Dynamics of bond-formation in some diatomics

Abstract

An understanding of molecular formation from the separated atoms is one of the important goals in quantum chemistry. Earlier interpretations of the bond formation are based on the spatial characteristics of the charge distribution and the electrostatic forces which they exert on the nuclei, via the Hellmann–Feynman theorem. One view of the bond formation based on the virial theorem emphasises the lowering of the potential energy due to the accumulation of density in the internuclear region as a result of electron sharing. The other view attaches importance to the lowering of the kinetic energy caused by the extension of the space of electron movement from atoms to molecules. The integrated virial kinetic energy theorem derived by Hurley shows that the kinetic energy must drop initially in the process of formation of a stable bond and greater the kinetic energy drop, the stronger is the bond formed. Thus, the behaviour of the kinetic energy provides a touchstone for the formation of a stable molecule. A general expression for the normalisation condition of the kinetic field functions is derived from the above theorem, whose satisfaction throws light on the quality of the wavefunctions. We have studied the role of the kinetic energy in the dynamics of the formation process of the stable, unstable and metastable diatomics from the separated atoms. As the accurate wavefunctions reported in the literature are very complex, we have generated the optimised, ab initio wavefunctions in terms of small configuration-interaction expansions using orbitals in elliptic coordinates. These wavefunctions satisfy not only the virial theorem but also the kinetic field normalisation condition. With these wavefunctions we have resolved the kinetic energy into its bond-parallel and bond-perpendicular components. Our analysis of H? X (¹?g?) and a states using the extended Hartree–Fock wavefunctions shows that the charge contraction and interference effects are important during the formation of a stable bond, while the unstable situation is accompanied by the orbital expansion at lower values of R (internuclear distance). The metastable ground state (¹?g?) of He?? dissociates into two He? ions. Even though the behaviour of the total kinetic energy in this case is different from that of the ground state of H?, the kinetic energy components show that the weak bonding in this state arises primarily from the interference effect and is similar to that of H?. Both the lowest and the first excited (³?g) states of He?? are weakly bonding and dissociate into He + He??. The weak bonding in these states was believed to be due to the ion-induced dipole interaction. Our analysis based on kinetic energy components clearly shows that the weak bonding in these states is preceded by charge transfer from the neutral atom to the ion followed by exciton resonance, rather than by polarisation of the 1s orbital of He by He?. A study of density difference contour maps of these states also confirms this view. We then studied the ground state and the weakly bound first excited (¹?) and the lowest (³?) states of HeH?. The ground state dissociates into He + H? and was assumed to arise from the polarisation of the He atom by H?. The behaviour of the parallel and perpendicular components of the kinetic energy shows that the bond formation is not preceded by the classical polarisation of He by H? but arises from the interference effect following the charge flow from He atom to H?. An analysis of the electron density on the nucleus also confirms this view. Both the first excited and the lowest states of HeH? dissociate into He? + H and the weak bonding in these states was thought to arise from the polarisation of H by He?. Our analysis, however, reveals that the bond formation in these states is preceded by charge transfer from the 1s orbital of H to the 2s orbital of He? rather than by polarisation of the 1s orbital of H by He?. The stronger bond in the (³?) state relative to the first excited (¹?) state is due to the greater extent of charge transfer from H to He? in the (³?) state than in the (¹?) state. The density difference contour maps of these states show unsymmetrical charge distribution in the internuclear region which arises due to charge transfer from H 1s orbital to 2s orbital of He?.