ON THE ELECTRON AFFINITIES OF PERFLUOROALKANES: A SYSTEMATIC DENSITY FUNCTIONAL STUDY by ANKAN PAUL (Under the Direction of Henry F. Schaefer) ABSTRACT The electron affinities of several perfluorolalkane (PFA) molecules have been investigated employing hybrid and pure density functional methods. The optimum structures of the neutral PFAs and their corresponding radical anions have been predicted employing pure and hybrid density functionals in conjunction with a double zeta basis set augmented with polarization and diffuse functions (DZP++). Electron affinities, structural features of neutrals and anions of (a) linear chain PFAs (n-PFAs) and branched chain PFAs with tertiary C-F bonds, (b) mono-cyclic PFAs (c-PFAs) and CF 3 - substituted c-PFAs, and (c) perfluoro-bicyclo[n, n, 0]alkanes (n,n,-BCPFAS), have been explored. Adiabatic electron affinity (AEA) trends for n- PFAs (general formula, n-C n F 2n+2 , with “n” corresponding to the carbon chain length) reveal that AEAs show a drastic enhancement moving from n=2 to n=3, beyond that they exhibit a slow increase with increments falling of steadily with extending chain length, terminating at n=7. The radical anions of n-PFAs show a characteristic structural feature, an exceptionally long C-F bond in the middle carbon of the chain. Branched PFAs with a tertiary C-F bond are found to possess higher AEA than the linear chain PFAs. Mono-cyclic PFAs (general formula of c-PFA, c-C n F 2n ,
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ON THE ELECTRON AFFINITIES OF PERFLUOROALKANES: A SYSTEMATIC
DENSITY FUNCTIONAL STUDY
by
ANKAN PAUL
(Under the Direction of Henry F. Schaefer)
ABSTRACT
The electron affinities of several perfluorolalkane (PFA) molecules have been
investigated employing hybrid and pure density functional methods. The optimum structures of
the neutral PFAs and their corresponding radical anions have been predicted employing pure and
hybrid density functionals in conjunction with a double zeta basis set augmented with
polarization and diffuse functions (DZP++). Electron affinities, structural features of neutrals and
anions of (a) linear chain PFAs (n-PFAs) and branched chain PFAs with tertiary C-F bonds, (b)
mono-cyclic PFAs (c-PFAs) and CF3- substituted c-PFAs, and (c) perfluoro-bicyclo[n, n,
0]alkanes (n,n,-BCPFAS), have been explored. Adiabatic electron affinity (AEA) trends for n-
PFAs (general formula, n-CnF2n+2, with “n” corresponding to the carbon chain length) reveal that
AEAs show a drastic enhancement moving from n=2 to n=3, beyond that they exhibit a slow
increase with increments falling of steadily with extending chain length, terminating at n=7. The
radical anions of n-PFAs show a characteristic structural feature, an exceptionally long C-F bond
in the middle carbon of the chain. Branched PFAs with a tertiary C-F bond are found to possess
higher AEA than the linear chain PFAs. Mono-cyclic PFAs (general formula of c-PFA, c-CnF2n,
and “n” corresponds to the carbon ring size) exhibit a peculiar trend of AEAs with increasing
ring size. The AEAs of c-CnF2n increase from n=3 to n=5 but then dramatically fall off for both
n=6 and n=7. It was noted that there is a change in the mode of binding the “extra electron”
beyond the 5-memebred ring. CF3- substituted c-PFAs display enhanced adiabatic electron
affinity due to the presence of tertiary C-F bonds. Adiabatic and vertical electron affinities were
computed for perfluoro-bicyclo[n, n, 0]alkanes, with “n” ranging from 1 to 4. All the n.n-
BCPFAs have tertiary C-F bonds. However, the mode of binding the “unpaired electron”
changes significantly over the different ring sizes for these bicyclic radical anions. The highly
strained 1, 1-BCPFA is predicted to have the highest AEA among the family of BCPFA
molecules that were examined.
INDEX WORDS: Perfluoroalkanes, Tertiary C-F bonds, Density Functional Theory,
Electron Affinity, and Spin Density.
ON THE ELECTRON AFFINITIES OF PERFLUOROALKANES: A SYSTEMATIC
DENSITY FUNCTIONAL STUDY
by
ANKAN PAUL
Bachelor of Science, Presidency College, University of Calcutta, India (1998)
Master of Science, Indian Institute of Science, India (2001)
A Thesis Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment
Ts is the kinetic energy of the non-interacting electrons and J[p] is the energy contribution from
coulombic repulsion of the non-interacting electron. The EXC[p] is the exchange-correlation
energy which includes energy corrections for the kinetic energy, energy correction for exchange
and coulombic self-interaction and electron correlation. Reformulating these functionals in terms
of orbitals and applying the variational principal with the constraint of orthonormality of the
orbitals the actual Kohn-Sham equations are obtained. The optimized orbitals are obtained by
self consistently solving the Kohn Sham equations. The Kohn-Sham equations are:
( ) iiieffi rv ϕεϕ =
+∇− 2
21
………………………………………………………………..eq(1.5)
where,
and the energy of the system is given by:
[ ] [ ])()()|'|/)()'((21][ rVrEdrrrrrE extXC
N
ii ρρρρερ ++−−= ∫∑ ………………………..eq(1.6)
where, [ ])()( rVdrVr extext ρρ =∫)
In the energy expression EXC, the exchange-correlation functional is unknown and so different
functionals have been developed to approximate that part.
6
1.3 EXCHANGE-CORRELATION FUNCTIONALS
Different methodologies have been pursued to design a proper exchange-correlation functional
which will provide for the exchange and correlation corrections. The early implementations of
the Kohn-Sham method used functionals, which were developed from electron gas data. The two
popular choices were spin unpolarized (LDF/LDA (Local Density Functional/Approximation)
[9] and spin polarized (LSD {Local Spin Density) where arguments require both α and β electron
densities [10], rather than a total density. Initially the LSDA functional, which treats electron
density locally as a uniform gas in conjunction of a spin polarization parameter, was widely used
to treat chemical problems. This functional employs the 1980 correlation functional of Vosko,
Wilk, and Nusair [11] and the exchange functional of Slater [12]. However, this correlation
functional over-binds the molecules and total energies are in error by up to 10%. Additionally,
correlation energies are overestimated by up to a factor of two. The LSDA functional’s original
form was abandoned, as it was found to over bind molecules. New families of functionals
originated to provide corrections to the LSDA functional. Out of those the most popular ones are:
the Generalized Gradient Approximation (GGA) based functionals and the hybrid functionals.
The GGA functionals employs a non-local component which is a derivative of the density.
Among the most popular GGA functionals is the “B” exchange functional [13] developed by
Becke. They are usually used in conjunction of the correlation functionals “LYP” and “P86” [14,
15]. The hybrid exchange functionals use a mixture of pure exchange with Hartree-Fock
exchange. The most commonly used exchange functionals are “B3” and “BH” [16, 17], both
developed by Becke. The B3 and BH hybrid functionals are widely used in conjunction with the
“LYP” correlation functionals, and usually known in scientific literature as the “B3LYP” and
“BHLYP” functionals. Throughout this thesis we have used both pure and hybrid functionals,
7
B3LYP, BLYP, and BP86. In particular cases we have also hybrid functionals like BHLYP and
KMLYP [18].
1.4 OVERVIEW OF CHAPTERS
Chapter 2 explores electron affinity trends in linear chain perfluoroalkanes (general
formula n-CnF2n+2) with increasing chain length. Linear chain Perfluoroalkanes (PFAs) are
known to bind electrons. Through the application of density functional theory, the unique
structural changes which are witnessed on electron attachment for linear PFA skeletons were
studied. Interestingly it was discovered that the “extra electron” in the PFA radical anions was
primarily localized in an elongated antibonding σ* orbital of the C-F bond attached to the central
carbon of the chain. Spin density plots revealed the extent of localization of the unpaired electron
in the radical anion. All the radical anions studied have a striking common structural feature, the
presence of a remarkably long C-F bond associated with the middle carbon of the chain. The
adiabatic electron affinities of all the linear chain PFAs are predicted to be positive (except for n-
C2F6 at KMLYP/DZP++ and BHLYP/DZP++). The electron affinities range from 0.23 eV to
0.70 eV at the B3LYP/DZP++ level of theory for linear chain PFAs for carbon chain length
ranging from 2 to 8. The AEAs increased from with increasing chain length from n=2 to n=7 and
then a slight decrease was observed for n=7 to n=8. We observe that there is a substantial surge
in AEA as we move from chain length n=2 to n=3 and then the increment in AEA falls with
increasing chain length. The particular trend of AEA is observed with increasing chain length of
the linear chain PFA is with the increase in -CF2 units in the chain the no. of negative inductive
effect exerting groups increase, hence conferring stability to the radical anion and at longer chain
length the inductive effect of distant –CF2 units are weak, so increase in AEA stops beyond a
certain chain length. The branched PFAs with tertiary C-F bonds have much higher AEA than
8
their linear chain counterparts. The i-C4F10 has an AEA of 1.23 eV as compared to the 0.45 eV of
n-C4F10. The i-C4F10 radical anion is stabilized by negative hyperconjugation and inductive
effect.
