J . Phys. Chem. 1987, 91, 3266-3272
3266
A Semiempirical Potential-Energy Surface for the C,H,F,
System
Lionel M. Raff Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078 (Received: November 24, 1986; In Final Form: February 24, 1987)
-
-
+ F2 CH2F-CH2F, C2H4 + F2 CH2-CH2F F, C2H4 F2 CH,=CHF + HF, CH2F-CH2F CH,=CHF + HF, CH2F-CH2F CH2-CH2F + F, CH,F-CH2F CH2=CH2 + 2 F, and CH2F-CH2F CH2=CHF + H + F are open on the surface. The surface predicts equilibrium geometries, reaction exo- or endothermicities, and fundamental frequencies for the nonradical reactants and products in fair-to-good accord with measured values. The accuracy for the radical products is less. The predicted barrier height for HF abstraction from 1,2-difluoroethane is in good agreement with the measured activation energy. The predicted barrier for the concerted, planar, four-center addition of F2 across the ethylene double bond is 12.3 kcal/mol. The strengths and deficiencies of the surface are discussed in detail. A semiempirical potential-energy surface for the C2H4F2system is reported. Reaction channels for C2H4 + +
+
-
+
t-,
I. Introduction During the previous several years, several research groups have reported studies of the chemistry of photochemical processes occurring under matrix isolation conditions at cryogenic temperatures. Reactions carried out under such conditions are found to exhibit several very interesting effects not seen for the corresponding solution or gas-phase reactions. Included among these are isotopic, orientational, and site selectivity. The reaction products obtained under matrix isolation conditions may be different from those obtained in the gas-phase or solution reactions and frequently the activation energies are significantly different. For some systems, mode-selective vibrational rate enhancement has been observed. Frei, Fredin, and Pimentel’S2 have reported results for several photochemically assisted reactions in cryogenic matrices. Several of the systems investigated exhibited mode-specified rate enhancement. Principal among these is the addition of molecular fluorine to ethylene: C,H,
+ Fz
+
CH2F-CH2F
(R1)
-
+ +
ergy surface should reveal the onset of many of the features associated with the dynamics of matrix-isolated reactions. The QCT results show that this is indeed the case.4 The dynamics for the 0 3 . N 0complex are found to exhibit mode-specific rate enhancement for reaction to form O2 + NO2 products, for vibrational predissociation (VP), and for intramode energy transfer. Structure specificity is also observed. We also find that excitation of the hindered internal rotation of NO about the O3 symmetry axis significantly influences the dynamic^.^ Unfortunately, the calculated dynamics for the vibrationally assisted reactions of the O,.NO van der Waals complex cannot be directly compared with the corresponding matrix-isolation studies since the presence of a “dark reaction” of the complex complicates the interpretation of the matrix isolation results.’*5 This problem does not exist for the ethylene-fluorine system. In addition, the chemistry of this system is more complex and interesting than that for the O,.NO reaction. In the gas phase, the primary products of the reaction are found to be fluorine atoms and fluoroethyl radicals6 C2H4
+ F2
+
‘CH2-CH2F
+F
(R2)
The quantum efficiency for R1 is found to increase over 5 orders of magnitude as the photon wavenumber increases from 953 to 4209 cm-I. However, the increase is neither smooth nor mono~ band of C2H4 at tonic. Excitation of the u2 + u , combination 3076 cm-l results in a quantum efficiency 3 times that obtained upon excitation of u I 1 at 2989 cm-’. In contrast, the quantum efficiency of ug at 3105 cm-I appears to be below that for the u2 u12 excitation. Knudsen and Pimenta13 have reported similar results for the reaction of allene with F, in N,, Ar, Kr, and Xe matrices at 12 K. As a first approach to the computational study of matrix-isolation chemistry, we have recently reported the results of quasi-classical trajectory (QCT) studies of vibrationally assisted re~ a complex actions of the 03.N0 van der Waals ~ o m p l e x . Such may be regarded as being a system intermediate between a bimolecular gas-phase system and one that is isolated in a matrix. It resembles the matrix system in that the molecules are held in close proximity with the individual molecular rotations partially quenched. On the other hand, it resembles the bimolecular system in that there are no third bodies to which vibrational energy may be transferred and the van der Waals binding forces are much less efficient in holding the molecules together than is a cryogenic matrix. Consequently, we expect that comparison of the reaction dynamics of the bimolecular gas-phase system with those of the corresponding van der Waals complex on the same potential-en-
In contrast, in the matrix-isolation experiments, the major products are either 1,2-difluoroethane or fluoroethylene and hydrogen fluoride depending upon the nature of the matrix material.’ No mode-specific rate enhancement has been found in the gas phase whereas there is good evidence for its presence in the Consequently, computational studies of the reaction dynamics of the bimolecular gas-phase system, the van der Waals complex, and the matrix-isolation reaction of this system could lead to a much improved understanding of the factors that influence the chemistry in each of these cases. The first requirement for the execution of such computational studies is the development of an acceptable potential-energy surface to represent the C2H4F2system. This is a formidable task which can only be accomplished with limited accuracy. The size and number of ab initio calculations required to characterize the entire surface are too great. This is particularly true in systems such as C2H, + F, where there exist several product channels and saddle-point regions that are important for the dynamics of the system. In addition, the use of arbitrary functional forms selected to achieve a least-squares fit of ab initio results often leads to difficulties unless physically motivated forms are used. Truhlar and Steckler8 have documented these difficulties in a recent review article. The above considerations suggest that the most productive line of attack will be semiempirical in nature. That is, we seek a global
( I ) Frei, H.; Fredin, L.; Pimentel, G. C. J . Chem. Phys. 1981, 74, 397. (2) Frei, H.; Pimentel, G. C. J. Chem. Phys. 1983, 78, 3698. (3) Knudsen, A. K.: Pimentel, G. C. J . Chem. Phys. 1983, 78, 6780. (4)Arnold, C.; Gettys, N. S.; Thompson. D. L.; Raff, L. M. J. Chem. Phys. 1986, 84, 3803.
