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As described above, some method such as quantum mechanics can be used to calculate the energy, E(r) , the gradient of the PES, that is, the derivative of the energy with respect to the position of the atoms, ∂E/∂r and the second derivative matrix of the system, ∂∂E/∂r i ∂r j, also known as the Hessian matrix, which describes the curvature of the PES at r.
A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N(t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be ...
To derive Darken's second equation the gradient in Gibb's chemical potential is analyzed. The gradient in potential energy, denoted by F 2, is the force which causes atoms to diffuse. [1] To begin, the flux J is equated to the product of the differential of the gradient and the mobility B, which is defined as the diffusing atom's velocity per ...
The Non-Covalent Interactions index, commonly referred to as simply Non-Covalent Interactions (NCI) is a visualization index based in the Electron density (ρ) and the reduced density gradient (s). It is based on the empirical observation that Non-covalent interactions can be associated with the regions of small reduced density gradient at low ...
As a concrete example of unconstrained internal variables, we might have a chemical reaction in which there are two types of particle, an A atom and an A 2 molecule. If N 1 {\displaystyle N_{1}} and N 2 {\displaystyle N_{2}} are the respective particle numbers for these particles, then the internal constraint is that the total number of A atoms ...
An electrochemical gradient is a gradient of electrochemical potential, usually for an ion that can move across a membrane. The gradient consists of two parts: The chemical gradient, or difference in solute concentration across a membrane. The electrical gradient, or difference in charge across a membrane.
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces.
Solubility of compounds in the stationary phase may rise or fall with , but not exponentially. is referred to as selectivity or polarity by gas chromatographers today. Isothermal Kovats index in terms of the physical properties becomes: