Energy Disposal in Reactions of Fluorine Atoms ... - ACS Publications

9 Energy Disposal i n Reactions of Fluorine Atoms w i t h Polyatomic H y d r i d e Molecules as Studied b y Infrared Downloaded by CALIFORNIA INST OF TECHNOLOGY on November 16, 2017 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0066.ch009

Chemiluminescence DENIS BOGAN* Chemical Dynamics Branch, 6180, Naval Research Laboratory, Washington, D C 20375 D. W. SETSER Department of Chemistry, Kansas State University, Manhattan, KS 66506

Understanding reactive collisions at the microscopic level is a long standing goal of chemical kinetics. The potential energy is the cause of chemical change and is responsible for rearrangements of chemical bonds and for the energy states of the product molecules. Through study of the energy disposal, i.e., the partitioning of energy to the various possible quantum states of the products, properties of the potential energy surface can be inferred. The principal experimental methods for measuring energy disposal have been crossed molecular beams (1,2), laser emission or probing (3,4), and infrared chemiluminescence. The basis for infrared chemiluminescence experiments is the analysis of the infrared emission emanating from vibrationally excited molecules. The results and interpretations of infrared chemiluminescence studies of the reactions of F atoms with polyatomic hydride molecules are reviewed and discussed herein. The infrared chemiluminescence technique has been pioneered by J. C. Polanyi (5-21). The University of Toronto group has concentrated on three-body reactions and more recently on reactions with vibrationally and translationally excited reagents (14-21). At Kansas State University attention has been directed to reactions of F atoms with polyatomic hydrides (22-33); a large body of data has been obtained and information theory has been used for interpretation (31,32). Other groups working in the HF infrared chemiluminescence field are those of Jonathan (40,41), (University of Southhampton), McDonald (34-39),(University of Illinois) and Y. K. Vasiljev (42), (Academy of Sciences, USSR). Interesting work with CO infrared chemiluminescence has been done by Smith (43,44) and others (38,45). *Postdoctoral fellow, Kansas State University, 1972-1974; National Research Council Associate, 1974-1976; Staff Scientist from 1976 at Naval Research Laboratory. © 0-8412-0399-7/78/47-066-237$10.00/0

Root; Fluorine-Containing Free Radicals ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

238

FLUORINE-CONTAINING FREE

HF i s p a r t i c u l a r l y amenable t o i n f r a r e d s t u d i e s for the f o l l o w i n g reasons: a)

Downloaded by CALIFORNIA INST OF TECHNOLOGY on November 16, 2017 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0066.ch009

tomic

i t has the l a r g e s t molecule,

RADICALS

chemiluminescence

t r a n s i t i o n p r o b a b i l i t i e s of

any

dia

b) t h e l a r g e v i b r a t i o n a l and r o t a t i o n a l e n e r g y s p a c i n g s f a c i l i t a t e t h e a s s i g n m e n t o f v i b r a t i o n a l and r o t a t i o n a l d i s t r i butions, c) t h e a c t i v a t i o n e n e r g i e s f o r 0-2 k c a l / m o l e ; h e n c e , the r e a c t i o n s emission,

F atom r e a c t i o n s a r e l o w ( 4 6 ) , a r e f a s t g i v i n g s t r o n g IR

d) f l u o r i n e atom r e a c t i o n s a r e h i g h l y e x o t h e r m i c s t r o n g l y n o n - B o l t z m a n n HF p r o d u c t d i s t r i b u t i o n s .

and

give

There a l s o a r e p r a c t i c a l needs f o r u n d e r s t a n d i n g the dynamics of r e a c t i o n s p r o d u c i n g H F , s i n c e t h i s k n o w l e d g e may f a c i l i t a t e s e l e c t i o n o f b e t t e r f u e l s and o p t i m i z a t i o n o f o p e r a t i n g c o n d i t i o n s f o r HF l a s e r s . M c D o n a l d and c o w o r k e r s ( 3 4 , 3 6 , 3 7 ) have s t u d i e d i n f r a r e d c h e m i l u m i n e s c e n c e f r o m p o l y a t o m i c p r o d u c t m o l e c u l e s formed by a d d i t i o n - d i s p l a c e m e n t r e a c t i o n s of the type F + CH =CHX 2

+

CH =CHF + Χ (X = H , C H , C l , B r ) , 2

3

(1)

a s w e l l a s r e a c t i o n s w i t h b e n z e n e and s u b s t i t u t e d b e n z e n e m o l e cules. V a l u a b l e i n s i g h t i n t o the energy d i s t r i b u t i o n i n p o l y atomic p r o d u c t m o l e c u l e s from u n i m o l e c u l a r r e a c t i o n s has been o b t a i n e d from t h i s work ( 4 7 ) . B a s i c s of

the I n f r a r e d Chemiluminescence

Technique

The e x p e r i m e n t s i n v o l v e m i x i n g f l u o r i n e atoms w i t h a h y d r i d e r e a g e n t w i t h o b s e r v a t i o n o f t h e e m i s s i o n f r o m t h e r e s u l t i n g HF product. F + HR

•>

HF+j + R

(2)

F l u o r i n e atoms u s u a l l y a r e p r o d u c e d by a m i c r o w a v e d i s c h a r g e t h r o u g h C F ^ o r S F ^ . F i g u r e 1 shows a s c h e m a t i c d i a g r a m o f a v e s s e l w i t h l i q u i d n i t r o g e n c o o l e d i n n e r w a l l s t h a t has been used for "arrested r e l a x a t i o n " experiments. Such a v e s s e l a r r e s t s v i b r a t i o n a l r e l a x a t i o n and p a r t i a l l y a r r e s t s r o t a t i o n a l r e l a x a tion. The maximum f r a c t i o n o f t h e s u r f a c e s h o u l d be c o o l e d f o r a r r e s t e d r e l a x a t i o n s t u d i e s w i t h HF b e c a u s e c o l l i s i o n s o f H F ^ j w i t h warm s u r f a c e s r e s u l t i n some r e l a x a t i o n w i t h s u b s e q u e n t r e e n t r y o f t h o s e m o l e c u l e s i n t o t h e cone o f s i g h t o f o b s e r v a t i o n . M i r r o r s u s u a l l y a r e p l a c e d i n s i d e t h e v e s s e l t o more e f f i c i e n t l y c o l l e c t the i n f r a r e d r a d i a t i o n .


9.

BOG AN

AND

Energy

SETSER

Disposal

in Reactions

of

239

Fluorine

I n f r a r e d r a d i a t i o n i s observed under steady s t a t e condi t i o n s , and the f o l l o w i n g equations can be w r i t t e n f o r each v i b r a t i o n a l (as shown) or r o t a t i o n a l l e v e l (6).

d[HF+] 0 = — τ — = k [RH][F]

+ ΣΑ, v

V

V


T

-

N

2k ,v-v»N v" z

V

z

V

f

- k N

v

p

Ξ [ H F ^ ] = concentration

v

N » + Ek v

»_ N » ' V

-

V

ΣΑ _ "Ν v" ν

ν

ν

(3)

v

of HF

i n state ν

k [ R H ] [ F ] = r a t e of format i o n of HF^, from the chemical reaction V

A »_ N » v

k

V

T

z 5

v -vN

A _ "N V

k

z j V

V

v

v

T

=

v

v

f

c o l l i s i o n a l r a t e i n t o s t a t e ν from v

= r a d i a t i v e r a t e out of ν i n t o

V

_ "N

kpN The

= r a d i a t i v e r a t e i n t o s t a t e ν from v

V

v

f

M

= c o l l i s i o n a l r a t e out of ν i n t o v"

= r a t e of removal by pumping of H F J

steady s t a t e expression f o r [HF^j k [RH][RF] V

[ H F

v

]

=

k

is f

N

+ Σ Α ' _ Ν ' + £kz,v -v v ν

ν

+ ΣΑ - " + E k ν

ν

v"

f

ν

z ? v

( 4 )

_ " v

v"

I f the r a t e of removal by pumping i s s i g n i f i c a n t l y greater than any of the r a d i a t i v e or c o l l i s i o n a l terms then the steady s t a t e becomes

[HF+]

=

k^RHHF] r .

