Ingmar Grenthe

Inorganic Chemistry, Royal Institute of Technology (KTH), S-10044 Stockholm, Sweden

Solution coordination chemistry; stoichiometry and structure, thermodynamics and dynamics –

the reciprocity of experiment and theory.

Classical coordination chemistry

•Metal ion, often with known coordination properties

•Ligands with known donor atoms and geometry

•Often dynamic equilibria between M and L

•pMm+ + qL M⇌ pLq; where the stoichiometric coefficients have values ranging from 0 < p < P and 0 < q < Q;

Several different complexes are in general presentsimultaneously in equilibrium systems.

In the experimtal study one determines the stoichiometryand equilbrium constants by varying the totalconcentrations of M and L and meauring the freeconcentration of one reactant or product, often using anion selective electrode.Mtot = [M] + [ML] + [ML2] + … + [MLQ]; Ltot =[ML] + 2[ML2] + … + Q[MLQ];

nL = ([ML] + 2[ML2] + … + Q[MLQ]) / ([M] + [ML] + [ML2] + … + [MLQ]) = (Ltot – [L]) / Mtot;

Limitations in the chemical information obtainedusing ”classical” methods.•No information on the number of donor atoms bonded in a poly-dentate ligand.•No information on the presence of isomers•No information on coordinated solvent molecules•No information on structure•In some cases one cannot distinguish between M(OH)n, M(O)(OH)n-2, ..., MOn/2, because of the so called ”proton ambiguity”, 2OH- = O2- + H2O

It is obvious that these facts will seriously impair anydiscussion of the ”microscopic” properties

Correlation diagrams

Can complex formation be described using QM methods and which are the problems?

M(aq) + L(aq) ML(aq), classical. ⇌Using QM it is necessary to taking first-sphere water into accountM(OH2)x + L(H2O)y ML(OH⇌ 2)z + (x +y –z)H2O;How about remaining solute solvent interactions?One possibility:M(OH2)x(PCM)+ L(PCM) ML(OH⇌ 2)z(PCM)+ (x –z)H2O(PCM); Model AOne can expect the PCM effect to depend strongly on charge and size of the reactants and products.

The following alternative chemical model (B) minimizes these variations:1. M(OH2)x(PCM)+ L(PCM) [M(OH⇌ 2)x](L)(PCM); outer-sphere complex formation 2. [M(OH2)x](L)(PCM) [ML(OH⇌ 2)x-1](H2O)(PCM);

Example: Zn2+(aq)+ NH3(aq) → Zn(NH3)2+(aq); is ΔGr

o = -13.1 kJ/molModel A: ΔGr

o = -41.2 kJ/molModel B: ΔGr

o = -16.6 kJ/molThe QM calculations have been made assuming Zn2+to be six-coordinated (Vallet and Grenthe, JACS, 2003, 125, 14941)

Ionic strength dependence of thermodynamic data

Experimental thermodynamic data at ionic strengthdifferent from zero should be extrapolated to the “pure water” standard state before being compared with QM data. Recalculation to zero ionic strength can be made using semi-empirical models of “extended” Debye – Hückel type.

An extensive discussion in my book Modeling in Aquatic Chemistry; it is out of print but can be downloaded free ofcharge from www.nea.fr, use the search function on the homepage to find the book and download Chapter IX.

The ionic medium method ensures that experimentscan be made in such a way that the activity coeff. ofreactants and products do not vary when the total concentration of M and L are varied in an experiment.At each ionic strength, I, we can the define a proper standard state where the activity of the solvent is unityand where the activity coefficients of reactants and products are unity. Data at different ionic strength can be referred to a common pure water standard stateusing semi-empirical (electrostatic) electrolyte models.

Methods for determination of the structure of complexes in solution.

All methods, LAXS, LANS, EXAFS provide ”one-dimensional” struture information in the form ofpair-distances between atoms and the number of suchdistances. The distances are often rather accurate, but not the number of the particular distances. This means that coordination numbers in general have errors of 10 – 25 %. The deduction of a three- dimensional modelfrom such date requires the comparison of different models; these and their relative energy can be obtainedfrom QM.

