JahnâTeller Effect of the Benzene Radical Cation - ACS Publications

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Jahn-Teller Effect of the Benzene Radical Cation: A Direct Ab Initio Molecular Dynamics Study Hiroto Tachikawa J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00292 • Publication Date (Web): 11 Apr 2018 Downloaded from http://pubs.acs.org on April 17, 2018

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The Journal of Physical Chemistry

Jahn-Teller Effect of the Benzene Radical Cation: A Direct Ab Initio Molecular Dynamics Study Hiroto TACHIKAWA* Division of Applied Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, JAPAN

Abstract: The benzene radical cation (Bz+) is a typical model molecule of the Jahn-Teller (J-T) active species. Bz+ has two structural forms due to the J-T effect. These are the compressed and elongated forms, expressed as Bz+(comp) and Bz+(elong), respectively. In Bz+(comp), the hexagonal structure of the benzene ring is compressed up and down, and in Bz+(elong), it is pulled up and down. From electron spin resonance experiments, it was found that Bz+ takes a compressed form in low-temperature Freon matrices (CF3Cl and CF2ClCFCl2), whereas the elongated form was found in argon matrices. However, the selectivity of these structural forms is still unclear. In this study, the ionization dynamics of isolated benzene (Bz) and benzene-M complexes (where M denotes counter-molecules, M = NH3, H2O, CF3Cl, CH4, CH3OH, Ar, SH2, ammonia dimer, or water dimer) have been investigated by means of the direct ab initio molecular dynamics (AIMD) method, in order to shed light on the Bz+ formation mechanism. The static ab initio calculations showed that Bz+(comp) is slightly more energetically stable than Bz+(elong), although the energy difference was only 0.1 kcal/mol at the CCSD/6-311++G(d,p) level. The direct AIMD calculations indicated that Bz+(comp) was formed from the Bz-M complexes when M was NH3, CF3Cl, or an ammonia dimer, whereas the ionization of Bz-M when M was H2O, CH4, CH3OH, SH2, or a water dimer, formed Bz+(elong). In the case of complexes with an argon dimer, Bz(Ar)2, both forms were obtained from a slight orientation change of Ar on Bz. A selective rule is discussed on the basis of the calculated results.

Corresponding Author: Hiroto Tachikawa, [email protected]

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1. Introduction The Jahn-Teller (J-T) effect is frequently found in several chemical and physical systems.1-6 The coupling between degenerate electronic states and asymmetric vibrations results in the energy minimum of the molecule being located in geometric structures with lower symmetry. Benzene (Bz) is a simple aromatic hydrocarbon and an important solvent for several organic solutes. The radical cation of the benzene molecule (Bz+) is J-T active and it has several other interesting characteristics.7-24 Figure 1 shows a schematic illustration of the types of structural deformation of Bz+ and the shifts of orbital energies due to the J-T effect (an expression of the potential energy curve is given in Scheme S1 in the supporting information). There are two types of deformation in Bz+: the compressed and elongated forms, which are expressed as Bz+(comp) and Bz+(elong), respectively. In Bz+(comp), the C–C bond lengths of R2 and R5 are shorter than the others, whereas in Bz+(elong) they are longer than the others. In 1983, Iwasaki et al. measured the electron spin resonance (ESR) spectrum of Bz+ in Freon matrices (CFCl3) at 4.2 K.25 They obtained clear evidence that the orbital degeneracy of the 2E1g benzene cation (D6h) is split into two electronic states (D2h): the unpaired electron occupies the b2g orbital with D2h symmetry (2B2g), giving major spin densities located at the 1,4-carbon positions of Bz+. This result was supported by isotope exchange (H/D) experiments with Bz+(D).26 On the basis of ab-initio calculations, Raghavachari et al. determined the J-T distorted structures of Bz+.27 They suggested that Bz+ has compressed and elongated forms at the ground state. The former and latter structures have 2B2g and 2B1g electronic states under D2h symmetry, respectively. At the MP2 level, the compressed structure

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(2B2g state) was predicted as the stable ground state. Huang and Lunell carried out more accurate ab-initio configuration interaction (CI) calculations for the benzene cation.28 Their configuration interaction with all single and double substitutions (CISD) calculations predicted that the benzene cation in the 2B2g state (compressed form) is more stable than in the 2B1g state (elongated form). The hyperfine coupling constants (HFCCs) of the hydrogen atoms of Bz+ in the compressed form are in good agreement with the experimental values obtained by Iwasaki et al.25 In 1999, Feldman et al. measured an ESR spectrum of the benzene radical cation in argon matrices at low temperature.29 They suggested that Bz+ in argon matrices shows the elongated form at 16 K. These results indicated that the benzene radical cation is capable of taking both structural forms: Bz+(comp) and Bz+(elong). Lund and co-workers investigated Bz+ in several matrices at low-temperature.30 Bz+ in Freon matrices has the compressed form as in the previous experiment. The ESR spectra observed in the other matrices were unresolved, and the electronic state of Bz+ was not determined. Thus, the structural form of the Bz+ is strongly dependent on the environment around the neutral Bz molecule before the ionization. However, the selectivity of the structural forms is still unclear. Also, the dynamics of Bz+, following the ionization of the parent Bz is not yet clearly understood. There is no information on the relaxation process from vertical ionized benzene cation, [Bz+]ver, to the distorted structures, Bz+(comp) or Bz+(elong). In particular, the reason why the compressed form is mainly formed in a low temperature matrix is still unclear. In the present study, the structural relaxation of benzene radical cation following the ionization of Bz was investigated by means of the direct ab-initio molecular dynamics (AIMD) method in order to elucidate the formation mechanism of the two forms of the

