Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn–Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment (μ), static dipole polarizability (α), and first hyperpolarizability (β), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of “adiabatic connection theorem” and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems

Determining the Optimal Duration of Progesterone Supplementation prior to Transfer of Cryopreserved Embryos and Its Impact on Implantation and Pregnancy Rates: A Pilot Study

Objective. To determine the optimal duration of progesterone supplementation prior to transfer of cryopreserved embryos and its impact on implantation and pregnancy rates. Study Design. Prospective randomised study. Materials and Methods. In an IVF unit of a tertiary centre, sixty-six patients undergoing cryopreserved embryo transfer cycles were included. Endometrial preparation was done with estradiol valerate. Once it reached a minimum of 7 mm, patients were allocated randomly into group I (n=39) and group II (n=27). Injectable progesterone 100 mg daily was then started for 3 and 4 days, respectively. This was followed by transfer of at least one thawed cleavage stage day 2 embryo of good quality. Groups I and II were compared in terms of clinical pregnancy and implantation rates. Results. In group I (3-day progesterone) and group II (4-day progesterone) the pregnancy rates were 41.02% (16/39) and 18.51% (5/27), respectively. On the other hand, the implantation rates were 16.82% (18/107) and 7.69% (6/78), respectively. The difference was statistically significant (p values 0.0172 and 0.0386, resp.). Conclusion. Progesterone supplementation for three days before the transfer of cleavage stage (day 2) cryopreserved embryos has significantly higher pregnancy and implantation rates, as compared to four-day supplementation

Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius r c . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) 3S, 1snp (n = 2–3) 3P, 1s3d 3D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to r c in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower r c regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed

Confined H

Ground and excited states of a confined negative hydrogen ion have been pursued under Kohn–Sham density functional approach by invoking a physically motivated work-function-based exchange potential. The exchange-only results are of near Hartree–Fock quality. Local parameterized Wigner-type, and gradient- and Laplacian-dependent non-local Lee–Yang–Parr functionals are chosen to investigate the electron correlation effects. Eigenfunctions and eigenvalues are extracted by using a generalized pseudospectral method obeying Dirichlet boundary condition. Energy values are reported for 1s$$^{2}$$ ($$^{1}$$S), 1s2s ($$^{3,1}$$S) and 1s2p ($$^{3,1}$$P) states. The performance of the correlation functionals in the context of confinement is examined critically. The present results are in excellent agreement with the available literature. Additionally, Shannon entropy and Onicescu energy are offered for ground and low-lying singly excited 1s2s ($$^{3}$$S) and 1s2p ($$^{3}$$P) states. The influence of electron correlation is more predominant in the weaker confinement limit, and it decays with an increase in confinement strength. In essence, energy and some information measures are estimated using a newly formulated density functional strategy

Protective Role of Black Tea Extract against Nonalcoholic Steatohepatitis-Induced Skeletal Dysfunction

Aim. This paper aimed to examine the chemoprotective actions of aqueous black tea extract (BTE) against nonalcoholic steatohepatitis- (NASH-) induced skeletal changes in rats. Material. Wistar rats (body wt. 155–175 g) of both sexes, aged 4–5 months, were randomly assigned to 3 groups; Group A (control), Group B (60% high-fat diet; HFD), and Group C (HFD + 2.5% BTE). Methods. Several urinary (calcium, phosphate, creatinine, and calcium-to-creatinine ratio) serum (alkaline phosphatase and serum tartrate-resistant acid phosphatase), and molecular markers of bone turnover (receptor activator of NF-κB ligand (RANKL), osteoprotegerin (OPG), and estrogen) were tested. Also, several bone parameters (bone density, bone tensile strength, bone mineral content, and bone histology) and calcium homeostasis were checked. Results. Results indicated that HFD-induced alterations in urinary, serum, and bone parameters as well as calcium homeostasis, all could be significantly ameliorated by BTE supplementation. Conclusion. Results suggest a potential role of BTE as a protective agent against NASH-induced changes in bone metabolism in rats