Application of NMR Spectroscopy to Studies of Aqueous Coordination

11 Application of NMR Spectroscopy to Studies of Aqueous Coordination Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 14, 2016 | http://pubs.acs.org Publication Date: May 5, 1996 | doi: 10.1021/ba-1995-0246.ch011

Chemistry of Vanadium(V) Complexes Debbie C . Crans, Paul K. Shin, and Kathleen B. Armstrong Department of Chemistry, Colorado State University, Fort Collins, C O 80523-1872

The structure and dynamic processes of a series of oxovanadium(V) complexes with multidentate ethanolamine- or EDTA (ethylenediaminetetraacetic acid)-derived ligands are characterized using multinuclear NMR spectroscopy. Coordination-induced shifts (CIS) are used to determine the connectivity in the complex. O NMR spectroscopy is used to identify geometries in aqueous solution. V NMR spectroscopy is used to determine the H -dependent formation constants of vanadate oxoanions. Dynamic processes are conveniently studied using ID and 2D magnetization transfer techniques. Examples of applications of qualitative and quantitative 2D exchange spectroscopy (EXSY) are given. The major source of error in the rate constants originates in the volume integrations of the EXSY spectra, which are very sensitive to baseline correction. For exchange between strong off-diagonal resonances, the error in the site-to-site rate constants can approximate 10%, but for exchange between weak signals the error can be 100% or more. Consequently, 2D EXSY spectroscopy is a promising tool with which mechanistic problems in both chemistry and biology may be investigated. 17

51

+

NUCLEAR MAGNETIC RESONANCE

( N M R ) s p e c t r o s c o p y is i n c r e a s i n g l y b e i n g a p p l i e d to structural, t h e r m o d y n a m i c , mechanistic, a n d dynamic studies of b i o i n o r g a n i c systems. T h e large n u m b e r o f N M R - a c t i v e n u c l e i provide several alternative handles w i t h w h i c h to study metal complexes by N M R spectroscopy ( i ) . P r o t o n and carbon-13 are particularly useful nuclei because the interpretation of their N M R spectra allows determination of the connectivity between metal a n d ligand i n diamagnetic metal complexes. Recent advances i n t h e N M R spectroscopy o f para0065-2393/95/0246-0303$09.08/0 © 1995 American Chemical Society

Thorp and Pecoraro; Mechanistic Bioinorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1996.

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304

M E C H A N I S T I C BIOINORGANIC CHEMISTRY

m a g n e t i c s p e c i e s s h o w t h a t s u c h m e t a l c o m p l e x e s c a n also b e s t u d i e d (2-4). I n t h i s c h a p t e r w e d e s c r i b e o u r s t u d i e s o f t h e s o l u t i o n s t r u c t u r e s o f a n u m b e r o f v a n a d i u m ( V ) c o m p l e x e s t h r o u g h t h e use o f N M R t e c h n i q u e s , i n c l u d i n g c o o r d i n a t i o n - i n d u c e d shifts ( C I S ) o f N M R r e s o n a n c e s , h e t e r o n u c l e a r c o r r e l a t i o n e x p e r i m e n t s , a n d i s o t o p i c l a b e l i n g . W e also h a v e u s e d N M R s p e c t r o s c o p y i n t h e d e t e r m i n a t i o n o f f o r m a t i o n constants a n d as a t o o l t o m o n i t o r a r e a c t i o n ' s p r o g r e s s . F i n a l l y , w e h a v e u s e d 2 D N M R exchange spectroscopy ( E X S Y ) to e x a m i n e q u a l i t a t i v e l y a n d q u a n titatively intra- and intermolecular processes i n aqueous vanadium(V) complexes. N M R s p e c t r o s c o p y is a v a l u a b l e t o o l i n b i o i n o r g a n i c c h e m i s t r y b e c a u s e s u c h a l a r g e n u m b e r o f e l e m e n t s h a v e N M R - a c t i v e n u c l e i (1). T a b l e I lists s p i n V2 n u c l e i a n d t h o s e n u c l e i w i t h s p i n l a r g e r t h a n V2 u p to a t o m i c n u m b e r 2 0 9 a n d t h e i r n a t u r a l abundances ( i ) . T h e p r a c t i c a l aspects o f s t u d y i n g a p a r t i c u l a r n u c l e u s b y N M R d e p e n d o n t h e p r o p erties of the nucleus and on the e x p e r i m e n t a l feasibility of the N M R e x p e r i m e n t . O n e i m p o r t a n t p r o p e r t y o f t h e n u c l e u s is its n a t u r a l a b u n d a n c e (1). B o t h Ή a n d V a r e p r e s e n t t o g r e a t e r t h a n 9 9 % , m a k i n g t h e m p a r t i c u l a r l y a m e n a b l e to s t u d y b y N M R s p e c t r o s c o p y . L o w n a t u r a l a b u n d a n c e n u c l e i s u c h as C a n d 0 (1.1 a n d 0 . 0 3 % , r e s p e c t i v e l y ) , r e q u i r e l o n g e r a c q u i s i t i o n t i m e s f o r d e t e c t i o n b y N M R , a n d i n t h e case of 0 , samples e n r i c h e d i n 0 must generally be p r e p a r e d . T h e spin q u a n t u m n u m b e r o f t h e p a r t i c u l a r n u c l e u s is a n e q u a l l y i m p o r t a n t property. T h e quadrupole moments of nuclei w i t h ί > h result i n r a p i d r e l a x a t i o n o f t h e i r N M R r e s o n a n c e s w i t h a c o n c o m i t a n t loss i n r e s o l u t i o n and sensitivity. A d d i t i o n a l properties affecting the quality of the N M R s p e c t r u m o f a g i v e n n u c l e u s i n c l u d e its m a g n e t o g y r i c r a t i o , its r e l a t i v e r e c e p t i v i t y , a n d its q u a d r u p o l e m o m e n t ( w h i c h affects t h e s i g n a l w i d t h ) (1). T h e s e n u c l e a r p a r a m e t e r s d i c t a t e t h e s e n s i t i v i t y o f a n u c l e u s a n d t h e i n f o r m a t i o n that m a y b e d e r i v e d f r o m its N M R s p e c t r u m . O f p r a c t i c a l i m p o r t a n c e is t h e N M R f r e q u e n c y at w h i c h t h e n u c l e u s r e s o n a t e s . S p e c trometers can be equipped w i t h broadband probes, w h i c h enable the d e t e c t i o n o f m o s t n u c l e i i n a d d i t i o n to Ή . N u c l e i o f w e a k m a g n e t i c s t r e n g t h s u c h as Y , R h , and F e , however, do require special i n s t r u m e n t a t i o n . A l s o o f p r a c t i c a l i m p o r t a n c e t o a n N M R e x p e r i m e n t is the presence o f paramagnetic species i n the sample that can adversely affect t h e s p e c t r u m . 5 1

1 3

1 7

1 7

1 7

l

8 9

1 0 3

5 7

Research Problems Suitable for NMR Spectroscopic Study T h e r e are a n u m b e r o f g e n e r a l p r o b l e m s o f interest to a c h e m i s t that c a n b e a d d r e s s e d b y N M R s p e c t r o s c o p y . N M R studies can be i n s t r u m e n t a l i n e l u c i d a t i n g the structure of n u c l e i c acids. T h e i n t e r a c t i o n of substrates w i t h cofactors

bioinorganic spectroscopic proteins and or other eel-



3

87

Ge(7.73, %)

Rb(27.85, / )

87

201

2

2

3

2

2

Hg(13.22, / )

3

Ba(11.32, / )

2

3

195

Pt(33.8)

Ag(48.18)

C(1.108) '

109

199

Hg(16.84)

Cd(12.26)

N(0.37)

113

15 19

205

T1(70.50)

Sn(8.58)

F(100)

119

37

2

2

2

3

2

9

2

Nb(100, / )

209

139

7

2

3

2

Bi(100, / )

7

2

La(99.911, / )

123

[ Sb(42.75, / )]

93

79

3

2

Cu(30.91, / )

7

Ti(5.51, / )

C1(24.47, / )

3

[ Br(50.54, %)]

65

49

3

Ne(0.257, / )

Li(92.58, / )

21

7

39 2

2

181

7

2

Ta(99.988, / )

I(100, %)

Mo(15.72,%)

3

2

Br(49.46, / )

5

2

Zn(4.11, / )

7

3

2

K(93.10, / )

3

2

V(99.76, / )

127

95

81

67

51

3

Na(100, / )

Be(100, / )

23

9

c

b

a

1

2

2

2

2

185

3

2

Xe(21.18, / )

43

7

2

Ca(0.145, / )

3

2

187

7

2

Re(62.93, %)

Cs(100, / )

113

133

[ In(4.28, %)]

85

Ga(39.6, / )

Mn(100, %) [ Rb(72.15,%)]

71

55

2

A1(100, %)

3

Tm(100)

Fe(2.19) 69

,7

B(80.42, / ) 27

n

Xe(26.44)

P(100)

129

31

[ Re(37.07, %)]

131

97

9

Kr(11.55, / )

3

2

[ Mo(9.46, %)]

83

69

3

Cr(9.55, / ) [ Ga(60.4, / )]

53

41

5

Mg(10.13, / )

B(19.58, 3)

Pb(22.6)

[ K(6.88, %)]

25

10

6,

207

2

Te(6.99)

Si(4.70)

125

29

NOTE: The boxes indicate nuclei used in N M R studies described in this chapter. If spin is no further information is provided. The natural abundance is indicated in parentheses. The spin (> / ) are indicated in parentheses after the natural abundance. If the entire nucleus is in brackets, this nucleus is not the most favorable nucleus for a particular element.

3

Os(16.1, / )

189

2

2

Sb(57.25, %)

9

2

3

Sr(7.02, / )

3

As(100, / )

137

3

2

Cu(69.09, / )

I Ba(6.59, / )]

135

3

Ti(7.28, %)

C1(75.53, / )

ln(95.72, %)

115

2

4

0

Spin >y spin given in parentheses after natural abundance

Q(3.7 X 10" , %)

121

2

75

73

3

63

Co(100, / )

59

2

47

7

35

Sc(100, / )

2

S(0.76, %)

7

l7

187Os(1.64) r

Rh(100)

N M R nuclei spin % nuclei

l

The NMR-Active Nuclei of Spin % and Those with Spin > /

He(1.3 Χ 10" )

103

3

Li(7.42, 1)

17

6

W(14.40)

45

D

183

Y(100)

H(-)

89

33

N(99.63, 1)

H(1.5 X 10

14

2

Yb(14.31)

Se(7.58)

171

77

1 Ή(99.985)|

Table I.


