The Chemistry of Combustion Processes - ACS Publications

7 Reactions of NH and N H with Ο and O2 Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on September 16, 2016 | http://pubs.acs.org Publication Date: April 16, 1983 | doi: 10.1021/bk-1983-0249.ch007

2

Theoretical Studies C. F. MELIUS and J. S. BINKLEY Sandia National Laboratories, Livermore, CA 94550

Calculations involving fourth-order Møller-Plesset perturbation theory with bond a d d i t i v i t y corrections were used to investigate the reactions of NH2 and NH with O and O . New heats of formation were used f o r NH (47 kcal-mole ) and NH (87 kcal-mole ). We find that the NH O complex is barely stable. Thus, the rate constant for NH + O should be very small with the most probable products at high temperatures being NHO+O. For NH+O, we find that the reaction forming HNO+O i s spin forbidden on the lower lying singlet surface. Thus, at room temperature the l i k e l y products are ΝO+OΗ and H+NO, which are accessible on the singlet surface. For NH+O and NH+O, we find that stable inter mediate complexes can be formed with no activation barrier. These can undergo direct dissociation by losing a hydrogen or can undergo a 1,2-hydrogen shift with further dissociation forming OH. The reaction path way involving molecular complex formation should dominate at room temperature while direct hydrogen abstraction by 0 atoms should dominate at high temperatures. 2

-1

-1

2

2

2

2

2

2

2

2

2

The r e a c t i o n s o f N H and NH w i t h 0 and 0 p l a y i m p o r t a n t r o l e s i n t h e o x i d a t i o n o f ammonia and f u e l bound n i t r o g e n s a s w e l l a s i n t h e r e d u c t i o n o f N0 's(l-12). However, t h e r a t e c o n s t a n t s f o r these r e a c t i o n s d i f f e r d r a s t i c a l l y i n t h e various chemical r e a c t i o n m o d e l s which have been d e v e l o p e d ( 1 - 6 ) . Even t h e e x p e r i m e n t a l l y measured r a t e c o n s t a n t s show a wide v a r i a t i o n and d i f f e r s i g n i f i c a n t l y from the corresponding i s o e l e c t r o n i c counter2

2

y

0097-6156/84/0249-0103506.00/0 © 1984 American Chemical Society Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on September 16, 2016 | http://pubs.acs.org Publication Date: April 16, 1983 | doi: 10.1021/bk-1983-0249.ch007

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PROCESSES

p a r t s i n v o l v i n g c a r b o n and oxygen ( 6 , 1 3 - 2 3 ) . F u r t h e r m o r e , i t i s n o t even c l e a r what t h e p r o d u c t s o f t h e s e r e a c t i o n s s h o u l d b e . To a i d t h e m o d e l e r s i n d e v e l o p i n g improved r e a c t i o n mechanisms as w e l l as t o a i d t h e e x p e r i m e n t a l i s t s i n t h e i r i n t e r p r e t a t i o n o f t h e d a t a , we have c a l c u l a t e d t h e e n e r g e t i c s o f m o l e c u l a r i n t e r m e d i a t e s and p r o d u c t s a r i s i n g f r o m t h e s e r e a c t i o n s . O u r a p p r o a c h was t o u s e t h e h i g h l y a c c u r a t e f o u r t h o r d e r M p l l e r P l e s s e t p e r t u r b a t i o n t h e o r y (24) with b o n d - a d d i t i v i t y c o r r e c t i o n s . (25) In t h e n e x t s e c t i o n , we b r i e f l y p r e s e n t t h e t h e o r e t i c a l a p p r o a c h . We t h e n p r e s e n t and d i s c u s s t h e r e s u l t s f o r t h e r e a c t i o n s NH +o , NH+0 , NH +0, and NH+0. 2

