X-HCOO$^{-}$ Complexes

According to the B3LYP level of theory using the basis set described above, the carboxylate anion has a C$_{2v}$ symmetry with C-O bond lengths of 1.270 Å and a $\widehat{OCO}$ bond angle of 130.3$^{o}$. In terms of charge location, the NBO [76] analysis reports the following: -0.844 e$^{-}$ of charge on the oxygen atoms and +0.702 e$^{-}$ of charge on the carbon atom.

a	b

Figure 1: a.-) Bidentate binding of the metal with the ligand. b.-) monodentate binding of the aluminum (III) cation with the ligand.

The metals we have studied present two different orientations when binding to the carboxylate anion, monodentate and bidentate, the former being much higher in energy. The different structures characterized in this section are shown in Figure 1 and the important geometrical parameters are given in Table 1.

Table 1.
Geometrical figures of the monodentate binding, and X-OOCY bidentate
complexes maintaining the symmetry of the COO-X cycle,
where X=Al, Mg and Y=H, CH$_{3}$ and CH$_{2}$CH$_{3}$.
Y	X		X-O			C-O			$\widehat{OCO}$
H	-		-			1.270			130.0
	Al		1.809			1.311			114.8
	Mg		1.963			1.292			119.3
(Monodentate)	Al		1.698			1.395-1.192			127.8
CH$_{3}$	-		-			1.272			128.8
(Staggered Isomer)	Al		1.788			1.332			112.2
	Mg		1.944			1.304			117.2
CH$_{2}$CH$_{3}$	-		-			1.273			128.7
(Staggered Isomer)	Al		1.813			1.318			113.3
	Mg		1.942			1.305			117.0
(Monodentate)	Al		1.698			1.428-1.198			115.5
(Monodentate)	Mg		1.821			1.359-1.213			122.3

In the case of bidentate bonding, the metal, both oxygens, and the carbon form a planar cycle with C$_{2v}$ symmetry. For the aluminum complex, the Al-O bond distance is 1.810 Å. There are significant changes in the geometry of the HCOO$^{-}$ fragment due to this bonding to the cation. The C-O bonds lengthen by 0.041 Å to 1.311 Å and the $\widehat{OCO}$ angle shrinks by 15.5$^{o}$ with a final value of 114.8$^{o}$to accommodate the bidentate bonding.

For the magnesium complex there are numerous signals of weaker metal-oxygen bonding. The Mg-O bond length is 1.963 Å, 0.154 Å longer than the Al-O bond (the covalent radius of magnesium is only 0.12 Å larger than that of aluminum) and the effect of complexation on the C-O bond length is much smaller; the C-O bond is lengthened by only 0.029 Å in the magnesium case. Clearly, to support bidentate bonding the $\widehat{OCO}$ angle must shrink substantially from its value in the free anion, but there again the magnesium cation causes less effect than the aluminum cation, the final $\widehat{OCO}$ angle being 119.3$^{o}$.

Previous calculations by Garmer and Gresh [41] reported an Mg-O distance of 1.94 Å, at HF level of theory, with a 6-631G(2d) basis set for magnesium (II) cation and SBK-31(2d) for the ligand atoms, and geometry optimizations performed with fixed ligand geometries. A slightly more recent work by Deerfield II et al [44] reported a distance of 1.933 Å calculated at the HF/6-31++G** level of theory. Additionally, we have performed MP2/6-31++G** calculations with the magnesium-carboxylate complex. This level of theory predicted a value of 1.982 Å for the Mg-O bond length while the B3LYP with the basis described above, estimates a bond length of 1.963 Å. From this result we consider that our standard level of theory reproduces these systems with reasonable accuracy.

An interesting comparison between the two cases can also be made by examining the natural charges as given by the NBO analysis (see Table 2). The aluminum (III) cation in complexing with the carboxylate anion has a final natural charge of +2.349 e$^{-}$, decreasing the negative charge on the oxygen atoms to -0.734 e$^{-}$, and increasing the positive charge on the carbon atom to +0.776 e$^{-}$. The magnesium (II) cation receives only -0.233 e$^{-}$ worth of charge from the anion upon complexation, a charge transfer only slightly more than one third that seen in the case of aluminum (III). Also of note in the Mg-OOCH$\rceil$$^{+}$ complex is that the negative charge on the oxygen atoms is actually increased upon complexation, though only very slightly (-0.847 e$^{-}$), and the positive charge on the carbon atom increases slightly to +0.721 e$^{-}$.