306



lular components i n a biological system can b e defined (5-7). I n addition, functional and structural models can be characterized (7-9). A l t h o u g h N M R s p e c t r o s c o p y is a v e r y p o w e r f u l t o o l , c o r r o b o r a t i v e s t u d i e s w i t h other experimental methods are essential to many applications. I n this chapter, w e focus o n m u l t i n u c l e a r N M R studies r e l a t e d to the b i o c h e m istry o f vanadium(V). T h e discovery o f the vanadium-containing haloperoxidases a n d n i trogenases, i n c o n j u n c t i o n w i t h t h e k n o w n insulin m i m e t i c activity o f v a n a d i u m , has i n c r e a s e d t h e i n t e r e s t i n v a n a d i u m c o o r d i n a t i o n c h e m i s t r y (10-12). B e c a u s e m a n y p r o t e i n s exist a n d f u n c t i o n i n a n a q u e o u s e n v i ronment, t h e elucidation o f the chemistry o f v a n a d i u m i n aqueous sol u t i o n is e s s e n t i a l f o r m i m i c k i n g a n d h e n c e u n d e r s t a n d i n g t h e f u n c t i o n s o f t h e s e p r o t e i n s . C o m p l e x e s c o n t a i n i n g v a n a d i u m ( V ) a r e d°, m a k i n g t h e m diamagnetic. A s such, they are ideal candidates for study b y N M R s p e c t r o s c o p y (JO, 12). T h e p r o p e r t i e s o f v a n a d i u m ( V ) a r e i n c o n t r a s t t o those of the paramagnetic vanadium(IV) complexes, w h i c h can b e s t u d i e d e f f e c t i v e l y b y e l e c t r o n p a r a m a g n e t i c r e s o n a n c e ( E P R ) s p e c t r o s c o p y (13, 14). S o l i d - s t a t e c h a r a c t e r i z a t i o n o f v a n a d i u m ( V ) c o m p l e x e s b y X - r a y crystallography reveals that t h e i r structures i n aqueous solution d o n o t always c o r r e s p o n d to their solid-state structures ( i 5 ) . These findings demonstrate t h e n e e d for structure e l u c i d a t i o n studies i n solution. V a n a d i u m ^ ) and vanadium(IV) derivatives show both similarities and diff e r e n c e s i n t h e i r c o o r d i n a t i o n b y m u l t i d e n t a t e l i g a n d s (16-23). T h e s e differences further illustrate t h e n e e d for solution-state investigation o f v a n a d i u m ( V ) d e r i v a t i v e s . W e d e s c r i b e h e r e s o m e a p p l i c a t i o n s o f H, C , 0 , a n d V N M R spectroscopy to the characterization of the struct u r a l a n d d y n a m i c p r o p e r t i e s o f a series o f aqueous v a n a d i u m ( V ) complexes. l

1 3

1 7

5 1

Experimental Parameters A l l samples for study b y N M R s p e c t r o s c o p y c o n t a i n e d D 0 a n d t h e i r p r e p aration h a v e b e e n d e s c r i b e d i n d e t a i l e l s e w h e r e (24-26). P r o t o n N M R s p e c t r a w e r e a c q u i r e d o n a B r u k e r A C P - 3 0 0 N M R s p e c t r o m e t e r (7.0 T ) u s i n g standard p a r a m e t e r s . C a r b o n - 1 3 N M R s p e c t r a w e r e a c q u i r e d w i t h a 2 0 0 p p m s p e c t r a l w i n d o w , a 9 0 ° p u l s e w i d t h a n d a r e l a x a t i o n d e l a y o f 7 0 0 ms. E x p o n e n t i a l l i n e - b r o a d e n i n g (2 H z ) was a p p l i e d to the free i n d u c t i o n d e c a y ( F I D ) p r i o r to F o u r i e r t r a n s f o r m a t i o n . Phase-sensitive c o r r e l a t i o n spectroscopy ( C O S Y ) a n d heteronuclear correlation ( H E T C O R ) spectra were acq u i r e d o n a B r u k e r A C P - 3 0 0 N M R s p e c t r o m e t e r (7.0 T ) u s i n g s t a n d a r d p a r a m e t e r s . T h e m i x i n g t i m e was 3 0 0 ms f o r the 2 D C E X S Y e x p e r i m e n t a n d 8 ms for the 2 D V E X S Y e x p e r i m e n t . B o t h e x p e r i m e n t s w e r e a c q u i r e d u s i n g parameters d e s c r i b e d p r e v i o u s l y (25, 26). T h e results f r o m t h e 2 D E X S Y e x p e r i m e n t , u s i n g these p a r a m e t e r s , w e r e e x a m i n e d b y c o m p a r i n g the exchange rate constants f r o m t h e 2 D E X S Y e x p e r i m e n t w i t h exchange rate constants f r o m a I D m a g n e t i z a t i o n transfer e x p e r i m e n t (27). T h e v a r i able t e m p e r a t u r e e x p e r i m e n t s w e r e c o n d u c t e d after c a l i b r a t i n g t h e p r o b e 2

1 3

5 1


11.

CRANS E T AL.

307

Chemistry of Vanadium(V) Complexes

using a m e t h a n o l standard (28). T h e 0 N M R s p e c t r u m of a sample e n r i c h e d i n 0 b y the a d d i t i o n of 1 5 % H 0 was r e c o r d e d at 41 M H z (7.0 T ) u s i n g a 9 0 ° p u l s e w i d t h a n d no r e l a x a t i o n d e l a y (28). T h e V N M R s p e c t r a w e r e r e c o r d e d at 5 2 . 6 M H z (4.7 T ) or 7 9 . 0 M H z (7.0 T ) u s i n g 9 0 ° p u l s e angles a n d no r e l a x a t i o n delay. 1 7

1 7

2

1 7

5 1


Structural Studies O n e - d i m e n s i o n a l N M R studies p r o v i d e information about the nuclear environment surrounding the nucleus. T h e theory of N M R and further experimental considerations have been described i n detail elsewhere (29). T h e c h e m i c a l s h i f t , δ, o f a n N M R s i g n a l , p r o v i d e s s t r u c t u r a l i n f o r m a t i o n , as d o e s its i n t e g r a t i o n ( r e l a t i v e t o o t h e r signals) a n d its c o u p l i n g pattern. T h e N M R spectra of most molecules exhibit complex c o u p l i n g patterns. A l t h o u g h c o u p l i n g i n f o r m a t i o n can be valuable, analysis of a s p e c t r u m m a y b e s i m p l i f i e d , a n d its s i g n a l - t o - n o i s e r a t i o ( S : N ) i n c r e a s e d t h r o u g h d e c o u p l i n g . A s a result, C N M R spectra are frequently r e corded decoupled from their attached protons. T h e combination of a * H spectrum and a decoupled C s p e c t r u m is v e r y p o w e r f u l i n e x p l o r i n g the solution-state structure of metal complexes w i t h organic ligands. T h e f o l l o w i n g e x a m p l e s i l l u s t r a t e t h e use o f N M R e x p e r i m e n t s i n p r o b i n g the structures of aqueous vanadium(V) complexes. 1 3

1 3

Application of H and C N M R Spectroscopy for Structural Studies of Vanadium(V) Complexes. V a n a d a t e c a n p o t e n t i a l l y f o r m 1

1 3

a series o f c o m p l e x e s w i t h m u l t i d e n t a t e l i g a n d s c o n t a i n i n g v a r i o u s f u n c tionalities. F o r example, vanadate can interact w i t h ethanolamine and e t h y l e n e d i a m i n e t e t r a a c e t i c a c i d ( E D T A ) - d e r i v e d ligands to f o r m c o m p l e x e s w i t h u p t o six m o i e t i e s c h e l a t e d t o t h e m e t a l . C h e l a t i o n t o t h e m e t a l w i l l shift t h e c h e m i c a l shifts o f t h e * H a n d C n u c l e i i n t h e l i g a n d , r e s u l t i n g i n d i s t i n c t a n d c h a r a c t e r i s t i c C I S s , d e f i n e d as δ ι - 5i . A s a result, * H a n d C N M R spectroscopy are w e l l - s u i t e d tools w i t h w h i c h to study the s o l u t i o n structures o f m e t a l c o m p l e x e s . T h e H N M R s p e c t r u m a n d t h e C N M R s p e c t r u m o f E D T A a n d its v a n a d a t e c o m p l e x ( V - E D T A ) a r e s h o w n i n F i g u r e 1. A l s o s h o w n i n F i g u r e 1 a r e t h e * H and C spectra of E D T A alone. Integration of the * H N M R resonances suggests t h a t a b o u t 7 5 % o f t h e E D T A l i g a n d is t i e d u p as V - E D T A . T h i s p e r c e n t a g e is c o n f i r m e d b y V N M R s p e c t r o s c o p y . T h e C N M R s p e c t r u m o f t h e f r e e l i g a n d c o n t a i n s t h r e e signals, w h e r e a s t h a t o f t h e l i g a n d c o m p l e x m i x t u r e c o n t a i n s e i g h t s i g n a l s . T h e five r e m a i n i n g s i g n a l s a r e c o n s i s t e n t w i t h a c o m p l e x t h a t c o n t a i n s t w o t y p e s o f a c e t a t e a r m s , as s h o w n i n t h e s t r u c t u r e i n F i g u r e 1. T h e c a r b o x y l a t e g r o u p c o o r d i n a t e d t o t h e v a n a d i u m (C^,) has a r e s o n a n c e w i t h a p o s i t i v e C I S v a l u e (5.1 p p m ) , a n d t h e c a r b o x y l a t e i n t h e p e n d e n t a r m ( C f ) has a n e g a t i v e C I S value ( - 1 . 4 p p m ) . T h e m e t h y l e n e groups have C I S values o f 5.3 a n d 1 3

ο ο π φ

6 Χ

i g a n d

1 3

l

1 3

1 3

5 1

1 3

X



1

1

JU

ι -

180

'

160

• - I '

EDTA

V-EDTA

I

0

"1

3 C

140

120 ppm

' I ' • ' ι '

1

A

C 5 b

C21\\

I

ο ο

3-

100

80

60

' ι ' »' I ' »' ι '

(

ο Llc2bXcil>

ο-

13

Figure 1. The *H and C NMR spectra of EDTA (bottom) and a mixture of vanadate (125 mM) and EDTA (167 mM) at pH 8.00 and 298 Κ (top).

—ι—•—ι—•—ι— —ι—•—ι—'—ι—•—ι—•—ι—•—ι—ι 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 2.8 ppm

EDTA

V-EDTA

pH 8.00 298 Κ Clf


11.

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309

3.4 p p m , f o r t h e b o u n d a r m ( C b ) a n d t h e f r e e a r m ( C f ) , r e s p e c t i v e l y , w h e r e a s the p o s i t i v e C I S v a l u e o f 2.6 p p m for the d i a m i n e p o r t i o n o f t h e c o m p l e x also p r o v i d e s e v i d e n c e o f c h e l a t i o n o f t h e v a n a d i u m b y t h e e t h y l e n e d i a m i n e b a c k b o n e . T h e c h e m i c a l shifts a n d c o u p l i n g p a t t e r n s o b s e r v e d i n the H N M R spectra p r o v i d e a d d i t i o n a l i n f o r m a t i o n to support this interpretation i n agreement w i t h the X - r a y structure of this c o m p o u n d (16, 17). D e t a i l e d d i s c u s s i o n o f t h e a s s i g n m e n t s o f t h e H N M R s i g n a l s , a l o n g w i t h t h e i r c o u p l i n g p a t t e r n , has b e e n d e s c r i b e d p r e v i o u s l y (30). 2

2

1


1

T h r o u g h o u t this chapter w e show partial C N M R spectra that i l l u s t r a t e t h e shifts i n t h e r e s o n a n c e f r e q u e n c i e s that o c c u r u p o n c o m p l e x a t i o n . T h e c a r b o x y l a t e C signals a p p e a r f r o m 1 7 0 t o 1 8 0 p p m , so that t h e i r o b s e r v a t i o n r e q u i r e s t h a t t h e N M R s p e c t r u m b e r e c o r d e d w i t h a m u c h g r e a t e r w i n d o w t h a n s h o w n i n t h e figures. G i v e n t h e l o w s e n s i t i v i t y of the C nucleus and the longer relaxation time of the carboxylate group, C N M R s p e c t r a c a n b e r e c o r d e d i n m u c h less t i m e i f t h e s p e c t r a l w i d t h is r e d u c e d to e x c l u d e t h e c a r b o x y l a t e r e s o n a n c e s . T h e 2 D C N M R s p e c tra discussed i n subsequent paragraphs w e r e therefore r e c o r d e d w i t h r e d u c e d spectral widths. F o l d o v e r of the carboxylate resonances was not a p p a r e n t i n these s p e c t r a . T h e c h e m i c a l shifts f o r t h e c a r b o x y l a t e s o f t h e c o m p l e x e s d e s c r i b e d h e r e h a v e b e e n d e t a i l e d e l s e w h e r e , b u t i n a l l cases, t h e y s u p p o r t t h e analysis d e s c r i b e d (26). 1 3

1 3

1 3

1 3

1 3

A n N M R spectrum can be complicated b y dynamic processes taking place on the timescale of the N M R experiment. T h e C N M R spectrum of the N-(2-hydroxyethyl)iminodiacetic acid ( H I D A ) - v a n a d i u m complex at p H 8 . 5 3 ( V - H I D A 1) p r o v i d e s a n e x a m p l e o f t h i s . B o t h t h e C a n d C resonances exhibit a temperature d e p e n d e n c e b e t w e e n 2 7 6 and 2 9 8 K . A s the temperature increases, the C signal broadens, and the C s i g n a l s h a r p e n s . T h e s p e c t r a are s h o w n at v a r i o u s t e m p e r a t u r e s i n F i g u r e 2, a l o n g w i t h t h e a s s i g n m e n t s o f c a r b o n r e s o n a n c e s C , C , a n d C i n the V - H I D A 1 complex. T h e c o r r e s p o n d i n g resonances f r o m the free l i g a n d are l a b e l e d L , L , a n d L . T h e carboxylate groups, C a n d L q , are not s h o w n . B e c a u s e o n l y the C a n d C signals s h o w t e m p e r a t u r e d e p e n d e n c e i n these spectra a n d i n t e r m o l e c u l a r exchange processes w o u l d have i n d u c e d similar changes i n all carbon resonances, w e c o n c l u d e t h a t t h e o b s e r v e d p r o c e s s i n t h i s t e m p e r a t u r e r a n g e is a n i n t r a molecular process. 1 3

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T h e l a r g e C I S v a l u e f o r C ( 1 1 . 2 p p m ) s h o w s t h a t t h i s a r m is c o o r d i n a t e d t o t h e v a n a d i u m a t o m . O n l y o n e c h e m i c a l shift is o b s e r v a b l e f o r C , a n d its m a g n i t u d e (5.6 p p m ) suggests t h a t i t is also c o o r d i n a t e d . F i g u r e 3 s h o w s a s c h e m a t i c r e p r e s e n t a t i o n o f five p o s s i b l e s t r u c t u r e s f o r t h e V - H I D A 1 c o m p l e x . G i v e n t h e fact t h a t s i x - c o o r d i n a t e c o m p l e x e s a r e m o s t l i k e l y , t h e d i s c u s s i o n h e r e is l i m i t e d to s u c h s t r u c t u r e s (26). A l t h o u g h the observed equivalency of the carboxylate arm resonances 4

2


310

MECHANISTIC BIOINORGANIC CHEMISTRY V-HIDA pH 8.53 (300 :150

C2

mM) 13


C

C

3

298 Κ

L

3

4* 283 Κ

273 Κ

ι

τ—τ

η

1

71 70

1—h

1

1

1

1

1—π

1

1

Figure 2. Partial C NMR spectra at 298, 283, and 273 Κ of 300 mM vanadate and 150 mM HIDA at pH 8.53. The V-HIDA 1 complex concen trations were 72 mM at 298 K, 93 mM at 283 K, and 115 mM at 273 K. The carbons assigned to the complex are labeled C and for the ligand L . 13

x

x

( C i a n d C ) is c o n s i s t e n t w i t h s t r u c t u r e B , a n y o f t h e o t h e r f o u r s t r u c t u r e s m i g h t also r e v e a l o n l y f o u r r e s o n a n c e s i n t h e i r C s p e c t r a i f r a p i d i n t r a m o l e c u l a r e x c h a n g e is t a k i n g p l a c e b e t w e e n t h e i n e q u i v a l e n t c a r b o x y l a t e s . T h e t r a n s effect c o m m o n l y e x h i b i t e d b y t h e s e c o m p l e x e s f a vors structure A i f the complex contains a tetradentate ligand and structure D i f the complex contains a tridentate ligand. T h e pendent arm i n structures C , D , and Ε must be exchanging rapidly w i t h the c o m p l e x e d a r m f o r t h e g e o m e t r y to b e c o n s i s t e n t w i t h t h e o b s e r v e d N M R data. L o w - t e m p e r a t u r e * H N M R spectra reveal an apparent decoalescence, consistent w i t h the observation b y C N M R spec troscopy. 2

1 3

1 3

T h e C s p e c t r u m f o r t h e V - H I D A c o m p l e x at h i g h p H ( V - H I D A 1 i n F i g u r e 2) is v e r y d i f f e r e n t f r o m its s p e c t r u m at l o w p H ( V - H I D A 2 1 3



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311

Figure 3. Five structural representations illustrating the connectivity in a dianionic 1:1 complex of V-HIDA 1. Further studies are necessary to deter mine the stoichiometry and the charge on the complex in solution because we have isolated and characterized (from solution) a 2:2 V-HIDA mixedvalence complex by X-ray crystallography (Mahroof-Tahir and Crans, Col orado State University, unpublished results). i n F i g u r e 4). O n e c o m p l e x is s t r o n g l y f a v o r e d at h i g h p H , t h e o t h e r at l o w p H . T h e p r e s e n c e o f t h e t w o c o m p l e x e s is c o n f i r m e d b y V NMR s p e c t r o s c o p y w h i c h s h o w s t w o d i f f e r e n t s i g n a l s at n e u t r a l p H . A t p H 5 . 1 3 , t h e C C I S v a l u e is 4 p p m s m a l l e r t h a n its v a l u e at p H 8 . 5 3 . B e c a u s e s t r o n g e r c o o r d i n a t i o n shifts C r e s o n a n c e s d o w n f i e l d , t h e s m a l l , p o s i t i v e C C I S v a l u e (2.4 p p m ) at p H 5 . 1 3 suggests w e a k i n t e r a c t i o n b e t w e e n the h y d r o x y l group and the v a n a d i u m center. T h e C I S for the C signal is v e r y s i m i l a r i n b o t h c o m p l e x e s . T h i s s i m i l a r i t y suggests t h a t t h e a m i n e nitrogens are similarly c o o r d i n a t e d i n the t w o complexes. 5 1

