We study the problem of finding unitary submatrices of the discrete Fourier transform matrix. This problem is related to a diverse set of questions on idempotents on ZN , tiling ZN , difference graphs and maximal cliques. Each of these is related to the problem of interpolating a discrete bandlimited signal using an orthogonal basis.

The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms a...

We present a first-principles computational study of solid 4He at T = 0 K and pressures up to ∼160 GPa. Our computational strategy consists in using van der Waals density functional theory (DFT-vdW) to describe the electronic degrees of freedom in this material, and the diffusion Monte Carlo (DMC) method to solve the Schrödinger equation describing the behavior of the quantum nuclei. For this, ...

The (13)C and (1)H isotropic chemical shift values computed at HF, BLYP, B3LYP, and MPW1PW91/6-311+G(2d,p) levels of theory, for the BLYP and B3LYP/6-31G(d,p) optimized geometries of adamantane, 2-adamantanone, and 2,4-methano-2,4-dehydroadamantane ([3.1.1] propellane) are reported and compared with the experimental data. Except for the "inverted" carbon atoms and some of their nearest neighbor...

Background To establish the chronic stability of defibrillation thresholds (DFTs) in a transvenous cardioverter/defibrillator (TCD) system, we studied 37 consecutive patients with TCD systems implanted for >6 months. Methods and Results DFT was measured by a step-down method at implant and 2 and 6 months later. The mean ejection fraction was 34.5±14.3%. Coronary artery disease with previous myo...

Single-molecule magnets are perspective materials for molecular spintronic applications. Predictions of magnetic coupling in these systems have posed a long standing problem, as calculations of this kind require a balanced description of static and dynamic electron correlation. The large size of these systems limits the choice of theoretical methods used. Two methods feasible to predict the exc...

This paper will look at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of discrete Fourier transform (DFT). We will develop an algorithm, called the quick Fourier transform (QFT), that will reduce the number of oating point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for p...

The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected dens...

This article starts with a brief history and idea interpretation of the Density Functional Theory (DFT), and then explains more detailedly about the original thought of Hohenberg and Kohn and their first and second theorem of the DFT. Next, it also introduces a methodology to treat the calculation based on DFT, which is the Kohn-Sham method based on the Local Density Approximation (LDA) treatme...

The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Har...