DCT (Discrete Cosine Transform) is an N-input sequence x(n) , 0≤n≤N-1 , as a linear transformation or combination of complex exponentials. As a result, the DFT coefficients are in general, complex even if x(n) is real.Suppose, we try to find out an orthogonal transformation which...
but also linear scaling methods are supported as the eigenvalue solver. Three calculation parts in ...
The results of these calculations suggest that the HR approximation should be applicable to atoms through the light actinides, so long as spin-orbit effects are unimportant. A comparison of very large basis-set results with results obtained using ordinary-size basis sets indicates that the valence...
If x[n] is real, it is possible to transform it into a complex sequence and use properties of the DFT to obtain X[k]. Example 11.28 In this example we compare the efficiency of the FFT algorithm, in terms of computation time as measured by the functions tic and toc, when computing ...
This chapter introduces the Hubbard model and its applicability as a corrective tool for accurate modeling of the electronic properties of various classes of systems. The attainment of a correct description of electronic structure is critical for predicting further electronic-related properties, including ...
Periodic DFT calculations Two different approaches are widely used for the atomic simulation of molecular crystals within periodic DFT calcula- tions: the rst approach exploits a linear combination of plane- wave functions as a basis set28 and the second one adopts a linea...
The KS orbitals are found as solutions of non-linear (Schrödinger-like) equations, where potentials depend on their own eigenfunctions through the electron density distribution. The unknown functional of a system of interacting electrons can be written as a sum of known ground-state kinetic ...
Finally, we obtained for fullerene, Y = 157.57X − 0.47, for fullerane, Y = 586.99X + 4.96, and for fulleryne, Y = 266.99X + 6.78, as a linear relation. We conclude that the effective mass of the electron is different in the three groups of fullerenes, ...
Transformation of uracil into 5-fluorouracil significantly changes its chemical and spectroscopic properties, as well as its in vivo activity. 5FU can also be considered as a derivative of a nucleobase thymidine where the methyl group is replaced by a fluorine atom. 5-Fluorouracil belongs to the ...
This finding suggests that Ti, a γ′ phase constituent, promotes Ni3Al growth kinetics, as expected. However, contrary to expectations, Cr exhibits a similar effect as a solid solution strengthening element. In our scenario, Cr may act like Re, segregating at phase interfaces to reduce solute...