(5)

P

FC

With proper design of the r e a c t i o n v e s s e l and with adjustment of flow r a t e s , i t i s p o s s i b l e i n p r a c t i c e to cause k [ R H ] [ F ] and k to dominate the steady s t a t e expression (eq. 5). Since [ H F J ] α I , the measured emission i n t e n s i t y from l e v e l v, then k α I f o r such experimental c o n d i t i o n s . A s i m i l a r a n a l y s i s can be derived f o r the r o t a t i o n a l populations of a given ν l e v e l . Unfor tunately, some r o t a t i o n a l r e l a x a t i o n i s always present, even i n V

v

v


v


240


RADICALS

the best experiments. For the a r r e s t e d r e l a x a t i o n apparatus, with molecules other than Ή2, CH4 or SiH^, the p r i n c i p a l pumping, under t y p i c a l c o n d i t i o n s , i s cryopumping by the l i q u i d n i t r o g e n cooled w a l l s . Since the HF emission i n t e n s i t y i s weak under a r r e s t e d r e l a x a t i o n c o n d i t i o n s , good l i g h t c o l l e c t i o n o p t i c s and a low f/number spectrometer must be used. For work at Kansas State U n i v e r s i t y , the apparatus c o n s i s t e d of a Welsh c e l l l i g h t c o l l e c t i o n system (48,49) w i t h i n the c o l d w a l l v e s s e l , a 0,25 meter f/4.3 g r a t i n g monochromâtor, HR-8 l o c k - i n a m p l i f i e r and cooled (77°K) PbS photo-conductive d e t e c t o r . The alignment procedure f o r the Welsh c e l l has been d e s c r i b e d (50). In our work the o p t i m i z a t i o n of alignment was done u s i n g a flame s i m u l a t o r cons t r u c t e d of nichrome wire wrapped on a g l a s s cane framework and placed i n the reagent mixing r e g i o n . The a b s o r p t i o n due to a t mospheric water was minimized by e n c l o s i n g the f o r e - o p t i c s and spectrometer i n a p l e x i g l a s s box which was continuously swept with pneumatically d r i e d a i r . Some work a l s o has been done u s i n g the "measured r e l a x a t i o n " technique (18,33,40,41) which can g i v e i n i t i a l v i b r a t i o n a l d i s t r i b u t i o n s and r e l a t i v e t o t a l r a t e constants f o r d i f f e r e n t RH molecules. T h i s technique u s u a l l y i n v o l v e s a flowing a f t e r g l o w apparatus with bulk flow v e l o c i t y i n the 100 m sec regime (33,40,41). In these experiments the r e a c t a n t s are mixed at v a r i o u s d i s t a n c e s , which can be converted to times, upstream of an o b s e r v a t i o n window. The observed r o t a t i o n a l populations are relaxed to a Boltzmann d i s t r i b u t i o n ; however, the v i b r a t i o n a l r e l a x a t i o n can be followed as a f u n c t i o n of time and can be ext r a p o l a t e d to o b t a i n the i n i t i a l populations at zero time. The HF"î* i n t e n s i t y from a given v , J l e v e l i s given by (51). 1

f

ΐ£.;ί'

f

= [HF+, ]A^«;j"; J t

(6)

A = E i n s t e i n c o e f f i c i e n t f o r spontaneous emission, the primed and double primed quantum numbers r e f e r to the upper and lower s t a t e s of the r a d i a t i v e t r a n s i t i o n , r e s p e c t i v e l y . The photon f l u x ( i n t e n s i t y ) a s s o c i a t e d with each r o t a t i o n a l l e v e l i s obtained from the observed i n t e n s i t y a f t e r c o r r e c t i o n f o r the v a r i a t i o n of the s p e c t r a l s l i t f u n c t i o n and the o v e r a l l spectrometer response with wavelength. The s p e c t r a l s l i t f u n c t i o n i s o f t e n given by the spectrometer manufacturer and can be determined experimentally (along with wavelength c a l i b r a t i o n ) by scanning mercury l i n e s i n higher o r d e r s . The s p e c t r a l s l i t f u n c t i o n i s t r i a n g u l a r , i . e . , a d i s c r e t e l i n e i s observed as a t r i a n g l e with width at h a l f height of S £ , which i s the e f f e c t i v e s p e c t r a l s l i t width. The spectrometer response f u n c t i o n i s determined from a c a l i b r a t e d b l a c k body source; f o r an i d e a l b l a c k body the energy i n c i d e n t upon an aperture of 2π e f


9.

BOGAN A N D SETSER

Energy

Disposal

in Reactions

of

241

Fluorine

s t e r a d i a n s i s (52): Rjldw = 2 7 r h c w 2

3

r~~~ [exp(—)

(7) -1]


and the photon radiancy i s

R

w

2ucw^dw

W

V4.W

[exp(^)

/Q\

-1]

h = Planck's constant, c = speed of l i g h t and w = frequency i n cm" . Since determination of r e l a t i v e p o p u l a t i o n s i s e q u i v a l e n t to r e l a t i v e number of photons, i s used. For a spectrometer with a t r i a n g u l a r s l i t f u n c t i o n a continuous source, such as a b l a c k body, gives a s i g n a l at a f i x e d w, that i s p r o p o r t i o n a l to the square of the s l i t width. For a l i n e spectrum, such as a v i b r a t i o n - r o t a t i o n spectrum, the i n t e n s i t y at a f i x e d w has a f i r s t power dependence on the s l i t width. The above experimental obser v a t i o n s can be understood from a d e t a i l e d a n a l y s i s of the e f f e c t s of s p e c t r a l s l i t width on r a d i a t i o n of l i n e and continuum charac t e r i s t i c s (52). I f the s p e c t r a l s l i t width of the instrument changes w i t h w, these c o n s i d e r a t i o n s must be i n c l u d e d i n a c q u i r ing the response curve. The E i n s t e i n c o e f f i c i e n t s , A, of equation 6 were c a l c u l a t e d from ( 9 ) . 1

f

v ,J

v",J"

64TT W

f

4

=

3

I„V ,J T

t

f

ι

3 h ( 2 J 4 d ) ' v",!"

1

2

ι ,

, , Q

| m |

K

}

v J M "'j i s the e l e c t r i c d i p o l e matrix element f o r the v i b r a t i o n r o t a t i o n t r a n s i t i o n and can be separated i n t o two terms; f

T

M

v

R»t

f

where = < v | μ | v" > i s the v i b r a t i o n a l t r a n s i t i o n matrix v element, |m| = J " + 1 f o r R branch (AJ = -1) t r a n s i t i o n s and J " for Ρ branch (AJ = +1) t r a n s i t i o n s , F ^ " = the v i b r a t i o n - r o t a t i o n i n t e r a c t i o n f a c t o r . We used the tabulated v a l u e s of H e r b e l i n and Emmanuel (53) f o r R^„, and c a l c u l a t e d the F^M v a l u e s from Herman, Rothery and Rubin (54). For room temperature experiments w i t h Boltzmann r o t a t i o n a l p o p u l a t i o n s , the simple two term F^n> expression of Herman and W a l l i s i s adequate (55). The Herman and W a l l i s e x p r e s s i o n begins to d e v i a t e from the Herman, Rothery and Rubin e x p r e s s i o n at J = 12 and the d i f f e r e n c e becomes i n c r e a s i n g l y s e r i o u s w i t h i n c r e a s i n g J . Because of the w dependence of f

f

3


242

FLUORINE-CONTAINING

RADICALS

A, accurate l i n e p o s i t i o n s are important and were c a l c u l a t e d from the Dunham expression (56). Appendix I contains a .summary of the E i n s t e i n c o e f f i c i e n t s and l i n e p o s i t i o n s f o r the Δν=1 and Δν=2 HF t r a n s i t i o n s o r i g i n a t i n g from l e v e l s up to v =5, J =18. For the a n a l y s i s of low r e s o l u t i o n HF s p e c t r a , the above information i s used to o b t a i n HFJJ r e l a t i v e populations v i a i t e r a t i v e computer s i m u l a t i o n of the observed spectrum. The computer program accepts estimated v i b r a t i o n a l - r o t a t i o n a l d i s t r i butions, and then f


F R E E

f

i ) a p p l i e s the A c o e f f i c i e n t s to o b t a i n l i n e strengths, i i ) performs the c o n v o l u t i o n of s p e c t r a l s l i t and s p e c t r o meter response f u n c t i o n s , i i i ) computes the r e s u l t a n t spectrum as a sum of i n d i v i d u a l , t r i a n g u l a r peaks, and iv)

p l o t s the spectrum.

The computed spectrum i s compared to the observed spectrum and adjustments i n the r e l a t i v e populations are made, and t h i s proc ess i s repeated u n t i l a s a t i s f a c t o r y f i t i s obtained. Many v i b r a t i o n a l - r o t a t i o n a l bands are overlapped, and the use of the e f f e c t i v e s p e c t r a l s l i t width i n the c a l c u l a t i o n leads to a f i t t i n g of peak areas. The f i n a l set of HF r e l a t i v e populations i s the r e s u l t o f f i t t i n g fundamental and f i r s t overtone s p e c t r a and averaging of s e v e r a l s p e c t r a . A l e a s t squares c r i t e r i o n , on peak height, was used to determine when the i t e r a t i v e s i m u l a t i o n proc ess had converged. An example of the agreement of experimental and simulated s p e c t r a i s shown as F i g u r e 2. For higher r e s o l u t i o n s p e c t r a i n which the r o t a t i o n a l l i n e s are r e s o l v e d , the sys tematic conversion of the area of each r o t a t i o n a l l i n e ( c o r r e c t e d for spectrometer response) to r e l a t i v e populations i s tedious but straightforward. V i b r a t i o n a l Energy D i s p o s a l In order to s p e c i f y the energy d i s p o s a l the mean energy available, = -ΔΗ© + E

a

+ ,

(11)

th

i n a r e a c t i v e c o l l i s i o n i s r e q u i r e d ; ΔΗ° i s the standard enthalpy change a t 0°K, Ε i s the a c t i v a t i o n energy and i s the mean thermal energy o f r e a c t i v e c o l l i s i o n s (57). The v i b r a t i o n a l energy i n the polyatomic molecule i s assumed to be u n a v a i l a b l e f o r d i s p o s a l to HF+, thus = 5/2 RT f o r a diatomic or l i n e a r t r i atomic reagent and 3 RT f o r a polyatomic reagent. The a c t i v a t i o n energy was s e t at 1.0 kcal/mole f o r o l e f i n i c and aromatic C-H bonds and 0.5 kcal/mole f o r other hydrocarbons and r e a c t i v e t

t


9.