(5) Frei, H.;Pimentel, G. C. J . Phys. Chem. 1981, 85, 3355. (6) Kapralova, G. A,; Chaiken, A. M.; Shilov, A. E. Kine?. Katal. 1967, 8 No. 3, 485. ( 7 ) Viswanathan, R.; Raff, L. M. J . Phys. Chem. 1983,87, 3251. ( 8 ) Truhlar, D.G.; Steckler, R. Chem. Rev., submitted for publication.
+
0022-3654/87/2091-3266$01.50/00 1987 American Chemical Society
Potential-Energy Surface for the C2H4F2System TABLE I: Atom Designations atom
carbons fluorincs hydrogens
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3267
0
(a) atom number
0
H
1 and 2 3 and 4 5 thri 8
STRUCTURE NO. 1
STRUCTURE NO. 2 Figure 2. Bonding structures 1 and 2. Atom numbers are enclosed in circles. TABLE II: Bond Angle Assignments structure 1
Figure 1. Interatomic distance notation for the C2H4F2 system. Atom numbers are enclosed in circles.
representation of the C2H4F2surface which correctly reproduces as many of the known chemical features of the system as possible. These include the exo- and endothermicities for each of the reaction channels, the measured fundamental vibration frequencies for the reactants and products, and the equilibrium bond lengths and bond angles for all reactants and products. In addition, the surface should yield reaction profiles and barrier heights that are in accord with the available kinetic data for the reactions in question. N o matter what is done, the system is so complex that any global representation of the potential-energy surface will necessarily be deficient in many respects. Nevertheless, if there are enough features of the surface that are in reasonable accord with experiment, then it should be possible to utilize the potential in various types of dynamics calculations to fully investigate van der Waals and matrix-isolation chemistry. In addition, such a surface would be useful in testing various approximate scattering theories in complex many-body systems. In this paper, we report the development of a first approximation to the C2H4F2potential-energy surface. Later papers will report the results of dynamics calculations using this surface. 11. Formulation
It is most convenient to express the potential-energy surface in terms of analytic functions of the interatomic distances and bond angles. For this purpose, we adopt the atom numbering given in Table I and the distance notation illustrated in Figure 1. The Ri (i = 1, 2) denote the interatomic distances between carbon no. 1 and the two fluorine atoms. The distances between this carbon
atoms forming angle
angle
2-1-5 2- 1-6 1-2-7 1-2-8 2-1-3 1-2-4 5- 1-6 5-1-3 6-1-3 7-2-8 7-2-4 8-2-4
01 01
83 04
85 86
07 08
0, 40 911 012
structure 2 atoms forming angle 2-1-5 2-1-6 1-2-7 1-2-8 1-2-3 2-1-4 5-1-6 5-1-4 6-1-4 7-2-8 1-2-3 8-2-3
angle 81
02
83 84
05 O6 91
98
99 4 0 811 012
and the four hydrogen atoms are labeled Ri ( i = 3,4, 5,6). The equivalent distances for carbon atom no. 2 are R, ( i = 7, 8 , 9, 10, 11, 12). RI3is the C-C distance. The fluorine-hydrogen distances are defined to be Ri ( i = 14, 15, 16, 17) and R, ( i = 18, 19, 20, 21) for fluorine atoms 1 and 2, respectively. Rz2 is the F-F separation. The six hydrogen-hydrogen distances are R, ( i = 23, 24, 25, 26, 27, 28), as shown. Since F2 can add across the ethylene double bond in either of two ways, we must consider the two possible bonding structures shown in Figure 2. In Figure 2a, fluorine atoms 3 and 4 are bonded to carbon atoms 1 and 2, respectively. The structure shown in Figure 2b has the bonding of the fluorine atoms reversed. We denote these two bonding structures as 1 and 2, respectively, and their corresponding potentials as V , and V2. There are 12 bond angles in 1,2-difluoroethane. These are assigned as shown in Table I1 for each of the two structures. We are also concerned with the CzH4 and CH,=CHF dihedral angles, 41 and 42. W e begin the formulation by taking the total potential of the C2H4F2system to be the exponentially weighted average of the VI and V, potentials V=
[vle-Avl
+ V , ~ - A ~ Z ] / [ ~ - A ~+ I e-Av~]
(1)
