where a = x 10-3 for units of kcal/mol

Transcription

1 Detemining the Enegy of Activation Paametes fom Dynamic MR Expeiments: -D. Rich Shoemake (Souce: Dynamic MR Spectoscopy by J. Sandstöm, and me) he esults contained in this document have been published: o Zimme, Shoemake, & Ruminski, Inoganica Chimica Acta, 359(2006) he most common (and oft inaccuate) method of detemining activation enegy paametes is though the detemination (often estimation) of tempeatue at which the MR esonances of 2 exchanging species coalesce. he coalescence tempeatue ( c ) is then used in conjunction with the maximum peak sepaation in the low-tempeatue (i.e. slow-exchange) limit ( ν in Hz). he biggest souce of eo using the method of coalescence is (1) accuately detemining c and (2) accuately detemining ν. Often, the isotopic chemical shifts of the exchanging species ae tempeatue dependent, so ν changes with tempeatue. If this happens, then the eo in estimation of the activation enegy baie ( ) can be vey lage. he ate constant (k ) in these calculations, fo nealy all MR exchange situations, is actually k 1 +k 2 in a system fo A exchanging with B, whee: A k 1 k 2 B he equation to estimate using the coalescence tempeatue is: = a log c whee a = x 10-3 fo units of kcal/mol ν a = x 10-2 fo units of kj/mol ote: at the coalescence tempeatue, k c = π υ/ 2 A second common method of detemining the enegy of activation (E a ) is by pefoming an Ahenius Plot. If one knows the exchange ate constant (k ) at seveal tempeatues (always in Kelvin), one can plot ln(k) vs. 1/. he slope = -E a /R and the Y-intecept is = ln(a), whee A is the Ahenius fequency facto (descibed below). Obtaining k at seveal tempeatues can be accomplished by using tansient exchange expeiments (i.e. 2D-EXCHSY o 1D-EXCHSY (aka GOESY)) using seveal mixing times, and measuing the buildup ate of the exchange coss-peak vs. mixing time at seveal tempeatues. Altenatively, the moe common method is to measue the 1D MR at many tempeatues (between the slow-exchange limit and fast-exchange limit), and then the exchanging esonances can be simulated using pogams like DMR o MEXICO. We have these simulation outines available in the lab within the SpinWoks softwae, witten by Kik Maat at the Univesity of Manitoba. Good simulation equies time, patience, and pactice. E a R he Ahenius equation is: k = A e. Bea in mind that E a, but E a is elated to in that E a = H + R (of couse = H - S and at this point we don t have S ). At a given tempeatue, you can get H fom E a because H = E a - R. (Remembe that if you use fo R, then R is in units of caloies, not kilocaloies.) Complete analysis of the activation enegy paametes equies the use of the Eying equation.

2 Eying Equation: k kb = κ h e R Assuming a tansmission coefficient (κ) = 1, you can calculate if you know k at any single tempeatue. A good estimate of can often be obtained if one has k at seveal tempeatues, and you can use the equation below to calculate at each tempeatue. kb = R ln ln( kate ) h o = R ln use R = fo caloies/mol k ate R = fo Joules/mol In Sandstöm s book (page 96) this has been conveted to a diffeent fom using base-10 logaithms: = a log k ate whee a= x 10-3 fo units of kcal/mol a= x 10-2 fo units of kj/mol Knowing using this equation, and knowing E a fom an Ahenius plot, one can get a good estimate of S without doing an Eying plot (descibed below). [( Ea R ) ] S = Eying Plot: Plot ln(k /) vs. 1/. Slope is - H /R ; Intecept is S /R {ote is ln(k b /h)} he dawback of the Eying Plot is that the Y-intecept (used to detemine S ) is nomally a lage extapolation fom the expeimental data. heefoe, if the linea fit of ln(k /) vs. 1/ is not extemely good, the eo in S can be quite lage. k ln H = R S + R k b + ln h {emembe: ln(k b /h) = } An example of these methods fo a eal dynamic system is pesented on the following page:

3 Example of using vaiable-tempeatue MR to evaluate the themodynamic paametes govening chemical exchange: Re- dpop (dipyido(2,3-a:3',2'-j)phenazine). On this molecule, the coodinating nitogens on the dpop exchange between bound and unbound to the Re. his molecule was synthesized in the laboatoy of D. Ron Ruminski, Univesity of Coloado at Coloado Spings (Inoganica Chimica Acta, 359(2006) ). O C O C Cl Re C O his low tempeatue 1 H MR shows distinct MR esonances fo the potons on the aomatic ings on opposite ends of the dpop ligand. he vaiable tempeatue MR specta, and the dynamic-mr simulations (DMR3 utility in the SpinWoks 2.4 softwae) ae shown below, including the tempeatues and the ates extacted fom the simulations.

4 Using the best estimate of coalescence tempeatue ( c ) = 314 Kelvin, and ν=52.5 Hz (at 248 Kelvin), = a log c = 15.3 kcal/mol. his is ou initial estimate of. ν An Ahenius plot of ln(k ) vs. 1/ gives a vey linea fit, with 2 = Using the Eying Equation, can be calculated fo evey ate at evey tempeatue (ote that S is usually << H so the tempeatue dependence of is usually undetectable within eo) emp Rate kcal/mol Aveage Std.Dev Fom the Ahenius plot, E a = 16.1 kcal/mol, so H = E a - R = 15.5 kcal/mol (using =314 Kelvin, which is the best estimate of the coalescence tempeatue, and mid-ange in the expeiments). Using =14.9 kcal/mol, and S = [( E R ) G ] a, S = 1.8 cal/(mol-kelvin).

5 A semi-independent method of obtaining H and S can be obtained by pefoming the Eying Plot discussed ealie. his is semi-independent because the Eying Equation was used to pefom the calculation above. he esults of the Eying Plot of the data obtained fom the vaiable-tempeatue MR is shown below. he slope yields a H = 15.5 kcal/mol, and S = 1.88 cal/(mol-kelvin). Clealy, these numbes agee vey well with the values calculated peviously. his document is a compilation of infomation that is eadily available in the liteatue, and in vaious textbooks and esouces; howeve, many find it difficult to pull out the useful infomation out of all of the mathematics. Hopefully, this document will be useful in claifying how these methods can be applied to eal-wold eseach poblems. -D. Rich Shoemake, Ph.D. last updated Decembe, 2009