Atoms-in-molecule approach

In the Atoms In Molecules approach (Section 9.3), the Laplacian (trace of the second derivative matrix with respect to the coordinates) of the electron density measures the local increase or decrease of electrons. Specifically, if is negative, it marks an area where the electron density is locally concentrated, and therefore susceptible to attack by an electrophile. Similarly, if is positive, it marks an area where the electron density is locally depleted, and therefore susceptible to attack by a... 

To summarize, therefore, it is reasonable to say that ab initio calculations of spin-orbit coupling constants may be successfully performed on atoms (although relativistic wavefunctions will be necessary for the heavier ones) and diatomic molecules (especially hydrides). For larger molecules, such methods may be too time-consuming and resort to semi-empirical techniques will be necessary. The atoms-in-molecules approach has proved extremely successful, but it should be possible to use semi-empirical wavefunctions with the full hamiltonian before long. This will be probably more useful with very large molecules. 

One of the most commonly employed procedures has been to simply extrapolate the molecular coupling from the available atomic parameters using the so-called atoms-in-molecules approach (72). Here (r,) is assumed to be constant for electrons with the same n and / quantum numbers. The values of are then assumed to be equal to the spin-orbit coupling constants n/, which are derived from atomic spectral data. This approach has been employed by Wadt (73) in all-electron studies, and by other groups (32,74) in effective potential calculations involving the rare-gas dimers and dimer ions. Ermler and co-workers used this approach coupled with AREP calculations to determine spectroscopic properties for various states of Au2 (42), Hg2, and HgTl (75). 

There may be many different functional representations of PESs based on a variety of mathematical techniques (e.g. polynomials or splines) and different physical models (e.g. atoms-in-molecule approach). Theoretically, all of them should work adequately in simulations of scattering, spectroscopic or thermodynamic properties. However, we believe... 

An excellent and comprehensive book written by the founder of the atoms-in-molecule approach. 

The molecular chemical hardness may be set equal to that of atomic species entering homopolar binding, according to molecule softness (5) based formulation rooted in the Bratsch atoms-in-molecule approach (Bratsch, 1985)... 

The results consist in the emergence of the so called atomic basins that include all the atomic nuclei but also their interspaces until the surface delimited by fulfillment of the zero flux condition of electronic density (Vp(r)-n- 0) according with Bader and co-workers atoms-in-molecules approaches. 

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