Some remarks on the stability of the ground and excited electronic states of the CF2++ dication

20 April 2001

Chemical Physics Letters 338 (2001) 189±194

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Some remarks on the stability of the ground and excited electronic states of the CF‡‡ dication 2 k * Jan Hrusa J. Heyrovsk y Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejskova 3, 18223 Prague 8, Czech Republic Received 7 December 2000; in ®nal form 20 February 2001

Abstract 1 ‡ The dissociation path of the ground state of CF‡‡ 2 … Rg † is investigated by means of the multi-reference averaged quadratic coupled cluster (AQCC) method using an ANO type basis set. Low lying electronically excited states involved 1 ‡ in the dissociation are also calculated. The CF‡‡ 8:5 kcal/ 2 … Rg † dication has to be considered as metastable (DEDiss ˆ mol). However, the dissociation into the ground states of the products (i.e., CF‡ …1 R‡ † and F‡ …3 P†) is spin forbidden. Further, the surface crossing of the ground-state potential energy surfaces (PES) with the lowest triplet surface (3 A0 )  The related barrier is calculated to be 5 eV. Ó 2001 Published by Elsevier occurs around the C±F distance of 1.85 A. Science B.V.

1. Introduction The CF‡‡ dication is a long-lived polyatomic 2 dication and has attracted considerable attention of both experimentalists [1±5] and theoreticians [6± 8]. The long lifetime, easy formation, and relatively high ion abundances in gas phase experiments, make the CF‡‡ dication one of the most promi2 nent small polyatomic dications. Despite tremendous experimental and theoretical e€ort, the mechanism of formation has not been conclusively determined. The CF‡‡ dication is usually produced upon 2 ionization and subsequent fragmentation of CF4 . The complete reaction sequence of its formation is entirely unknown. Already the ground state (2 T1 )

*

Fax: +420-858-2307. E-mail address: [email protected] (J. Hrusak).

of CF‡ 4 is unstable towards dissociation into CF‡ ‡ F and is thus dicult to access by spec3 trometric techniques. The electronically excited states of CF‡ 4 preferentially dissociate into frag‡ ‡ mentation channels leading to CF‡ 3 ; CF2 ; CF and ‡ F ions in various electronic states [9] and this almost excludes the direct formation of CF‡‡ 2 . The reaction ‡‡ CF‡ 4 ! CF2 ‡ 2F ‡ e …or F2 †

CF‡‡ 2

…1†

formation. However, formally allows direct due to the poor Franck±Condon factors and the short life-time of the highly excited CF‡ 4 it does not seem probable. Very recently, by examining the dissociative photoionization of CF4 a new CF‡‡ 2 appearance potential (AP) of 41.7 eV was measured [10]. This value is considerably lower than both previously listed AP's of 44:3  0:3 eV [11] and 42:9  0:3 eV [12]. The authors link the formation of CF‡‡ (and CF‡‡ 2 3 ) to the fragmentation

0009-2614/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 2 7 7 - 9

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J. Hrusak / Chemical Physics Letters 338 (2001) 189±194

of the metastable parent ion CF‡‡ that is directly 4 formed upon photoionization of CF4 . Because of a large scattering of the data, no particular dissociation pathway could be given. However, these ®ndings are in line with our ab initio calculations. We found a large Jahn±Teller distortion of CF‡‡ 3 [13]. This system may be rationalized as a CF‡‡ 2  aFCF ˆ 162°) with an substructure (RCF ˆ 1:186 A,  The obvious similarF attached (RCF ˆ 1:552 A). 1 ‡ ity in geometry to the isolated CF‡‡ 2 … Rg †  (RCF ˆ 1:156 A, aFCF ˆ 180° [8]), the weak bond to the spectator ¯uorine, the assumption of the CF‡‡ 3 dication being formed hot, and as a consequence of the geometry, favorable Franck±Condon factors, are all in line with the dissociation scheme (2), ‡‡ CF‡‡ ! CF‡‡ 4 3 ‡ F ! CF2 ‡ F

…2†

With respect to the process of formation of CF‡‡ 2 in an ion source of a mass spectrometer, there is another fact that should be noted. Depending on the experimental conditions (energy regime and the molecular precursor used) di€erent ratios of ground and excited states of CF‡‡ are formed [1]. 2 Besides indirect evidence of the presence of excited states in the gas phase experiments (the occurrence of an excited state at 4 eV) [3,4], however, there is no experimental or theoretical information available on these excited states of CF‡‡ 2 . Koch and Frenking [6] established the structure  of the ground state of CF‡‡ 2 . Their MP2/6-31G calculations led to a linear structure with rather  high p-bond short CF bond (RCF ˆ 1:166 A), population, and charge delocalization over the whole skeleton. The calculated structure and harmonic frequencies were very close to those of the isoelectronic neutral CO2 . Recently, the CF‡‡ 2 ground state has been reinvestigated using high level ab initio techniques [8] and its DHf was determined to be 687 kcal/mol. Another important feature of this interesting species is its remarkable stability towards dissociation. The reaction enthalpy for the dissociation ‡ 1 ‡ ‡ 1 1 ‡ CF‡‡ 2 … Rg † ! CF … R † ‡ F … D†