Chapter 3 is a report on the investigation of electron affinity trends in mono-cyclic PFAs
(general chemical formula, c-CnF2n) with increasing ring size. The adiabatic electron affinities,
the vertical electron affinities and vertical detachement energies have been computed for 2 to 7
membered PFA rings. A DFT study revealed that the structural changes which are observed on
electron attachment to c-PFAs vary over the different ring sizes. The 3- , 4- and 5- membered
PFA rings form a delocalized radical anion whereas the 6- and 7- membered rings form radical
anions which are more localized in nature. The 3- , 4- and 5- membered radical anions have
planar to near planar structures where the “unpaired electron” is delocalized over the molecular
plane through overlap of the C-F σ* orbitals. However, the 6- and 7- membered ring PFA radical
anions prefer puckered structural forms and the “unpaired electron” is localized in an
exceptionally long C-F bond. The AEA trends reveal that the AEAs of the mono-cyclic PFAs
increase with increasing ring size ranging from to 3- to 5- membered rings and beyond that a
dramatic drop in AEA was observed for the 6- and 7- membered rings. Ring strain and
planarization energy of these PFA rings have been implicated to explain the observed AEA
trends. The zero-point corrected AEA ranges from 0.4 eV to 1.0 eV at the B3LYP/DZP++ level
of theory for the c-PFAs. CF3- substitution of these cyclic PFAs leads to substantial increase in
AEAs. Generally it was observed that the presence of tertiary C-F bonds enhances the electron
binding ability of a PFA molecule.
Chapter 4 extends the exploration of electron affinities studies to a family of PFAs
which inherently possess tertiary C-F bonds, perfluoro-bicyclo[n, n, 0]alkanes (n,n,-BCPFAs).
9
The adiabatic and vertical electron affinities of n.n.-BCPFAs (for n=2 to n=4) have been
computed using hybrid density functional methods. The structural in these bicyclic rings vary
significantly with varying ring size. The cis isomer of 1,1 BCPFA is the only PFA molecule
which binds an electron in the bridgehead C-C σ*, as compared to the C-F σ* orbital in other
PFAs. All the BCPFAs studied exhibited substantially high AEAs as compared to those of the
previous mono-cyclic and linear PFAs. The zero point corrected AEAs of the BCPFAs range
from 0.9 eV to 2.3 eV at the B3LYP/DZP++ level of theory.
1.5 REFERENCES
[1] Hartree, D. R. Proc. Camb. Phil. Soc.1928, 24, 426.
[2] Slater, J. C. Phys. Rev. 1930, 35, 210.
[3] (a) Fermi, E. Rend. Accad. Lincei 1927, 6, 602. (b) Thomas, L. H. Proc. Camb. Phil. Soc.
1927, 23, 542.
[4] Slater, J. C. Phys. Rev. 1951, 81, 385.
[5] Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864.
[6] Kohn, W.; Sham, L. J. Phys. Rev. 1964, 136, B864.
[7] Rienstra-Kiracofe, C. J.; Tschumper, G.S.; Schaefer, H. F. Chem. Rev. 2002, 102, 231.
[8] Richardson, N. A.; Weselowski, S. S.; Schaefer, H. F. J. Am. Chem. Soc. 2002, 124, 10163.
[9] Dirac, P. A. M. Proc. Cambridge Philos. Soc. 1930, 26, 376. [10] Von Weiszäcker, C. F. Z. Phys. 1935, 96, 431. [11] Vosko, S. J.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. [12] Slater, J. C. Quantum Theory of Molecules and Solids: The Self-Consistent Field for
Molecules and Solids, Vol. IV. McGraw-Hill: New York, 1974.
[13] Becke, A. D. Phys. Rev. A. 1988, 38, 3098. [14] Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B., 1988, 37, 785.
10
[15] Perdew, J. P. Phys. Rev B, 1986, 33, 8822.
[16] Becke, A. D. J. Chem. Phys., 1993, 98, 5648.
[17] Becke, A. D. J. Chem. Phys., 1993, 98, 1372.
[18] Kang, J. K.; Musgrave, C. B. J. Chem. Phys. 2001, 115, 11040.
CHAPTER 2
DO LINEAR CHAIN PERFLUOROALKANES BIND AN ELECTRON?1
1 Ankan Paul, Chaitanya S. Wannere and Henry F. Schaefer Journal of the Physical Chemistry A 2004, 108, 9428. Reprinted by permission of the American Chemical Society, Copyright 2004.
12
2.1 ABSTRACT
The adiabatic electron affinities (AEAs), vertical electron affinities (VEAs) and vertical
detachment energies (VDEs) of linear chain perfluoroalkanes (PFAs), n-CnF2n+2 (n=2 to 8) are
structures for the longer neutral n-PFAs with C2 symmetry show that the n-PFA backbone is
helical in nature, in concordance with previous reports in the literature [53, 54]. Information
about the dihedral angles along the C-C backbones of the n-PFAs is summarized in Table 2.5.
Analysis of the bond lengths shows that the B3LYP method predicts the shortest bond lengths
19
for both C-C and C-F bonds among all the three functionals, whereas BLYP predicts the longest
bonds.
2.4.2. RADICAL ANIONS OF LINEAR CHAIN PFAS
The optimized bond lengths and the corresponding molecular geometries of n-CnF2n+2 (n = 2 to
8) are indicated in Figures 2.1b through 2.7b respectively. The study of the optimized structures
of the molecular anions reveals that drastic changes occur within the molecular framework on
electron attachment. The linear chain PFA anions show a consistent change in geometry
compared to those of their corresponding neutral species. The most conspicuous change occurs
for one of the C-F bonds, namely that located on the central carbon for the odd numbered n-PFA
anion and on one of the central carbons in even numbered n-PFA anions. Molecular geometry
optimization using three different functionals (with subsequent vibrational frequency analysis)
imposing C2v symmetry on CnF2n+2, where n is odd, leads to single large imaginary frequency
which shows distortion towards the asymmetric stretch of the C-F bonds on the central -CF2 unit.
While C3F8 and C7F14 prefer Cs symmetry, C5F12 prefers C1 geometry. Imposing Cs symmetry
on C5F12 followed by geometry optimization and harmonic frequency analysis shows a presence
of very small imaginary frequency at all levels of theory (e.g., 11i cm-1 at B3LYP/DZP++),
which corresponds to torsional twisting of the -CF2 units in the molecular framework. In all the
odd numbered PFA anions significant C-F bond length elongation occurs on one of the two C-F
bonds located in the center of the chain. For example, with B3LYP/DZP++ the C-F bond length
in question in C3F8 is exceptionally long, 2.046 Å (Figure 2.2b), whereas at the same level of
theory C-F bond length in the neutral molecule has a typical value, 1.351 Å. In C5F12 the longest
C-F bond has a length of 2.012 Å and the longest C-F bond in C7F16 measures up to 2.009 Å at
B3LYP/DZP++ level of theory. Moreover, there is C-C bond shortening in the anionic species
20
compared to their neutral analogues for the C-C bonds, which are associated with the central
carbon in the chain. The C-C bond distances associated with the central carbon in C3F8 are
about 1.484 Å at the B3LYP/DZP++ level, whereas in the neutral C3F8 the same C-C bond has
slightly longer distance, 1.567 Å. In addition, C-F bonds that are trans to the longest C-F bonds
also are slightly elongated compared to the quasi-syn ones. Similar bond length patterns are also
observed in the other odd numbered n-PFA anions.
The structural features of even numbered n-PFA anions are similar in nature to those of
the odd numbered chains. The optimized structures of all the even numbered n-PFA anions
exhibit an exceptionally long C-F bond, which is located on one of the central carbons in the
chain. n-C2F6 prefers a Cs structure (Figure 2.1b) and the other even numbered n-PFA anions
prefer C1 structures as minima. Analysis of the optimized geometries of n-C4F10 (Figure 2.3b)
at all the three levels of theory reveals the presence of an exceptionally long C-F bond (2.028 Å
at B3LYP/DZP++) on the second carbon from the end of the chain. In the vicinity of the
exceptionally long C-F bond in C4F10 we observe C-C bond shortening and slight elongation of
C-F bond trans to the longest C-F bond, similar to those observed for the odd numbered PFA
anions. All the other even numbered n-PFA anions show similar structural features. The longest
C-F bond in C6F14¯ is associated with the third carbon from the end of the chain and for C8F18
the fourth carbon from the end of the chain holds the longest C-F bond. In C6F14 the longest C-F
bond has a length of 2.006 Å and the longest C-F bond in C8F18 is 2.030 Å long at
B3LYP/DZP++ level of theory. For C4F10 and C6F14
we were able to detect other low- lying
minima possessing C2h symmetry. The C2h minimum for the C4F10 anion lies above the C1
structure by 17 kcal/mol, whereas the C2h minimum for C6F14 is 13 kcal/mol higher in energy
than the C1 minimum (B3LYP/DZP++).
