Interatomic force

VAN DER WAALS FORCES. Interatomic or intermolecular forces of attraction due to the interaction between fluctuating dipole moments associated with molecules not possessing permanent dipole moments. These dipoles result from momentary dissymmetry in the positive and negative charges of the atom or molecule, and on neighboring atoms or molecules. These dipoles tend to align in antiparallel direction and thus result in a net attractive force. This force varies inversely as the seventh power of the distance between ions. 

This approach is the most useful for engineering purposes since it expresses fracture events in terms of equations containing measurable parameters such as stress, strain and linear dimensions. It treats a body as a mechanical continuum rather than an assembly of atoms or molecules. However, our discussion can begin with the atomic assembly as the following argument will show. If a solid is subjected to a uniform tensile stress, its interatomic bonds will deform until the forces of atomic cohesion balance the applied forces. Interatomic potential energies have the form shown in Fig. 1 and consequently the interatomic force, whidi is the differential of energy with respect to linear separation, must pass throt a maximum value at the point of inflection, P in Fig. 1. 

Cutting force Interatomic forces F = tF i = E- jsei yV/ Plastic deformation/ friction... 

Forces, interatomic, from infrared and Raman studies, 9 Free internal rotation, 202. ... 

Van der Waals Forces Interatomic and intermolecular forces of electrostatic origin. These forces arise due to die small instantaneous dipole moments of the atoms. They are much weaker than valence-bond forces and inversely proportional to the seventh power of the distance between the particles (atoms or molecules). 

Pethica J B 1986 Comment on interatomic forces in scanning tunnelling microscopy giant corrugations of the graphite surface Phys. Rev. Lett. 57 3235... 

The dynamics of ion surface scattering at energies exceeding several hundred electronvolts can be described by a series of binary collision approximations (BCAs) in which only the interaction of one energetic particle with a solid atom is considered at a time [25]. This model is reasonable because the interaction time for the collision is short compared witii the period of phonon frequencies in solids, and the interaction distance is shorter tlian the interatomic distances in solids. The BCA simplifies the many-body interactions between a projectile and solid atoms to a series of two-body collisions of the projectile and individual solid atoms. This can be described with results from the well known two-body central force problem [26]. 

Fig. 4, top). In particular we asked, what interatomic interactions cause the experimentally observed unbinding forces. 

Tbis tecbnic ne is available only for the MM-i- force field. As is true for the conjugate gradient methods, yon should noi use this algorithm when the initial interatomic forces are very large (meaning, the molecular structure is far from a inmiimim). 

Note You can superimpose harmonic restraining forces to interatomic distances, angles, or dihedrals that you have set up as named selections. Yon can also restrain atoms to points in space. See Using Geometric Restraints" on page SI and "Restraints" on page 105. 

Brenner D W, O A Shendreova and D A Areshkin 1998. Quantum-Based Analytic Interatomic Force and Materials Simulation. In Lipkowitz K B and D B Boyd (Editors). Reviews in Computationc Chemistry Volume 12. New York, VCH Publishers, pp. 207-239. 

There are forces other than bond stretching forces acting within a typical polyatomic molecule. They include bending forces and interatomic repulsions. Each force adds a dimension to the space. Although the concept of a surface in a many-dimensional space is rather abstract, its application is simple. Each dimension has a potential energy equation that can be solved easily and rapidly by computer. The sum of potential energies from all sources within the molecule is the potential energy of the molecule relative to some arbitrary reference point. A... 

The steepest descent method is a first order minimizer. It uses the first derivative of the potential energy with respect to the Cartesian coordinates. The method moves down the steepest slope of the interatomic forces on the potential energy surface. The descent is accomplished by adding an increment to the coordinates in the direction of the negative gradient of the potential energy, or the force. 

Assuming that the interatomic force term F(t) varies linearly with time, the equations above can be rewritten in a form which produces more accurate simulations ... 

Recommended values for the force constant are 7.0 kcal/mol M for an interatomic distance, 12.5 kcal/mol degree for an angle, and 16.0 kcal/mol degree for a dihedral angle. Use the recommended values and then, if the internal coordinate is not sufficiently restrained, try a larger force constant. 

The primary requirement for carrying out MD simulations is a suitable interatomic potential for the description of forces acting between atoms in the cascade. A general discussion on MD can be found (47) and detailed summaries of the use of MD in ion—soHd interactions are also available (43,48). 

To obtain a metallurgical bond between two metals, the atoms of each metal must be brought sufficiently close so that their normal forces of interatomic attraction produce a bond. The surfaces of metals and alloys must not be covered with films of oxides, nitrides, or adsorbed gases. When such films are present, metal surfaces do not bond satisfactorily (see Metal surface treatments). 

The forces which hold atoms together (the interatomic bonds) which act like little springs, linking one atom to the next in the solid state (Fig. 4.1). 

As we showed in Chapter 6 (on the modulus), the slope of the interatomic force-distance curve at the equilibrium separation is proportional to Young s modulus E. Interatomic forces typically drop off to negligible values at a distance of separaHon of the atom centres of 2rg. The maximum in the force-distance curve is typically reached at 1.25ro separation, and if the stress applied to the material is sufficient to exceed this maximum force per bond, fracture is bound to occur. We will denote the stress at which this bond rupture takes place by d, the ideal strength a material cannot be stronger than this. From Fig. 9.1... 

Since empirical force fields do not accurately estimate the true interatomic forces, it is difficult a priori to say how accurate the fast multipole approximation to the exact Coulomb potential and forces (exact in terms of the sum over partial charges) should be. Probably a good rule is to make sure that at each atom the approximate electrostatic force is within a few percent relative error of the true electrostatic force, obtained by explicitly summing over all atom pairs, i.e., IF — FJ < 0.05 F , for all atoms i, where F is the... 

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

It may be that in years to come, interatomic potentials can be estimated experimentally by the use of the atomic force microscope (Section 6.2.3). A first step in this direction has been taken by Jarvis et al. (1996), who used a force feedback loop in an AFM to prevent sudden springback when the probing silicon tip approaches the silicon specimen. The authors claim that their method means that force-distance spectroscopy of specific sites is possible - mechanical characterisation of the potentials of specific chemical bonds . 

Chemicals exist as gases, liquids or solids. Solids have definite shapes and volume and are held together by strong intermolecular and interatomic forces. For many substances, these forces are strong enough to maintain the atoms in definite ordered arrays, called crystals. Solids with little or no crystal structure are termed amorphous. 

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