4

1 3

4

2

F i g u r e 4 is a 2 D C Ή H E T C O R s p e c t r u m o f t h e V - H I D A 2 s a m p l e at p H 5 . 1 3 . T h e H E T C O R e x p e r i m e n t is o n e e x a m p l e o f t h e m a n y N M R e x p e r i m e n t s n o w i n r o u t i n e use (others i n c l u d e insensitive n u c l e i e n hanced by polarization transfer ( I N E P T ) , distortionless enhanced po l a r i z a t i o n t r a n s f e r ( D E P T ) , a n d n u c l e a r O v e r h a u s e r effect ( N O E ) ) t h a t a l l o w one to i d e n t i f y N M R - a c t i v e n u c l e i that are e i t h e r c o u p l e d to one a n o t h e r o r i n c l o s e p r o x i m i t y ( J , 5, 6, 2 9 ) . T h e b r o a d r e s o n a n c e a s s i g n e d to C i n F i g u r e 4 correlates w i t h a * H resonance assigned to a m e t h y l e n e p r o t o n o f a p e n d e n t (or less t i g h t l y h e l d ) a r m o f t h e c o m p l e x . T h i s c r o s s peak t h e r e f o r e enables the C signal to p r o v i d e c o r r o b o r a t i v e e v i d e n c e for the * H assignment a n d v i c e versa. V a r i a b l e - t e m p e r a t u r e * H N M R spectra w e r e r e c o r d e d , a n d t h e y support the i n t e r p r e t a t i o n that the V H I D A 2 complex contains a pendent or w e a k l y coordinated arm. C o n sidering the modest positive C I S of C , it m a y b e a h y d r o x y e t h y l a r m i n t h i s c o m p l e x t h a t is s t i l l p r o t o n a t e d a n d p e n d e n t o r w e a k l y coordinated. 1 3

4

1 3

4

Application of 0 N M R Spectroscopy for Structural Studies of Vanadium(V) Complexes. I s o t o p i c - l a b e l i n g e x p e r i m e n t s w i t h 1 7


Thorp and Pecoraro; Mechanistic Bioinorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1996. x

x

Figure 4. A HETCOR spectrum of the V-HIDA 2 complex 100 mM vanadate and 300 mM HIDA at pH 5.13 and 318 K. The carbons assigned to the complex are labeled C and those assigned to the ligand L .


*

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313

N M R - a c t i v e n u c l e i c a n o f t e n assist t h e c h e m i s t i n d i s t i n g u i s h i n g b e t w e e n t w o o r m o r e l i k e l y s t r u c t u r e s f o r a m o l e c u l e . O n e s u c h e x a m p l e is t h e use o f 0 N M R spectroscopy to distinguish b e t w e e n four possible structures for the c o m p l e x o f v a n a d i u m a n d t r i - 2 - p r o p a n o l a m i n e ( T P A ) i n a q u e o u s s o l u t i o n (15). A n a l o g o u s a n a l y s i s w a s c a r r i e d o u t w i t h t h e complex of vanadium and triethanolamine (TEA), and the solution s t r u c t u r e was c o m p a r e d t o t h e s t r u c t u r e d e t e r m i n e d b y X - r a y c r y s t a l l o g r a p h y (15, 31). A n a l y s i s o f t h e C I S C v a l u e s f o r t h i s s y s t e m s h o w s that the V - T P A c o m p l e x contains two 2 - p r o p a n o l arms along w i t h the c e n t r a l a m i n e c h e l a t i n g t h e v a n a d i u m c e n t e r w i t h o n e - a r m p e n d e n t (15). X - r a y c r y s t a l l o g r a p h y shows that the solid-state V - T P A c o m p l e x isolated from organic solvents contains tetradentate T P A w i t h five-coordinate v a n a d i u m , i n w h i c h t h e n i t r o g e n is b o u n d i n a n a x i a l p o s i t i o n . T h e s t r u c ture for the aqueous V - T P A c o m p l e x c o u l d , h o w e v e r , contain either five- o r s i x - c o o r d i n a t e v a n a d i u m w i t h e i t h e r a n a x i a l o r a n e q u a t o r i a l b o n d t o t h e n i t r o g e n (see F i g u r e 5). A d d i t i o n o f 0 - l a b e l e d w a t e r t o a solution containing T P A and vanadate w o u l d exchange the 0 into the oxo p o r t i o n o f t h e c o m p l e x . A n 0 N M R spectrum of the solution w o u l d allow the four structural possibilities to b e distinguished from one an other. T h e two complexes w i t h five-coordinate vanadium w o u l d have two 0 signals i n a 1:1 i n t e n s i t y r a t i o i f t h e n i t r o g e n is a x i a l a n d o n l y o n e s i g n a l i f t h e n i t r o g e n is e q u a t o r i a l ( a s s u m i n g t h e c i s o r t r a n s h y 1

7


1 3

1 7

1

1

1

7

7

7

Alternative Heteronuclei:

1040

1000

1 7

0

960

920

880

ppm

Figure 5. Four structural possibilities for the V-TPA complex. The number of Ο NMR signals predicted for each structure and the experimentally observed Ο NMR spectrum are shown below the structures. 17

17


314


d r o x y p r o p y l g r o u p d o e s n o t affect t h e c h e m i c a l shift o f t h e o x y g e n a t o m e n o u g h to o v e r c o m e the b r o a d 0 signals). T h e exchange b e t w e e n l a b e l e d o x y g e n s i n t h e V - T P A c o m p l e x is p r e s u m e d t o b e f a i r l y s l o w o n t h e 0 N M R t i m e s c a l e as s h o w n f o r r e l a t e d c o m p l e x e s (25). I f t h e c o m p l e x was six-coordinate, t w o or t h r e e resonances w o u l d b e e x p e c t e d i n the 0 N M R spectrum. If two resonances w e r e observed, their intensity r a t i o s h o u l d b e 1:2, a n d i f t h r e e r e s o n a n c e s w e r e o b s e r v e d , t h e i n t e n s i t y ratio should be 1:1:1. Because the s p e c t r u m s h o w n i n F i g u r e 5 shows t w o signals i n a 1:1 r a t i o w i t h a c h e m i c a l shift d i f f e r e n c e o f m o r e t h a n 4 0 p p m , w e c o n c l u d e that the aqueous structure of the V - T P A c o m p l e x is five-coordinate w i t h the v a n a d i u m - n i t r o g e n b o n d axial. 1 7

1 7


1 7

Thermodynamic Studies N M R s p e c t r o s c o p y c a n also b e u s e d to d e t e r m i n e t h e f o r m a t i o n constants of various complexes. W e illustrate this b y quantificating the d i s t r i b u t i o n of vanadate oligomers i n aqueous solution b y V N M R spectroscopy. M o r e o v e r , t h e c h e m i c a l shifts a r e v e r y s e n s i t i v e t o p r o t o n a t i o n o f t h e oxovanadium species, a n d V spectra can p r o v i d e information on the s p e c i f i c p r o t o n a t i o n state o f t h e a n i o n s i n s o l u t i o n . 5 1

5 1

A q u e o u s s o l u t i o n s o f v a n a d a t e c o n t a i n a m i x t u r e o f m o n o m e r (V\), d i m e r (V ), t e t r a m e r (V ), a n d p e n t a m e r (V ) (32). O n l y V has b e e n c h a r a c t e r i z e d b y X - r a y c r y s t a l l o g r a p h y (33, 34). T h e s p e c i a t i o n i n a q u e o u s s o l u t i o n is w e l l - c h a r a c t e r i z e d b y V N M R s p e c t r o s c o p y b e c a u s e e a c h a n i o n i c s p e c i e s has a d i s t i n c t s i g n a l (in c o n t r a s t t o o t h e r m e t h o d s u s e d f o r q u a n t i f i c a t i o n o f v a n a d a t e o x o a n i o n s ) (12). B e c a u s e v a n a d i u m is a q u a d r u p o l e a n d e a c h o f its o l i g o m e r s r e l a x w i t h s i m i l a r r e l a x a t i o n t i m e s (32), i n t e g r a t i o n o f V N M R s p e c t r a g i v e s a c c u r a t e r e l a t i v e p e r 2

4

5

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5 1

centages of the various vanadate species present i n solution. A s s u m i n g t h a t a l l o f t h e v a n a d i u m is p r e s e n t i n t h e f o r m o f v a n a d i u m ( V ) , w e c a n calculate the concentration of each species. F i g u r e 6 shows the V N M R s p e c t r a r e c o r d e d at 0 . 5 , 1.0, a n d 5 m M t o t a l v a n a d a t e c o n c e n t r a t i o n s i n t h e p r e s e n c e o f 1 5 0 m M i m i d a z o l e a n d at p H 8 . 0 . G r a p h i c a l r e p r e sentation of the p H - d e p e n d e n t e q u i l i b r i a b e t w e e n V ! and V and bet w e e n V i a n d V a r e also i n c l u d e d i n F i g u r e 6. P l o t t i n g t h e V a n d V c o n c e n t r a t i o n s d e t e r m i n e d f r o m t h e i n t e g r a t e d V N M R s p e c t r a as a function of [ V J a n d [V^ , respectively, gives straight lines, w i t h the H - d e p e n d e n t f o r m a t i o n c o n s t a n t as t h e s l o p e (35). 5 1

2

4

2

4

5 1

2

4

+

Q u a n t i t a t i v e solution-state N M R studies can b e v e r y i m p o r t a n t for b i o i n o r g a n i c studies because the active species cannot often be chara c t e r i z e d b y o t h e r m e a n s i n s o l u t i o n (15, 32, 35, 36).

Kinetics and Dynamic Processes M e t a l - l i g a n d complexes can undergo many types of dynamic processes (including complex formation). D y n a m i c processes can vary from l i g a n d -


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Chemistry of Vanadium (V) Complexes

51 V NMR o f Vanadate S o l u t i o n s at Various Concentrations

V

«

a A


1

0.5

315

^

mM

mM

"i

1

1

1

B u f f e r : 150 mM

1

1

Γ

i m i d a z o l e , pH 8.0

1

Figure 6. V NMR spectra of 0.5, 1.0, and 5.0 mM total vanadate in 150 mM imidazole at pH 8.0. The Vj (—555 ppm) and V (—579 ppm) resonances are indicated by arrows. The V resonance (—573 ppm) is upfield of the Vj and downfield of the V resonance, and the V resonance (—585 ppm) is furthest upfield. The W -dependent equilibrium constants K and K are defined, and plots of [V ] as a function of [Vj\ and [V ] as a function of [Vj\ are shown for a study carried out at constant ionic strength. The data shown in these plots were reported previously as assay conditions for studies of 6-phospho gluconate dehydrogenase from sheep liver (Data are from ref erence 35). 51

4

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c o m p l e x exchange to c o n f o r m a t i o n a l i n t e r c o n v e r s i o n s w i t h i n the c o m p l e x . N M R t e c h n i q u e s exist w i t h w h i c h t h e s e p r o c e s s e s m a y b e i n v e s t i g a t e d , i n c l u d i n g v a r i a b l e t e m p e r a t u r e N M R s p e c t r o s c o p y , as d i s c u s s e d in T h e r m o d y n a m i c Studies. These N M R techniques include monitoring the time-course of a reaction b y one-pulse N M R experiments, coales cence point determination, lineshape analysis, a n d I D a n d 2 D magne t i z a t i o n t r a n s f e r t e c h n i q u e s (37). T h i s s e c t i o n f o c u s e s m a i n l y o n t h e a p p l i c a t i o n o f q u a l i t a t i v e a n d q u a n t i t a t i v e 2 D E X S Y N M R m e t h o d s to s t u d y i n t r a - a n d i n t e r m o l e c u l a r p r o c e s s e s (38).