21
The structural changes that occur on attaching an electron to a PFA may be explained
with the help of spin density plots. All the spin density plots for the molecular anions (Figure
2.10) were obtained at the B3LYP /DZP++ level of theory. For all the n-PFA anions the spin
density is mainly associated with their corresponding longest C-F bonds. The elongation of the
C-F bonds is due to the addition of an extra electron to an antibonding C-F σ* orbital. An
increase in the electron density in the C-F σ* orbital leads to a lengthening of the respective C-F
bond. The shortening of the C-C bonds which are associated with the carbon bearing the
exceptionally long C-F bond, and also the observed lengthening of the C-F bonds trans to the
longest C-F bond, can be explained on the basis of a negative hyperconjugation-like
phenomenon. The half filled C-F σ* orbital corresponding to the longest C-F bond in the anions
mentioned above may have substantial overlap with the empty trans C-F σ* orbital. This in
effect leads to negative hyperconjugation-like phenomenon (see Figure 2.11). In Figure 2.11 we
show how the overlap of a half filled C-F σ* orbital with an empty C-F σ* orbital trans to it can
lead to C-F bond lengthening and C-C bond shortening.
2.4.3. ELECTRON AFFINITIES OF LINEAR CHAIN PFAS
Examination of the AEA data in Table 2.1 reveals that the BLYP method rather
consistently predicts the highest EAs for all the species, while B3LYP estimates for the AEAs
are the lowest. The zero-point corrected AEAs are consistently higher than the corresponding
uncorrected values. This of course reflects the smaller ZPVEs of the anions. The AEA
predictions show a monotonic increase with increasing chain length for n-CnF2n+2, from n=2 to
n=7. C8F18 and C7F16 have similar AEA values. All the linear chain PFAs, with the exception of
C2F6, have positive AEAs. The high pressure electron attachment studies on straight chain n-
PFAs reveal that for n > 2 nondissociative electron attachment occurs [23,24]. C2F6 undergoes
22
only dissociative electron attachment, whereas the other longer chain n-PFAs exhibit both
dissociative and nondissociative electron attachment [24]. Based on electron attachment studies
of C3F8, C4F10, C5F12 and C6F14, Christophorou and co-workers have suggested that these
molecules possess positive electron affinities [23, 24, 26, 29, 30]. Our findings lend an
explanation to their experimental observation. As noted earlier, the extra electron in the n-PFA
anionic species occupies the C-F σ* orbital. The presence of the more negative inductive effect
exerting CF2 groups may lower the energy of the C-F σ* orbital, leading to an increase in AEA.
The extra electron goes to the central carbon C-F bond for odd carbon containing PFA anions.
For even carbon PFA anions, the “last” electron goes to the C-F bond on one of the central
carbons, as those specific carbons have the maximum number of -CF2 groups in their vicinity.
From C2F6 to C7F16 the AEA increases as the number of negative inductive effect exerting –CF2
unit increases. The incremental change in AEA along the series of n-PFA decreases as we move
from n=2 to n=7. This can be rationalized by the understanding that the increase in negative
inductive effect on addition of –CF2 units away from the electron binding center weakens with
the increasing chain length. As one moves from C7F16 to C8F18 we observe that the increase in
the AEA ceases, plausibly pointing to the idea that the further addition of -CF2 groups far away
from the electron binding center has negligible effect.
The VEAs show a similar trend. None of the straight chain PFAs investigated has a
positive VEA. Analysis of the predictions shows that the VEA increases with the chain length of
the PFAs. The VEA results indicate that among the neutral straight chain PFA molecules the
LUMO is high lying. The LUMO energy is lowered with chain length growth due to the increase
in the number of negative-inductive-effect exerting CF2 groups [33]. The observed trend in VEA
is in agreement with the previous experimental reports [24, 33]. Though all three density
23
functionals predict the right trend they consistently overestimate the VEAs compared to the
experimentally reported values [24, 33]. The VEA data reveal that if a linear chain PFA has to
bind an electron adiabatically it has to lower the energy of its LUMO. We observe through
molecular geometry optimization of the molecular anions that drastic changes within the
molecular framework take place upon electron attachment. Bond elongation leads to a lowering
of the energy of the corresponding antibonding σ* orbital, giving rise to a low energy orbital that
can efficiently bind an electron.
The VDEs indicate that all the molecular anionic species considered in this work are
bound with respect to electron loss. Earlier it was demonstrated by King et. al. that C2F6 is
unbound with respect to electron loss [41]. King et. al. based their predictions on a D3d geometry
for the C2F6 anion. In contrast to their results, we have found that a Cs structure is the global
minimum for the C2F6 anion. The Cs minimum is 15 kcal/mol energetically lower than the D3d
minimum at B3LYP/DZP++ level of theory! When the optimized Cs geometry of C2F6 is taken
into consideration for the VDE computations we find that it has a positive VDE, indicating C2F6
may form a bound anion. The high predicted VDEs for the longer chains show that all these
molecular anions can exist.
2.4.4. ELECTRON AFFINITIES OF BRANCHED CHAIN C4F10 AND C5F12
The theoretical AEAs of branched C4F10 (perfluoro-iso-butane, i-C4F10) and C5F12 (perfluoro-iso-
pentane, i-C5F12) are listed in Table 2.4. Branched C4F10 has a much higher AEA than that for the
linear chain n-C4F10 (1.09eV and -0.36eV respectively). This trend persists for the AEAs of the
C5F12 isomers. The optimized anionic i-C4F10 shows a substantial elongation of the tertiary C-F
bond (2.039 Å) (see Fig. 2.9b) as compared to that for the neutral C3 symmetry structure (1.366
Å) (see Fig. 2.9a). The tertiary C-F bond is the longest bond in the molecular anion of branched
24
C4F10. Tertiary C-F bond length elongation is also observed in i-C5F12. This prediction lends
support to the generally accepted mechanism of defluorination of perfluorodecalin by reducing
agents like Na in organic media, where it is believed that a molecular anion is formed, followed
by cleavage of the tertiary C-F bond [35, 36]. Christophorou and co-workers reported the
formation of a stable parent anion species on electron attachment to i-C4F10 [23]. Our predicted
geometry for i-C4F10 is a plausible molecular structure for the parent anion species formed on
electron attachment to i-C4F10. The lengthening of the tertiary C-F bond in the molecular anion
of i-C4F10 also indicates that a defluorination step will involve cleaving of the exceptionally long
tertiary C-F bond in the subsequent step [35, 36]. In branched C5F12 there is one C-F tertiary
bond along with secondary and primary C-F bonds. In the optimized molecular geometry of the
anion at B3LYP/DZP++ again we encounter an exceptionally long tertiary C-F bond. This
indicates that the extra electron prefers to go to the tertiary C-F bond. The spin density plots (see
Fig. 2.10) for the branched anions reveal that the extra electron is accommodated in their tertiary
C-F σ* orbitals. The enhanced AEA of PFA with tertiary C-F bonds may be explained on the
basis of the tertiary C-F bonds having the maximum number of negative hyperconjugative-effect
exerting C-F bonds trans to it. Through the negative hyperconjugative effect the empty C-F σ*
orbitals trans to the longest C-F bond help to delocalize the extra charge through σ*- σ*
interactions between the C-F bonds, as demonstrated earlier. The geometric changes in moving
from the branched neutrals to the branched anions show the same structural effects as expected
from negative hyperconjugation; the shortening of the C-C bond associated with elongated C-F
bond bearing carbon and the lengthening of the C-F bonds which are trans in orientation to the
elongated C-F bonds.
25
2.5 CONCLUDING REMARKS
Through this work we have shown that the straight chains PFAs (with the exception of
C2F6) have substantial adiabatic electron affinities. In addition, the VEA predictions reveal that
none of the straight chain PFAs possesses a positive VEA. Moreover, the VEA increases with
extension of the chain length of a PFA. Analysis of the VDE data shows that all the straight
chain molecular anions considered in this research are bound with respect to electron loss. The
C2F6 anion, which was thought to possess a negative VDE [41], has a more energetically
favorable Cs minimum which possesses a positive VDE. Spin density studies of the anions
convincingly establish that the n-PFAs bind the extra electron in a C-F σ* antibonding orbital. It
was also observed that branched PFAs possessing tertiary C-F bonds have much higher AEAs
compared to those of their straight chain analogues indicating that branched chain molecules can
be better candidates for electron attachment studies.
ACKNOWLEDGEMENTS
Ankan Paul would like to thank Dr. Alexey Timoshkin and Mr. Lubos Horny for their insightful
comments and discussions. This research was supported by National Science Foundation under
Grant CHE-0136184.
