United atoms, calculations

June et al. (85) presented united-atom calculations for butane and for hexane in silicalite, whereby the bond and dihedral angles of the alkanes were allowed to vary. In addition, the calculation of hexane took account of an additional intramolecular Lennard-Jones potential for nonbonded atoms more than three bonds apart (which prevents the alkane crossing over itself). The interaction parameters for the alkane molecules were taken from Ryckaert and Bellmans (3), and those governing the interaction of the alkanes with the zeolite from a previous study of the low-occupancy sorption of alkanes in silicalite (87). Variable loadings of alkanes were considered from 1 to 8 molecules per unit cell were considered, and calculations were allowed to run for 500 ps for diffusion at 300 K. 

United Atom force fieldsare used often for biological polymers. In th esc m oleciiles, a reduced ii nm ber of explicit h ydrogen s can have a notable effect on the speed of the calculation. Both the BlOn and OPLS force fields are United Atom force fields. AMBER con tain s both aU nited and an All Atom force field. 

The OPLS force field is described in twtt papers, one discussing parameters for proteins W. L. Jorgensen and J. Tirado-Rives,/. Amer. (. hem. Soc., 110, 1557 (iy8K) and on e discii ssin g param eters for n iicleotide bases [J. Pranata, S. Wiersch ke, and W. L. Jorgen sen. , /.. Amer. Chem. Soc.. 117, 281(1 ( 1991)1. The force field uses the united atom concept ftir many, but not all. hydrttgens attached to carbons to allow faster calculation s on macromolecular systems. The amino and nucleic acid residue templates in HyperChein automatically switch to a united atom representation where appropriate when th e OPLS option is selected. 

Caution If you are new to computational chemistry, do not use United Atoms for AMBER calculations. This HyperChem option is available for researchers who want to alter atom types and parameters for this force field. 

AMBER was first developed as a united atom force field [S. J. Weiner et al., J. Am. Chem. Soc., 106, 765 (1984)] and later extended to include an all atom version [S. J. Weiner et al., J. Comp. Chem., 7, 230 (1986)]. HyperChem allows the user to switch back and forth between the united atom and all atom force fields as well as to mix the two force fields within the same molecule. Since the force field was developed for macromolecules, there are few atom types and parameters for small organic systems or inorganic systems, and most calculations on such systems with the AMBER force field will fail from lack of parameters. 

In order to determine electrode corrosion quantitatively, Adzic et al. [43], used the following approach. The H content of the charged electrode, expressed as the number of H atoms, n, per formula unit, was calculated from Qimx by the Faraday equation, Eq.(12),... 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

Perhaps the most widely discussed source of uncertainty in electrostatic calculations is the location of the solute/solvent boundary. The most common treatment is to place the boundary at the surface of a set of overlapping spheres centered at the nuclei. But what radius should one use for those spheres One common answer is van der Waals radii times I.2.46 In our own quantum mechanical solvation models,12 27 and those of several others59, 69, these radii are empirical parameters. Recently Barone et al.70 have modified the PCM to use charge-dependent united-atom spheres instead of all-atom spheres, and they optimized the electrostatic radii for a... 

The next two steps in the procedure of Leonard and Ashman are the conversion of the diagonal elements from atomic units into force field units and calculation of scaling factors for bond lengths and angles. The calculated force constants had to be scaled down by approximately 25% and 70% to yield force constants comparable in numerical size with those included in MM2. Neither force constants nor scaling factors can be incorporated directly into a different force field. A modification of the described procedure that meets the requirements of CVFF was developed. Fragments with known force field parameters were chosen. After a full geometry optimization (HF/6-31G ) second derivatives and vibrational frequencies were calculated. The force... 

The fourth term is a polarisation term. Here E(z) = di/z/dz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of erA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value... 

Negative of the Energies (Atomic Units) of Some Atoms Calculated with the Potential Wx Equation 7.34... 

Figure 7 Comparison of melt structure factor and single-chain structure factor for PB (upper panel, calculated as scattering from the united atoms only) and a bead-spring melt (lower panel, in Lennard-Jones units).

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