…3†

is calculated to have a very high endothermicity (76.5 kcal/mol [6]). On the contrary the dissociation reaction (4)

‡ 1 ‡ ‡ 3 1 ‡ CF‡‡ 2 … Rg † ! CF … R † ‡ F … P†

…4†

is calculated to be exothermic by 12 [6] and 9.6 kcal/mol [8]. However, it is (since leading to the triplet state of the F‡ ) forbidden by the spin conservation principle. The fairly small spin±orbit coupling is then re¯ected in surprisingly long lifetime of the ion. The limited knowledge of CF‡‡ motivated us to 2 explore parts of the potential energy surfaces (PES) for the low lying excited states up to the dissociation. The ab initio calculations of PES for excited states are particularly complicated. Due to the density of states and the occurrence of many surface crossings in the dissociation channels, reliable theoretical description can be achieved only with the use of high level ab initio methods and requires the use of a multi-con®gurational wavefunction. In this Letter, we use the averaged quadratic coupled cluster (AQCC) method [14], which has been shown to give reliable results for systems of similar size and complexity [15,16]. Both the vertical and adiabatic excitation and dissociation energies of the CF‡‡ dication are calculated. 2 2. Computational details In our previous study [8], we have applied the coupled cluster singles and doubles approach [17,18], including the e€ect of connected triples determined by perturbation theory (CCSD(T)) [19±21] with di€erent basis sets, in the calculations of ground-state properties of CF‡‡ 2 . These groundstate calculations can serve as a benchmark for the multi-reference (MR)-based methods applied in this study. Here, both the ground- and the excitedstate properties were uniformly recalculated. In particular, the non-variational AQCC method [14] was used. This method is approximately size-consistent and was previously successfully applied to the 1 B1 excited state of SO2 [15,16]. The full valence reference space was employed in the complete active space self-consistent ®eld (CAS±SCF) calculations. Only the 1s orbitals of carbon and of ¯uorine were kept frozen in the calculations. The use of the internal contraction scheme allowed inclusion of up to 400 million con®guration

J. Hrusak / Chemical Physics Letters 338 (2001) 189±194

state functions (CFS). The ANO contraction (14s9p4d3f/5s4p2d1f) of the Gaussian basis set was used [22]. In addition, one Gaussian g-type function on each atom was added to the ANO basis set in order to check the basis set dependency. However, the e€ect of this g-function was only small  and DBDE ˆ 0.9 kcal/mol) and for (Dr ˆ 0:002 A the scan it caused too high computational costs. Thus, the calculations were performed with the (14s9p4d3f/5s4p2d1f) basis set. For the dissociation pathway, the scan was performed based on state-averaged CAS with equal weights for the R and the two P states (for the linear conformation). The subsequent AQCC calculations became computationally demanding, especially when the symmetry was lowered to the Cs point group. In order to manage the size of the problem, it appeared to be necessary to lower the number of references in the AQCC expansion. Thus, we selected all references of which the weight in the CAS expansion is larger than 0.005. Using larger cuto€s often results in deviations of the relative AQCC energies. This scattering of the calculated energies is obviously due to the di€erent number of references at particular structures of the PES [15]. The dissociation pathway was followed in the linear conformation of the CF‡‡ ground state by 2 ®xing the second CF bond to the AQCC calculated  equilibrium CF bond distance (RCF ˆ 1:154 A). 3 0 For the lowest triplet state A (corresponding to 3 B1 and 3 B2 in C2v , i.e., to the 3 P state) a relaxed scan was also performed in the bent geometry. Further, the individual electronic states of CF‡‡ 2 were calculated in the C2v symmetry. The isolated fragments F, F‡ , and CF‡ were calculated in their high spin and low spin states (i.e., 2 P; 3 P; 1 D; 1 R; 1 P; 3 R, and 3 P, respectively). All the calculations were performed with the MO L P R O 98 program. 3. Results and discussion In order to describe the PES of excited states it is necessary to use a multi-reference method. Since the formulation of the MR coupled clusters equation is rather complicated, there is currently no MR-CC method available, which would be