BOGAN A N D SETSER

Energy

Disposal

Sfi reagent ι ,1


liq.No it,

in Reactions

of

Fluorine

243

microwave

- discharge

I\

τ "1

C-Z-- =) to trap TRAP GATE VALVE PUMP

Figure 1. Schematic of an arrested relaxation re action vessel used at Kansas State University, taken from (24). See (11) for a drawing of the reaction vessel used by the Toronto group.

r z x z i z i _ i . . i . . . r _ x z i z x z r 1.ι~τ L; V'= -i I : ' r r m _ L ν '=5 Figure 2. HF emission spectrum from the F + H CO reaction showing the match between the low resolution experimental spectrum from the monochromator and the computer-simulated spectrum, taken from (32) 2


244


h y d r i d e s . The v a l u e s s e l e c t e d by Perry and P o l a n y i (20) were used f o r H , HD and D . I f a v a i l a b l e , standard bond energies were used f o r D^ggiR-H); these were c o r r e c t e d to Do(R-H) by sub t r a c t i o n of 1.4 kcal/mole, D°(H-F) = 135.4 kcal/mole (58). T h i s c a l c u l a t i o n of assumes that r e a c t i o n i s from the ( 3 / 2 ) ground s t a t e , and that the ( ? i / 2 ) s t a t e , which i s 1.15 kcal/mole higher i n energy can be ignored. The o b s e r v a t i o n (59) of Br( P-^/ ) product channel from the F + HBr r e a c t i o n sug gests that formation of the upper s p i n - o r b i t s t a t e s can be impor t a n t . The B r ( P y ) s t a t e may be formed from the r e a c t i o n of the F ( P ^ / ) s t a t e , but f u r t h e r work i s r e q u i r e d to prove t h i s . Two recent t h e o r e t i c a l papers bear on t h i s s u b j e c t . T u l l y (73) p r e d i c t e d that P^/2 y 0.14 as r e a c t i v e as Ρ / 300°K; and t h i s , combined w i t h 300°K Boltzmann f a c t o r , p r e d i c t s that only 2% of r e a c t i v e t r a j e c t o r i e s w i l l o r i g i n a t e from P^/2* Tully (73) and J a f f e et a l . (74) p r e d i c t f a c i l e crossovers between the two s u r f a c e s i n the entrance v a l l e y a t r _ > 2A. Uncertainties i n bond energies are as great as the 1.15 k c a l s e p a r a t i o n between the F atom s t a t e s and a s c e r t a i n i n g the presence of F( P-^/2) from the highest observed HF*^ energy would be d i f f i c u l t . 2

2

F

2 p

F

2


RADICALS

a

s

2

a

2

2

1

2

2

2

2

i

s

o n l

2

a

3

2

t

2

B

o

t

n

2

A summary of the HF v i b r a t i o n a l d i s t r i b u t i o n s , , and the highest observed HF energy from F + HR r e a c t i o n s i s given i n Appendix I I . The column l a b e l l e d thermochemical a v a i l a b l e energy was c a l c u l a t e d from (11). The column l a b e l l e d observed cut o f f i s the energy of the highest observed HF v i b - r o t a t i o n a l s t a t e . Data from d i f f e r e n t l a b o r a t o r i e s and from deuterated molecules are i n c l u d e d i n order to f a c i l i t a t e q u a n t i t a t i v e comparison. No attempt has been made to assess the q u a l i t y of the data except to omit work known to be suspect or to add comments as footnotes. The v=0 p o p u l a t i o n s , given f o r some e n t r i e s , were obtained from s u r p r i s a l p l o t s (62) or from rule-of-thumb estimate, as d e s c r i b e d i n the o r i g i n a l p u b l i c a t i o n s . In g e n e r a l , the HF^ v i b r a t i o n a l d i s t r i b u t i o n s have the form of a b e l l shaped curve w i t h a maximum at f y ^0.5 ; i . e . , v=2 f o r ^100 kcal/mole R-H bonds and v=3 or 4 f o r weaker R-H bonds; fy = Ey/. In almost a l l cases, there i s an a b s o l u t e i n v e r s i o n between the v=l and v=2 l e v e l s . The v a l u e s are remarkably constant, ranging from 0.45-0.70 i n v i r t u a l l y a l l cases. T h i s i n d i c a t e s that the polyatomic r a d i c a l s , which have g r e a t l y v a r y ing numbers of i n t e r n a l s t a t e s , have l i t t l e e f f e c t on the HF v i b r a t i o n a l energy d i s p o s a l ; hence, l i t t l e of the a v a i l a b l e energy i s p a r t i t i o n e d to the r a d i c a l products. The obvious i n f e r ence i s that the r a d i c a l can be t r e a t e d as a s t r u c t u r e l e s s par t i c l e f o r v i b r a t i o n a l energy d i s p o s a l . However, on c l o s e r i n s p e c t i o n , s u b t l e d i f f e r e n c e s appear. For example, F + H£ and F + CH^ have s i m i l a r ; but, the r e l a t i v e p o p u l a t i o n of v=3 i s markedly lower f o r CH^ and i s consequently lower, 0.70 vs 0.60. The thermochemical energy and the observed energy c u t o f f c o i n c i d e f o r H ; however, Ε(cutoff) f a l l s ^2 kcal/mole short of E(thermo) f o r CH^. These two d i f f e r e n c e s presumably i n d i c a t e (24) v

2



9.

BOGAN AND SETSER

Energy Disposal in Reactions of Fluorine

245

that some energy i s r e t a i n e d i n the CH3 group as i t r e l a x e s from the t e t r a h e d r a l geometry of methane to the planar geometry of methyl. The e f f e c t i s a conformational s t a b i l i z a t i o n of C H 3 o c c u r r i n g l a t e i n the e x i t channel. Since the H atom i s r a p i d l y t r a n s f e r r e d from the C to F, such an e f f e c t i s maximized. For some reagents, much l a r g e r e f f e c t s a r i s i n g from t h i s f e a t u r e have been observed. The best examples are F + toluene (30,31) and F + propene (35). In these cases, the e f f e c t s are much more pronounced because of the much l a r g e r resonance s t a b i l i z a t i o n energy of the benzyl and a l l y l r a d i c a l s . Dynamical complications can obscure the s i m p l i c i t y of the above i n t e r p r e t a t i o n . These i n c l u d e complex encounters, where the s e p a r a t i o n of HF^j from R i s slow enough to permit exchange of v i b r a t i o n a l energy between them and delayed secondary encounters where HF+j c o l l i d e s w i t h R f o l l o w i n g a d i r e c t r e a c t i o n (63,64). Complex and secondary encounters seem not too s e r i o u s f o r v i b r a t i o n a l energy d i s p o s a l f o r simple polyatomics, such as methane, s u b s t i t u t e d methane, and formaldehyde; however, they appear to become i n c r e a s i n g l y s e r i o u s w i t h i n c r e a s i n g b u l k i n e s s of the p o l y atomic r a d i c a l , f o r example i n the s e r i e s CH^ ( s l i g h t ) , CH^CH^ (more s e r i o u s ) , C(CHg)^ (severe)(31). Models f o r V i b r a t i o n a l Energy D i s p o s a l At t h i s p o i n t i t i s a p p r o p r i a t e to ask: what models e x i s t f o r understanding the dynamics of hydrogen a b s t r a c t i o n by f l u o r i n e atoms (or the s i m i l a r case, CI + HI (65)). The dominant f e a t u r e of the three-body dynamics i s the r a p i d t r a n s f e r of the H atom to the a t t a c k i n g F (64), which r e s u l t s i n simultaneous change i n the Rp_ and RJJ_£ coordinates and a h i g h degree of mixed energy r e l e a s e g i v i n g a h i g h f r a c t i o n of HF v i b r a t i o n a l energy. Since the l i g h t H atom cannot t r a n s f e r much momentum, the momenta of both heavy atoms, one of which i s now incorporated i n the newly formed HF, remain n e a r l y the same as t h e i r v a l u e s p r i o r to the H t r a n s f e r (66). A f t e r the t r a n s f e r of the H to F the HF continues to approach the donor atom; the subsequent s c a t t e r i n g resembles hard sphere e l a s t i c s c a t t e r i n g (65). During the s c a t t e r i n g , c o n s i d e r able i n t e r a c t i o n between the HF and the polyatomic fragment can occur. To the extent that t h i s model a p p l i e s , the products w i l l have r e l a t i v e l y small amounts of t r a n s l a t i o n a l energy, f o r thermal r e a c t a n t s , and the r e a c t i o n e x o e r g i c i t y must be p a r t i t i o n e d p r i m a r i l y to v i b r a t i o n and, to a l e s s e r extent, r o t a t i o n of the p r o duct HF. Some d i s c r e t i o n must be e x e r c i s e d i n a p p l y i n g t h i s model to F + polyatomic r e a c t i o n s because i n t e r n a l degrees o f freedom of R can take up energy; n e v e r t h e l e s s , i t i s c l e a r from the obs e r v a t i o n of s i m i l a r and the i n v e r t e d v i b r a t i o n a l d i s t r i b u t i o n s t h a t three-body behavior f r e q u e n t l y dominates the energy d i s p o s a l of the F + polyatomic r e a c t i o n s . The F + HC1 and HBr r e a c t i o n s p r o v i d e "standard" three-body systems o f bond e n e r g i e s of vL03 and 88 kcal/mole, r e s p e c t i v e l y , f o r comparison to the H



h

10

6

5

4

59

40(31)

