Atomic and Molecular Properties

Many atomic and molecular properties depend on the electron density, and some depend on the gradient of the electron density evaluated at certain positions in space. 

Electronegativities, which have no units, are estimated by using combinations of atomic and molecular properties. The American chemist Linus Pauling developed one commonly used set of electronegativities. The periodic table shown in Eigure 9 7 presents these values. Modem X-ray techniques can measure the electron density distributions of chemical bonds. The distributions obtained in this way agree with those predicted from estimated electronegativities. 

Schwerdtfeger, P. (1991) Relativistic and Electron Correlation Contributions in Atomic and Molecular Properties. Benchmark Calculations on Au and Au2. Chemical Physics Letters, 183, 457 163. Neogrady, P., Kello, V., Urban, M. and Sadlej, A.J. (1997) Ionization Potentials and Electron Affinities of Cu, Ag, and Au Electron Correlation and Relativistic Effects. International Journal of Quantum Chemistry, 63, 557-565. 

The empirical law of absorbance is all well and good but what are the atomic and molecular properties that control how much electromagnetic radiation is absorbed by a specific transition ... 

The development of the method started in the mid 1920 s with the work of Thomas and Fermi [8, 9]. The aim was to formulate an electronic structure theory for the solid state, based on the properties of a homogeneous electron gas, to which we introduce a set of external potentials (i.e. the atomic nuclei). The original formulation, with later additions by Dirac [10] and Slater [11], was, however, inadequate for accurate description of atomic and molecular properties, and it was not until the ground-breaking work of Kohn and coworkers in the mid 1960 s that the theory was put in a form more suited to computational chemistry [12,... 

The significance of the electrostatic potential is not limited to reactivity. It is indeed a fundamental quantity, in terms of which such intrinsic atomic and molecular properties as energies and electronegativities can be expressed rigorously. (For detailed discussions see Politzer et al. [18-23] and March [24].) In this chap-... 

What atomic and molecular properties explain the macroscopic properties of the fabric used to make these protective gloves ... 

I tried to consistently distinguish between the quantum mechanics of atomic and molecular properties on the one hand and quantum collision theory on the other. The present discussion follows the same pattern. 

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

The latter choice insures that the values of atomic and molecular properties are of balanced magnitudes (typically of order unity on a per-atom basis). Atomic units are therefore well adapted to exhibit simple numerical and graphical relationships between molecular properties, whereas the corresponding comparisons often require strange multiplicative factors (such as those defining the meter and second) if expressed in SI units. 

The application of quantum-mechanical methods to the prediction of electronic structure has yielded much detailed information about atomic and molecular properties.13 Particularly in the past few years, the availability of high-speed computers with large storage capacities has made it possible to examine both atomic and molecular systems using an ab initio variational approach wherein no empirical parameters are employed.14 Variational calculations for molecules employ a Hamiltonian based on the nonrelativistic electrostatic nuclei-electron interaction and a wave function formed by antisymmetrizing a suitable many-electron function of spatial and spin coordinates. For most applications it is also necessary that the wave function represent a particular spin eigenstate and that it have appropriate geometric symmetry. 

A.-M. Martensson-Pendrill. In S. Wilson (ed.). Methods in Computational Chemistry, Vol.5 Atomic and Molecular Properties, pp. 99-156, Plenum Press, New York, 1992. 

The science of materials may have begun in the blacksmith s forge, but the materials of tomorrow will be formulated by understanding how the properties of matter are determined by the arrangements of its atoms and molecules. Scientists understand and invent new materials by considering the properties and interactions of individual particles and predicting how those properties translate into bulk properties. This chapter continues the important task of relating atomic and molecular properties to the structure and properties of bulk matter. 

His early work on atomic and molecular properties and dispersion energies involved the development and application of ab initio pseudostate techniques for the reliable evaluation of atomic and molecular multipolar properties and dispersion energies for small species.216 This was followed by the development and application of practical constrained dipole oscillator strength (DOSD) techniques, based on a combination of experimental and theoretical input, for the reliable evaluation (errors < 1-2%) of the dominant dipolar... 

The idea of calculating atomic and molecular properties from electron density appears to have arisen from calculations made independently by Enrico Fermi and P.A.M. Dirac in the 1920s on an ideal electron gas, work now well-known as the Fermi-Dirac statistics [19]. In independent work by Fermi [20] and Thomas [21], atoms were modelled as systems with a positive potential (the nucleus) located in a uniform (homogeneous) electron gas. This obviously unrealistic idealization, the Thomas-Fermi model [22], or with embellishments by Dirac the Thomas-Fermi-Dirac model [22], gave surprisingly good results for atoms, but failed completely for molecules it predicted all molecules to be unstable toward dissociation into their atoms (indeed, this is a theorem in Thomas-Fermi theory). 

This chapter introduces the core concepts of what is now called classical physics (mechanics, electricity, magnetism, and properties of waves). Today we think of classical physics as a special case in a more general framework which would include relativistic effects (for particles with velocities which approach the speed of light) and quantum effects, which are needed for a complete description of atomic behavior. Nonetheless, we will find that this classical perspective (with a few minor corrections) serves as an excellent starting point for understanding many atomic and molecular properties. 

In reality, molecules each occupy some space, so the empty volume of the container decreases as the concentration N/ V increases. In addition, there is generally some attraction even at distances substantially larger than the nominal diameter of the molecules, and the repulsive part is somewhat soft so that collisions are not instantaneous. The exact form of this interaction must be calculated by quantum mechanics, and it depends on a number of atomic and molecular properties as discussed in Chapter 3. For neutral, nonpolar molecules, a convenient approximate potential is the Lennard-Jones 6-12 potential, discussed in Chapter 3 Table 3.5 listed parameters for some common atoms and molecules. 

Moreover, to understand why SF6 exists as a stable compound whereas SC16 does not, we need to know something about the properties of the S, F, and Cl atoms. As another illustration, it may be asked why the P043- ion is quite stable but N043 is not. Throughout this descriptive chemistry book, reference will be made in many instances to differences in chemical behavior that are based on atomic and molecular properties. Certainly not all chemical characteristics are predictable from an understanding of atomic and molecular structure. However, structural principles are useful in so many cases (for both comprehension of facts and prediction of properties) that a study of atomic and molecular structure is essential. 

Nudear attraction integrals on one hand, and repulsion mtegrals on the other hand, are the first elements of a general integral formulation connected with atomic and molecular properties as well as with relativistic corrections. A good review of all the possible related operators involved in this family can be found in the GTO firamework within the work of Matsuoka [68a,b] and in the excellent textbook of McWeeny [72], if detailed operator information and physical signifi( ce are sought. 

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