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Theoretical investigation on the existence of the SiF−6 anion
Volume 184,number 4
CHEMICALPHYSICSLETTERS
27 September I99 1
Theoretical investigation on the existence of the SiF; anion G.L. Gutsev Institute of Chemical Physics, USSR Academy of Sciences,Chernogolovka, Moscow Region 142432, USSR
Received 20 May I99 1;in final form 28 June 1991
The octahedral configurations of SiFa-, n =O, 1 and 2, are considered within the framework of a density functional approach. It is found for the first time that the SiF; anion is stable towards dissociation. The SiF; anion possesses a high first ionization potential, z 7 eV. and the adiabatic electron affinity of SiF, is estimated to be z 5 eV. The large adiabatic correction is stipulated by the dissociative character of the neutral molecule.The most striking feature of the SiF,, SiF; , SiFa- series consists of the nonstability of species formed after both attachment and detachment ofan electron to the SiF; anion.
1. Introduction The problem of stable anions having no stable neutral precursors is considered in recent theoretical investigations. The best known species of this kind is SiH, whose stability in the gas phase was established experimentally [ 11, and was subsequently confirmed in ab initio calculations [ 21. However, no stable state appears to exist [3] for its neutral precursor SiHS. The same question should be addressed to the next member of the hypervalent SiXs series, i.e. SiF,. This species belongs to the superhalogen class [ 41 and possesses a high electron affinity (EA ) , which was estimated to be 6.3 eV according to results of Hartree-Fock-Slater (HFS) calculations [ 41. However, stability of both the neutral molecule and its anion has not been considered. The results of recent calculations [ 51 allow the prediction for SiFS to be stable at least by 3 kcal/mol, and these calculations predict the high stability, by 73 kcal/mol, of the SiFr anion towards the lowest dissociation channel SiF; +SiF, t F-. The SiF; anion, but not the neutral molecule, was detected experimentally [6] as well as in the preceding case. Some analogy between unstable SiHS, weakly stable SiFs and their highly stable anions may be anticipated in the case of the SiF; anion and its dianion SiFi- which is known to exist [ 71 in salts. On the other hand, the central atom in SiF; possesses the same formal valency as in SiF,. Elsevier Science Publishers B.V.
The present work aims at theoretical consideration of the octahedral configurations of the SiFs, SiF; , SiFi- series in order to gain insight into their stability and electronic characteristics. The calculations are carried out within a local spin-density ap proximation (LSDA) which was shown to be reliable [ 81 in calculations on the electronic affinity of molecules and radicals, and which yields an EA estimate within the limit of 0.3 eV with respect to the most reliable experimental data.
2. Calculationaldetails The original complex of programs [9] based on the discrete variational approach for solving the LSDA equations [ lo] and supplemented [ 111 with geometry optimization subroutines is applied to calculations on the geometrical and electronic structures. The triple-zeta ST0 basis sets [ 121 of F and Si, augmented with two sets of the polarization 3dfunctions (with exponents 2.5 and 1,O) at each atom, is used in the standard MO LCAO expansion. The same basis sets are used for all three species considered. Total energies are calculated both in the LSDA variant which employs the Vosko-Wilk-Nusair [ 131 exchange-correlation potential and with the inclusion of non-local (NL) corrections due to Becke [ 141 to the LSDA exchange potential. The latter approach 305
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will be denoted as LSDA/NL below. Further details may be found elsewhere [ 81. The reliability of our approach may be assessed in the case of SiF,, whose experimentally measured [ 151 value of D, (SiF,+SiF,+F) is 6.95 eV. Theoretical values obtained within the same basis as used in the present work are 7.08 and 6.95 eV on the LSDA and LSDA/NL level, respectively. The second severe test is presented by the calculations on the atomic EA, because the ASCF approach is quite crude for the fluorine EA. The typical LCAO value is 1.19 eV [ 161 and the best numerical Hartree-Fock value 1.363eV [ 17 1. Only a substantial account of the electronic correlation brings [ 18,191 the calculated values close to the experimental value [20] of 3.399(9) eV. For the silicon atom the ASCF approach affords a more reliable value of 0.95-0.97 eV [ 211 versus the experimental value of 1.385 eV [20]. The EAs of F and Si are 2.79, 3.16, 3.45 eV and 1.11, 1.12, 1.18 eV on the HFS, LSDA and LSDA/ NL levels of the theory, respectively, with the use of the basis set indicated above. Thus, it may be concluded that the LSDA/NL approach accounts for much of the electronic correlation, and results obtained on this level are usually close to those on the Cl-SD level.
