Molecular modelling kinetic energy

Imagine a model hydrogen molecule with non-interacting electrons, such that their Coulomb repulsion is zero. Each electron in our model still has kinetic energy and is still attracted to both nuclei, but the electron motions are completely independent of each other because the electron-electron interaction term is zero. We would, therefore, expect that the electronic wavefunction for the pair of electrons would be a product of the wavefunctions for two independent electrons in H2+ (Figure 4.1), which I will write X(rO and F(r2). Thus X(ri) and T(r2) are molecular orbitals which describe independently the two electrons in our non-interacting electron model. 

Robinson, E.A., Johnson, S.A., Tang, T.-H., Gillespie, R.J. (1997). Reinterpretation of the lengths of bonds to fluorine in terms of an almost ionic model. Inorganic Chemistry, 36, 3022-3030. Schinder, H.L. Becke, A.D. (2000). Chemical contents of the kinetic energy density. Journal of Molecular Structure (THEOCHEM), 527, 51-61. 

Molecular modeling work performed by Sasol researchers on fee cobalt (100) shows that increased coverage of 50% atomic carbon will induce a clock type reconstruction (Figure 4.3) similar to that observed for the classic case of Ni (100).28 The adsorption energy of the carbon is stabilized by 15 kJ/mol compared to the unreconstructed surface, resulting in a more stable surface.28 The reconstruction results in a shorter distance between the carbon and cobalt but also an increase in coordination of the cobalt atoms and, thus, fewer broken bonds. The barrier for the carbon-induced clock reconstruction was found to be very small (1 kJ/mol), which suggested that the process is not kinetically hindered. The... 

These two methods are different and are usually employed to calculate different properties. Molecular dynamics has a time-dependent component, and is better at calculating transport properties, such as viscosity, heat conductivity, and difftisivity. Monte Carlo methods do not contain information on kinetic energy. It is used more in the lattice model of polymers, protein stmcture conformation, and in the Gibbs ensemble for phase equilibrium. 

For the electro-nuclear model, it is the charge the only homogeneous element between electron and nuclear states. The electronic part corresponds to fermion states, each one represented by a 2-spinor and a space part. Thus, it has always been natural to use the Coulomb Hamiltonian Hc(q,Q) as an entity to work with. The operator includes the electronic kinetic energy (Ke) and all electrostatic interaction operators (Vee + VeN + Vnn)- In fact this is a key operator for describing molecular physics events [1-3]. Let us consider the electronic space problem first exact solutions exist for this problem the wavefunctions are defined as /(q) do not mix up these functions with the previous electro-nuclear wavefunctions. At this level. He and S (total electronic spin operator) commute the spin operator appears in the kinematic operator V and H commute with the total angular momentum J=L+S in the I-ffame L is the total orbital angular momentum, the system is referred to a unique origin. 

Kinetic Molecular Theory model that defines an ideal gas and assumes the average kinetic energy of gas molecules is directly proportional to the absolute temperature... 

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