Theoretical

2

2

2

Approach

The method i s d i v i d e d i n t o two d i s t i n c t s t e p s . The f i r s t s t e p c o n s i s t s o f ab i n i t i o c o m p u t a t i o n o f t h e t o t a l e n e r g i e s o f t h e d e s i r e d m o l e c u l e . T h i s i s accomplished by f i r s t d e t e r m i n i n g t h e t h e o r e t i c a l e q u i l i b r i u m geometry o f t h e molecule u s i n g t h e 6-31G*(26j b a s i s and s p i n - r e s t r i c t e d H a r t r e e - F o c k ( 2 7 ) t h e o r y f o r c l o s e d - s h e l l m o l e c u l e s and s p i n - u n r e s t r i c t e d H a r t r e e - F o c k (28) t h e o r y f o r o p e n - s h e l l m o l e c u l e s . U s i n g t h e s e g e o m e t r i e s two a d d i t i o n a l c a l c u l a t i o n s a r e p e r f o r m e d . Z e r o - p o i n t v i b r a t i o n a l c o r r e c t i o n s a r e d e r i v e d u s i n g a n a l y t i c a l l y computed (29) s e c o n d d e r i v a t i v e s o f t h e energy with r e s p e c t t o the i n t e r n a l degrees o f freedom. In t h e second c a l c u l a t i o n e l e c t r o n c o r r e l a t i o n e f f e c t s are d e t e r m i n e d u s i n g M f l l l e r - P l e s s e t p e r t u r b a t i o n t h e o r y c a r r i e d o u t t o f o u r t h - o r d e r (24) u s i n g t h e 6-31G** ( 2 6 ) b a s i s ( d e n o t e d MP4/6-31G**). Combining t h e d a t a f r o m t h e s e two c a l culations leads to a v i b r a t i o n a l l y corrected, electron-correlated t o t a l energy f o r a given molecule. These t h e o r e t i c a l c a l c u l a t i o n s a r e s u b j e c t t o s y s t e m a t i c e r r o r s a r i s i n g f r o m b a s i s s e t t r u n c a t i o n and n e g l e c t o f h i g h e r p e r t u r b a t i o n o r d e r e l e c t r o n c o r r e l a t i o n e f f e c t s . T h e r e f o r e , we have added a s e c o n d s t e p t o o u r p r o c e d u r e i n which we a t t e m p t t o a c c o u n t f o r t h e s e d e f i c i e n c i e s by a d d i n g e m p i r i c a l l y d e r i v e d B o n d - A d d i t i v i t y - C o r r e c t i o n (BAC) f a c t o r s t h a t a r e based on t h e t y p e s o f bonds p r e s e n t i n t h e g i v e n m o l e c u l e . The c o r r e c t i o n f a c t o r s f o r NH (9.4 k c a l - m o l e " ) and OH (10.7 k c a l - m o l e " ) bonds are o b t a i n e d a s t h e d i f f e r e n c e between t h e t h e o r e t i c a l and 1

1

Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


7.

MELIUS AND BINKLEY

Reactions of NH and NH with Ο and 0 2

2

105

e x p e r i m e n t a l e n e r g i e s f o r c o m p l e t e d i s s o c i a t i o n o f NH3 and ΟΗ2, r e s p e c t i v e l y , a v e r a g e d o v e r t h e number o f Dnds i n t h e m o l e c u l e . In a s i m i l a r f a s h i o n , c o r r e c t i o n f a c t o r s f o r t h e n i t r o g e n - o x y g e n and o x y g e n - o x y g e n bond t y p e s a r e d e v e l o p e d f r o m a c o m p a r i s o n o f the t h e o r e t i c a l r e s u l t s with v a r i o u s experimental values o f Ν-0-Η c o n t a i n i n g m o l e c u l a r s p e c i e s . In t h i s c a s e t h e bond a d d i t i v i t y c o r r e c t i o n s depend b o t h on t h e bond d i s t a n c e a s w e l l a s t h e bond t y p e . An a d d i t i o n a l c o r r e c t i o n f a c t o r f o r s p i n c o n t a m i n a t i o n i n the s p i n - u n r e s t r i c t e d Hartree-Fock wavefunction i s i n c l u d e d . U s i n g t h e t h e o r e t i c a l l y computed t o t a l e n e r g i e s , Δ Η £ v a l u e s were be o b t a i n e d f o r t h e a p p r o p r i a t e Η, N, 0 - c o n t a i n i n g s p e c i e s . T h i s p r o c e d u r e t a c i t l y assumes t h e t r a n s f e r a b i l i t y o f t h e c o r r e c t i v e f a c t o r s f r o m one m o l e c u l e t o a n o t h e r and i s s u b j e c t t o a n y l i m i t a t i o n s imposed b y t h e o r i g i n a l e x p e r i m e n t a l v a l u e s . The f u l l d e t a i l s and a c r i t i c a l a n l y s i s o f t h i s p r o c e d u r e w i l l be p u b l i s h e d separately. R e s u l t s and D i s c u s s i o n The c a l c u l a t e d h e a t s o f f o r m a t i o n f o r v a r i o u s s t a b l e and metas t a b l e i n t e r m e d i a t e s and p r o d u c t s f o r t h e r e a c t i o n s NH2+O2, ΝΗ+Ο2, NH +0, and Ν Η + 0 a r e shown i n F i g u r e s 1-4. The h e a t s o f f o r m a t i o n f o r t h e p o l y a t o m i c s a g r e e w i t h known e x p e r i m e n t a l h e a t s o f f o r m a t i o n t o w i t h i n s e v e r a l k c a l - m o l e " . The e x c e p t i o n s a r e NH and NH2 where t h e e x p e r i m e n t a l e s t i m a t e s v a r y w i d e l y . ( E x p e r i m e n t a l v a l u e s f o r N H r a n g e f r o m 40-46 k c a l - m o l e " w h i l e e x p e r i m e n t a l v a l u e s f o r NH r a n g e f r o m 81-90 k c a l - m o l e " ) . We t h e r e f o r e have used o u r r e c e n t l y c a l c u l a t e d v a l u e s o f ΔΗ^(ΝΗ2) = 47 k c a l - m o l e " and Δ Η ^ ( Ν Η ) = 87 k c a l - m o l e " a s b e i n g t h e most r e l i a b l e ( 2 5 ) . Included i n t h e f i g u r e s a r e schematic curves which connect v a r i o u s i s o m e r s w i t h each o t h e r and w i t h r e a c t a n t s o r p r o d u c t s . T r a n s i t i o n s t a t e p o t e n t i a l e n e r g y b a r r i e r s have n o t been c a l c u l a t e d f o r t h e s e p r o c e s s e s . However, we have i n c l u d e d t h e s e s c h e m a t i c c u r v e s ( w i t h an i n d i c a t i o n o f w h e t h e r t h e t r a n s i t i o n s t a t e b a r r i e r s h o u l d be l a r g e , s m a l l , o r n o n e x i s t e n t ) i n o r d e r t o h e l p t h e r e a d e r f o l l o w p o s s i b l e r e a c t i o n mechanisms. 2

