recently 
 we reported on an analysis of the infrared spectrum of 
 c2f4 . by observation 
 of many combination and difference bands , including many from two c - containing isotopologues , and by comparison with mp2 and 
 density - functional calculations , all 12 fundamentals could be assigned , 
 although only five are ir active .
the geometry 
 was deduced from ro - vibrational analysis of strong ir active bands 
 and by comparison with theoretical calculations .
however , it is also 
 instructive to correlate anharmonic constants with some peculiarities 
 of the reactions of c2f4 .
accordingly , in this 
 work more anharmonic constants ( altogether 54 ) are derived from the 
 spectra , and a complete set ( 78 ) is calculated .
the earlier vibrational 
 assignments of c2f4 were reported at a time 
 when the unusual properties of this molecule were barely known .
explained this property by positing that the electron attraction 
 of fluorine leads to a preference of sp- over sp - type carbon : radical addition converts both 
 c atoms from sp to sp hybridization , which 
 stabilizes the primary product , lowers the transition state , and thus 
 accelerates the reaction .
alder reactions , for example , 
 which was again explained by stabilization of radical intermediates .
( borden also presented an alternative but related description based 
 on delocalization of unpaired radicalic electrons to accepting  * 
 orbitals of cf groups . )
the preference 
 for carbon sp hybridization can also be expected to lower 
 the force constants for the pyramidalization ( wagging ) vibrations 
 ( 7 , 8 ) and/or increase their anharmonicity . 

furthermore , torsion ( 4 ) should be facilitated by 
 rehybridization and in fact quantum chemistry confirmed this for a 
 90 twist .
another spectacular property of c2f4 is how 
 readily it can dissociate thermally to two cf2 molecules .
a c = c bond energy of only 2.95 ev is derived , less than that of a typical c  c single 
 bond ( 4 ev ) .
the low dissociation energy is caused by stabilization 
 of the resulting two difluorocarbenes by back - bonding from nonbonding 
 fluorine electrons to the empty carbon p - orbital .
this also explains why cf2 has a singlet 
 ground state which is more stable than the triplet ( by 2.458 ev , taken 
 from the band origin of the phosphorescence spectrum ) . whereas in the previous work
, only cc stretching is considered 
 as the dissociation coordinate , it was argued in ref ( 16 ) that pyramidalization 
 must also be involved .
this idea is supported in the present work 
 by the large value found for the anharmonic constant x18 coupling cc stretch with trans pyramidalization .
the 
 magnitude of x18 as compared to the much 
 smaller x17 ( coupling cc stretch with 
 cis pyramidalization ) also supports a valence - bond analysis of weak 
 double bonds , which was reviewed in ref ( 19 ) .
the samples in natural isotopic abundance were either taken from 
 commercial c2f4 ( hoechst ) , that contained a 
 trace of the cyclic dimer , or prepared from c2f4br2 + zn in a high - boiling 
 alcohol ( diethylene glycol ) ; the comparison allowed for recognizing 
 absorptions of impurities .
a sample enriched in c to 
 50% was prepared from chclf2 by co2 laser isotope 
 separation with enriched cf2 as the primary product .
ir spectra of c2f4 in natural isotopic 
 abundance 
 and isotopically enriched were recorded between 370 and 4000 cm with 0.2 cm resolution by a perkinelmer 
 ftir spectrometer in garching . at the 
 synchrotron lab ,
the isotopically enriched sample was measured at 
 moderate 0.1 cm resolution in the far ir region 
 from 100 to 600 cm ( capturing the band at 210 
 cm ) , and at high resolution for the ir active 
 cf stretch bands , see ref ( 1 ) .
the present work focuses on anharmonic constants of c2f4 . only where the constants were 
 expected to be different for ccf4 and c2f4 ( e.g. , in the case of 
 fermi resonance )
theoretical values of the anharmonic constants xij were obtained from anharmonic 
 vibrational 
 frequency calculations performed using gaussian 03 revision c02 at the mp2 level using 
 dunning - type correlation - consistent ( cc - pvtz ) orbitals .
the molecular force field at this level of theory 
 was shown in the previous study to reproduce the fundamental wavenumbers 
 and the isotopic shifts of c2f4 very satisfactorily 
 ( for details , see ref ( 1 ) ) , and hence was an appropriate choice for computing xij values .
the calculations were performed for each of 
 the c2f4 , ccf4 , and c2f4 isotopologues .
the spectra were measured previously and the 
 fundamentals extracted 
 from them , using a limited number of anharmonic constants ( from combination 
 and hot bands ) where necessary . for convenience 
 table 1
lists the fundamentals again . in this 
 work we derived a large set of experimental anharmonic constants from 
 combination bands and  in particular for the lower - wavenumber 
 vibrations  from hot bands , and report a complete set of theoretically 
 computed values .
symmetry types refer to a d2h molecule with z axis along the cc bond and the y axis perpendicular 
 to the plane , as used in ref ( 1 ) for easier comparison with the c2v symmetric ccf4 ; the more conventional designation with x axis along the cc bond and z axis perpendicular 
 to the plane is given in parentheses .
revised value ( instead of 210 cm ) , based on a more definite 
 assignment of a hot - band structure and x10,10 , see supporting information .
band origins from high - resolution 
 spectra ; low - resolution values are 1338.4 
 and 1187.0 .
upright : 
 experimental values . 
 in parentheses : values calculated by mp2/pvtz . where two values or 
 a range are given for the experimental data
, it may indicate ( a ) a 
 dependence of the effective xij on the involved levels due to perturbations ( fermi resonances , 
 section 4.4 ) or ( b ) an uncertainty due to error 
 limits ( e.g. , where broad bands are involved ) or an uncertain assignment . 

