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MOLECULAR DYNAMICS STUDIES OF AQUEOUS SOLUTIONS
D. Bounds
To cite this version:
D. Bounds. MOLECULAR DYNAMICS STUDIES OF AQUEOUS SOLUTIONS. Journal de
Physique Colloques, 1984, 45 (C7), pp.C7-113-C7-117. �10.1051/jphyscol:1984711�. �jpa-00224272�
JOURNAL DE PHYSIQUE
Colloque C7, suppl6ment a u n09, Tome 45, septembre 1984 page C7-113
MOLECULAR DYNAMICS S T U D I E S OF AQUEOUS S O L U T I O N S
D . G . ~ o u n d s *
Department o f T h e o r e t i c a Z C h e m i s t r y , 1 S o u t h Parks Road, Oxford O X 1 3TG, U. K.
Rksumk
-
Des s i m u l a t i o n s de dynamique mo+kculaire+ont 'tk r 6 $ + i s k e s s_ur une s k r i e de s o l u t i o n s contenant l e s i o n s L i,
~ a * , K,
Ca", N i ou C 1.
Lesp o t e n t i e l s ion-eau o n t k t 6 obtenus p a r d e s c a l c u l s q u a n t i q u e s en u t i l i s a n t l a mkthode du g r a d i e n t rkcemment dbveloppke. Dans l a p l u s grande p a r t i e d e s c a s 06 d e s r k s u l t a t s expkrimentaux e x i s t e n t , l e s c a l c u l s s o n t en accord r a i - sonnable. Dans quelques c a s , il s e r a i t u t i l e d ' o b t e n i r de nouveaux r k s u l t a t s s t r u c t u r a u x p a r l a d i f f u s i o n d e s n e u t r o n s .
A b s t r a c t a s e r l e s
~ 1 - i o n s .
-
M o l e c u l a r dynamics s i m u l a t i o n s h a v e b e e n p e r f o r m e d on o f s o l u t i o n s c o n t a i n i n g ~ i + , ~ a + , K+, CaS+, N i + + , o r, The i o n - w a t e r p o t e n t i a l s were o b t a i n e d from quantum m e c h a n i c a l c a l c u l a t i o n s u s i n g t h e r e c e n t l y d e v e l o p e d g r a d i e n t method. I n most c a s e s where e x p e r i m e n t a l r e s u l t s a r e a v a i l a b l e t h e MD r e s u l t s a r e i n r e a s o n a b l e a g r e e m e n t . I n some c a s e s a r e m e a s u r e m e n t o f t h e n e u t r o n s t r u c t u r a l d a t a may b e w o r t h w h i l e .
INTRODUCTION
The f a c t o r s which i n f l u e n c e t h e dynamics o f i o n s i n aqueous s o l u t i o n , and t h e n a t u r e o f t h e h y d r a t i o n s h e l l s which s u r r o u n d them, h a v e been t h e s u b j e c t s o f many i n v e s t i g a t i o n s . Because t h e s o l v a t i o n s h e l l i s b e l i e v e d t o h a v e a s t r o n g i n f l u e n c e on i o n i c m o t i o n s , i t s s t r u c t u r e i s o f c o n s i d e r a b l e i n t e r e s t . The most d i r e c t way o f s t u d y i n g t h e s t r u c t u r e o f t h e s o l v a t i o n s h e l l i s by n e u t r o n s c a t t e r i n g u s i n g t h e f i r s t o r d e r d i f f e r e n c e method [ I ] , a n d t h e quantum l e a p i n o u r know- l e d g e o f i o n i c s o l u t i o n s o v e r t h e l a s t few y e a r s h a s come l a r g e l y from t h e a p p l i c a t i o n o f t h i s t e c h n i q u e .
However, measurements o f i o n - i o n c o r r e l a t i o n s by s e c o n d o r d e r d i f f - e r e n c e s a r e s t i l l v e r y d i f f i c u l t . Measurements o f i o n - w a t e r c o r r e l a - t i o n s r e q u i r e s i g n i f i c a n t amounts o f beam t i m e a n d t h e i r i n t e r p r e t a - t i o n i s n o t a l w a y s unambiguous. S i m u l a t i o n s t u d i e s c a n be a u s e f u l a i d i n u n r a v e l l i n g s u c h d a t a and may s u g g e s t new e x p e r i m e n t s .
F u r t h e r m o r e , c o m p u t e r s i m u l a t i o n s g i v e a much more d e t a i l e d model f o r s o l u t i o n s t h a n i s o b t a i n a b l e from any e x p e r i m e n t a l t e c h n i q u e .