3. Results and discussion Optimized bond lengths are 1.633, 1.661 and 1.699 A for the octahedra1 configurations of SiF,, SiF; and SiF:- , respectively. The experimental bond length of SiFi- is known [ 71 to be equal to 1.706 A in the FeSiF,.6H,O salt. This value is quite close to that computed for the isolated dianion. Using the results of preliminary calculations [ 51 on the constituents, we are able to calculate the dissociation energies through the different channels. The values obtained as the total energy differences (i.e. without zero-point energy and basis-set-superposition-error corrections) of a species and its corresponding conslituents are displayed in table 1. It is seen that both SiF6 and SiFg- are unstable towards dissociation through the channels SiF6+SiF,t F, and SiFi- +SiF, +F-, respectively. At the same time, the anion SiF; is quite stable, by 0.87 eV 306
27 September I99 I
CHEMICAL PHYSICS LE-lTERS
Table 1 Dissociation energies (in eV) through the lowest channels of SiF,, SiF;, and SiFi-
Channel
LSDA
LSDA/NL
SiF&iF,+F, -&iF$tF +SiF,tF?
-1.08 I .22 5.86
-1.99 0.32 4.38
1.74
SiF; +SiF; tF +SiF,+Fy +SiF, + F+SiF; t F, SiFi-+SiF, t F-SIFT t Fy 4 SIFT t F,
2.8 1 4.61 6.02 -
1.24 3.48 5.57
0.87 1.42 3.91 5.02 -1.90 2.07 4.07
(20.06 kcal/mol ) on the LSDA/NL level. On the LSD.4 level, the stability is even higher, but it is known [22] that this approximation tends often to some overestimation (within w 1 eV) of the dissociation energies, and the LSDA/NL level affords the more reliable values. Thus, the SiF,- anion presents a stable species which has no stable neutral precursor. The ground state of the anion is ‘T,, and it may suffer Jahn-Teller distortions. However, the isoelectronic PF6 possesses the octahedral ground-state configuration [23]. Reduction in symmetry Oh-‘DZh leads to creation of the degenerate states ‘Bng,n= I3, which are placed ~0.2 eV above the octahedral ‘T,, state. Formal valency of the central atom in SiF; is the same as in SiFS, and both species possess one ligand hole. The more stable character of the anion may be related to properties of the ligand frame [ 241. The F6 frame allows for more delocalization of the hole than the FS. The second reason appears to be related to the screening effect influencing the ligand hole by the delocalized external electron of SiF; . Let us consider the vertical and adiabatic EAs of SiF, and SiF;! calculated as differences in total energies of their initial and final states in the octahedral geometrical configurations. By definition,
EA,,,=E,,,(M,R,)-E,,,(M-,R,) ,
(1)
EA,,=E,,,(M,R,)-E,,,(M-,R,),
(2)
where R, and R; stand for the equilibrium geometries of a neutral system M and its anion M-, re-
CHEMICAL PHYSICS LETTERS
Volume 184, number 4
27 September 1991
Table 2 Adiabatic a1 and vertical EAs (in eV) of SiFS, SiF, and SiF; Property
Approach
SiFS
SiF6
SiF;
diff
limit
diff
limit
EA.*
LSDA
6.09
6.84
5.53
0.18
1.42
EA,
LSDA/NL LSDA
6.49
7.04
5.14
0.6s
2.58
EL,,
5.82
6.81
0.18
a) “diff” denotes values obtained according to eq. (2), and “limit” stands for those due to eq. (3)) see teat.
