10 Potential Energy Surfaces for Fluorine-Hydrogen Systems †
Downloaded by UNIV OF SYDNEY on March 19, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0066.ch010
CHARLES F. BENDER * Theoretical Atomic and Molecular Physics Group, University of California, Lawrence Livermore Laboratory, Livermore, CA 94550 HENRY F. SCHAEFER,. III.** Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 During t h e past decade, there has been a genuine e x p l o s i o n of i n t e r e s t i n the r e a c t i o n s o f atomic and molecular f l u o r i n e and hydrogen. As i s u s u a l l y the c a s e , experimental s t u d i e s have led the way, due i n c o n s i d e r a b l e measure t o t h e tremendous impact o f the HF l a s e r . In a d d i t i o n t o t r a d i t i o n a l k i n e t i c s (1_), the most successful experimental techniques have been i n f r a r e d c h e m i l u m i nescence ( 2 ) , chemical l a s e r s ( 3 ) , crossed molecular beams ( 4 ) , and l a s e r - i n d u c e d f l u o r e s c e n c e JS). T h i s experimental research has y i e l d e d a great deal o f important i n f o r m a t i o n concerning these elementary r e a c t i o n s . In a d d i t i o n , t h i s work has s t i m u l a t e d a keen i n t e r e s t i n the d e t a i l e d understanding on the molecular l e v e l of how these simple r e a c t i o n s occur. Given t h e above background, i t i s h a r d l y s u r p r i s i n g t h a t there has been c o n s i d e r a b l e t h e o r e t i c a l a c t i v i t y d i r e c t e d toward f l u o r i n e hydrogen systems. From a t h e o r e t i c a l v i e w p o i n t , t h e understanding o f such r e a c t i o n s has two components: f i r s t , the p o t e n t i a l energy surface ( o r surfaces) on which t h e p e r t i n e n t r e a c t i o n o c c u r s , and s e c o n d l y , the dynamics which occur given t h e potential surface(s). The amount o f d e t a i l e d experimental i n f o r mation now a v a i l a b l e f o r f l u o r i n e hydrogen r e a c t i o n s i s s u f f i c i e n t t o c h a l l e n g e the most s o p h i s t i c a t e d t h e o r i s t s o f both t h e e l e c t r o n i c s t r u c t u r e and dynamics s c h o o l s . Since dynamical c o n s i d e r a t i o n s a r e taken up i n a d i f f e r e n t chapter o f the present volume, we w i l l be concerned here w i t h the p o t e n t i a l surface h a l f of the t h e o r e t i c a l problem. C l e a r l y , however, we must keep i n mind the e s s e n t i a l complementarity o f these two pieces o f t h e puzzle. This work was performed under the auspices o f the U . S . Energy Research and Development A d m i n i s t r a t i o n under c o n t r a c t No. W-7405-Eng-48. *M. H. F e l l o w . * J . S. Guggenheim F e l l o w , 1976-1977. ©
0-8412-0399-7/78/47-066-283$05.00/0
Root; Fluorine-Containing Free Radicals ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Downloaded by UNIV OF SYDNEY on March 19, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0066.ch010
284
FLUORINE-CONTAINING
FREE RADICALS
In an i n t e r d i s c i p l i n a r y volume such as the p r e s e n t , i t does not seem a p p r o p r i a t e to g i v e any s o r t o f d e t a i l e d coveraqe t o the t h e o r e t i c a l methods c u r r e n t l y i n use ( £ , 7 J . I t must be n o t e d , however, t h a t the Hartree-Fock or S e l f - C o n s i s t e n t - F i e l d (SCF) method remains a t the core of e l e c t r o n i c s t r u c t u r e t h e o r y . A l though SCF theory i s sometimes adequate i n d e s c r i b i n g p o t e n t i a l energy s u r f a c e s , t h i s has turned out more often not to be the c a s e . That i s , e l e c t r o n c o r r e l a t i o n , which i n c o r p o r a t e s the instantaneous r e p u l s i o n s of p a i r s of e l e c t r o n s , can have a q u a l i t a t i v e e f f e c t on the topology of f l u o r i n e hydrogen p o t e n t i a l s u r faces. Without f u r t h e r i n t r o d u c t i o n , i t seems a p p r o p r i a t e to proceed to a d i s c u s s i o n o f s p e c i f i c systems f o r which ab i n i t i o p o t e n t i a l surface f e a t u r e s have been p r e d i