S i m u l a t i o n s o f i o n i c s o l u t i o n s h a v e been a l m o s t e n t i r e l y r e s t r i c t e d t o a l k a l i o r h a l i d e i o n s a n d , w i t h t h e e x c e p t i o n o f t h e work o f S z a s z e t a l . [ 2 1 , t o a s i n g l e i o n s u r r o u n d e d by w a t e r m o l e c u l e s [ 3 , 4 1 . Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984711
C7-114 JOURNAL DE PHYSIQUE
Many of t h e b e s t e x p e r i m e n t a l d a t a a r e f o r more c o m p l i c a t e d i o n s s u c h a s t r a n s i t i o n m e t a l s [ 5 ] , o r i n c o n c e n t r a t e d s o l u t i o n s where t h e r e a r e n o t enough w a t e r m o l e c u l e s t o s o l v a t e a l l i o n s f u l l y . The aims o f t h e p r e s e n t r e s e a r c h program a r e t o s t u d y t h e i o n s on which n e u t r o n measurements h a v e b e e n made, a n d t o s i m u l a t e c o n c e n t r a t e d s o l u t i o n s c o n t a i n i n g b o t h p o s i t i v e a n d n e g a t i v e i o n s . I n t h i s comm- u n i c a t i o n we r e p o r t some p r e l i m i n a r y r e s u l t s f o r a q u e o u s s o l u t i o n s c o n t a i n i n g a s i n g l e ~ i + , ~ a + , ,'K Ca
+ + ,
~ i + + o r ~ 1 - i o n .SIMULATION METHODS
A l l c a l c u l a t i o n s h a v e been c a r r i e d o u t by t h e method o f m o l e c u l a r dynamics i n t h e ( ? J , V , E ) e n s e m b l e . The s y s t e m c o n s i s t e d o f one i o n and 64 r i g i d w a t e r m o l e c u l e s i n a c u b i c box w i t h t h e u s u a l p e r i o d i c boundary c o n d i t i o n s . S i m u l a t i o n s on ~ i ' , Na', ,K' ~ 1 - a n d F- i o n s which u s e d a d i f f e r e n t s e t o f p o t e n t i a l s t o t h o s e u s e d h e r e h a v e shown l i t t l e d e p e n d e n c e on s y s t e m s i z e between 64 and 125 w a t e r mol- e c u l e s y s t e m s [ 4 ] . The e q u a t i o n s o f m o t i o n were i n t e g r a t e d u s i n g t h e Verlet a l g o r i t h m a n d t h e geometry o f t h e w a t e r m o l e c u l e s w a s p r e - s e r v e d by t h e c o n s t r a i n t s method o f R y c k a e r t , C i c c o t t i a n d B e r e n d s e n
[ 6 ] . The e l e c t r o s t a t i c e n e r g y which a r i s e s b o t h from t h e i o n - w a t e r i n t e r a c t i o n s was summed u s i n g t h e Ewald method. T h e s e t e c h n i q u e s h a v e b e e n d e s c r i b e d f u l l y by Impey, Madden and McDonald [ 4 ] . For. t h e a l k a l i i o n s and
e l - ,
a t i m e s t e p o f 5 x 10-15s g i v e s s a t i s - f a c t o r y e n e r g y c o n v e r g e n c e when t h e a t o m i c masses o f t h e most abun- d a n t i s o t o p e s o f t h e i o n s and t h o s e o f ~ ~ a r e t a k e n . 0 ' ~ F o r t h e Ca++
and ~ i + + r u n s , e q u a l masses were u s e d f o r a l l a t o m s . A minimum o f 2000 t i m e s t e p s was a l l o w e d f o r e q u i l i b r a t i o n and s t a t i s t i c s were a c c u m u l a t e d o v e r a p p r o x i m a t e l y 5000 s t e p s . Runs of d o u b l e t h i s l e n g t h f o r ~ a + + show no s i g n i f i c a n t c h a n g e i n thermodynamic p r o p e r - t i e s o r t h e p a r t i a l r a d i a l d i s t r i b u t i o n f u n c t i o n s , b u t l o n g e r r u n s a r e c e r t a i n l y n e c e s s a r y f o r N i+ + .
