Unphysical atom

The dummy junction atom or link atom approach introduces so-called link atoms to satisfy the valence of the atoms on the QM side of the QM/MM interface. Usually this atom is a hydrogen, but other atom types have also been used, e.g. halogens such as fluorine or chlorine. The link atom method can be used with both the Warshel-type QM/MM methods and ONIOM methods. The link atom method has been criticised because it introduces extra unphysical atoms to the system, which come with associated extra degrees of freedom. Another problem is that a C-H bond is clearly not chemically exactly equivalent to a C-C bond. Despite these problems, the simplicity of the link atom method means that it is used widely in the QM/MM modelling of proteins and other biological molecules. ... 

Conceptually the hybrid orbital approach is to be preferred over the link atom method as no unphysical atoms are introduced into the system. Undoubtedly the HO method will become more popular but, as we shall see in section 4, link atoms have been the most widely used when studying macromolecular systems, in large part because they are simpler to implement. 

Similarly, in studies of lamellar interfaces the calculations using the central-force potentials predict correctly the order of energies for different interfaces but their ratios cannot be determined since the energy of the ordered twin is unphysically low, similarly as that of the SISF. Notwithstcinding, the situation is more complex in the case of interfaces. It has been demonstrated that the atomic structure of an ordered twin with APB type displacement is not predicted correctly in the framework of central-forces and that it is the formation of strong Ti-Ti covalent bonds across the interface which dominates the structure. This character of bonding in TiAl is likely to be even more important in more complex interfaces and it cannot be excluded that it affects directly dislocation cores. 

In these equations, (24)-(26), orthonormal orbits are denoted by indices Vs. Equation (26) means that the orbiting electron interacting with itself, that is self-interaction, exists. This is unphysical. In order to remove this unphysical term, the SIC is taken into account by the following procedure. The SIC for the LDA in the density functional method has been treated for free atoms and insulators [16], and found an important role in determining the energy levels of electrons. However, no established formula is known to take into account the SIC for semiconductors and metals. As a way of trial, in the present calculation, the atomic SIC potential is introduced for each angular momentum in a way similar to the SIC potential for atoms [17] as follows ... 

One way to solve the problem of unphysically short atomic distances is to project onto the Rpm subspace only those grid points included in a selected strip (gray area), with width of a (cos a + sin a) in the A per subspace. The slope of RPai shown in Fig. 1 is 0.618..., an irrational number related to the golden mean [( /5 + l)/2 = 1.618...]. As a result, the projected ID structure contains two segments (denoted as L and S), and their distribution follows a ID quasiperiodic Fibonacci sequence [2] (c.f. Table 1). From another viewpoint, the ID quasiperiodic structure on the par subspace can be conversely decomposed into periodic components (square lattice) in a (higher) 2D space. The same strip/projection scheme holds for icosahedral QCs, which are truly 3D objects but apparently need a more complex and abstract 6D... 

V — —This is clearly unphysical except in the united atom limit. However, generally it does not affect the result of interest to the chemists. 

Here, is the distance between atoms i andj, C(/ is a dispersion coefficient for atoms i andj, which can be calculated directly from tabulated properties of the individual atoms, and /dampF y) is a damping function to avoid unphysical behavior of the dispersion term for small distances. The only empirical parameter in this expression is S, a scaling factor that is applied uniformly to all pairs of atoms. In applications of DFT-D, this scaling factor has been estimated separately for each functional of interest by optimizing its value with respect to collections of molecular complexes in which dispersion interactions are important. There are no fundamental barriers to applying the ideas of DFT-D within plane-wave DFT calculations. In the work by Neumann and Perrin mentioned above, they showed that adding dispersion corrections to forces... 

This rescaling reflects the idea that any increase of electronic charge at a center, as a consequence of an enrichment of the basis functions describing it, is unphysical if, lacking equipoise, atoms bonded to it suffer from poorer basis set descriptions. The parameter introduced in Eq. (8.4) is there to correct this imbalance if we follow Mayer s claim [172,173] that Mulliken s half-and-half partitioning of overlap terms between the concerned atoms should not be tampered with. It is felt that the way depends on the basis sets used for describing atoms k and I deserves attention as part of an effort aimed at letting X.rtsi approach Mulliken s limit A = 1 as closely as possible. 

The existence of many ionic structures in MCVB wave functions has often been criticized by some workers as being unphysical. This has been the case particularly when a covalent bond between like atoms is being represented. Nevertheless, we have seen in Chapter 2 that ionic structures contribute to electron delocalization in the H2 molecule and would be expected to do likewise in all cases. Later in this chapter we will see that they can also be interpreted as contributions from ionic states of the constituent atoms. When the bond is between unlike atoms, it is to be expected that ionic stmctures in the wave function will also contribute to various electric moments, the dipole moment being the simplest. The amounts of these ionic structures in the wave functions will be determined by a sort of balancing act in the variation principle between the diagonal effects of the ionic state energies and the off-diagonal effect of the delocalization. 

We notice that this wave function contains terms where both electrons are located at the same atom. These terms are clearly unphysical at large separations, since they correspond to the dissociation to H+ + H", which has an energy around 320 kcal/mol above H + H. It is only the middle terms in the wave function that describe correctly the dissociated products. 

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