a preferred value is indicated by bold face . for further details on 
 the derivation of each xij and some isotopic data ,
the anharmonic constants xij were calculated from observed 
 combination and difference bands 
 by assuming that anharmonic shifts are additive : for binary combination 
 bands ( i  j ) and for overtones 
 we used1and2with obvious extensions for more complicated 
 combinations .
( the xij values are mostly negative , as usual . ) the left - hand side of these 
 equations should be read as  wavenumber of ( name )  . for hot bands ( satellite transitions near i that originate from a thermally populated 
 lower level j ) we used3again 
 with obvious extensions .
one can often 
 observe sequences of equidistant q branches , corresponding to hot 
 bands starting from higher levels mj , or combination of such sequences ( from mj + nk ) .
equation 3 implies that the distance of a ( first ) hot band from the fundamental 
 directly indicates the corresponding anharmonic constant .
combination 
 bands allow for a direct assignment , whereas hot bands must be identified 
 by their intensity ( controlled by the boltzmann factor ) . in a number 
 of cases
the supporting information ( si ) compiles the sources for each xij in table s2 , whereas table s1 lists the observed 
 bands ( with hot bands ) and their isotopic shifts .
two examples of 
 hot bands , whose shifts are dominated by the large x18 anharmonicity , are shown in figure 1 .
absorbance spectra demonstrating the large x18 derived shifts for hot - bands originating in 8 .
the spectra were recorded 
 in the garching laboratory , with pressure and path length of 2 bar 
 and 10 cm ( for the lower trace of each panel ) , and 140 mbar and 4 
 m ( upper trace ) , respectively . for levels involving more than two quanta of vibration , anharmonic 
 shifts
this helped to decide between different 
 assignments of combination bands in a few cases where the harmonic 
 sums were similar to each other .
however , such additivity need not 
 apply when the levels involved are subject to fermi resonance , producing 
 shifts that depend on the separation of nearby interacting levels . 

we use eqs 13 to 
 obtain the experimental values , and hence , table 2 reports phenomenological xij , some of which show a spread in the values suggestive of fermi 
 resonances ( in particular x18 , x26 , and x77 ) .
fermi 
 resonances can also be recognized if the apparent xij or the hot - band structure depends 
 on the isotopologue . for c2f4 ,
fermi resonances 
 were identified ( see section 4.4 and si ) between:5 and 2+6 ( discussed already in ref ( 1)),1 and 5+6 ( indicated by the hot - band structure 
 of 1-combinations , which are different in the mixed 
 isotopologue),2 and 27 ( causing irregularities 
 in overtone levels of 7 , also contributing to the 
 large magnitude of x27 and x77).2 and 23 , identified from the 
 mp2 calculations .
5 and 2+6 ( discussed already in ref ( 1 ) ) , 1 and 5+6 ( indicated by the hot - band structure 
 of 1-combinations , which are different in the mixed 
 isotopologue ) , 2 and 27 ( causing irregularities 
 in overtone levels of 7 , also contributing to the 
 large magnitude of x27 and x77 ) . 2 and 23 , identified from the 
 mp2 calculations .
the mp2/cc - pvtz calculations 
 reproduced the observed wavenumbers 
 and isotopic shifts very well . supporting 
 the overall vibrational analysis
exceptions are 15 ( x22 , x28 , x29 , x2,10 , x2,11 , x36 , x3,10 , x45 , x59 , x5,11 , x66 , x68 , x77 , x88 , x10,11 ) out of 54 cases where an observed value is available 
 for comparison . some of these will be discussed below .
as already 
 described in the introduction , the peculiar 
 reactions of c2f4 have to do 
 with cc stretching and carbon pyramidalization . the discussion will 
 focus on these coordinates ( sections 4.14.3 ) . for 
 a planar geometry , 