1

1

2

1

1

1

NH?+Q?. S e v e r a l r e a c t i o n schemes have been p r o p o s e d f o r NH2+Û2 ( Δ Η v a l u e s f o r a l l r e a c t i o n s were computed i n t h i s s t u d y ) : NH +0 *-Ν0+Η 0 proposed by Gesser ( 7 ) , 2

2

2

Δ Η = -83 k c a l - m o l e "

1


(1)

CHEMISTRY OF COMBUSTION PROCESSES


106

Figure 1. C a l c u l a t e d energies o f p o s s i b l e intermediates and products f o r the r e a c t i o n o f NH^ ®2' V e r t i c a l s c a l e represents ΔΗ at OK. Connecting curves s c h e m a t i c a l l y i n d i c a t e p o s s i b l e r e a c t i o n pathways. +

Ν + H0

120-

Figure 2.

Same as i n Figure 1 f o r NH + 0,


2

MELIUS AND BINKLEY

Reactions of NH and NH with Ο and 0 2

2


7.

F i g u r e h.

Same as i n F i g u r e 1 f o r NH + 0.


107

108


NH +o 2

*-ΗΝ0+0Η

2

Δ Η = -10 k c a l - m o l e "

PROCESSES

1

(2)

1

(3)

f i r s t p r o p o s e d b y H u s a i n and N o r r i s h ( 8 ) , NH +o Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on September 16, 2016 | http://pubs.acs.org Publication Date: April 16, 1983 | doi: 10.1021/bk-1983-0249.ch007

2

*-ΝΗ 00

2

Δ Η = -5 k c a l - m o l e "