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benzene cation (compressed and elongated structures). Also, the ionization dynamics of complexes of Bz with M = NH3, H2O, CF3Cl, CH4, CH3OH, Ar, SH2, (H2O)2, and (NH3)2 were investigated to elucidate the effect of the counter molecule (M) on the electronic states of Bz+, and also to shed light on the preferential formation of Bz+(comp or elong) in low-temperature matrices.

2. Computational details The geometries of the neutral benzene (Bz) and of the benzene radical cation (Bz+) were fully optimized with the MP2, MP4SDQ, and CCSD methods. Also, the CAM-B3LYP functional was used in the density functional theory (DFT) calculation. The basis sets used were aug-cc-pVDZ, aug-cc-pVTZ, 6-311G(d,p), and 6-311++G(d,p). The HFCCs were calculated using optimized geometries. The standard Gaussian 09 program package was used for static ab initio and DFT calculations. In the direct AIMD calculation of Bz+, the geometry of Bz was first fully optimized at the MP2/6-311++G(d,p) level. Next, the trajectories of Bz+ following the ionization of Bz were calculated at the MP2/6-311++G(d,p) level under the assumption of vertical ionization at the neutral state. The optimized structure of Bz obtained at the MP2/6-311++G(d,p) level was used for the initial structure of Bz+, at time zero. The velocity Verlet algorithm was used with a time step of 0.05 fs to solve the equation of motion of the system. The velocity and momentum of each atom was set to zero at time=0 fs: the excess energy of [Bz+]ver was zero at time=0 fs. The electronic states of Bz+ and the total energy (potential energy plus kinetic energy) were carefully monitored during the reaction. We confirmed that the total energies of the two states were individually kept during the reaction. The drifts of the total energies in all trajectory

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calculations were less than 0.01 kcal/mol. Two electronic states, 2B2g and 2B1g, were examined for Bz+. The initial density matrixes for these states were obtained by the complete active space self-consistent filed (CASSCF) method with five electrons distributed into six orbitals, namely, CASSCF(5,6). Using the density matrix (the initial guess), the trajectories for the benzene radical cations at the 2B2g and 2B1g states were then propagated at the MP2/6-311++G(d,p) level. One trajectory was calculated for each electronic state, and the trajectory was started from the optimized structure of Bz. In the direct AIMD calculation of Bz+-M, the optimized geometries of neutral Bz-M complexes obtained at the MP2/6-311++G(d,p) level were used for the initial structure of Bz+-M at time zero. The velocity and momentum of each atom was set to zero at time=0 fs: the excess energy of [Bz-M+]ver was zero at time=0 fs. One trajectory was calculated from the optimized structure of each complex. The direct AIMD calculations were carried out at the CAM-B3LYP/6-311G(d,p) level. Only the ground state of Bz+-M was calculated.

3. Results 3.1. Structures of neutral benzene (Bz) and radical cations of benzene (Bz+) First, the structure of Bz was optimized under D6h symmetry. The C–C and C–H bond lengths of Bz were calculated to be R1 = R2 = 1.400 Å and r(C–H) = 1.087 Å. The optimized structures of the benzene radical cations (Bz+) are given in Figure 2. Two stable forms were obtained for Bz+: Bz+(comp) and Bz+(elong). Their bond lengths were R1 = R3 = R4 = R6 = 1.431 Å and R2 = R5 = 1.377 Å in Bz+(comp), indicating that the structure of Bz+(comp) is compressed up and down. In contrast, Bz+(elong) had bond