59

HBr

HI

HI

21 21

41

42

4

CH

CH,

21

4

2

11

18

CH

Primary C-H

24(31)

12

8

40(31)

HBr

30

24

10

15

64 68

13

64

35

35

35

0.61 0.59

33.6

0.59

0.60

0.56

0.58

33.6

33

g

26

67

19

17

11

13

g

67

14

17

g

51

30

30

23 14

g

51

19

26

29

14

g

35.6

10

36. l

34.3

0.53

0.53 35

35.6

60

40

HC1

24

13

52

11

17(31)

0.64

34.2

35.2

25

43

0.63 34.3

23

7

2

20

2 HC1

D

f

25

41

23

8

3

20

HD (DF)

0.59

9

67

4

e

34.1

27

57

16

35 f

35

26

55

19

42 20

0.65

33.6

35.0

37

49

14

41

0.66

0.70

34.7

35.0

34

0.66

34.7

35.0

30

53

15

20

34.7

20

2

>

35.0

2

V

0.66

24

Ρ(ν)

29

3

25

Phenol

a

Distribution =0 1

9h

Ketones,

Ref.

( p a g e 5)

32

Aldehydes,

Reactant

Appendix I I Continued


I

^

Π Ο

M

I

to

ο


q.

m. η o. p.

j. k. 1.

i.

h.

g.

f.

d. e.

c.

b.

2

f

v

v

was n o t done i n t h e o r i g i n a l w o r k , t h e r e f e r e n c e i n p a r e n t h e s i s s h o u l d be c o n s u l t e d . In other c a s e s Ρ(0) was e s t i m a t e d by e x t r a p o l a t i o n o f t h e d i s t r i b u t i o n t o v=0; t h e s e a r e d e n o t e d b y a s u p e r s c r i p t E . These e s t i m a t e s a r e c o n s i d e r a b l y l a r g e r t h a n t h o s e o b t a i n e d from e x t r a p o l a t i o n of the s u r p r i s a l p l o t s . F o r room t e m p e r a t u r e e x p e r i m e n t s u n l e s s n o t e d o t h e r w i s e ; t h e u n i t s a r e k c a l / m o l e . The v a l u e s a r e r o u n d e d t o t h e n e a r e s t k c a l / m o l e u n l e s s t h e bond e n e r g i e s a r e v e r y w e l l known. T h i s i s t h e g i v e n by e q . 11 i n t h e t e x t . I f more t h a n one t y p e o f C - H bond i s p r e s e n t , t h e f o r t h e w e a k e r bond i s g i v e n f i r s t , f o l l o w e d b y t h e f o r t h e s t r o n g e r bond i n p a r e n t h e s e s . M o s t bond e n e r g i e s w e r e t a k e n f r o m B e n s o n and O N e a l (82). * I f P(0) i s l i s t e d i n t h e t a b l e , i t was u s e d t o c a l c u l a t e < f y > ~ Σ P(v)f . M c D o n a l d and c o w o r k e r s u s e t h e r m a l d i s s o c i a t i o n o f F ^ a s t h e F atom s o u r c e and t h e a v a i l a b l e e n e r g y c o u l d be s l i g h t l y h i g h e r t h a n t h e v a l u e s q u o t e d f r o m o t h e r l a b o r a t o r i e s u s i n g m i c r o w a v e d i s s o c i a t i o n o f C F . o r S F , a s t h e F atom s o u r c e . W i t h i n t h e r o u n d - o f f l i m i t s , t h e a r e t h e 4 6 ' same a s t h e room t e m p e r a t u r e v a l u e s . The a c t i v a t i o n e n e r g i e s and z e r o p o i n t e n e r g i e s a r e d i f f e r e n t a n d l e a d t o u n e q u a l a v a i l a b l e e n e r g i e s ; s e e (20). T h e s e e x p e r i m e n t s were done i n a f l o w i n g a f t e r g l o w a p p a r a t u s w h i c h g i v e s a B o l t z m a n n d i s t r i b u t i o n o f r o t a t i o n a l l e v e l s and a c u t o f f l e v e l i s n o t o b s e r v a b l e . T h e s e v a l u e s w e r e o b t a i n e d by e x t r a p o l a t i o n o f t h e m o d e l I I I s u r p r i s a l p l o t s . I f model I I or I w e r e u s e d , t h e r e l a t i v e p o p u l a t i o n o f v=0 w o u l d be h i g h e r b y f a c t o r s o f ^2 and 3 r e s p e c t i v e l y . R e c e n t l y a c q u i r e d r e s u l t s (80) u s i n g a n i m p r o v e d r e a c t i o n v e s s e l and i n t e r f e r o m e t r i c o b s e r v a t i o n o f t h e e m i s s i o n s u g g e s t t h e ν ^ Λ ^ r a t i o i s somewhat h i g h e r t h a n g i v e n i n t h e t a b l e . The a d d i t i o n o f F t o CH^CN f o l l o w e d by HF e l i m i n a t i o n may compete w i t h d i r e c t a b s t r a c t i o n . The bond e n e r g y was assumed t o be t h e same a s f o r C«H^. The v ^ / v r a t i o p r o b a b l y i s t o o h i g h . See r e f . (32; f o r u p d a t i n g o f t h e ( C H ^ ^ O d a t a . Similar c h a n g e s p r o b a b l y a p p l y |o ( C H ^ ^ S . The h i g h e s t o b s e r v e d H F ^ j e n e r g y was s e t e q u a l t o t h e t h e r m o c h e m i c a l e n e r g y . The bond e n e r g y was assumed t o be t h e same a s f o r C ^ H ^ . The bond e n e r g y was assumed t o be t h e same a s f o r C ^ H ^ . V e r y f a s t V - V r e l a x a t i o n w i t h o u t a n a p p r e c i a b l e change i n J may h a v e a f f e c t e d t h e s e d a t a ; t h u s , i s a l o w e r l i m i t . P o o r q u a l i t y d a t a due t o weak e m i s s i o n ; r e a c t i o n c h a n n e l s o t h e r t h a n d i r e c t a b s t r a c t i o n may c o n t r i b u t e to the observed e m i s s i o n .


3

to H-

§

§ §"· | ^ ^ IT

^ g -§ | ^ 3

QTQ

-J

g ^ H g

>

g ξ

ω

5°


252


RADICALS

polyatomic systems. P r o d u c t d i s t r i b u t i o n s c a n be o b t a i n e d v i a c l a s s i c a l t r a j e c t o r y c a l c u l a t i o n s on s e m i - e m p i r i c a l , p o t e n t i a l energy s u r f a c e s (63). "Computer e x p e r i m e n t s " a r e performed on the s u r f a c e u s i n g s e l e c t e d d i s t r i b u t i o n s of r e a c t a n t s t a t e s . For comparison w i t h experimental d a t a , the c l a s s i c a l product energies are " r e q u a n t i z e d " b y d i v i d i n g t h e c l a s s i c a l c o n t i n u u m o f HF v i b r a t i o n - r o t a t i o n s t a t e s i n t o b i n s w h i c h c o r r e s p o n d t o t h e known v , o r J * energy s t a t e s . C o m p a r i s o n o f t h e c a l c u l a t e d and e x p e r i m e n t a l energy d i s t r i b u t i o n s r e v e a l s the a p p r o p r i a t e n e s s of the t r i a l s u r f a c e and a d j u s t m e n t s c a n be made t o d e v e l o p a more c o r r e c t surface. E x t e n s i v e t r a j e c t o r y c a l c u l a t i o n s h a v e b e e n done f o r F + H ( 6 7 - 7 1 ) , F + HC1 (17) and C l + H I (65) w h i c h i s s i m i l a r t o F t H C 1 . A r e p r e s e n t a t i v e ( n o t o p t i m i z e d ) LEPS s u r f a c e f o r F + HC i s shown i n F i g u r e 3. The r e s u l t s f r o m s u c h a s u r f a c e a r e i n moderate accord w i t h the v i b r a t i o n a l energy d i s p o s a l f o r F + CH^X r e a c t i o n s . A l t h o u g h the s u r f a c e i s of the v e r y r e p u l s i v e t y p e , a l a r g e f r a c t i o n of the e x o e r g i c i t y i s r e l e a s e d as Ey b e c a u s e o f t h e m i x e d e n e r g y r e l e a s e c h a r a c t e r i s t i c o f t h e F - H - C mass c o m b i n a t i o n . T r a j e c t o r y c a l c u l a t i o n s f o r F + HC1 (17) a r e i n good a g r e e m e n t w i t h e x p e r i m e n t a l v i b r a t i o n a l and r o t a t i o n a l d i s t r i b u t i o n s o f HF . F o r F + HC1 and C l + H I t h e t r a j e c t o r y c a l c u l a t i o n s and t h e e x p e r i m e n t a l d a t a show c o n s i d e r a b l e i n v e r s e c o r r e l a t i o n between E* and E ^ ( v i d e i n f r a ) . f

