpca.6b03761 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Optimized structures of naphthalene dimer in the ground and excited states (PDF)
AUTHOR INFORMATION
Corresponding Author
*A. A. Bagaturyants. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation, project no. 14-43-00052. REFERENCES
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DOI: 10.1021/acs.jpca.6b03761 J. Phys. Chem. A XXXX, XXX, XXX−XXX