Monitoring Complex Formation by N M R Spectroscopy. T h e rates o f s l o w r e a c t i o n s a r e m e a s u r e d b y e i t h e r m o n i t o r i n g t h e f o r m a t i o n of product or the disappearance of starting materials. W h e n complex f o r m a t i o n (or a p p r o p r i a t e d y n a m i c p r o c e s s ) is s l o w o n t h e t i m e s c a l e o f t h e N M R e x p e r i m e n t , its k i n e t i c s m a y b e s t u d i e d b y N M R . I n t h i s c a s e , slow complex formation may be followed by the observation of distinct


316


resonances for the c o m p l e x (product), intermediates, or starting materials. If the reaction progresses over the course of hours, days, or w e e k s , the reaction progress toward completion can be m o n i t o r e d by r e c o r d i n g t h e I D N M R s p e c t r a as a f u n c t i o n o f t i m e (39). I n s u c h cases, t h e N M R analysis s i m p l y represents an analytic t e c h n i q u e that allows quantification of the various species i n v o l v e d i n the reaction. T h e s e reactions


a r e a l l s t u d i e d i n t h e i r e a r l y stages b e f o r e t h e y r e a c h c o m p l e t i o n .

Chemical Exchange Processes at E q u i l i b r i u m . C h e m i c a l e x c h a n g e p r o c e s s e s a r e o f t e n fast, a n d w h e n t h e s y s t e m is at e q u i l i b r i u m , t h e i r k i n e t i c s c a n also b e s t u d i e d b y N M R . T h e s e t y p e s o f p r o c e s s e s c a n b e s t u d i e d b y c l a s s i c l i n e - s h a p e a n a l y s i s (rate c o n s t a n t s a p p r o x i m a t i n g 1 0 s ) o r m a g n e t i z a t i o n t r a n s f e r m e t h o d s (rate constants a p p r o x i m a t i n g 1 0 " s" ) (37). I n g e n e r a l , m e t h o d s t h a t r e q u i r e t h e f e w e s t a s s u m p t i o n s a b o u t r e l a x a t i o n t i m e s , r e l a x a t i o n m e c h a n i s m s , c h e m i c a l shift d i f f e r e n c e s , a n d t e m p e r a t u r e d e p e n d e n c e are most r e l i a b l e . C o a l e s c e n c e - p o i n t a n d band-shape simulation methods often assume t e m p e r a t u r e invariance o f c h e m i c a l shifts. B a n d - s h a p e analysis r e q u i r e s k n o w l e d g e o f l i n e w i d t h s in the absence of exchange. M a g n e t i z a t i o n transfer techniques and 2 D exchange techniques do not require k n o w l e d g e of temperatured e p e n d e n t c h e m i c a l shifts o r l i n e w i d t h s . A l t h o u g h o n e o f t h e s e m e t h o d s m a y p r e s e n t advantages o v e r t h e o t h e r s f o r a g i v e n s y s t e m , it is a d v i s a b l e to d e t e r m i n e any g i v e n rate constant b y m o r e t h a n one m e t h o d or b y using more than one nucleus. 4

- 1

2

1

T h e I D m a g n e t i z a t i o n t r a n s f e r m e t h o d is w e l l - k n o w n a n d is m o s t effective for d e t e r m i n i n g exchange rate constants for t w o - a n d t h r e e site e x c h a n g e s y s t e m s (40). T h e I D m a g n e t i z a t i o n t r a n s f e r e x p e r i m e n t may be conducted b y using either selective or nonselective pulse m e t h ods. B e c a u s e s e l e c t i v e p u l s e s (41) o f t e n s p i l l o v e r t o n e a r b y r e s o n a n c e s , less c o n v e n i e n t n o n s e l e c t i v e m e t h o d s a r e p r e f e r a b l e i n cases i n w h i c h t h e r e is o v e r l a p i n t h e s p e c t r a l r e g i o n o f i n t e r e s t a n d h a r d w a r e p r o h i b i t s s e l e c t i v e i r r a d i a t i o n (42, 43). W e u s e d a I D m a g n e t i z a t i o n t r a n s f e r e x p e r i m e n t to m e a s u r e t h e c h e m i c a l e x c h a n g e b e t w e e n v a n a d a t e m o n o m e r a n d d i m e r . T h e s e r e s u l t s a r e d e t a i l e d e l s e w h e r e (27). F o r exchange i n m u l t i s i t e systems, b o t h line-shape analysis a n d I D magnetization transfer methods b e c o m e tedious a n d t i m e - c o n s u m i n g . Because 2 D magnetization transfer methods ( 2 D E X S Y ) p r o v i d e s i m u l taneous quantitative information about every exchange process taking p l a c e i n a s y s t e m , t h e y p r e s e n t a n a t t r a c t i v e a l t e r n a t i v e to s t u d y i n g t h e d y n a m i c s of c o m p l e x systems.

Qualitative 2D

E X S Y Spectroscopy of Vanadium(V)

Com-

plexes. T h e 2 D E X S Y e x p e r i m e n t is s i m i l a r to t h e 2 D n u c l e a r O v e r h a u s e r effect ( N O E S Y ) s p e c t r o s c o p y e x p e r i m e n t ) u s e d t o e s t i m a t e i n -


11.

CRANS E T AL.


317

ternuclear distances i n a m o l e c u l e . B o t h N O E S Y a n d E X S Y experiments use t h e s a m e p u l s e s e q u e n c e ( 9 0 - f - 9 0 ° - f - 9 0 - f ) w i t h N O E s a n d chemical exchange taking place, respectively, d u r i n g the second delay t i m e (the m i x i n g t i m e t ). T h e 2 D E X S Y s p e c t r u m t h e r e b y p r o v i d e s offd i a g o n a l c r o s s - p e a k s b e t w e e n shifts f o r e a c h p a i r o f e x c h a n g i n g sites i n a multisite system. T h e signal intensities of the cross-peaks, b e i n g p r o p o r t i o n a l to the rate of exchange, w i l l l e a d to s i m u l t a n e o u s q u a n t i t a t i v e information about each exchange process i n a potentially complex m u l t i s i t e e x c h a n g e s y s t e m (44). o

1

o

m

2


m

W e first i l l u s t r a t e t h e use o f 2 D C E X S Y s p e c t r a to e x a m i n e the exchange b e t w e e n ligand and complex i n an aqueous solution of H I D A a n d V - H I D A 2 c o m p l e x at p H 5 . 1 3 . F i g u r e 7 s h o w s t h e p a r t i a l 2 D C E X S Y s p e c t r u m r e c o r d e d at 3 1 8 K . T h e t e m p e r a t u r e m o s t a p p r o p r i a t e for r e c o r d i n g the 2 D E X S Y s p e c t r u m was d e t e r m i n e d b y a p r e l i m i n a r y series o f v a r i a b l e t e m p e r a t u r e C N M R s p e c t r a . T h e t e m p e r a t u r e at w h i c h s i g n i f i c a n t e x c h a n g e is o b s e r v e d d u r i n g t h e t i m e s c a l e o f t h e e x p e r i m e n t w i t h o u t e x c e s s i v e l i n e - b r o a d e n i n g is t h e p r e f e r r e d t e m p e r a t u r e to p e r f o r m the 2 D E X S Y e x p e r i m e n t . T h e s e p r e l i m i n a r y studies are c r i t i c a l , b e c a u s e t h e d y n a m i c p r o c e s s e s are v e r y s e n s i t i v e t o t e m p e r a t u r e , a n d t h e t e m p e r a t u r e r a n g e f o r f a v o r a b l e m e a s u r e m e n t s is l i m i t e d . F u r t h e r m o r e , e x p e r i m e n t a l p a r a m e t e r s s u c h as s w e e p w i d t h , r e l a x a t i o n d e lay, and pulse w i d t h must be defined i n p r e l i m i n a r y experiments. T h e 2 D experiment yields a 2 D map with C spectra along each dimension. If exchange occurs on the timescale of the experiment, an off-diagonal r e s o n a n c e b e t w e e n t h e e x c h a n g i n g sites w i l l b e o b s e r v e d . I n F i g u r e 6 off-diagonal resonances are o b s e r v e d b e t w e e n C a n d L , b e t w e e n C a n d L , a n d b e t w e e n C a n d L . T h e i n t e g r a t e d i n t e n s i t i e s o f t h e s e offdiagonal resonances are d i r e c t l y p r o p o r t i o n a l to the exchange rate b e tween the ligand and the complex. T h e spectrum in F i g u r e 6 clearly illustrates the exchange b e t w e e n the carbon atoms i n the l i g a n d a n d those i n the complex. 1 3

1 3

1 3

1 3

2

3

4

2

3

4

I n m a n y c o m p l e x e s , i n t r a m o l e c u l a r e x c h a n g e is also t a k i n g p l a c e . A 2 D E X S Y s p e c t r u m that reveals the presence of b o t h i n t e r - a n d i n t r a m o l e c u l a r e x c h a n g e p r o c e s s e s is s h o w n i n F i g u r e 8. T h e s t r u c t u r e o f t h e a q u e o u s V - T E A c o m p l e x is a n a l o g o u s t o t h e V - T P A c o m p l e x d e scribed i n previous paragraphs, w i t h two b o u n d (C b and C b) arms, and o n e f r e e ( C a n d C ) a r m (15). T h e C E X S Y s p e c t r u m s h o w n i n F i g u r e 8 w a s a c q u i r e d at 2 7 8 Κ a n d r e v e a l s s e v e r a l o f f - d i a g o n a l p e a k s . T h e solid lines connecting C and L , C f and L , C b and L , and C and L indicate exchange b e t w e e n the c o m p l e x a n d the free l i g a n d . Offd i a g o n a l r e s o n a n c e s a r e also o b s e r v e d b e t w e e n C b a n d C f a n d b e t w e e n C b and C f . Quantification of this exchange process and the i n t e r m o lecular exchange process show that the C b -> C f a n d C b C f offdiagonal signals are the result of i n t r a m o l e c u l a r exchange. T h e V - T E A 4

4 f

3

1 3

3 f

4 b

4

4

4

3

3

3 f

3

4

3

4

3

4

4

3


3


13

The C

EXSY spectrum of the V-HIDA

2 complex formed

in 100 mM vanadate

and 300

mM

I*.

x

HID A at pH 5.13 and 318 K. The carbons assigned to the complex are labeled C and those of the ligand as

Figure 7.

