CASPT2 Study on the Low-lying Electronic States of 1,3,5-C₆H₃Cl₃⁺ Ion

Abstract

The multiconfiguration second-order perturbation theory (CASPT2) and complete active space self-consistent field (CASSCF) methods were employed to calculate the geometries and energy levels for the low-lying electronic states of 1,3,5-$C_6H_3Cl{_3}^+$ ion. The CASPT2 values for the 1,3,5-$C_6H_3Cl{_3}^+$ ion were in reasonable agreement with the available experimental values. The current calculations augmented previous theoretical investigations on the ground state and assigned the low-lying excited electronic states of the 1,3,5-$C_6H_3Cl{_3}^+$ ion. The Jahn-Teller distortion in the excited electronic state for the 1,3,5-$C_6H_3Cl{_3}^+$ ion were reported for the first time.

Introduction

Halobenzene ions have long attracted a great deal of interest for its great significance for environmental protection.1,2 The 1,3,5-C6H3Cl3 + ion has been investigated by spectroscopic studies.3-8 The experimental adiabatic ionization potential (AIP) values and vertical ionization potential (VIP) values for the 1,3,5-C6H3Cl3 + ion were reported by Maier et al..3 Assignments of electronic states are fundamental to under-standing of the experimental facts. On the basis of the energy orderings of the four highest-occupied molecular orbitals (HOMOs) in the electronic configurations of the ground-state 1,3,5-C6H3Cl3 (…12e′4 3a2′2 3a2″2 3e″4) molecule, the four lowest-lying states of the 1,3,5-C6H3Cl3 + ion could be assigned to X2E″, A2A2″, B2A2′ and C2E′, respectively. One of the main topics of interest in the spectroscopic investi-gation of highly symmetric cations such as 1,3,5-C6H3Cl3 + is the Jahn-Teller effect because of the degenerate 2E″ and 2E′ states. The Jahn-Teller effect splits the degenerate electronic states involved in D3h symmetry (2E″ and 2E′) to correspond-ing electronic states in low (such as C2v) symmetry. So those four electronic states mentioned above for the 1,3,5-C6H3Cl3 + ion were assigned to X2E″, B2A2″, C2A2′, and D2E′, respectively, in which the X2E″ and D2E′ states correspond to the points of the conical intersection of the Jahn-Teller potential energy surfaces (PESs).

The Jahn-Teller effect for the 1,3,5-C6H3Cl3 + ion in the ground electronic state has been investigated by mass-ana-lyzed threshold ionization (MATI) spectroscopy4 and wave-length resolved emission spectra.5 Most of these focus on the Jahn-Teller active vibrational mode of the ground electronic state and the Jahn-Teller stabilization energy of the ground state.

Theoretical studies of the 1,3,5-C6H3Cl3 + ion have been few. The ground state of the 1,3,5-C6H3Cl3 + ion were previ-ously calculated by using the DFT9 and GRHF10 methods. In the literature we have found no reported theoretical studies on excited electronic states of 1,3,5-C6H3Cl3 + ion, and there are neither experimental nor theoretical studies on the Jahn-Teller distortion in the higher electronic state (2E′) for the 1,3,5-C6H3Cl3 + ion reported. The molecular configurations distortion owing to the Jahn-Teller effect and the corre-sponding electronic states in low symmetry are of particular interest herein.

It is known that the CASSCF (complete active space self-consistent field)11 and CASPT2 (multiconfiguration second-order perturbation theory) methods12,13 are effective for theoretical studies of excited electronic states of molecules and molecular ions.14-17 In the present work the six lowest-lying electronic states of the 1,3,5-C6H3Cl3 + ion were studied using the CASPT2 and CASSCF methods. The Jahn-Teller distortion in the X2E″ and D2E′ states, equilibrium geometries and excitation energies of the states were calculated. These results are described and discussed below, and the assign-ments for the X, A, B, C, D, and E states of 1,3,5-C6H3Cl3 + ion based on our CASPT2 calculations are presented. Only the 1,3,5-isomers of the C6H3Cl3 + ion were involved. So the “1,3,5-” designation will be omitted from hereon.

