Properties from Atomic Structures

Statistical Mechanics Predicts Macroscopic Properties from Atomic Structures 

To predict the properties of materials from the forces on the atoms that comprise them, you need to know the energy ladders. Energy ladders can be derived from spectroscopy or quantum mechanics. Here we describe some of the quantum mechanics that can predict the properties of ideal gases and simple solids. This will be the foundation for chemical reaction equilibria and kinetics in Chapters 13 and 19. Our discussion of quantmn mechanics is limited. We just sketch the basic ideas with the particle-in-a-box model of translational freedom, the harmonic oscillator model for vibrations, and the rigid rotor model for rotations. 

Evidence for the quantization of energies comes from atomic spectroscopy. Spectroscopy measures the frequency v of electromagnetic radiation that is absorbed by an atom, a molecule, or a material. Absorption of radiation by matter leads to an increase in its energy by an amount As = hv, where h = 6.626176 X 10 Js is Planck s constant. This change. As, is the difference from one energy level to another on an encrg ladder. 

Atoms and simple molecules absorb electromagnetic radiation only at certain discrete frequencies, rather than as continuous functions of frequency. For example, Eigure 11.1 shows the infrared absorption spectrum of hydrogen bromide. Discrete absorption frequencies imply discrete energy spacings. This is the basis for quantum mechanics. 

The basis for predicting quantum mechanical energy levels is the Schrodinger equation, which can be expressed in compact form  

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He even proposed the existence of polyvalent atoms producing "sponge or net like" molecular mass in 1878. Towards the end of his career, he advanced the hypothesis that natural organic substances-those most closely associated with life, proteins, starch, and cellulose-may consist of very long chains, and derive their special properties from this structure. 

In effect, in the new variables the Schrodinger equation can be written in a form in which the constants of nature do not appear. All the unusual bond angles and properties of atomic structure that life exploits in non-relativistic atoms will arise in identical fashion in a world with new values of a and nie. They come from the ubiquitous geometrical factors of order Itt that detemiine the eigenvalues of the Schrodinger equation. The double helices of its DNA molecules will differ only in size its water molecules will display the same remarkable properties that flow from its special bond angles but will differ solely in overall scale. 

What are the principal differences in physical and chemical properties between any one metal from Group I and any one metal from Group IV and any one transition metal How far can you explain these differences in terms of their different atomic structures ... 

We denote the topological distance between atoms i and j (i.e., the number of bonds for the shortest path in the structure diagram) dy, and the properties for atoms i and j are referred to as pi and pj, respectively. The value of the autocorrelation function a d) for a certain topological distance d results from summation over all products of a property p of atoms i and j having the required distance d. 

Structure determines properties and the properties of atoms depend on atomic struc ture All of an element s protons are m its nucleus but the element s electrons are dis tributed among orbitals of varying energy and distance from the nucleus More than any thing else we look at its electron configuration when we wish to understand how an element behaves The next section illustrates this with a brief review of ionic bonding... 

Multiple Chiral Centers. The number of stereoisomers increases rapidly with an increase in the number of chiral centers in a molecule. A molecule possessing two chiral atoms should have four optical isomers, that is, four structures consisting of two pairs of enantiomers. However, if a compound has two chiral centers but both centers have the same four substituents attached, the total number of isomers is three rather than four. One isomer of such a compound is not chiral because it is identical with its mirror image it has an internal mirror plane. This is an example of a diaster-eomer. The achiral structure is denoted as a meso compound. Diastereomers have different physical and chemical properties from the optically active enantiomers. Recognition of a plane of symmetry is usually the easiest way to detect a meso compound. The stereoisomers of tartaric acid are examples of compounds with multiple chiral centers (see Fig. 1.14), and one of its isomers is a meso compound. 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

In NMR the magnetic-spin properties of atomic nuclei within a molecule are used to obtain a list of distance constraints between those atoms in the molecule, from which a three-dimensional structure of the protein molecule can be obtained. The method does not require protein crystals and can be used on protein molecules in concentrated solutions. It is, however, restricted in its use to small protein molecules. 

There are a number of properties of molecules that are additive to a reasonable approximation, i.e. the value of such a property of a given molecule is an approximate sum of the values of the properties of either the atoms or bonds present. It has been shown that the dielectric constant is related to some additive properties and it is thus possible to make some estimate of dielectric properties from consideration of molecular structure. 

Computing the vibrational frequencies of molecules resulting from interatomic motion within the molecule. Frequencies depend on the second derivative of the energy with respect to atomic structure, and frequency calculations may also predict other properties which depend on second derivatives. Frequency calculations are not possible or practical for all computational chemistry methods. 

From a structural point-of-view the bulk metallic state, that is, fee lattice (with varying densities of defects such as twins and stacking faults) is generally established in gold nanoparticles of about 10 nm diameter and upwards. However, such particles still display many unusual physical properties, primarily as the result of their small size. Shrinking the size of gold particles has an important effect it increases both the relative proportion of surface atoms and of atoms of even lower coordination number, such as edge atoms [49] and these atoms in turn are relatively mobile and reactive. 

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