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lengths of R1 = R6 = 1.389 Å and R2 = R5 = 1.454 Å. These geometrical parameters suggest that Bz+(elong) has a structure pulled up and down. Figure 3 shows stick diagrams of the C–C bond lengths of Bz, Bz+(comp), and Bz+(elong). The bond lengths of neutral benzene (Bz) were six degenerated at R = 1.400 Å. In Bz+(comp), the bond lengths were split into two groups (1.377 and 1.431 Å). The short and long bond lengths were 2 and 4 degenerated, respectively (with a ratio of degeneracy of the short to long bond lengths of 2:4). In contrast, this ratio was drastically changed to 4:2 in Bz+(elong), where the short and long bond lengths were 1.389 and 1.454 Å. Thus, the structures of Bz+ are clearly described by the degeneracy ratio of their bond lengths. The energy difference between Bz+(comp) and Bz+(elong) was calculated at several levels of theory. The results are given in Table 1. At the CCSD/6-311++G(d,p) level, this difference was calculated to be –0.10 kcal/mol, indicating that Bz+(comp) is 0.10 kcal/mol more stable, in energy, than Bz+(elong). The relative energies calculated by several other methods showed a similar trend. The heights of the activation barriers were calculated and the results are given in Table S1. The height is defined as energy difference between [Bz+]ver and E(comp or elong), where [Bz+]ver means the benzene radical cation at the vertical ionization point from parent neutral benzene molecule, and E(comp) means the total energy of the compressed from. The heights of the activation barrier, Ea(comp) and Ea(elong), were calculated to be 3.6 and 3.5 kcal/mol, respectively, indicating that the conformational change between both structures can easily occur at room temperature.

3.2. Hyperfine coupling constants of Bz+.

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The HFCCs give important information on the electronic states and structure around a radical species. In the present study, the HFCCs of Bz+ were calculated and compared with the experimental values obtained by Iwasaki et al. (expl-1)25 and by Feldman et al. (expl-2).29 The calculated HFCCs of the Bz+(comp) and Bz+(elong) are given in Table 2, together with their experimental values. The most sophisticated calculation is at the CCSD/6-311++G(d,p) level. In Bz+(comp), the HFCCs of H(2,3,5,6) and H(1,4) were calculated to be –1.6 and –12.5 G, respectively, which are in good agreement with the Iwasaki's experiments.25 The HFCCs calculated for Bz+(elong) were H(1,4) = 2.0 G and H(2,3,5,6) = –8.9 G; the latter are in reasonable agreement with expl-2, although there is as yet no experimental data for the HFCCs of H(1,4) in expl-2. The MP2/aug-cc-pVTZ level of theory gave HFCCs close to the experimental values, H(2,3,5,6) = –2.8 G and H(1,4) = –9.4 G (the experimental values were –2.4 and –8.2 G, respectively). Thus, the present calculations strongly supported previous experiments.

3.3. Ionization of benzene to the 2B2g state. The time evolution of the bond lengths of Bz+ at the 2B2g state are given in Figure 4. All bond lengths of Bz+ were 1.400 Å at time zero. After the ionization, the lengths were separated into two groups: shortened and elongated bonds. The R2 and R5 (this group will be denoted R2-R5 throughout this paper) were rapidly shortened, whereas R1, R3, R4, and R6 (denoted R1-R6) were elongated. The elongated bonds reached their limited values at 12 fs (R1-R6 = 1.451 Å). The shortened bonds reached their first shortest point (R2-R5 = 1.358 Å) at 10 fs. After that, these bonds vibrated periodically. The average value of each bond length was calculated in the time range 10–120 fs. The

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average bond lengths are given as stick diagrams. The bond lengths were calculated to be R2 = R5 = 1.3671 Å, and R1 = R3 = R4 = R6 = 1.4332 Å. The ratio of degeneracy was 2:4, indicating that the structure of Bz+ remained as Bz+(comp) during the simulation.

3.4. Ionization of benzene to the 2B1g state. The time evolution of the bond lengths in Bz+ at the 2B1g state are given in Figure 5. The bond lengths were separated into two groups after the ionization: shortened and elongated bonds, as in the ionization to the 2B2g state. R1-R6 was rapidly shortened, whereas R2-R5 was elongated. The shortened bonds reached their first lowest value (1.375 Å) at 10 fs, and vibrated periodically as a function of time. The elongated bonds reached their limit values at 12 fs (1.495 Å). The average value of each bond length was obtained in the time range 10–120 fs. The average bond lengths were calculated to be R1-R6 = 1.3883 Å, and R2-R5 = 1.4557 Å. The ratio of degeneracy was 4:2, indicating that the structure of Bz+ remained as Bz+(elong). Thus, one can distinguish the structure of the Bz+s using their ratio of degeneracy. The structures of both forms remained after the ionization in short time propagation.

3.5. Structures of the benzene-M complexes To elucidate the effect of a counter molecule (M) on the structural form of the Bz+ moiety after ionization, the ionization dynamics of model systems were investigated by means of direct AIMD. The optimized structures of the model systems Bz-M (M = NH3, H2O, CF3Cl, CH4, CH3OH, and H2S), are illustrated in Figure S1 in the supporting

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information. The structures of the Bz-M neutral complexes were fully optimized at the MP2/6-311++G level. A hydrogen atom was oriented toward the benzene when M = NH3, CH4, and CH3OH, while the dipole moments of H2O and H2S were oriented toward the center of benzene when M = H2O and H2S.