where A is a coupling parameter. In the limit of infinite A , we have
3268 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 V = min [Vl,V2]
(2)
That is, the system potential energy becomes the smaller of the potentials for the two bonding structures. For brevity, we describe the formulation of Vi only. The form of the potential for the second bonding structure is obvious from the symmetry of the system and the definitions given in Tables I and I1 and in Figure 1. In physical terms, we choose to represent the VI potential as the sum of bond stretching interactions plus bending potentials for each of the 12 angles along with torsional terms for the C2H4and CH2=CHF molecules. Each of these interactions is multiplied by appropriate switching functions so as to give the potential the correct asymptotic limits. In addition, each term is parametrized to allow the total potential to be fitted to the measured fundamental frequencies, equilibrium structures, and heats of reaction. The total potential for structure 1 is taken to be
Raff AI(RCF,RCH,R~~;W,A,U) = 12 - eXP(-U(RcF - R’cF)’) exP(-A(RcH - R’CH)’)] [ I - exd-o(R22 - R°FF)2)l (10) That is, Morse potentials operate between all H F pairs. These w,A,g) function potentials are attenuated by the AI(RcF,RcH,R~~; whenever the hydrogen atom bonds to a carbon or whenever a bonding interaction between fluorine and either carbon or the second fluorine atom exists. In eq 10, the notation RcF represents the instantaneous distance between the fluorine atom in the H F bond and carbon. A similar definition applies to R C H . In all equations, the notation R’,, denotes the equilibrium a-fl bond distance. The carbon-hydrogen interactions are pH(R,) = DCH[exp(-2aCH(R~- R°CH)) -
exp(-aCH(R~ - R°CH))l ( l
where DCH = DdCH- (DdCH- D,CH)S(Ri,R,,R4,Rs,R,,,R12;7,fl) (12)
F F ( R I ) + p F ( R s ) + PF(R2,) + i p C H ( 8 , )+
As in eq 5-7, DdCHand DsCH are the well depths for the C-H potential for double and single carbon-carbon bonds, respectively. “cH and R°CHare taken to be constant. The carbon-fluorine interactions are simple Morse functions:
r=l
6
c
FCF(8,)
+ VHCH(8,) + V H C H ( 8 l ’ ) + 5PCF(8,) + 1=8
i=5
12
2 VHCF(8,)+ VTC2H4(41)+ VTC2H~F(42) (3)
/=I I
The Vafl(RI)terms are bond stretching potentials for the bond whose distance is R,. These potentials are, in general, functionally dependent upon several interatomic distances. The notation Pfl(R,)therefore serves only to identify the bond involved. It does not specify the complete functional dependence of the term. The Vaflr(8,) are bending potentials for the angle 8,. The ethylene torsional potential is VTC2H4(41). The torsional potential for CH2=CHF is VTC2H3F(42).Again, the notation specifies only the angle involved in the bending motion and not the complete functional dependence of the term. These terms are defined as follows. The carbon-carbon interaction, Fc(R13), is a Morse-type function whose “parameters” vary with interatomic distance. FC(Ri3) = D c c [ ~ x P ( - ~ ~ c c -( RRcc)! I ~ - 2 exp(-%AR13 - R c c ) ~(4) ~
pF(R,)= D C F [ ~ X P ~ ~ % F-( R°CF)l RI - 2 exp(-“CF(Rr - R°CF)ll (13) The fluorine-fluorine bond interaction is given by PF(R22) = DFF[eXP(-2aFF(R22 - R°FF)] - exp(-aFF(R22 R°FF))1A2(Ri,R8;6) (I4) where A2(R,&; 6 ) = O.S[tanh (6(Rl- R°CF)) tanh (6(R8- ROCF)}] (15)
+
The F2interaction is attenuated by the A2(R1,R8;6)function as either fluorine atom forms a bonding interaction with carbon. All of the bending potentials have the quadratic form
~/.leye,) = osk,,,[o,
k,,, = k0,p,A3(R,,R,r)
Dcc = DdCC- (DdCC- D,CC)S(Ri,R3,R4,Rs,R,,,R,2;7,fl) (5) =
adcc
- (adcc
-
a,Cc)S(Ri,R3,R4,Rs,R,irR12;~,P) (6)
Rcc = RdCC- (RdCC- R,Cc)S(Ri,R,,R4,Rs,Ri~,Ri2;~,P) (7) with S(Rl,R3&R8>RI I,Rl2;73fi) = tanh2 [y(eXp(-fl[Rl + R3 R4 - ~R’cH- R’cF]) exp(-P[& + Rll + R12 - 2R°CH - R’CF])~] (8)
+
