Electronic charge distribution molecules

For a molecule with a continuous electron charge distribution and nuclear point charges, the expression becomes ... 

In the 1920s it was found that electrons do not behave like macroscopic objects that are governed by Newton s laws of motion rather, they obey the laws of quantum mechanics. The application of these laws to atoms and molecules gave rise to orbital-based models of chemical bonding. In Chapter 3 we discuss some of the basic ideas of quantum mechanics, particularly the Pauli principle, the Heisenberg uncertainty principle, and the concept of electronic charge distribution, and we give a brief review of orbital-based models and modem ab initio calculations based on them. 

For gas-phase molecules the assumption of electronic adiabaticity leads to the usual Bom-Oppenheimer approximation, in which the electronic wave function is optimized for fixed nuclei. For solutes, the situation is more complicated because there are two types of heavy-body motion, the solute nuclear coordinates, which are treated mechanically, and the solvent, which is treated statistically. The SCRF procedures correspond to optimizing the electronic wave function in the presence of fixed solute nuclei and for a statistical distribution of solvent coordinates, which in turn are in equilibrium with the average electronic structure. The treatment of the solvent as a dielectric material by the laws of classical electrostatics and the treatment of the electronic charge distribution of the solute by the square of its wave function correctly embodies the result of... 

The theory of molecular structure based on the topology of molecular charge distribution, developed by Bader and co-workers (83MI2 85ACR9), enables certain features to be revealed that are characteristic of the systems with aromatic cyclic electron delocalization. To describe the structure of a molecule, it is necessary to determine the number and kind of critical points in its electronic charge distribution, i.e., the points where for the gradient vector of the charge density the condition Vp = 0 is fulfilled. 

This book is about electronic charge distributions, chemical bonds, bond energy additivity in organic molecules, and the description of their relevant thermochemical properties, such as the energy of atomization, the enthalpy of formation, and the like, using computer-friendly methods. 

Another approach to providing atomic charges is to fit the value of some property which has been calculated based on the exact wavefunction with that obtained from representation of the electronic charge distribution in terms of a collection of atom-centered charges. In practice, the property that has received the most attention is the electrostatic potential, 8p. This represents the energy of interaction of a unit positive charge at some point in space, p, with the nuclei and the electrons of a molecule (see Chapter 4). 

For hetercnuclear diatomic molecules, the atomic energy-level mismatch does not vanish, so that <5 0. Hence, the electronic charge distribution... 

These Au nanoparticles, protected by a monolayer of thiolated ligands, display interesting properties, such as single-electron charging and molecule-like HOMO-LUMO energy gaps, and can be used in optical and chemical sensing [70, 71]. Their physicochemical properties are closely related to their size and size distribution. Therefore, the ability to synthesize nano particles in a size-controlled... 

Polarizability is the relative tendency of a charge distribution o(r), that is, the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, F, which may be caused by the presence of a nearby ion or dipole. The interaction of an electronic charge distribution with a uniform electric field gives an energy contribution,... 

The electronic charge distribution of H2 is inversion symmetric and, therefore, H2 is necessarily non-polar. The HD molecule possesses a nearly identical electronic cloud. Nevertheless, HD does feature a (weak) permanent dipole moment. It is of a non-adiabatic nature and arises from the fact that the zero-point motion of the proton takes place with a greater amplitude than that of the deuteron. As a consequence, the side of the proton is slightly more positively charged than that of the deuteron if the HD molecule is in the vibrational ground state. 

If we limit our description to the initial step of the whole process, i.e. the vertical electronic transition (absorption and emission), we can safely assume a Franck-Condon like response of the solvent, exactly as for the solute molecule the nuclear motions inside and among the solvent molecules will not be able to follow immediately the fast changes in the solute electronic charge distribution and thus the corresponding part of the... 

When a polar molecule and a non-polar molecule approach each other, the electric field of the polar molecule distorts the electron charge distribution of the non-polar molecule and produces an induced dipole moment within it. The interaction of the permanent and induced dipoles then results in an attractive force. This induction contribution to the electrostatic energy is always present when two polar molecules interact with each other. 

The fuzzy membership function defined above reflects the actual electronic charge distribution of functional group within the given molecule X, without directly involving any other density contributions from other functional groups of the molecule. 

Dispersion interactions arise because there are rapid fluctuations in electronic charge distributions. Even a nonpolar molecule A has an instantaneous dipole moment /W< n8tant) that induces a dipole moment in molecule B that interacts with the instantaneous dipole to produce the instantaneous energy ... 

The most characteristic feature, however, will be observed in the structure of the vibrational satellites. The change of the electronic charge distribution due to an electronic transition is experienced by the whole molecule, in particular of both the deuterated and the protonated ligands. Thus, the emission spectrum will exhibit ligand satellites of both protonated and deuterated ligands. It is very important that these satellites belong to the same electronic 0-0 transition. 

Methods to Reproduce the Molecular Electrostatic Potential (MEP). The electrostatic potential surrounding the molecule that is created by the nuclear and electronic charge distribution of the molecule is a dominant feature in molecular recognition. Williams reviews (42) methods to calculate charge models to accurately represent the MEP as calculated by ab initio methods by use of large basis sets. The choice between models (monopole, dipole, quadrapole, bond dipole, etc.. Fig. 3.12) depends on the accuracy with which one desires to reproduce the MEP. This desire has to be balanced by the increased complexity of the model and its resulting computational costs when implemented in molecular mechanics. 

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