Atom truncation

This is similar to the simple atom-atom truncation except that dipolar groups will never be split by the cutoff distance. There is still the problem of discontinuities, but these are less extreme than in the case of atom-atom truncations. In cases where water is explicitly included, this approach exhibits the curious phenomena of hot water and cold protein if the entire system is coupled to a heatbath. This is because the more mobile atoms (the water) are subjected to more discontinuities which makes them hotter than the less mobile atoms (the protein) (Levitt, M., Weizmann Institute, personal communication, 1986.). It should be noted that this is one of the most commonly used methods of truncation for simulations where CHARMM is not used. For the group-group truncation, these calculations are in progress and will be reported elsewhere. For this type of truncation, both methods where the list is updated on... 

Fig. 1.28. (a) Electron density of the methyl cation in the plane of the atoms (truncated at C) (b) gradient vector field Vp(r) of the electron density distribution terminating at H (Ijj), C (If-) the bond path and critical point (11) and the zero flux surfaces (111) partitioning the ion into C and H atoms. From E. Kraka and D. Cremer, in Theoretical Models of Chemical Bonding, Part 2, Z. B. Maksic, ed., Springer Verlag, Berlin, 1990, pp. 459, 461. 

Both AMBER and CHARMM based calculations show spontaneous transitions between the A and B forms of DNA. CHARMM based calculations using both Ewald sums and atom truncation for the treatment of electrostatics show spontaneous transitions from the B form to the A form (9,7,5). Simulations with AMBER stay in the vicinity of the B form of DNA while those started in the A form shift to the B fomi (6). RNA simulations with AMBER if started in the A form stay A, however, if started in the B form stay in the B form (20). A form RNA simulations using CHARMM stay A (5) RNA simulations starting in the B form have yet to be performed with CHARMM. 

Fig. 4. Radial distribution of atoms corresponding to platinum clusters in Pt/NaY (from [150]). a Experimental distribution obtained by Fourier transform of X-ray scattering data b distribution calculated for a 40-atom truncated tetrahedron with the same symmetry and size as the supercage...

Figure 2. Distribution of interatomic distances in platinum clusters encaged in Y-zeolites. Curve a, distribution calculated for a AO-atom truncated f.c.c. tetrahedron (see Fig. 3). Curve b, experimental distribution obtained with the RED technique from X-ray scattering data. Curve c, calculated distribution for a mixture of AO-atom truncated tetrahedra and of six-atom octahedra.

The atomic structure of a surface is usually not a simple tennination of the bulk structure. A classification exists based on the relation of surface to bulk stnicture. A bulk truncated surface has a structure identical to that of the bulk. A relaxed surface has the synnnetry of the bulk stnicture but different interatomic spacings. With respect to the first and second layers, lateral relaxation refers to shifts in layer registry and vertical relaxation refers to shifts in layer spacings. A reconstructed surface has a synnnetry different from that of the bulk synnnetry. The methods of stnictural analysis will be delineated below. 

In applying minimal END to processes such as these, one finds that different initial conditions lead to different product channels. In Figure 1, we show a somewhat truncated time lapse picture of a typical trajectory that leads to abstraction. In this rendering, one of the hydrogens of NHaD" " is hidden. As an example of properties whose evolution can be depicted we display interatomic distances and atomic electronic charges. Obviously, one can similarly study the time dependence of various other properties during the reactive encounter. 

For large systems comprising 36,000 atoms FAMUSAMM performs four times faster than SAMM and as fast as a cut-off scheme with a 10 A cut-off distance while completely avoiding truncation artifacts. Here, the speed-up with respect to SAMM is essentially achieved by the multiple-time-step extrapolation of local Taylor expansions in the outer distance classes. For this system FAMUSAMM executes by a factor of 60 faster than explicit evaluation of the Coulomb sum. The subsequent Section describes, as a sample application of FAMUSAMM, the study of a ligand-receptor unbinding process. 

Of the five possible shapes, the cube/parallelepiped and the truncated octahedron have been most widely used, with some simulations in the hexagonal prism. The formulae used to translate a particle back into the central simulation box for these three shapes are given in Appendix 6.4. It may be preferable to use one of the more common periodic cells even if there are aesthetic reasons for using an alternative. This is because the expressions for calculating the images may be difficult and inefficient to implement, even though the simulation would use fewer atoms. 

The atomic symbol is one or two letters chosen to represent an element ("H" for "hydrogen," etc.). These symbols are used internationally. Typically, a symbol is the truncated name of the element or the truncated Latin name of the element. Click here for... 

The electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using principles of physics, chemists can predict how atoms will react based upon the electron configuration. They can predict properties such as stability, boiling point, and conductivity. Typically, only the outermost electron shells matter in chemistry, so we truncate the inner electron shell notation by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules. 

MM methods are defined atom by atom. Thus, having a carbon atom without all its bonds does not have a significant affect on other atoms in the system. In contrast, QM calculations use a wave function that can incorporate second atom effects. An atom with a nonfilled valence will behave differently than with the valence filled. Because of this, the researcher must consider the way in which the QM portion of the calculation is truncated. 

A few of the earliest methods did truncate the atom on the dividing line between regions. Leaving this unfilled valence is reasonable only for a few of the very approximate semiempirical methods that were used at that time. 

Example For two atoms having point charges of 0.616 and -0.504 e and a constant dielectric function, the energy curve shows a switching function turned on (Ron) at a nonbonded distance of 10 A and off (Roff) at a distance of 14 A. Compare the switched potential with the abruptly truncated potential. 

The use of QM-MD as opposed to QM-MM minimization techniques is computationally intensive and thus precluded the use of an ab initio or density functional method for the quantum region. This study was performed with an AMi Hamiltonian, and the first step of the dephosphorylation reaction was studied (see Fig. 4). Because of the important role that phosphorus has in biological systems [62], phosphatase reactions have been studied extensively [63]. From experimental data it is believed that Cys-i2 and Asp-i29 residues are involved in the first step of the dephosphorylation reaction of BPTP [64,65]. Alaliambra et al. [30] included the side chains of the phosphorylated tyrosine, Cys-i2, and Asp-i 29 in the quantum region, with link atoms used at the quantum/classical boundaries. In this study the protein was not truncated and was surrounded with a 24 A radius sphere of water molecules. Stochastic boundary methods were applied [66]. 

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