Density functional theory in quantum chemistry by Takao Tsuneda
By Takao Tsuneda
In this booklet, density practical idea (DFT) is brought in the total context of quantum chemistry. DFT has turn into the main usually used concept in quantum chemistry calculations. despite the fact that, to date, there was no publication at the basics of DFT that makes use of the terminology and method of quantum chemistry, that is customary to many chemists, together with experimentalists. This publication first experiences the elemental thoughts and old heritage of quantum chemistry after which explains these of DFT, exhibiting how the latter matches into the larger photo. contemporary attention-grabbing themes of DFT in chemistry also are unique. particularly, the actual meanings of state of the art exchange-correlation functionals and their corrections are defined intimately. due to its unconventionality, this booklet is bound to be of significant curiosity not just to chemists but additionally to sturdy nation physicists.
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11) which appears similar to the Hamiltonian of the helium atom. However, the equation is more difficult to solve than it appears, because the hydrogen molecule has two atomic nuclei. Actually, the position vectors of the electrons must be considered for each atomic nucleus, although these are represented as rn in Eq. 11). To solve this problem, the concept of the molecular orbital was introduced. The concept of the molecular orbital was used by Hund for the first time to explain the electronic states of molecules (Hund 1926).
44) This is in contrast to the classical state of a particle at rest in a hole, for which the sum of the kinetic energy and potential energy is zero. This nonzero energy is called the zero-point energy. • Given the momentum of a molecule, the expectation value of the momentum hpi is always zero for real eigenfunctions. x/. 45) dx is always imaginary and therefore hpi is not identical to the complex conjugate hpi except for hpi D 0. x/; 2m dx increases as the curvature of the eigenfunction grows.
Now, let us consider the eigenstates of the translational motions of molecules in the box potential. For the simplest one-dimensional box potential with width a (Fig. 6 Molecular Translational Motion 21 where m is the mass of the molecule. x/ D a These eigenvalues and eigenfunctions have the following characteristics (Gasiorowicz 1996). 44) This is in contrast to the classical state of a particle at rest in a hole, for which the sum of the kinetic energy and potential energy is zero. This nonzero energy is called the zero-point energy.