3.6. Ionization of the benzene-ammonia complex A neutral complex of benzene with an ammonia molecule, Bz–NH3, is a model for the N–H––π interaction system. In the neutral state, the N–H bond of NH3 is oriented toward the center of mass of Bz. The distances of the N and H atoms from the Bz plane were calculated to be 3.624 and 2.464 Å, respectively, and the C–N bond distance was 3.624 Å. The snapshots of Bz+(NH3) after ionization are given in Figure 6. At time zero, the structure of Bz+(NH3) corresponds to that of the neutral state. At 73 fs, its energy decreased to –11.0 kcal/mol, and the C–N bond distance became 3.147 Å. The N atom of NH3 was oriented toward one of the carbon atoms of Bz+. The NH3 molecule gradually approached the carbon atom (2.517 Å at 106 fs). At 148 fs, the C–N distance was 1.544 Å, where a new C–N bond formed. The adduct complex (Bz–NH3)+ was formed, and the stabilization energy was 23.5 kcal/mol. The time evolution of the bond lengths of Bz+ after the ionization of Bz+(NH3) is given in Figure 7. All bond lengths of Bz+ were 1.400 Å at time zero. After the ionization, the lengths were separated into two groups: R2-R5 were shortened, whereas R1-R6 were elongated. The average value of each bond length was obtained in the time range 10–120 fs. The average bond lengths were calculated to be R2 = R5 = 1.3721 Å, R1 = R4 = 1.4179 Å, and R3 = R6 = 1.4137 Å. The ratio of degeneracy (shorter to

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longer) was 2:4, indicating that, after the ionization of Bz–NH3, the structure of Bz+ takes the compressed form.

3.7. Ionization of the benzene-water 1:1 complex A neutral complex composed of benzene and water molecules, Bz(H2O)n, is a prototype

model for an

aromatic-water hydrophobic

interaction.

Also,

the

benzene-water complex has been recently receiving much attention as a π–OH interaction. The ionization of the benzene-water complex results in the formation of Bz+ and an ion-molecule complex represented by [Bz–H2O]+. In this section, the initial structural relaxation process of [Bz–H2O]+, following the ionization of Bz–H2O, was investigated by means of the direct AIMD method. First, the structure of the Bz–H2O neutral complex was fully optimized at the MP2/6-311++G level. The optimized structure is illustrated in Figures S1 and S2B (time = 0 fs); in it the dipole moment of H2O was oriented toward the center of mass of Bz. The oxygen atom of the water molecule was located at 3.207 Å from the benzene surface. The time evolution of the potential energy of [Bz-H2O]+, following ionization, is plotted in Figure S2. After ionization, the potential energy vibrated in the range –3.0–(–2.0) kcal/mol due to the deformation of the benzene ring. The time evolution of the bond lengths of Bz+ and the averages of the C–C bond lengths of Bz+, are plotted in Figure S4. The time range for the average was chosen as 0–120 fs. The bond lengths were split into two groups: R2-R5 was elongated, whereas R1-R6 was shortened. The ratio of shorter and longer bond lengths was calculated to be (R1-R6:R2-R5) = 4:2, indicating that the benzene ring of Bz–H2O was deformed to the elongated structure

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after the ionization. The HOMOs of Bz–NH3 and Bz–H2O are given in Figure S4. The HOMO of Bz–NH3 consisted of an orbital symmetric in relation to the Cs plane of Bz, whereas in Bz–H2O it was an asymmetric orbital. When ionization occurs, the electron is removed from these orbitals.

3.8. Ionization of the benzene-(argon dimer) complex First, the structures of the Bz(Ar)2 neutral complex were fully optimized at the MP2/6-311++G level. Two optimized structures were obtained as shown in Figure 8. The argon dimer was stabilized in the parallel (Bz(Ar)2(parallel)) and perpendicular (Bz(Ar)2(perpendicular)) positions above the benzene ring. Bz(Ar)2(perpendicular) was 0.2 kcal/mol more stable in energy than that in the parallel position. In Bz(Ar)2, the argon atoms interacted with the π-orbital of Bz. The direct AIMD calculations were carried out from these stationary positions. The results are given in the Supporting Information (Figure S5). Bz(Ar)2(parallel) showed the compressed form, whereas Bz(Ar)2 (perpendicular) the elongated one. These results indicate that a slight positional change of the argon atoms strongly affected the structural forms of Bz+, after the ionization of Bz(Ar)2. For comparison, the structure of Bz-Ar 1:1 complex was optimized, and the optimized structure is given in Figure S6. The Bz-Ar complex has a D6h symmetry as well as the Bz molecule. The 2B1g and 2B2g states of Bz+-Ar are doubly degenerate. Therefore, there is no orbital splitting in Bz-Ar and both the compressed and elongated

structures of Bz+-Ar are obtained after the ionization of Bz-Ar as well as free Bz.