Table 2.
NBO charges of the monodentate binding and X-OCCY bidentate
complexes maintaining the symmetry of the COO-X terminus, where
X=Al, Mg and Y=H, CH$_{3}$ and CH$_{2}$CH$_{3}$.
Y		X		X	O	C
H			-	-	-0.844	0.702
			Al	2.349	-0.734	0.776
			Mg	1.767	-0.847	0.721
(Mono)			Al	2.089	-1.046/-0.162	0.768
CH$_{3}$			-	-	-0.842	0.841
(Staggered Isomer )			Al		2.295 -0.766	0.933
			Mg	1.944	-0.870	0.890
CH$_{2}$CH$_{3}$			-	-	-0.844	0.841
(Staggered Isomer )			Al	2.145	-0.756	0.932
			Mg	1.748	-0.874	0.894
(Mono)			Al	2.086	-0.943/-0.261	0.884
			Mg	1.760	-1.045/-0.550	0.868

In examining the molecular orbitals for these systems we find that the main HCOO$^{-}$ cation interaction originates from the HOMO of the HCOO$^{-}$ moiety (Fig. 2) which is one of the two in-plane oxygen lone pair orbitals. Donation is from this molecular orbital into the empty $s$-orbital of the metal cation. This is easily appreciated through inspection of Figures 3 and 4. The relative stregth of the interactions is also evident in these figures, the aluminum case (Fig. 3) showing much larger metal participation than the magnesium case (Fig. 4).

Other interactions between the two fragments can also be found. Figures 5 and 6 demonstrate the donation from the $\pi$-system of the HCOO$^{-}$ fragment into an empty $p$-orbital of the metal. These two figures are out-of-plane cuts along the C-M axis with the oxygen atoms above and below the plane. Again it is obvious that the aluminum (III) cation attracts more electron density than does the magnesium (II) cation. In the aluminum case, yet another interaction is worthy of note. The second in-plane oxygen lone pair molecular orbital is stabilized by donation into the in-plane $p$-orbital of aluminum (see Figure 7). This interaction can be found in the case of magnesium also, but the stabilization is minimal and the orbital which corresponds to Figure 7 is, in this case, the HOMO while the HOMO of the aluminum complex is the out-of-plane oxygen lone pair orbital.

The NBO analysis agrees with this picture. It reports one bond between the aluminum atom and each of the carboxylate's oxygen atoms. The bonds are formed by an in-plane sp$_{y}$ aluminum hybrid and the oxygen in-plane $p$-orbitals. These orbitals are centered mainly on the oxygen atoms, but they also have a participation from aluminum of 11.75 $\%$ which is enough, according to the NBO program, to be reported as a bond.

Figure 2: The HOMO orbital	Figure 3: a$_{1}$ orbital of the
of the carboxylate ($^{-}$OOCH)	Al-OOCH$\rceil^{+2}$ complex
anion, which corresponds to the	(HOMO-2) showing donations
oxygen in-plane $p$-lone-	from the in-plane oxygen
pairs.	lone pairs to an empty
	$s$-orbital of the aluminum.
	-->
Figure 4: 7 a$_{1}$ orbital	Figure 5:2 b$_{1}$ orbital
of the Mg-OOCH$\rceil^{+}$ complex (HOMO-2),	(HOMO-3), which is out of the
showing donations from the in-plane	O-C-O plane. In this orbital,
oxygen lone pairs to an empty $s$-orbital	donation of the carboxylate
of the magnesium.	$\pi$-system into an empty
	aluminum $p$-orbital is observed.
Figure 6: 2 b$_{1}$ orbital	Figure 7:2 b$_{2}$ (HOMO-1)
(HOMO-3), which is out-of the O-C-O plane.	orbital of the Al-OOCH$\rceil^{+2}$
In this orbital, donation of the carboxylate	complex, demonstrating a donation
$\pi$-system into an empty magnesium	from the second in-plane oxygen
$p$-orbital is observed.	lone-pair orbital into an
	aluminum in-plane $p$-orbital.

Examining the second-order interactions, the most energetic are between the Al-O bonding orbitals and their opposite Al-O antibonding orbitals. Each of these having energy of 13.75 kcal/mol.

The NBO analysis localizes the $\pi$-system of the carboxylate anion showing a lone pair on O$_{1}$ and a C-O$_{2}$ $\pi$-bond. Donations from these localized orbitals into the out-of-plane $p$-orbital of aluminum have energetic values of 7.73 kcal/mol and 8.21 kcal/mol respectively giving a numerical value to the $\pi$$\rightarrow$$p$-orbital donation witnessed in Figure 5. The interactions between the two in-plane oxygen lone-pairs with the empty $p$-orbital of the aluminum atom have values of 3.27 kcal/mol each.

In addition to these interactions that are observed by looking at the MO's, some other interactions are reported by the NBO analysis such as a donation from the $\sigma$$_{C-O}$ orbital to the opposite $\sigma$$^{*}_{Al-O}$ antibonding orbital, as a consequence of the localization of the Al-OOC-cycle, where each bond donation contributes 5.32 kcal/mol. Finally, the NBO analysis reports interaction between both Al-O bonding orbitals and the C-H antibonding orbital, with an energetic contribution of 8.52 kcal/mol.

