Bond length variations: electron number profiles and transferable atomic sizes - Ganguly, Parthasarathy; Kulkarni, Bhakti S.; Pal, Sourav (Journal of Molecular Structure, 2009)
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(M)r(nZ)(c)(M) and for X atom is C(X)r(nZ)(c)(X). The ``axle'' size, DMX, is usually the ordinary (similar to 4a(H)/3 where a(H) is the Bohr radius of the hydrogen atom) or elongated (similar to 2a(H)) bond length of the hydrogen molecule. The ``hub'' and ``axle'' sizes could be characterized ``charge-transfer'' (C(M) = pi(2/3) = 2.144; C(X) = pi(4/3)/2 = 2.300 and D(MX) = 4a(H)/3) or ``neutral'' (CM 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 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 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 Bin, out being related inversely to the Slater orbital exponent. (C) 2009 Elsevier B.V. All rights reserved.
Keywords: B3LYP; Bond length; Bond-stretch isomer; DFT; Diatomic molecule