Stabilization Studies of Metal-Chelating Complexes

                              via Computational Methods

By

Kweku Acquah, Eihab Jaber

 

Abstract

The bidentate chelating ligands of a metal ion are known to result in a more stable molecule due to the chelate effect when compared with monodentate ligands on the same metal ion. In this work, we examine the enthalpic contribution to the stabilization of the metal ion complexes as the ligands change from monodentate to bidentate and subsequently, as the molecule itself become more macrocyclic.  Copper (II), Cadmium (II), and Nickel (II), were used as the subject metal ions, and the monodentate and bidentate chelating ligands were NH3 ,-. and ethyldiamene (EN), respectively. The equilibrium values for Ni(en) and Cd(en), were 46.9, and 337.5, respectively. Our findings suggest that different equilibrium positions are established upon addition of new ligand interactions, favoring the bidentate chelating ligand interactions over the monodentate ligands interactions. The selection of the metals were irrational hence to avoid random data, silver and palladium were added to provide a rational data and patterns in groups versus columns of the metals in the periodic table.

Introduction

            Research in inorganic chemistry has been conducted over the years with regard to the thermodynamic properties of chelating ligands.  More specifically, it has been theorized and is widely believed that the closed end macrocyclic ligands of a metal ion result in differing metal ion selection when compared with their open-ended monodentate counterparts.

            Here, we examine a comparison of entropy and enthalpy within four metal based molecules; one set with ethylenediamine (EN) chelating ligands ranging from 1-3 and the other with six Ammonia (NH3) ligands.   The ethylenediamine chelating ligands represent a means to approach a macrocyclic molecule by comparing bidentate versus monodentate ligand correlation. The six Ammonia ligands represent a means to explain the behavior and the overall stability of the monodentate ligand whiles the ethylenediamine represents a means to explain the behavior and the overall stability of the bidentate ligand.

            It is quite obvious that a bigger molecule would have more entropy associated to it as compared to a smaller molecule. The questions that was considered before carrying out the experiment was what happens to the molecule as the size of the ligand increases and becomes more macrocyclic (i.e. from EN to TN to TIRON, etc.), how should entropy and molecular stability correlate from a computational point of view? Also how much contribution does entropy and enthalpy has over the stabilization of the molecule and which one precedes over the other; in other words is the reaction entropy driven or enthalpy driven? The predicted results was that metals would prefer to have a bidentate ligand bond compared to a monodentate ligand bond; and the more the ligand bonds, the more stable the molecule will become. This prediction is due to the fact that a bidentate ligand has two nodes whereby it can form two bonds to the central metal whiles the monodentate ligand only has one node and is able to form one bond to the central metal. In theory it is easier to dissociate a monodentate ligand than a bidentate ligand because the monodentate ligand only forms individual bonds whiles the bidentate ligand form bonds as a group (pairs).

 

Methods and Basis Sets

 

            All computations were carried out using GAUSSIAN 03.  The Computational Methods that were used for these calculations include: Hartree-Fock (HF) and Density Functional Theory (DFT) B3LYP & LANL2DZ.

            Hartree-Fock is a computational method derived from Ab initio methods. Ab initio method is a mathematical approach known as model chemistry which describes a mathematical approach to solving the Schrodinger’s equation. Ab initio method states that if one knows the structure of the molecule, one should be able to perform a complete calculation of that molecule completely from mathematical principles.1 Hartree-Fock is the most basic among the theories and is also known as the self-consistent field theory. The self consistent field theory looks at one electron as the starting electron and calculates the potential of its movement by freezing the distribution of all the electrons and treating their average distribution as centrosymmetric. The advantage of this theory is that it is accurate and precise in molecular modeling and also takes less time. The disadvantage of this theory is the inability to incorporate electron-electron repulsion; hence it is mostly used to verify data and calculations.

            Density Functional Theory (DFT) is a computational method that derives properties of the molecule based on determination of the electron density of the molecule and it is independent of the number of electrons.1 Hartree-Fock is mainly concerned with the wavefunction, which is a mathematical construct; DFT concentrates only on the density of the electron and is more concerned with the physical characteristics of the molecule. The mathematical aspect of DFT is functional implying that it is a function of a function. DFT is a function of the x-y-z coordinates of the individual electron. The method in DFT used for this research is B3LYP which is a hybrid DFT. It is a combination of Hartree-Fock approximation to the exchange energy and a DFT approximation to the exchange energy, all combined with functional that includes electron correlation.

Methods & Basis Set Descriptions:

 

-       DFT – B3LYP  Beck 3-term correlation functional, Lee, Yang and Parr – Exchange Functional Hybrid

-       LanL2DZ – Los Alamos National Laboratory 2-Double-Zeta

-       Basis Sets – example: 3-21, 3 Slater Equations for the Inner shell electrons, 2 and 1 Slater Equations for the Valence electrons.