In eq 5 , DdCCand Dscc are the potential well depths for the carbon-carbon double and single bonds, respectively. a d c c and ‘a: are the curvature parameters and RdCCand R F C are the equilibrium bond distances for double and single bonds, respectively, in eq 6 and 7. The switching function defined by eq 8 alters the Morse parameters in eq 5 from those characteristic of carbon-carbon single bonds to those appropriate for the carboncarbon double bond as either of the following reactions occur CHZF-CH2F CH,=CH, + F2 (R3)
(16)
where
where
“CC
- eoaBr]2
(17)
= 8dnBr - (8dn/.ler- 8s*PY)S(Ri,R3,R4,R,,R~ i9Ri2;7,P) (18)
with A ~ ( R , , R ~ ;=~ )exp[-r((R, -
+ ( R , - Ro,)211
(19)
In eq 17-19, R, and R, are the two interatomic distances forming and Ro,are the corresponding equilibrium the aPy angle and p,, bond distances. and 8//.leY are the equilibrium angles for carbon-carbon double and single bonds, respectively. Equation 17 attenuates the bending force constant, kaB7,as either of the two bonds forming the angle begins to undergo dissociation. The C2H, torsional potential is given by VTC2H4(@l)=
k,@12A4(RI,R!3;t)
(20)
where k , is the torsional force constant and 4, is the C2H4 dihedral angle with 4, = 0 for the planar conformation. The A4(RI,RS,t) function attenuates the torsional potential as either fluorine atom adds across the ethylene double bond. Its form is
+
CHIF-CH2F
-+
CH,=CHF
+ HF
(R4)
The H F interactions are VHF(R,) = 0.jDHF[eXP(-2aHF(RI - R ’ H F ) J - 2 exp(-aHF(R, R’HF)11A I(Rc~&xd?nW,A,o) (9) where
A4(Rl,Rg;t) = tanh (t(Rl - A’cF))tanh (t(R8 for A4(R1,R,;t)> 0; A4(R1,RB;t)= 0 otherwise Roc,)} (21)
The torsional potential for CH2=CHF must take into account the fact that there are four possible ways to form the fluoroethylene molecule depending upon which fluorine atom bonds to carbon and which hydrogen atom is abstracted. If we denote the four
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3269
Potential-Energy Surface for the CzH4FzSystem TABLE III: Equilibrium Morse "Parameters" for Diatomic Pairs
diatomic pair 7-6
c-c F-F H-F C-H C-F H-H
D.Tfl. eV 3.925 00 1.650 04 6.1 1450 4.842 30 5.01800 4.74000
A-1
Rod. A
1.686 40 2.901 65 2.21980 1.8 10 00 1.991 00 1.974 00
1.57000 1.41801 0.917 10 1.07 1 00 1.39800 0.74000
C&yfl,
TABLE I V Bending Potential Parameters angle ~ 0 - 7koasu,eV/rad2 B,"@y, rad 3.450 1.90241 C-C-H C-C-F 6.507 1.902 41 H-C-H 3.444 1.902 41 H-C-F 4.627 1.90241
rad 2.094 2.094 2.094 2.094
TABLE V Carbon-Carbon Double Bond Parameters and Torsional Force Constants Darameter value Darameter value Ddcc,eV 6.454 DdCH,eV 5.048 1 adcC, A 2.200 k,, eV/rad 4.50 RdCC,A 1.353 TABLE VI: Switching and Attenuation Parameters parameter value parameter 6, A-' Y 2.500 fl, A-I 2.850 r, A-2 w , A-2 2.300 6 , A-l A, A-2 2.300 A , eV-l 6,A-2 2.300
value 2.000 0.44804 1.ooo 15.000
CH,=CHF molecules in structure 1 by the index (i = 1, 2, 3, 4), the CH2=CHF torsional potential has the form
carbon double bonds. Two parameters are used to adjust the rate at which the double bond-single bond parameters are switched. The five attenuation functions, A , , AI, A3, A4, and AScontain six parameters. The remaining parameters are the torsional force constant and the coupling constant. The equilibrium Morse potentials are adjusted to fit the experimentally measured well depths, fundamental frequencies, and bond distances for FZ, HF, and H2 diatomic pairs. The Morse parameters for the C-C, C-H, and C-F pairs are adjusted to fit the structure, energetics, and fundamental frequencies of reactants and products. The results of this fitting are given in Table 111. The equilibrium carbon-carbon single- and double-bond angles are taken to be the tetrahedral angle and 120°, respectively. The four bending force constants, the torsional force constant, and the double-bond curvature parameter, adcc,are adjusted to the 12 measured fundamental vibration frequencies of CzH4and to the C-F and X-C-F (X = H, C) stretching and bending frequencies. Ddcc, DdCH,and RdCCare fitted to the measured c=c and C-H bond energies in C2H4 and to the measured equilibrium carboncarbon distance in ethylene, respectively. The values of these parameters are given in Tables IV and V. The best values for the remaining nine parameters in the