Molecular kinetic/potential energy

The word kinetics stems from the Greek klvclv, to move, and reaction kinetics is the science of how fast chemical reactions proceed. Beyond that broad definition, reaction kinetics means different things to different practitioners. Ask a chemical physicist and he may think of molecular beams, potential-energy profiles along pathways, or ab initio calculations of rates of which he is proud if their results are correct within an order of magnitude. Ask a development chemist and he might see in his mind tabulations of rates under a variety of conditions, and of... 

Molecular mechanics potential energy functions have been used to calculate binding constants, protein folding kinetics, protonation equilibria, active site coordinates, and to design binding sites [4,5]. 

Vibrations are considered in terms of the classical expressions governing motion of nuclei vibrating about their equilibrium positions with a simple harmonic motion (40). The potential and kinetic potential energies of molecules are defined in terms of the coordinates most appropriate to the molecular structures. All relative motions of atoms about the center of mass (vibrations) are linear combinations of a set of coordinates, known as normal coordinates. For every normal mode of vibration, all coordinates vary periodically with the same frequency and pass through equilibrium simultaneously. 

Chakraborty A, Zhao Y, Lin H, Tiuhlm DG (2006) Combined valence bond-molecular mechanics potential-energy surface tmd direct dynamics study of rate constants and kinetic isotope effects for the H + C2H6 reaction. J Chem Phys 124 044315... 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The total energy in an Molecular Orbital calculation is the net result of electronic kinetic energies and the interactions between all electrons and atomic cores in the system. This is the potential energy for nuclear motion in the Born-Oppenheimer approximation (see page 32). 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

Anhydrous NaC102 crystallizes from aqueous solutions above 37.4° but below this temperature the trihydrate is obtained. The commercial product contains about 80% NaC102. The anhydrous salt forms colourless deliquescent crystals which decompose when heated to 175-200° the reaction is predominantly a disproportionation to C103 and Cl but about 5% of molecular O2 is also released (based on the C102 consumed). Neutral and alkaline aqueous solutions of NaC102 are stable at room temperature (despite their thermodynamic instability towards disproportionation as evidenced by the reduction potentials on p. 854). This is a kinetic activation-energy effect and, when the solutions are heated near to boiling, slow disproportionation occurs ... 

The Dirac operator incorporates relativistic effects for the kinetic energy. In order to describe atomic and molecular systems, the potential energy operator must also be modified. In non-relativistic theory the potential energy is given by the Coulomb operator. 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

Importantly, all biological procedures are operating at a temperature of 310 Kelvin, not at 0 Kelvin as the potential energy is calculated by the force fields. The kinetic energy must also be considered. Molecules and proteins at room temperature change the conformation at least at the surface and in loop region. Molecular dynamics simulation (MD) is an approach to tackle these kinetic and stability problems. 

An explanation of potential energy involves an explanation of force both terms are simply another way of saying that we know nothing about the thing to be explained. A distinct advance is made when a force can be explained in terms of the kinetic energy of a system in motion, an illustration of which is afforded by the kinetic theory of gases, which replaced the supposed forces of repulsion between the molecules of gases (the existence of which is disproved by Joule s experiment, 73) by molecular impacts. 

While thermodynamics does not describe the nature of this internal energy, it is helpful to consider the insights gained from kinetic molecular theory. According to this theory, the internal energy can be partitioned into kinetic and potential energy terms associated with various motions and positions of the nuclei of the atoms or molecules that make up the gas, and with energies associated with their electrons. 

---