2.6 REFERENCES:
[1] Slinn, D. S. L.; Green, S. W. In Preparation, Properties and Industrial Applications of
Organofluorine Compounds; Banks, R. E, Ed.; Ellis Horwood: Chichester, 1982; p 45.
[2] Green, S. W.; Slinn, D. S. L.; Simpson, R. N. F.; Woytek, A. J. in Organofluorine Chemistry,
Principles and Commercial Applications; Banks, R. E., Smart, B. E.; Tatlow, J. C., Eds;
Plenum: New York, 1994; p 89.
[3] Barthel-Rosa, L. P.; Gladysz, J. A. Coord. Chem. Rev. 1999, 190-192, 587.
26
[4] Kajdas, C.; Industrial Lubricants. In Chemistry and Technology of Lubricants; Mortier, R.
M.; Orszulik, S. T.; Ed.; VCH Publishers, Inc.; New York, 1992.
[5] Eastoe, J.; Bayazit, Z.; Martel, S.; Steytler, D. C.; Heenan, R. K. Langmuir 1996, 12, 1423.
[6] Ogino. K.; Abe, M. Mixed Surfactant Systems; M. Dekker, Inc.; New York, 1993.
[7] Eger, E. I; Jonescu, P.; Laster, M. J.; Gong, D.; Hudlicky, T.; Kending, J. J.; Harris, A.;
Trudell, J. R.; Pohorille, A. Anesth. Analg. 1999, 88, 867.
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29
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Table 2.1. Adiabatic electron affinities of linear chain CnF2n+2 in eV (n = 3 to 8). Zero point corrected EAs are shown in parentheses.
Molecules
B3LYP
BLYP
BP86
C2F6
-0.52
(-0.37)
-0.33
(-0.19)
-0.43
(-0.29)
C3F8
0.26
(0.39)
0.43
(0.56)
0.35
(0.48)
C4F10
0.40
(0.53)
0.57
(0.70)
0.50
(0.63)
C5F12
0.50
(0.65)
0.68
(0.83)
0.60
(0.74)
C6F14
0.56
(0.69)
0.73
(0.87)
0.67
(0.81)
C7F16
0.58
(0.71)
0.75
(0.89)
0.69
(0.83)
C8F18
0.52
(0.66)
0.71
(0.85)
0.64
(0.78)
30
Table 2.2. Vertical electron affinities of linear chain CnF2n+2 in eV (n = 2 to 8).
a. Hunter, S. R.; Christophorou, L. G.; J. Chem. Phys. 1984, 80, 6150. b. Ishii, I.; McLaren, R.; Hitchcock, A. P.; Jordan, K. D.; Choi, Y.; Robin, M. B. Can. J. Chem. 1988, 66, 2104.
Molecules
B3LYP
BLYP
BP86
Expt.1
A
Expt.2
B
C2F6
-1.17
-1.16
-1.05
-4.6
C3F8
-1.03
-0.96
-0.96
-2.55
-3.34
C4F10
-0.92
-0.77
-0.78
-1.95
-2.37
C5F12
-0.85
-0.60
-0.61
-1.55
-1.64
C6F14
-0.63
-0.36
-0.36
-1.20
-1.20
C7F16
-0.53
-0.19
-0.20
-
-
C8F18
-0.36
-0.07
-0.06
-
-
31
. Table 2.3. Vertical detachment energies of linear chain CnF2n+2 in eV (n = 2 to 8).
Table 2.4. Comparison of AEA of branched chain PFAs to those of their straight chain analogues. Zero point corrected EAs are shown in parentheses.
Method
Branched-C4F10
n-C4F10
Branched-C5F12
n-C5F12
B3LYP/DZP++
1.11 eV
(1.23 eV)
0.40 eV (0.53 eV)
1.21 eV
(1.33 eV)
0.50 eV (0.65)
Molecules
B3LYP
BLYP
BP86
C2F6
3.08
2.81
2.68
C3F8
3.41
3.31
3.16
C4F10
3.43
3.24
3.16
C5F12
3.50
3.31
3.23
C6F14
3.51
3.31
3.21
C7F16
3.55
3.33
3.23
C8F18
3.65
3.42
3.32
32
Table 2.5. Dihedral angles along the carbon backbone of n-PFAs for n=4 to 8. (The carbons are numbered from one end of the chain)
1b Figure 2.1. Optimized molecular geometries of: (a) Neutral n-C2F6 (D3d symmetry), (b) Anionic n-C2F6 (Cs symmetry). All bond lengths reported are in Angstroms.
34
B3LYP 1.484BLYP 1.490BP 86 1.487
2.0462.0732.031
1.3651.3821.374
1.3521.3721.366
1.4011.4361.426
1.3481.3681.361
1.351 1.369
1.363
B3LYP 1.567BLYP 1.584BP86 1.577
1.339 1.358
1.352
1.339 1.358
1.351
2a
2b Figure 2.2. Optimized molecular geometries of: (a) Neutral n-C3F8 (C2v symmetry), (b) Anionic n-C3F8 (Cs symmetry). All bond lengths reported are in Angstroms
35
B3LYP 1.341 BLYP 1.364BP86 1.355
1.4891.4991.494 1.483
1.4941.491
2.0282.0401.998
1.3631.3811.373
1.3501.3691.363
1.3481.3671.361
1.4001.4281.419
1.4111.4661.448
1.3331.3531.347
1.5711.5831.577
1.3621.3781.374
1.3661.3851.380
3a
3b
Figure 2.3. Optimized molecular geometries of: (a) Neutral n-C4F10 (C2 symmetry), (b) Anionic n-C4F10 (C1 symmetry). All bond lengths reported are in Angstroms.
1.352 1.369 1.362
1.570 1.586
1.588
1.570 1.588
1.581
1.337 1.359 1.352
1.337 1.359
1.352
B3LYP 1.339BLYP 1.359BP86 1.352
36
1.340 1.359 1.353
B3LYP 1.339BLYP 1.358BP86 1.352
1.573 1.591 1.583
1.337 1.356
1.349 1.352 1.371
1.364
1.349 1.368
1.361
1.352 1.371 1.364
1.571 1.589
1.582
1.340 1.361 1.353
B3LYP 1.366BLYP 1.387BP86 1.381
1.572 1.587 1.580
1.404 1.442 1.430
1.362 1.380 1.373
1.419 1.461 1.448
1.362 1.382 1.377
1.567 1.581 1.574
1.481 1.487 1.482
1.332 1.352 1.346
1.487 1.494 1.491 1.364
1.3811.374
2.012 2.022 1.976
1.350 1.370
1.363
1.332 1.352 1.342
1.358 1.378
1.371
4a
4b
Figure 2.4. Optimized molecular geometries of: (a) Neutral n-C5F12 (C2v symmetry), (b) Anionic n-C5F12 (C1 symmetry). All bond lengths reported are in Angstroms.
37
1.349 1.368
1.361
1.576 1.594
1.586
1.351 1.370
1.363
1.340 1.359 1.353
B3LYP 1.571BLYP 1.589BP86 1.582
1.352 1.371
1.364
1.351 1.371 1.363 1.337
1.356 1.349
1.339 1.358
1.352
1.574 1.592
1.584
5a
5b Figure 2.5. Optimized molecular geometries of: (a) Neutral n-C6F14 (C2 symmetry), (b) Anionic n-C6F14 (C1 symmetry). All bond lengths reported are in Angstroms.
B3LYP 1.350BLYP 1.367BP86 1.363
1.3321.3521.346
1.3571.3781.370
1.5671.5821.574
1.4831.4901.486
1.4841.4901.486
1.5781.5941.586
1.4181.4571.444
1.4131.4531.442
2.0062.0111.964
1.3631.3801.373
1.3481.3691.362
1.3511.3611.374
1.5741.5921.584
1.3531.3751.368
1.3451.3641.357
1.3421.3611.354
1.3601.3781.371
1.3611.3811.376
38
1.363 1.378
1.372 2.009 2.008 1.963
1.348 1.369
1.363
1.583 1.597
1.590
1.357 1.375
1.368
1.484 1.491
1.487
1.417 1.459
1.4471.574 1.592
1.585
1.345 1.363 1.357
1.3421.361
1.358
1.353 1.375
1.368
B3LYP 1.351BLYP 1.371BP86 1.363
6a
6b Figure 2.6. Optimized molecular geometries of: (a) Neutral n-C7F16 (C2v symmetry), (b) Anionic n-C7F16 (Cs symmetry). All bond lengths reported are in Angstroms.