switching function S ( R 1 , R 3 , R 4 , R 8 ,l,R12;y,/3) Rl and the five attenuation functions are more difficult to determine. Their values, along with the coupling constant, influence some of the heats of reaction and the potential barriers for the various reaction channels. Due to the arbitrary semiempirical form of eq 3, no parameter set could be determined which reproduced the measured data for all of these properties. Nevertheless, the functional form of eq 3 is sufficiently flexible that it is possible to obtain values for these parameters which give barrier heights and heats of reaction in fair to excellent accord with experiment. Table VI lists the values used. 111. Properties of the Surface
4
VTc2H'F(c#J2)= Ck&2:AS(RiH,Rfie) i= 1
where c#J21 is the CH,=CHF dihedral angle for molecule i and R I Hand R,Fare the C-H and C-F distances for the hydrogen and fluorine atoms forming the H F molecule, respectively. The attenuation function, A s , is given by
A5(RlH,RlF;e) = tanh [t(R," - R o C H )tanh ] [ t ( R I F> 0, A5(RlH,RlF;e) = 0 otherwise R o C F ) ] for As(R,H,RIF;e) (23) Equation 3 contains 41 adjustable parameters. Eighteen of these are the equilibrium well-depth, curvature, and bond distance parameters for the six possible diatomic pairs. Eight parameters give the equilibrium bending force constants and associated equilibrium angles for the four different bends in C2H4F2. Five parameters are associated with well depths, curvature, equilibrium C-C bond distance, and the equilibrium bond angle for carbon-
III.A. Equilibrium Structures and Heats of Reaction. The Morse parameters for F2, H2, and H F have been fitted to the measured equilibrium bond lengths, dissociation energies, and fundamental vibration frequencies. So these properties are in good accord with experiment. The equilibrium structures for the polyatomic species have been determined by using trajectories in which all momenta are set to zero each time the kinetic energy attains a maximum. This procedure is repeated until the structure converges to a local minimum. By sampling different initial configurations, the equilibrium structures predicted by eq 1 can be determined. The results are given in Table VI1 where H,FC-H refers to a C-H distance for a carbon atom to which a fluorine atom is bonded. Similarly, H,C-H is a C-H distance for a carbon atom to which no fluorine atom is bonded. Analogous notation is used for the various azimuthal angles. The predicted structure for C2H4is in excellent accord with that reported by Galloway and Barker9 who found R(C-H) =
TABLE VII: Equilibrium Structures and Energies' C2H4F2
variable distances
eclipsed
C-F H,FC-H H,C-H
1.402 1.071
c-c
1.570
angles C-CH,-H C-CF-H C-C-F energy
trans 1.398 1.072 1.570
CH2-CH2F 1.398 1.073 1.071 1.570 109.06
109.57 109.27 -33.3297
109.56 109.27 -33.3292
108.93 109.10 -28.3986
+F
CH,=CHF
+H +F
1.398 1.07 1 1.O7lb 1.071' 1.353 1 19.99d 119.99e 120.00 120.01 -26.6163
'
CH2=CH2
+ 2F
1.071 1.353 119.98
-26.6464
"Distances are in angstroms. Angles are given in degrees. All energies are given relative to the separated atoms taken to be the energy zero (in
eV). bC-H distance eclipsed by hydrogen. eC-H distance eclipsed fluorine. dC-C-H angle for hydrogen eclipsed by hydrogen. 'C-C-H angle for hydrogen eclipsed by fluorine.
3270 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
Raff
TABLE VIII: Equilibrium Structure and Energy for CH,-CH,P
group CH2F R(C-H) R(C-F) LC-C-F LC-C-H CH2 R(C-H) LC-C-H R(C-C) energy
eq 1
SCF (6-31G basis)
1.073 1.398 109.10 108.93
1.082 1.419 110.48 112.13
1.071 109.06 1.570 -28.3986
1.072 120.01 1.484
WAVE N
Figure 3. Calculated spectral density, eq 26, for C2H4.
ODistances are in angstroms. Angles are given in degrees. Energy is in electrovolts.
TABLE X Comparison of Computed and Measured Vibration Frequencies for Ethylene"
TABLE 1X: Heats of Reaction (kcal/mol)
reaction C2H4 + Fz CH2F-CH2F C2H4 + F2 CHz-CHlF + F C2H4 + F2 CH,=CHF + HF -+
4
4
mode ea 1
exma
-1 16.07 -2.4 -102.3
-1 16.1 -14.0 -108.9
Reference 1.
