Theoretical Study of the Gas-Phase Reaction : SF 6 + CO + SF 5 + + FCO

Cálculos teóricos utilizando conjuntos de funções de base com potenciais efetivos de caroço (pseudopotencial ECP) foram efetuados para um grande número de sistemas moleculares relacionados a SF 6 . Utilizou-se cálculos do tipo Hartree-Fock (HF), MP2 e QCISD(T). Foram feitos estudos para propriedades de estrutura eletrônica como geometrias moleculares, energias de dissociação de ligação e de ionização adiabática. No caso de estruturas moleculares, observou-se existir boa concordância entre os dados obtidos com pseudopotencial e aqueles disponíveis na literatura. Para propriedades relacionadas com energias, os métodos com pseudopotencial reproduzem a tendência observada usando cálculos mais sofisticados. O estudo da reação de SF6 com CO foi caracterizado pela formação de um complexo íon-molécula reagente passando por um estado de transição e originando um complexo íon-molécula produto. Nesta reação, nem o estado de transição, nem o complexo íon-molécula reagente puderam ser localizados usando energias e forças do método HF, pois a reação prossegue sem barreiras formando SF 5 + + FCO, sem uma barreira potencial associada ao processo. O uso de cálculos a partir de metodologia CASSCF(7,7)/B0 foi necessário para caracterizar o complexo íon-molécula reagente como ponto estacionário. Finalmente, estudos mais detalhados foram feitos para averiguar as mudanças na energia e na distribuição de cargas com o avanço da reação de reagentes para produtos. Observou-se que a reação SF 6 + CO SF 5 +


Introduction
2][3] On the cosmic scale, the chemistry that produces molecules in interstellar clouds is dominated by ion-molecule reactions.Shrinking down to our own planet, the upper atmosphere is a plasma, and contains electrons and various positive ions.Certain anthropogenic chemical compounds 4 (including SF 6 and perfluorocarbons) can probably not be destroyed within the troposphere or stratosphere, but may be removed by reactions with ions or electrons in the ionosphere.SF 6 is a highly potent greenhouse gas used in the industry for insulation and current interruption in electric transmission and distribution equipment.It represents about 15% of total European fluorinated greenhouse gas emissions. 5ecent years have seen a massive growth in the industrial use of plasmas, particularly in the fabrication of microelectronic devices and components. 6The chemistry within the plasma, much of which involves ion-molecule and electron-molecule reactions, determines the species that etch the surface, and hence the outcome and rate of an etching process.Much of the chemistry that is often labeled as 'organic' or 'inorganic' involves ion-molecule reactions, usually carried out in the presence of a solvent.For instance, S N 2 reactions, such as OH -+ CH 3 Cl, fall into this category.To gain a clearer picture of how these reactions occur, it is advantageous to study them removed from the (very great) perturbations due to the solvent.The experimental analysis is very difficult in many situations.So, the theoretical calculations can be useful.What can theoretical calculations add to the experimental data?It is possible to calculate the energies of each of the species involved in a specific reaction pathway, and so establish whether the reaction is exothermic.Theory is particularly powerful for providing energies of transient species such as ions, where experiments are usually only able to supply bounds.Inevitably there are questions about the accuracy of the energies provided by theoretical calculations, since all computational approaches contain approximations.Theory can be used to map out the detailed pathway that connects reactions to products. 7or an ion-molecule reaction there may be three stationary points, a reactant ion-molecule complex, a transition state, and a product ion-molecule complex.For some exothermic reactions, there may be only one stationary point, a product ion-molecule complex.Examining the minimum energy pathway produced by theoretical calculations can then identify barriers and bottlenecks to reactions, and hence may reveal why some exothermic reactions have rate coefficients less than the predictions of capture theory.
The molecule SF 6 is widely used in plasmas for processing of materials, and the fabrication of microelectronic components. 611][12][13] Richard D. Ernst and coworkers 14 have observed the high reactivity between SF 6 and low valent organometallic compounds of titanium and zirconium.They suggest that SF 6 may prove useful for preparing compounds "not normally obtained through other reactions." There has been much theoretical work on the energies of SF n , SF n + , and SF n -molecules.The rate constants and product ion distributions have been measured for the reactions of many ions and also electrons with SF 6 .Until this work there had been no attempt to use theoretical methods to map out the detailed pathway of any ion-molecule reaction of SF 6 .On the basis of experimental evidence it has been asserted that the reaction of SF 6 with CO + proceeds via F -abstraction.