spectively. The octahedral configuration of SiF6 is unstable; therefore, let us supplement the EA values calculated for this configuration by the subscript “diff”. Table 2 presents these values together with data for SiFs given for comparison. It is seen that octahedral (metastable) SiF6 is the superhalogen whose AEad(diff ) exceeds that of SiFs by z 0.5 eV, i.e. by a value which is roughly equal to the difference in the dissociation energies of SiFs and SiF;. The vertical EA of SiF, is close to its EAad( diff ) due to the small change in bond lengths occurring after the attachment of an extra electron. The first ionization potential of SiF; is also close to EAad(diff ), confirming the superhalogen [4] nature of the neutral SiF,(O,). The adiabatic EA by definition is the difference between total energies of the most stable states of the neutral and its anion. Because of the dissociative character of the neutral, we need to change eq. (2) as follows: EA,d =R,,,(M, R,) -&,(M-,
R, )+Do(M)
2 (3)
where M stands for SiF6, R, refers to its equilibrium octahedral structure, and Do is the negative dissociation energy through the lowest channel. Using eq. (3), one may estimate EA, of SiF6 as 5.53 and 5.05 eV on the LSDA and LSDA/NL levels of theory, respectively. These values are presented in table 2 in the columns designated as “limit”. Let us turn to results of calculations on the dianion. According to data presented in table 2, it is stable to the loss of an electron, which is in line with our theoretical estimations [ 241 of the value of the second EA for the six-membered fluorine frames. On
the other hand, this dianion is unstable towards dissociation to the highly stable anion SiF; and F-. The same situation has been met earlier for the dianion BeFi- where a barrier to the dianion dissociation was found [ 25 1, thus confirming the existence of its metastable state. Because of the close resemblance of both systems, the same conclusion seems to be valid for SiFi- , and the octahedral configuration of this dianion appears to have an appreciable lifetime of the vibrational levels as well. Strictly speaking, the same arguments may be applied when estimating EAad of SiF; as those used in the case of its neutral precursor. In order to obtain the value of EA,,, we should account for the dissociative character of the dianion and make the corresponding changes in eq. (3) i.e. E&,=&(M-,R,) -E,,,(M’-,R:-)-Do(M2-),
(4)
where again R, refers to the octahedral contigurations. Combining data of both tables, one obtains quite a large value for the EAadof SiF; , namely, 1.42 and even 2.58 eV on the LSDA and LSDA/NL levels of theory, respectively. Other examples of doubly charged anions have been considered among the hexafluorides of transition metals both theoretically [ 261 and experimentally [ 27 1, and it was found that the corresponding neutral systems should possess a second positive EA. However, the problem of stability to dissociation of these dianions has not been investigated.
4. Conclusions According to results of calculations within the density functional method, the SiF; anion is stable 307
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CHEMICALPHYSICSLETTERS
towards dissociation, whereas its neutral precursor appears to be unstable. The existence of SiF; may be related to the existence of the weakly stable SiF, because both these hypervalent systems possess one ligand hole. The more stable character of the SiF; anion seems to be related to delocalization of the hole over the larger number of ligand atoms, and some screening effect influencing the hole from the external delocalized electron. The neutral SiF6 may be attributed to superhalogens because its estimated EAad exceeds 5 eV. Due to the unstable character of the neutral precursor, the first ionization potential of SiF; is much higher than EAad, indicating the quasi-superhalogen character of this species. The SF; anion presents an interesting system which dissociates after attachment or detachment of an electron. The SiFg- dianion is shown to be unstable towards dissociation, though it is stable to the loss of an electron in its metastable octahedral state. Thus, the neutral SiF6 molecule possesses a positive second EA with respect to this metastable state. The second EA, of SiF6 is quite large, 2.58 eV on the LSDA/ NL level of theory, and refers to the difference between total energies of the stable anion and products of the dianion dissociation.