1.349 1.368 1.361
1.577 1.595 1.587
1.351 1.370
1.363B3LYP 1.352BLYP 1.371BP86 1.364
1.574 1.592
1.584
1.339 1.358 1.352
1.340 1.359
1.353 1.571 1.589
1.582 1.351 1.370
1.363
1.351 1.370 1.363
1.337 1.356
1.349
39
2.030 2.032 1.983
1.367 1.382 1.375
1.482 1.489
1.485
1.341 1.361
1.355
1.367 1.387
1.378
1.340 1.359
1.353
1.571 1.589
1.582
1.355 1.373
1.366
1.350 1.370
1.363
1.341 1.370
1.363
1.352 1.372
1.378
1.579 1.594
1.586
1.413 1.452
1.4411.355 1.373
1.366 1.4821.489
1.485
1.418 1.459
1.446
1.343 1.361
1.354
1.577 1.591
1.583
1.364 1.384
1.377 1.342 1.363 1.356
B3LYP 1.353BLYP 1.374BP86 1.367
1.339 1.359 1.352
1.571 1.589
1.582
7a
7b Figure 2.7. Optimized molecular geometries of: (a) Neutral n-C8F18 (C2 symmetry), (b) Anionic n-C8F18 (C1 symmetry). All bond lengths reported are in Angstrom
1.351 1.370 1.363
1.352 1.371 1.364
1.574 1.592
1.584 1.577
1.596 1.588
1.351 1.370 1.363
1.577 1.595
1.584
1.339 1.357 1.364
1.352 1.371
1.364
1.351 1.374
1.363
1.349 1.368 1.361
B3LYP 1.337BLYP 1.356BP86 1.349
1.340 1.359 1.353
40
1.572
1.341
1.340
1.366
1.337
8a
8b
Figure 2.8. Optimized molecular geometries at the B3LYP/DZP++ level of theory: (a) Neutral branched C4F10 (C1 symmetry), (b) Anionic branched C4F10 (C1 symmetry). All bond lengths reported are in Angstroms.
2.039
1.349
1.495
1.354
1.390
41
1.3661.352
1.5791.582
1.573
1.338
1.341
1.338
1.3401.339
1.339
1.353
1.5731.338
1.338
1.339
9a
9b Figure 2.9. Optimized molecular geometries at the B3LYP/DZP++ level of theory: (a) Neutral branched C5F12 (C1 symmetry), (b) Anionic branched C5F12 (C1 symmetry). All bond lengths reported are in Angstroms.
2.034
1.352
1.349
1.387
1.5041.496
1.497
1.352
1.387
1.351
1.364
1.408
1.570
1.332
1.357
1.348
42
(a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 2.10. Spin density plots for molecular anions at B3LYP/DZP++, (a) n-C2F6
Electron density moved into C-F σ∗ orbital increases the C-F bond length
Overlap shortens the C-C bond
Filled orbital on carbanion center
Partly filled C-F σ∗ orbital corresponding tothe longest C-F bond in the PFA radical anion
Electron density moved into the C-F σ∗ orbital increases the anti-periplanar C-F bond length
Overlap shortens the C-C bond
(a) Negative hyperconjugation in the carbanion
(b) Interaction of the partly filled C-F σ∗ orbital of PFA radical anion with anti-periplanar C-F σ∗ orbital
Figure 2.11. Comparison between (a) negative hyperconjugation in carbanions and (b) the interaction of the partly-filled C-F σ* radical anion SOMO with empty anti-periplanar C-F σ* orbital.
CHAPTER 3
THE PECULIAR TREND OF MONOCYCLIC PERFLUOROALKANE ELECTRON
AFFINITIES WITH INCREASING RING SIZE1
1 Ankan Paul, Chaitanya S. Wannere, Paul V. R. Schleyer and Henry F. Schaefer submitted to Journal of the American Chemical Society, 12/09/2005.
45
3.1 ABSTRACT
The adiabatic electron affinities (AEAs), vertical electron affinities (VEAs) and vertical
detachment energies (VDEs) of cyclic perfluoroalkanes, c-CnF2n (n = 3 to 7), and their
monotrifluoromethyl derivatives were computed using various pure and hybrid density
functionals with DZP++ (polarization and diffuse function augmented double-ζ) basis sets. The
theoretical AEA of c-C4F8 at KMLYP/DZP++, 0.70 eV, agrees with the 0.63 ± 0.05 eV
experimental value. c-C3F6(-), c-C4F8(-), and c-C5F10(-) are unusual in preferring planar ring
structures with Dnh symmetries. The ZPE corrected AEAs of c-CnF2n increase from n=3 (0.24
eV) to n=5 (0.77 eV) but then dramatically fall off to 0.40 eV for both n=6 and n=7. All the other
functionals predict the same trend. This is due to a change in the structural preference: Cs c-
C6F12(-) and C1 c-C7F14(-) are predicted to favor non-planar rings, each with an exceptionally
long C-F bond. (There also is a second, higher energy D3d minimum for C6F12(-).) The SOMOs
as well as the spin density plots of the c-PFA radical anions reveal that he “extra” electron is
largely localized on the unique Fs in the larger n=6 and n=7 rings, but is delocalized in the
multiatom SOMO’s of the 3 to 5 membered ring radical anions. The computed AEAs are much
larger than the corresponding VEAs; the latter are not consistent with different functionals. The
AEAs are substantially larger when a c-CnF2n fluorine is replaced by a –CF3 group. This behavior
is general: PFAs with tertiary C-F bonds have large AEAs. The VDEs for all the anions are
substantial, ranging from 1.89 eV to 3.64 eV at the KMLYP/DZP++ level.
3.2 INTRODUCTION
The exceptional properties of perfluoroalkanes (PFAs) not only elicit scientific interest, but also
have led to multifarious industrial applications [1, 2]. The attributes of chemical inertness,
extreme hydrophobicity, thermal stability, low viscosity, and low dielectric constant make PFAs
excellent candidates for lubricants, sealants, surfactants, oxygen carriers, anesthetics, and inert
46
solvents [3-9]. The unusual solubility trend of PFAs has led to the emergence of a new field
called “fluorous biphase chemistry” [10]. The concern of the present theoretical paper, the strong
electron attaching properties of the PFAs, has also been exploited in tracer studies in atmospheric
dispersion investigations [11]. The remarkable chemical inertness of PFAs arises from the
unusually strong C-F bonds. Their chemical passivity has earned them the reputation of
“immortal molecules” [12]. The notion of immortality is further corroborated by their unusually
long lifetimes in the atmosphere. Given the fact that these molecules possess the notorious
attributes of global warming potential, their long lifetimes could be of great concern [13].
Recently Morris et. al. have shown that electron attachment can reduce the lifetime of
perfluorocyclobutane in the atmosphere from 3200 years to 1400 years [14].
Chemical reactivity can be induced in PFAs through free electrons and reducing media.
Seminal research by Tatlow and co-workers, as well as by Macnicol and Robertson has shown
that PFAs can be defluorinated by using reducing agents [15, 16]. Macnicol and Robertson used
an organic reductant, sodium benzenethiolate to reduce trans-perfluorodecalin to C10(SPh)10 [16].
Reductive defluorination of PFA proceeds through electron transfer from the electron-rich
reagent to the PFA. Particularly, now it is known that PFAs with tertiary C-F bonds are more
prone to undergo reduction [17]. Tertiary C-F bonds in PFAs have been implicated as the
“Achilles heel”, a potentially fatal feature towards chemical transformation in these unusually
inert molecules [17, 18]. Richmond and co-workers has shown defluorination of
perfluoromonomethylcyclohexane and perfluorodecalin can be achieved using organometallic
nucleophiles at room temperature [17b, 17c]. Crabtree’s group has made also significant
contributions in developing reagents and photosensitization techniques to defluorinate PFAs
using various transition metal containing organometallic reagents [17d-17f]. Reductive
47
defluorination of saturated perfluoroalkanes has led to the emergence of the challenging frontier
of “C-F” bond activation in chemistry [19]. Though there are numerous reports on defluorination
of PFAs possessing tertiary C-F bonds, reactions involving defluorination of PFAs devoid of
tertiary C-F bonds are rare, indicating lower propensity of PFAs without tertiary C-F bonds
towards electron attachment. Richmond and co-workers has developed a Zr based reagent which
defluorinates perfluorocyclohexane, one of the very rare examples of reduction through electron
transfer to a PFA san the tertiary C-F bond [20].
PFAs attach electrons excellently. Extensive experimental electron attachment studies
have demonstrated that both cyclic and acyclic PFAs [21-47] bind low energy electrons and can
have positive electron affinities [22-25, 35-37]. Cyclic PFAs are known to be better electron
scavengers than their acyclic analogues [48]. The electron affinities of PFAs are crucial in
determining their reactivity. Electron attachment to the PFAs in reducing environments forms
radical anions; defluorination through fluoride ion loss follows [15-19].
c-C4F8 (perfluorocyclobutane) has been the most thoroughly investigated cyclic PFA,
both experimentally and theoretically. Electron attachment yields C4F8¯ over a wide range of
electron energies below 200meV [32, 45]. Bound radical anion of c-C4F8 has been generated
with γ-radiation at 130 K in a neopentane matrix and characterized by ESR spectroscopy [49].