Trajectory calculations provide detailed microscopic insight for three-body r e a c t i o n s . However, such c a l c u l a t i o n s f o r l a r g e r s y s t e m s a r e much more d i f f i c u l t , a s w e l l a s c o s t l y . Another approach i s the use of i n f o r m a t i o n t h e o r y , p a r t i c u l a r l y s u r p r i s a l analysis. These methods h a v e b e e n d e v e l o p e d b y L e v i n e , B e r n s t e i n a n d c o w o r k e r s f o r t h r e e - b o d y r e a c t i o n s ( 6 2 , 7 2 , 7 3 ) and we h a v e e x tended the a n a l y s i s i n o r d e r to d e a l w i t h p o l y a t o m i c r a d i c a l p r o duct (31). S u r p r i s a l a n a l y s i s i s a q u a n t i t a t i v e framework f o r comparison of an observed d i s t r i b u t i o n to a r e f e r e n c e ( p r i o r ) distribution. A n a t u r a l and c o n v e n i e n t r e f e r e n c e i s t h e s t a t i s t i c a l phase space d i s t r i b u t i o n ( 7 4 ) . A c c e s s i b l e s t a t e s are those f o r m e d by t r a j e c t o r i e s w h i c h c o n s e r v e e n e r g y and a n g u l a r momentum. The l i m i t a t i o n s t o t h e p r o d u c t s t a t e s a l l o w e d b y a n g u l a r momentum i s d i f f i c u l t to e v a l u a t e ( 7 5 , 7 6 ) . Fortunately for fast react i o n s , t h e l a r g e i m p a c t p a r a m e t e r s c o n t r i b u t e a l a r g e amount o f o r b i t a l a n g u l a r momentum t o t h e r e a c t i v e c o l l i s i o n and t h i s p e r m i t s t h e n e g l e c t o f t h e a n g u l a r momentum c o n s t r a i n t i n t h e c o m p u t a t i o n of the p r i o r d i s t r i b u t i o n (32). The s u r p r i s a l a s s o c i a t e d w i t h t h e o b s e r v a t i o n o f a g i v e n v i b r a t i o n a l l e v e l i s (62) I(f ) y

= -In

P(f )/P (f ); v

e

v


(12)


BOGAN A N D SETSER

Energy

Disposal

in Reactions

of

Fluorine

Figure 3. A LEPS potential energy surface (collinear) representing the F -f- HC three-body reaction, from (64). This particular surface has a low potential energy barrier which occurs at a large R H F distance.



254


RADICALS

w h e r e P° i s t h e p r i o r d i s t r i b u t i o n a n d Ρ i s t h e o b s e r v e d d i s t r i bution. The s u r p r i s a l i s a l o c a l m e a s u r e o f t h e d i f f e r e n c e b e tween t h e e x p e r i m e n t a l a n d p r i o r p o p u l a t i o n s . The s u r p r i s a l w i l l be z e r o i f t h e e x p e r i m e n t a l and p r i o r p o p u l a t i o n s a r e i n e x a c t agreement. F o r an experiment w i t h f i x e d a v a i l a b l e energy E , P ° ( f ) i s d e f i n e d by v* P°(f ) = ρ(ν,Ε)/Σ p(v,E) (13) v=0 The maximum a c c e s s i b l e ν i s v * and ρ ( ν , Ε ) i s t h e d e n s i t y o f p r o d u c t s t a t e s a t e n e r g y E , w i t h ν q u a n t a f i x e d i n HF v i b r a t i o n . The d e n s i t y o f HF + R p r o d u c t s t a t e s i s (31) Ε - E (HF) ν, J p ( v , E ) - E(2J+1) / ρ (Ε )p ( E - E J Ε «0

(HF) - Ε ) dE .

(14)

The r o t a t i o n a l d e g e n e r a c y o f HF i n s t a t e J i s 2 J + 1 , p^(E^) i s t h e i n t e r n a l s t a t e d e n s i t y o f R a t e n e r g y Ε and ρ,^(Ε^) i s t h e t r a n s l a t i o n a l s t a t e d e n s i t y f o r E ^ = E - E ^ - E . The e v a l u a t i o n o f (14) c a n be done a t s e v e r a l l e v e l s o f c o m p l e t e n e s s . We h a v e c h o s e n 3 p r i o r m o d e l s , i d e n t i f i e d by t h e Roman n u m e r a l s b e l o w (31). I.

The t h r e e - b o d y m o d e l , w h e r e R i s t r e a t e d a s a s t r u c t u r e l e s s p a r t i c l e . I n t h i s m o d e l p^(E^) = 1 . 0 a n d E ^ = 0 .

II.

The t h r e e - b o d y m o d e l e x t e n d e d t o a l l o w R t o a c q u i r e r o t a t i o n a l but not v i b r a t i o n a l energy.

III.

A complete model a l l o w i n g a l l i n t e r n a l degrees of f r e e dom o f R t o a c q u i r e e n e r g y . F o r s u b s t i t u t e d m e t h a n e s , i t was u s e f u l t o employ a r e d u c e d m o d e l I I I , named I I I - R , i n w h i c h l a r g e m o l e c u l e s were t r e a t e d a s a s i x - b o d y s y s t e m , C H ^ X , w i t h X a s t r u c t u r e l e s s atom o f a p p r o p r i a t e

The e v a l u a t i o n o f (14) was done n u m e r i c a l l y f o r m o d e l s I I I and I I I - R (31). F o r m o d e l s I (62) and I I ( 3 1 ) , i n t e g r a t i o n o v e r J y i e l d s r e s u l t s w h i c h a r e i n e x c e l l e n t a g r e e m e n t w i t h e x a c t summa t i o n s and p e r m i t s e q u a t i o n (14) t o be r e d u c e d so a s t o g i v e p a r t i c u l a r l y simple expressions for the p r i o r d i s t r i b u t i o n s .

p; = α v

p

-

îi

HC1 + I

I (Exp)

= 0.45

F + H

2

->

HF + Η

(22)

£(Εχρ) = 0.21

W i t h i n e x p e r i m e n t a l e r r o r , t h e f i r s t two r e a c t i o n s g i v e g ( E x p ) = g ( I ) , f o r a l l ν l e v e l s , and t h e r e i s l i t t l e r o t a t i o n a l d i s equilibrium. The F + Η r e a c t i o n h a s d i f f e r e n t mass r e l a t i o n s h i p s (H + L L ) a n d d y n a m i c s t h a n t h e F + HR (H + L H ) cases. F o r t h i s r e a s o n , o n l y t h e f i r s t two r e a c t i o n s a r e s u i t a b l e t h r e e - b o d y r e f e r e n c e s f o r c o m p a r i s o n w i t h F + HR r e a c t i o n s . F i g u r e s 7-8 show t h e t r i a n g u l a r c o n t o u r p l o t s f o r t h e d e t a i l e d r e l a t i v e r a t e c o n s t a n t s f o r HF f o r m a t i o n from F + HC1, and ( C H ^ ^ O . For the three-body case, the contour p l o t i d e n t i f i e s t h e v i b r a t i o n a l , r o t a t i o n a l and t r a n l a t i o n a l e n e r g i e s a s s o c i a t e d w i t h a g i v e n HF s t a t e , p r o v i d i n g t h a t t h e atom i s formed i n a u n i q u e e l e c t r o n i c s t a t e . However, f o r t h e p o l y a t o m i c c a s e t h e r e s i d u a l e n e r g y , - E^.(HF) - E ( H F ) , c a n b e i n i n t e r n a l energy of t h e R fragment,as w e l l as t r a n s l a t i o n . T h e (ΟΗβ^Ο r e a c t i o n i s an example. The a b s e n c e o f e m i s s i o n f r o m v=4 and f h e f a i l u r e f o r any of t h e v i b r a t i o n a l - r o t a t i o n a l l e v e l s t o r e a c h t o t h e t h e r m o c h e m i c a l l i m i t i s a t t r i b u t e d t o t h e CH^OCH radical s t a b i l i z a t i o n energy. T h i s energy which a p p a r e n t l y i s not a v a i l a b l e t o H F ' , d i s p l a c e s t h e c o n t o u r p l o t away f r o m t h e d i a g o n a l l i n e connecting f and f = 1.0. There a r e obvious d i f f e r e n c e s b e t w e e n t h e c o n t o u r p l o t f o r F + HC1 and t h a t o f t h e p o l y a t o m i c c a s e w h i c h seem t o b e w e l l beyond t h e u n c e r t a i n t i e s i n v o l v e d i n e x t r a p o l a t i n g t o t h e i n i t i a l J d i s t r i b u t i o n s . The i m p o r t a n t d i f f e r e n c e s a r e : a) The v a l u e s o f g ( E x p ) f o r t h e p o l y a t o m i c c a s e s a r e ^ 0 . 2 , w i t h t h e v a l u e s f o r v = l b e i n g somewhat l e s s t h a n for the other ν l e v e l s . Thus, the strong inverse c o r r e l a t i o n b e tween v i b r a t i o n a l and r o t a t i o n a l e n e r g y , found f o r t h e t h r e e - b o d y F ψ HC1 r e a c t i o n , no l o n g e r seems t o h o l d , b) F o r f 3f 0.4 t h e HF d i s t r i b u t i o n u s u a l l y does n o t e x t e n d t o t h e energy l i m i t denoted by t h e d i a g o n a l l i n e . R