2

f i r s t p r o p o s e d b y J a y a n t y , e t a l . ( 1 3 ) and f a v o r e d by Hack, e t a l . (14), and NH +o *-ΝΗ+Η0 Δ Η = +45 k c a l - m o l e " (4) f i r s t p r o p o s e d b y Takeyama and Miyama ( £ ) . As c a n be seen f r o m F i g u r e 1, NH 00 does n o t f o r m a v e r y s t a b l e complex, h a v i n g a N H - 0 bond e n e r g y o f l e s s t h a n 6 k c a l - m o l e " . Our c a l c u l a t i o n s a r e c o n s i s t e n t w i t h t h e e s t i m a t e s by P a g s b e r g , e t a l . ( 1 5 ) and Benson ( 1 6 ) and i m p l y t h a t t h e i n t e r p r e t a t i o n o f t h e e x p e r i m e n t a l r a t e d a t a by Hack, e t a l . ( 1 4 ) s h o u l d be r e e x a m i n e d w i t h r e s p e c t t o f o r m i n g p r o d u c t s , s i n c e t h e 1,3-hydrogen s h i f t t o f o r m ΗΝ00Η s h o u l d have a s i g n i f i c a n t b a r r i e r . T h u s , i t i s u n l i k e l y t h a t r e a c t i o n s ( 1 ) and ( 2 ) a s w e l l as ( 4 ) v i a t h e ΗΝ00Η complex w i l l have l a r g e r a t e c o n s t a n t s . T h e r e c e n t t h e o r e t i c a l c a l c u l a t i o n s o f Pouchan and C h a i l l e t ( 1 7 ) , u s i n g a l e s s s o p h i s t i c a t e d s u b s e t o f t h e method employed h e r e , f i n d NH 00 t o be unbound b y 13 k c a l - m o l e " . However, t h e i r c o n c l u s i o n s a r e c o n s i s t e n t with ours i n tending t o r u l e out r e a c t i o n (3). Thus, w h i l e t h e r e a r e s e v e r a l e x o t h e r m i c p r o d u c t s f o r t h e r e a c t i o n o f N H + 0 ( e . g . , Η0Ν0+Η, ΗΝ0+0Η, N 0 + H , and N0+H 0), t h e r e a r e no s i m p l e r e a c t i o n pathways t o f o r m them. Based on F i g u r e 1, we b e l i e v e t h e most p r o b a b l e r e a c t i o n t o be 1

2

2

2

2

2

2

1

1

2

2

2

2

NH +0 —*-Η Ν0+0 2

2

2

2

Δ Η = +30 k c a l - m o l e "

2

1

(5)

as s u g g e s t e d b y Benson ( 1 6 ) , p a r t i c u l a r l y a t t h e h i g h e r tempera t u r e s i n f l a m e c o n d i t i o n s . Such a mechanism i s c o n s i s t e n t w i t h t h e o b s e r v a t i o n t h a t a t room t e m p e r a t u r e t h e measured r a t e c o n stant f o r NH +0 i s n e g l i g i b l y small (), and used b y and b y A z u h a t a , e t a l . ( 4 ) i n t h e i r r e a c t i o n pathway i n v o l v e s t h e more d i r e c t f o r m i n g HNO, i . e . ,

ΝΗ+0 —*-ΗΝ0+0

Δ Η = -1 k c a l m o l e "

2

1

(7)

W h i l e t h e r e h a s been some c o n c e r n t h a t r e a c t i o n ( 7 ) may be e n d o t h e r m i c , o u r c a l c u l a t e d h e a t o f f o r m a t i o n f o r NH o f 87 k c a l - m o l e " implies that (7) i s e s s e n t i a l l y thermal n e u t r a l . R e a c t i o n ( 7 ) i s f a v o r e d b y Z e t z s c h and Hansen ( 2 0 ) as b e i n g s i m p l e r t h a n ( 6 ) and i s used by F u j i i , e t a l . (j5), M i l l e r , e t a l . (1), and L y o n , e t a l . (2) i n t h e i r m o d e l i n g e f f o r t s . In e i t h e r c a s e , t h e a c t i v a t i o n b a r r i e r used by t h e m o d e l e r s i s s m a l l ( 3 k c a l - m o l e " ) o r a b s e n t . The r a t e c o n s t a n t f o r NH+0? p r o d u c t s a t room t e m p e r a t u r e i s s m a l l ( 5 . 1 x 1 0 ^ c c m o l e ^ s e c " as measured by Z e t z s c h and Hansen ( 2 0 ) ; < 2 x l 0 c c m o l e " s e c " as measured b y P a g s b e r g , e t a l . ( 1 5 ) ) , a l t h o u g h a r a t e c o n s t a n t o f 3 . 6 x 1 ο c c m o l e ^ s e c " was measured i n d i r e c t l y by M c C o n n e l l 1

