United atom approximation

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. 

As input to the UHBD program we need the PDB coordinate file for acetic acid, which has the format (assuming the united atom approximation) ... 

The properties of the diatomic hydrides MH can be derived from the density distribution of the united-atom approximation (see e. g. (79, 80) for the potential-energy-curves) of the neutral united atom (M-f 1). Platt (28, 98) used this approximation to calculate the frequencies via the force constants of these diatomic hydrides through purely electrostatic arguments. To make the hydride from the united atom one proton is removed from the nucleus without distortion of the charge cloud of the united atom (i. e. the removal of the proton is considered to be a small perturbation). If ro is the radius at which the effective nuclear charge is unity, the proton should be moved to ro. i- e- to the radius beyond which lie a total number of 1.00 electrons. If the proton is replaced outside ro, the excess electrons will attract it, and it will be repelled if it is situated inside the nucleus. This is just the situation for the vibrating motion of a proton attached to another atom through a stable chemical bond a small displacement (-i-iir) from ro will subject the proton to an added force... 

Lynden-Bell and coworkers examined the validity of this approximation by simulating systems with fully explicit methyl groups (i.e. aU hydrogens) as well as united atom models. They found that the united atom approximation leads to a higher density in both the liquid and crystalline states. As a consequence, the dynamics of the united atom system are somewhat slower than for the case of the explicit atom model. 

Net atomic charges of about -0.2 at each H were calculated with an ab initio MO-SCF method [2], with the semiempirical CNDO/2 method [11], and with another semiempirical method using localized bond orbitals for Cl [12]. A lower value came from an EH calculation [3]. A radial electron density distribution was calculated within the united-atom approximation [10]. Two different dipole moments were obtained with an MO-SCF calculation (yielding also quadrupole and octupole moments) [2] and with the electron propagator theory (EPT) [13]. 

The geometrical structure of gaseous PH2 in its X Ai ground state appears to be similar to that of ground-state PH2 (with an internuclear distance of r=1.42 A and an interbond angle of a = 92° see p. 72). This was inferred from a sharp increase of the photodetachment cross section at threshold, measured by ion cyclotron resonance [2, 3] and from the predominance of the (0, 0, 0)<-(0, 0, 0) transition in the PH2, X Bi PH, X A photoelectron spectrum [4]. r=1.34 0.05 A and a = 92 5 were taken from the isoelectronic H2S molecule (and used to calculate the thermodynamic functions of PH, see p. 109) [5]. r and a have also been theoretically calculated by several ab initio MO methods, i.e., at an MP2 [6, 7], a CEPA (coupled electron pair approximation) [8], and an HF level [9 to 15]. r was also obtained from a united-atom approximation [16] a was also calculated by a semiempirical (CNDO/2) method [17] and estimated by extended Huckel calculations [18]. 

X and x were also calculated for different origins by a variational method yielding the susceptibilities of localized P-H bonds [16] and for the origin at the center of mass by an ab initio sum-over-states (SOS) configuration interaction method [17]. x =-40.93 was obtained from a united-atom approximation, and x was estimated to be 16.35 (or 7.70) [18]. 

An orthogonal set of approximations involves the structural representation of the polymer. As an example. Fig. 1 shows four different ways in which the structure of polyisoprene might be represented in an MD or BD simulation. The top structure (a) is an atomic representation of the polyisoprene repeat unit. The second structure (b) results from coUapsing all the hydrogens onto their parent carbons (the united atom approximation). The third structure (c) further collapses the three carbon centers in the fairly rigid double bond unit into a single pseudo-atom. Any of these three structures might be used in a simulation of local polymer dynamics. The fourth structure (d) shows a bead-... 

Molecular dynamics studies of penetrant diffusion have so far been performed for polyethylene, polyisobutylene and polydimethylsiloxane. Calculated diffusion coefficients have not been in particularly good agreement with experiment. In the case of polyethylene, modeled using the united atom approximation, diffusion coefficients were much higher than expected and the activation energies too small although much better results have been obtained using PE IV. Reliable comparisons with experimental data are made difficult by uncertainties as to the true diffusion coefficients... 

Fig. 13 Lipid-packing defects in atomistic and CG simulations. Left Molecular models of lipids using a united-atom representation (top) or a CG representation (bottom). Polar atoms/beads, grey hydrophobic atoms/beads, yellow/orange. Middle Top view of lipid bilayers using a surface representation in AA ad CG simulations. Right Top view of the lipid bilayers in the middle panel plus detected lipid-packing defects (blue, see Vanni etal. for additional details on the methodology to identify them) for the two bilayers. Moving from a united-atom (approximately 50 atoms per lipid) to a CG representation (approximately 15 beads per lipid) does not prevent a correct quantification of this microscopic membrane property.

The united atom approximation reduces a group of atoms, for example CH3, CH2, to a unique atom considered as an effective and single center of interaction. This procedure has the advantage of reducing the time of computation. 

Levinthal (1966) and Katz and Levinthal (1972) described protein molecules in a united atom approximation and used a molecular modeling system in conjunction with an interactive computer graphic program. More recently (Honig et al, 1976), the same group developed a procedure based... 

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