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CASPT2 Study on the Low-lying Electronic States of 1,3,5-C<sub>6</sub>H<sub>3</sub>Cl<sub>3</sub><sup>+</sup> Ion
CASPT2 Study on the Low-lying Electronic States of 1,3,5-C6H3Cl3+ Ion
Bulletin of the Korean Chemical Society. 2014. May, 35(5): 1511-1515
Copyright © 2014, Korea Chemical Society
  • Received : October 13, 2013
  • Accepted : January 30, 2014
  • Published : May 20, 2014
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About the Authors
Shu-Yuan Yu
Department of Chemistry and Material Science, Langfang Normal College, Langfang 065000, People’s Republic of China
Cheng-Gen Zhang
College of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
Shu-Jun Wang
Department of Chemistry and Material Science, Langfang Normal College, Langfang 065000, People’s Republic of China

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 6 H 3 Cl 3 + ion. The CASPT2 values for the 1,3,5-C 6 H 3 Cl 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 6 H 3 Cl 3 + ion. The Jahn-Teller distortion in the excited electronic state for the 1,3,5-C 6 H 3 Cl 3 + ion were reported for the first time.
Keywords
Introduction
Halobenzene ions have long attracted a great deal of interest for its great significance for environmental protection. 1 2 The 1,3,5-C 6 H 3 Cl 3 + 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-C 6 H 3 Cl 3 + 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-C 6 H 3 Cl 3 (…12 e 4 3 a 2 2 3 a 2 2 3 e 4 ) molecule, the four lowest-lying states of the 1,3,5-C 6 H 3 Cl 3 + ion could be assigned to X 2 E″, A 2 A 2 ″, B 2 A 2 ′ and C 2 E′, respectively. One of the main topics of interest in the spectroscopic investi-gation of highly symmetric cations such as 1,3,5-C 6 H 3 Cl 3 + is the Jahn-Teller effect because of the degenerate 2 E″ and 2 E′ states. The Jahn-Teller effect splits the degenerate electronic states involved in D 3 h symmetry ( 2 E″ and 2 E′) to correspond-ing electronic states in low (such as C 2 v ) symmetry. So those four electronic states mentioned above for the 1,3,5-C 6 H 3 Cl 3 + ion were assigned to X 2 E″, B 2 A 2 ″, C 2 A 2 ′, and D 2 E′, respectively, in which the X 2 E″ and D 2 E′ 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-C 6 H 3 Cl 3 + ion in the ground electronic state has been investigated by mass-ana-lyzed threshold ionization (MATI) spectroscopy 4 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-C 6 H 3 Cl 3 + ion have been few. The ground state of the 1,3,5-C 6 H 3 Cl 3 + ion were previ-ously calculated by using the DFT 9 and GRHF 10 methods. In the literature we have found no reported theoretical studies on excited electronic states of 1,3,5-C 6 H 3 Cl 3 + ion, and there are neither experimental nor theoretical studies on the Jahn-Teller distortion in the higher electronic state ( 2 E′) for the 1,3,5-C 6 H 3 Cl 3 + 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) methods 12 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-C 6 H 3 Cl 3 + ion were studied using the CASPT2 and CASSCF methods. The Jahn-Teller distortion in the X 2 E″ and D 2 E′ 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-C 6 H 3 Cl 3 + ion based on our CASPT2 calculations are presented. Only the 1,3,5-isomers of the C 6 H 3 Cl 3 + 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 C 6 H 3 Cl 3 + ion studied in the present work have planar geometries in D 3h symmetry and in C 2v symmetry (resulting from the Jahn-Teller distortion), and the geometries and atom labels used for the C 6 H 3 Cl 3 + ion are shown in Figure 1(a), (b), and (c) .
