X-HCONH$_{2}$ Complexes

Using the B3LYP method and the basis set described above, two different C$_{s}$ isomers have been located for the formamide, a planar structure (1 in Fig. 1) and a transition state with an imaginary frequency which corresponds to the rotation of the NH$_{2}$ (ts1). Two tautomers are known for the formamide, (see 2.n and 3 in Fig. 1). However, as stated above, only the rotomers of tautomer 2 have been studied in this work. All four rotomers of 2 present C$_{s}$ symmetry. A transition state was also found, which connects the formamide and the tautomer ts2, with an imaginary frequency corresponding to the passing of the hydrogen atom from the nitrogen to the oxygen.

The formamide structure 1 is the most stable of all the studied structures (see Table 1) and the rotation barrier of the NH$_{2}$ is 16.77 kcal/mol. Structure 2.1 is 12.81 kcal/mol higher in energy and is the global minimum of the tautomer. The other three tautomer 2 rotomers are around 5 kcal/mol higher in energy. Recall that Tortajada et al. [82] reported an energy difference between 1 and 2.1 of 11.50 and 11.40 kcal/mol at the G2 and G2(MP2) levels of theory respectively. Finally, ts2 lies 43.50 kcal/mol above structure 1, which agrees well with the values of 46.6 and 45.9 kcal/mol at the G2 and G2(MP2) levels of theory respectively reported by Tortajada et al..

The geometries of these HCONH$_{2}$ species are shown in Table 2. We focus our attention on the atoms which will be involved in the metal binding. The geometric features of the formamide and its NH$_{2}·$ rotation transition state are very similar, with the only remarkable difference being in the C-N bond, which measures 1.457 Å in the transition state structure, and 1.376 Å in the formamide ground state. As can be seen, the effect of ``turning off'' the C-N $\pi$ interaction is significant. Similarly, the geometries of the tautomer and its rotomers are nearly identical (except, of course, for the rotations).

The formamide and its tautomer present different binding possibilities, monodentate binding to the oxygen in the formamide (xo1, xots1), and either to the oxygen (xo2.1, xo2.3, xo2.4) or nitrogen (xn2.1, xn2.3, xn2.4) of the tautomer. Bidentate binding is also possible in both compounds (xbts1, xb2.2).

The aluminum-formamide interaction presented only oxygen monodentate Alo1 and bidentate binding Albts1 possibilities (note that Alots1 is a transition state). The B3LYP/DZ(p,d) wave function for the Alo1 isomer in C$_{s}$ symmetry experiences RHF-UHF instability. We have located a C$_{1}$ complex where the Aluminum is out of the NCO plane by 47$^{o}$ which is a stable minimum. The formamide-tautomer 2.n aluminum (III) binding, however, presented Al-N monodentate (Aln2.1, Aln2.3 and Aln2.4) and bidentate Alb2.2 bindings. All of these complexes have C$_{s}$ symmetry except the Aln2.3 structure which has C$_{1}$ symmetry with the aluminum 17$^{o}$ out of the NCO plane.

The geometric parameters of these complexes are shown in Table 2. Among the aluminum complexes, in the oxygen monodentate complex, logically, we observe that the C-O bond is elongated, while the C-N bond shrinks, similarly, the opposite effect is detected in the nitrogen binding aluminum complexes. The Al-O bond in Alo1 measures 1.711 Å, and the C-O bond is 0.14 Å longer and the C-N bond 0.07 Å shorter than in 1. In the nitrogen-metal monodentate binding complexes, the shortest Al-N bond is found in the Aln2.4 complex, with a value of 1.836 Å while this bond has a length of 1.856 Å in Aln2.1.

In the bidentate binding modes, X-O and X-N bond lengths are 1.907 and 1.879 Å respectively in Alb2.2 and 1.855 and 2.024 Å respectively in Albts1. The C-O bond elongates by 0.038 Å in both complexes, while the C-N bond shrinks by 0.043 and 0.022 Å in Albts1 and Alb2.2 respectively. Looking at the ligand after binding to the aluminum, we see that both bidentate modes alter the geometry less than the monodentate modes.

Structurally related magnesium (II) complexes were also located in our B3LYP/DZ(p,d) having C$_{s}$ symmetry. A Mgots1 structure was not found, instead Mgo1.1 was present; all of these complexes have C$_{s}$ symmetry. The geometrical features of these compounds are shown in Table 2, as expected, various signals of weaker bonding in the magnesium complexes are observed, e.g., longer metal-ligand bond lengths and smaller effects of complexation suffered by the ligand.

