Question

Briefly define the following terms and discuss their role in molecular modelling

a. Periodic boundary conditions

b. Steepest descents minimization

c. Force field parameterisation

d. Bonded potential

e. Cross terms

f. Harmonic potential

g. Morse potential

Answer 1

Periodic boundary conditions (PBC):

Periodic boundaries are used when physical geometry of interest and expected flow pattern and the thermal solution are of a periodically repeating nature. It has the advantage to reduce the computation time.

Periodic boundary conditions (PBC) are used in molecular dynamics simulations to avoid problems with boundary effects caused by finite size, and make the system more like an infinite one, at the cost of possible periodicity effects.

The existence of PBC means that any atom that leaves a simulation box by, say, the right-hand face, then enters the simulation box by the left-hand face. In the example of a large protein, if you look at the face of the simulation box that is opposite to the one from which the protein is protruding, then a hole in the solvent will be visible. The reason that the molecule(s) move from where they were initially located within the box is (for the vast majority of simulations) they are free to diffuse around. And so they do. They are not held in a magic location of the box. The box is not centered around anything while performing the simulation. Molecules are not made whole as a matter of course. Moreover, any periodic cell shape can be expressed as a parallelepiped (a.k.a. triclinic cell), and GROMACS does so internally regardless of the initial shape of the box.

Steepest descents minimization:

These visual issues can be fixed after the conclusion of the simulation by judicious use of the optional inputs to trjconv to process the trajectory files. Similarly, analyses such as RMSD of atomic positions can be flawed when a reference structure is compared with a structure that needs adjusting for periodicity effects, and the solution with trjconv follows the same lines. Some complex cases needing more than one operation will require more than one invocation of trjconv in order to work.

One of the active areas of research in computational chemistry is that in which the structures of molecules, and structures of transition state species in chemical reactions are determined. For the simplest case, the determination of the internuclear distance between two hydrogen atoms in an H2 molecule, the equilibrium distance is the minimum in the function that describes how the potential energy changes with the internuclear distance between the atoms. The equilibrium distance can be determined visually after plotting the potential energy for the interacting atoms as a function of internuclear distance. Data for such plots are easy to obtain even if specialized software is not available.

Force field parameterisation

Molecular mechanics force fields, which are commonly used in biomolecular modeling and computer-aided drug design, typically treat nonbonded interactions using a limited library of empirical parameters that are developed for small molecules. This approach does not account for polarization in larger molecules or proteins, and the parametrization process is labor-intensive. Using linear-scaling density functional theory and atoms-in-molecule electron density partitioning, environment-specific charges and Lennard-Jones parameters are derived directly from quantum mechanical calculations for use in biomolecular modeling of organic and biomolecular systems. The proposed methods significantly reduce the number of empirical parameters needed to construct molecular mechanics force fields, naturally include polarization effects in charge and Lennard-Jones parameters, and scale well to systems comprised of thousands of atoms, including proteins. The feasibility and benefits of this approach are demonstrated by computing free energies of hydration, properties of pure liquids

Cross terms

Cross-conjugation is a special type of conjugation in a molecule, when in a set of three Pi bonds only two pi-bonds interact with each other byconjugation, the third one is excluded from interaction. ... The type ofconjugation affects reactivity and molecular electronic transitions.

Morse potential

The study of exactly solvable problems has attracted much attention of many authors since the early development of quantum mechanics. To our knowledge, the exact solvable physical problems are few in quantum mechanics except for several well-known exactly solvable quantum systems like the hydrogen atom, harmonic oscillator and others. Due to its mathematical advantages, the harmonic oscillator model has been widely used to describe the interaction force of the diatomic molecule. Nevertheless, it is well known that the real molecular vibrations are anharmonic. Among many molecular potentials, the Morse potential as an ideal and typical anharmonic potential permits an exactly mathematical treatment and it has been the subject of interest since it was proposed by Morse in 1929 [293]. In particular, the Morse potential will reduce to the harmonic oscillator in the harmonic limit.