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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 C 6 H 3 Cl 3 + ion, and the CASSCF frequency calculations were performed for all the calculated C 2v and D 3h states. On the basis of the CASPT2 energies of the X 2 B 1 ground state (see below) and the excited states calculated at the respective CASPT2 and CASSCF optimized geometries of the C 6 H 3 Cl 3 + ion, we obtained the CASPT2//CASPT2 and CASPT2// CASSCF adiabatic excitation energy values (denoted as CASPT2 T 0 and CASPT2//CASSCF T 0 , 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 X 2 B 1 ground state of the C 6 H 3 Cl 3 + ion, we obtained the CASPT2 vertical excitation energy values (denoted as CASPT2 T v ) for the excited states. On the basis of the CASPT2 energies of the X 2 B 1 and excited states calculated at the experimental ground-state geometry of 1,3,5-C 6 H 3 Cl 3 molecules, 6 we obtained the CASPT2 relative energy values (denoted as CASPT2 T v ′) for the electronic states of the C 6 H 3 Cl 3 + ion.
CASPT2 and CASSCF optimized geometriesafor the 11A1′(X1A1′) state of the 1,3,5-C6H3Cl3molecule and for the 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1states of the C6H3Cl3+ion (bond lengths are given in Å and bond angles in degrees; for atom labelings, seeFigure 1)
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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 C 6 H 3 Cl 3 + 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-C 6 H 3 Cl 3 molecule. The highest sym-metry point-group is D 2h for the CASSCF wavefunction in MOLCAS software, so the C 2v point-group, the sub-group of D 3h , was used in the present work. Based on the HF/6-31+G(d,p) calculations, the ground-state 1,3,5-C 6 H 3 Cl 3 mole-cule has the following electron configuration: …(4 b 1 ) 2 (2 a 2 ) 2 (14 b 2 ) 2 (21 a 1 ) 2 (15 b 2 ) 2 (5 b 1 ) 2 (3 a 2 ) 2 (6 b 1 ) 2 (22 a 1 ) 0 (23 a 1 ) 0 (16 b 2 ) 0 (4 a 2 ) 0 (7 b 1 ) 0 (17 b 2 ) 0 (24 a 1 ) 0 (25 a 1 ) 0 (8 b 1 ) 0 …. Our active space corresponded to a segment of this sequence from 14 b 2 to 7 b 1 , augmented with 8 b 1 for C 6 H 3 Cl 3 + . 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 Cl 1 , and two p orbitals of Cl 2 and Cl 3 . Labeling these orbitals (six occupied plus six virtual) within the C 2v point-group in the order a 1 , a 2 , b 2 , and b 1 , 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 C 6 H 3 Cl 3 + 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.
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The vibrational mode for the imaginary frequency.
Results and Discussion
Optimized Geometries. As a non-linear polyatomic system, the C 6 H 3 Cl 3 + ion ( D 3h ) in the degenerate X 2 E″ and D 2 E′ states should experience the Jahn-Teller geometry distortion and reduce the symmetry from D 3h to C 2v . The X 2 E″ state splits into one 2 B 1 state and one 2 A 2 state at two different C 2v geometries, and the D 2 E′ state splits into one 2 A 1 state and one 2 B 2 state at two different C 2v geometries.
In Table 1 , the CASPT2 and CASSCF optimized geometries for the 1 2 B 1 , 1 2 A 2 , 1 2 A 2 ″, 1 2 A 2 ′, 2 2 B 2 , and 1 2 A 1 states of the C 6 H 3 Cl 3 + ion are given, together with the CASPT2 and CASSCF optimized geometries and experimental geometry 6 for the 1 1 A 1 ′ ground state of the 1,3,5-C 6 H 3 C l3 molecule. The CASSCF frequency calculations produced no imaginary frequencies for the 1 2 B 1 , 1 2 A 2 ″, 1 2 A 2 ′, and 2 2 B 2 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 1 2 A 2 and 1 2 A 1 states produced the unique imaginary frequency of the b 2 sym-metry and represent saddle points. The vibrational modes for the imaginary frequencies of the 1 2 A 2 and 1 2 A 1 states are similar, they principally involving the C-C-C bending in the phenyl ring that likely reduces the molecular symmetry from D 3h to C 2v . This is consistent with the conclusions of the previous experiment 5 8 that the C-C-C bending mode is the most active Jahn-Teller mode in C 6 H 3 Cl 3 + ion. And the vibrational mode for the imaginary frequency is shown schematically in Figure 2 .
