Electron-Density Distributions in Hydride Molecules. The Ammonia Molecule

Abstract

An electron-density distribution is determined for the ammonia molecule in its equilibrium configuration by requiring the distribution to exert forces on the nuclei equal and opposite to the nuclear forces of repulsion. The density distribution so obtained is compared with those determined by SCF calculations. All of the density functions are tested by comparing the calculated and observed values for the following molecular properties: (i) the forces on the nuclei, (ii) the dipole moment, (iii) the electric-field gradient at the nitrogen nucleus, (iv) the diamagnetic susceptibility, and (v) the diamagnetic contribution to the nuclear shielding constant.

Quantum chemical study of the umbrella inversion of the ammonia molecule

“…However, the glimpses of the symmetric or asymmetric distribution of charge density within the skeleton of the molecule may be obtained by measurement or theoretical calculation of dipole moment. It is already mentioned that Bader and Jones [9] concluded from a theoretical calculation that the reason for the asymmetry of charge distribution in ammonia, hence the existence of the dipole moment, is due to the hybridization of s and p orbitals of the N atom. Coulson [18] established that the magnitude of dipole moment of a molecule containing a lone pair orbital is directly proportional to the extent of the s character of the s-p hybrid accommodating the lone pair electron.…”

“…A good number of self-consistent field (SCF) molecular orbitals (MO) theoretical calculations with Slater-type orbitals (STOs) as well as SCF basis sets on the electronic structure, dipole moment, ionization potential, dissociation energy, and barrier height of ammonia molecule have been reported [3 -8]. Bader and Jones [9] computed electron density distribution in ammonia within the framework of the Hellmann-Feynman electrostatic theorem and concluded that the large resultant force on the N and H nuclei and asymmetry of charge distribution in the molecule stem from the large amount of sp hybridization. Hybridization is in reality a process of charge density reorganization within an atom by blending the necessary atomic orbitals (AOs) in its chemical response to other atoms just prior to the event of formation of bonds with them.…”

“…Coulson [18] established that the magnitude of dipole moment of a molecule containing a lone pair orbital is directly proportional to the extent of the s character of the s-p hybrid accommodating the lone pair electron. A rationale of dipole moment variation of ammonia as a function of conformational evolution in terms of the suggestions of Bader and Jones [9] and Coulson [18] is attempted.…”

Unraveling reaction mechanisms by means of Quantum Chemical Topology Analysis

“…Its prominence derives from the Hohenberg-Kohn theorem (HKT), [41] which has shown the existence of a functional relation between the ground-state electron distribution and the ground-state wave function of electronic systems. However, in 1963, a year before the historical discovery of the foundations of modern DFT, Bader and Jones wrote: [42] "The manner in which the electron density is disposed in a molecule has not received the attention its importance would seem to merit." Unlike the energy of a molecular system which requires a knowledge of the second-order density matrix for its evaluation, [43] many of the observable properties of a molecule are determined in whole or in part by the simple 3D electron density distribution.…”

A constrained Roothaan–Hartree–Fock method

“…[12]. The "zeroeth order" RHF equations are solved for two values of A where the difference h between them E, and E, are the eigenvalues, and ( U U~K K ) and ( U K~U K ) are electron repulsion and exchange integrals.…”