1

1

1 0

1 1

1

1


1


110

PROCESSES

To a s s i s t i n d i s t i n g u i s h i n g between t h e p o s s i b l e r e a c t i o n pathways and r a t e c o n s t a n t s , we p r e s e n t t h e c a l c u l a t e d e n e r g e t i c s o f t h e NH+0 s y s t e m i n F i g u r e 2. The s y s t e m i s c o m p l i c a t e d i n t h a t t h r e e p o t e n t i a l e n e r g y s u r f a c e s must be c o n s i d e r e d . We c a n i m m e d i a t e l y r u l e o u t t h e q u i n t e t s u r f a c e s i n c e no l o w - l y i n g i n t e r mediate s t a t e s o r f i n a l products e x i s t f o r t h i s surface. The l o w e s t r e a c t i o n pathway e x i s t s f o r t h e s i n g l e t s u r f a c e , f o r which t h e Η Ν 0 0 i n t e r m e d i a t e ( s t a b i l i z e d b y t h e N-0 bond e n e r g y which i s e s t i m a t e d t o be 22-29 k c a l - m o l e " ) c a n be f o r m e d w i t h o u t any s i g n i f i c a n t b a r r i e r . The Η Ν 0 0 s p e c i e s i s i s o e l e c t r o n i c w i t h o z o n e , a b i r a d i c a l s i n g l e t s p e c i e s ( 2 8 - 3 0 ) . The Η Ν 0 0 s p e c i e s c a n u n d e r g o r i n g c l o s u r e f o l l o w e d b y s c i s s i o n o f t h e 0-0 bond t o f o r m t h e s t a b l e n i t r o h y d r i d e i s o m e r . Our c a l c u l a t i o n s i n d i c a t e t h a t t h e a c t i v a t i o n e n e r g y f o r t h i s r i n g c l o s i n g and r e o p e n i n g s h o u l d be l e s s t h a n t h e 22-29 k c a l - m o l e " bond e n e r g y formed from t h e i n c o m i n g NH+0 . Having f o r m e d n i t r o h y d r i d e , t h e r e i s s u f f i c i e n t i n t e r n a l e n e r g y t o b r e a k t h e N-H bond t o f o r m H+N0 , i . e . ,


2

1

1

2

2

NH+0

*-Η+Ν0

2

Δ Η = -28 k c a l m o l e "

2

1

(8)

o r t o u n d e r g o a 1,2-hydrogen s h i f t t o f o r m t h e more s t a b l e Η 0 Ν 0 which c a n decompose t o f o r m Ν0+0Η ( r e a c t i o n ( 6 ) ) a s w e l l a s H+N0 ( r e a c t i o n ( 8 ) ) . Under t h e a p p r o p r i a t e c o n d i t i o n s one c o u l d f o r m t h e Η Ν 0 0 complex r a t h e r than t h e more s t a b l e Η 0 Ν 0 . I t s h o u l d be noted t h a t t h e d i r e c t d i s p l a c e m e n t r e a c t i o n f o r m i n g HN0+0( P) ( r e a c t i o n ( 7 ) ) c a n n o t o c c u r t h r o u g h t h e s t a b l e H N O O ^ A ) complex but must o c c u r on t h e h i g h e r l y i n g t r i p l e t s u r f a c e . Removing t h e 0 atom f r o m Η Ν Ο Ο ^ Α ' ) would p r o d u c e H N 0 ( A ) + 0 ( P ) a n a l o g o u s t o t h e i s o e l e c t r o n i c r e a c t i o n 0 ( Ρ ) + 0 ( Σ g ) - ^ 0 ( 2 g) + 0 ( P ) . However, u n l i k e 0 + 0 , t h i s r e a c t i o n i s e n d o t h e r m i c b y 19 k c a l - m o l e " , which would e x p l a i n why t h e r a t e c o n s t a n t f o r NH+0 i s s m a l l e r than t h a t f o r t h e i s o e l e c t r o n i c 0+0 (29) exchange reaction. R e a c t i o n ( 7 ) w i l l o c c u r on t h e t r i p l e t s u r f a c e t h r o u g h t h e metastable HN00( A') i n t e r m e d i a t e . T h i s i n t e r m e d i a t e i s c a l c u l a t e d t o be o n l y s l i g h t l y e n d o t h e r m i c ( 4 k c a l - m o l e " ) . T h e r e s h o u l d be a v e r y s m a l l a c t i v a t i o n b a r r i e r on t h e i n c o m i n g r e a c t i o n path. Of greater s i g n i f i c a n c e i s the outgoing r e a c t i o n 2

3

1

3

3

3

3

2

3

3

2

2

1

2

2

3

1


7.