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3.9. Summary of the ionization dynamics of the benzene-M complexes Similar calculations were carried out for the other complexes. The results are summarized in Table 3 and in Figures S7, S8, and S9. The notation “Symmetry” in Table 3 means the symmetry of the highest occupied molecular orbital (HOMO) of Bz-M relative to the Cs plane of Bz. From the ionization of Bz-M (M = NH3, CFCl3, (Ar)2 with parallel position, and ammonia dimer), the product Bz+ was calculated to be Bz+(comp), whereas that of Bz-M (M = H2O, CH4, CH3OH, SH2, (Ar)2 in perpendicular position, and water dimer) lead to Bz+(elong). The structural forms of product Bz+ were dependent on the symmetry of the HOMO of M in Bz-M. The relation of structural form to symmetry will be discussed in section 4.2.

3.10. Effect of zero-point energy (ZPE) on the J-T deformation The importance of the zero-point energy (ZPE) on the reaction mechanism has been highlighted in previous studies.32-40 In this section, the effects of ZPE on J-T deformation was examined. First, ZPE simulations of a neutral system, Bz(H2O), were carried out at the CAM-B3LYP/6-311G(d,p) level. Second, the geometries and velocities of the atoms were selected from the ZPE simulations. Next, direct AIMD calculations were carried out for the cation systems. A resulting sample trajectory is presented in Figure S10 in the supporting information. The C-C bond lengths vibrated randomly as a function of time. No clear evidence of J-T distortion was obtained. Zero-point energies of Bz and Bz-H2O were 63.5 and 78.0 kcal/mol, respectively. These energies are significantly larger than those of J-T splitting energies (0.1-1.0 kcal/mol). Therefore, the J-T effect did not clearly occur under the ZPE condition.

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3.11. Effect of initial geometry on the product state of Bz+. In the present study, only one trajectory was run from the optimized structure of Bz and Bz-M, because the existence probability of structure becomes maximum at the equilibrium point. To check the initial geometry on the product structure of Bz+, the trajectories were run from several initial geometries. The optimized structures obtained at the MP2/6-31G(d) and MP2/6-311G(d,p) levels were chosen as the initial geometries. The results of direct AIMD calculations for Bz and Bz-M are given in Tables S2 and S3, respectively. It was clearly shown that the product state of Bz+ is not dependent on both initial structure and level of theory used.

4. Discussion 4.1. Summary In the present study, the J-T effect on the structures and electronic states of Bz+ was investigated by means of the direct AIMD method. The Bz+ cation has two structural forms: compressed and elongated. The compressed form was more stable in energy than the elongated one, although their energy difference was significantly small (0.1 kcal/mol at the CCSD/6-311++G(d,p) level). The initial structural change of Bz+, following the ionization of the parent neutral complex (Bz-M), was also investigated to elucidate the effect of a counter molecule (M) on the structural form of Bz+, which was strongly dependent on the electronic states and orientation of the counter molecule (M) on Bz.

4.2. Selection rule for the structural form of Bz+ in Bz-M In this section, the selectivity of structural forms is discussed. The electronic state of

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Bz+ was affected by the shape of the HOMO and the orientation of M with respect to Bz. If the HOMO of M interacted with the symmetric orbital of Bz for the Cs plane, the compressed form of Bz+ was preferentially formed after the ionization of Bz-M. In contrast, if the HOMO of M interacted with the asymmetric HOMO of Bz, the elongated form was obtained. The schematic illustration of orbital interactions between Bz and M is given in Figure 10. The HOMO of Bz has two orbitals for the Cs plane, symmetric (ΨB(sym)) and asymmetric (ΨB(asym)). The dotted line indicates the Cs plane of Bz. Figure 9A shows the interactions of Bz with NH3. The HOMO of NH3 consists of the non-bonding orbital of NH3 (n-orbital) and it can interact with the symmetric orbital of Bz (ΨB(sym)) in the Bz–NH3 complex. After the interaction of the HOMO of Bz with the n-orbital of NH3, three split orbitals are formed, φ(sym), φ(asym), and φ*(sym). Here, φ(sym) is in the lowest energy level and is composed of bonding interactions between the ΨB(sym) of Bz and the n-orbital of NH3. In contrast, φ*(sym) is in the highest energy level and consists of anti-bonding interactions. In the ionization of Bz–NH3, the electron is removed from φ*(sym), and Bz+ takes the compressed form. The asymmetric orbital of Bz, ΨB(asym), does not interact with the n-orbital of NH3, and it leads to φ(asym) in Bz–NH3. In the case of H2O, the HOMO of H2O consisted of the n-orbital with asymmetry (Fig. 9B). This orbital can interact with ΨB(asym) of Bz. Therefore, the HOMO of Bz–H2O becomes φ*(asym). The elongated form is preferentially formed after the ionization of Bz–H2O.