Electron spin resonance studies confirm that the radical anion has a cyclic structure [50]. The
experimentally estimated adiabatic electron affinity of c-C4F8 has been controversial. Miller and
co-workers’ 1994 rate constant measurements of electron attachment to c-C4F8 and subsequent
equilibrium constant determination, estimated the adiabatic electron affinity (AEA) to be 0.63 eV
[41]. Later, Hiraoka et. al. deduced a higher value, 1.05 ± 0.05 eV.46 Recently, Miller and co-
workers challenged Hiraoka et. al.’s findings and confirmed that the AEA of c-C4F8 is 0.63 ±
48
0.05 eV [47]. Their G3(MP2) computations gave 0.59 eV. A similar value of 0.64 eV was
suggested by Gallup based on ab initio MP2/6-311G(dps) computations [51].
Our comprehensive recent study of the electron affinities of straight chain n-PFAs
included an assessment of the AEA trend with increasing chain length [52]. The
perfluorocycloalkanes (c-PFAs), c-CnF2n s are known to possess better electron scavenging
properties than that of the straight chain PFAs [48]. Liebman, based on qualitative molecular
orbital arguments, suggested over three decades ago that electron affinities of c-PFAs would be
higher than their straight chain counterparts [48]. The bonding of c-PFAs depends on ring size.
The angle strain is very large in the smaller rings and only diminishes in the larger rings. Hence,
the nature of the C-C and C-F bonds in the small c-PFAs can be different from that of straight
chain PFAs. These considerations encouraged the present computational exploration of the
consequences of electron binding to c-PFAs: the patterns and trends in AEAs with increasing
ring size and the unusual changes in geometries produced by electron attachment. Furthermore,
electron attachment has been implicated as a primary process of removal of
perfluorocyclobutane, a global warming gas from the atmosphere. Electron affinity trends can
provide insight about the vulnerability of PFAs, the potential global warming agents, to electron
attachment and. hence, are likely to indicate, which of these molecules will have smaller
atmospheric lifetime.
The extensive work on electron attachment of perfluorocarbons has revealed that
perfluoro-monomethyl-cycloalkanes, CF3-c-PFA, with the general molecular formula CF3-c-
CnF2n-1), exhibit excellent electron binding properties [53-63]. Like perfluoro-
monomethylcyclohexane, which has been investigated thoroughly [53-57], CF3-c-PFAs possess
tertiary C-F bonds. Since acyclic PFAs with a tertiary C-F can have high adiabatic electron
49
affinities [52], we investigated the effects of -CF3 substitution on the electron binding properties
of c-PFAs here.
3.3 COMPUTATIONAL METHODS
We computed energies, optimized structures, and harmonic vibrational frequencies using
the GAUSSIAN 94 program [64] and the five generalized gradient approximation (GGA)
exchange correlation functionals, BHLYP B3LYP, BLYP, BP86, and KMLYP, described briefly
below:
B3LYP (as implemented in GAUSSIAN 94) is a hybrid of exact, “Hartree-Fock”
exchange with local and gradient-corrected exchange and correlation terms, as proposed by
Becke [65], but with certain modifications to the correlation part. Instead of using the LSDA [66]
and PW91 [67] functional for local correlation, the B3LYP implementation [68] in GAUSSIAN
94 uses a mixture of LYP [69] and the VWN [70] correlation functional.
BHLYP is another hybrid functional, which combines Becke’s “half-and-half” exchange
functional [71], which is a 50-50 hybrid of exact exchange and local spin density approximation,
and the correlation part is described by the LYP functional.
BLYP uses Becke’s pure exchange functional 72 in conjunction to the LYP functional [68].
BP86 combines Becke’s pure exchange functional [72] with Perdew’s P86 [73, 74]
correlation correction.
KMLYP is a recently formulated hybrid functional [75], which combines the HF
exchange functional (ExH) and the Slater exchange functional (Ex
S). The description of
correlation is provided by a combination of the LYP functional (EcLYP) and the correlation
functional of Vosko, Wilk and Nusair (EcVWN). The KMLYP energy functional may be expressed
as: E = Ek + Eze + Eee + ExS + a(Ex
H - ExS) + b(Ec
LYP - EcVWN) + Ec
VWN
50
Where Ek is Kohn-Sham kinetic energy functional, Eze is the nuclear–electron Coulomb energy
functional, and Eee is the classical electron-electron coulomb repulsion energy functional. The
KMLYP parameters were a = 0.557 and b = 0.448 [75].
All computations employed double-ζ basis sets with polarization and diffuse functions. These
[81] Chang, C. H.; Porter, R. F.; Bauer, S. H. J. Mol. Struct. 1971, 7, 89.
[82] Chen, X.; Lemal, D. M. J. Org. Chem. 2004, 69, 8205.
[83] This conclusion was tested and confirmed by computations on the 1,3,5-tris-equatorial-
perfluorocyclohexane radical anion. The C3v symmetry of its neutral precursor was not
retained, even though this might have permitted delocalization of the extra electron
simultaneously to three axial C–F bonds. Instead, a lower symmetry minimum with only a
single, elongated C–F bond was favored. Moreover, the AEA of perfluoro-1,1-dimethyl-
cyclobutane, which does not have a tertiary C-F bond ( 0.92 eV B3LYP/DZP++ +ZPE ) was
substantially lower than the AEA of CF3-c-C5F11.
69
Table 3.1.Planarization energies (in kcal/mol) computed as the difference between the energy of the c-PFA species in Dnh symmetry and the energy of the same species in its most favorable conformational minimum.
− 48.25 50.60 Table 3.2.Adiabatic electron affinities of cyclic perfluoroalkanes in eV with the DZP++ basis set. Zero-point corrected AEAs are shown in parentheses.
Molecule
KMLYP
B3LYP
BLYP
BP86
BHLYP
c-C3F6 Neutral – D3h Anion- D3h
0.07 (0.24)
0.47 (0.64)
0.69 (0.85)
0.73 (0.89)
-0.12 (0.06)
c-C4F8 Neutral- D2d Anion-D4h
0.52 (0.70)
0.85 (1.04)
1.05 (1.23)
1.13 (1.30)
0.28 (0.47)
c-C5F10 Neutral- Cs Anion-Cs
0.59 (0.77)
0.94 (1.12)
1.17 (1.35)
1.25 (1.42)
0.33 (0.51)
c-C6F12 Neutral- D3d Anion- Cs
0.27 (0.40)
0.68 (0.82)
0.89 (1.04)
0.94 (1.16)
0.19 (0.33)
c-C7F14 Neutral- C2 Anion- C1
0.27 (0.40)
0.64 (0.77)
0.83 (0.98)
0.80 (0.96)
0.18 (0.32)
70
Table 3.3. Comparison of AEAs for cyclic with straight chain PFAs at B3LYP/DZP++. Zero-point energy corrected results are in parentheses.
No. of carbons in the ring
or chain
AEA of c-CnF2n
AEA of n-CnF2n+2
[a]
n=3
0.47
(0.64)
0.26
(0.39)
n=4
0.85
(1.04)
0.40
(0.53)
n=5
0.94
(1.12)
0.50
(0.65)
n=6
0.68
(0.82)
0.56
(0.69)
n=7
0.64
(0.77)
0.58
(0.71) [a] Reference 53.
71
Table 3.4. Adiabatic electron affinities of geometry constrained cyclic perfluoroalkanes in eV. (Zero-point corrections are not included)
Neutral and anion constrained to Dnh
symmetry
B3LYP/DZP++
KMLYP/DZP++
c-C3F6
0.47
0.07
c-C4F8
0.86
0.53
c-C5F10
1.13
0.82
c-C6F12
1.18
0.91
c-C7F14
1.08
0.86
Table 3.5.Vertical electron affinities of cyclic perfluoroalkanes in eV. (Zero-point corrections are not included)
Molecule
KMLYP
B3LYP
BLYP
BP86
BHLYP
c-C3F6 -1.11 -0.71
-1.17
-0.72
-1.33
c-C4F8 -0.80
-0.40 -0.18 -0.25 -0.99
c-C5F10
-0.77 -0.22 0.04 0.08 -1.0
c-C6F12
-0.66 -0.33 -0.01 -0.01 -0.87
c-C7F14
-0.61
-0.30
0.05 0.06
-0.81
72
Table 3.6.Vertical detachment energies of cyclic perfluoroalkanes anions in eV. (Zero-point corrections are not included)
Table 3.7. Adiabatic electron affinities of CF3-monosubstituted PFAs in eV. Zero-point corrected AEAs are shown in parentheses.
6b Figure 3.6. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C3F5 (Cs symmetry), (b) Anionic branched CF3-c-C3F5 (Cs symmetry). All bond lengths reported are in Angstroms.