MELIUS AND BINKLEY

111

Reactions of Ν H and NH with Ο and 0 2

3

2

3

p a t h ( H N 0 0 ( A ' ) — • H N 0 + 0 ( P ) ) which must undergo a t w o - e l e c t r o n a v o i d e d c u r v e c r o s s i n g v i a a b r e a k i n g o f p l a n a r symmetry, g i v i n g r i s e t o an a d d i t i o n a l 5-15 k c a l - m o l e " e n e r g y b a r r i e r . Thus, t h e a c t i v a t i o n e n e r g y f o r r e a c t i o n ( 7 ) s h o u l d be l a r g e r t h a n t h e 3 k c a l - m o l e " used by t h e m o d e l e r s . T a k i n g both s u r f a c e s i n t o a c c o u n t , we c o n c l u d e t h a t t h e room t e m p e r a t u r e p r o c e s s s h o u l d be dominated by r e a c t i o n s ( 6 ) and ( 8 ) on t h e s i n g l e t s u r f a c e w h i l e a t h i g h t e m p e r a t u r e s , r e a c t i o n ( 7 ) should dominate. 1


1

NHp+Q. Two s e t s o f p r o d u c t s have been p r o p o s e d (22,23) f o r t h e r e a c t i o n o f N H w i t h a t o m i c oxygen: 2

ΝΗ +0 —*-HN0+H

Δ Η = -28 k c a l - m o l e "

1

(9)

NH +o — * - 0 Η + Ν Η

Δ Η = -9 k c a l - m o l e "

1

(10)

2

and 2

T h e r e h a s been some q u e s t i o n as t o whether o r n o t r e a c t i o n (10) i s e n d o t h e r m i c o r e x o t h e r m i c . Based on o u r c a l c u l a t e d h e a t s o f f o r m a t i o n o f NH and NH , r e a c t i o n (10) s h o u l d be e x o t h e r m i c by 9 k c a l - m o l e " . The r a t e c o n s t a n t f o r NH +0 a t room t e m p e r a t u r e i s 2.1 χ l O ^ c c m o l e " s e c " a s measured by G e h r i n g , e t a l . ( 2 2 ) . T h i s i s s m a l l e r t h a n t h e measured r a t e c o n s t a n t s f o r t h e i s o e l e c t r o n i c s p e c i e s C H and OH r e a c t i n g w i t h 0 atom. Our t h e o r e t i c a l r e s u l t s (shown i n F i g u r e 3) i n d i c a t e t h a t b o t h r e a c t i o n s ( 9 ) and (10) a r e p o s s i b l e . On t h e d o u b l e t s u r f a c e , NH +0 s h o u l d f o r m t h e H N0 i n t e r m e d i a t e w i t h o u t an a c t i v a t i o n b a r r i e r . T h i s complex c a n r e a d i l y d i s s o c i a t e t o f o r m HNO+H (Reaction ( 9 ) ) . The r a d i c a l i n t e r m e d i a t e i s s u f f i c i e n t l y e x o t h e r mic t h a t i t c a n a l s o undergo a 1,2-hydrogen s h i f t t o f o r m HNOH which c a n d i s s o c i a t e t o f o r m e i t h e r HNO+H o r NH+OH ( R e a c t i o n s ( 8 ) or ( 9 ) ) . T h e r e s h o u l d a l s o be s u f f i c i e n t e n e r g y f o r H N0 t o d i s s o c i a t e t o N0+H 2

1

2

1

1

1

3

2

2

2

2s

NH +0 2

*-Ν0+Η

2

Δ Η = -85 k c a l - m o l e "

1

(11)

However, t h e dominant r e a c t i o n i s e x p e c t e d t o be t h e d i r e c t d i s placement r e a c t i o n (9) with s m a l l e r branching r a t i o s f o r r e a c t i o n s (10) and even l e s s f o r ( 1 1 ) .


112


PROCESSES

On t h e q u a r t e t s u r f a c e , no i n t e r m e d i a t e complex e x i s t s t h a t i s s t a b l e w i t h r e s p e c t t o NH +o . However, h y d r o g e n a b s t r a c t i o n ( r e a c t i o n (10)) can occur, having a small a c t i v a t i o n b a r r i e r . On t h e o t h e r hand, t h e r e i s no pathway t o t h e e x o t h e r m i c p r o d u c t s N ( S ) + H o. T h u s , we c o n c l u d e t h a t a t room t e m p e r a t u r e , t h e r e a c t i o n NH +o s h o u l d be d o m i n a t e d by r e a c t i o n ( 9 ) w i t h some s m a l l e r b r a n c h i n g p r o b a b i l i t y f o r r e a c t i o n s (10) and ( 1 1 ) , a l l o c c u r r i n g on t h e d o u b l e t s u r f a c e w i t h no a c t i v a t i o n e n e r g y . A t h i g h e r t e m p e r a t u r e s , t h e h y d r o g e n a b s t r a c t i o n r e a c t i o n (10) s h o u l d d o m i n a t e . We f i n d no r e a s o n t o e x p e c t t h e NH +o r e a c t i o n r a t e a t room t e m p e r a t u r e t o be a p p r e c i a b l y s m a l l e r t h a n i t s i s o e l e c t r o n i c c o u n t e r p a r t s , CH3+0 and OH+0. 2

