Long-range interatomic force

W. Byers Brown and D. M. Whisnant. Long range interatomic forces. Chem. Phys. Lett., 7 239, 1970. 

In the description of the technique, the particular aspects that make it different of other schemes aimed at the computation of IFCs in solids or molecules [1-9] will be emphasized. These aspects are connected to the central use of a variational principle in order to find the changes in the wavefunctions due to atomic displacements, on one hand, and to find the change in electronic energy due to the changes in wavefunctions, on the other hand. Some technical details, related with the presence of relatively long-ranged interatomic force constants, caused by... 

The van der Waals forces are present universally, regardless of the species and polarity of the interacting atoms or molecules. The forces can be attractive or repulsive, but mostly attractive and long-range, effective from a distance longer than 10 nm down to the equilibrium interatomic distance (about 0.2 nm). 

An exact determination of the relative values of P for the BPTI and villin simulations is not possible, because some algorithmic developments reduce computational costs (particularly methods that allow one to increase the size of the time step and to efficiently treat long-range interactions), while others increase the costs (e.g., more detailed force fields and appropriate boundary conditions). But we can place reasonable bounds on the historical growth rate of P by using r=l and r=2 as lower and upper limits on the costs of calculating interatomic interactions. 

The effects of pressure on the properties of perovskite fes and rls are manifestations of the influence of pressure on the soft fe mode frequency of the host lattice [14,24], This frequency is determined by a delicate balance between short-range and long-range forces, and these forces exhibit markedly different dependences on interatomic separation, or pressure. Specifically, pressure increases the soft-mode frequency at constant temperature, which reduces the polarizability of the host lattice, thereby reducing Ac. The result is a shift of the transition temperature, Tc (or Tm), to lower temperatures and a suppression of the e (T) response in the high temperature paraelectric phase [14,24],... 

Interatomic Force Constants (IFCs) are the proportionality coefficients between the displacements of atoms from their equilibrium positions and the forces they induce on other atoms (or themselves). Their knowledge allows to build vibrational eigenfrequencies and eigenvectors of solids. This paper describes IFCs for different solids (SiC>2-quartz, SiC>2-stishovite, BaTiC>3, Si) obtained within the Local-Density Approximation to Density-Functional Theory. An efficient variation-perturbation approach has been used to extract the linear response of wavefunctions and density to atomic displacements. In mixed ionic-covalent solids, like SiC>2 or BaTiC>3, the careful treatment of the long-range IFCs is mandatory for a correct description of the eigenfrequencies. 

Actual calculations that have been carried out are still confined almost entirely to atoms, so that the title Intermolecular Forces is almost a misnomer, Interatomic Forces being much closer to the state of the art. Some calculations are aimed primarily at understanding the short-range, repulsive region of interaction. These are discussed in Section 3, while Section 4 covers recent results on the long-range region. 

The calculation of vibration spectra in terms of force constants is similar to the calculation of energy bands in terms of interatomic matrix elements. Force constants based upon elasticity lead to optical modes, as well as acoustical modes, in reasonable accord with experiment, the principal error being in transverse acoustical modes. The depression of these frequencies can be understood in terms of long-range electronic forces, which were omitted in calculations tising the valence force field. The calculation of specific heat in terms of the vibration spectrum can be greatly simplified by making a natural Einstein approximation. 

It is known that the method used to truncate the interatomic interactions can have an important effect. It has been demonstrated that the dielectric properties of simulated water are a sensitive function of the extent to which the long-range electrostatic interactions are included [40]. Simulations of phospholipid membrane-water systems showed that the behavior of the water near the membrane is incorrectly described if the electrostatic interactions are truncated at too short a distance, and hot water/cold-protein behavior is observed [10]. Given the importance of the potential/force truncation, we have investigated this issue for the copper system being simulated. This has been done in terms of the same properties as were used in examining convergence. 

In AFM, several forces contribute to the deflection of the cantilever. The force most commonly associated with AFM is an interatomic force called the van der Waals forces. Figure 3.10 shows the dependence of the short-range repulsive force and the long-range van der Waals forces on the distance between the tip and the sample. 

---