Computational Methods
The scale of the problem must be reduced if any results are obtained.In order to obtain energies that may approach chemical accuracy ( 10 kJ mol -1 ) calculations must take account of electron correlation.The 'ideal' methodology would have been a multi-reference configuration interaction all electron calculation with several large, flexible basis sets to enable extrapolation to the complete basis set limit.By the standards of high level ab initio quantum chemistry, the system SF 6 + CO + is large.So, performing accurate calculations (methodology and basis sets) on these systems represents a significant challenge.Morgon et al. [15][16][17][18][19][20] have been developing techniques to tackle such problems.These are centered around the use of effective core potentials (ECP), 21 in which the inner electrons are represented by an effective potential derived from calculations on atoms.The electronic wavefunction itself then only contains the outer electrons.Basis functions for these outer electrons are generated so that when used with the effective core potential important data are reproduced accurately.In fact two sets of basis functions were used, a small basis (usually called basis B0) and a larger basis, with extra diffuse and polarization functions (basis sets designated as B1).These diffuse functions are obtained by observing the convergent behavior of the weight functions (graphical display of the linear combination of basis functions 15,22 ) of the outer atomic orbitals (s and p).Calculations with basis B1 are naturally much more expensive than those employing basis B0, so it is important to have computational schemes that perform the minimum number of calculations using basis B1.Optimization of the molecular geometries and vibrational analysis are carried out at HF/B0 level.The harmonic frequencies confirm that the stationary points correspond to minima and are used to compute the zero-point energies.Further optimization is carried out at MP2/B0 level.At the MP2 equilibrium geometry corrections to the total energies are performed at higher level of theory.First, this is done to the QCISD(T)/B0 level, and later by addition of extra Theoretical Study of the Gas-Phase Reaction: SF 6 + CO + SF 5 + + FCO functions (s, p, d and f) at MP2/B1 level.Thus, these results coupled to additive approximations for the energy yield an effective calculation at a high level of theory, This scheme has been tested on a range of smaller systems, and shown to give good results.
All of these calculations were performed using the Gaussian98 program. 23It should be noted that the absolute values of the calculated energies have no real significance, as no common energy zero for different atoms has been used.This arises from how the effective core potentials are constructed.When differences are formed, the differences between the zeros cancel, to leave for instance the difference in energy between the products and reactants of a reaction.