 

Calculation Details

The CAS (CASSCF and CASPT2) calculations were carried out using the MOLCAS 7.8 quantum-chemistry software.18 With a CASSCF wavefunction constituting the reference function, the CASPT2 calculations were perform-ed to compute the first-order wavefunction and the second-order energy in the full-CI space. A contracted atomic natural orbital (ANO-L) basis set,19-21 Cl[5s4p2d1f]/F[4s3p2d]/ C[4s3p2d]/H[3s2p1d], was used. It was assumed that the electronic states of the C6H3Cl3 + ion studied in the present work have planar geometries in D3h symmetry and in C2v symmetry (resulting from the Jahn-Teller distortion), and the geometries and atom labels used for the C6H3Cl3 + ion are shown in Figure 1(a), (b), and (c).

Figure 1.Atom labelings for the C6H3Cl3 + ion used in the present work, (a) in D3h symmetry, (b) and (c) in C2v symmetry resulting from the Jahn-Teller distortion.

The CASPT2 and CASSCF geometry optimization calculations were performed for the electronic states of the C6H3Cl3 + ion, and the CASSCF frequency calculations were performed for all the calculated C2v and D3h states. On the basis of the CASPT2 energies of the X2B1 ground state (see below) and the excited states calculated at the respective CASPT2 and CASSCF optimized geometries of the C6H3Cl3 + ion, we obtained the CASPT2//CASPT2 and CASPT2// CASSCF adiabatic excitation energy values (denoted as CASPT2 T0 and CASPT2//CASSCF T0, respectively) for the excited states. On the basis of the CASPT2 energies of the X2B1 and excited states calculated at the CASPT2 geometry of the X2B1 ground state of the C6H3Cl3 + ion, we obtained the CASPT2 vertical excitation energy values (denoted as CASPT2 Tv) for the excited states. On the basis of the CASPT2 energies of the X2B1 and excited states calculated at the experimental ground-state geometry of 1,3,5-C6H3Cl3 molecules,6 we obtained the CASPT2 relative energy values (denoted as CASPT2 Tv′) for the electronic states of the C6H3Cl3 + ion.

Table 1.aOnly geometric parameters in the heavy-atom frame-works are given. bThe experimental geometry of the ground-state 1,3,5-C6H3Cl3 molecule, see Ref. 6

In the CAS calculations for the low-lying states of the C6H3Cl3 + ion, 11 electrons were active and the active space included 12 orbitals [CAS (11,12)]. The choice of active space stemmed from the molecular orbital (MO) sequence of the ground-state 1,3,5-C6H3Cl3 molecule. The highest sym-metry point-group is D2h for the CASSCF wavefunction in MOLCAS software, so the C2v point-group, the sub-group of D3h, was used in the present work. Based on the HF/6-31+G(d,p) calculations, the ground-state 1,3,5-C6H3Cl3 mole-cule has the following electron configuration: …(4b1)2 (2a2)2 (14b2)2 (21a1)2 (15b2)2 (5b1)2 (3a2)2 (6b1)2 (22a1)0 (23a1)0 (16b2)0 (4a2)0 (7b1)0 (17b2)0 (24a1)0 (25a1)0 (8b1)0…. Our active space corresponded to a segment of this sequence from 14b2 to 7b1, augmented with 8b1 for C6H3Cl3 +. The selected active space is composed of six π/π* orbitals of the phenyl ring, two σ/σ* orbitals of C–Cl, two p orbitals of Cl1, and two p orbitals of Cl2 and Cl3. Labeling these orbitals (six occupied plus six virtual) within the C2v point-group in the order a1, a2, b2, and b1, this active space was named (3234). In CAS calculations for electronic states of a molecular ion, we often take a “segment” of the electron configuration of the ground-state molecule constituting our active space. The “segment” includes many (sequential) occupied MOs for not missing primary ionization states and includes a few of virtual MOs for describing shake-up ionization character of some ionic states. And this way of the choice of the active space has been justified by our previous published works on electronic states of halobenzene ions,15-17 in which the CASPT2 calculations predict more accurate results for the electronic states of these ions. At the same time, the testing CASPT2 Tv′ calculations for the C6H3Cl3 + ion using larger active spaces, CAS(15,12) and CAS(15,14) were performed [Details are given in the supporting information (SI1)] and the calculated Tv′values are similar to the CASPT2 Tv ′ values obtained in the CAS(11,12) calculations. In all the CASPT2 calculations the weight values of the CASSCF reference functions in the first-order wave functions were larger than 0.75.

