Bond length variations: Electron number profiles and transferable atomic sizes

A profile of the number of electrons with distance along the M–X bond in gas-phase diatomic molecules has been obtained from electron density plots calculated using DFT B3LYP 6-311G∗∗ method for some representative molecules. This “number profile” is compared with that expected from the partitioning of the 1D bond-distance into atom-specific transferable “hub” or core atomic sizes of the M and X atoms and another “axle” size which is associated with a pair of (bonding) electrons. The “hub” size is proportional to a core atom-specific size, rnZc with rnZc(M) ⩾ rnZc(X). For “single bonds”, the “hub” size for M atom is CMrnZc(M) and for X atom is CXrnZc(X). The “axle” size, DMX, is usually the ordinary (∼4aH/3 where aH is the Bohr radius of the hydrogen atom) or elongated (∼2aH) bond length of the hydrogen molecule. The “hub” and “axle” sizes could be characterized “charge-transfer” (CM = π2/3 = 2.144; CX = π4/3/2 = 2.300 and DMX = 4aH/3) or “neutral” (CM or CX = 1, 2, … and DMX = 2aH). We use a new “static” or “peripatetic” classification for the core sizes which is derived from a new condition for metallization in elements based on atomic size. The charge-transfer distance, dMX±, is usually found for “static” conditions while the “neutral” description is usually found when X = F or for “peripatetic” conditions. Such a partitioning is seen to agree with that from the plot of the total number of electrons, Nel, vs r along a bond axis. The Nel vs r plots from each atom are described by a simple hydrogen-atom-like function which differ away (“out”) or towards (“in”) the M–X bond. Thus Nin,out(M,X) = (ZM,X ± 1)exp (−r/Bin,out) where the minus sign is associated with M and plus sign with X and Bin,out being related inversely to the Slater orbital exponent.