R

y

P l o t s of f v £ ( 1 - f ) t e n d t o b e l i n e a r a n d y i e l d a mean v a l u e of g(Exp) from t h e s l o p e . F o r t h e CH^OCH a n d CH 0 r e a c t i o n s Q 2 ) , g ( E x p ) was ^0.2 w h i c h i s t h e t h e o r e t i c a l v a l u e o f g ( I I ) (32). T h i s suggests t h a t t h e a v a i l a b l e r o t a t i o n a l energy i s p a r t i t i o n e d s t a t i s t i c a l l y between H F ^ and R. T h i s c a n e x p l a i n o b s e r v a t i o n (a) a b o v e . A p o s s i b l e e x p l a n a t i o n f o r (b) c a n be o b t a i n e d f r o m c o n s i d e r a t i o n o f t h e a n g u l a r momentum c o n servation equation, R

P



262

FLUORINE-CONTAINING F R E E

Figure 7. Contour plot of the detailed rate constants for formation of HF in a given ν J state for the F -j- HCl reac tion. The 0.5 contour has been omitted for sake of clarity; the dotted contour is the 0.05 value. Based upon a sur prisal analysis, the relative population of ν = 0 is ~ 0.10.


RADICALS

9.

BOGAN AND SETSER



K C A L / M O L E

_9

1

18

1 J 1 , F • CH3OCH3— H F" • CH OCH

ρ

r

1

2

3

Figure 8. Contour plot of the detailed rate constants for formation of HF in given v j states for the F + (CH ) 0 reaction, from (32). The failure of HF\j to acquire energy up to the thermochemical limit is attributed to the presence of the CH OCH stabilization energy which is retained in the radi cal. This stabilization energy displaces the contour plot from the dotted diagonal line. s

2

2

s


263

264

FLUORINE-CONTAINING

L + J = L

f

+

FREE

+

RADICALS

(23)

->.

L = o r b i t a l and J = r o t a t i o n a l a n g u l a r momentum; t h e p r i m e d q u a n t i t i e s denote p r o d u c t s . The m e a s u r e d t o t a l r a t e c o n s t a n t s ( 4 6 , 33) y i e l d t h e t h e r m a l r e a c t i o n c r o s s s e c t i o n , σ , w h i c h c a n b e £ converted to L (62). T y p i c a l l y Ύ, >_ 2Oh c o r r e s p o n d i n g t o σ ί 20A, h o w e v e r , J a t 300°K i s a l s o l a r g e , 8ft f o r m e t h a n e , 19ti f o r e t h a n e and 27fi f o r ( C H « ) 0 . Since J i s o n l y a b o u t 2% l e s s t h a n Τ ( a t 300°K f o r b o t h RH and R ) , t h e r o t a t i o n a l e n e r g y a c q u i r e d by HF c o u l d be l i m i t e d by t h e a n g u l a r momentum ( a l t h o u g h E J ( R ) i s l o w b e c a u s e o f t h e l a r g e moments o f i n e r t i a ) o f t h e p o l y a t o m i c R. This could constrain Ε (HF) t o l e s s t h a n ( - E ) , p a r t i c u l a r l y i n the lower v i b r a t i o n a l l e v e l s . I t must be s t r e s s e d t h a t the c u r r e n t l y a v a i l a b l e data f o r r o t a t i o n a l energy d i s p o s a l are q u i t e l i m i t e d (32). T h e s e c o n c l u s i o n s may be m o d i f i e d a s b e t t e r data are accumulated (80).


0

2

R

v

R - H Bond D i s s o c i a t i o n E n e r g i e s Bond d i s s o c i a t i o n e n e r g i e s , and h e n c e , ΔΗ° (R) c a n ]j>e o b t a i n e d by s e t t i n g t h e e n e r g y o f t h e h i g h e s t o b s e r v e d H F ^ j v i b r a t i o n - r o t a t i o n s t a t e e q u a l t o o f e q n . 1 1 . The a c c u r a c y o f bond e n e r g i e s o b t a i n e d f r o m c h e m i l u m i n e s c e n c e i s d e p e n d e n t u p o n a)

the presence of a measurable l e v e l of chemiluminescence f r o m H F ^ j l e v e l s n e a r t h e l i m i t i m p o s e d by ,

b)

the correctness

c)

t h e energy s p a c i n g between J s t a t e s region,

d)

the absence

of

of

t h e assumed a c t i v a t i o n e n e r g y ,

a sizeable radical

i n the

cut-off

s t a b i l i z a t i o n energy.

Of c o u r s e , n o r m a l p r e c a u t i o n s o f c h e m i c a l p u r i t y must b e exercised. The a b s e n c e o f a r a d i c a l s t a b i l i z a t i o n e n e r g y , and a l s o t h e a b s e n c e o f i m p u r i t i e s ( d e f i n e d a s two o r more t y p e s o f R - H b o n d s ) and m u l t i p l e r e a c t i o n c h a n n e l s , c a n b e i n f e r r e d f r o m a l i n e a r v i b r a t i o n a l s u r p r i s a l p l o t w i t h i n the three-body model (I) (31,32). Requirement b , i s not s e r i o u s because a l l a c t i v a t i o n e n e r g i e s a r e n e a r l y z e r o and f a l l i n t h e r a n g e 0 - 1 . 5 k c a l / m o l e (46). The r o t a t i o n a l e n e r g y s p a c i n g i n c r e a s e s a s J ( J + 1 ) and t h e s p a c i n g s e x c e e d 1 k c a l / m o l e a t J % 9. In f a v o r a b l e c a s e s bond e n e r g i e s , a c c u r a t e t o 1-2 k c a l / m o l e , c a n b e o b t a i n e d by t h i s m e t h o d . T h i s approaches the accuracy of the b e s t a l t e r n a t i v e methods ( 8 2 ) . The c h e m i l u m i n e s c e n c e method a c t u a l l y g i v e s u p p e r l i m i t bond e n e r g i e s and t h i s i s a u s e f u l c h e c k on l e s s d i r e c t m e t h o d s . T a b l e I s u m m a r i z e s some o f t h e bond e n e r g i e s t h a t h a v e b e e n o b t a i n e d f r o m c h e m i l u m i n e s c e n c e data.


Root; Fluorine-Containing Free Radicals ACS Symposium Series; American Chemical Society: Washington, DC, 1978. consensus v a l u e Ε .A. A.P.

83

100.7

33

£105.0

3,5

85 87 HBr + C l

(24)

I n f o r m a t i o n on r e a g e n t e n e r g y c o n s u m p t i o n i s o b t a i n e d f r o m t h e d e p l e t i o n s p e c t r u m o f HC1 i n t h e p r e s e n c e o f B r , and i n f o r m a t i o n on t h e p r o d u c t e n e r g y r e l e a s e i s o b t a i n e d f r o m t h e HBr c h e m i l u m inescence spectrum. P r e d i c t i o n s of m i c r o s c o p i c r e v e r s i b i l i t y d e r i v e d from the forward (exothermic) r e a c t i o n s a r e b e i n g t e s t e d and, i n g e n e r a l , confirmed (17-21). The g e n e r a l r e s u l t s a r e t h a t v i b r a t i o n a l energy i s h i g h l y e f f e c t i v e i n promoting endothermic reactions w h i c h have the b a r r i e r i n the c o o r d i n a t e o f s e p a r a t i o n , w h i l e t r a n s l a t i o n a l energy i s l e s s e f f e c t i v e . For exo thermic r e a c t i o n s , w i t h the b a r r i e r i n the c o o r d i n a t e of


9.

BOGAN AND SETSER


approach, the reverse i s t r u e . R o t a t i o n a l energy has l e s s on b o t h f o r w a r d and r e v e r s e r e a c t i o n s .