Figure 2.The vibrational mode for the imaginary frequency.

 

Results and Discussion

Optimized Geometries. As a non-linear polyatomic system, the C6H3Cl3 + ion (D3h) in the degenerate X2E″ and D2E′ states should experience the Jahn-Teller geometry distortion and reduce the symmetry from D3h to C2v. The X2E″ state splits into one 2B1 state and one 2A2 state at two different C2v geometries, and the D2E′ state splits into one 2A1 state and one 2B2 state at two different C2v geometries.

In Table 1, the CASPT2 and CASSCF optimized geometries for the 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1 states of the C6H3Cl3 + ion are given, together with the CASPT2 and CASSCF optimized geometries and experimental geometry6 for the 11A1 ′ ground state of the 1,3,5-C6H3Cl3 molecule. The CASSCF frequency calculations produced no imaginary frequencies for the 12B1, 12A2″, 12A2′, and 22B2 states, indicating that the CASSCF geometries of the four states correspond to energy minima in the respective PESs, and thus the CASPT2 and CASSCF optimized geometries were considered to be the predicted equilibrium geometries. The CASSCF frequency calculations for the 12A2 and 12A1 states produced the unique imaginary frequency of the b2 sym-metry and represent saddle points. The vibrational modes for the imaginary frequencies of the 12A2 and 12A1 states are similar, they principally involving the C-C-C bending in the phenyl ring that likely reduces the molecular symmetry from D3h to C2v. This is consistent with the conclusions of the previous experiment5,8 that the C-C-C bending mode is the most active Jahn-Teller mode in C6H3Cl3 + ion. And the vibrational mode for the imaginary frequency is shown schematically in Figure 2.

The CASPT2 optimized geometry for the 11A1′ground state of the 1,3,5-C6H3Cl3 molecule was almost identical to the experimental geometry,6 while the C-Cl bond length values in the CASSCF optimized geometries were 0.007 Å larger than the experimental value, respectively. For the ionic states of the C6H3Cl3 + ion (12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1), the CASSCF calculations predicted longer C-Cl bond lengths than the CASPT2 calculations. The CASPT2 calculations predicted more accurate geometries for the ground-state halobenzene molecules than the CASSCF calculations based on our previous studies.15-17 It was ex-pected that the CASPT2 calculations would predict accurate geometries for the ground and excited states of the C6H3Cl3 + ion.

As shown in Table 1, the CASPT2 geometries for the 22B2 and 12A1 states (the two Jahn-Teller component states of D2E′) are noticeably different. The C1-Cl1 bond length is longer than the C3-Cl2 bond length in the 22B2 state while the C1-Cl1 bond length is shorter than the C3-Cl 2 bond length in the 12A1 state, and the differences of the two C-Cl bond lengths are almost equal for the two states. The C1-C2 and C3-C4 bond lengths are longer than the C2-C3 bond length (0.012 and 0.022 Å, respectively) in the 22B2 state, while the C1-C2 and C3-C4 bond lengths are shorter than the C2-C3 bond length (0.004 and 0.010 Å, respectively) in the 12A1 state. This signifies that the carbon frameworks of the CASPT2 geometries (C2v) for the two states (22B2 and 12A1) are regular hexagons distorted to significant extents because of the Jahn-Teller effect, and that one of the carbon frames is “flattened” and the other is “elongated” [see Figure 1(b) and (c)]. The CASPT2 geometries for the 12B1 and 12A2 states (the two Jahn-Teller component states of X2E″) are also notably different. The carbon frameworks of the CASPT2 geometries (C2v) for the two states (12B1 and 12A2) are regular hexagons distorted to great extents because of the Jahn-Teller effect, and one of the carbon frames is “flatten-ed” and the other is “elongated” [see Figure 1(b) and (c)].

Excitation Energies. In Table 2 the CASPT2 and CASPT2//CASSCF T0 values for the 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1 states of the C6H3Cl3 + ion are given, along with the CASPT2 Tv and Tv′ values for the six states. The experi-mental T0 value for the B state and the experimental Tv′ values for the B, C, and D states are also listed in Table 2. By checking the CASSCF wavefunctions, the 12B1, 12A2, 12A2′ (12B2 in C2v symmetry), 22B2, and 12A1 states could be characterized as primary ionized states. Our CASPT2 and CASPT2//CASSCF T0 calculations indicated that 12B1 is the ground state of the C6H3Cl3 + ion. On the basis of our CASPT2 T0 values the X, A, B, C, D, and E states of the C6H3Cl3 + ion were assigned to the 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1 states, respectively. The CASPT2 T0value of 1.98 eV for the 12A2″ state was in good agreement with the experimental T0 value of 1.91 eV for the B state.3 The CASPT2//CASSCF T0 values for the six states were similar to the CASPT2 T0 values for the respective states.

