AIM analysis

A much less basis set dependent method is to analyze the total electron density. This is called the atoms in molecules (AIM) method. It is designed to examine the small effects due to bonding in the primarily featureless electron density. This is done by examining the gradient and Laplacian of electron density. AIM analysis incorporates a number of graphic analysis techniques as well as population analysis. The population analysis will be discussed here and the graphic techniques in the next chapter. 

The five second-moment spherical tensor components can also be calculated and are defined as the quadrupolar polarization terms. They can be seen as the ELF basin equivalents to the atomic quadrupole moments introduced by Popelier [32] in the case of an AIM analysis ... 

Unusual arene-cadmium 7r-complexes have been recently prepared and structurally characterized. For example, the /w /zz-bcn/i porphyrin complex 194, which can be obtained by reaction of the free base with CdCl2, possesses a cadmium atom that is bound to the Mfez-phcnylcnc unit of the ligand in an apparent /-fashion (Figure 32). The resulting Cd-C distance of 2.71 A is shorter than the sum of the van der Waals radii.252 Despite this relatively short contact, DFT calculations and AIM analysis point to the weakness of the interaction. Comparable weak arene-cadmium 7r-interactions are also observed in the /wra-benziporphyrin cadmium chloride complex 195.253... 

The C-H BDE in peptides is even lower than that of the S-H BDE in thiols as a consequence of the exceptional stability of the radical products due to captoda-tive stabilization (Viehe et al. 1985 Armstrong et al. 1996). Yet, the observed rate constants for the reaction of CH3 and CH2OH with, e.g., alanine anhydride are markedly slower than with a thiol. This behavior has been discussed in terms of the charge and spin polarization in the transition state, as determined by AIM analysis, and in terms of orbital interaction theory (Reid et al. 2003). With respect to the repair of DNA radicals by neighboring proteins, it follows that the reaction must be slow although thermodynamically favorable. 

In the ethane case, however, the AIM analysis helps in understanding the overlap of the bonds and the location of the electrons as derived from the density picture, but it does not tell us anything about the origin of the rotational barrier. For that, we need methods that quantitatively give us energies that can be associated with the effects of donor-acceptor bonding (hyperconjugation) and electron-electron repulsion (Pauli repulsion) as noted above. 

The atoms-in-molecules (AIM) analysis of electron density, using ab initio calculations, was considered in Section 5.5.4. A comparison of AIM analysis by DFT with that by ab initio calculations by Boyd et al. showed that results from DFT and ab initio methods were similar, but gradient-corrected methods were somewhat better than the SVWN method, using QCISD ab initio calculations as a standard. DFT shifts the CN, CO, and CF bond critical points of HCN, CO, and CH3F toward the carbon and increases the electron density in the bonding regions, compared to QCISD calculations [107]. 

Fig. 10. Atomic charges for TNDAP - upper number from AIM analysis, lower from kappa refinement.

In this section, characterization of H-bonding of water clusters using the AIM approach is presented. Computational details of AIM analysis of water clusters are given elsewhere [243]. Stabilization energies (SEs) of all water clusters have been calculated using the supermolecule approach and corrected for BSSE using the counterpoise (CP) procedure suggested by Boys and Bernardi [181]... 

It is well known that water-mediated interaction stabilizes structure of biomolecules [1, 138, 247-250]. Therefore, several model molecular systems have been chosen to probe the water-mediated interactions in biomolecules and a large amount of experimental and theoretical work has been published over the years on this subject [78, 138, 251-258]. Since phenol is the simplest aromatic alcohol resembling chromophore of an aromatic amino acid, hydration of phenol molecules has been studied to understand H-bonding and solute-solvent interaction in biological systems. Several experimental and theoretical calculations have been made on the phenol-water clusters [259-273]. Recently, we have made a comprehensive analysis on structure, stability, and H-bonding interaction in phenol (P1-4), water (W1-4), and phenol-water (PmW (w = 1-3, n = 1-3, w + n < 4)) clusters using ab initio and DFT methods [245]. In this section, electronic structure calculations combined with AIM analysis on phenol-water clusters are presented. 

We can finally comment on the validity of the AIM analysis of bond critical point in solids. Its validity has been recently questioned [18,83] on the basis of a recent finding that the topological features of the electron density of a complex... 

This system is being studied at a higher calculation level, in order to determine the energetic, the energy decomposition pattern and perform an AIM analysis. 

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