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, r_nZ^c with r_nZ^c(M) ≥ r_nZ^c(X). For "single bonds", the "hub" size for M atom is C_Mr_nZ^c(M) and for X atom is C_Xr_nZ^c(X). The "axle" size, D_MX, is usually the ordinary (~4a_H/3 where a_H is the Bohr radius of the hydrogen atom) or elongated (~2a_H) bond length of the hydrogen molecule. The "hub" and "axle" sizes could be characterized "charge-transfer" (C_M = π^2/3 = 2.144; C_X = π^4/3/2 = 2.300 and D_MX = 4a_H/3) or "neutral" (C_M or C_X = 1, 2, ... and D_MX = 2a_H). 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, d_MX^±, 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) = (Z_M,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.