The molecular structures of the four models examined are pictorially represented in Figure 1 below.  In each case, M refers to the metal ion; Cu(II), Cd(II) and Ni(II) have been examined herein.

Figure 1

 

 

            Figure 1 (a) shows the structure of the bond formation between the ethylenediamine ligand and the central metal. Figure 1 (b) Shows the structure of two ethylenediamine ligand and the central metal. Figure (c) Shows the bond formation of three ethylenediamine ligand and the central metal atom. Figure 1 (d) shows the monodentate ligand formation structure whereby the central metal is bonded to six Ammonia molecules. The sizes of the molecules differ by observation of the structures of the molecules. Entropy is increased upon addition of the ligands which works against the stabilization of the molecule but in terms of enthalpy, the addition of ligands increase the stability of the molecules. A macrocyclic approach can also be observed in these figures.

            Due to the nature of these metal complexes, geometry optimizations were not performed. Optimization of molecules of that size results could take days to optimize even with the fastest machines and tools. The monodentate and bidentate ligands are rigid enough in structure that only frequency calculations were performed at Hartree-Fock and DFT theory levels. The percent errors of the Gibbs free energy of the molecules when optimized are unnoticeable compared when compared to the frequency simulations which makes the optimization irrelevant. Gibbs free energy as well as Enthalpy for each complex was calculated directly by GAUSSIAN 03, dependent on the basis set used. 

Data and Calculations

 

Table 1

 

		HF3-21g	HF6-31g (d)	B3LYP-LANL2DZ
NH3	ΔG kcal/mol	-35048.25391	-35244.19139	-35471.64118
ΔH kcal/mol	-35034.57419	-35230.51419	-35457.93197
ΔS kcal/mol	0.045881999	0.04587358	0.045980919
EN	ΔG kcal/mol	-118049.471	-118707.4083	-119241.046
ΔH kcal/mol	-118026.9465	-118686.169	-119221.1934
ΔS kcal/mol	0.075547447	0.071237065	0.066585725
Ni(II)	ΔG kcal/mol	-940890.6464	-945336.6219	-105529.8175
ΔH kcal/mol	-940879.2897	-945325.2652	-105518.4609
ΔS kcal/mol	0.038090478	0.038090478	0.038090478
Cu(II)	ΔG kcal/mol	-1023438.131	-1028273.822	-122416.0345
ΔH kcal/mol	-1023426.291	-1028261.981	-122404.1933
ΔS kcal/mol	0.039713185	0.03971529	0.03971529
Cd(II)	ΔG kcal/mol	-3413782.664	-1301094.323	-29601.25815
ΔH kcal/mol	-3413770.706	-1301062.6	-29589.30032
ΔS kcal/mol	0.04010676	0.106399935	0.04010676

 

 

Table 2

		HF3-21g	HF6-31g (d)	B3LYP-LANL2DZ
Cu(NH3)6	ΔG kcal/mol		-1239457.972	-335720.0896
ΔH kcal/mol	-1239428.9	-335693.1299
ΔS kcal/mol	0.097507667	0.090423318
log k	-206.0734381	347.7660402
Cu(en)	ΔG kcal/mol	-1141389.22	-1146841.849	-242507.5384
ΔH kcal/mol	-1141367.628	-1146820.525	-242485.8956
ΔS kcal/mol	0.072421999	0.071519092	0.072590374
log k	-72.14933419	-102.2173475	623.6933757
Cu(en)2	ΔG kcal/mol	-1259469.704	-1265577.193	-361812.212
ΔH kcal/mol	-1259443.214	-1265551.281	-361786.0825
ΔS kcal/mol	0.088846913	0.086908504	0.087638827
log k	-49.40619411	-81.73006775	670.3554459
Cu(en)3	ΔG kcal/mol	-1377316.749	-1383997.782	-481283.6357
ΔH kcal/mol	-1377286.594	-1383966.246	-481251.2914
ΔS kcal/mol	0.101140342	0.105774845	0.108483567
log k	-197.8571733	-292.0722452	839.3056699

 

 

 

 