V-HIDA


C5 /

11.

CRANS E T AL.


V-TEA (400 : 600 mM) pH 9.01 278 K

^0

/

C4b

I

\C4b

319

EXSY

HO^C3f C4f

•

Cf Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 14, 2016 | http://pubs.acs.org Publication Date: May 5, 1996 | doi: 10.1021/ba-1995-0246.ch011

3

I

L

3

>

Cf

L

4

[

4

4•

C3b

C4b

13

- -

1

I I

I -4

ψ

C

Figure 8. The C EXSY spectrum of the V-TEA complex 400 mM vanadate and 600 mM HIDA at pH 9.01 and 278 K. The carbons assigned to the complex are labeled C and those of the ligand as L . 13

x

X

c o m p l e x is a n e x a m p l e o f a c o m p l e x i n w h i c h i n t r a - a n d i n t e r m o l e c u l a r processes are o c c u r r i n g o n the same timescale. O b s e r v a t i o n of b o t h p r o cesses o f t e n r e q u i r e s t h a t E X S Y s p e c t r a b e r e c o r d e d at m o r e t h a n o n e t e m p e r a t u r e . T h e s c i e n t i s t has s o m e

flexibility

in choosing the temper

a t u r e at w h i c h t o s t u d y a s p e c i f i c s y s t e m . D e c r e a s i n g t h e t e m p e r a t u r e c o u l d decrease the intermolecular exchange b e y o n d detection and c o u l d p o s s i b l y a l l o w o b s e r v a t i o n o f t h e faster i n t r a m o l e c u l a r p r o c e s s w i t h o u t i n t e r f e r e n c e f r o m t h e s l o w e r i n t e r m o l e c u l a r r e a c t i o n also. I n t h e c a s e of the V - T E A system, temperatures m u c h lower than 2 7 8 Κ c o u l d not b e a c c e s s e d , g i v e n t h e f r e e z i n g p o i n t o f w a t e r . S p e c t r a r e c o r d e d at h i g h e r temperatures show greater contribution from the intermolecular process relative to the i n t r a m o l e c u l a r process. E v e n w i t h o u t quantification, this is e v i d e n c e t h a t a l l o f t h e o b s e r v e d e x c h a n g e is n o t d u e t o o n e p r o c e s s . O t h e r c o m p l e x e s s u c h as t h e V - E D T A c o m p l e x (45) a n d t h e V - T r i c i n e [ N - [ t r i s ( 2 - h y d r o x y m e t h y l ) m e t h y l ] g l y c i n e ] - v a n a d i u m c o m p l e x (25) a l l o w observation o f intra- and intermolecular processes w i t h o u t the interfer ence o f the other process.


320


F i n a l l y , w e w i l l describe a complex multisite i n t e r m o l e c u l a r exc h a n g e s y s t e m b e t w e e n t h e v a n a d a t e o l i g o m e r s . T h i s s y s t e m is s t u d i e d b y 2D V E X S Y NMR s p e c t r o s c o p y . A 2D E X S Y s p e c t r u m is s h o w n i n F i g u r e 9. V a n a d i u m - 5 1 r e l a x e s m u c h m o r e r a p i d l y t h a n carbon-13 a n d as a r e s u l t , t h e 2D V E X S Y e x p e r i m e n t is p e r f o r m e d w i t h m i x i n g t i m e s o f a p p r o x i m a t e l y 10 ms ( c o m p a r e d to t h e m i x i n g t i m e o f 300 m s f o r t h e 2D C E X S Y e x p e r i m e n t ) . A t p H 8.6, o f f - d i a g o n a l r e s o n a n c e s are o b served b e t w e e n all of the resonances. W e therefore c o n c l u d e that the Vi, V , V , a n d V a l l e x c h a n g e w i t h o n e a n o t h e r (32). B e c a u s e t h e v a n adate o x o a n i o n s a r e a l l d i f f e r e n t s p e c i e s , t h i s s o l u t i o n r e p r e s e n t s a n e x ample of a multisite intermolecular exchange system. 5 1

5 1


1 3

2

4

5

Quantification of E X S Y data produces a " m a p " of individual sitet o - s i t e r a t e c o n s t a n t s . B e c a u s e a l l o f t h e d a t a are d e r i v e d f r o m a s i n g l e e x p e r i m e n t , t h i s m e t h o d is p r e f e r a b l e to a n a l o g o u s ID m e t h o d s w h e n e v e r t h e n u m b e r o f e x c h a n g i n g sites i n t h e s y s t e m e x c e e d s t w o .

Quantitation and Interpretation of 2D E X S Y Spectra.

Quan-

t i f i c a t i o n o f t h e E X S Y e x p e r i m e n t is a c c o m p l i s h e d t h r o u g h a s e r i e s o f

-540

-560

-580

ppm

Figure 9. The 2D V EXSY NMR spectrum of a 10 mM total vanadate solution containing KCl to obtain an ionic strength of 0.4 at pH 8.6 (32). The vanadate oligomers V (-542 ppm), V (-562 ppm), V (-574 ppm), and V (—579 ppm) are indicated. 51

1

2

4

5


11.

CRANS E T AL.


321

matrix manipulations c a r r i e d out b y c o m p u t e r . E a c h of the magnetiza t i o n s rrii o f a n E X S Y s p e c t r u m m a y b e e x p r e s s e d b y e q u a t i o n 1, w h e r e nii is t h e m a g n e t i z a t i o n ' s d e v i a t i o n f r o m its e q u i l i b r i u m v a l u e ( M — M ) a n d m is t h e c o r r e s p o n d i n g m a t r i x (38). T h i s e x p r e s s i o n i n c l u d e s relaxation terms i n a d d i t i o n to e x c h a n g e terms for e a c h o f the e x c h a n g e p a t h w a y s f r o m site i. T h e η m a g n e t i z a t i o n s o f a n η-site e x c h a n g e s y s t e m m a y b e e x p r e s s e d as r o w s i n t h e η Χ η m a g n e t i z a t i o n m a t r i x M s h o w n i n e q u a t i o n 2. C a l c u l a t i o n o f t h e e x c h a n g e m a t r i x R ( e q u a t i o n 3) is g e n erally accomplished by a matrix diagonalization method, w h i c h linearizes t h e s u m o f e x p o n e n t i a l s i n t h e i n t e g r a t e d f o r m o f e q u a t i o n 2. I n e q u a t i o n 3, R is t h e e x c h a n g e m a t r i x , t is t h e m i x i n g t i m e , M is t h e m a g n e t i z a t i o n m a t r i x , M is t h e m a t r i x o f e q u i l i b r i u m m a g n e t i z a t i o n s , X is t h e m a t r i x that diagonalizes M , X its i n v e r s e , a n d Λ is t h e d i a g o n a l m a t r i x o f exchange a n d relaxation rate constants. {


i 0

m

0

-

1

(1)

(2) R = -tvT'Vn

(MM,,- )] = - t o T W n A j X " ] 1

1

(3)

M a t r i x representation allows the c o m p o n e n t s of the r e s u l t i n g ex change m a t r i x R to b e r e a d i l y i n t e r p r e t e d . C o u p l i n g terms (off-diagonal elements) of the exchange matrix p r o v i d e site-to-site rate constants. E a c h site-to-site rate constant ( w h i c h m a y represent a series o f e l e m e n t a l steps) is p r o v i d e d d i r e c t l y f r o m t h e o f f - d i a g o n a l e l e m e n t s o f t h e e x c h a n g e m a t r i x R ^ . R e l a x a t i o n i n f o r m a t i o n is c o n t a i n e d o n l y i n t h e d i a g o n a l e l e ments (R = Τχ + Σ]1ι kij). T h u s u n l i k e i n I D d y n a m i c m e t h o d s ( m a g netization-transfer a n d l i n e - w i d t h analysis), quantification of a single E X S Y e x p e r i m e n t separates each of the exchange rate constants f r o m each other a n d f r o m the relaxation rate constants. if

ί_1

N o t e , h o w e v e r , that the exchange rate constants i n the rate matrix are not necessarily rate constants for e l e m e n t a l c h e m i c a l reactions. T h e o b s e r v e d pseudo-first-order rate constants i n R are d e p e n d e n t o n the f r a c t i o n a l p o p u l a t i o n s at v a r i o u s sites a n d a r e o f t e n m a d e u p o f s e v e r a l e l e m e n t a l r a t e c o n s t a n t s . T h e r a t e c o n s t a n t s f o r t h e e l e m e n t a l steps o f a c h e m i c a l reaction must therefore be d e r i v e d from the observed rate constants w i t h a g i v e n m e c h a n i s m i n m i n d . C o n s i d e r a t i o n s for i n t e r p r e t i n g the m e a s u r e d m a g n e t i z a t i o n transfer rates have b e e n discussed (38) for b o t h i n t r a - (46) a n d i n t e r m o l e c u l a r systems (32). I n t h e f o l l o w i n g section we show a few examples. I n t h e case o f t h e V - T E A c o m p l e x , t h e t w o e q u i v a l e n t c o o r d i n a t e d arms exchange w i t h the pendent a r m i n an i n t r a m o l e c u l a r process ( F i g -


