Electronic structure calculations are now indispensible for understanding chemical phenomena. Density functional theory (DFT), which is simple, conceptual, and applicable to large systems, has emerged as a powerful computational tool to tackle molecular electronic structures. DFT efficiently calculates electronic structure with high accuracy, and its algorithm is suitable for parallel computing...

Periodic density functional theory (DFT) calculations have recently emerged as a popular tool for assigning solid-state nuclear magnetic resonance (NMR) spectra. However, in order for the calculations to yield accurate results, accurate structural models are also required. In many cases the structural model (often derived from crystallographic diffraction) must be optimised (i.e., to an energy ...

| Some applications of the Discrete Fourier Transform (DFT) in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged in general commutative rings. I. The (Usual) Discrete Fourier Transform Let be a primitive N th root of uni...

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationsh...

The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomi...

Density functional (DFT) calculations at M05-2x/aug-cc-pVDZ level were used to analyze the interactions between dimethyl sulfoxide (DMSO) dimers. The structures obtained have been analyzed with the Atoms in Molecules (AIMs) and Natural Bond Orbital (NBO) methodologies. Four minima were located on the potential energy surface of the dimers. Three types of interactions are observed, CH•••O, CH•••...

Tetrazole-containing compounds have been the subject of much recent research because of theirpotential as high energy density materials (HEDMs). In this work, theoretical studies on the 1Htetrazolylderivatives of tetrahedrane were done at the density functional theory (DFT) method withthe 6-31G(d) basis set without any symmetrical restrictions in order to find the structural andenergetically pr...

The interaction of a nitrosyl hydride (HNO) molecule with B12N12 nanocage was explored by means of density functional calculations. It was found that HNO prefers to be adsorbing on a boron atom of the cage with adsorption energy of -0.65 eV. This adsorption process significantly shifts the HOMO-LUMO gap (Eg) of the cage to lower energies, thereby reducing Eg of the cage from 6.84 to 2.45 eV. Ti...

Magnesium oxide nanotubes of finite length are investigated by the Density Functional Theory (DFT) at the B3LYP/6-31G (d) level. The (6, 0) zigzag and (4, 4) armchair of MgO nanotubes were considered and nuclear magnetic resonance properties including isotropic and anisotropic chemical shielding parameters (CSI and CSA) were calculated for 25Mg and 17O atoms of the optimiz...