Regular Approximation Method Research Articles

DFT and TDDFT exploration on electronic transitions and bonding aspect of DPA and PTDC ligated transition metal complexes.

In this study, we have investigated the structure, reactivity, bonding, and electronic transitions ofDPAandPDTC along with theirNi-Zncomplexes usingDFT/TD-DFT methods. The energy gap between the frontier orbitals was computed to understand the reactivity pattern of the ligands and metal complexes. From the energies of FMO's, the global reactivity descriptors such as electron affinity, ionization potential, hardness (η), softness (S), chemical potential (μ), electronegativity (χ), and electrophilicity index (ω) have been calculated. The complexes show a strong NLO properties due to easily polarization as indicated by the narrow HOMO-LUMO gap. The polarizability and hyperpolarizabilities of the complexes indicate that they are good candidates for NLO materials. Molecular electrostatic potential (MEP) maps identified electrophilic and nucleophilic sites on the surfaces of the complexes. TDDFT and NBO analyses provided insights into electronic transitions, bonding, and stabilizing interactions within the studied complexes. DPA and PDTC exhibited largerHOMO-LUMO gapsand more negative electrostatic potentials compared to their metal complexes suggesting the higher reactivity. Ligands (DPA and PDTC) had absorption spectra in the range of250nm to 285nm while their complexes spanned250nm to 870nm. These bands offer valuable information on electronic transitions, charge transfer and optical behavior. This work enhances our understanding of the electronic structure and optical properties of these complexes. Gaussian16 program was used for the optimization of all the compounds. B3LYP functional in combination with basis sets, such as LanL2DZ for Zn, Ni and Cu while 6-311G** for other atoms like C, H, O, N, and S was used. Natural bond orbital (NBO) analysis is carried out to find out how the filled orbital of one sub-system interacts with the empty orbital of another sub-system. The ORCA software is used for computing spectral features along with the zeroth order regular approximation method (ZORA) to observe its relativistic effects. TD-DFT study is carried out to calculate the excitation energy by using B3LYP functional.

Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts

Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts

Global weak solutions for the two-component Novikov equation

<p style='text-indent:20px;'>The two-component Novikov equation is an integrable generalization of the Novikov equation, which has the peaked solitons in the sense of distribution as the Novikov and Camassa-Holm equations. In this paper, we prove the existence of the <inline-formula><tex-math id="M1">$ H^1 $</tex-math></inline-formula>-weak solution for the two-component Novikov equation by the regular approximation method due to the existence of three conserved densities. The key elements in our approach are some a priori estimates on the approximation solutions.</p>

Parabolic Biased Infinity Laplacian Equation Related to the Biased Tug-of-War

Abstract In this paper, we study the parabolic inhomogeneous β-biased infinity Laplacian equation arising from the β-biased tug-of-war u t - Δ ∞ β ⁢ u = f ⁢ ( x , t ) , {u_{t}}-\Delta_{\infty}^{\beta}u=f(x,t), where β is a fixed constant and Δ ∞ β {\Delta_{\infty}^{\beta}} is the β-biased infinity Laplacian operator Δ ∞ β ⁢ u = Δ ∞ N ⁢ u + β ⁢ | D ⁢ u | \Delta_{\infty}^{\beta}u=\Delta_{\infty}^{N}u+\beta\lvert Du\rvert related to the game theory named β-biased tug-of-war. We first establish a comparison principle of viscosity solutions when the inhomogeneous term f does not change its sign. Based on the comparison principle, the uniqueness of viscosity solutions of the Cauchy–Dirichlet boundary problem and some stability results are obtained. Then the existence of viscosity solutions of the corresponding Cauchy–Dirichlet problem is established by a regularized approximation method when the inhomogeneous term is constant. We also obtain an interior gradient estimate of the viscosity solutions by Bernstein’s method. This means that when f is Lipschitz continuous, a viscosity solution u is also Lipschitz in both the time variable t and the space variable x. Finally, when f = 0 {f=0} , we show some explicit solutions.

Application of 204mPb Perturbed Angular Correlation of γ-rays Spectroscopy in Coordination Chemistry

(204m)Pb perturbed angular correlation of γ-rays (PAC) spectroscopy has been applied successfully for the first time to detect the nuclear quadrupole interaction in a lead(II) coordination compound in a molecular crystal [tetraphenylarsonium lead(II) isomaleonitriledithiolate ([AsPh(4)](4)[Pb(2)(i-mnt)(4)])]. The recorded parameters from a powder crystalline sample are ν(Q) = 0.178(1) GHz and η = 0.970(7). The electric field gradient (EFG) was determined at the PW91/QZ4P level including relativistic effects using the two-component zeroth-order regular approximation method for both the [Pb(i-mnt)(2)](2-) monomer and the [Pb(2)(i-mnt)(4)](4-) dimer. Only the EFG for the latter compares favorably with the experimental data, indicating that the picture of this complex as a prototypical hemidirected coordination geometry with a stereochemically active lone pair on lead(II) is inadequate. Advantages and limitations of (204m)Pb PAC spectroscopy as a novel technique to elucidate the electronic and molecular structures of lead-containing complexes and biomolecules are presented.

Behavior of papain in mixed micelles of anionic–cationic surfactants having similar tails and dissimilar head groups

The mixed micellar behavior of anionic surfactant, sodium dodecylsulfate (SDS) and cationic surfactant, dodecylethyldimethylammonium bromide (DDAB) at varying mole fractions of DDAB, i.e. α DDAB in aqueous solution of papain has been investigated with the aid of spectroscopy and physiochemical measurements. Thermodynamic parameters have been computed over the entire mole fraction range of DDAB. The Clint equation and the regular approximation method have been used to investigate the interactions between mixed surfactants in the presence of protein. The two surfactants have similar tails, however, the charges on respective polar head groups are expected to have significant effect on their colloidal behavior. The cmc values of mixed surfactants have been estimated from fluorescence, conductivity, surface tension, ultrasonic speed and density measurements. The results show that lower and higher mole fractions of DDAB give negative departure from ideality whereas intermediate mole fractions have positive deviation. The aggregation number, N agg of mixed micelles has also been calculated. The turbidity or cloudiness at intermediate mole fractions demonstrates a reduction in the background free monomer concentration due to neutralization of the monomers of opposite charge. The effect of concentration of papain on mixed micellar behavior indicates that with increase in the concentration of protein, the cac and cmc values increase. The unfolding of polypeptide chain in the presence of mixed surfactant has been observed.

Infinite-Order Regular Approximation by the Metric Perturbation

The regular approximation methods for the reduction of the Dirac equation to a fully equivalent two-component form are considered in the framework of the perturbation theory. The usual Dirac hamiltonian is first transformed with the change of metric. Then, the change of metric is considered as a perturbation to the zeroth-order (ZORA) problem. General formulae for perturbation corrections to the ZORA wave function and energy are expressed solely in terms of the two-component solutions. The method presented in this paper gives the energy- independent scheme for the step-by-step generation of the infinite-order results which are equivalent to solutions of the Dirac equations. Several formal and computational aspects of the infinite-order regular approximation are discussed. It is concluded that, because of the use of well-behaved operators, the high-order regular approximation methods can be considered as competitive to high-order Douglas-Kroll approaches.