Initial Tests
There have been several attempts to produce a consistent set of energies for the SF n , and SF n + molecules.Of importance to this study are the G2 calculations of Irikura, 24 and the higher level calculations of Bauschlicher & Ricca (B&R). 25G2 is a set of rules, containing empirical corrections, for obtaining energies which perform well in tests against experimental data.Bauschlicher & Ricca's work did not call upon empirical rules, but did look very carefully at the effect of basis set size.Their results appear to the best currently available in the literature.We used them to perform a series of tests on the energies produced by the ECP-based QCISD(T)/B1//MP2/B0 energies (equation 1).Specifically, comparisons were made between the structures of the SF n and SF n + molecules, S-F bond dissociation energies (BDE) and the adiabatic ionization energies (AIE) of SF n molecules.
A comparison of molecular geometries, considering the ground states, for SF 6 , SF n , and SF n + (n = 1 -5) is presented in Table 1.The adiabatic ionization energies of the SF n (n = 1 -5) given by process SF n SF n + + e -, can also be obtained from the energies of the neutral SF n molecules and the SF n + cations, to provide another test of the quality of the energies produced from the QCISD(T)/B1//MP2/B0 calculations.The results can be found in Table 2.The first observation must be the excellent agreement between our values and those of Bauschlicher and Ricca (average error of 0.01 eV).
The results for the bond dissociation energies of the neutral SF n molecules are tabulated in Table 3.These can be compared against dissociation energies from high level theoretical calculations (Bauschlicher and Ricca's results at RCCSD(T) level which have been extrapolated to the complete basis set limit) and also against a set of dissociation energies obtained from the G2 (results obtained from Irikura 24 and G3 calculations. The general conclusions from these tables and graphs are that the ECP-based 21 calculations produce excellent optimized molecular geometries and the energy obtained using QCISD(T)/B1//MP2/B0 does a good job of reproducing the trends in the adiabatic ionization energies (AIE) and bond dissociation energies (BDE).The values of IE and BDE calculated in this work were compared with the medium values of previous results and are in the range of 0.05 to 0.49 eV (Table 2), and 0.97 to 7.70 kJ mol -1 (Table 3), respectively, and the calculations with this scheme are naturally much less expensive than procedures employing G2, G3, and complete basis sets.

The reaction between SF 6 and CO +
The experimental observations concerning the reaction between SF 6 and CO + are that it is a fast reaction (k = 9.2 × 10 -10 cm 3 molecule -1 s -1 ), with an efficiency approaching 100%. 13The only observed ion product is SF 5 + .Without identification of the neutral product(s) it is not possible to say for certain, on the basis of the experimental data, how the reaction proceeds.
It could be by dissociative charge transfer: or F -abstraction: On the basis of other evidence, and in particular that Kr + , 13 which has a very similar recombination energy to CO + , does not react with SF 6 , it is strongly believed that the reaction proceeds by an F -transfer mechanism.The experimental results 13 involving the CO + reagent ion and SF 5 + product ion (100%) show that when the proposed neutral products are CO + F or FCO, the enthalpies ( have the values of +16 kJ mol -1 and -133 kJ mol -1 , respectively.This hypothesis can be tested through theoretical calculations.It is possible to map out the minimum energy pathway between the separated reactants and products.
The high rate constant implies that there can be little or no activation energy barrier to the reaction.Characterization of the pathway requires the identification of three stationary points on the potential energy surface (together with the separated reactants and products).These are the reactant ion-molecule complex, the transition state, and the product ion-molecule complex.Initial HF/B0 searches starting from a variety of start geometries failed to find either a reactant ion-molecule complex or a transition state.Each run either aborted for one reason or another, or optimized to a product ion-molecule complex comprising SF 5 + and FCO.No runs terminated with a complex made up of SF 5 + + F + CO.The reaction clearly proceeds by a F -transfer mechanism, but the transition state had not been found.The system SF 6 /CO + is difficult because of the high symmetry of the molecules, and the open shell electronic structure.This implies that there are likely to be several molecular orbitals for the system with energies close to (but above) the highest occupied molecular orbital.A single determinant electronic wavefunction of the type used in Hartree-Fock calculations is then a poor description of the system.A better starting wavefunction was obtained using the CASSCF(7,7)/B0 (Complete a Values in parentheses are given by: x i is the experimental measurement or previous theoretical result.