cc dissociation correlates c2h4 and c2f4 with a pair of carbenes in their lowest triplet states ( figure 2a ) . because 
 the energy of forming these products is practically the same for the 
 two molecules
, one could also expect that the potential energy curves 
 coincide and the cc stretch force constants are equal .
in fact , already 
 early force - field calculations showed no substantial difference ( 889 
 n / m for c2f4 and 
 940
furthermore , 
 the short cc distance ( 132 pm , which is 1 pm shorter than in ethylene ) and the high cc stretch wavenumber ( 1873.8 cm , compared to 1625.4 cm   for ethylene ) do not point to a weakened bond . 
 as early as 1965 , the low dissociation energy of c2f4 was attributed to switching over to a channel producing two 
 singlet carbenes and to the stabilization ( by 2.458 ev , see introduction ) of singlet cf2 by back bonding , so that this channel is energetically favored by 4.9 ev .
this path hence leads over an avoided 
 crossing of potential surfaces ( figure 2a ) . 

if the avoidance is strong , one could expect an influence at least 
 on the anharmonicity x11 ( 1 is dominated by cc stretching ) , even if not on the force 
 constant at the bottom of the potential energy well .
table 2 shows that the magnitude of x11 ( calculated 7.8 cm ) is not unusually 
 large for such a high - frequency vibration , though noticeably larger 
 than for ethylene ( x22 = 2.3 cm  ) . that the increase 
 in magnitude is only moderate
can be taken as a sign that the avoidance 
 along this coordinate is not very strong .
hence , the back reaction 
 ( recombination ) will have a high barrier in planar geometry . whereas 
 the measured recombination barrier is not , in fact , zero , it is only 
 minor ( 9 kj / mol = 0.09 ev  ) .
so , 
 a lower - energy path must lead around the barrier , out of the drawing 
 plane of figure 2a , that is , with distortion 
 different from cc stretch .
potentials for ground - state cc dissociation 
 of c2f4 , leading over an avoided crossing to 
 two singlet carbenes . 
 in ( a ) it is assumed that the one - sided pyramidalization ( q7 + q8 ) begins only after overcoming the barrier , whereas 
 ( b ) shows the preferred path , where this distortion is already fully 
 developed on the barrier and is preceded by a trans pyramidalization 
 ( q8 ) , while the cc distance is steadily increasing .
it was argued in ref ( 16 ) that recombination of 
 two cf2 molecules should 
 be easiest if one of them points with its filled n orbital 
 to the empty p orbital of the other .
hence , the dissociation 
 path will change from pure cc stretch to include also pyramidalization 
 ( figure 2b ) , and the potential should be lowered 
 in energy in the direction of q7 ( the coordinate of 7 ) and/or q8 . in turn
in fact x18 has an unusually large magnitude , although x17 is in the normal range ( table 2 ) .
( the magnitude of x18 is not 
 caused by secondary effects such as fermi resonance , as we shall see 
 in section 4.4.3 . )
we can conclude that on 
 stretching the cc bond the molecule first bends toward trans pyramidalization 
 ( q8 ) ( figure 2b ) .
the one - sided 
 nonplanar bending ( figure 2 ) is a superposition 
 of q7 and q8 .
the reason why q8 is 
 active earlier than q7 can be understood by a valence - bond 
 model for weak double bonds . in this model
several symmetric arrangements 
 of carbenes ( a  c 
 of scheme 2 ) were considered : whereas with 
 two triplet carbenes all arrangements ( a  d ) lead to bonding 
 interaction , with two singlet carbenes bonding occurs only in the 
 trans - bent case ( c ) ; this corresponds to a double donor 
one can add that the cis - bent case with singlet carbenes would 
 lead only to antibonding ( scheme 2d ) .
malrieu 
 and trinquier derived a criterion for trans - bending ( deriving even 
 the angle ) by comparing the standard double - bond energy with the singlet 
their findings were confirmed by many examples , in particular with 
 heavier - element homologues .
we can apply 
 this rule not only to the equilibrium geometry of c2f4 but also to its dissociation path , if we consider in the 
 comparison the double - bond energy that is reduced on extension of 
 this bond .
the rule thus predicts that on cc extension c2f4 is distorted from planar geometry to a trans - bent structure , 
 and this rationalizes the large magnitude of x18 . in the triplet case ,
the interaction 
 can be bonding in all arrangements . in the singlet case , ( a )
is antibonding , 
 ( b ) nonbonding , ( c ) bonding , ( d ) antibonding .
more recently , borisov et al . found evidence 
 for trans pyramidalization 