Example (Vallet and Grenthe, C.R Chimie, 2007, 10, 905):The uranyl ion forms the moderately strong complex UO2(SO4) with sulfate; how is the sulfate coordinated?

Model CoordNumb.

U – Oyl U – OH2

U - Osulf

U - Oaver U - S

Mono 5 1.759 2.48(3) 2.22 2.43(8) 3.61

Chel 5 1.765 2.46(3) 2.37 2.42(4) 3.07

Mono 6 1.760 2.52(3) 2.41 2.51(6) 3.13

EXAFS 5.4 1.77(1) - - 2.41(2) 3.11(2)

Energy difference between mono and chel 5 kJ/mol. This is a small value and consistent with the experimental observation that the mode of coordination of sulfate varies with the water activity.

Determination of reaction mechanism – how do chemical reactions occur? Experimental data: rate equation, rate constant and activation parameters. The rate equation is used to deduce a possiblestoichiometric mechanisms for the reaction; activation parameters can be calculated using QM.

Example (Macak et al. Dalton Trans. 2006, 3638), the exchange reaction: U17O2

2+ + UO2F+ U⇌ 17O2F+ + UO22+

follows the rate equationv = kobs[UO2

2+][UO2F+] kobs = 5.5×103 M-1s-1 at 25.0 oC, ∆H≠ = 31 kJ/mol and ∆S≠ = -56 J.K-1.mol-1

Possible stoichiometric exchange mechanisms:dissociative, (H2O)[(H2O)4UAO2F+]..[UBO2(OH2)5

2+] (H2O)[(H2O)4UAO2

+-F-UBO2(OH2)42+],(H2O)

[(OH2)5UAO22+]..[(FUBO2(OH2)4

+],(H2O); Model D associative, (H2O)[(H2O)4UAO2F+]..[UBO2(OH2)5

2+] (H2O)[(H2O)4UAO2

+- F-UBO2(OH2)52+]

[(OH2)5UAO22+]..[(FUBO2(OH2)4

+],(H2O); Model A

Using QM, we can calculate the relative energy of the precursor, intermediates and corresponding transitionstates; the latter can be compared with experiment:Model A , ∆H≠ = 49.6 kJ/mol; Model B, ∆H≠ = 30.9 kJ/mol and experiment ∆H≠ = 31 kJ/mol.

Chemical reactivity and chemical bonding.

Example, the rate for the isotope exchange reaction (Szabó and Grenthe, Inorg. Chem. 2007, 46, 9372):U17O2

2+(aq) + H2O UO⇌ 22+(aq) + H2

17O;follows the rate equation

The half-life for the exchange with UO22+(aq) is larger

than 105 hours, for UO2(OH)+ larger than 104 hours while it is 0.13 sec for (UO2)2(OH)2

2+, a change of more than a factor of 109

;

2,2

2222

2

222

OHUOk

H

UOkv obstotobs

Possible explanations for the large variation in reactivity:•Weakening of the ”yl”-bond as a result of strong σ- donation from coordinated hydroxide (Clark et al. Inorg. Chem. 1999, 38, 1456 and Ingram et al. Dalton Trans. 2006, 2403). Burns et al.(Inorg. Chem. 2000,39, 5297; ibid, 2001, 40, 5491) have discussed how the basicity and lability of the uranyl oxo ligands are affected by coordination of other strong donors in the equatorial plane of uranyl(VI) complexes. • Competing participation of uranium 6d orbitals in both the U - Oyl and U – OH -bonds (Clark et al.)

Concluding remarks:

•It is necessary to be familiar with both the languages used by experimental and theoretical chemistry.•Look carefully into the often hidden assumptions used in the analysis of experimental data.•Careful consideration of the pros and cons of different QM methods is certainly important, but perhaps even more so exploring the different chemical models that are required in any QM calculation.•Comparison of experimental and QM studies requires testing of different models.•Do we have sufficient confidence in the methods used to describe solvents? Do they give the same answers?

Correlation diagrams