The CASPT2 optimized geometry for the 1 1 A 1 ′ground state of the 1,3,5-C 6 H 3 Cl 3 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 C 6 H 3 Cl 3 + ion (1 2 B 1 , 1 2 A 2 , 1 2 A 2 ″, 1 2 A 2 ′, 2 2 B 2 , and 1 2 A 1 ), 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 C 6 H 3 Cl 3 + ion.
As shown in Table 1 , the CASPT2 geometries for the 2 2 B 2 and 1 2 A 1 states (the two Jahn-Teller component states of D 2 E′) are noticeably different. The C 1 -Cl 1 bond length is longer than the C 3 -Cl 2 bond length in the 2 2 B 2 state while the C 1 -Cl 1 bond length is shorter than the C 3 -Cl 2 bond length in the 1 2 A 1 state, and the differences of the two C-Cl bond lengths are almost equal for the two states. The C 1 -C 2 and C 3 -C 4 bond lengths are longer than the C 2 -C 3 bond length (0.012 and 0.022 Å, respectively) in the 2 2 B 2 state, while the C 1 -C 2 and C 3 -C 4 bond lengths are shorter than the C 2 -C 3 bond length (0.004 and 0.010 Å, respectively) in the 1 2 A 1 state. This signifies that the carbon frameworks of the CASPT2 geometries ( C 2v ) for the two states (2 2 B 2 and 1 2 A 1 ) 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 1 2 B 1 and 1 2 A 2 states (the two Jahn-Teller component states of X 2 E″) are also notably different. The carbon frameworks of the CASPT2 geometries ( C 2v ) for the two states (1 2 B 1 and 1 2 A 2 ) 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 T 0 values for the 1 2 B 1 , 1 2 A 2 , 1 2 A 2 ″, 1 2 A 2 ′, 2 2 B 2 , and 1 2 A 1 states of the C 6 H 3 Cl 3 + ion are given, along with the CASPT2 T v and T v ′ values for the six states. The experi-mental T 0 value for the B state and the experimental T v ′ values for the B, C , and D states are also listed in Table 2 . By checking the CASSCF wavefunctions, the 1 2 B 1 , 1 2 A 2 , 1 2 A 2 ′ (1 2 B 2 in C 2v symmetry), 2 2 B 2 , and 1 2 A 1 states could be characterized as primary ionized states. Our CASPT2 and CASPT2//CASSCF T 0 calculations indicated that 1 2 B 1 is the ground state of the C 6 H 3 Cl 3 + ion. On the basis of our CASPT2 T 0 values the X, A, B, C, D , and E states of the C 6 H 3 Cl 3 + ion were assigned to the 1 2 B 1 , 1 2 A 2 , 1 2 A 2 ″, 1 2 A 2 ′, 2 2 B 2 , and 1 2 A 1 states, respectively. The CASPT2 T 0 value of 1.98 eV for the 1 2 A 2 ″ state was in good agreement with the experimental T 0 value of 1.91 eV for the B state. 3 The CASPT2//CASSCF T 0 values for the six states were similar to the CASPT2 T 0 values for the respective states.
Calculated energetic results (in eV) for the 12B1, 12A2, 12A2″, 12A2′, 22B2, and 12A1states of the C6H3Cl3+ion: CASPT2 and CASPT2//CASSCF adiabatic excitation energy (T0) values, CASPT2 vertical excitation energy (Tv) values, and CASPT2 relative energy (Tv′) values calculated at the experimental groundstate geometry of the 1,3,5-C6H3Cl3moleculea
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aThe experimental geometry of the ground-state 1,3,5-C6H3Cl3 molecule, see Ref. 6. bRef. 3
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A slice through the Jahn-Teller potential energy surface.