J. Braz. Chem. Soc. 78
Theoretical Study of the Gas-Phase Reaction: SF 6 + CO + SF 5 + + FCO Active Space Self Consistent Field) method.It was then possible to locate the reactant ion-molecule complex.This geometry was then used in the subsequent HF/B0 calculations of frequencies, and MP2/B0, QCISD(T)/B0, and MP2/B1 calculations of the energy of the reactant ionmolecule complex.The electronic energies for systems in SF 6 /CO + reaction are summarized in Table 4.
The relative energies of the separated reactants, the reactant ion-molecule complex, the transition state, the product ion-molecule complex, and the separated products Xat the QCISD(T)/B1//MP2/B0 level -equation 1, are displayed in Figure 1.There are no strong forces in the product ion-molecule complex, and minimum energy structures corresponding to a variety of different structures were found by HF/B0 followed by MP2/B0 optimizations.The transition state lies far in energy below the separated reactants, it is unlikely to act as a significant bottleneck to the reaction, which is consistent with the experimental observation that the reaction is not less than 70% efficient. 13his transition state (TS) ( i = 478.80cm -1 ) shows a close approach of the CO + to the SF 6 , and that when first formed the SF 5 + unit has approximately C 4v symmetry (for the isolated SF 5 + molecule the equilibrium geometry has D 3h symmetry).The Figure 2 shows the intrinsic reaction coordinate (IRC) pathway.The IRC was calculated using HF/B0 theory.The reaction path is formed through the computation of an IRC a The effects of spin-orbit coupling on the energies have been neglected.b The HF/B0 vibrational wavenumbers are scaled by the standard factor 0.8929.
c Values in parentheses are given by: x i is the value of the previous theoretical result.using the Gonzalez-Schlegel second order method 26 to connect the reactant to the transition state and then to the product.The IRC is interpreted as the pathway of a concerted mechanism involving a single TS.To investigate the reaction pathway further (Figure 1), the HF/B0 energy and the charge distribution (as expressed by the Mulliken atomic charges) were calculated as the F -was abstracted from the SF 6 .At each separation of the F from the S the energy was optimized (subject to the constraint that the SF 5 unit retained C 4v symmetry), and the Mulliken atomic charge were calculated, subsequently the atomic charges were summed to give the charges on the SF 5 , F and CO units (Figure 3).Due to the time required to perform the many geometry optimizations the calculations were limited to the HF/B0 level.Inspection of the energy plot shows a smooth variation (there is no maximum corresponding to a transition state in HF/B0 calculations on this system).The charges also vary smoothly as the S-F distance extends.This smooth variation of the charges and energies is expected for a reaction occurring on the potential energy surface for a single electronic state of the overall system.This is further proof that the SF 6 + CO + reaction occurs via a F -transfer mechanism (with the value of 103.86 kJ mol -1 ).
Additional information can be given by the kinetic constant calculation for the SF 6 + CO + SF 5 + + FCO reaction.The reaction rate constant (k) was determined using the Conventional Transition-State Theory (CTST). 27,28onsidering a unimolecular process the CTST formula can be applied to calculate k: (2)   where is the tunneling factor, k B and h are the Boltzmann and Planck constants, respectively.Q SF represent the partition functions corresponding to the reactant complex and transition state, and were obtained from the Gaussian98 output.E a involves the difference between the high-level energies (QCISD(T)/B1) of reactant complex and TS, including ZPE corrections.The effect is essential in cases where high barriers and large frequencies occur, and this is not the case in the present reaction, so the = 1 was considered.The value of k calculated at 298 K is approximately equal to 3.9 × 10 -11 cm 3 molecule -1 s -1 , and this value is close to the experimental value, 13 k exp = 9.2 × 10 -10 cm 3 molecule -1 s -1 at 300 K.

Table 1 .
Molecular geometries and ground state symmetries for SF 6 , SF n , and SF n + (n = 1 -5) calculated at the MP2 level a .Where there are chemically distinct types of fluorine atom in a molecule, the subscript 1 refers to the less numerous or axial type.Distances are in Å and angles in degrees 24Results at MP2=Full/6-31G* calculations.24;b Our results at the MP2/B0 level are in parentheses.

Table S1 .
Small Basis Set (B0) Two sets of basis functions were used in this work, a small basis (B0) and a larger one, with extra diffuse and polarization functions (B1).The effective core potential (ECP) used was SBKJC potential 21 for all atoms.Study of the Gas-Phase Reaction: SF 6 + CO + SF 5 + + FCO J. Braz.Chem.Soc.S2

Table S2 .
Larger Basis Set (B1): Small Basis Set plus extra diffuse and polarization functions