4


2

2

2

NH+0. The r e a c t i o n NH+0 i s , i n many r e s p e c t s , a n a l o g o u s t o t h e r e a c t i o n o f NH +o. Two s e t s o f r e a c t i o n p r o d u c t s have been used i n c o m b u s t i o n m o d e l i n g , (1,3,5,) i . e . , 2

NH+0

*-Ν0+Η

Δ Η = -74 k c a l - m o l e "

1

(12)

NH+0

*-0Η+Ν

Δ Η = -24 k c a l - m o l e "

1

(13)

and

1

F o r r e a c t i o n ( 1 2 ) an a c t i v a t i o n e n e r g y o f 5 k c a l - m o l e " i s used w h i l e f o r r e a c t i o n (13) t h e a c t i v a t i o n e n e r g y used i s v e r y small (0.1 k c a l - m o l e " ) . I n F i g u r e 4, we p r e s e n t t h e r e s u l t s f o r t h e i s o m e r i c c o m p l e x e s on t h e l o w e s t s i n g l e t ( A ) and t r i p l e t ( A") s u r f a c e s . These r e s u l t s a r e c o n s i s t e n t with o t h e r work on t h e HNO s y s t e m ( 3 4 , 3 5 ) . The HNO r a d i c a l i n t e r m e d i a t e s c a n be formed from NH+0 w i t h o u t an e n e r g y b a r r i e r . The f o r m a t i o n e n e r g y o f t h e c o m p l e x e s i s s u f f i c i e n t t o e i t h e r d i s s o c i a t e t o H+NO ( r e a c t i o n ( 1 2 ) ) o r a l l o w t h e 1,2-hydrogen s h i f t ancj d i s s o c i a t i o n t o OH+N ( r e a c t i o n ( 1 3 ) ) . The A " s u r f a c e i s d i r e c t l y a n a l o g o u s t o t h e d o u b l e t s u r f a c e f o r NH +o ( F i g u r e 3 ) . F o r t h e A s u r f a c e t h e d o m i n a n t p r o d u c t s h o u l d be NO+H t h o u g h some N+OH c a n be f o r m e d . On t h e o t h e r hand, HNO formed on t h e Ϊ-Α' s u r f a c e c a n o n l y d i s s o c i a t e t o H+NO s i n c e f o r m a t i o n o f OH+N i s s p i n f o r b i d d e n . A t h i g h e r t e m p e r a t u r e s , t h e d i r e c t h y d r o g e n a b s t r a c t i o n r e a c t i o n c a n o c c u r , p a r t i c u l a r l y on the q u i n t e t s u r f a c e , r e q u i r i n g a small a c t i v a t i o n energy. T h u s , f o r NH+0 we c o n c l u d e t h a t t h e r e a c t i o n r a t e s h o u l d be 1

1

I

3

3

3

M

2


7.

MELIUS AND BINKLEY

Reactions of NH and NH

2

with Ο and 0

2

113

f a s t , w i t h no a c t i v a t i o n e n e r g y f o r r e a c t i o n s (12) and (13) g o i n g t h r o u g h t h e HNO i n t e r m e d i a t e and w i t h a s l i g h t a c t i v a t i o n e n e r g y f o r t h e d i r e c t hydrogen a b s t r a c t i o n r e a c t i o n ( 1 3 ) .