Analyzing the natural charge distribution of the complexes, we also observe that the charge transfer is larger at the aluminum complexes. While the aluminum gains -0.52 e$^{-}$ upon complexation , magnesium only receives a transfer of -0.05 e$^{-}$ in the Xo1 complexes. The charge transfer to the aluminum atom in the bidentate complex is very similar to that seen in the monodentate Alo1 complex, but the Mgb2.2 complex demonstrates a charge transfer almost three times greater than that seen in the corresponding monodentate complex. These charge transfers are slightly smaller than those found earlier for the bidentate X-COO$\rceil^{+2}$ complexes described in the previous chapter. In these complexes, a charge of -0.651 e$^{-}$ was transfered to aluminum and -0.233 e$^{-}$ to magnesium (the NBO charges are shown in Table 3).

In the aluminum (III) complexes, the most stable binding occurs in the Alb2.2 complex, with a binding energy of 331.86 kcal/mol, while the monodentate to oxygen and to nitrogen (the strongest, Aln2.3) binding energies are 322.57 and 316.83 kcal/mol respectively. Recall that we are comparing the binding energies with respect to two different ligands, the formamide and its tautomers. In the magnesium complexes, the tightest bond occurs also in the Mgb2.2 complex, where the binding energy is 125.38 kcal/mol but that is only 1 kcal/mol stronger than the bonding found in the Mgo1 structure.

Finally, the Mgo2.1 complex, namely the only monodentate metal-oxygen binding minimum on the tautomer surface, has a binding energy of only 84.66 kcal/mol.

Comparing these binding energies with those in the X-COOH$\rceil^{+/+2}$ complexes, the binding energies here are much smaller. Aluminum and magnesium had bidentate binding energies of 710.21 kcal/mol and 364.37 kcal/mol respectively in the X-COOH $\rceil^{+2/+3}$ complexes, which are more than twice the binding energies of the X-ONH$_{2}$CH $\rceil^{+2/+3}$ complexes. This binding energy difference it is largely due to the negative charge of the HCOO$^{-}$ ligand. The monodentate Al-OCOH$\rceil^{+2}$ binding energy is also significantly larger than the monodentate binding to the formamide in around 350 kcal/mol larger.

Previous calculations concerning magnesium (II) cation and formamide were performed by Garmer and Gresh [41], but they only focused on the formamide ground state, i.e., our Mgo1 complex. They report an Mg-O bond length of 1.80 Å at the HF level of theory using a 6-631G(2d) basis set for the magnesium [88], and a SBK-31(2d) set for the ligand atoms. Their binding energy of 121.1 kcal/mol at the MP2//HF level of theory, compares well with our value of 124.30 kcal/mol.

The X-O bonding, leads to a charge transfer occurring from the ligand to the metal cation. To garner a better understanding of this process, we have performed Bader$'$s topological analysis, and observed that the metal cation activates the C-O bond, hence the oxygen atom gains negative charge by depopulating the C=O bond. Let us look at Mgo1 to illustrate the point. Upon metal binding, the energy density of the C-O bond critical point becomes less negative (changes from -0.635 to -0.526, see Table 4) and the bond length elongates (about 0.070 Å). The energy density of the C-N bond critical point becomes more negative (around 0.05 in our example), and the C-N bond shrinks. Observe that this applies to either Al or Mg X-O bindings. Similarly, the bonding of the metal to the nitrogen causes the C-N energy density to become less negative and the C-O energy density to become more negative. In the bidentate bonding modes, both C-O and C-N bonds are activated after the metal binding (the energy densities are lower after the metal bonding), so that the bonds are longer than in the uncomplexed ligands (see Tables 2 and 4).

Finally, we mention another difference between the aluminum (III) and magnesium (II) complexes. According to the Bader analysis, it is easy to discriminate between covalent and ionic bonds. When the energy density at the bond critical point is larger than zero the bond can be classified as an ionic bond, while if it is less than zero then the bond is considered covalent [78]. Yañez [82] group in their aluminum (I) and magnesium (I) formamide study, reported electrostatic interactions between aluminum (I) and formamide, and at the xb2.2 complex, they only located bond critical points between the cation and the nitrogen atom but not with the oxygen.

In our study, as it is shown in Table 4, we see that for aluminum (III) ligand binding, all but the Alo1 and the Al-O bond in Alb2.2, are covalent bonds, while all of the magnesium (II) bonds are reported as ionic in the Bader analysis. Comparing with the formamide and aluminum (I) and magnesium (I) interactions [82], the structure analogous to xo1 was found to be bind most tightly for both monocations, both of them having similar binding binding energies around 48 kcal/mol (significantly lower than in our case). They found xb2.2 complex binding to be only 3 kcal/mol lower for magnesium (I) and 7 kcal/mol lower for aluminum (I). In terms of cation-ligand bonding, in the xb2.2 complex, they located bond critical points only between the cation and the nitrogen atom; no critical point existed between the metal and the oxygen [82].