A.B. Sannigrahi

Three-center bond index

Abstract The bond index for a multi-center bond has been defined from a generalized SCF density matrix. Using this definition, we have calculated the three-center bond indices ( I ABC ) for a number of molecules. It has been observed that I ABC is positive and appreciably high (⩾ 0.1) only for those three-center bonds which can be obtained from localized MO calculations. In other cases, I ABC is either negative or very close to zero.

Ab initio theoretical study of three-centre bonding on the basis of bond index

Abstract Various methods of derivation of a multi-centre bond index and its physical significance are briefly discussed. The usefulness of the bond index model for the study of three-centre (3c) bonding is illustrated by taking a number of examples chosen from earlier calculations. The origin of the sign of 3c bond indices ( I ABC ) predicted for three-centre two-electron (3c-2e) and three-centre four-electron (3c-4e) bonds is investigated using simple models with different bonding topologies. Some examples are given highlighting the role of I ABC in elucidating the nature of bonding in controversial molecules. The bond index and the effective pair population models are compared and shown to be equivalent for an RHF wave function and even-centre bond indices. It is concluded that despite some inherent limitations such as the basis set sensitivity the bond index model provides a quite satisfactory description of 3c bonding.

Ab initio SCF study of maximum hardness and maximum molecular valency principles

Ab initio SCF calculations using the 6-31G** basis set have been performed on a number of molecules in order to test the validity of maximum hardness and maximum molecular valency principles. It has been observed that the former is valid under a variety of bonding situations, while the latter breaks down in the case of highly ionic molecules.

Effect of a general nonsingular transformation of the AO basis set on MO calculations of valency

Abstract The effect of a general nonsingular transformation of the AO basis set on MO calculations of valency has been studied, taking as examples a number of molecules with varying degrees of ionicity and using a variety of basis sets. The nonsingular transformation used is of the form Φ=χ S − n , where {χ a } is the nonorthogonal AO basis set with overlap matrix S , and n can take any finite value. It has been observed that n =0.5, which corresponds to Lowdins symmetric orthogonalization, generally predicts maximum valencies and minimum charge separation.

Comparison of atomic charges, valencies and bond orders in some hydrogen-bonded complexes calculated from Mulliken and Löwdin SCF density matrices

Abstract Atomic charges, valencies and bond orders in six H-bonded systems, (H2O)2, (HF)2 and HnFn+1− (n = 1 to 4) have been calculated using 4-31G, 6-31G* and 6-31G** (only in the case of (HF)2 and HF2−) basis sets and employing definitions based on Mulliken and Lowdin SCF density matrices. The definitions based on the former and the 6-31G* basis set are found to give results in conformity with the classical valence theory. The covalent bonding is highly exaggerated by the alternative definitions based on the Lowdin density matrix. The H-bond formation is found to be accompanied by decrease in total valency, and the valency and atomic charge of bridging hydrogen. A clear distinction between normal and strong H-bonding can be made on the basis of bond order and overlap population of the intermolecular HX (X = F or O) bonds and the amount of charge transferred from the proton acceptor to the donor molecule.

Some remarks on multi-center bond index

Abstract The basic mathematical structure and the inherent limitations of the bond index model are critically examined. It is then compared with a similar model where the bonding indices are defined in terms of multi-center effective pair populations derived from pair densities. The two models, although they differ in the basic approach, are shown to be equivalent for bond indices of even rank deduced from an RHF wavefunction.

Ab initio SCF study of the nature of bonding in Si2H2 and Si2H4

Abstract Ab initio SCF calculations using several basis sets have been performed on a number of structural isomers of Si 2 H 2 and Si 2 H 4 , and their nature of bonding has been studied on the basis of bond index, valency and localized molecular orbitals (LMOs). Excepting the transition states, the stability of the Si 2 H 2 isomers is found to increase with decreasing molecular valency and increasing inert-pair effect in Si. In the case of Si 2 H 4 also, the most stable structure is associated with the least molecular valency. Analysis of the LMOs reveals that Si exhibits rather complicated hybridization.

On the nature of multicenter bonding in simple atomic clusters

Abstract The electronic structure of simple atomic clusters (C3 and B 3 + ) has been analyzed using multicenter bond indices and orbital localization. It has been shown that unusually high values of 3-center XXX bond indices in these molecules are due to multiple 3-center bond.

Hardness and bond index profiles of hydrogen-bonded complexes with single-minimum and double-minimum potentials

Abstract The dissociation reaction, H 3 N · HF → H 3 N + HF and the proton-transfer reaction (F-H · Cl) − → (F· H-Cl) − have been studied at the HF//6-31G ∗∗ level in order to understand the progress of these reactions in terms of global and local reactivity parameters. Both the reactions are found to obey the maximum hardness principle. The potential energy curve for the proton transfer reaction passes through a transition state wherein the hardness is at a minimum. In this reaction bond index profiles of the bonds being broken and formed intersect at the point corresponding to the maximum in the potential energy curve. Condensed Fukui functions have been calculated at different stages of dissociation of H 3 N · HF. Variation of reactivity of a particular site towards electrophilic, nucleophilic or radical attack is properly reflected in these values.

Theoretical study of multi-centre bonding using a delocalised MO approach

Abstract The nature of the bonding in about thirty electron-deficient molecules has been studied on the basis of two-centre and multi-centre (mainly three-centre) bond indices and atomic valencies calculated from ab initio SCF density matrices using 4-31G (or 6-31G) and 6-31G∗ (or 6-31G∗∗) basis sets. For comparison, the density matrices corresponding to non-orthogonal and symmetrically orthogonalised basis functions have been employed. The nature of the bonding deduced on the basis of bond indices and valencies has been confirmed by localised MO calculations. It has been observed that a three-centre bond is invariably associated with a positive and significantly high value (⩾0.1) of the bond index. For a four-centre bonding interaction the corresponding bond index is generally positive, but rather small.