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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
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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
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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
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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.
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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
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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
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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
7.
MELIUS AND BINKLEY
Reactions of NH and NH with Ο and 0 2
2
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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
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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
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Δ Η = -83 k c a l - m o l e "
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Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
(1)
CHEMISTRY OF COMBUSTION PROCESSES
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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
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Figure 2.
Same as i n Figure 1 f o r NH + 0,
Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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MELIUS AND BINKLEY
Reactions of NH and NH with Ο and 0 2
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7.
F i g u r e h.
Same as i n F i g u r e 1 f o r NH + 0.
Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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NH +o 2
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Δ Η = -10 k c a l - m o l e "
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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
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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
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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 "
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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
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Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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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 . ,
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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
Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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
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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 ) .
Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
112
CHEMISTRY OF COMBUSTION
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
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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
Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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 ) .
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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.
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CHEMISTRY OF COMBUSTION
114
PROCESSES
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7.
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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
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115
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RECEIVED
December 21, 1983
Sloane; The Chemistry of Combustion Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
