Atomic cores

Ch em uses Slater atom ic orbitals to con struct sent i-em pirical molecular orbitals. I he complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and arc not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

The use of RECP s is often the method of choice for computations on heavy atoms. There are several reasons for this The core potential replaces a large number of electrons, thus making the calculation run faster. It is the least computation-intensive way to include relativistic effects in ah initio calculations. Furthermore, there are few semiempirical or molecular mechanics methods that are reliable for heavy atoms. Core potentials were discussed further in Chapter 10. 

The total energy in an Molecular Orbital calculation is the net result of electronic kinetic energies and the interactions between all electrons and atomic cores in the system. This is the potential energy for nuclear motion in the Born-Oppenheimer approximation (see page 32). 

Many problems with MNDO involve cases where the NDO approximation electron-electron repulsion is most important. AMI is an improvement over MNDO, even though it uses the same basic approximation. It is generally the most accurate semi-empirical method in HyperChem and is the method of choice for most problems. Altering part of the theoretical framework (the function describing repulsion between atomic cores) and assigning new parameters improves the performance of AMI. It deals with hydrogen bonds properly, produces accurate predictions of activation barriers for many reactions, and predicts heats of formation of molecules with an error that is about 40 percent smaller than with MNDO. 

The XPS chemical shift, for an atomic core orbital with principal and orbital... 

Other techniques in which incident photons excite the surface to produce detected electrons are also Hsted in Table 1. X-ray photoelectron Spectroscopy (xps), which is also known as electron spectroscopy for chemical analysis (esca), is based on the use of x-rays which stimulate atomic core level electron ejection for elemental composition information. Ultraviolet photoelectron spectroscopy (ups) is similar but uses ultraviolet photons instead of x-rays to probe atomic valence level electrons. Photons are used to stimulate desorption of ions in photon stimulated ion angular distribution (psd). Inverse photoemission (ip) occurs when electrons incident on a surface result in photon emission which is then detected. 

The description of the atomic distribution in noncrystalline materials employs a distribution function, (r), which corresponds to the probability of finding another atom at a distance r from the origin atom taken as the point r = 0. In a system having an average number density p = N/V, the probability of finding another atom at a distance r from an origin atom corresponds to Pq ( ). Whereas the information given by (r), which is called the pair distribution function, is only one-dimensional, it is quantitative information on the noncrystalline systems and as such is one of the most important pieces of information in the study of noncrystalline materials. The interatomic distances cannot be smaller than the atomic core diameters, so = 0. 

The spectra of Figure 3 illustrate two further points. All the C Is peaks in Figure 3a are of equal intensity because there are an equal number of each type of C atom present. So, when comparing relative intensities of the same atomic core level to get composition data, we do not need to consider the photoionization cross section. Therefore, Figure 3c immediately reveals that there is four times as much elemental Si present as Si02 in the Si 2p spectrum. The second point is that the chemical shift range is poor compared to the widths of the peaks, especially for the solids in Figures 3b and 3c. Thus, not all chemically inequivalent atoms can be distin-... 

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

The most elementary all valence electron NDO model is that known as Ippmplete neglect of differential overlap (CNDO). Segal and Pople introduced (his in 1966. Only valence electrons are explicitly treated, the inner shells being tijicen as part of the atomic core. The ZDO approximation is applied to the WO-electron integrals, so that... 

Effective core potentials (ECP) replace the atomic core electrons in valence-only ab initio calculations, and they are often used when dealing with compounds containing elements from the second row of the periodic table and above. 

Ab initio ECPs are derived from atomic all-electron calculations, and they are then used in valence-only molecular calculations where the atomic cores are chemically inactive. We start with the atomic HF equation for valence orbital Xi whose angular momentum quantum number is 1 ... 

Rumpf, m. body (of an en ne, etc.) core (of an atom or ion) trimk, torso hull (of a ship) (Aero.) fuselage, -elektron, n. inner electron (as distinguished from an optical or valence electron), -fl che, /. (Geol.) peneplain. -wirkung, /. (atomic) core effect. Rumsprit, m. double rum. 

The Car-Parrinello simulations were performed using the MOTECC-90 computer code [13]. All considered systems consist of 64 atoms in a cubic unit cell with a length of 23.4 a.u. and periodic boundary conditions. The plane-wave cut-off was chosen to be 6 Ryd. The atomic cores were described by the pseudopotentials of Bachelet et al. [14]. 

In the same way, if we remove a positive atomic core from a piece of... 