 on extension of the cc bond also from molecular orbital calculation 
 ( at high level : mller  plesset perturbation theory of 
 second , third and fourth order ) : the 
 authors found that the onset is relatively sudden on cc extension 
 to 142 pm and that the distortion lowers the energy appreciably .
( the 
 large x18 anharmonicity is an indication 
 that this pyramidalization already begins not far from the s0 minimum .
in fact , a cc stretch by 10 pm  from 132 to 142 pm 
is 
 just about the vibrational amplitude in the 1 = 
 1 level . )
although borisov et al . did not find an energy minimum with 
 such a distortion , they suggested that it plays a crucial role in 
 the low - energy real intermediate found by buravtsev , kolbanovskii 
 et al . in thermal reactions of c2f4 and recombination 
 of cf2 ( see ref ( 31 ) and literature quoted therein and section 4.3 ) .
one could suppose that in order to lower the activation 
 energy 
 for dissociation the only necessary deviation from simple cc stretching 
 is distortion toward the 8 coordinate ( q8 ) .
however , there is experimental 
 evidence that the asymmetric pyramidalization ( corresponding to superposition 
 of q7 and q8 as in figure 2b ) is already crucial in the transition state : the pre - exponential 
 factor found in the rate of thermal c2f4 dissociation 
 ( 2.8  10 s  ) is clearly larger than would be typical for 
 a simple bond splitting ( 10 s ) .
this 
 corresponds to a raised entropy of activation , such as that which 
 happens if an additional degree of freedom is activated in the transition 
 state .
the most plausible candidate is free internal rotation , as 
 it can be expected in the asymmetric structure with a single dative 
 bond but not in symmetric geometry with double donor  acceptor 
 bond .
this picture is also consistent with a stepwise cleavage of 
 the double donator  acceptor bond on c2f4 dissociation and its stepwise formation on cf2 recombination .
it is worth noting that the molecule with one - sided pyramidalization 
 has an electron distribution ( figure 2b ) that 
 is zwitterionic and correlates in planar geometry with the 2ag state with two  electrons excited to  * , as 
 already pointed out in ref ( 16 ) .
a fully analogous dissociation path can also be 
 expected for the 
 other systems considered by malrieu and trinquier .
in fact , according 
 to ref ( 32 ) ground - state 
 ( ir induced ) dissociation of diazomethane ( h2cnn ) follows 
 a path with a pyramidalized methylene group to produce n2 + singlet ch2 ; the out - of - plane deformation was experimentally 
 confirmed . in the backward reaction ,
n2 points with its 
 n electron pair to the empty p orbital of the singlet 
 methylene ( see refs ( 32 and 33 ) for a calculated potential in two dimensions , which would look similar 
 for c2f4 ) .
hence , 
 the out - of - plane deformation on dissociation of c2f4 is not an isolated phenomenon . applying 
 their energetic criterion to the equilibrium geometry of c2f4 , trinquier and malrieu found that this molecule is 
 not far from the limit , where it would become nonplanar , and suggested 
 that the 8 force constant may be significantly lower 
 than that of ethylene .
this is in fact 
 confirmed in the following way : analytical expressions for a valence 
 force field model for planar x2y4 were given 
 by herzberg . besides the masses mx and my , bond lengths l1 ( for xx ) and l2 ( xy ) and the angle  ( half of yxy ) , both 7 and 8 only depend on the force constant for pyramidalization 
 ( k/l2 ) . with equilibrium distances and angles from ref ( 1 ) and i = ( 2ci )
one derives this force constant from 
 7 and 8 ( with identical results 
 for c2f4 and c2f4):4both values should be identical 
 in this valence - force field model .
in fact for ethylene , the value 
 is 22.9 n / m , whether derived from 7 or 8 .
the pyramidalization force constant 
 derived from 7 of c2f4 is 
 slightly higher than in ethylene ( by 17% ) , but the same quantity derived 
 from 8 is only 49% of the ethylene value .
( of course , 
 these values are not quantitatively meaningful , as the discrepancy 
 highlights that a pure valence - force field model is not sufficient 
 for wagging of c2f4 . )
so in fact the restoring 
 force for the 8 vibration is significantly smaller 
 than in ethylene and than that expected on the basis of the same pyramidalization 
 force constant as for 7 .
this is consistent with 
 the prediction of the valence - bond model favoring the trans - bent geometry .
the slightly raised force constant for 7 could 
 be due to repulsive nonbonding interaction in cis pyramidalization . 