Table 2.aThe experimental geometry of the ground-state 1,3,5-C6H3Cl3 molecule, see Ref. 6. bRef. 3

Figure 3.A slice through the Jahn-Teller potential energy surface.

Based on our CASPT2 T0 results the 12A2 state is higher in energy than the 12B1 state by 0.014 eV. As described above, the geometries of the 12B1 and 12A2 states (the two Jahn- Teller component states of X2E″) are regular hexagons distorted into “flattened” and “elongated” [see Figure 1(b) and (c)] carbon frames, respectively, and the CASSCF frequency calculations produced no imaginary frequency for the 12B1 state and one imaginary frequency for the 12A2 state. These facts indicate that the symmetry distortion of C6H3Cl3 + from D3h to C2v by the Jahn-Teller effect splits the ground electronic state X2E″ into 12B1 and 12A2 states, and 12B1 (C2v), 12A2 (C2v), and X2E″ (D3h) correspond to the global minimum (Xmin), the saddle point (Xmax), and the conical intersection (X0) on the PES, respectively, as shown in Figure 3. The relative energy of the X0 and Xmin ( EX 0– EX min) is generally accepted as the total Jahn-Teller stabilization energy. The CASPT2 value of Jahn-Teller stabilization energy for the ground state is 0.090 eV, which is in reasonable agreement with the experimental value of 547 cm˗1 (0.068 eV).8

The CASPT2 T0 value for the 12A1 state is larger than that for the 22B2 state by 0.08 eV. As described above, the geometries of the 22B2 and 12A1 states (the two Jahn-Teller component states of D2E′) are also “flattened” and “elon-gated” distortions of regular hexagonal [see Figure 1(b) and (c)] carbon frames, respectively, and the CASSCF frequency calculations produced no imaginary frequency for the 22B2 state and one imaginary frequency for the 12A1 state. These facts indicate that the symmetry distortion of C6H3Cl3 + from D3h to C2v by the Jahn-Teller effect splits the excited elec-tronic state D2E′ into 22B2 and 12A1 states, and 22B2 (C2v), 12A1 (C2v), and D2E′ (D3h) correspond to the global minimum (Xmin), the saddle point (Xmax), and the conical intersection (X0) on the PES, respectively, as shown in Figure 3. The CASPT2 value of Jahn-Teller stabilization energy for the excited state is 0.151 eV.

As shown in Table 2, the CASPT2 Tv and Tv′ orderings for the 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1 states are the same as the CASPT2 T0 ordering. The CASPT2 Tv′ values of 1.90 and 2.09 eV for the 12A2″ and 12A2′ states are in good agreement with the experimental Tv′ values of 1.91 and 2.17 eV for the B and C states evaluated using the experimental VIP values, respectively (the deviations being smaller than 0.08 eV).3

 

Conclusion

Geometries and energy levels for the low-lying electronic states of the C6H3Cl3 + ion were calculated by using the CASPT2 and CASSCF methods in conjunction with the ANO-L basis set. The CASPT2 values for the C6H3Cl3 + ion were in reasonable agreement with the available experi-mental values. Based on our CASPT2 and CASSCF T0 calculations, we assigned the X, A, B, C, D, and E states of C6H3Cl3 + to 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1, respectively.

The Jahn-Teller distortion in the excited electronic state for the C6H3Cl3 + ion were reported for the first time. The symmetry distortion of C6H3Cl3 + from D3h to C2v by the Jahn-Teller effect split the ground state X2E″ into 12B1 and 12A2 states and split the excited state D2E′ into 22B2 and 12A1 states. The carbon frameworks of the CASPT2 geo-metries for the two Jahn-Teller component states of C6H3Cl3 + ion were regular hexagons distorted to be “elongated” or “flattened ” carbon frames, respectively, because of the Jahn-Teller effect.