c t e d . In the present paper, s p e c i a l emphasis w i l l be placed on the r e l a t i o n s h i p between t h e o r e t i c a l p r e d i c t i o n s and experimental o b s e r v a t i o n s . F + H? ·» FH + H Three p r o g r e s s i v e l y more r e l i a b l e p o t e n t i a l surfaces have been reported f o r t h i s key r e a c t i o n , which has become the focus o f an enormous amount o f s c i e n t i f i c r e s e a r c h . In the f i r s t ( 8 ) , a double z e t a (DZ) b a s i s set was adopted. This n o t a t i o n i m p l i e s t h a t two b a s i s f u n c t i o n s are used t o d e s c r i b e each o r b i t a l of the separated atoms. That i s , f o r f l u o r i n e I s , I s ' , 2 s , 2 s ' , 2 p , 2 ρ ' , 2py, 2 p * , 2 p , and 2 p f u n c t i o n s are adopted. Such a b a s i s i s c l e a r l y twice as l a r g e as the t r a d i t i o n a l minimum b a s i s used i n q u a l i t a t i v e d i s c u s s i o n s o f e l e c t r o n i c s t r u c t u r e . Using the DZ b a s i s and both SCF and c o n f i g u r a t i o n i n t e r a c t i o n (CI) methods, the r e s u l t s i n Table I were o b t a i n e d . I t seems reasonable to conclude t h a t the SCF r e s u l t s obtained w i t h t h i s b a s i s are i n poor agreement w i t h experiment, w h i l e the CI r e s u l t s are much improved but even y e t i n o n l y f a i r agreement. This con c l u s i o n was i n i t i a l l y a s u r p r i s e to u s , s i n c e such techniques often y i e l d r a t h e r r e l i a b l e r e s u l t s , f o r example, i n the p r e d i c t i o n of e q u i l i b r i u m molecular s t r u c t u r e s (9}. The most obvious ( i n 1 i g h t of previous research ( 6 , 7 j i n t h i s area) extension o f the DZ b a s i s i s the a d d i t i o n of p o l a r i z a t i o n f u n c t i o n s , i . e . , a set of d f u n c t i o n s on f l u o r i n e and sets of ρ f u n c t i o n s on each Η atom. The b a s i s thus obtained i s l a b e l e d DZ + Ρ and the ensuing r e s u l t s are summarized i n Table I (10). There we see once again t h a t the SCF approximation y i e l d s a b a r r i e r height much l a r g e r than experiment. And i n f a c t even i f one goes to a complete set of o n e - e l e c t r o n f u n c t i o n s , the Hartree-Fock l i m i t b a r r i e r height w i l l be ^25 kcal l a r g e r than the t r u e b a r r i e r . This inherent i n a b i l i t y of the SCF approximation to even q u a l i t a t i v e l y d e s c r i b e r e p u l s i v e p o t e n t i a l surfaces must be viewed as one of the most important developments of our research to d a t e . x
χ
v
z
z
1
Root; Fluorine-Containing Free Radicals ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Root; Fluorine-Containing Free Radicals ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
^Reference 14
^Experimental a c t i v a t i o n energy; see Reference 1
R e f e r e n c e 13
^Reference 12
R e f e r e n c e 11
^Reference 10
Reference 8
Experiment
e
0.778
f
31.3 31.5 ± 0 . 5
3.3 1.6
1.48
Large B a s i s Extended CI
1976
31.0
2.2
0.777
1.43
Polanyi-Schreiber SE-I^
1974
31.8
1.1
0.76
e
1.54
Muckerman V
1972
34.4
1.7
0.767
b
1.54
DZ + Ρ C I
1972
13.2
29.3
0.836
b
1.18
DZ + Ρ SCF
1972
20.4
5.7
-0.6
0.81
34.3
9
Exothermicity (kcal/mole)
1.37
a
r (H-H)
B a r r i e r Height (kcal/mole)
0.81
r (F-H)
Saddle P o i n t Geometry (angstroms) 1.06
DZ C o n f i g u r a t i o n I n t e r a c t i o n ( C I )
a
1971
(SCF)
1971
Surface
2
Some f e a t u r e s of ab i n i t i o and s e m i - e m p i r i c a l p o t e n t i a l energy surfaces f o r F + H FH + H
Double Zeta (DZ) Self-Consistent-Field
Year
Table I .
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to
CO
sa
CO
ο S" 5
a
286
FLUORINE-CONTAINING FREE
F o r t u n a t e l y , the j u d i c i o u s use of CI y i e l d s a c h e m i c a l l y reasonable DZ + Ρ surface f o r F + H ( F i g u r e 1 ) . In p a r t i c u l a r , the p r e d i c t e d c l a s s i c a l b a r r i e r height of 1.66 kcal i s i n f o r t u i t o u s l y c l o s e agreement w i t h the experimental a c t i v a t i o n energy. F u r t h e r , the e x o t h e r m i c i t y of the BOPS surface i s