4.3. Comparison with the experimental values. The present calculations of the HFCCs of Bz+ were in good agreement with previous

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experiments25,29 and theoretical calculations obtained by Huang and Lunell.28 The previous experiments showed that the structural form of Bz+ is dependent on the matrices: Bz+(comp) is formed in Freon matrices, whereas Bz+(elong) is only found in argon matrices. In case of the other matrices (krypton, xenon, sulfur hexafluoride), unresolved spectra of Bz+ were found. This may be due to the fact that both structural forms are mixed in these matrices. The present calculations showed that the structural form of Bz+ is very sensitive to the environment around Bz, especially in rare gases (Ar). In Bz-(Ar)2, the structural form of Bz+ was strongly affected by the orientation of (Ar)2 on Bz, and both compressed and elongated forms were formed. The present calculation predicted that Bz–H2O, Bz–CH3OH and Bz(H2O)2 complexes would form Bz+(elong). From this result, the idea for an experiment can be proposed here. It is known that the mixture of H2O and alcohol makes glass matrices at low temperatures. Therefore, an ESR experiment of Bz in H2O/alcohol matrices may be possible. The results of present study allow us to predict that Bz+(elong) would be preferentially formed in the H2O/alcohol matrices.

5. Concluding remarks In the present study, only the initial process of Bz+ after the ionization of Bz-M was examined. The contribution of the stability of the Bz+-M complex to the structural form of Bz+ was not considered as origin of the deformation of Bz+. Such calculations will be performed in the near future. In the present study, we employed the Bz-M complex as a model system for Bz+ in order to shed light on the selection rule for the structural forms of Bz+ in several media. This model may be far from the real matrices systems. However, the results obtained in this work provide useful information on the selection

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rules for Bz+ interacting with several media.

Acknowledgments. The author acknowledges partial support from JSPS KAKENHI Grant Numbers 18K05021, 15K05371 and MEXT KAKENHI Grant Number 25108004.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI:

Potential energy curves of Jahn-Teller distortion of a benzene radical cation, Heights of activation barrier (in kcal/mol) for compressed and elongated forms, optimized structures of the neutral benzene-M complexes Bz-M (M = NH3, H2O, CF3Cl, CH4, CH3OH, and SH2), Time evolution of potential energy of Bz+-H2O following the ionization, molecular orbitals of of Bz-NH3 (left) and Bz-H2O, Stick diagrams of C-C bond lengths of Bz+(Ar)2 (parallel), and Bz+(Ar)2 (perpendicular), optimized structure of the neutral benzene-M complexes Bz-Ar 1:1 complex, effect of zero point vibration (ZPV) on Jahn-Teller effect on Bz+(H2O).

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Multiphoton Ionisation Mass Spectroscopy with Application to Benzene. Chem. Phys. 1982, 66, 105-127. (15) Walter, K.; Weinkauf, R.; Boesl, U.; Schlag, E. W. Spectroscopy of the Benzene cation: Resonance-enhanced Multiphoton Dissociation Spectra of the B̃ (E2g)←X̃ (E1g) Transition. Chem. Phys. Lett. 1989, 155, 8-14. (16) Riedle, E.; Neusser, H. J.; Schlag, E. W. Electronic Spectra of Polyatomic Molecules with Resolved Individual Rotational Transitions: Benzene. J. Chem. Phys. 1981, 75, 4231-4240. (17) Satink, R. G.; Piest, H.; von Helden, G.; Meijer, G. The Infrared Spectrum of the Benzene-Ar Cation. J. Chem. Phys. 1999, 111, 10750-10753. (18) Bakker, J. M.; Satink, R. G.: von Helden, G.; Meijer, G. Infrared Photodissociation Spectroscopy of Benzene-Ne, Ar Complex Cations. Phys. Chem. Chem. Phys. 2002, 4, 24-33. (19) Eiding, J.; Schneider, R.; Domcke, W.; Koppel, H.; von Niessen, W. Ab initio Investigation of the Multimode Dynamical Jahn-Teller Effect in the X̃ 2E1g State of the Benzene Cation. Chem. Phys. Lett. 1991, 177, 345-351. (20) Lindner, R.; Muller-Dethlefs, K.; Wedum, E.; Haber, K.; Grant E. R. On the Shape of C6H6+. Science 1996, 271, 1698-1702. (21) Muller-Dethlefs, K.; Peel, J. B. Calculations on the Jahn-Teller Configurations of the Benzene Cation. J. Chem. Phys. 1999, 111, 10550-10554. (22) Bondybey, V. E.; English, J. H.; Miller, T. A.; Shiley, R. H. The Laser-induced Fluorescence Spectrum of the 1,2,3-Trifluorobenzene Radical Cation. J. Mol. Spectrosc. 1980, 84, 124-131. (23) Sears, T. J.; Miller, T. A.; Bondybey, V. E. Jahn-Teller Distortions in C6H3F3+ and C6H3Cl3+. J. Chem. Phys. 1980, 72, 6070-6080. (24) Takeshita, K. A Theoretical Study on the First Ionic State of Benzene with Analysis of Vibrational Structure of the Photoelectron Spectrum. J. Chem. Phys. 1994, 101, 2192-2197. (25) Iwasaki, M.; Toriyama, K.; Nunome, K. E.S.R. Evidence for the Static Distortion of 2E1g Benzene Cations giving 2B2g with D2h Symmetry in Low Temperature Matrices. J. Chem. Soc. Chem. Commun. 1983, 6, 320-322. (26) Toriyama, K.; Okazaki, M. ESR Detection of the Isotopic-site-preference in the Jahn-Teller Distorted Benzene Cation Radicals Produced in MCM-41, Silica Gel, and Halocarbons. Chem. Lett. 2003, 32, 1020-1021. (27) Raghavachari, K.; Haddon, R. C.; Millar, T. A.; Bondybey, V. E. Theoretical Study of Jahn-Teller Distortions in C6H+6 and C6F+6. J. Chem. Phys. 1983, 79, 1387-1395.

