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Separable Embedding Potential

As was noted in the preceding section the use of atomic pseudopotentials (or effective core potentials-ECPs) considerably simplifies the quantum-mechanical description of polyatomic systems (molecules and crystals) as the much more localized and chemically inert core electrons are simulated by ECP introduction. The choice of the norm [Pg.304]

Recently introduced new separable potentials [488,490] have several kinds of ap -plications 1) when some special region of a covalently bonded sohd or very large molecule is modeled by a modest-sized cluster, each dangling bond at the cluster surface can be saturated in a way that exactly reproduces the bond in the complete system 2) a similar approach can be used at the matching surface in an embedding scheme for calculations on the same type of systems 3) application to atomic effective core potentials where the new potential operator avoids the possibility of ghost states that sometimes plague the widely used pseudopotentials. [Pg.305]

The important property of the introduced embedding potential is its separability. Let the nonlocal operator V(r) depend on the space variable r only and be represented by the integral operator V  [Pg.305]

As an example of separable potentials we mention the semilocal ECP, see (8.14), which have a form similar to (8.24), but where = Vi r) are functions of the radial variable. These semilocal potentials are separable only in the angular variables (in which these potentials are nonlocal) as the separability is the property of nonlocal potentials. [Pg.306]

Separable nonlocal ECPs were extensively studied [474,491-494]. The nonlocal separable potentials application is complicated by the problem of ghost states [495] i.e. extra bound states with levels, under the reference atomic eigenenergy. For semilocal ECPs, used in modern computer LCAO codes, this problem does not occur [493], for the embedding potential this problem has to be taken into acconnt. [Pg.306]


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 ... [Pg.307]

Approximations to the exact (in the Hartre Fock approximation) separable embedding potential were introduced in [490] that enable one to incorporate this potential into existing molecular calculation packages. The test calculations on the (CH3)20 molecule were performed that showed good accuracy of the potential. [Pg.309]

The electrostatic free energy of a macromolecule embedded in a membrane in the presence of a membrane potential V can be expressed as the sum of three separate terms involving the capacitance C of the system, the reaction field Orffr), and the membrane potential field p(r) [73],... [Pg.143]

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. [Pg.663]

Center for Healthcare Technologies at Lawrence Livermore National Laboratory in Livermore, potentially capable to measure pH at or near the stroke site29. The probe is the distal end of a 125 pm fibre tapered up to a diameter of 50 pm. A fluorescent pH-indicator, seminaphthorhodamine-1-carboxylate, is embedded inside a silica sol-gel matrix which is fixed to the fibre tip. Excitation of the dye takes place at 533 nm and the emission in correspondence of the acid (580 nm) and basic (640 nm) bands are separately detected. The use of this ratiometric technique obviates worrying about source fluctuations, which have the same effects on the two detected signals. The pH sensor developed was first characterised in the laboratory, where it showed fast response time (of the order of tens of seconds) and an accuracy of 0.05 pH units, well below the limit of detection necessary for this clinical application (0.1 pH units). The pH sensor was also tested in vivo on rats, by placing the pH sensor in the brain of a Spraque-Dawley rat at a depth of approximately 5 mm30. [Pg.425]

It may come as a surprise to some that two commensurate surfaces withstand finite shear forces even if they are separated by a fluid.31 But one has to keep in mind that breaking translational invariance automatically induces a potential of mean force T. From the symmetry breaking, commensurate walls can be pinned even by an ideal gas embedded between them.32 The reason is that T scales linearly with the area of contact. In the thermodynamic limit, the energy barrier for the slider to move by one lattice constant becomes infinitely high so that the motion cannot be thermally activated, and hence, static friction becomes finite. No such argument applies when the surfaces do not share a common period. [Pg.78]

Consider now two point charges q and -q which are separated by a distance d (Fig. 5.4). This configuration of charges is called a dipole with dipole moment p = pez, where p = qd. If the charges are embedded in a uniform unbounded medium with permittivity em, the potential of the dipole at any point P is... [Pg.138]

In any case, the position and width of the peaks are not affected by the value of the frequency or by the geometry of the electrode (see embedded graphs in Fig. 7.31) since the potential and the time-geometrical dependences of the response can be separated. On the other hand, the peak height is affected in the usual way, such that the higher the frequency, the higher the peak. [Pg.515]

In all the systems considered above the photosensitizer was embedded in the membrane symmetrically, i.e. identical S molecules are located near both the inner and the outer surfaces of the vesicle membranes. Of great interest would also be to create asymmetric membranes providing a specially organized gradient of the redox potential across the lipid bilayer. Asymmetry of a membrane can be realized, e.g. if one locates the molecules with different redox potentials within the membrane near its inner and outer interfaces. An asymmetric membrane containing the components required for photochemical separation of charges at the lipid // water... [Pg.19]

This approach can be used to model non-bonded interactions in molecular mechanics instead of using empirical potentials. The rule of thumb, equation (6.6) predicts effective strain-free zero-order bond lengths. As no interaction is possible at separations larger than 2 x rc, the maximum d0(obs) for C- C is 3.70 A, and hence do = 3.70 — 0.28/4 cs 3.6A d0(C---H) 2.75 — 0.19/5 = 2.55A. The separation between non-bonded H atoms depends on the atom to which they are linked - the H ionization sphere is completely embedded within that of the larger atom. As a first approximation d0(H- H)= do(C- H) is assumed. [Pg.228]


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