such a geometry would be involved in the hypothetical transition state 
 of the diels 
alder addition of c2f4 to 
 butadiene , a reaction that has not been observed .
it was argued that 
 an increased energy associated with this distortion might contribute 
 to inhibiting the reaction .
however , an 
 increase in the force constant of only 17% is hardly sufficient to 
 support this explanation , and the other effects discussed in ref ( 7 ) , in particular the competing 
 fast radical reactions , are probably more important . applying 
 again the force - field formulas of herzberg ,
the force constant for torsion , k/l2 , is found to be 30.3 
 n / m for both ethylene and tetrafluoroethylene .
that is , near the potential 
 minimum the c = c bond in c2f4 behaves 
 just like a normal double bond .
consequently , the torsional barrier 
 at a 90 twist ( which is a measure of the  bond strength ) 
 would be identical for both molecules ( 2.8 ev ) if the two c  cf2 groups remained planar ; this was confirmed by a high - level 
 calculation .
however , pyramidalization 
 lowers this barrier by 0.57 ev ( at mp2 level , consistent with ref ( 35 ) ) .
if this stabilization is activated early along q4 , 
 it could give rise to substantially negative values for x44 and especially for x47 and x48 .
however , x44 and x47 are actually slightly positive 
 ( 0.8 and 0.3 cm ) and x48 has no unusual magnitude ( 0.7 to 1.05 cm ) .
evidently , the stabilizing effect of pyramidalization becomes 
 effective only at high torsional angles .
the corresponding values 
 for ethylene are 2.4 , 8.9 , and 7.2 cm , respectively .
the nondiagonal anharmonicities xi4 and x4j are 
 generally smaller in magnitude than in ethylene . but this may simply 
 have to do with the relative vibrational amplitudes , which are much 
 larger for torsion of ch2 than of cf2 due to 
 the relative masses . in the twisted - pyramidalized structure 
 of c2f4 ,
the triplet ( t1 ) is only 
 0.013 ev lower than the singlet 
 ( s0 ) .
it 
 can therefore act as a real intermediate and undergo radical - type 
 reactions , further assisted by its low energy that is calculated at 
 2.1 ev .
this has been a widespread interpretation 
 of some peculiarities of c2f4 reactions ( see , 
 for example ref ( 7 ) ) .
however , buravtsev , kolbanovskii et al . found in shock - tube experiments 
 ( with c2f4 diluted by ar and adiabatically compressed ) 
 an intermediate at much lower energy ( 0.8 to 1 ev ) with uv and visible 
 absorption ( 235 and 500 nm ) ( see refs ( 31,36 , and 37 ) and the 
 literature quoted there ) .
they supposed it to be a singlet diradicaloid 
 of c2f4 with a geometry corresponding not to 
 an energy minimum but to a point on a slope of the potential ( see , 
 for example ref ( 31 ) ) .
however , as these points are not stationary there are too many 
 ( nearly ) isoenergetic locations with shifted electronic transitions , 
 so that the electronic absorption would be smeared out .
it was therefore 
 suggested that the observed intermediate 
 is another low - energy isomer , tetrafluoro - ethylidene cf3cf ( electronic absorption in an ar matrix : ) .
however , its energy ( 1.9 ev  ) seems to be nearly as high as that of the twisted - pyramidalized 
 triplet .
( in one study the twisted - pyramidalized c2f4 triplet is calculated at 0.90 ev , but computational details are not given , and previous theoretical 
 results are not discussed . )
some more anharmonicities of table 1 have unusually large magnitudes or show a range 
 of values and/or deviate from prediction . in many of them
fermi resonances 
 play a role , as will be explained here . in section4.4.3 , however , it is shown that x18 is hardly influenced by such effects and its large magnitude mainly 
 results from the overall shape of the potential energy surface .
fermi resonances mix two nearby levels of the 
 same symmetry , which differ by three units in the quantum numbers . 

