Where θ is finite temperature of the thermal equilibrium system, A is the free energy of \(\theta ,v(r)\) electron system and S is entropy of electron system under \(\theta ,v(r)\).Ī pure state molecule electron system, not a mixed one, can be supposed to be a thermodynamic system. In the variational equation which gives the electron density corresponding to minimum energy in DFT, Euler-Lagrange (EL) equation, an undefined multiplier μ is the energy per electron and electron migration measure. The aim of this paper is to lay foundations for the principles and methods which could determine the energy of molecules and their atomic charges by thermodynamic formalization, rather than the quantum theory. WFT, DFT and its varieties are all different in calculation accuracy and velocity, but both formalization of the variable quantity of energy minimization and the solution of the variational equation are based on the quantum theoretical formalization. Over the past decades, much effort has been made to improve the calculation accuracy of DFT 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22.
Therefore, less accurate DFT based on electron density has been created and used 14, 15, 16, 17, 18, 19, 20.
However, it is infeasible for calculating the molecules with a large quantity of atoms, because the more quantity of atoms is given, the longer it takes to calculate. Of course, the ab initio method of WFT is widely used for calculating the properties of the molecules because of its high accuracy 9, 10, 11, 12, 13. In quantum theory for calculating molecular energy, atomic charge, structures and properties, excellent successes were achieved in calculation for many projects by establishment to ab initio and semi-empirical method of wave function theory (WFT) 1, 2, 3, 4, 5, 6 in that electron wave function is variable quantity of energy minimization and density-function theory (DFT) 7, 8 in that electron density is variable quantity.
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