Table 3

		HF3-21g	HF6-31g (d)	B3LYP-LANL2DZ
Ni(NH3)6	ΔG kcal/mol	-1151061.916	-1156582.033	-318871.0834
ΔH kcal/mol	-1151033.951	-1156555.026	-318843.3223
ΔS kcal/mol	0.093795013	0.090583273	0.093110992
log k	-86.72268883	-161.1467512	375.0549551
Ni(en)	ΔG kcal/mol	-1058876.061	-1063631.938	-225632.3136
ΔH kcal/mol	-1058855.105	-1063610.782	-225611.4671
ΔS kcal/mol	0.07028575	0.070959248	0.069919536
log k	-46.97638128	-302.212572	631.7545558
Ni(en)2	ΔG kcal/mol	-1176760.476	-1182462.527	-345101.3635
ΔH kcal/mol	-1176735.889	-1182437.074	-345077.0117
ΔS kcal/mol	0.082467631	0.085372088	0.081676272
log k	-168.022017	-211.876457	798.9638741
Ni(en)3	ΔG kcal/mol	-1294911.443	-1301094.323	-464350.9385
ΔH kcal/mol	-1294881.452	-1301062.6	-464319.5386
ΔS kcal/mol	0.100591021	0.106399935	0.105316025
log k	-93.58875083	-267.3277309	805.2188014

 

 

 

 

Table 4

		HF3-21g	B3LYP-LANL2DZ
Cd(NH3)6	ΔG kcal/mol		-242803.5544
ΔH kcal/mol	-242776.6693
ΔS kcal/mol	0.090172861
log k	273.1399536
Cd(en)	ΔG kcal/mol	-3531371.876	-149337.1152
ΔH kcal/mol	-3531350.822	-149314.6346
ΔS kcal/mol	0.070616185	0.07540012
log k	-337.5364362	362.8755183
Cd(en)2	ΔG kcal/mol	-3649759.091	-268965.4829
ΔH kcal/mol	-3649732.504	-268939.3295
ΔS kcal/mol	0.089171034	0.087718805
log k	-89.8483117	646.9224783
Cd(en)3	ΔG kcal/mol	-3767518.767	-388058.4911
ΔH kcal/mol	-3767488.981	-388026.2697
ΔS kcal/mol	0.099904896	0.10807105
log k	-302.3722586	538.3572448

 

 

 

 

RESULTS AND DISCUSSIONS

 

The underlying definition of Gibbs free energy (∆G) is a correlation between enthalpy (∆H) and entropy (∆S) at a constant temperature (T). The Gibbs free energy is defined as the enthalpy of the reaction minus the product of entropy and temperature.

To determine the equilibrium constant (log k), the Gibbs free energy of a molecule (ΔG˚) is equate to the ∆G of its components. .  Therein, ∆G of the metal (M) and ligands (L) are subtracted from ∆G of the product molecule. , the number of ligands (x) required to form the product molecule must be multiplied by the ∆G of the individual ligand.  The subsequent value is then related to log k as .

Table 1 reflects the calculated values of Gibbs free energy as well as enthalpy derived directly from GAUSSIAN 03 simulations for monodentate and bidentate ligands as well as the entropy values. Entropy and the equilibrium constant were calculated manually based on the Gibbs free energy equation () and the standard Gibbs free energy.  While the results vary by basis set, a trend is noticeable with regard to Gibbs free energy and enthalpy.  In all cases of Nickel as the subject metal ion, the enthalpy contribution was greater in the (EN)3 complex than the monodentate amine model.  However, this data also suggests that the enthalpic contribution did not exceed the monodentate ligand complex until the metal ion was held by two bidentate ligands as shown in Table 2. Table 3 indicates a similar trend with regard to the analysis of copper metal ion.  With regard to the equilibrium constant (k), a larger k value reflects a product favored reaction.  In this respect, the variance of basis set produces differing results.  Under the premise that DFT B3LYP/LANL2DZ is the most preferable of the levels of theory utilized herein for 3rd+ row transition metals, the data suggests that Ni(en)3 is the preferred complex for formation of the 4 ligand sets.  Similarly, Cu(en)3 shares this trait; however Cd(en)2 is the preferred complex according to the data obtained for its ligand sets in table 4.

Conclusion

In all cases, the G value for 2+ bidentate ligands was lower than that of the monodentate complex.  This aids in affirming the chelate effect in that a lower G value reflects higher spontaneity and thus a more stable molecule.  Further, stability increases from monodentate to bidentate ligands despite an increase in each system’s entropy.  Each of these results confirms via computational chemistry that the stabilization of a metal ion-bidentate ligand complex is enthalpy driven; a matter that was in question with regard to metal ion selection until only recent years.

Future Works

            Metals are complex in its natural states as well as bond formations in a reaction. One of the future works being considered is to expand the amount of central metals being used and also to be rational when it comes to selection of the metals. The metals are not going to be chosen randomly but as a group and family and then optimize to get a better understanding of their interactions with non metals. This will help categorize and explain the complex behavior of metals more accurately.

 

 

 

 

                  (1)                  James B Foresman, A. F. exploring chemistry with electronic structure methods, 2nd ed.; Gaussian, Inc.: Pittsburgh, 1996.