Molecular geometry from molecular tensegrity: a case study of gas-phase MX2 compounds - Ganguly, Parthasarathy (Current Science, 2006)
We define a tensegrity factor, t(00)(+/-), for X-M-X linkages of gas-phase MXn compounds (X is an atom of an insulating element) that is a measure of the matching of `ideal' 1,2-(single-bonded) M-X distance, d(MX)(00), to the `ideal' (non-bonded) 1,3-X–-X distances, d(MX)(00). The actually observed 1,3-distance, d(XX) is given (within 1% error) by 2CR(X)/F-S, where F-S (= 2-1.41(00)(+/-)) is shown to be an ab initio quantity with no adjustable parameter, no dependence on actual M-X distance or bond order and with 2CR(X) depending only on whether M is an atom of an insulating element (2CR(X) =d(XX)(00)) or whether M is metallic (2CR(X) = 1.1d(XX)(00)). This is illustrated for gas-phase MX2 compounds.
Keywords: gas-phase; molecular geometry; MX2 compounds; tensegrity

Molecular tensegrity: predicting 1,3-X–-X distance in gas-phase MXn (n <= 4) compounds from atomic sizes - Ganguly, Parthasarathy (Current Science, 2006)
This article extends an earlier definition(1) and use of molecular tensegrity for obtaining quantitatively the 1,3-non-bonded distances in gas-phase MX2 compounds to nearly 160 gas-phase MXn (n <= 4) inorganic compounds (including those of transition metal elements), once a transferable `core' atomic size is specified. The simple principles behind this methodology (involving only linear equations), its quantitative character, its transparency, its portability and its generality account very simply for molecular geometry in such compounds without requiring earlier theoretical methodologies. We also establish clear distinction in the prescription for obtaining the 1,3-distance when M is an atom of a metallic or insulating element.
Keywords: Atomic size; gas phase; molecular tensegrity; non-bonded distance

Van der waals and polar intermolecular contact distances: quantifying supramolecular synthons - Ganguly, Parthasarathy; Desiraju, Gautam R. (Chemistry-an Asian Journal, 2008)
Crystal structures are viewed as being determined by ranges and constraints on interatomic contact distances between neighboring molecules. These distances are considered to arise from environment-dependent atomic sizes, that is, larger sizes for isotropic, van der Waals type contacts and smaller sizes for more-polar, possibly ionic contacts. Although the idea of different, or anisotropic, radii for atoms is not new, we developed a method of obtaining atomic sizes that is based on a theoretical framework. Using different atomic sizes for the same atom in different environments, we were able to rationalize some structural observations and anomalies. For example, benzene with the Pbca structure may be described in terms of two types of C center dot center dot center dot H interactions: a longer contact largely of the van der Waals type, and a shorter, structure-determining type (C delta-center dot center dot center dot H delta+), which we term ``n-polar''. Our approach is illustrated with three examples: 1) the equivalence in crystal packing of fluorobenzene, benzonitrile, pyridine N-oxide, and pyridine/HF 1:1 molecular complex, all of which take the not-so-common tetragonal P4(1)2(1)2 space group and are practically isomorphous; 2) the similarity of the Pa3 acetylene and Pbca benzene crystal structures; and 3) the equivalence between an increase in pressure and an increase in the ``n-polar'' contacts in Pbca benzene; in other words, the equivalence between hydrostatic pressure and chemical pressure. In the context of crystal engineering, we describe a method whereby the topological information conveyed in a supramolecular synthon is recast in a more quantitative manner. A particular synthon, and in turn the crystal structure to which it leads, is viable within small ranges of distances of its constituent atoms, and these distances are determined by chemical factors.
Keywords: atomic radii; benzene crystal; engineering; supramolecular chemistry; van der Waals radii

Atomic sizes from atomic interactions - Ganguly, Parthasarathy (Journal of Molecular Structure, 2009)
We obtain an atomic size, r(nZ)(c), in the presence of an interaction (represented by an electron-hole pair, e(-)h(+) as in vacuum polarization techniques) as a sum of contribution, r(nv), from the interaction of n(val) valence sand p-electrons and a contribution r(RG) from inner filled shell electrons with rare-gas configuration. The method is applicable to all elements for a given electron configuration that is usually available simply from the position of the elements in the periodic table. The sizes thus obtained are close to other ``core sizes'' obtained in the literature. The transition metal elements are treated as group II elements. This method gives sizes for the actinide and trans-actinide elements without requiring relativistic corrections. The importance of these sizes in interpreting interatomic distances in terms of electronic configuration is illustrated for actinide elements. (C) 2009 Elsevier B.V. All rights reserved.
Keywords: Atomic size; Ionic radii; Vacuum polarization

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