For the magnesium complex, the NBO analysis does not show any bond per se between the magnesium (II) and the carboxylate moiety. Instead the NBO analysis reports that magnesium (II) and carboxylate units are held together by second-order interactions, which are in accordance with the molecular orbitals described above. The most important interactions are donations from the in-plane oxygen $p$-orbital lone pairs to the magnesium empty $3s$-orbital with a energy contribution of 20.92 kcal/mol. These interactions are analogous to those which are given as Al-O bonds in the AlOOCH$\rceil$$^{+2}$ case except that in this case the participation of the metal is not large enough for these to be considered bonds in the NBO report.

More evidence of weaker Mg-OOCH$\rceil$$^{+}$ interaction is that the donation from C-O$_{2}$ $\pi$ bond into the magnesium $p$-orbital has an energy of only 2.31 kcal/mol, and the O$_{1}$ out-of-plane lone-pair donation contributes only 2.22 kcal/mol (corresponding values were 8.21 kcal/mol and 7.73 kcal/mol in the aluminum complex). Also the oxygen in-plane lone-pair donations to the magnesium in-plane p-orbital has an energy of only 2.71 kcal/mol. All of these interactions are weaker than their corresponding interactions in the aluminum complex.

Still, the Bader analysis of these complexes reveals more differences between the aluminum and magnesium complexes. According to the Bader analysis it is easy to differentiate between covalent and ionic bonds, looking at the energy density sign at the bond critical points (H(r$_{c}$)). The H(r$_{c}$) for the aluminum complex is -0.002 and +0.013 for magnesium, i.e., covalent and ionic bonds respectively. The Bader analysis also shows us how the C-O bonds are activated after binding to aluminum (or magnesium), i.e., H(r$_{c}$) is less negative, and these C-O bonds elongate. Aluminum provokes a larger change than magnesium in the H(r$_{c}$) that is in agreement with the larger elongation of the C-O bonds occurred in the aluminum complex. This trend is repeated along the bidentate X-COOY series (see Table 3).

Following the molecular orbital, NBO, and Bader analyses, it is certainly expected that the aluminum (III) interaction with the carboxylate anion would be much stronger than that of magnesium (II). While the magnesium-carboxylate interaction energy is -364.37 kcal/mol, the aluminum (III) interaction energy is -710.21 kcal/mol. Garmer and Gresh also reported a binding energy for the Mg-OOCH$\rceil$$^{+}$ complex of -362.7 kcal/mol which agrees with ours.

Another type of binding between aluminum (III) cation and the carboxylate anion was also found, where the metal cation binds only to one oxygen of the carboxylate. This bond length is 1.698 Å and has an angle $\widehat{AlOC}$ of 156.2$^{o}$. There is a charge transfer to the aluminum atom of aproximately 1 e$^{-}$ in this isomer. The natural charge on aluminum atom in this monodentate case is +2.089 e$^{-}$. The oxygen which binds the aluminum atom has a natural charge of -1.046 e$^{-}$ while the other oxygen only supports a charge of -0.162 e$^{-}$. The carbon atom has a natural charge of +0.768. As D. W. Deerfield et. al. we have not located either an homologous magnesium monodentate complex[44].

According to the NBO theory, the Al-O bond in this monodentate complex is a $\sigma$ bond between the $s$-orbital of the aluminum and an oxygen in-plane $p$-orbital. The contribution of the aluminum in this bond is 31 $\%$, while its contribution was around 11 $\%$ per bond for the bidentate complex. The second-order interactions are important in this complex and stronger than they were in the bidentate case. The most important donation is that of the $\sigma$$_{Al-O}$ to the $\sigma$$_{C-O}^{*}$ orbital with an energy contribution of 35.30 kcal/mol. The donation from one of the oxygen's in-plane lone pairs to an empty aluminum in-plane $p$-orbital has an energetic value of 29.17 kcal/mol. This oxygen lone-pair also donates some charge to the $\sigma$$_{Al-O}^{*}$ orbital, contributing 26.72 kcal/mol. The binding energy of the monodentate binding is only 26 kcal/mol lower than the aluminum (III) bidentate binding mode; it has an energy of 684.41 kcal/mol.

The Bader analysis describes the Al-O bond to be ionic, i.e., positive H(r$_{c}$), while in the bidentate complex it was described as a covalent bond. When the aluminum (III) cation binds the oxygen, the adjacent C-O bond is activated and at the same time the contrary C-O bond gains in negative energy density (see Table 3) at the bond critical point. Concomitantly, the C-O bond interacting with the aluminum lengthen from 1.292 to 1.395 Å while the contrary C-O bond shrinks (see Table 1).