267 effect


Energy D i s p o s a l from U n i m o l e c u l a r R e a c t i o n s The m a j o r i t y o f u n i m o l e c u l a r p r o c e s s e s y i e l d p o l y a t o m i c products. F u r t h e r m o r e t h e e n e r g y r a n d o m i z a t i o n q u e s t i o n makes the i n t e r n a l energy d i s t r i b u t i o n of t h e l a r g e r R fragment o f interest. A n a l y s i s of t h e i n f r a r e d chemiluminescence from v i b r a t i o n a l l y e x c i t e d p r o d u c t s ought t o y i e l d a g r e a t d e a l o f i n f o r m a t i o n about t h e dynamics of such r e a c t i o n s . McDonald and c o w o r k e r s have had n o t a b l e s u c c e s s i n t h i s v e r y d i f f i c u l t f i e l d (34,36,37). P o l y a t o m i c v i b r a t i o n a l - ^ t r ans i t i o n s have E i n s t e i n A c o e f f i c i e n t s on t h e o r d e r of 1 sec , compared t o a p p r o x i m a t e l y 200 s e c f o r H F , and t h e f r e q u e n c i e s o f t h e s e t r a n s i t i o n s l i e i n a r e g i o n w h e r e d e t e c t o r s e n s i t i v i t i e s a r e

2

HF^ j + CHC1

(26a)

2

C H F C 1 * + H C 1 * j + CFC1 2

where * denotes v i b r a t i o n a l e x c i t a t i o n a r i s i n g from t h e e x o e r g i c i t y of the a c t i v a t i n g r e a c t i o n . S i m i l a r l y , the r e a c t i o n s of H atom w i t h C C l ^ B r and C F ^ I a l l o w t h e o b s e r v a t i o n o f ; CX

3

+ H

->

CX H* 3

•*

HX* j + C X

2

(X = C 1 , F ) .

(26b)

I n a l l t h r e e r e a c t i o n s y s t e m s , t h e v = l l e v e l had t h e g r e a t e s t r e l a t i v e p o p u l a t i o n s (v=0 c o u l d n o t be o b s e r v e d ) . There i s l i t t l e p o t e n t i a l energy r e l e a s e i n these t h r e e - c e n t e r e d e l i m i n a t i o n r e a c t i o n s and t h e o b s e r v e d d i s t r i b u t i o n s a r e r o u g h l y c o n s i s t e n t w i t h s t a t i s t i c a l d i s t r i b u t i o n s . The t o t a l v i b r a t i o n a l e n e r g y r e l e a s e d to the carbene fragments (:CC1CH C1 or :CFCH F) r e c e n t l y h a s b e e n m e a s u r e d (96,97) and t h e m a g n i t u d e o f t h e a v e r a g e e n e r g y 2

2


9.

BOGAN AND SETSER


269

and the breadth of the d i s t r i b u t i o n a r e c o n s i s t e n t w i t h s t a t i s t i c a l predictions. The C H C F 3


CH

3

3

reaction,

+ CF

3

-> C H C F * -> HF^ j + C H C F 3

3

2

2

(27)

i s an example of a four-centered e l i m i n a t i o n from a c h e m i c a l l y a c t i v a t e d molecule. In t h i s case there i s a s i g n i f i c a n t pot e n t i a l energy r e l e a s e s i n c e the a c t i v a t i o n energy of the r e v e r s e r e a c t i o n (HF + CH = C F -> C H C F ) i s ^42 kcal/mole endoergic. The energy of the C H C F formed by the r a d i c a l recombination p l a c e s the system 30 kcal/mole above the e x i t channel b a r r i e r . The HF product was e x c i t e d up to v=4, (42.4 kcal/mole) showing that some of the p o t e n t i a l energy, a s s o c i a t e d w i t h the r e v e r s e reaction,was p a r t i t i o n e d to HF v i b r a t i o n . Chemical l a s e r e x p e r i ments (3) have conf irmed the HF v i b r a t i o n a l d i s t r i b u t i o n measured by i n f r a r e d chemiluminescence. The energy contained i n the o l e f i n fragment has been assigned (98) by o b s e r v a t i o n of the u n i molecular r a t e constant, k , f o r i s o m e r i z a t i o n of m e t h y l c y c l o butene i n the f o l l o w i n g sequence. 2

2

3

3

3

3

The < f ( m e t h y l c y c l o b u t e n e ) > was 0.57 which corresponds to o n l y 28% of the p o t e n t i a l energy, assuming t h a t the energy i n excess of the t h r e s h o l d energy was p a r t i t i o n e d s t a t i s t i c a l l y to methylcyclobutene. For the C F C H r e a c t i o n was 0.13 which corresponds to only a s m a l l f r a c t i o n of the p o t e n t i a l energy. By d i f f e r e n c e a l a r g e f r a c t i o n of the p o t e n t i a l energy i s r e l e a s e d as t r a n s l a t i o n a l energy. R e c o i l energy measurements (99,100) f o r HCl e l i m i n a t i o n from c h l o r o a l k a n e ions support t h i s c o n c l u s i o n . D i s c u s s i o n of the dynamics of the HX e l i m i n a t i o n r e a c t i o n s i s given elsewhere (101,102). 3

3

Ac knowledgments We wish to thank Dr. K e i e t s u Tamagake f o r p e r m i s s i o n t o i n clude the r e s u l t s from h i s study of the F + HCl r e a c t i o n i n t h i s paper. P r o f e s s o r P o l a n y i provided p r e p r i n t s of recent work f o r which we are g r a t e f u l . D.J.B. a l s o wishes to acknowledge h e l p f u l d i s c u s s i o n s w i t h Drs. D.S.Y. Hsu and J . W. Hudgens. The i n f r a r e d


270


RADICALS

chemiluminescence program a t Kansas S t a t e U n i v e r s i t y has been s u p p o r t e d by t h e N a t i o n a l S c i e n c e F o u n d a t i o n ( M P S 7 5 - 0 2 7 9 3 ) .


APPENDIX I ,

R a d i a t i v e T r a n s i t i o n P r o b a b i l i t i e s f o r HF

T h e E i n s t e i n c o e f f i c i e n t s , e q . 9 and 1 0 , f o r HF v i b r a t i o n r o t a t i o n t r a n s i t i o n s c a n be e x p r e s s e d a s t w o ^ q u a n t i t i e s A ^ „ , t h e p u r e v i b r a t i o n a l E i n s t e i n c o e f f i c i e n t , and F „ , the v i b r a v

,J

t i o n - r o t a t i o n i n t e r a c t i o n f a c t o r , p l u s o t h e r t e r m s d e p e n d i n g upon J and J " . V a l u e s o f A , f r o m s e v e r a l d i f f e r e n t w o r k e r s a r e ν reported i n Table I I . Table I I . E i n s t e i n C o e f f i c i e n t s f o r HF V i b r a t i o n a l T r a n s i t i o n s f

V

t

v Α „

v -v"

f

A

1

γ

, -1. (sec )

reference

(103)

(53)

(104)

(51)

1-0

189

189

189

216

2-1

324

320

323

385

3-2

410

398

406

513

4-3

602

453

430

446

5-4

460

421

450

2-0

23.6

23.4

22.9

3-1

66.2

67.9

65.4

4-2

124

131

124

5-3

193

207

195

In determining r e l a t i v e v * , J p o p u l a t i o n s from i t e r a t i v e s i m u l a t i o n of the s p e c t r a , r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s a r e r e q u i r e c since t r a n s i t i o n p r o b a b i l i t i e s having a constant systematic error w i l l g i v e t h e same r e s u l t a s t h e c o r r e c t a b s o l u t e v a l u e s . The p u b l i s h e d r e s u l t s f r o m t h e ^ r o u p a t KSU i n c l u d i n g (27) a n d a l l o t h e r s p r i o r t o 1974 u s e d A ^ , , v a l u e s ^ c a l c u l a t e d f r o m t h e method o f Heaps and H e r z b e r g (51) and F , , ' „ v a l u e s f r o m Herman and W a l l i s (55). B e g i n n i n g w i t h ( 2 9 j and (30) all w o r k r e p o r t e d f r o m K S U , w i t h t h e e x c e p t i o n o f ( 2 7 ) , u s e d A ,, f r o m H e r b e l i n and Emmanuel (53) and F ^ , , ' „ f r o m H e r m a n , R o t h e r y and R u b i n , i^±). f

f


BOGAN A N D SETSER

9.

Energy

Disposal in Reactions of

Fluorine

Table I I I . E i n s t e i n C o e f f i c i e n t s f o r Spontaneous E m i s s i o n f o r HF F u n d a m e n t a l a n d F i r s t O v e r t o n e T r a n s i t i o n s V


J

= f

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1-0 J" 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ν = 1-0 J

f

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

J" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

R Branch A A

v J v J f

, f

,

f

f f

(

s

e

c

-1. )

VJ" 4001 4039 4075 4110 4143 4174 4203 4231 4256 4280 4302 4321 4339 4355 4368 4380 4389 4396

61.3 71.6 74.4 74.6 73.6 71.8 69.6 67.1 64.4 61.5 58.4 55.3 52.2 49.0 45.8 42.6 39.5 36.5 Ρ Branch .v J !

