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Solution coordination chemistry; stoichiometry and
structure, thermodynamics and dynamics –
the reciprocity of experiment and theory.
Ingmar Grenthe
Inorganic Chemistry, Royal Institute of Technology (KTH),
S-10044 Stockholm, Sweden
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 ⇌ MpLq; where the stoichiometric
coefficients have values ranging from 0 < p < P
and 0 < q < Q;
Several different complexes are in general present
simultaneously in equilibrium systems.
In the experimtal study one determines the stoichiometry
and equilbrium constants by varying the total
concentrations of M and L and meauring the free
concentration of one reactant or product, often using an
ion 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 obtained
using ”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 any
discussion 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 account
M(OH2)x + L(H2O)y ⇌ ML(OH2)z + (x +y –z)H2O;
How about remaining solute solvent interactions?
One possibility:
M(OH2)x(PCM)+ L(PCM) ⇌ ML(OH2)z(PCM)+
(x –z)H2O(PCM); Model A
One 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(OH2)x](L)(PCM);
outer-sphere complex formation
2. [M(OH2)x](L)(PCM) ⇌ [ML(OH2)x-1](H2O)(PCM);
Example:
Zn2+(aq)+ NH3(aq) → Zn(NH3)2+(aq); is ΔGro = -13.1 kJ/mol
Model A: ΔGro = -41.2 kJ/mol
Model B: ΔGro = -16.6 kJ/mol
The 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 strength
different 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 of
charge 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 experiments
can be made in such a way that the activity coeff. of
reactants 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 unity
and where the activity coefficients of reactants and
products are unity. Data at different ionic strength can
be referred to a common pure water standard state
using semi-empirical (electrostatic) electrolyte models.
Methods for determination of the structure of complexes
in solution.
All methods, LAXS, LANS, EXAFS provide ”onedimensional” struture information in the form of
pair-distances between atoms and the number of such
distances. 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 model
from such date requires the comparison of different
models; these and their relative energy can be obtained
from 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
Coord U – Oyl U –
Numb.
OH2
Mono
5
1.759
Chel
5
Mono
6
EXAFS 5.4
U - Oaver
U-S
2.48(3) 2.22
2.43(8)
3.61
1.765
2.46(3) 2.37
2.42(4)
3.07
1.760
2.52(3) 2.41
2.51(6)
3.13
2.41(2)
3.11(2)
1.77(1) -
UOsulf
-
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 possible
stoichiometric mechanisms for the reaction; activation
parameters can be calculated using QM.
Example (Macak et al. Dalton Trans. 2006, 3638), the
exchange reaction: U17O22+ + UO2F+ ⇌ U17O2F+ + UO22+
follows the rate equation
v = kobs[UO22+][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)52+] 
(H2O)[(H2O)4UAO2+-F-UBO2(OH2)42+],(H2O) 
[(OH2)5UAO22+]..[(FUBO2(OH2)4+],(H2O); Model D
associative, (H2O)[(H2O)4UAO2F+]..[UBO2(OH2)52+] 
(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 transition
states; 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):
U17O22+(aq) + H2O ⇌ UO22+(aq) + H217O;
follows the rate equation
v
 
H 
2 2
2 tot
 2
kobs UO


kobs UO2 2 OH 
2
2

 2, 2
;
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)22+, a change of more
than a factor of 109
Possible explanations for the large variation in
reactivity:
•Weakening of the ”yl”-bond as a result of strong σdonation 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