Bond length variations: Electron number profiles and transferable atomic sizes

Abstract: 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, rnZ c with rnZ c (M)⩾ rnZ c (X). For “single bonds”, the “hub” size for M atom is CMrnZ c (M) and for X atom is CXrnZ c (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, N el, vs r along a bond axis. The N el 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 N in,out(M,X)=(ZM,X ±1)exp(−r/B in,out) where the minus sign is associated with M and plus sign with X and B in,out being related inversely to the Slater orbital exponent. [Copyright &y& Elsevier]