the fermi - induced 
 repulsion of the levels depends in a nonlinear way on both the magnitude 
 of the fermi interaction parameter and on the original ( i.e. , unperturbed ) 
 energetic distance of the levels .
this separation will , in general , 
 change ( a ) on isotopic substitution and ( b ) on adding a quantum of 
 another vibration ( i.e. , in analogous combination bands ; similarly 
 also in higher overtones , in which case a quantum number dependence 
 must also be taken into account ) .
another method of characterizing fermi resonance interactions relies 
 on intensity borrowing caused by the mixing of levels . according 
 to the mp2 calculations , the great majority of xij change by 1 cm on isotopic substitution
the few exceptions are 
 listed in table 3 and are compared to experimental 
 values . identified ( fr13 ) and
the interpretation in the line  influenced by  
 is based on the assumption that an xij is affected by such a resonance if at least one 
 of the levels i and j is involved in the fermi interaction .
the table shows that 
 the calculated isotopic shift is sometimes 
 much larger than in the experiment , for instance x26 , x27 .
also x56 for c2f4 is probably 
 too large , as the two observed bands 5+6+11 and 5+6+12 are close to their harmonic positions 
 ( table s1 in si ) .
it seems that at the 
 present level of theory , the calculation does not reliably reproduce 
 the fermi resonance induced shifts , at least the stronger ones .
this 
 is not surprising given the highly sensitive and nonlinear dependence 
 of fermi shift on the  unperturbed  level separations . 

the same deficiency will also affect those xij connected with at least one level ( or a 
 combination thereof ) involved in a resonance listed above ( examples 
 in figure 3a ) .
in fact , 10 of the 15 deviations 
 listed at the end of section 3 can be attributed 
 in this way to the resonances fr1 and fr2 with possible contributions 
 of fr3 .
the exceptions are x36 , x3,10 , x66 , x68 , and x88 . in 
 all 42 other cases
it is worthwhile to consider 
 the two strongest fermi resonances , 
 fr1 ( 2/27 ) and fr2 ( 5/2+6 ) , in c2f4 in some detail .
the effect of these resonances 
 is summarized in figure 3 . some levels involved 
 in fermi resonances and observed transitions . 

solid arrows : ir , broken arrows : raman ; double arrows ( with interaction matrix element ) indicate repulsion 
 between level pairs .
the anharmonic shifts involving x77 are only nominal , because the fermi perturbation is 
 strong :  6x77  = 18.1 is 
 less than 3 times 
(= 8.2 ) and  4x77  is only 
 9.9 . ( but  2x77  +  4x77  =  6x77  , as is obvious from the level scheme , and the raman 
 anharmonic shifts practically coincide with those from the ir spectra . ) 
 ( b ) three - level fermi resonance 5/2+6/27+6 and 
 their combinations with 9 for c2f4 and c2f4 . 