191

suitable for the system under study. Previously, we have tested several modi®cations of the con®guration-interaction (CI) methods. It is well known that CI (and MR-CI) methods su€er from the sizeinconsistency error and, therefore, are inadequate for description of dissociation processes. The two modi®cations of the CI methods (ACPF [23] and AQCC [14]) were formulated and implemented into the program. These methods are able to recover most of the size-inconsistency error of the CI methods, and particularly, the AQCC method seemed to be most promising [15,16]. The geometrical parameters for the ground and excited states of CF‡‡ (applying C2v symmetry 2 constraint) and the corresponding excitation energies are summarized in Table 1. The CF‡ geometries and energies are also included for completeness. All the bond parameters were optimized at the AQCC level using the ANO basis set and comparison with the available data gives an estimate of the reliability of the presented results. ‡ For the ground state (1 R‡ g ) of CF the AQCC  is slightly optimized bond length (RCF ˆ 1:1615 A) longer than the reported experimental result  [24] as well as the result of our (RCF ˆ 1:154 A)  previous CCSD(T) calculations (RCF ˆ 1:157 A) [8]. Such ¯uctuations in bond length are not unusual and can probably be attributed to the different basis set size. The AQCC calculations of the ®rst excited state  again (3 P) result in a bond length of 1.220 A, somewhat longer than the data from previous  and calculations (CCSD(T) [8]: RCF ˆ 1:214 A 1 3  MR-CI [25]: RCF ˆ 1:224 A. The R ! P separation, which is calculated to be 4.70 eV at the AQCC level, is in excellent agreement with the previous data (CCSD(T): 4.79 eV and MR-CI: 4.77). The other electronic states (3 R; 3 D, and 1 P) were found to lie quite high (7.04, 7.10, and 7.91 eV, respectively) and thus do not interfere within the reaction window. Similarly, the AQCC optimized CF bond length for the ground state 1 ‡ 1  is in agreement R … A1 † of CF‡‡ (RCF ˆ 1:154 A) 2 with the result of the CCSD(T)/cc-pVQZ calcula [8]). tion (RCF ˆ 1:150 A The four lowest vertical ionization energies listed in Table 1 were calculated at the AQCC 2 equilibrium geometry of the CF‡ 2 … A1 † ground

J. Hrusak / Chemical Physics Letters 338 (2001) 189±194

192

Table 1 Energy and structure of the low lying CF‡ and CFn‡ 2 ions ERe1 (eV)

Geometry

State

This work

Literature

CF‡

1

R‡ 3 P

137:282362 137:109676

0.0 4.70

3

R D 1 P 2 A1

137:023785 137:021636 136:991449 237:021091

7.04 7.10 7.91 0.0

0.0 [8] 4.79 [8] 4.77 [25]

R‡ g A1 3 B1 3 A2 1 A2 1 B1 3 B1 1 B1 3 A2 1 A2

236:267593a 236:199269a 236:042209a 236:030144a 236:027612a 236:021795a 236:059994 236:044463 236:042993 236:040862

20.46 0.0 4.27 4.60 4.67 4.83 5.64 6.07 6.11 6.17

3

CF‡ 2 CF‡‡ 2 Vert. Vert. Vert. Vert. Vert.

a

ETot (Hartree)

Syst.

1

1

20.57 [8]

This work  1.161 A  1.220 A 1.826 1.899 1.281 1.221

 A  A  A  125.1° A,

1.154 1.221 1.221 1.221 1.221 1.221 1.274 1.293 1.293 1.291

 A,  A,  A,  A,  A,  A,  A,  A,  A,  A,

180.0° 125.1° 125.1° 125.1° 125.1° 125.1° 106.2° 103.4° 116.6° 115.6°

Literature  [8], 1.154 A  [24] 1.157 A  [8], 1.224 A  [25] 1.214 A

1.222 1.232 1.150

 124.5° [26] A,  A, 124.4° [6]  180.0° [8] A,

 125.1°) of CF‡ ; ERel energies are given relative to the ground state …1 A1 † of bent CF‡‡ . Calculated at the AQCC geometry (1.221 A, 2 2

