All atoms

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

The total interaction between two slabs of infinite extent and depth can be obtained by a summation over all atom-atom interactions if pairwise additivity of forces can be assumed. While definitely not exact for a condensed phase, this conventional approach is quite useful for many purposes [1,3]. This summation, expressed as an integral, has been done by de Boer [8] using the simple dispersion formula, Eq. VI-15, and following the nomenclature in Eq. VI-19 ... 

Note that the van der Waals forces tliat hold a physisorbed molecule to a surface exist for all atoms and molecules interacting with a surface. The physisorption energy is usually insignificant if the particle is attached to the surface by a much stronger chemisorption bond, as discussed below. Often, however, just before a molecule fonus a strong chemical bond to a surface, it exists in a physisorbed precursor state for a short period of time, as discussed below in section AL7.3.3. 

In this section, we concentrate on the relationship between diffraction pattern and surface lattice [5], In direct analogy with the tln-ee-dimensional bulk case, the surface lattice is defined by two vectors a and b parallel to the surface (defined already above), subtended by an angle y a and b together specify one unit cell, as illustrated in figure B1.21.4. Withm that unit cell atoms are arranged according to a basis, which is the list of atomic coordinates within drat unit cell we need not know these positions for the purposes of this discussion. Note that this unit cell can be viewed as being infinitely deep in the third dimension (perpendicular to the surface), so as to include all atoms below the surface to arbitrary depth. 

In the inner loops of MD and MC programs, we consider an atom and loop over all atoms j to calculate the... 

Burnham C J, Li J C, Xantheas S S and Leslie M 1999 The parametrization of a Thole-type all-atom polarizable water model from first prinoiples and its applioation to the study of water olusters (n = 2-21) and the phonon speotrum of ioe Ih J. Chem. Phys. 110 4566-81... 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

In special cases (as in colloidal solutions) some particles can be considered as essential and other particles as irrelevant , but in most cases the essential space will itself consist of collective degrees of freedom. A reaction coordinate for a chemical reaction is an example where not a particle, but some function of the distance between atoms is considered. In a simulation of the permeability of a lipid bilayer membrane for water [132] the reaction coordinate was taken as the distance, in the direction perpendicular to the bilayer, between the center of mass of a water molecule and the center of mass of the rest of the system. In proteins (see below) a few collective degrees of freedom involving all atoms of the molecule, describe almost all the... 

To facilitate conformational transitions in the before-mentioned adenylate kinase, Elamrani and co-workers scaled all atomic masses by a large factor thus allowing the use of a high effective simulation temperature of 2000K ([Elamrani et al. 1996]). To prevent protein unfolding, elements of secondary structure had to be constrained. 

In order to solve the classical equations of motion numerically, and, thus, to t)btain the motion of all atoms the forces acting on every atom have to be computed at each integration step. The forces are derived from an energy function which defines the molecular model [1, 2, 3]. Besides other important contributions (which we shall not discuss here) this function contains the Coulomb sum... 

Preparation of a Brookhaven Protein Data Bank (PDB)-formatted [10] file containing the coordinates and appropriate names of all atoms, including all polar and aromatic hydrogens. 

Levitt Warshel [17, 18] were the first to show that reduced representations may work they used Ca atoms and virtual atoms at side chain centroids. OOBATAKE Crippen [24] simplified further by only considering the Ca atoms. This is snfficient since there are reasonably reliable methods (Holm Sander [11, 12]) that compute a full atom geometry from the geometry of the Ca atoms. (All atom representations are used as well, but limited to the prediction of tiny systems such as enkephalin.)... 

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

Among the main theoretical methods of investigation of the dynamic properties of macromolecules are molecular dynamics (MD) simulations and harmonic analysis. MD simulation is a technique in which the classical equation of motion for all atoms of a molecule is integrated over a finite period of time. Harmonic analysis is a direct way of analyzing vibrational motions. Harmonicity of the potential function is a basic assumption in the normal mode approximation used in harmonic analysis. This is known to be inadequate in the case of biological macromolecules, such as proteins, because anharmonic effects, which MD has shown to be important in protein motion, are neglected [1, 2, 3]. 

The treatment of conjugated systems in terms of electron systems that extend smoothly over all atoms allows the treatment of a variety of structural phenomena, as may be explained with a spedes that shows hindered rotation and with the nitro group. 

To obtain an effective algorithm for substructure searching the factorial degree of the brute force algorithm has to be drastically deaeased. In the next sections we discuss several approaches where combination leads to a much more effective and apphcable approach for substructure searching. In the process of searching the isomorphism between Gq and a substructure of Gx, the partial mappings Gq —> Gj can be used as well. In these cases, not all atoms from Gq are mapped and, for those which are not, the array value Mj is set to 0. 

The temperature T of a system is related to the mean kinetic energy of all atoms N via Eq. (36), where kg is the Boltzmann constant and the average of the squared velocities of atom i. 

Figure 7-14. All-atom and united-atom representation of the amino acid isoleucine. In this example, 13 atoms, which are able to form explicit non-bonding interactions, are reduced to only four pseudo-atoms,...

Figure 10.3-16. Graphical representation of the chemical structure of the reactants and products of a chemical reaction a) as a 2D image b) with structure diagrams showing all atoms and bonds of the reactants and products to indicate how this information is stored in a connection table.

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. 

Temperature also determines step size. An acceptable time step for room temperature simulations is about 0..5-1 fs for All Atom system s or for sim Illation s that do not con strain hydrogen atoms. For United Atom systems or systems containing only heavy atoms, you can use steps of 1-2 fs. 

An esliniaie of the hybridization state of an aioin in a molecule can be obtained from the group ol ihc periodic table that the atom resides in (which describes the number of valence elecironsi and the connectivity (coordination of the atom ). The IlyperChem default sch em e uses ih is estiin ate to assign a h ybridi/ation slate to all atom s from th e set (n ii 11, s, sp, sp, sp2-- and sp The special... 

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