Acknowledgement This investigation was supported by the National Science and Engineering Research Council of Canada (NSERC ), whose grant for the international collaboration is gratefully acknowledged. I am very appreciative of the University of Calgary for the generous gift of computer time and the access to their Cyber-205 facilities. Special thanks are due to Professor Tom Ziegler for hospitality as well as to Dr. V. Tschinke and Dr. L. Fan for assistance. The reception of results of calculations on the dianion BeFi- prior to publication from Professor A.I. Boldyrev is gratefully acknowledged. I would like to express my gratitude to the referee for his remarks,
308
27 September1991
References
[l] D.J. Hajdaszand R.R. Squires, J. Am. Chem. SOC.I08 (1986) 3139. [2] A.E. Reed and P. von R. Schleyer,Chem. Phys. Letters 133 (1987) 553; G. Sini, P.C. Hiberty and S.S. Shaik, Chem. Commun. (1989) 773; G. Sini, G. Ohanessian, PC. Hiberty and S.S.Shaik,J. Am. Chem. Sot. 112 (1990) 1407; M.S. Gordon, T.L. Windus, L.W. Burgraffand L.P. Davis, 3. Am. Chem. Phys. 112 (1990) 7167. [ 3 ] MS. Gordon, D.R. Gano and J.A. Boatz,J. Am. Chem. Sot. 105 (1983) 5771; A. Demolliens,0. Eisenstein, P.C. Hiberty, J.M. Lefour,G. Ohanessian, S.S. Shaik and F. Volatron, J. Am. Chem. SOC. 111 (1989) 5623; F. Volatron, P.Maitre and M. PClissier,Chem. Phys. Letters 166 (1990) 49; J. Mot and H. Ratajczak,Chem. Phys. Letters, in press. [4] G.L. Gutscv and A.I. Boldyrev,Chem. Phys. 56 (1981) 277; Advan. Chem. Phys. 6 1 ( 1985) 169;Usp. Khim. 56 (1987) 889, in Russian. [ 5 ] G.L. Gutsev and T. Ziegler,to bc published. [ 61 H.C. Clark and K.R. Dixon. Chem. Commun. ( 1967) 717. [ 71W.C. Hamilton, Acta Cryst. 15 (1962) 353; B.M. Gimarc, Molecularstructure and bonding (Academic Press, New York, I979) [8] T. Ziegler and G.L. Gutsev. J. Comput. Chem., submitted for publication; G.L. Gutsev and T. Ziegler, J. Phys. Chem., submitted for publication; G.L. Gutsev, J. Phys. Chem. 95 (1991), in press. [9] E.J. Baerends, D.E. Ellis and P. Ros, Chem. Phys. 2 (1973) 41. [IO] S. Lundqvist and N.H. March, eds. Theory of the inhomogeneous electron gas (Plenum Press, New York, 1983). [ 111 L. Versluisand T. Ziegler,J. Chem. Phys. 88 (1988) 322. [ 121J.G. Snijders,E.J. Baerendsand P. Vemooijs,At. Data Nucl. Data Tables 26 (1982) 483. [13]S.J. Vosko,L. WilkandM.Nusair, Can. J. Phys. 58 (1980) 1200. [ 141A.D. Becke,Phys. Rev. A 38 ( 1988) 3098. [ 151D.F. McMillan and D.M. Golden, Ann. Rev. Phys. Chem. 33 (1982) 493. [16] J.V. Ortiz, J. Chem. Phys. 86 (1987) 308. [ 171 S. Fraga, Handbook of atomic data (Elsevier, Amsterdam, 1976). [ 18] B.H. Botch and T.H. DunningJr., J. Chem. Phys. 76 ( 1982) 6046. [ 191J.V. Ortiz, Chem. Phys. Letters 136 (1987) 387. [20] H. Hotop and W.C. Lineberger, J. Phys. Chem. Ref. Data 14 (1985) 731.
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[21] J. Anglada, P.J. Bruna, SD. Peyerimhoff and R.J. Buenker, J. Phys. B 16 (1983) 2469; Y. Guo, S. Manoli and M.A. Whitehead, Phys. Rev. A 38 (1988) 1120. [22] A.D. Becke, Intern. J. Quantum Chem. 27 (1985) 585: V. Tschinke and T. Ziegler,in: Density matrices and density functionals, eds. R. Erdahl and V.H. Smith Jr. (Reidel, Dordrecht, 1987) pp. 467-477. [23] G.L. Gutsev, unpublished results. [24] G.L. Gutsev and A.I. Boldyrec,J. Phys. Chem. 94 (1990) 2256.
27 September 1991
[25] H.-G. Weikert, L.S. Cederbaum, F. Tarantelli and Al. Boldyrev,Z. Physik B ( 199I ), in press. [26] Y. Sakai andE. Miyoshi, J. Chem. Phys. 87 ( 1987) 2885; E. Miyoshi,Y. Sakai,A. Murakami,H. Iwaki,H. Terashima, T. Shoda andT. Kawaguchi,J. Chem. Phys. 89 (1988) 4193; Y. Sakai and E. Miyoshi, J. Chem. Phys. 89 ( 1988) 7363. [27]M.V. Korobov, S.V. Kuznetsov, L.N. Sidorov, V.A. Shipachevand V.N. Mit’kin, Intern. J. Mass Spectrom. Ion Phys. 87 ( 1989) 13.