 aFCF ˆ 125:1°). Its geometry state (RCF ˆ 1:221 A, agrees well with the previous MR-CISD results of  aFCF ˆ 124:5°) and also Cai [26] (RCF ˆ 1:222 A, with the MP2 calculations of Koch et al. [6]  aFCF ˆ 124:5°). The lowest excited (RCF ˆ 1:232 A, state in each symmetry representation was calculated. Even at the bent geometry the 1 A1 (corresponding to 1 R‡ g in the linear arrangement) is the most stable state of CF‡‡ 2 . A series of four states (3 B1 ; 3 A2 ; 1 A2 , and 1 B1 ) of CF‡‡ 2 , with excitation energies in the range 4±5 eV is accessible upon vertical ionization. It should be noted in passing, that the experiments of Leone [3] indicated the existence of an excited state in this region. The position of the lowest 3 B1 state (being 4.27 eV less stable than 1 A1 ) veri®es that the CF‡‡ 2 ground state is clearly separated in the Franck±Condon region. For these particular excited states the geometry was optimized at the AQCC level in order to get the adiabatic excitation energies (Table 1). It should be noted however, that these energies were calculated for the C2v symmetry structures of the excited states. Thus the listed structures might be saddle points for the Cs C2v ! Cs transition on a double-minimum PES or even not stationary points for some repulsive (triplet) states. Unfor-

tunately, no comparisons are possible due to the lack of experimental data. It was noted previously [15,16] that the excitation energies are not so sensitive to the size of the basis set as are the dissociation energies and thus the presented values may serve as an estimate of the electronic spectra. The dissociation reaction (4) is calculated to be exothermic by 8.5 kcal/mol in agreement with the previous results of 12 [6] and 9.6 kcal/mol [8], respectively. Besides the above-mentioned dissociation channels of CF‡‡ (3) and (4) another channel 2 appears to be principally accessible, ! CF‡ …3 P † ‡ F‡ …3 P† CF‡‡ 2

…5†

The lowest dissociation asymptotes (3)±(5) can be obtained directly from the 3 P ! 1 D excitation energy of F‡ (2.59 eV [25]) and from the calculated 1 R ! 3 P separation of CF‡ (4.70 eV). The next excited state of F‡ (1 S; 5.75 eV [25]) as well as the 1 D of CF‡ (7.04 eV) are already too high to be considered in our calculation. The restricted PES scan along the dissociation pathway CF‡‡ ! CF‡ ‡ F‡ 2

…6†

J. Hrusak / Chemical Physics Letters 338 (2001) 189±194

193

Fig. 1. Calculated energy pro®le for the low lying electronic states of CF‡‡ calculated at the AQCC level for the linear nuclear ar2 rangement. The 3 A0 state corresponds to the calculation at bent geometry (a ˆ 125°).

 is depicted in Fig. 1. The in the range 0.9±3.0 A 1 ‡ Rg ground state exhibits a deep minimum at 1.153  (linear conformation), which lies 0.37 eV above A the asymptote (3) and is clearly separated from all  the the other states. At a distance of about 1.9 A dissociative surface is crossed by the repulsive triplet surface leading to the ground-state asymptote (4). The crossing point lies 4.9 eV above the 1 ‡ Rg minimum. An impression about the shape of the triplet PES can be obtained by looking to second curve which represents the corresponding

triplet state (a 3 A0 ) at the bent geometry (a ˆ 125°). From the comparison of the 3 B1 and 3 0 A curves, it is obvious that the angular dependency, which is important in the Franck±Condon region, is not very pronounced in the dissociation path. Further, the ion±dipole interaction favors the linear dissociation and the dissociation pathway at the bent geometry is slightly higher in energy. However, neither the position nor the high of the SO-barrier is a€ected signi®cantly. The spin± orbit coupling elements for the singlet±triplet

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J. Hrusak / Chemical Physics Letters 338 (2001) 189±194

transition were not calculated and thus, no information on transition probabilities can be given. A high density of states and many surface crossings occurring characterize the energy range above 6 eV. The minima appearing at the adiabatic surfaces are very shallow. Only the second 1 A1 state shows a pronounced well before dissociating into the asymptote (3). These presented data do carry only limited information, since a detailed multi-dimensional scan would be needed for further analysis. This, however, is at present quite costly and not possible by using the described computational procedure. It appears to be necessary to project out the individual higher roots in Cs symmetry (to prevent root-¯ipping problems occurring at larger RCF ) and to calculate each state separately. It is obvious that the knowledge of the complete PES (including spin±orbit coupling) would be of critical importance in elucidation of the dissociation dynamics of CF‡‡ 2 . We are currently working towards construction of the part of the PES's along the dissociation channels (3) and (4) in order to investigate theoretically the dissociation dynamics. However, some appropriate spectroscopic experiments would be highly desirable. Acknowledgements This work was supported by the grant #ME272=1998 awarded by the Ministry of Education of the Czech Republic. The support of the grant #203=00=0652 of the Grant agency of the Czech Republic is also acknowledged. My thanks also belong to Prof. S. Iwata for helpful discussions. References [1] C.J. Proctor, C.J. Porter, J.H. Beynon, Int. J. Mass Spectrom. Ion Phys. 41 (1982) 251.

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