193 131 120 116 114 113 113 112 112 111 110 109 108 107 106 104 102 100 98.2

f

3920 3878 3834 3788 3742 3694 3644 3594 3542 3490 3436 3381 3326 3270 3213 3155 3097 3038 2978


272 V


J

=

F

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

FLUORINE-CONTAINING

2-1 J "

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ν = 2-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

ν = 2-0

R Branch A

v J v"J" f

f

106 125 132 135 136 135 134 132 129 126 123 120 116 113 109 105 100 96.3

J

3827 3864 3899 3932 3964 3994 4022 4048 4072 4095 4115 4134 4151 4166 4178 4189 4198 4204

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

J" 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ν = 2-0

Ρ Branch 322 216 195 186 181 178 175 172 169 167 164 161 158 155 152 148 144 140 136

1

3750 3709 3666 3623 3578 3531 3484 3435 3385 3335 3283 3230 3177 3122 3067 3012 2955 2898 2841

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 4 7 8 9 10 11 12 13 14 15 16 17 18 19

F R E E RADICALS

R Branch w ' V J ' v f J

V J " 7.66 9.03 9.49 9.64 9.65 9.58 9.46 9*. 31 9.14 8.95 8.75 8.54 8.33 8.11 7.88 7.66 7.43 7.21

7789 7824 7856 7884 7910 7932 7951 7966 7979 7987 7993 7995 7993 7988 7980 7968 7953 7934

Ρ Branch 23.8 16.1 14.7 14.2 13.9 13.8 13.7 13.7 13.7 13.7 13.7 13.7 13.7 13.6 13.6 13.5 13.4 13.3 13.2


7710 7666 7619 7569 7516 7460 7402 7341 7278 7212 7143 7072 6999 6924 6847 6767 6685 6602 6516

BOGAN AND SETSER

9. V


J

= f

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

3-2 J" 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ν = 3-2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Energy

ν = 3-1

R Branch v'J v"J" 1

129 149 154 154 150 146 140 134 127 120 113 105 98.0 90.6 83.4 76.3 69.4 62.7

v J' 3659 3694 3727 3759 3789 3818 3845 3870 3893 3915 3934 3952 3968 3981 3993 4003 4011 4017

J

F

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 v

3584 3544 3504 3461 3418 3373 3328 3281 3233 3184 3134 3083 3031 2979 2925 2872 2817 2762 2706

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

J

of

Fluorine

273

R Branch

f

Ρ Branch 410 280 258 250 247 246 246 245 245 244 243 242 240 238 235 232 228 224 219

Disposal in Reactions

A

L F

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 = 3-1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

A

v J f

f

v"J" 22.4 26.7 28.2 28.9 29.2 29.3 29.2 29.0 28.8 28.4 28.1 27.7 27.3 26.9 26.4 25.9 25.5 25.0

v J VJ< f

1

7448 7482 7512 7539 7564 7585 7603 7617 7629 7637 7641 7643 7641 7636 7627 7615 7599 7581

Ρ Branch 68.5 46.0 41.7 39.9 39.0 38.4 38.0 37.7 37.4 37.2 36.9 36.7 36.4 36.1 35.8 35.4 35,0 34.6 34.2


7372 7329 7284 7236 7185 7131 7075 7016 6955 6891 6825 6756 6685 6612 6537 6460 6381 6300 6217

274

FLUORINE-CONTAINING


v = 4-3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 v

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 = 4-3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

R Branch 138 158 162 160 155 148 141 132 124 115 106 97.4 88.7 80.2 71.9 63.9 56.2 49.0

ν = 4-2 3494 3528 3560 3590 3619 3647 3672 3696 3718 3739 3757 3774 3789 3801 3812 3821 3828 3833

Ρ Branch 445 307 284 277 276 276 277 278 279 279 279 278 277 275 273 270 266 262 257

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 v

3422 3384 3345 3304 3262 3219 3175 3130 3084 3036 2988 2939 2889 2838 2787 2735 2682 2629 2575

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-

4-2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

F R E E RADICALS

R Branch 42.1 48.7 50.3 50.1 49.2 47.8 46.3 44.5 42.7 40.9 39.0 37.1 35.2 33.3 31.5 29.7 28.0 26.3

7116 7148 7177 7204 7227 7247 7264 7277 7288 7295 7299 7300 7297 7291 7282 7270 7254 7235

Ρ Branch 135 92.6 85.8 83.9 83.6 84.0 84.8 85-.6 86.5 87.4 88.2 89.0 89.6 90.1 90.6 90.8 91.0 90.9 90.8


7043 7002 6958 6912 6862 6811 6756 6699 6640 6578 6514 6448 6379 6308 6235 6161 6084 6005 5925

9.

BOGAN A N D SETSER


ν = 5-4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ν = 5-4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Energy

R Branch 134 154 157 153 148 140 132 124 115 105 96.2 87.1 78.2 69.6 61.3 53.4 46.0 39.0

3333 3365 3396 3425 3453 3479 3504 3526 3547 3566 3584 3599 3613 3625 3635 3643 3649 3653

Ρ Branch 438 303 282 276 275 276 278 279 280 282 282 282 281 280 277 275 271 267 262

Disposal in Reactions of

Fluorine

ν

R Branch

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

- 5-3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ν = 5-3 3264 3228 3190 3151 3110 3069 3026 2983 2938 2892 2846 2798 2750 2701 2651 2601 2549 2498 2446

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

66,0 75.7 77.1 76.0 73.6 70.6 67.3 63.8 60.2 56.6 53.0 49.4 46.0 42.6 39.4 36.2 33.2 30.4

275

6792 6823 6851 6876 6898 6916 6932 6945 6955 6961 6964 6964 6961 6955 6945 6932 6916 6896

Ρ Branch 216 150 140 138 139 140 143 145 147 150 152 154 156 158 159 160 161 162 162


6722 6682 6640 6595 6548 6498 6445 6390 6332 6273 6210 6146 6080 6011 5940 5867 5793 5716 5638


276

FLUORINE-CONTAINING FREE RADICALS

The experimental v a l u e s of S i l e o and C o o l c l o s e l y agree with the semi-empirical c a l c u l a t i o n s o f Meredith and Smith (104) and of H e r b e l i n and Emanuel (53). The E i n s t e i n c o e f f i c i e n t s o f S i l e o and C o o l , which were published during the p r e p a r a t i o n o f t h i s review, are based on a l a r g e data base and a s t r a i g h t f o r w a r d com p u t a t i o n a l procedure and t h e i r r e s u l t s are recommended. S i l e o and Cool present an e x c e l l e n t d i s c u s s i o n that p l a c e s t h e i r work i n p e r s p e c t i v e to previous s t u d i e s . l

v The use of the new A v a l u e s i n r e a n a l y s i s o f data reported p r i o r t o 1974 would not cnange the v=l-4 v i b r a t i o n a l d i s t r i b u t i o n s beyond the experimental l i m i t of e r r o r . However, f o r r e a c t i o n s y i e l d i n g very high v i b r a t i o n a l l e v e l s , such as H + F«, the r e l a t i v e populations are a l t e r e d s i g n i f i c a n t l y (53,18), by the new t r a n s i t i o n p r o b a b i l i t i e s . For J a, 12 i t i s not p o s s i b l e t o simultaneously f i t both the P- and R-branch l i n e i n t e n s i t i e s f o r the same ν l e v e l i f the v i b r a t i o n - r o t a t i o n i n t e r a c t i o n f a c t o r s of Herman and W a l l i s (55) are used. The problem becomes e s p e c i a l l y severe i n the r e g i o n of the head formation of the R-branch. As the degree of r e l a x a t i o n was reduced by Improvement o f apparatus and technique, t h i s problem prompted us t o switch t o the Herman, Rothery and Rubin (54) f o r m u l a t i o n . The r e s u l t i n g t r a n s i t i o n p r o b a b i l i t i e s a r e l i s t e d i n Table I I I . These were c a l c u l a t e d using a computer program w r i t t e n by Johnson and Bogan (105). The o r i g i n a l paper of HRR (54) contains s e v e r a l t y p o g r a p h i c a l e r r o r s i n the equations^ however, the g r a p h i c a l d i s p l a y o f the numerical v a l u e s f o r F „ ' „ i s c o r r e c t . The v a l u e s of the v i b r a t i o n i n t e r a c t i o n f a c t o r s ' d e r i v e d from Table I I I , d i f f e r a t high J from the v a l u e s of F i g u r e 2 i n r e f . 54, because we have used a more accurate v a l u e of θ = M /M,r ; i . e . , the r a t i o of the f i r s t two terms of o l e the d i p o l e moment expansion d i v i d e d by r = 0.917 A. HRR (54) used θ = 1.18, we used θ = 1.32, S i l e o and Cool (103) g i v e θ = 1.287 (Table ¥ ) .

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280

FLUORINE-CONTAINING

FREE RADICALS

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