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27 September I99 1
Theoretical investigation on the existence of the SiF; anion G.L. Gutsev Institute of Chemical Physics, USSR Academy of Sciences,Chernogolovka, Moscow Region 142432, USSR
Received 20 May I99 1;in final form 28 June 1991
The octahedral configurations of SiFa-, n =O, 1 and 2, are considered within the framework of a density functional approach. It is found for the first time that the SiF; anion is stable towards dissociation. The SiF; anion possesses a high first ionization potential, z 7 eV. and the adiabatic electron affinity of SiF, is estimated to be z 5 eV. The large adiabatic correction is stipulated by the dissociative character of the neutral molecule.The most striking feature of the SiF,, SiF; , SiFa- series consists of the nonstability of species formed after both attachment and detachment ofan electron to the SiF; anion.
1. Introduction The problem of stable anions having no stable neutral precursors is considered in recent theoretical investigations. The best known species of this kind is SiH, whose stability in the gas phase was established experimentally [ 11, and was subsequently confirmed in ab initio calculations [ 21. However, no stable state appears to exist [3] for its neutral precursor SiHS. The same question should be addressed to the next member of the hypervalent SiXs series, i.e. SiF,. This species belongs to the superhalogen class [ 41 and possesses a high electron affinity (EA ) , which was estimated to be 6.3 eV according to results of Hartree-Fock-Slater (HFS) calculations [ 41. However, stability of both the neutral molecule and its anion has not been considered. The results of recent calculations [ 51 allow the prediction for SiFS to be stable at least by 3 kcal/mol, and these calculations predict the high stability, by 73 kcal/mol, of the SiFr anion towards the lowest dissociation channel SiF; +SiF, t F-. The SiF; anion, but not the neutral molecule, was detected experimentally [6] as well as in the preceding case. Some analogy between unstable SiHS, weakly stable SiFs and their highly stable anions may be anticipated in the case of the SiF; anion and its dianion SiFi- which is known to exist [ 71 in salts. On the other hand, the central atom in SiF; possesses the same formal valency as in SiF,. Elsevier Science Publishers B.V.
The present work aims at theoretical consideration of the octahedral configurations of the SiFs, SiF; , SiFi- series in order to gain insight into their stability and electronic characteristics. The calculations are carried out within a local spin-density ap proximation (LSDA) which was shown to be reliable [ 81 in calculations on the electronic affinity of molecules and radicals, and which yields an EA estimate within the limit of 0.3 eV with respect to the most reliable experimental data.
2. Calculationaldetails The original complex of programs [9] based on the discrete variational approach for solving the LSDA equations [ lo] and supplemented [ 111 with geometry optimization subroutines is applied to calculations on the geometrical and electronic structures. The triple-zeta ST0 basis sets [ 121 of F and Si, augmented with two sets of the polarization 3dfunctions (with exponents 2.5 and 1,O) at each atom, is used in the standard MO LCAO expansion. The same basis sets are used for all three species considered. Total energies are calculated both in the LSDA variant which employs the Vosko-Wilk-Nusair [ 131 exchange-correlation potential and with the inclusion of non-local (NL) corrections due to Becke [ 141 to the LSDA exchange potential. The latter approach 305
Volume 184, number 4
will be denoted as LSDA/NL below. Further details may be found elsewhere [ 81. The reliability of our approach may be assessed in the case of SiF,, whose experimentally measured [ 151 value of D, (SiF,+SiF,+F) is 6.95 eV. Theoretical values obtained within the same basis as used in the present work are 7.08 and 6.95 eV on the LSDA and LSDA/NL level, respectively. The second severe test is presented by the calculations on the atomic EA, because the ASCF approach is quite crude for the fluorine EA. The typical LCAO value is 1.19 eV [ 161 and the best numerical Hartree-Fock value 1.363eV [ 17 1. Only a substantial account of the electronic correlation brings [ 18,191 the calculated values close to the experimental value [20] of 3.399(9) eV. For the silicon atom the ASCF approach affords a more reliable value of 0.95-0.97 eV [ 211 versus the experimental value of 1.385 eV [20]. The EAs of F and Si are 2.79, 3.16, 3.45 eV and 1.11, 1.12, 1.18 eV on the HFS, LSDA and LSDA/ NL levels of the theory, respectively, with the use of the basis set indicated above. Thus, it may be concluded that the LSDA/NL approach accounts for much of the electronic correlation, and results obtained on this level are usually close to those on the Cl-SD level.
