Abstract
The Density Functional Theory is at the core of all modern ways of computing accurate electron energies under all aggregation states of the matter.
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Notes
- 1.
The probability does not depend on the direction.
- 2.
In the RPA, electrons are assumed to respond only to the total electric potential V(r) which is the sum of an external perturbing potential Vext(r) and a screening potential Vsc(r). Vext(r) is assumed to oscillate, so that the model yields a dynamic dielectric function. However, the contribution to the dielectric function is assumed to average out, so that only the potential at wave vector k is effective.
- 3.
- 4.
The entire formalism is easily generalized to spin unrestricted problems also, in terms of local spin densities \(\rho _{\alpha } ,\rho _{\beta }\).
- 5.
The 2c sub-set is composed of 56 heats of formation at 298 K + 42 ionization potentials + 25 electron affinities + 10 total energies.
- 6.
Part of the problems of the original approach (Grimme 2004), resides in the combination rule employed for the composed coefficients that gave too much weight to the smaller coefficient (lighter atom).
- 7.
When the electron density n(r) has a marked spatial dependence, such as in the case of strongly fluctuating spin and charge degrees of freedom in correlated metals, this approximation breaks down (Imada et al. 1998).
- 8.
The Hamiltonian must be Hermitian: if there is an amplitude for hop** between i and j nearest neighbors, then there must be also an amplitude for the reverse process (i.e. hop** between j and i)., and the H.c. term is compulsory.
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Ottonello, G.A. (2024). DFT Functionals. In: Quantum Geochemistry. Springer Geochemistry. Springer, Cham. https://doi.org/10.1007/978-3-031-21837-8_10
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DOI: https://doi.org/10.1007/978-3-031-21837-8_10
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