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(28) Huang, M.; Lunell, S. Accurate Configuration Interaction Calculations of the Hyperfine Interactions in the Benzene Cation. J. Chem. Phys. 1990, 92, 6081-6083. (29) Feldman, V. I.; Sukhov, F. F.; Orlov, A. Yu. An ESR Study of Benzene Radical Cation in an Argon Matrix: Evidence for Favourable Stabilization of 2B1g Rather than 2

B2g State. Chem. Phys. Lett. 1999, 300, 713-718. (30) Feldman, V. I.; Sukhov, F.; Orlov, A.; Kadam, R.; Itagaki, Y.; Lund, A. Effect of Matrix and Substituent on the Electronic Structure of Trapped Benzene Radical Cations. Phys. Chem. Chem. Phys. 2000, 2, 29-35. (31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (32) Wang, X.; Bowman J. M. Zero-point Energy is Needed in Molecular Dynamics Calculations to Access the Saddle Point for H + HCN → H2CN* and cis/trans-HCNH* on a New Potential Energy Surface. J. Chem. Theory Comput. 2013, 9, 901-908. (33) Han, Y.-C.; Bowman, J. M. Reactant Zero-Point Energy is needed to Access the Saddle Point in Molecular Dynamics Calculations of the Association Reaction H + C2D2 → C2D2H. Chem. Phys. Lett. 2013, 556, 39-43. (34) Cotton, S. J.; Miller, W. H. The Symmetrical Quasi-Classical Model for Electronically Non-adiabatic Processes applied to Energy Transfer Dynamics in Site-Exciton Models of Light-Harvesting Complexes. J. Chem. Theory Comput. 2016, 12, 983−991. (35) Sibert III, E. L.; Hynes, J. T.; Reinhardt, W. P. Classical Dynamics of Highly Excited CH and CD Overtones in Benzene and Perdeuterobenzene. J. Chem. Phys. 1984, 81, 1135-1144. (36) Lu, D.-h.; Hase, W. L. Classical Trajectory Calculation of the Benzene Overtone Spectra. J. Phys. Chem. 1988, 92, 3217-3225. (37) Wyatt, R. E.; Iung, C.; Leforestier, C. Quantum Dynamics of Overtone Relaxation in Benzene. ii. 16 Mode Model for Relaxation From CH(v=3). J. Chem. Phys. 1992, 97, 3477-3486. (38) Stock, G. Classical Simulation of Quantum Energy Flow in Biomolecules. Phys. Rev. Lett. 2009, 102, 118301. (39) Lu, D.-h.; Hase, W. L. Classical Mechanics of Intramolecular Vibrational Energy Flow in Benzene. v. Effect of Zero Point Energy Motion. J. Chem. Phys. 1989, 91,

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7490-7497. (40) Tachikawa, H., Effects of Zero Point Vibration on the Reaction Dynamics of Water Dimer Cations following Ionization, J. Comput. Chem., 2017, 38, 1503-1508.