3. Results and discussion Optimized bond lengths are 1.633, 1.661 and 1.699 A for the octahedra1 configurations of SiF,, SiF; and SiF:- , respectively. The experimental bond length of SiFi- is known [ 71 to be equal to 1.706 A in the FeSiF,.6H,O salt. This value is quite close to that computed for the isolated dianion. Using the results of preliminary calculations [ 51 on the constituents, we are able to calculate the dissociation energies through the different channels. The values obtained as the total energy differences (i.e. without zero-point energy and basis-set-superposition-error corrections) of a species and its corresponding conslituents are displayed in table 1. It is seen that both SiF6 and SiFg- are unstable towards dissociation through the channels SiF6+SiF,t F, and SiFi- +SiF, +F-, respectively. At the same time, the anion SiF; is quite stable, by 0.87 eV 306
27 September I99 I
CHEMICAL PHYSICS LE-lTERS
Table 1 Dissociation energies (in eV) through the lowest channels of SiF,, SiF;, and SiFi-
Channel
LSDA
LSDA/NL
SiF&iF,+F, -&iF$tF +SiF,tF?
-1.08 I .22 5.86
-1.99 0.32 4.38
1.74
SiF; +SiF; tF +SiF,+Fy +SiF, + F+SiF; t F, SiFi-+SiF, t F-SIFT t Fy 4 SIFT t F,
2.8 1 4.61 6.02 -
1.24 3.48 5.57
0.87 1.42 3.91 5.02 -1.90 2.07 4.07
(20.06 kcal/mol ) on the LSDA/NL level. On the LSD.4 level, the stability is even higher, but it is known [22] that this approximation tends often to some overestimation (within w 1 eV) of the dissociation energies, and the LSDA/NL level affords the more reliable values. Thus, the SiF,- anion presents a stable species which has no stable neutral precursor. The ground state of the anion is ‘T,, and it may suffer Jahn-Teller distortions. However, the isoelectronic PF6 possesses the octahedral ground-state configuration [23]. Reduction in symmetry Oh-‘DZh leads to creation of the degenerate states ‘Bng,n= I3, which are placed ~0.2 eV above the octahedral ‘T,, state. Formal valency of the central atom in SiF; is the same as in SiFS, and both species possess one ligand hole. The more stable character of the anion may be related to properties of the ligand frame [ 241. The F6 frame allows for more delocalization of the hole than the FS. The second reason appears to be related to the screening effect influencing the ligand hole by the delocalized external electron of SiF; . Let us consider the vertical and adiabatic EAs of SiF, and SiF;! calculated as differences in total energies of their initial and final states in the octahedral geometrical configurations. By definition,
EA,,,=E,,,(M,R,)-E,,,(M-,R,) ,
(1)
EA,,=E,,,(M,R,)-E,,,(M-,R,),
(2)
where R, and R; stand for the equilibrium geometries of a neutral system M and its anion M-, re-
CHEMICAL PHYSICS LETTERS
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27 September 1991
Table 2 Adiabatic a1 and vertical EAs (in eV) of SiFS, SiF, and SiF; Property
Approach
SiFS
SiF6
SiF;
diff
limit
diff
limit
EA.*
LSDA
6.09
6.84
5.53
0.18
1.42
EA,
LSDA/NL LSDA
6.49
7.04
5.14
0.6s
2.58
EL,,
5.82
6.81
0.18
a) “diff” denotes values obtained according to eq. (2), and “limit” stands for those due to eq. (3)) see teat.