UI(Ag) V2(Ag) U3(Ag)
U4(A") vs(B1,) u6(Blg)
U7(BI~) 1.071 A, R ( C = C ) = 1.353 A, and an H-C-H angle of 119.92'. Electron diffraction measurements on gas-phase 1,Zdifluoroethane have given values in the following ranges:1w121.103 A < R(C-H) < 1.13 A; 1.384 A < R(C-F) < 1.394 A; 1.502 A < R(C-C) < 1.535 A; 108.3' < L(C-C-H) < 11 1.0'; and 108.3' < L(CC-F) < 11 1.2'. The equilibrium bond lengths and angles given in Table VI1 are in good agreement with these results. However, the experimental measurements show the gauche form of 1,2difluoroethane to be the most stable conformation.'O The rotation barrier between trans and gauche forms lies in the range 1.4-2.4 kcal/mol. In contrast, eq 1 predicts both conformers to have nearly identical energies with little or no internal rotation barrier. The experimentally measured C-H bond lengths in fluoroethylene all lie in the range 1.076-1.090 The values predicted by eq 1 are therefore low by 0.006-0.01 5 A. The measured C = C equilibrium distance is 1.333 A compared to 1.353 A given by the potential surface. The equilibrium C-F bond length is 1.348 A.12Equation 1 yields 1.398 A. The experimental C-C-F angle is 120.98' in good agreement with the result given in Table VII, but the measured C-C-H angles are uniformly larger than the 120.0° values given by eq 1. The measured results are 121.41°, 123.92', and 127.7Oo.l2 The gas-phase structures of the radical species are not wellknown. We have carried out a b initio calculations at the S C F level using GAUSSIAN 82 with a 6-31G basis set to determine the equilibrium structure for the fluoroethyl radical. A comparison of the results with those given by eq 1 is reported in Table VIII. The C-C-H and C-C-F angles tend to be too small. Equation 1 predicts that the C H 2 group will essentially be sp3 hybridized whereas the S C F calculations show the C-C-H bond angle for this group to more characteristic of sp2 hybridization. The equilibrium bond lengths given by eq 1 and the S C F results are in fair accord. The predicted heats of reaction for various reaction channels are compared with the measured values in Table IX. The average absolute error for these results is 6.1 kcal/mol. 1II.B. Fundamental Vibration Frequencies. Ethylene. The C-H and C=C curvature parameters, the C-C-H and H-C-H (9) Galloway, W. S.; Barker, E. F. J . Chem. Phys. 1942, 10, 88. (10) (a) Fernholt, L.; Kveseth, K. Acra. Chem. Scand. A 1980, 34, 163.
(b) Friesen, D.; Hedberg, K. J . Am. Chem. SOC.1980, 102, 3987. ( 1 1) van Schaick, E. J. M.; Geise, H. J.; Mijlhoff, F. C.; Renes, G. J . Mol. Struct. 1973, 16, 23. (12) Carlos, Jr., J. L.; Karl, Jr., R. R.; Bauer, S. H. J . Chem. Soc., Faradav Trans. 2 1974. 70. 177. (1 3) Herzberg, G: Infrared and Raman Spectra; van Nostrand: Princeton, NJ, 1945; p 326. (14) Herzberg, G. Infrared and Raman Spectra; van Nostrand: Princeton, NJ, 1942; p 107.
uS(B2g)
u9(B2u) uIO(B2,,) u,,(B3J
uI2(B3J
description C-H stretch H-C-H bend C=C stretch out-of-plane C-H stretch C-C-H bend out-of-plane out-of-plane C-H stretch C-C-H bend C-H stretch H-C-H bend
kptb
vcalcd
3019 1623 1342 825 3272
1050 949 943 3106 995 2990 1444
(eq 1)
3065 1829 1331 744 3304 1126 785 785 3126 1106 3024 1563
'Wavenumbers are given in cm-'. *Reference 13. bending force constants, and the C2H4 torsional force constant have all been adjusted to fit the 12 fundamental vibration frequencies of ethylene. The fundamental frequencies on the model surface have been obtained by computation of the spectral intensity. The spectral intensity is calculated directly from the Fourier transforms, C,(mAv), of a set of momentum components, bond angles, or bond lengths N
C,(mAv) = N-' Cexp[27rinm/A$Sol(nAt)
(24)
I='
In eq 24, S,(nAt) represents either a momentum component, bond angle, or bond length at time t = nAt (n = 0, 1, 2, ..., A') in a trajectory of duration 7. The resolution, Av, of the transform depends upon the length of the trajectory Av = 2 a / r
(25)
The spectral intensity, g(mAv), is defined to be the sum of the normalized power spectra for each Sa(mAv): g(mAv) =
C[ F a a
12/ C I C e ( mAv) I2I m
(26)
Figure 3 shows the calculated spectral density for C2H4 where the S,(nAt) are the four C-H bond distances, the C=C bond distance, the four C-C-H angles, the two H-C-H angles, and the CH2=CH2 dihedral angle. The spectral resolution is 6.83 cm-l. The four C-H stretching modes appear at frequencies between 3000-3300 cm-'. The fundamental frequencies for each of the modes is somewhat uncertain due to the statistical noise and the limited spectral resolution. If we use the nominal peak maxima, the results are 3024, 3065, 3126, and 3304 cm-', which is in very good accord with the measured frequencies. The two modes corresponding primarily to H-C-H bends are seen at 1563 and 1829 cm-l. The C=C stretch appears at 1331 cm-I. The two C-C-H bending modes are nearly degenerate. We might interpret the band around 1100 cm-I as consisting of two peaks at 1106 and 1126 cm-'. These are in fair agreement with the 995- and 1050-cm-' bands seen in the IR. The low-frequency out-of-plane modes are seen in Figure 3 below 800 cm-I. Only two peaks can be resolved. These appear
Potential-Energy Surface for the CZH4F2System
The Journal of Physical Chemistry, Vol. 91. No. 12, 1987 3271 TABLE XI: Comparison of Computed and Measured Vibration Frequencies for 1,2-Difluoroethane mode descriotion obsdb calcd rocking 355 416 rocking 320 rocking
Figure 4. Calculated spectral density, eq 26, for 1,2-difluoroethane.