Conclusions The c a l c u l a t i o n a l a p p r o a c h used h e r e i n v o l v i n g f o u r t h - o r d e r M j a l l e r - P l e s s e t p e r t u r b a t i o n t h e o r y w i t h bond a d d i t i v i t y c o r r e c t i o n s (BAC-MP4), h a s been shown t o be a p o w e r f u l t o o l f o r d e t e r m i n i n g h e a t s o f f o r m a t i o n o f m o l e c u l a r s p e c i e s and f o r a n a l y z i n g p o s s i b l e r e a c t i o n p a t h w a y s . F o r N H and NH r e a c t i n g w i t h 0 and 0 we have been a b l e t o d i s t i n g u i s h between l i k e l y and u n l i k e l y r e a c t i o n p r o d u c t s b a s e d on t h e s t a b i l i t y o f v a r i o u s r e a c t i o n i n t e r m e d i a t e s compared t o t h e r e a c t a n t s and p r o d u c t s . The r e a c t i o n s s t u d i e d h e r e a r e t y p i c a l o f many systems i n t h a t t h e y a r e complex, i n v o l v i n g m u l t i p l e p o t e n t i a l e n e r g y s u r f a c e s w i t h c o m p e t i n g p a t h w a y s , even when t h e same p r o d u c t c h a n n e l e x i s t s . T h u s , t h e o r e t i c a l r e s u l t s such a s t h e s e can be h e l p f u l b o t h i n a n a l y z i n g e x p e r i m e n t a l r a t e c o n s t a n t s a s w e l l as i n com p u t e r m o d e l i n g o f r e a c t i o n s y s t e m s . A d d i t i o n a l work i s needed t o a d d r e s s t h e r e a c t i o n pathways f o r p r o d u c t s g o i n g t o o t h e r p r o d u c t s , s i n c e o t h e r p a r t s o f t h e p o t e n t i a l e n e r g y s u r f a c e may be i n v o l v e d . We a r e c u r r e n t l y i n t h e p r o c e s s o f d e v e l o p i n g an a p p r o a c h f o r c a l c u l a t i n g t r a n s i t i o n s t a t e e n e r g y b a r r i e r s (which were o n l y i n c l u d e d s c h e m a t i c a l l y i n t h i s p a p e r ) , which can be o f comparable accuracy t o the r e s u l t s presented here. 2

2

Acknowledgments The a u t h o r s would l i k e t o g i v e p a r t i c u l a r t h a n k s t o Dr. R. J . B l i n t o f General Motors f o r encouraging our i n v e s t i g a t i o n o f t h e s e N-H-0 r e a c t i o n s and p r o v i d i n g e n l i g h t e n i n g d i s c u s s i o n s i n v o l v i n g t h e p o s s i b l e r e a c t i o n m e c h a n i s m s . T h e a u t h o r s would a l s o l i k e t o thank D r s . J . A. M i l l e r , W. A. G o d d a r d , and M. J . F r i s c h f o r h e l p f u l discussions i n v o l v i n g various aspects o f t h i s r e s e a r c h . T h i s work was s u p p o r t e d by t h e U. S. Department o f E n e r g y , B a s i c E n e r g y S c i e n c e , C h e m i c a l P h y s i c s Program.



114

PROCESSES


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7.

23. 24.


25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

MELIUS A N D BINKLEY

Reactions of ΝH and NH with Ο and 0 2

2

115

E . A. Albers, K. Hoyermann, H. Gg. Wagner, and J. Wolfrum, 12th Symp. (Int.) Combust. Proc., 12th, 1969, 313. R. Krishnan, M. J. F r i s c h , and J. A. Pople, J. Chem. Phys. 1980, 72, 4244; R. Krishnan and J. A. Pople, Int. J. Quant. Chem., 1978, 14, 91. J . S. Binkley and C. F . Melius, to be published. P. E. Hariharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213. C. C. J. Roothaan, Rev. Mod. Phys., 1951, 23, 19. J . A. Pople and R. K. Ne sbet, J. Chem. Phys., 1954, 22, 571. J . A.Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Int. J. Quant. Chem., 1979, 513, 225. P. J. Hay, T. H. Dunning, and W. A. Goddard, J. Chem. Phys., 1975, 62, 3912. K. Yamaguchi, S. Yabushita, and T. Fueno, J. Chem. Phys., 1979, 71, 2321. A. J. Varandas and J. N. Murrell, Chem. Phys. L e t t . , 1982, 88, 1. L . B. Harding and W. A. Goddard, J. Amer. Chem.Soc.,1978, 100, 7180. P. J. Bruna, Chem. Phys., 1980, 49, 39; P. J. Bruna and C. M. Marian, Chem. Phys. Lett, 1979, 67, 109. O. Nomura and S. Iwata, Chem. Phys. Lett., 1979, 66, 523.

RECEIVED

December 21, 1983


The Chemistry of Combustion Processes - ACS Publications

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