the indicated level energies are from the spectra except those in 
 parentheses , which are calculated .
the broken horizontal lines are 
 the estimated unperturbed positions ( see the si ) , and the signed numbers are the calculated shifts .
the 16.4 cm magnitude of the interaction term ( with its expected dependence 
 on quantum numbers ) has been derived 
 from band shifts and intensities for a series of levels built on 2/27 for all three isotopologues .
bands for 
 27+x ( x = 9 , 11 ) borrow their entire intensity from 2+x . the detailed analysis 
 is provided in si .
it 
 is also evident that x77 , x27 and x22 are affected by 
 the fermi resonance ( and probably other x2i , if the level separations differ ) and that x77 is level dependent because of the varying 
 separation .
the fermi term is almost entirely responsible for the 
 + 8.2 cm shift of 27 for c2f4 and those of the heavier isotopologues 
 ( table 3 under fr1 ) . in the latter
the fermi - induced 
 shift is increased , because the levels 2 and 27 ( before perturbation ) are closer together than in c2f4 and are practically degenerate in c2f4 .
the success of these calculations 
 shows that the additional mixing of 2 with 23 ( fr3 ) is apparently a weak perturbation at most .
the 
 fermi resonance fr2 between 5 and 2+6 was qualitatively discussed in ref ( 1 ) .
a more complete understanding 
 of the resonance shifts and pattern of intensity borrowing requires 
 the three - level scheme shown in figure 3b ; 
 this figure also shows combinations with 9 , as they 
 are all ir active and were directly observed .
analysis based on this 
 model has enabled the magnitude of the fermi term to be determined 
 as 11 cm ; the fr1 term of 16.4 cm was used without change .
significantly , the model predicts varying 
 fr shifts that even differ in sign ( originating from the different 
 repulsions in figure 3b ) and can thus account 
 for the unusual isotopic shifts observed between c2f4 and c2f4 . 

it explains a substantial deviation of the observed isotopic shift 
 5 = 51.9 from the value of 5 = 43.1 
 expected from the teller  redlich product rule , which is valid 
 for harmonic oscillators .
additionally 
 the relative intensities of combination bands and their isotopic dependence 
 are well predicted .
it is also remarkable that according to the model 
 the largest part of the anharmonicity x26 is due to fermi resonance .
as described in ref ( 1 ) , the lower symmetry in ccf4 leads to strong mixing of 5 with 9 ( which are nearly degenerate in c2f4 ) .
the two levels repel each other 
 ( even in the harmonic approximation ) and give rise to two infrared - active 
 transitions .
it is sometimes difficult to disentangle them and their 
 combination bands from the spectra .
if the large magnitude of some 
 anharmonicities is caused by fermi resonance , a crucial question is 
 whether this might also be the case for x18 .
if so , the conspicuous value of x18 could be largely a matter of the character of the resonance and 
 less a consequence of global features of the potential for dissociation , 
 which we considered in section 4.1 .
in fact , 
 weak perturbations of the 1 level and its combinations 
 by the 1/5+6 fermi resonance are indicated by the slight x18 dependence on the level and on isotopic substitution and 
 the change of the hot - band structure of 1 combinations 
 in ccf4 , as explained in the si .
a quantitative estimate of the strength 
 of the 1/5+6 interaction can be deduced from the intensities of 5+6 combinations relative to those of the corresponding 
 1 combinations , assuming that the former borrow 
 their full strength from the latter .
the 5+6+12 band ( 2444.3 cm ) 
 has 12% the strength of the 1+12 band ( 2428.7 cm ) , see figure 1a .
similarly , the 5+6+11 shoulder ( 3072 cm ) is < 1% as intense as 1+11 ( 3056.2 cm ) and clearly visible only with longer 
 path length than shown in figure 1b .
from both 
 observations , one can estimate a fermi term ( w ) of 
 no more than 2.5 cm , causing a shift ( and 
 consequent change in x18 ) of < 0.5 cm .
this is actually an upper bound , because such weak 
 bands can also be expected without intensity borrowing .
hence , fermi 
 resonance affects the magnitude of x18 only by a little ( by < 3% ) , and we can maintain the conclusions 
 of section 4.1 on the shape of the potential .
a large set of anharmonic 
 constants of c2f4 was derived from spectroscopic 
 data , and a complete set was calculated . 