at 744 and 785 cm-I, which is 80-160 cm-' below the observed values for these modes. A comparison between the results obtained on the model surface and experiment is given in Table X. The average absolute deviation is 88 cm-I. 1,2-Difluoroethane. The C-F curvature parameter and the H-C-F and C-C-F bending force constants are adjusted to give reasonable C-F stretching and bending frequencies for 1,2-difluoroethane. With only three adjustable parameters, it is clearly not possible to fit the entire C2H4FZvibrational spectrum. Nevertheless, the results are in fair accord with measured values. Klaboe and Nie1se1-1'~have reported extensive Raman and IR spectra for 1,Zdifluoroethane in the gas, liquid, and solid states at five different temperatures between 25 and 180 "C. They have identified 16 fundamentals in the gas-phase spectra. Strong bands corresponding to C-F stretches are observed at 1088 and 1246 cm-I. The four C-H stretching fundamentals are seen at 2895, 2966, 2987, and 2994 cm-I. Six fundamentals corresponding to C H 2 F deformation modes are observed between 897 and 1462 cm-I. Finally, Klaboe and N i e l ~ e nhave ' ~ identified three rocking modes at 320, 498, and 780 cm-I. Figure 4 shows the computed spectral density for S,(nAt) chosen to be the 24 Cartesian momentum components of 1,2difluoroethane. These results were obtained from the power spectra of a trajectory integrated for 2.59 X 10-'2s to give a spectral resolution of 6.83 cm-I. The modes corresponding to the translations and rotations appear at low frequency, as expected. There are clearly three modes whose fundamental frequencies are between 300 and 500 cm-'. The nominal peak positions indicate these fundamentals are at 355,416, and 505 cm-'. Apparently these modes correspond to the rocking fundamentals identified by Klaboe and Nie1~en.I~ Between 700 and 1000 cm-l, there are three closely spaced modes. The intense band a t 778 cm-' is in near-quantitative agreement with the rocking fundamental observed by Klaboe and Nielsen at 780 cm-'.I5 The peak maxima for the other two bands are 840 and 874 cm-I. The first of these is very close to the observed C-C stretch at 857 cm-I.l5 The 874-cm-' band apparently corresponds to a CH2F deformation mode. The C-F stretching modes are seen at 1065 and 1229 cm-' in Figure 4. Experimentally, these fundamentals are at 1088 and 1246 cm-'.15 Figure 4 shows at least three, and possibly four, modes between 1300 and 1600 cm-I. The three intense bands have peak maxima at 1379, 1488, and 1577 cm-I. The small shoulder on the lowfrequency side of the 1577-cm-' band lies at 1556 cm-'. Klaboe and Nielsen15 observe four fundamentals corresponding to CHzF deformations between 1274 and 1462 cm-l. The four C-H stretching modes are closely bunched between 2921 and 3078 cm-I. The peak maxima suggest that these fundamentals are at 2921, 2935, 2955, and 3078 cm-', which is in fair agreement with the observed I R spectrum.IS Table XI compares the calculated frequencies with those observed by Klaboe and N i e l ~ e n . 'The ~ average absolute deviation between the two is 62 cm-I. In general, there is good agreement for the rocking modes, the C-C stretch, and the C-F and C-H (15) Klaboe, P.; Nielsen, J.
R.J . Chem. Phys. 1960, 33, 1764.
rocking C-C stretch CH2Fdeformn C-F stretch CH2F deformn C-F stretch CH2Fdeformn CH2F deformn CH2F deformn CH2F deformn C-H stretch C-H stretch C-H stretch C-H stretch
897
505 778 840 874
1088
1065
498 780
857 1112
1246
1229
1274 1295 1402 1462 2895
1379 1488 1556 1577 2921 2935
2966 2987 2994
2955 3078
"Wavenumbers are given in cm-'. bReference 15.