I n a l l c a s e s t h e volume o f t h e box c o r r e s p o n d e d t o t h e d e n s i t y o f w a t e r a t ~ O C .POTENTIALS
The p o t e n t i a l u s e d f o r t h e w a t e r - w a t e r i n t e r a c t i o n s i s t h e model de- s i g n a t e d TIP4P by J o r g e n s e n e t a l . [ 7 ] . T h i s r a t h e r s i m p l e model c o n s i s t s o f a L e n n a r d - J o n e s 1 2 - 6 p o t e n t i a l between t h e oxygen atoms t o g e t h e r w i t h a s e t o f 3 c h a r g e s p e r m o l e c u l e : one on e a c h hydrogen and t h e o t h e r d i s p l a c e d away from oxygen on t h e C 2 a x i s . T h i s model g i v e s a s a t i s f a c t o r y d e s c r i p t i o n o f t h e s t r u c t u r e o f p u r e w a t e r [ 7 ] . The i o n - w a t e r p o t e n t i a l i s a l s o made up o f an e l e c t r o s t a t i c i n t e r -
a c t i o n between t h e i o n i c c h a r g e and a s e t o f c h a r g e s r e p r e s e n t i n g t h e w a t e r m o l e c u l e , t o g e t h e r w i t h some atom-atom t e r m s . The w a t e r c h a r g e d i s t r i b u t i o n i s t h a t which i s u s e d f o r t h e w a t e r - w a t e r p o t e n - t i a l . I t i s i m p o r t a n t t o k e e p t h e w a t e r c h a r g e d i s t r i b u t i o n f i x e d f o r a l l i n t e r a c t i o n t y p e s , s i n c e Rossky h a s shown [ 8 ] t h a t i f d i f f - e r e n t c h o i c e s are made f o r d i f f e r e n t i o n s it i s p o s s i b l e t o o b t a i n a n e g a t i v e s o l v e n t d i e l e c t r i c c o n s t a n t . The r e m a i n i n g atom-atom p a r t o f t h e p o t e n t i a l i s w r i t t e n a s :
f o r t h e c a t i o n - w a t e r p o t e n t i a l s , and a s :
f o r t h e c h l o r i d e - w a t e r p o t e n t i a l . The c o n s t a n t s A , B , C , D were t a k e n from quantum m e c h a n i c a l c a l c u l a t i o n s on t h e i s o l a t e d i o n - w a t e r s y s t e m s [ 9 1 . The quantum c a l c u l a t i o n s u s e d l a r g e g a u s s i a n b a s i s s e t s and a r e o f s i m i l a r q u a l i t y t o t h e b e s t i o n - w a t e r p o t e n t i a l s p u b l i s h e d t o d a t k [ l o ] .
SIMULATION RESULTS
The p o s i t i o n s of t h e m a j o r p e a k s i n t h e p a r t i a l r a d i a l d i s t r i b u t i o n f u n c t i o n s a r e shown i n T a b l e 1. They a r e compared w i t h t h e e x p e r i - m e n t a l r e s u l t s which a r e most a p p r o p r i a t e a n d w i t h t h e MD r e s u l t s o f Impey
,
Madden and McDonald [ 4 ] who u s e d a d i f f e r e n t s e t of p o t e n t i a l s .T h e r e i s a s y s t e m a t i c t r e n d f o r t h e peak p o s i t i o n s t o b e o v e r - e s t i m a t e d f o r a l l c a t i o n s . However, i t i s c u s t o m a r y t o d i s c u s s t h e l o c a l o r d e r a r o u n d t h e i o n i n t e r m s o f t h e a n g l e s 8 a n d Y d e f i n e d i n F i g u r e 1. Wherever comparison w i t h e x p e r i m e n t i s p o s s i b l e , t h e v a l u e s o f 9 and Y a r e s a t i s f a c t o r y .
F i g u r e 1
JOURNAL DE PHYSIQUE
T a b l e 1 I o n - w a t e r peak p o s i t i o n s
I on T/K R ~ ~ / K B/o c o o r d i n a t i o n number
~ i + 304 2.04
Exp [Ill 1.9520.02
I M M 141 278 1.98
~ a + 287 2.35
I M M [4] 2 8 2 2.29
K + 293 2.86
I M M [4] 274 2.76
~ a + + 2 8 6 2.54
E x p t [I21 293 2.4620.03
~ i + + 316 2.17
E x p t [5] 294 2.0720.02
~ 1 - 2 79 3.23
Expt [5] 294 3.2020.04
I M M [4] 2 8 7 3.29
T h e r e a r e o n l y two i o n s f o r w h i c h - i t i s p o s s i b l e t o t e s t b o t h t h i s model a n d t h e K i s t e n m a c h e r , P o p k i e , C l e m e n t i / M a t s u o k a , C l e m e n t i
,
Yoshimine (KPC/MCY) model which was u s e d i n [41 a g a i n s t e x p e r i m e n t . F o r ~ i + , t h e KPC/MCY model i s somewhat c l o s e r w h i l e f o r ~ 1 - t h e p r e s e n t v a l u e s a r e c o n s i d e r a b l y b e t t e r . No o t h e r s i m u l a t i o n s a p p e a r
++ + + ++
t o h a v e b e e n r e p o r t e d f o r Ca o r N i
.