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Table 1. Optimized geometrical parameters (R1 and R2 in Å ) and relative energies (∆E in kcal/mol) calculated at several levels of theory. The relative energy is defined by ∆E = E(compressed) - E(elongated).

compressed

elongated

∆E

R1

R2

R1

R2

kcal/mol

CAM-B3LYP/6-311G(d,p)

1.424

1.361

1.382

1.446

-0.13

CAM-B3LYP/6-311++G(d,p)

1.424

1.362

1.382

1.446

-0.13

MP2/6-311G(d,p)

1.430

1.376

1.389

1.454

-2.27

MP2/aug-cc-pVDZ

1.437

1.385

1.396

1.460

-2.33

MP2/aug-cc-pVTZ

1.424

1.370

1.382

1.447

-2.15

MP2/6-311++G(d,p)

1.431

1.377

1.389

1.454

-2.29

MP4SDQ/6-311++G(d,p)

1.434

1.374

1.392

1.456

-2.29

CCSD/6-311++G(d,p)

1.435

1.374

1.394

1.456

-0.10

Table 2. Isotropic hyperfine coupling constants of proton of Bz+ (in gauss). compressed

elongated

H(2,3,5,6)

H(1,4)

H(1,4)

H(2,3,5,6)

B3LYP/6-311++G(d,p)

-1.4

-10.6

1.5

-7.5

CAM-B3LYP/6-311++G(d,p)

-1.3

-10.9

1.9

-7.7

MP2/6-311G(d,p)

-2.8

-10.6

-4.3

-6.3

MP2/aug-cc-pVDZ

-2.8

-10.4

-4.4

-6.2

MP2/aug-cc-pVTZ

-2.8

-9.4

-4.8

-5.5

MP2/6-311++G(d,p)

-2.8

-10.6

-4.4

-6.3

MP4SDQ/6-311++G(d,p)

-2.0

-11.3

-0.6

-7.5

CCSD/6-311++G(d,p)

-1.6

-12.5

2.0

-8.9

B3LYP/6-311++G(d,p)

-1.4

-10.6

1.5

-7.5

expl-1 (ref.25)

-2.4

-8.2

-6.4

expl-2 (ref.29) calc-1 (ref.28)

-1.4

-9.6

21


+1.0

-6.6


Page 22 of 34

Table 3. Structural forms of product Bz+ after the ionization of Bz-M complexes obtained by the direct AIMD calculations. “Symmetry” means the symmetry of HOMO of M relative to the Cs plane of benzene of Bz-M. complex, Bz-M

symmetry

product structure of Bz+

Bz(NH3)

sym

compressed

Bz(H2O)

asym

elongated

Bz(CFCl3)

sym

compressed

Bz(CH4)

asym

elongated

Bz(CH3OH)

asym

elongated

Bz(Ar)2 parallel

sym

compressed

Bz(Ar)2 perpendicular

asym

elongated

Bz(SH2)

asym

elongated

Bz(NH3)2

sym

compressed

Bz(H2O)2

asym

elongated

22


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Figure captions

Figure 1. Schematic energy diagram of Jahn-Teller distortion of a benzene radical cation.

Figure 2. Optimized structure of the benzene radical cations in the compressed form, Bz+(comp), and the elongated form, Bz+(elong), calculated at the MP2/6-311++G(d,p) level.

Figure 3. (A) Stick diagrams of C-C bond lengths of neutral benzene, (B) Bz+(comp), and (C) Bz+(elong) calculated at the MP2/6-311++G(d,p) level. The values indicate the C-C bond length in Å. Figure 4. (A) Time evolution of the C-C bond lengths of Bz+(2B2g) following the ionization of neutral benzene Bz. (B) Stick diagram of C-C bond lengths of Bz+. The values indicate the C-C bond length in Å. Direct AIMD calculation was carried out at the MP2/6-311++G(d,p) level. Figure 5. (A) Time evolution of the C-C bond lengths of Bz+(2B1g) following the ionization of neutral benzene Bz. (B) Stick diagram of C-C bond lengths of Bz+. Direct AIMD calculation was carried out at the MP2/6-311++G(d,p) level. Figure 6. (A) Time evolution of potential energy of Bz+-NH3 following the ionization of neutral complex Bz-NH3. (B) Snapshots of Bz+-NH3 following the vertical ionization of Bz-NH3. Direct AIMD calculation was carried out at the CAM-B3LYP/6-311G(d,p) level.

23



Page 24 of 34

Figure 7. (Left) Time evolution of the C-C bond lengths of Bz+ in Bz+-NH3 following the ionization of Bz-NH3. (Right) Stick diagram of C-C bond lengths of Bz+ in Bz+-NH3. Direct AIMD calculation was carried out at the CAM-B3LYP/6-311G(d,p) level. Figure 8. Optimized structures of the neutral benzene-argon dimer complexes Bz-(Ar)2 with

parallel

(upper)

and

perpendicular

forms

(lower)

calculated

at

the

MP2/6-311++G(d,p) level. Figure 9. Schematic illustration of orbital interaction between Bz and M derived from the present study results. (A) M = NH3 and (B) M = H2O.

24


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Figure 1.

25



Figure 2.

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Figure 3.

27



Figure 4.

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Figure 5.

29



Figure 6.

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Figure 7.

31



Figure 8.

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Figure 9.

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TOC abstract

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JahnâTeller Effect of the Benzene Radical Cation - ACS Publications

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JahnâTeller Effect of the Benzene Radical Cation - ACS Publications