most of the calculated and experimental values agree very well , and 
 nearly all deviations can be attributed to fermi resonances . the values 
 were used to interpret peculiarities of the potential and reactions 
 of this molecule .
the facile thermal cc dissociation of c2f4 is due to curve crossing of the ground state 
 ( 1ag ) with 
 the two - electron excited zwitterionic 2ag state .
the crossing 
 barely alters the properties of the potential curve ( cut purely as 
 a function of cc stretch ) near the equilibrium geometry ; the force 
 constant for cc stretching ( 1 in c2f4 , 2 in c2h4 ) is nearly 
 identical for the two molecules .
only a slightly larger magnitude 
 of the anharmonicity x11 compared to the 
 corresponding x22 of ethylene provides 
 a hint of a weakly avoided crossing in planar geometry of c2f4
. however , the large magnitude of x18 leads us to conclude that the dissociation path bends 
 early toward 
 q8 , i.e. to trans pyramidalization of the two carbon atoms 
 ( figure 2b ) .
this is rationalized by a valence - bond 
 model , which describes the stretched cc bond as a double donor  acceptor 
 bond ( scheme 2c ) .
it is also consistent with 
 the tendency of fluorine to induce sp hybridization at 
 carbon , although this preference alone would also allow cis pyramidalization , 
 q7 , which is not involved early in dissociation .
on further 
 cc stretching , one of the two donor  acceptor bonds breaks , 
 and the pyramidalization becomes fully one - sided already in the transition 
 state ( figure 2b ) . in this way , free internal 
 rotation of the cf2 groups becomes possible , providing 
 an additional degree of freedom that rationalizes the high pre - exponential 
 factor in the rate constant of dissociation .
this structure with perpendicular 
 arrangement of the two cf2 groups appears very plausible 
 for the back reaction .
thus , one cf2 group approaches with 
 its filled n orbital the empty p orbital of the other 
 cf2 group ( figure 2b ) .
the easy 
 trans pyramidalization on minor cc stretching is probably also the 
 reason that the corresponding 8 force constant is 
 lowered , although all other force constants are similar to those in 
 ethylene .
the preference of fluorine for sp hybridization 
 at 
 carbon has been invoked to explain not only the easy radical addition 
 and other reactions , but also the low - lying , twisted - pyramidalized 
 triplet , which is nearly isoenergetic with the singlet that has a 
 saddle point there .
this is indicated by x44 , x47 , and x48 , which have no unusual values .
very recently , 
 high - level theoretical studies investigated 
 electronic ground and excited states of c2f4 and their dependence on some coordinates , mainly 
 to discover the fate of this molecule after electronic excitation 
 and make comparisons with a corresponding time - resolved experiment 
 ( ref ( 16 ) ) . for the 
 ground state , the stabilizing effect of pyramidalization in the twisted 
 molecule was confirmed .
interestingly , the excited molecule enters 
 the s1/s0 conical intersection from the 2ag state , where the molecule has a large one - sided pyramidalization , 
 a 90 cc twist and a cc bond length ( 1.51  ) similar to 
 that of a single bond . in the present work ,
the transition state for 
 s0 dissociation was said to result from avoided crossing 
 of the 2ag and 1ag ( i.e. , s0 ) states , 
 also with large one - sided pyramidalization but at longer cc distances 
 and perhaps without twist
. it would be interesting to check whether 
 these geometrical differences are large enough to generate an excited - state 
 barrier , because evidence was found in ref ( 16 ) that cc dissociation does not begin in the excited 
 state .
 compared to ethylene and its nonfluorinated 
 derivatives , c2f4 is peculiar in many reactions . 
 
 it very easily 
 adds to radicals and prefers formation of four - membered rings over 
 diels  alder reactions . 
 this has been rationalized by the preference 
 of fluorine for carbon sp3 hybridization , which is possible 
 on opening of the double bond . 
 another property , the thermal dissociation 
 of the c = c bond , has been explained by the stabilization of 
 the product ( cf2 ) by back - bonding . 
 here , it is attempted 
 to correlate such properties with vibrational constants , in particular 
 for c = c stretching and twisting and for carbon pyramidalization . 
 
 the only force constant found to be lowered compared to ethylene is 
 that for trans pyramidalization ( 8 ) , and cc bond 
 softening on 8 distortion is indicated by the conspicuously 
 large magnitude of anharmonic constant , x18 . 
 both observations can be rationalized by a valence - bond model that 
 predicts a trans bent structure on weakening the cc bond . 
 conclusions 
 are drawn about the dissociation path and peculiarities of the potential . 
 
 other anharmonicities , both experimental and calculated and some in 12c13cf4 and 13c2f4 , are also discussed . in particular 
 some strong fermi 
 resonances are identified and their effects accounted for . 
Introduction
Methods
Results
Discussion
Conclusion