Pseudoatom potential

Another application of such a combined approach is presented by the results our calculations on the electronic structure of the PdCl dianion in Table 4. The calculations were performed both selfconsistently and nonselfconsistently with the superimposed atomic electronic densities and potentials [54]. In the pseudopotential calculations, all four chlorine atoms were considered as pseudoatoms. 

As an example of a pseudopotential simulation of boundary conditions for clusters representing some ionic compounds, let us consider the MgO case [79], which has been considered previously [80], [81] within a bare cluster model. The MgO crystal (the rock-salt lattice) was simulated by a cluster MggOg (see Fig. 3) placed in several embeddings comprised of a different number of pseudoatoms possessing the effective potentials and placed at the lattice sites. 

Recently, a new kind of analytic pseudo-potentials, directly in a fully nonlocal form, has been proposed [129,160]. Coefficients are fitted to minimize penalty functions, like atomic properties, to ensure that these properties are well reproduced for the pseudoatom. It has been further generalized for use in the context of QM/MM situations [161] or to include semi-empirically the long-range van der Waals attraction [161,162]. 

The radial deformation of the valence density is accounted for by the expansion-contraction variables (k and k ). The ED parameters P, Pim , k, and k are optimized, along with conventional crystallographic variables (Ra and Ua for each atom), in an LS refinement against a set of measured structure factor amplitudes. The use of individual atomic coordinate systems provides a convenient way to constrain multipole populations according to chemical and local symmetries. Superposition of pseudoatoms (15) yields an efficient and relatively simple analytic representation of the molecular and crystalline ED. Density-related properties, such as electric moments electrostatic potential and energy, can readily be obtained from the pseudoatomic properties [53]. 

The simulation by Bareman et al. involved 90 chains, each of which was made up of 20 identical pseudoatoms meant to represent methylene groups and the terminal methyl. Changes in chain conformations, including bond-bending and chain torsional motions, were allowed, with potentials known to provide good representations of short-chain alkanes. Interchain interactions were computed from pairwise additive Lennard-Jones 12-6 potentials. A 9-3 potential, which is appropriate for the interaction of a L-J particle above the surface of a bulk medium, was taken for the interaction of each methylene with the surface, with a well depth 5 times deeper than that for the CHj—CH2 interaction. The simulations were carried out with periodic boundary conditions for three fixed areas, 21,26, and 35 A per chain. 

Harris and Rice have specifically attempted to model PDA in their simulations. The amphiphiles are made up of pseudoatoms representing one methyl, 13 methylenes, and a COOH head, each of which has appropriate potential parameters and mass. Like Bareman et al. they accounted for intramolecular interactions with bending and torsional potentials appropriate for hydrocarbons. A Lennard-Jones 12-6 potential was used for intermolecular interactions and for interactions between pseudoatoms on the same chain separated by more than three bonds, with parameters that... 

In LDA calculations, pseudopotentials (or effective core potentials) are almost always used to increase the efficiency of calculations, even for calculations involving hydrogen. This allows smoother wavefunctions, which in turn reduces the number of basis functions. It has been found that transferability (the ability of a pseudoatom to mimic a full-core atom) is governed by norm conservation [39], and pseudopotentials are constructed so that the pseudo-orbitals match the full-core orbitals outside the core. 

Volkov, A., Koritsanszky, T, and Coppens, P. [2004]. Combination of the exact potential and multipole methods [EP/MM] for evaluation of intermolecular electrostatic interaction enei ies with pseudoatom representation of molecular electron densities, Chem. Phys. Lett 391, pp. 170-175, dol 10.1016/j.cplett.2004.04.097. von Lilienfeld, 0. A., Tavernelli, 1., Rothlisberger, U., and Sebastian , D. [2004]. Optimization of effective atom centered potentials for London dispersion forces in density functional theory, Phys. Rev. Lett 93,15, p. 153004. 

The NAST [16, 34] model represents each nucleotide by one pseudoatom at the C3 atom of the ribose group. NAST utilizes MD simulations and a force field parameterized from solved rRNA structures. NAST relies upon information from an accurate secondary structure and can also include experimental constraints. These constraints are modeled by a harmonic energy term. The bonded energy terms of distance, angle, and dihedral are further modeled by a harmonic potential, parameterized according to a Boltzmann inversion. Non-bonded interactions are modeled by a Lennard-Jones potential with a hard sphere radii of 5 A. Due to the low-resolution representation of one pseudoatom per nt, the conversion from the CG model to the all-atom model is complex and may produce steric overlaps. In order to overcome this difficulty, Jonikas et al. developed a program C2A [35] which is able to insert and minimize the all atom structure. 

Bernauer et al. [18] introduced a knowledge-based model that doesn t employ a conventional force field. Rather, interatomic distances are constrained to stay within prescribed bounds and follow a certain position distribution. Using these distance-based potentials, there is no need to explicitly account for electrostatics or other terms, as they are already captured. Bernauer et al. have two model resolutions, a CG model and an all atom. The CG model consists of five pseudoatoms one at the phosphate, C4 of the ribose, and one on the C2, C4, and C6 atoms of the nucleobase. The knowledge-based potentials required the use of a set of presolved structures the authors chose these structures based on stringent accuracy requirements. The authors score their potentials by implementing an REMD protocol. 

The Siesta (Spanish Initiative for Electronic Simulations with Thousands of Atoms) method [383,384,400] achieves linear scaling by the exphcit use of locahzed Wannier-like functions and numerical pseudoatomic orbitals confined by a spherical infinite-potential wall [401]. As the restriction of the Siesta method we mention the difficulty of the all-electron calculations and use of only LDA/GGA exchange-correlation functionals. 

The separable embedding potential (8.31) was apphed to model the single chemical bond between the atom A of the cluster and the atom B of the cluster environment [488]. To simulate the effect of the cluster environment the atom B is replaced by a pseudoatom Bps at the same position as the actual atom B. The influence of the pseudoatom on the cluster is described by the potential that was assumed to have the following form ... 

The pseudoatoms are introduced to terminate the wave functions of the quantum cluster in such a way that the structure and forces on the quantum cluster are as close as possible to those of the same subsystem within an allquantum system. The pseudoatoms are therefore placed along a straight line between the quantum oxygen and the classical silicon, at a fixed distance from the oxygen [d = 1.82 Aq (Bohr)]. Also, they do not carry any kinetic energy, so as not to exert any direct influence on the dynamics of the system. Lastly, to obtain an interface as smooth as possible, the same classical potential is used for modeling both the interactions between classical and quantum ions and the interactions between classical and classical ions. 

In the transparent interface method, the forces on each atom are derived from the gradient of the total potential energy in Eq. [71]. However, the constraint forces acting on quantum atoms at the boundary, due to the constaints imposed on the pseudoatoms, are neglected in this approach, leading to an approximation of the Hamiltonian equations that provides correct forces and dynamics (within the limit of a classical force field) but violates energy conservation. 

The Hamiltonian integrals and the overlap integrals are calculated with atom-centered localized atomic orbitals under a two-center approximation. These atom-centered orbitals are constructed by solving modified KS equations of spherical pseudoatoms with confinement potentials ... 

---