Based on our CASPT2 T 0 results the 1 2 A 2 state is higher in energy than the 1 2 B 1 state by 0.014 eV. As described above, the geometries of the 1 2 B 1 and 1 2 A 2 states (the two Jahn- Teller component states of X 2 E″) 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 1 2 B 1 state and one imaginary frequency for the 1 2 A 2 state. These facts indicate that the symmetry distortion of C 6 H 3 Cl 3 + from D 3h to C 2v by the Jahn-Teller effect splits the ground electronic state X 2 E″ into 1 2 B 1 and 1 2 A 2 states, and 1 2 B 1 ( C 2v ), 1 2 A 2 ( C 2v ), and X 2 E″ ( D 3h ) correspond to the global minimum ( X min ), the saddle point ( X max ), and the conical intersection ( X 0 ) on the PES, respectively, as shown in Figure 3 . The relative energy of the X 0 and X min ( E X 0 E X 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 T 0 value for the 1 2 A 1 state is larger than that for the 2 2 B 2 state by 0.08 eV. As described above, the geometries of the 2 2 B 2 and 1 2 A 1 states (the two Jahn-Teller component states of D 2 E′) 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 2 2 B 2 state and one imaginary frequency for the 1 2 A 1 state. These facts indicate that the symmetry distortion of C 6 H 3 Cl 3 + from D 3h to C 2v by the Jahn-Teller effect splits the excited elec-tronic state D 2 E′ into 2 2 B 2 and 1 2 A 1 states, and 2 2 B 2 ( C 2v ), 1 2 A 1 ( C 2v ), and D 2 E′ ( D 3h ) correspond to the global minimum ( X min ), the saddle point ( X max ), and the conical intersection ( X 0 ) 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 T v and T v ′ orderings for the 1 2 B 1 , 1 2 A 2 , 1 2 A 2 ″, 1 2 A 2 ′, 2 2 B 2 , and 1 2 A 1 states are the same as the CASPT2 T 0 ordering. The CASPT2 T v ′ values of 1.90 and 2.09 eV for the 1 2 A 2 ″ and 1 2 A 2 ′ states are in good agreement with the experimental T v ′ 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 C 6 H 3 Cl 3 + ion were calculated by using the CASPT2 and CASSCF methods in conjunction with the ANO-L basis set. The CASPT2 values for the C 6 H 3 Cl 3 + ion were in reasonable agreement with the available experi-mental values. Based on our CASPT2 and CASSCF T 0 calculations, we assigned the X, A, B, C, D , and E states of C 6 H 3 Cl 3 + to 1 2 B 1 , 1 2 A 2 , 1 2 A 2 ″, 1 2 A 2 ′, 2 2 B 2 , and 1 2 A 1 , respectively.
The Jahn-Teller distortion in the excited electronic state for the C 6 H 3 Cl 3 + ion were reported for the first time. The symmetry distortion of C 6 H 3 Cl 3 + from D 3h to C 2v by the Jahn-Teller effect split the ground state X 2 E″ into 1 2 B 1 and 1 2 A 2 states and split the excited state D 2 E′ into 2 2 B 2 and 1 2 A 1 states. The carbon frameworks of the CASPT2 geo-metries for the two Jahn-Teller component states of C 6 H 3 Cl 3 + ion were regular hexagons distorted to be “elongated” or “flattened ” carbon frames, respectively, because of the Jahn-Teller effect.
Acknowledgements
We express our thanks for financial support from the National Science Foundation of China (Nos. 21303078 and 21373217), the Hebei Province Science Foundation for Youths (B2012408008) and the Educational Commission of Hebei Province (Y2012023).
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