F
H
x
x
Figure 5. Planar pathway for concerted HF elimination from 1,2-difluoroethane. 0
_I fl
2b.00
4b.00
60.00
I 3.00
STEP NUMBER Figure 6. Reaction profile for the planar, concerted elimination of HF
from 1,2-difluoroethane. stretches The calculated frequencies for the high-frequency CH2F deformation modes are generally too high by about 100 cm-I. III.C. Barrier Heights and Reaction Profiles. We have determined approximate reaction profiles and barrier heights for reactions R1, R3, and R 4 occurring via concerted, planar elimination pathways. Figure 5 illustrates the type of reaction path examined. We assume the H F elimination reaction occurs in a plane containing the two carbon atoms and the H F molecule undergoing elimination. For a small abstraction distance, 6, the angles a and /3 shown in Figure 5 are varied until the minimumenergy configuration is obtained. At each point, the backside hydrogens, the second fluorine atom, and the C-C distance are relaxed to their most stable configurations. This process is repeated
3272 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
Raff
0
15'4'312
-1
-xi B
"5
> '
6
">T
t J
W
W v,
r "0.00
20.00
40.00
60.00
4.0
t Il1
I I
3.0
80.00
STEP NUMBER
Figure 7. Reaction profile for the planar, concerted elimination of F2 from 1,2-difluoroethane.
until reaction R4 is essentially complete. A similar procedure is used for reaction R3. The calculated reaction profile for the planar, concerted elimination of H F from 1,2-difluoroethane is shown in Figure 6. Each unit along the abstraction coordinate represents a displacement, 6, of 0.1 A. The saddle-point position corres onds to a total displacement of C-H and C-F bonds of 1.1 . The HF abstraction barrier along this path is 64 kcal/mol. Pritchard, Venugopalan, and Graham16 and Pritchard and Bryant" have examined the decomposition of hot 1,2-difluoroethane obtained by photolysis of CH2FCOCH2F. Benson and Haugen'* have used RRK theory to fit their data and have thereby obtained an activation energy for H F elimination of 62 f 3 kcal/mol. The barrier height obtained on the model surface is in good agreement with this result. Figure 7 shows the calculated reaction profile for the planar, concerted elimination of F2 from 1,2-difluoroethane. Each unit along the abscissa represents a 0.1-8, displacement of each C-F bond. The saddle-point position therefore corresponds to a total displacement of 2.0 A. The calculated F2abstraction barrier is 128.4 kcal/mol. Figure 7 also shows that the back reaction, R1, has a barrier of 12.3 kcal/mol. This back-reaction barrier is dependent upon the value chosen for the coupling parameter in eq 1. In the limit of large A , the back-reaction barrier is 13.9 kcal/mol. The countour map for F2 planar elimination along a C2,pathway is given in Figure 8. The saddle point for the 12.3 kcal/mol back-reaction barrier is seen to lie at a C2H4-F2 center-of-mass separation of about 3.0 with an F2 distance about 1.45 A.
w
F-F DISTANCE
(i)
Figure 8. Potential-energy contour map for a C, approach of F, to C,H,. The F2 bond axis lies parallel to the C2H4plane. At each point on the surface, the internal CzH4structure is relaxed to its most stable configuration for the specified F2-C2H4center-of-mass separation and F2 distance. Energies are given in electronvolts relative to the separated atoms taken to be the energy zero. Region B corresponds to reactants F2 + C2H4while the region denoted by A is 1,2-difluoroethane.
IV. Discussion The semiempirical potential-energy surface formulated in section I1 describes many of the C2H4F2properties with fair to good accuracy. Equilibrium geometries are generally correct to within 0.05 A for the bond lengths and a few degrees for the bond angles. The error for the reaction endo- and exothermicities varies from 1 1.6 kcal/mol for reaction R 2 to essentially zero for reaction R1. The fundamental vibration frequencies for C2H4and
1,2-difluoroethane are reproduced with fair accuracy. The predicted barrier height for reaction R4 is in good accord with the measured activation energy.16-'* Although many of the topographical features of the surface are accurate, others are not. In some cases, the errors may be large and serious in their effect upon particular properties of the system. Apart from the inaccuracies that have been documented in section 111, other errors are present. The simple function given in eq 3 cannot correctly represent the interaction regions of such a complex system. The geometries, fundamental frequencies, and barrier heights of the various transition states are unknown, but it is unlikely that they are accurately represented by eq 3. We therefore can regard the potential described by eq 1 as being only an approximate representation of the true surface whose topographical features are almost entirely unknown. In spite of its obvious defects, eq 3 provides a very convenient starting point for the theoretical study of the reaction dynamics of complex, many-body systems. The global functions employed in eq 3 have a relatively simple form that will facilitate various types of dynamics studies. Furthermore, many of the features of the surface are sufficiently accurate that the results of dynamics calculations may be nearly correct. This is particularly true if the property under investigation is not very sensitive to those topographical features of the surface that are the least accurate. Finally, the availability of this surface and the dynamics studies that follow will provide the impetus for further calculations that will eventually lead to improved potential surfaces for the system.
(16) Pritchard, G. 0.;Venugopalan, M.; Graham, T. F. J . Phys. Chem. 1964, 68, 1786. ( 1 7 ) Pritchard, G. 0.;Bryant, J . T. J . Phys. Chem. 1965, 69, 1085. (18) Bensoii, S. W.; Haugen, G. J . Phys. Chem. 1965, 69, 3898.
Acknowledgment. All calculations in this work were carried out on a VAX 11/780 purchased, in part, with funds provided by a grant from the Department of Defense University Instrumentation Program, AFOSR-85-0115.
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