79
F
F
C
F F
F
C
F
C
C
F
C
F
F
F
B3LYP 1.356KMLYP 1.323
1.3451.311
1.5461.516
1.3431.310
1.3411.308
1.3421.310
1.5841.548
1.5781.545
1.3391.307
1.3431.311
F
F
F
F
CC
C
F
FC
F
F
C
F
F
B3LYP 1.955KMLYP 1.884
1.4861.465
1.3831.342
1.3531.319
1.4911.469
1.5621.535
1.3941.352
1.3571.321
1.3631.327
1.3641.328
7a
7b
Figure 3.7. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C4F7 (Cs symmetry), (b) Anionic branched CF3-c-C4F7 (Cs symmetry). All bond lengths reported are in Angstroms.
80
FF
FF
CC
F
C C
F
F
F
F
CC
F
F
F
B3LYP 1.374KMLYP 1.339
1.3371.304
1.3421.309
1.3411.310
1.3521.319
1.3451.313
1.3431.311
1.5561.523
1.5621.529
1.5791.545
1.5851.553
F
F
F
F
CC
F
F
CCF
F
C
F
C
F
F
F
B3LYP 2.016KMLYP 1.955
1.3591.324
1.4811.463
1.4041.358
1.3831.341
1.3511.318
1.5691.542
1.5721.544
1.3641.331
1.3491.314
1.4881.464
8a
8b Figure 3.8. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C5F9 (Cs symmetry), (b) Anionic branched CF3-c-C5F9 (Cs symmetry). All bond lengths reported are in Angstroms
81
FF
F
F
C
F
C
C
F
C
F
F
F
C
F
F
CC
F
F
F
B3LYP 1.371KMLYP 1.337
1.3501.317
1.3481.315
1.3471.3141.3521.318
1.3531.320
1.3411.315
1.3381.305
1.3401.307
1.5751.540 1.572
1.537
1.5701.535
1.5701.535
FF
FF
FCC
CC
F
F
F
F
C
F
C
FCF
F
F
B3LYP 2.034KMLYP 1.935
1.5161.480
1.5011.471
1.4381.360
1.3811.327
1.4091.344
1.3681.316
1.5811.534
1.5691.522
1.3681.313
1.3851.331
1.3811.325
1.3771.324
9a
9b Figure 3.9. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C6F11 (Cssymmetry), (b) Anionic branched CF3-c-C6F11 (Cs symmetry). All bond lengths reported are in Angstroms.
82
(a) (b) (c) (d)
(e) Figure 3.10. Spin density plots for molecular anions at B3LYP/DZP++, (a) c-C3F6
(b) c-C4F8, (c) c-C5F10, (d) c-C6F12 and (e) c-C7F14 .
83
(a) (b)
(c) (d) Figure 3.12. SOMO plots for molecular anions at B3LYP/DZP++, (a) c-C3F6
(b) c-C4F8, (c) c-C5F10, and (d) c-C6F12.
84
(a) (b)
(c) (d)
Figure 3.12. SOMO plots for molecular anions at B3LYP/DZP++, (a) c-C3F6 (b) c-C4F8, (c) c-
C5F10, and (d) c-C6F12.
85
F
Electron density moved into C-F σ∗ orbital increases the C-F bond length
Overlap shortens the C-C bond
Filled orbital on carbanion center
Partly filled C-F σ∗ orbital corresponding tothe longest C-F bond in the PFA radical anion
Electron density moved into the C-F σ∗ orbital increases the anti-periplanar C-F bond length
Overlap shortens the C-C bond
(a) Negative hyperconjugation in the carbanion
(b) Interaction of the partly filled C-F σ∗ orbital of PFA radical anion with anti-periplanar C-F σ∗ orbital
Figure 3.13. Comparison between (a) negative hyperconjugation in carbanions and (b) the interaction of the partly-filled C-F σ* radical anion SOMO with empty anti-periplanar C-F σ* orbital.
86
Figure 3.14. Plot of computed zero-point corrected AEAs with respect to the ring size of cyclic perfluoroalkanes.
Zero Point Corrected AEAs of Cyclic PFAs
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 2 4 6 8
Number of Carbons in the Ring
AEA
s in
eV B3LYP
KMLYPBHLYPBLYPBP86
87
Figure 3.15. Plot of computed zero-point corrected AEAs with respect to increasing ring size of CF3-c-PFAs.
Zero-Point Corrected AEA Trends with Increasing Ring Size of Perfluoro-monomethyl-cycloalkanes
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 1 2 3 4 5 6 7
Number of Carbons in the Ring
Zero
-poi
nt c
orre
cted
AEA
in e
V
B3LYPKMLYP
CHAPTER 4
HIGH ELECTRON AFFINITIES OF PERFLUOROBICYCLO [N, N, 0] ALKANES1
1 Ankan Paul, Paul V. R. Schleyer and Henry F. Schaefer To be submitted to Journal of Physical Chemistry A
89
4.1 ABSTRACT
The adiabatic electron affinities (AEAs), vertical electron affinities (VEAs) of bicyclo [n, n, 0]
(where n= 1, 2, 3, 4) perfluoroalkanes (n,n-BCPFA) were computed using hybrid density
functionals with DZP++ (polarization and diffuse function augmented double-ζ) basis sets. The
perfluoro bicyclo [1, 1, 0] butane (1,1-BCPFA) exhibits exceptionally high electron affinity at all
the levels of theory (2.07 eV at the KMLYP/DZP++ level of theory). The perfluoro [2, 2, 0]
octane has the lowest electron adiabatic electron affinity among all the molecules studied. The
zero-point corrected AEAs of the n.n-BCPFAs examined range from 0.92 eV to 2.07 eV at the
KMLYP/DZP++ level of theory. The structural changes which occur over the different ring sizes
are varied and are dictated by the mode of binding the electron by the n.n-BCPFA. Spin density
and SOMO plots reveal 1,1-BCPFA binds the electron in a C-C σ* orbital, whereas the 2,2,-
BCPFA binds the electron in an orbital which is delocalized over the entire molecule. The 4,4-
and 5,5-BCPFA bind the electron in a C-F σ* orbital which is localized on an exceptionally long
tertiary C-F bond. The 1,1-BCPFA radical anion exhibits an exceptionally long bridgehead C-C
bond. Whereas, the 2,2-BCPFA radical anion shows slightly elongated C-F bonds and slightly
shortened C-C bond. The 3,3-BCPFA, both the cis and trans forms and the trans form of 4,4-
BCPFA radical anions show the presence of an exceptionally long tertiary C-F bond.
4.2 INTRODUCTION
Perfluoroalkanes (PFAs) are known for their exceptional stability, owing to the presence
of highly strong C-F bonds. This class of molecules has numerous industrial applications due to
their chemical inertness, low viscosity, and low dielectric constant [1]. The PFAs are also
profusely used as gaseous dielectrics [2]. Negative plasmas of PFAs are used in semi-conductor
industry for SiO2 surface etching [3]. Electron attachment is the most important facet in PFA
90
chemistry. PFAs show very low reactivity. However, they become vulnerable only in presence of
electrons. The seminal work on reduction of PFA by Tatlow and co-workers opened up a new
frontier in PFA chemistry [4]. McNicol and Robertson showed PFA molecules can be reduced
using organic thio-enolate anions in less harsher conditions [5]. PFAs with tertiary C-F bonds are
more likely to undergo reduction than those without one [6]. A tertiary C-F bond in a PFA is the
“Achilles’ Heel”, and reducing environment leads to loss of the Fluorine from the tertiary C-F
bond.
The chemistry of PFAs is dominated by reactions initiated by electron attachment [6].
The propensity of PFAs to form molecular radical anions has thoroughly been studied in electron
attachment experiments on acyclic and cyclic and perfluoro-monomethyl substituted and bicyclic
PFAs [7, 8]. Electron Affinities of some PFAs have been experimentally determined to be
positive [7a-7d]. The isolation of c-C4F8¯ radical anion in neopentane matrix and subsequent
ESR study has shown the radical anions of PFAs are bound species [8]. c-C4F8 is known to have
a positive AEA and electron attachment has been implicated as a major pathway for the removal
of the octafluorocyclobutane from atmosphere [9]. Considering the fact, that PFAs are known for
their exceptionally high global warming potential and very long lifetimes in atmosphere [10],
their vulnerability towards electron attachment can plausibly provide a channel which can reduce
their atmospheric life expectancy. PFAs with high electron affinities are more likely to attach
electrons and this will plausibly provide a channel for removal of these species from the
atmosphere. Electron affinities for these molecules are a significant indicator for their propensity
to react. Through our previous investigations we have shown that linear straight-chain PFAs
have lower electron affinities than the cyclic-PFAs [11, 12]. The striking facet of our previous
investigations is the discovery that some cyclic PFAs can form radical anions where the extra
91
electron is delocalized over the entire molecule [12]. Moreover, it was shown that presence of
tertiary bonds can increase the adiabatic electron affinity of PFAs.
