Atomization method, 189 core

Within the computational scheme described in the course of this work, the available information about the atomic substructure (core+valence) can be taken into account explicitly. In the simplest possible calculation, a fragment of atomic cores is used, and a MaxEnt distribution for valence electrons is computed by modulation of a uniform prior prejudice. As we have shown in the noise-free calculations on l-alanine described in Section 3.1.1, the method will yield a better representation of bonding and non-bonding valence charge concentration regions, but bias will still be present because of Fourier truncation ripples and aliasing errors ... 

A complete description of droplet generator and of several atomization methods appears in a previous paper [8]. Simple air-stripping or piezoelectric drop generators were employed. The core liquid typically consisted of a polyanion solution, while the receiving bath contained a polycation(s) solution and, in many instances, a divalent cation. 

The calculation of PAES intensities largely reduces to the calculation core annihilation probabilities for positrons in the surface state [11]. This follows from the fact that almost all of the core hole excitations of the outer cores relax via Auger emission and that almost all of the positrons incident at low energies become trapped in a surface state before annihilation. First-principles calculations of the positron states and positron annihilation characteristics at metal and semiconductor surfaces are based on a treatment of a positron as a single charged particle trapped in a "correlation well" in the proximity of surface atoms. The calculations were performed within a modified superimposed-atom method using the corrugated-mirror model of Nieminen and Puska [12]. 

The synthesis of large clusters such as [A Ris]3- (Chapters 2 and 3) proceeds by A1 atom cluster-core build up. Cluster-core growth is terminated at some point by external ligands. The method of Schnockel is a variation of metal-atom vapor-deposition techniques and relies on (a) the reversibility of the equilibrium between the liquid metal, e.g., Al, and gaseous metal halide, e.g., AICI3, with gaseous subhalide, e.g., A1C1 (b) the shift in equilibrium position with temperature and (c) competitive rates at similar temperatures of subhalide disproportionation to metal... 

Author" Ref. Atoms Method Type Core Valence Basis Set... 

C oniparing ihc corc-core repulsion ol lhe above two ec nations with those in the MNDO method, it can be seen that the only dil -ference is in the last term. The extra terms in the AMI core-core repulsion deline spherical Ciaiissian Tun ctioii s — the a. h, and c are adjustable parameters. AMI has between two and I onr Gaussian full ctiori s per atom, ... 

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

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. 

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