F o r Ca,
t h e main s t r u c - t u r a l f e a t u r e s a r e i n a c c o r d w i t h t h e n e u t r o n r e s u l t s a n d we have t h e r e f o r e c h o s e n t h i s i o n f o r a s t u d y o f t h e e f f e c t s o f t e m p e r a t u r e and p r e s s u r e on t h e s t r u c t u r e o f t h e s o l v a t i o n s h e l l .A f u l l d e s c r i p t i o n o f t h e N i + + r e s u l t s i s n o t y e t p o s s i b l e . How- e v e r , many of t h e o b s e r v e d f e a t u r e s o f N i + + h y d r a t i o n a r e v i s i b l e i n t h e s i m u l a t i o n r e s u l t s . The m a j o r d i s c r e p a n c y i s t h e c o o r d i n a - t i o n number which i s e s t i m a t e d , t e n t a t i v e l y , t o b e n e a r e r 8 t h a n t h e v a l u e of 6 which i s w i d e l y q u o t e d [5, 131. I t must be empha- s i s e d t h a t much l o n g e r r u n s a r e n e e d e d t o achieve d e p e n d a b l e v a l u e s . However, a r e - e x a m i n a t i o n o f t h e n e u t r o n r e s u l t s a s a f u n c t i o n o f c o n c e n t r a t i o n s u g g e s t s t h a t t h e v a l u e may w e l l b e g r e a t e r t h a n 6 a t h i g h d i l u t i o n .
I t h a n k R.W. I m p e y f o r a c o p y of h i s MD p r o g r a m , a n d J . E . E n d e r b y a n d G.W. N e i l s o n f o r u s e f u l d i s c u s s i o n s of t h e e x p e r i m e n t a l d a t a . T h i s r e s e a r c h w a s c a r r i e d o u t u n d e r SERC g r a n t G R / C / 4 1 6 1 6 .
*
R a m s a y M e m o r i a l F e l l o w 1 9 8 2-
8 4 . REFERENCES[ I ] SOPER, A . K . , N E I L S O N , G.W., ENDERBY, J . E . a n d HOWE, R . A . , J . P h y s . C10 ( 1 9 7 7 ) 1 7 9 3 .
[ 2 1 S Z A S Z , G . I . , H E I N Z I N G E R , K. a n d R I E D E , W . O . , Z , N a t u r f o r s c h . , 36 ( 1 9 8 1 ) 1 0 6 7 .
[ 3 ] M E Z E I , M . a n d BEVERIDGE, D . L . , J . C h e m . P h y s . , 7 4 ( 1 9 8 1 ) 6 9 0 2 . [ 4 ] IMPEY, R.W., MADDEN, P . A . a n d McDONALD, I . R . , J . P h y s . C h e m
.,
8 7 ( 1 9 8 3 ) 5 0 7 1
.
[ 5 ] NEILSON, G.W. a n d ENDERBY, J . E . , P r o c . R o y . S o c . L o n d . , A 3 9 0 ( 1 9 8 3 ) 3 5 3 .
[ 6 ] RYCKAERT, J . P . , C I C C O T T I , G . and BERENDSEN, H . J . C . , J . C o m p u t . P h y s . , 2 3 ( 1 9 7 7 ) 3 2 7 .
[ 7 I JORGENSEN
,
W . L .,
CHANDRASEKHAR, J .,
MADURA, J . D.,
IMPEY, R. W..a n d K L E I N , M. L.
,
J . C h e m . P h y s. ,
7 9 ( 1 9 8 3 ) 9 2 6 . [ e l ROSSKY, P . R . , M o l e c . P h y s . , 4 8 ( 1 9 8 3 ) 6 1 5 .[ 9 ] BOUNDS, D.G. a n d BOUNDS, P . J . , Molec. P h y s . , 5 0 ( 1 9 8 3 ) 2 5 ; i b i d , 5 0 ( 1 9 8 3 ) 1 1 2 5 .
[ I 0 1 DACRE, P . D . , Molec. P h y s . , 5 1 ( 1 9 8 4 ) 6 3 3 .
[ I l l NEWSHOME, J . R . , NEILSON, G.W. a n d ENDERBY, J . E . , J . P h y s . C 1 3 ( 1 9 8 0 ) L 9 2 3 .
[ I 2 1 HEWISH, N . A . , NEILSON, G.W. a n d ENDERBY, J . E . , N a t u r e , 2 9 7 ( 1 9 8 2 ) 1 3 8 .
[ I 3 1 GIAQUINTA, P . V . , T O S I , M . P . a n d MARCH, N . H . , P h y s . C h e m . L i q . , 1 3 ( 1 9 8 4 ) 1.