spectively. The octahedral configuration of SiF6 is unstable; therefore, let us supplement the EA values calculated for this configuration by the subscript “diff”. Table 2 presents these values together with data for SiFs given for comparison. It is seen that octahedral (metastable) SiF6 is the superhalogen whose AEad(diff ) exceeds that of SiFs by z 0.5 eV, i.e. by a value which is roughly equal to the difference in the dissociation energies of SiFs and SiF;. The vertical EA of SiF, is close to its EAad( diff ) due to the small change in bond lengths occurring after the attachment of an extra electron. The first ionization potential of SiF; is also close to EAad(diff ), confirming the superhalogen [4] nature of the neutral SiF,(O,). The adiabatic EA by definition is the difference between total energies of the most stable states of the neutral and its anion. Because of the dissociative character of the neutral, we need to change eq. (2) as follows: EA,d =R,,,(M, R,) -&,(M-,
R, )+Do(M)
2 (3)
where M stands for SiF6, R, refers to its equilibrium octahedral structure, and Do is the negative dissociation energy through the lowest channel. Using eq. (3), one may estimate EA, of SiF6 as 5.53 and 5.05 eV on the LSDA and LSDA/NL levels of theory, respectively. These values are presented in table 2 in the columns designated as “limit”. Let us turn to results of calculations on the dianion. According to data presented in table 2, it is stable to the loss of an electron, which is in line with our theoretical estimations [ 241 of the value of the second EA for the six-membered fluorine frames. On
the other hand, this dianion is unstable towards dissociation to the highly stable anion SiF; and F-. The same situation has been met earlier for the dianion BeFi- where a barrier to the dianion dissociation was found [ 25 1, thus confirming the existence of its metastable state. Because of the close resemblance of both systems, the same conclusion seems to be valid for SiFi- , and the octahedral configuration of this dianion appears to have an appreciable lifetime of the vibrational levels as well. Strictly speaking, the same arguments may be applied when estimating EAad of SiF; as those used in the case of its neutral precursor. In order to obtain the value of EA,,, we should account for the dissociative character of the dianion and make the corresponding changes in eq. (3) i.e. E&,=&(M-,R,) -E,,,(M’-,R:-)-Do(M2-),
(4)
where again R, refers to the octahedral contigurations. Combining data of both tables, one obtains quite a large value for the EAadof SiF; , namely, 1.42 and even 2.58 eV on the LSDA and LSDA/NL levels of theory, respectively. Other examples of doubly charged anions have been considered among the hexafluorides of transition metals both theoretically [ 261 and experimentally [ 27 1, and it was found that the corresponding neutral systems should possess a second positive EA. However, the problem of stability to dissociation of these dianions has not been investigated.
4. Conclusions According to results of calculations within the density functional method, the SiF; anion is stable 307
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towards dissociation, whereas its neutral precursor appears to be unstable. The existence of SiF; may be related to the existence of the weakly stable SiF, because both these hypervalent systems possess one ligand hole. The more stable character of the SiF; anion seems to be related to delocalization of the hole over the larger number of ligand atoms, and some screening effect influencing the hole from the external delocalized electron. The neutral SiF6 may be attributed to superhalogens because its estimated EAad exceeds 5 eV. Due to the unstable character of the neutral precursor, the first ionization potential of SiF; is much higher than EAad, indicating the quasi-superhalogen character of this species. The SF; anion presents an interesting system which dissociates after attachment or detachment of an electron. The SiFg- dianion is shown to be unstable towards dissociation, though it is stable to the loss of an electron in its metastable octahedral state. Thus, the neutral SiF6 molecule possesses a positive second EA with respect to this metastable state. The second EA, of SiF6 is quite large, 2.58 eV on the LSDA/ NL level of theory, and refers to the difference between total energies of the stable anion and products of the dianion dissociation.
Acknowledgement This investigation was supported by the National Science and Engineering Research Council of Canada (NSERC ), whose grant for the international collaboration is gratefully acknowledged. I am very appreciative of the University of Calgary for the generous gift of computer time and the access to their Cyber-205 facilities. Special thanks are due to Professor Tom Ziegler for hospitality as well as to Dr. V. Tschinke and Dr. L. Fan for assistance. The reception of results of calculations on the dianion BeFi- prior to publication from Professor A.I. Boldyrev is gratefully acknowledged. I would like to express my gratitude to the referee for his remarks,
308
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References
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