The atom in a molecule: A density matrix approach

Abstract

A method based on first-order density matrices is proposed to define an atom in a molecule, which is in accord with a previously given definition using density functional theory. The promotion energy Ep is expressed in terms of a defined division function α(r). By minimizing Ep with respect to α(r), one can obtain α(r), by which an atom in a molecule is uniquely determined. It is shown that such an ‘‘atom’’ satisfies a local virial theorem, depicted intuitively, Some other properties of the atom in a molecule are also discussed. Comparison is made with a definition due to Bader, and an approximate but simple approach to determine an atom in a molecule is proposed.

On the resolution of the optical rotatory power of chiral molecules into atomic terms. A study of hydrogen peroxide

“…The concept of atoms-in-molecules ͑AIM͒ as spatial domains bounded in space is deeply rooted within the preliminary assumption that a molecular structure can be theoretically defined and experimentally observed. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] In a fully a priori context, an axiomatic foundation for the idea of AIM has been attempted by Ayers, on the demand of maximum transferability of properties of atoms from molecule to molecule, 21 and found consistent with the partitioning scheme of Hirshfeld. 5 Experimental evidence on the fact that atoms and functional groups conserve some peculiar properties in a wide range of different molecular environments has long been known, see, for instance, the work of Pascal on magnetic susceptibilities, [22][23][24][25] and that of Denbigh 26 and Vogel 27 for electric dipole polarizabilities of molecules in static fields.…”

X-Ray diffraction studies on electron density in organic crystals

“…64 ' 65 However, the condition of the fulfillment of the principle of minimum action not only for the entire system (molecule) but also for its subsystems (atoms) requires that atoms be bounded by zero flux surfaces, as is done in Bader's theory. In this case, the atom in a molecule is described by the same equations of motion and theorems (for example, the virial theorem or the Ehrenfest theorem) as those applicable to the total system.…”

An empirical charge transfer potential with correct dissociation limits

“…This broad range of accuracy and the fact that Eqs. (45) and (46) are well-behaved for any R makes it tempting to use NDOL in general. However, near equilibrium bond lengths, Fig.…”

“…First, to define q, we invoke a density-functional-theory [39][40][41] (DFT) motivated atom-in-molecule 18,42,43 pseudo-atom concept within the context of the EVB approach. We assume the availability of a practical density decomposition strategy 18,[43][44][45][46][47][48] to define the pseudo-atom densities. The charge is defined as an average over the difference between two pseudo-atom densities.…”