The depth of this potential minimum will play a part similar to that of the depth of the minimum in Fig. 8a. The energy represented by the vertical arrow in Fig. 9a is the work required to detach a positive atomic core from the surface of the metallic lattice and to leave it at rest in a vacuum. No name for this quantity has come into general use. We shall denote it by Y, c, corresponding to the D of Fig. 8a. 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

Electrodes and Galvanic Cells. In connection with Fig. 9 in See. 11 we discussed the removal of a positive atomic core from a metal. The same idea may be applied to any alloy that is a metallic conductor. When, for example, some potassium has been dissolved in liquid mercury, the valence electron from each potassium atom becomes a free electron, and we may discuss the removal of a K+ core from the surface of the amalgam. The work to remove the K+ into a vacuum may be denoted by Ycr When this amalgam is in contact with a solvent, we may consider the escape of a K+ into the solvent. The work Y to remove the positive core into the solvent is much smaller than Yvac. 

This represents a violation of the number of quantum states, since a two-fold increase in terms of the atomic core seems to occur on the introduction of an additional electron. Bohr s response was to maintain adherence to the... 

The electrons within the atom are actually not quantised in parabolic coordinates, but instead, on account of the central field of the atom core, in polar co-ordinates. It would, then, not be logical to attempt to select favoured values of m and n3. Instead, we shall calculate the quantity... 

The expert is aware that the electron s history has no significance, but a learner may well expect there to be a greater attraction between an atomic core and the bonding electron that belongs to that atom (Taber, 1998). Such beliefs may seem rather bizarre for those used to thinking of chemistry in terms of fundamental concepts (such as energy and forces), but actually reflect one of the basic principles of magic that seem to commonly influence people s intuitions about the natural world (Nemeroff Rozin, 2000). Indeed the notion that a past association leaves some... 

In effect the chemist, and chemistry teacher, explains the observed chemical behaviour of matter (substances) - colour changes, precipitation from solution, characteristic flame colours, etc. - in terms of the very differenthQ miom of the quanticles that are considered to form the materials at the sub-microscopic level. Much of this involves the reconfiguration of systems of negative electrons and positively charged atomic cores (or kernels ) due to electrical interactions constrained by the allowed quantum states. 

Their ability to achieve a high chromophore density (for example, it is possible to introduce three conjugated chains about a single N-atom core in contrast to the two more normally possible with a linear macromolecule) [84]... 

High-energy radation can be imaged with a-Si H, either directly or via a converter [3], A thick film is required for direct detection, due to the weak interaction of the radiation with the material. A converter usually is a phosphor, which emits in the visible, and thin a-Si H films are needed. X-rays with an energy up to 100 keV eject the electrons from the inner atomic core levels to high levels in the conduction band. The emitted electrons create electron-hole pairs due to ionization. These pairs can be detected in the same way as in p-i-n photodiodes. 

If these structural features are not well represented by a mild redistribution of random independent constituents from an initially given prior prejudice, and arise instead from some degree of correlation between the scatterers, they cannot be expected to be satisfactorily dealt with by the method. For these reasons, substructures which scatter well beyond the experimental resolution should be left out of the subset of scatterers distributed at random. The data sets commonly collected for charge density studies do not as a rule extend beyond 0.4 A resolution, but scattering from the atomic core does extend well beyond this limit.2... 

It is therefore clear that MaxEnt redistribution of all electrons, using a uniform prior prejudice and carried out in the absence of very high-resolution diffraction measurements, cannot be expected to reproduce a physically acceptable picture of atomic cores. The reconstruction of total electron densities from limited-resolution diffraction measurements amounts to a misuse of the MaxEnt method, especially when the prior prejudice is uniform. 

When low-temperature studies are performed, the maximum resolution is imposed by data collection geometry and fall-off of the scattered intensities below the noise level, rather than by negligible high-resolution structure factor amplitudes. Use of Ag Ka radiation would for example allow measurement of diffracted intensities up to 0.35 A for amino-acid crystals below 30 K [40]. Similarly, model calculations show that noise-free structure factors computed from atomic core electrons would be still non-zero up to O.lA. 

The MaxEnt valence density for L-alanine has been calculated targeting the model structure factor phases as well as the amplitudes (the space group of the structure is acentric, Phlih). The core density has been kept fixed to a superposition of atomic core densities for those runs which used a NUP distribution m(x), the latter was computed from a superposition of atomic valence-shell monopoles. Both core and valence monopole functions are those of Clementi [47], localised by Stewart [48] a discussion of the core/valence partitioning of the density, and details about this kind of calculation, may be found elsewhere [49], The dynamic range of the L-alanine model... 

BUSTER has been run against the L-alanine noisy data the structure factor phases and amplitudes for this acentric structure were no longer fitted exactly but only within the limits imposed by the noise. As in the calculations against noise-free data, a fragment of atomic core monopoles was used the non-uniform prior prejudice was obtained from a superposition of spherical valence monopoles. For each reflexion, the likelihood function was non-zero for a set of structure factor values around this procrystal structure factor the latter acted therefore as a soft target for the MaxEnt structure factor amplitude and phase. 

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