322


u r e 8). T h e p o p u l a t i o n o f t h e c a r b o n s i n t h e c o o r d i n a t e d a r m s a r e t w i c e t h a t o f t h e c a r b o n s i n t h e f r e e a r m a n d b e c a u s e mass b a l a n c e m u s t b e m a i n t a i n e d , t h e f o r w a r d a n d r e v e r s e r a t e c o n s t a n t s a r e r e l a t e d as s h o w n i n e q u a t i o n 4: 2fc(C

^C

4 f

)

=

fc(C ^C ) 4f

(4)

4b

N e i t h e r fc(C -> C f ) n o r fc(C f C ) r e p r e s e n t s t h e " t r u e rate c o n s t a n t f o r e x c h a n g e " (k ) b e c a u s e s u c h a r a t e c o n s t a n t s h o u l d n o t d e p e n d o n the p o p u l a t i o n of each site. F u r t h e r m o r e , o n l y those p a t h w a y s that r e s u l t i n m a g n e t i z a t i o n t r a n s f e r w i l l b e o b s e r v e d a n d so t h e r a t e o f m a g n e t i z a t i o n t r a n s f e r is n o t t h e s a m e as t h e r a t e o f t h e u n d e r l y i n g p r o c e s s . I n t h i s case t h e m e a s u r e d r a t e c o n s t a n t fc(C C f ) expresses the rate by which C is c o n v e r t e d t o C f . I n d e g e n e r a t e c h e m i c a l e x c h a n g e processes, the intermediate species (whether this be an intermediate or a t r a n s i t i o n state) c a n d e c a y b a c k to t h e g r o u n d - s t a t e s t r u c t u r e o r p r o c e e d t o p r o d u c t . T h e e x c h a n g e t a k i n g p l a c e i n t h e V - T E A c o m p l e x is s u c h a p r o c e s s b u t is o n l y o b s e r v e d i f C is c o n v e r t e d t o C f . T h e " t r u e " r a t e constant characterizes a c h e m i c a l event, w h i c h s h o u l d reflect e v e r y passage to t h e t r a n s i t i o n state w h e t h e r o r n o t t h e passage c o n t i n u e s o n t o o b s e r v a b l e p r o d u c t . T h e c h e m i c a l e v e n t has b e e n d e f i n e d as t h e f o r mation of a species on the m u l t i d i m e n s i o n a l reaction m a n i f o l d from w h i c h t h e final c o n n e c t i v i t y o f t h o s e n u c l e i u n d e r g o i n g e x c h a n g e a r e d e t e r m i n e d s t a t i s t i c a l l y (46). I n t h e case o f t h e V - T E A c o m p l e x , l i k e l y i n t r a m o l e c u l a r exchange m e c h a n i s m w o u l d r e q u i r e that all three arms (one p e n d e n t a n d t w o c h e l a t e d arms) h a v e a n e q u a l l i k e l i h o o d o f e x c h a n g i n g d u r i n g t h e c h e m i c a l e v e n t . A c c o r d i n g l y fc h w i l l b e r e l a t e d to fc(C C f) and fc(C f C ) as s h o w n i n e q u a t i o n 5: 4b


4 b

4

4

4 b

chem

4b

4 b

4

4

4 b

4

c

4b

4

4

kchem

_

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em

4 b

C f ) - 3k(C {

4b

C )

4

4

(5)

4 b

A s e c o n d e x a m p l e is i l l u s t r a t e d b y t h e V - T r i c i n e s y s t e m (25). Its E X S Y s p e c t r u m , r e v e a l i n g i n t r a m o l e c u l a r e x c h a n g e , is s h o w n i n F i g u r e 10. T h e V - T r i c i n e c o m p l e x differs f r o m the V - T E A c o m p l e x i n that the t w o - p e n d e n t h y d r o x y m e t h y l a r m s are i n e q u i v a l e n t (an A B C system) (46). T h e rate constants d e t e r m i n e d for the c o o r d i n a t e d a r m e x c h a n g i n g w i t h e a c h p e n d e n t a r m [fc(C C f) and fc(C C f ) ] a r e v e r y s i m i l a r (25). A s s u m i n g t h e c h e m i c a l e v e n t is t h e f o r m a t i o n o f a s i n g l e s p e c i e s f r o m w h i c h t h e t w o p e n d e n t a r m s a n d t h e c h e l a t e d a r m is d e r i v e d , e a c h r a t e r e p r e s e n t s o n l y o n e - t h i r d o f t h e e x c h a n g e r a t e as s h o w n i n e q u a t i o n 6: 4b

5

C ) = 3fc(C 5 f

4b

4 f

^C

)

=

3fc(C

5f

6 b

6

C ) = 3fc(C 4 b

6f

C )


4 b

(6)

11.

2D *3c (75.4 MHz) E X S Y N M R Experiment


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c / 5

6

Figure 10. 2D C EXSY NMR spectrum recorded at 75.4 MHz (7.05 T) at 0 °C (273 Κ) of a solution containing 412 mM total vanadate and 500 mM total Tricine at pH 7.1. This solution contains 406 mM V-Tricine, 0.38 mM V and 94 mMfree Tricine. The microscopic exchange rates were determined from the integrations. (Adapted from reference 25.) 13

lf

H o w e v e r , as s e e n i n F i g u r e 1 0 , e x c h a n g e b e t w e e n t h e t w o p e n d e n t a r m s is also s u p p o r t e d b y a n o t h e r o f f - d i a g o n a l r e s o n a n c e (k(C f C f)). This cross-peak w o u l d not b e observed i f there w e r e only a single i n t r a m o l e c u l a r m e c h a n i s m f o r e x c h a n g e as a s s u m e d a b o v e . T h i s c r o s s p e a k is t h e r e f o r e l i k e l y t o r e s u l t f r o m y e t a n o t h e r d y n a m i c p r o c e s s t a k i n g p l a c e f o r w h i c h s e v e r a l m e c h a n i s m s c a n b e p r o p o s e d (25). Q u a n t i f i c a t i o n o f t h e r a t e c o n s t a n t s is i m p o r t a n t w h e n e v a l u a t i n g t h e m e r i t o f s p e c i f i c competing exchange pathways. 5

6

A s d e s c r i b e d for the i n t r a m o l e c u l a r systems, analyses o f i n t e r m o l e c u l a r e x c h a n g e p r o c e s s e s a r e also d e p e n d e n t o n t h e m e c h a n i s m o f t h e r e a c t i o n . A s i m p l e i n t e r m o l e c u l a r e x c h a n g e p r o c e s s is t h a t b e t w e e n v a n a d a t e d i m e r ( V ) a n d v a n a d a t e m o n o m e r (Vx). T w o l i k e l y m e c h a n i s m s f o r f o r m a t i o n o f d i m e r a r e s h o w n i n e q u a t i o n s 7 a n d 8. T h e first i n v o l v e s the c o m b i n a t i o n o f t w o m o n o m e r s (equation 7). T h e second involves the c o m b i n a t i o n o f m o n o m e r a n d d i m e r (equation 8). R e c o r d i n g 2 D V E X S Y s p e c t r a at a n u m b e r o f v a n a d a t e c o n c e n t r a t i o n s a l l o w s d i s t i n c t i o n b e t w e e n t h e t w o . A p l o t o f t h e f o r w a r d r a t e (fc(vi—v2)[Vi]) as a f u n c t i o n o f [ V x ] w o u l d b e l i n e a r f o r e q u a t i o n 7 b u t n o t f o r e q u a t i o n 8. A l i n e a r 2

5

2


1

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r e l a t i o n s h i p w a s i n fact o b s e r v e d (27). T h i s i l l u s t r a t e s t h e use o f q u a n titative 2 D E X S Y for m e c h a n i s t i c analyses. S u c h analyses r e q u i r e q u a n titative estimates of the uncertainties i n the rate constant calculation. O n l y a few q u a n t i t a t i v e attempts have b e e n m a d e to estimate the errors i n t h e r a t e c o n s t a n t s o b t a i n e d f r o m 2 D E X S Y e x p e r i m e n t s (47, 48). A p p l i c a t i o n of 2 D E X S Y to m e c h a n i s t i c studies r e q u i r e s that progress b e m a d e i n t h i s a r e a , a n d w e w i l l d e s c r i b e b r i e f l y o u r efforts e s t i m a t i n g errors from V E X S Y spectra.


5 1

V + Vx ç± x

Vi + V

2

τ±

v

(7)

2

V + Vx

(8)

