Quantum mechanical theory, atomic charge

Qm QM RECON Mean absolute atomic charge Quantum mechanics An algorithm for the rapid reconstruction of molecular charge densities and charge density-based electronic properties of molecules, using atomic charge density fragments precomputed from ab initio wave functions. The method is based on Bader s quantum theory of atoms in molecules. 

Despite the fact that Bohr s stopping power theory is useful for heavy charged particles such as fission fragments, Rutherford s collision cross section on which it is based is not accurate unless both the incident particle velocity and that of the ejected electron are much greater than that of the atomic electrons. The quantum mechanical theory of Bethe, with energy and momentum transfers as kinematic variables, is based on the first Born approximation and certain other approximations [1,2]. This theory also requires high incident velocity. At relatively moderate velocities certain modifications, shell corrections, can be made to extend the validity of the approximation. Other corrections for relativistic effects and polarization screening (density effects) are easily made. Nevertheless, the Bethe-Born approximation... 

In the past decade, many new techniques have been developed and applied to the study of interfaces. While earlier measurements involved only macroscopic characteristics of the interface (e.g., surface charge, surface tension, and overall potential drop), new spectroscopic techniques have opened a window to the microstructure of the interface, and insight at the atomic level in this important region is now possible. Parallel to these discoveries and supported by them, more realistic theoretical models of the interface have been developed that combine quantum mechanical theories of metal surfaces and the statistical mechanics of solutions. 

The negative hydrogen ion (H ), or hydrogen with an extra electron attached, is a glaring example of the necessity of quantum mechanical theory to describe atomic behavior. Classical physics, considering only electrostatic forces among the three charged particles, predicts that this ion should not exist in a stable, bound state. Yet H has been observed experimentally for decades. 

In more elaborate discussions, closer consideration of the definition of bond orders is needed, along the lines, for example, of the quantum-mechanical theories which have been referred to earlier and which yield information about the average density of electronic charge on the various atoms of a molecule (p. 255). 

The Concept of Atomic Charge in the Quantum Mechanical Theory of Atoms in Molecules... 

Soon after it was established that the discharge stage has a finite rate, efforts began to be made to develop a quantum-mechanical theory of an elementary act. The first important step in this direction was taken by Gurney[6]. He clearly formulated the basic idea that the transfer of an electron from a metal to an ion in solution (or in the reverse direction) can be accomplished only when the energy levels of the initial and the final states turn out to be virtually identical (for example, an electron on the Fermi level in a metal + a singly-charged ion in solution is the initial state and an electron + an ion, i.e. the atom in solution is the final state). 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

The units we use in daily life, such as kilogram (or pound) and meter (or inch) are tailored to the human scale. In the world of quantum mechanics, however, these units would lead to inconvenient numbers. For example, the mass of the electron is 9.1095 X J0 31 kg and the radius of the first circular orbit of the hydrogen atom in Bohr s theory, the Bohr radius, is 5.2918 X 10 11 m. Atomic units, usually abbreviated as au, are introduced to eliminate the need to work with these awkward numbers, which result from the arbitrary units of our macroscopic world. The atomic unit of length is equal to the length of the Bohr radius, that is, 5.2918 X 10 n m, and is called the bohr. Thus 1 bohr = 5.2918 X 10"11 m. The atomic unit of mass is the rest mass of the electron, and the atomic unit of charge is the charge of an electron. Atomic units for these and some other quantities and their values in SI units are summarized in the accompanying table. 

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