Trans perfluorodecalin (perfluoro-[4, 4, 0] bicycloalkane), composed of two fused
perfluorocyclohexane rings is known to undergo reduction under milder conditions than the
perfluorocyclohexane [13]. Tertiary C-F bonds in trans-perfluorodecalin are vulnerable to
electron attachment facilitating facile reduction. The radical anion formation of trans
perfluorodecalin is a key step in the reduction reactions of perfluorodecalin, which have been
developed over several years [6]. Perusal of chemical literature on perfluoroalkanes reveals the
scarcity of information regarding the structural features of the PFA radical anions which are the
key intermediates involved in the major reaction pathways of PFA reduction chemistry.
Moreover, electron attachment studies on perfluorodecalin are rare [8o]. Though, the reeduction
chemistry of perfluorodecalin employing different chemical reagents is well known, but there
have been no theoretical study related to its key step of reduction involving the radical anion
formation. In the current work we extend our investigation of electron affinities of PFAs to the
family of perfluorobicyclo[n, n, 0]alkanes. n,n-BCPFAs actually provide unique examples of
cyclic PFA frameworks which inherently possess a pair of tertiary C-F bonds. Our previous
investigations on tertiary C-F bond possessing PFAs have shown presence of tertiary C-F bonds
lead to high AEAs [11, 12]. Additionally for smaller bicyclic rings angle strain plausibly can
contribute to intriguing features in electron attachment properties. The perfluoro-bicyclo[n,n,0]
alkanes possess unique molecular frameworks which can provide the opportunity to study the
effect of angle strain and the simultaneous presence of tertiary C-F bonds in dictating electron
attachment properties to PFAs. In this cureent body of work we have elucidated the structural
92
facets of neutral and radical anion forms and the adiabatic and vertical electron affinities of 5
n.n-BCPFAs (n ranging from 1 to 4) have been computed.
4.3 COMPUTATIONAL METHODS
The GAUSSIAN 94 program [14] was used to compute total energies, optimized
structures and harmonic vibrational frequencies for all the molecules with three hybrid
functionals, B3LYP, BHLYP and KMLYP, These three functionals are described below briefly:
B3LYP (as implemented in GAUSSIAN 94) is a hybrid of exact, “Hartree-Fock”
exchange with local and gradient-corrected exchange and correlation terms, as proposed by
Becke [15], but with certain modifications to the correlation part. Instead of using the LSDA [16]
and PW91 [17] functional for local correlation, the B3LYP implementation [18] in GAUSSIAN
94 uses a mixture of LYP [19] and the VWN [20] correlation functional.
BHLYP is a hybrid functional originally proposed by Becke, which in its original form
combines Becke’s “half-and-half” exchange functional (BH), a 50-50 hybrid of exact exchange
and local spin density approximation [20], and the correlation part is described by the LYP
functional [19]. The GAUSSIAN 94 implementation of this functional is a bit different. The
GAUSSIAN 94 version of this functional is shown below:
Table 4.1. Adiabatic electron affinities of BCPFAs. Zero point corrected EAs are shown in
parentheses.
Molecules
B3LYP
BHLYP
KMLYP
1,1-BCPFA
2.19
(2.29)
1.96
(2.07)
2.08
(2.19)
2,2-BCPFA
1.10
(1.29)
0.49
(0.68)
0.74
(0.93)
cis-3,3-BCPFA
1.60
(1.72)
1.15
(1.27)
1.28
(1.40)
trans-3,3-BCPFA
1.89
(2.00)
1.52
(1.62)
.1.70 (1.81)
trans-4,4-BCPFA
1.77
(1.89)
1.36
(1.47)
1.48
(1.59)
106
Table 4.2. Vertical electron affinities of BCPFAs. Zero point corrected EAs are shown in
parentheses.
Molecules
B3LYP
BHLYP
KMLYP
1,1-BCPFA
-0.15
-0.53
-0.27
2,2-BCPFA
0.31
-0.32
-0.07
cis-3,3-BCPFA
0.62
-0.07
0.15
trans-3,3-BCPFA
0.49
-0.24
0.04
trans-4,4-BCPFA
0.46
-0.28
0.01
107
F
F
C F
C
C
F C
F
F
B3LYP 1.422 BHLYP 1.396KMLYP 1.378
1.3731.3551.338
1.9811.9621.944
1.4691.4581.450
95.295.595.7
84.884.584.3
FF
F
C
CC
FF
CF
B3LYP 1.320 BHLYP 1.308KMLYP 1.295
1.6891.6021.571
1.4771.4651.456
1.3561.3341.319 1.360
1.3361.320
1a
1b Figure 4.1. Optimized molecular geometries of: (a) Neutral 1,1-BCPFA (C2v symmetry), (b) Radical Anionic 1,1-BCPFA (D2h symmetry). All bond lengths reported are in Angstroms and angles are in degrees.
108
F
F
F
CF
C
F
C
F
C FC
C
F
F
F
BHLYP 1.327KMLYP
1.3231.309
1.3281.314
1.3301.316
1.5611.546
1.5781.565
1.5611.547
1.5421.526 1.322
1.308
F
F
F
C
C
F
C
F
F
CF
F
C
CF
F
1.5351.5041.512
1.4431.4201.396
1.3931.3681.352
1.3721.3531.338
1.5241.5041.495
1.5561.5421.528
2a
2b
Figure 4.2: Optimized molecular geometries of: (a) Neutral 2,2-BCPFA (C2 symmetry ), (b) Radical anionic form of 2,2-BCPFA (C2v symmetry). All bond lengths reported are in Angstroms.
109
F
F
F
F
C
C
F
F
F
C
C
C
C
F
F
FF
C
C
F
F
F
1.5711.5581.541
B3LYP 1.363BHLYP 1.345 KMLYP 1.329 1.564
1.5481.533
1.5771.5621.546
1.5801.5601.545
1.5661.5481.532
1.3431.3251.311
1.3411.3231.309
1.3491.3311.316
1.3491.3311.317
1.3531.3351.320
1.3421.3241.310
F
F
C
FF
F
CC
C
F
F
F
C
C
F
C
F
C
F
F
F
F
B3LYP 1.893BHLYP 1.910KMLYP 1.839
1.4131.3811.365
1.4981.4861.475
1.3901.3671.350
1.3591.3401.325
1.3541.3341.3201.497
1.4891.476
1.5621.5481.533
1.5591.5441.5291.558
1.5451.530
1.3601.3401.326
3a
3b
Figure 4.3: Optimized molecular geometries of: (a) Neutral cis 3,3-BCPFA (C2 symmetry), (b) Radical Anionic form of cis 3,3-BCPFA (Cs symmetry). All bond lengths reported are in Angstroms
110
F F
F F
C C
F F
F
C
C C
C
F
F F
C C
F F
F F
B3LYP 1.380 BHLYP 1.361KMLYP 1.344
1.3431.3251.314
1.6011.5821.566
1.3431.3261.311
1.5471.5321.517
1.5511.5361.521
1.3431.3281.311
F
F
F
F
C
C
F
C
C
F
F
F C
F
C
C
F
C
FF
FF
B3LYP 1.347BHLYP 1.327KMLYP 1.313
1.4301.3921.368
2.0312.0402.021
1.4701.4701.466
1.4751.4701.463
1.5611.5551.544
1.5901.5731.556
1.5831.5671.551
1.3571.3361.3211.394
1.3691.350
1.3471.3271.3121.363
1.3451.332
1.3641.3471.332
4a
4b
Figure 4.4: Optimized molecular geometries of: (a) Neutral trans 3,3-BCPFA (C2h symmetry), (b) Radical Anionic form of trans 3,3-BCPFA (Cs symmetry). All bond lengths reported are in Angstroms.
111
F
F
F
F
F
CCC
F
F
CC
F
F
F
F
CC
F
F
CCC
F
F
F
F
F
B3LYP 1.374 BHLYP 1.355KMLYP 1.339 1.350
1.3311.317
1.3481.3291.315 1.574
1.5581.540
1.5731.5561.538
1.5681.5501.534
1.3511.3321.318
1.3481.3301.316 1.560
1.5431.528
F
F
F
F
F
C
C
F
F
C
C
F
FC
C
F
F
CC
F
F
C
C
F
F
F
F
F
B3LYP 1.990BHLYP 1.976KMLYP 1.924
1.4921.4871.473
1.5031.4931.479
1.4311.403
1.3971.3721.355
1.5691.554 1.551
1.5361.521
1.3591.3401.326
1.3461.3271.313
1.3651.3451.330
1.5651.5491.533
1.5581.5421.526
1.3601.3401.325 1.355
1.3371.322
1.3481.329
5a
5b
Figure 4.5: Optimized molecular geometries of: (a) Neutral trans 4,4-BCPFA (C2h symmetry), (b) Radical Anionic form of trans 4,4-BCPFA (Cs symmetry). All bond lengths reported are in Angstroms.