2

Error Estimation on 2D EXSY Experiments and Data Analysis. E s t i m a t i n g e r r o r s i n a 2 D E X S Y m e a s u r e m e n t is c o m p l i c a t e d b y t h e fact t h a t t h e e x p e r i m e n t is d e s i g n e d t o p r o v i d e a l l o f t h e e x c h a n g e rate constants f r o m a single e x p e r i m e n t . Statistical errors are f r e q u e n t l y not r e p o r t e d nor d e t e r m i n e d , because the t i m e a n d expense of the E X S Y experiment often p r o h i b i t s generation of a statistically significant n u m b e r o f r e p e t i t i o n s (48). A s a r e s u l t , e r r o r e s t i m a t i o n has f o c u s e d o n m o d e l i n g r a n d o m s o u r c e s o f e r r o r (47, 48). W e e x a m i n e d v a r i o u s s o u r c e s o f b o t h r a n d o m a n d systematic e r r o r to d e t e r m i n e the m a j o r c o n t r i b u t o r s to e r r o r a n d to e v a l u a t e t h e i r m a g n i t u d e s i n t h e r a t e constants f o r e x c h a n g e in a n u m b e r of vanadate systems. W e describe here o u r results on b o t h t w o - a n d four-site systems. E r r o r s are p r o p a g a t e d to the rate constants f r o m the v o l u m e i n t e grals. T h e r e are a n u m b e r sources o f e r r o r i n the m e a s u r e m e n t o f the v o l u m e integrals f r o m w h i c h the site-to-site rate constants for exchange are d e r i v e d . T h e s e have b e e n discussed i n the l i t e r a t u r e a n d i n c l u d e errors d u e to noise, baseline i m p e r f e c t i o n , i n c o r r e c t p h a s i n g , e x p e r i m e n t a l a r t i f a c t s , i n a d e q u a t e d i g i t i z a t i o n , a n d t r u n c a t i o n (49). O u r e r r o r estimates w e r e o b t a i n e d f r o m an e m p i r i c a l estimation of the integration e r r o r a n d f r o m the e r r o r i n the integrals due to noise i n the s p e c t r u m . W e f o u n d that the p r e c i s i o n of v o l u m e i n t e g r a t i o n was l i m i t e d p r i m a r i l y b y t h e n e e d f o r b a s e l i n e c o r r e c t i o n . T h i s is e s p e c i a l l y t r u e i n t h e case o f si γ N M R s p e c t r a , b e c a u s e t h e s p e c t r a o f t h i s n u c l e u s a r e s u s c e p t i b l e t o r o l l i n g b a s e l i n e s (50). F i g u r e 11 s h o w s t h e c o n t o u r p l o t s o f t h e 2 D V E X S Y s p e c t r u m o f a t w o - s i t e s y s t e m ( 4 0 m M t o t a l v a n a d a t e at p H 1 0 . 9 ) i n w h i c h Vx e x changes w i t h V . Quantification of the E X S Y spectrum and calculation o f the e r r o r p r o p a g a t e d to the rate constants f r o m the i n t e g r a t i o n p r e cision gives a 2 5 % e r r o r o n the rate constant. T h e results (both the rate constants a n d the errors) c o r r e s p o n d n i c e l y to the results o b t a i n e d f r o m a I D m a g n e t i z a t i o n t r a n s f e r e x p e r i m e n t o n t h e s a m e s a m p l e (27). T h e E X S Y s p e c t r u m o f a s a m p l e c o n t a i n i n g 1 2 . 5 m M t o t a l v a n a d a t e at 1.0 5 1

2


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•

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1 l Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 14, 2016 | http://pubs.acs.org Publication Date: May 5, 1996 | doi: 10.1021/ba-1995-0246.ch011

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Figure 11. 2 D V EXSY NMR spectra recorded at23°C of three different vanadate solutions. A two-site system was observed in a solution containing 40 mM total vanadate at ionic strength of 0.4 M and pH 10.9. Two four-site systems were recorded at 10 and 12.5 mM total vanadate. The calculated rate constants are shown next to the off-diagonal resonances in all three maps. The errors were propagated to the rate constants from the integration precision and are also shown next to the off-diagonal resonance. 5 2

M i o n i c s t r e n g t h a n d p H 8 . 6 is s h o w n i n F i g u r e 1 1 a l o n g w i t h t h e c a l c u l a t e d rate constants a n d t h e i r errors. T h e exchange b e t w e e n vanadate oligomers was a n t i c i p a t e d to b e v e r y similar to that i n t h e sample s h o w n i n F i g u r e 9 (32). N e v e r t h e l e s s , less e x c h a n g e is o b s e r v e d w i t h t h e m i n o r


326


resonances ( V and V ) i n this sample, a n d several off-resonance crosspeaks are zero. T h e errors, d e t e r m i n e d b y r e p e a t e d v o l u m e integrations, o n the rate m a t r i x r a n g e d f r o m 2 0 % to > 1 0 0 % . A s a n t i c i p a t e d , the e r r o r s a s s o c i a t e d w i t h l a r g e o f f - r e s o n a n c e signals w e r e s m a l l ( ν V , V -> V i , V i V , V V i ) , w h e r e a s w e a k o f f - r e s o n a n c e signals r e s u l t i n l a r g e e r r o r s f r o m 5 0 % to 1 0 0 % (V — V , V — V V — V ) . 2

5

:

2

4

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2

4

5

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A s a m p l e c o n t a i n i n g 1 0 . 0 m M t o t a l v a n a d a t e i n 0 . 2 M K C I at p H 8.6 w a s also a n a l y z e d . T h e s p e c t r u m a n d its a s s o c i a t e d r a t e c o n s t a n t m a t r i x is s h o w n i n F i g u r e 1 1 . A l t h o u g h t h e I D s p e c t r u m m i g h t l e a d o n e t o c o n c l u d e t h a t t h e q u a l i t y o f t h i s s p e c t r u m is t h e s a m e as t h a t o f the previous sample, close i n s p e c t i o n of the rate constants a n d errors reveal that h i g h e r errors w e r e o b t a i n e d o n this measurement. A l t h o u g h the range of errors w e r e similar, a greater fraction of small cross-reso n a n c e s l e d t o o v e r a l l g r e a t e r u n c e r t a i n t i e s . I n a d d i t i o n t o w e a k e r offd i a g o n a l signals, greater baseline d i s t o r t i o n c o n t r i b u t e d significantly to the higher relative errors. T h e s e examples illustrate the source a n d size of the e x p e r i m e n t a l e r r o r s o n a t w o - a n d a f o u r - s i t e s y s t e m . T h e y also h i g h l i g h t t h e i m p o r tance of estimating the errors, because mechanistic interpretations often r e q u i r e fairly precise estimates of the rate parameters i n v o l v e d . I f care is t a k e n t o m i n i m i z e t h e n o i s e i n t h e s p e c t r u m ( t h r o u g h s i g n a l a v e r a g i n g ) a n d i f t h e e l e c t r o n i c s o f t h e s y s t e m a r e set u p t o m i n i m i z e b a s e l i n e distortion, relative errors < 2 5 % should easily be obtained i n even c o m plex multisite systems.

Summary A p p l i c a t i o n s of N M R spectroscopy to s t r u c t u r a l , t h e r m o d y n a m i c , a n d d y n a m i c processes have b e e n described. A b r i e f discussion of the types o f p r o b l e m s a p p r o p r i a t e f o r s t u d y b y t h i s t e c h n i q u e has b e e n i n c l u d e d . H a n d C N M R s p e c t r o s c o p y has b e e n a p p l i e d t o d e f i n e t h e l i g a n d coordination in complexes. These experiments, combined with 0labeling experiments, allowed deduction of the coordination n u m b e r of the vanadium atom. Integration of N M R spectra allowed measurement of the f o r m a t i o n constants a n d e q u i l i b r i u m constants. 2 D C and V E X S Y experiments were used in a qualitative and quantitative manner to e x a m i n e i n t r a - a n d i n t e r m o l e c u l a r d y n a m i c p r o c e s s e s , o f w h i c h s e v e r a l e x a m p l e s a r e d i s c u s s e d . T h e i n t e r p r e t a t i o n o f t h e r a t e m a t r i x a n d its r e l a t i o n s h i p t o t h e c h e m i c a l p r o c e s s e s u n d e r e x a m i n a t i o n w e r e also d e s c r i b e d . 2 D E X S Y s p e c t r o s c o p y has g r e a t p o t e n t i a l as a t o o l w i t h w h i c h t o p r o b e m e c h a n i s m s i n c o m p l e x r e a c t i o n s ; h o w e v e r , s u c h uses o f t e n requires estimation of errors. T h e major source of error i n 2 D V E X S Y N M R studies o n a t w o - a n d four-site vanadate system w e r e f o u n d to b e b a s e l i n e d i s t o r t i o n a n d t h e e r r o r s w e r e e s t i m a t e d . O u r r e s u l t s suggest l

1 3

1 7

1 3

5 1

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that quantification of 2D EXSY experiments can be sufficiently accurate to make it a powerful mechanistic tool in studies of dynamic processes.


Acknowledgment We thank the National Institutes of Health and the American Heart Association for funding most of this work. We also thank Christopher D. Rithner and Christopher R. Roberts for stimulating discussions and Christopher D. Rithner for technical assistance. References 1. Harris, R. K.; Mann, Β. E. NMR and the Periodic Table; Harris, R. K.; Mann, Β. E., Eds.; Academic: New York, 1978. 2. Holz, R. C.; Que, L., Jr.; Ming, L.-J. J. Am. Chem. Soc. 1992, 114, 44344436. 3.

4. 5. 6. 7. 8.

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Beer, R. H.; Lippard, S. J. Inorg. Chem. 1993, 32, 1030-1032. Dec, S. F.; Davis, M. F.; Maciel, G. E.; Bronnimann, C. E.; Fitzgerald, J. J.; Han, S.-S. Inorg. Chem. 1993, 32, 955-960. Wüthrich, K. NMR in Biological Research: Peptides and Proteins; Wüthrich K., Ed.; Elsevier: New York, 1976. Oppenheimer, N. J.; James, T. L. In Spectral Techniques and Dynamics. Methods of Enzymology; Oppenheimer, N. J.; James, T. L., Eds.; Academic: San Diego, CA, 1989; Vol. 176, Part A. Gorenstein, D. G. Phopshorus-31 NMR. Principles and Applications; Gorenstein, D. G., Ed.; Academic: Orlando, FL, 1984. Berkowitz, Β. Α.; Balaban, R. S. Methods Enzymol. 1989, 176, 330-494. Boyd, J.; Brindle, Κ. M.; Campbell, I. D.; Radda, G.Κ.J.Magn. Reson. 1984, 60, 149-155.

10. Chasteen, N. D. Vanadium in Biological Systems: Physiology and Bioche istry; Chasteen, N. D., Ed.; Kluwer Academic: Boston, MA, 1990. 11. Butler, Α.; Carrano, C. J. Coord. Chem. Rev. 1991, 109, 62-105. 12. Rehder, D. Angew. Chem. Int. Ed. Engl. 1991, 30, 148-167. 13. Chasteen, N. D. In Biological Magnetic Resonance; Reuben, J., Ed.; Plenum Press: New York, 1981; pp 53-119. 14. Eaton, S. S.; Eaton, G. R. In Vanadium in Biological Systems: Physiology and Biochemistry; Chasteen, N. D., Ed.; Kluwer Academic Publishers: Bos ton, 1990; p. 199-222.

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Kangjing, Z.; Xiaoping, L. J. Struct. Chem. 1987, 6, 14-16. 19. Kojima, Α.; Okazaki, K.; Ooi, S.; Saito, K. Inorg. Chem. 1983, 22, 116818.

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for review July 19, 1993. ACCEPTED revised manuscript January 24,

1994.


Application of NMR Spectroscopy to Studies of Aqueous Coordination

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