Atomic charge physical quantity

All equations given in this text appear in a very compact form, without any fundamental physical constants. We achieve this by employing the so-called system of atomic units, which is particularly adapted for working with atoms and molecules. In this system, physical quantities are expressed as multiples of fundamental constants and, if necessary, as combinations of such constants. The mass of an electron, me, the modulus of its charge, lei, Planck s constant h divided by lit, h, and 4jt 0, the permittivity of the vacuum, are all set to unity. Mass, charge, action etc. are then expressed as multiples of these constants, which can therefore be dropped from all equations. The definitions of atomic units used in this book and their relations to the corresponding SI units are summarized in Table 1-1. 

The second-order expansion given in eqn (6.96) recovers all of the physical quantities needed to describe a quantum system and determine its properties the charge density p and its gradient vector field Vp define atoms and determine many of their properties in a stationary state the current density determines the system s magnetic properties and the change in p in a time-dependent system and, finally, the stress tensor determines the local and average mechanical properties of the system. Thus, one does not need all the... 

The internal spin interaction Hamiltonian Hmt can be decomposed into spatial Tm[ ua(l) ] and spin Sm degrees of freedom Hin (t) = 2mTm[ ua(t) ]Sm. The spatial contribution, hereafter an NMR interaction rank-2 tensor T, is a stochastic function of time Tm[ ua(t) because it depends on generalized coordinates < ( ) of the system (atomic and molecular positions, electronic or ionic charge density, etc.) that are themselves stochastic variables. To clarify the role of these coordinates in the NMR features, a simple model is developed below.19,20 At least one physical quantity should distinguish the parent and the descendant phase after a phase transition. For simplicity, we suppose that the components of the interaction tensor only depend on one scalar variable u(t) whose averaged value is modified from m to m + ( at a phase transition. To take into account the time fluctuations, this variable is written as the sum of three terms, i.e. u(t) — m I I 8us(t). The last term is a stationary stochastic process such that — 0, where <.) denotes a... 

However, charges, dipoles, etc. do not correspond to real physical phenomena when assigned to atomic centers. Similarly, point-charge representations of lone pairs do not represent real physically observable quantities. With this understood, one can appreciate that atomic charges and so on can be looked upon not as physical quantities, but rather as adjustable parameters. These parameters can be fit to best reproduce certain desired quantities, either experimental or theoretical [14,19-21]. Of most relevance are those which are geared toward the electrostatic interactions of the molecule in question. 

Atomic Charges. Whereas the MEP is a well-defined, physically significant quantity that can be accurately calculated from a reasonably accurate wave function, there is no unique, well-defined answer to the question What is the charge on a particular atom in a molecule (The terms atomic charge, net atomic charge, and partial atomic charge are used synonymously.)... 

Typical chemical concepts are not as sharp as typical physical concepts. A nice example is that of atomic charge densities which were analyzed [21] in terms of factor analysis and were found to be scalar quantities (different possible definitions do not lead to the same numerical values, but these correlate satisfactorily), at variance with aromaticity [22, 23] which turned out to be a multidimensional half-ordered concept [23]. Primas [17] suggested that molecular structure is a genuine chemical concept, which has no counterpart in rigorous quantum mechanics. On the other hand, situations where molecular structures become undefined do show up in chemistry, or at least in molecular spectroscopy. Quantum phenomena apparently have a stronger tendency to survive in chemistry than in mac-... 

The dielectric polarization, or simply polarization, within dielectric materials is a vector physical quantity, denoted by P, and its module is expressed in C.m Electric polarization arises due to the existence of atomic and molecular forces and appears whenever electric charges in a material are displaced with respect to one another under the influence of an apphed external electric field strength, E. On the other hand, the electric polarization represents the total electric dipole moment contained per unit volume of the material averaged over the volume of a crystal cell lattice, V, expressed in cubic meters (m ) ... 

The atomic charges, which as we have said are often derived from the MEP, are thus often employed for two distinct, even if connected, purposes, namely the evaluation of the energy (or better, the electrostatic component of the energy) and obtaining the MEP. In a very accurate representation, it is correct to use a physically well-defined quantity for two different aims, but approximate representations could be good for one type of application and completely inadequate for the second. Apparently this is not the case for the PD atomic charges, which are often employed for both purposes. 

Prom Table 8.5 it follows that the correlation between charges calculated with different methods is similar to that for the dipole moments. However, it should be remembered that atomic charges are not physically observable quantities and they strongly depend on their definition and on the basis employed in calculations. 

The analysis of electronic wavefunctions provides an indispensable connection between the highly complex formalism of contemporary electronic structure calculations and the simple language of chemistry. The benefits of rigorous quantification of common chemical concepts extend far beyond its interpretive value. The computed atomic charges, bond orders, and other quantities facilitate systematization of experimental and theoretical data, permit rationalization of empirical observations, and elucidate chemical and physical mechanisms responsible for the observed phenomena. It is safe to predict that analysis of electronic wavefunctions will play an increasingly important role in future chemical research. 

The electrostatic potential V r) that is created in the space around a molecule by its nuclei and electrons is a well-established guide to chemical reactivity and molecular interactive behavior. " Unlike many of the other quantities used now and earlier as indices of reactivity, e.g., atomic charges, the electrostatic potential is a real physical property, one that can be determined experimentally by diffraction methods as well as computationally. However, V r) is most commonly obtained computationally. With the recent advances in computer technology, it is currently being applied to a variety of significant chemical systems. 

When considering the thermodynamics of nucleation and the mechanism of the elementary acts of single ions attachment and detachment to and from a growing cluster or a crystal surface, it proves convenient to work not with molar but with molecular quantities. For that reason the molecular unit to be used in Chapters 1 and 2 ofthis book will be not a mol but uparticle - atom, ion or molecule - and aU physical quantities like chemical and electrochemical potential, electric charge etc. will be referred to this unit. In what follows we consider the conditions that characterize the thermod5Uiamic equilibrium in chemical and electrochemical systems. 

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