All-electron basis sets for H to Xe specific for ZORA calculations:Applications in atoms and molecules

A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.

All-electron ZORA triple zeta basis sets for the elements Cs-La and Hf-Rn

Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constructed.To correctly describe electrons distant from atomic nuclei,the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA.At the ZORA-B3LYP theoretical level,these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms,bond length,dissociation energy,and harmonic vibrational frequency of diatomic molecules.Then,these results are compared with the theoretical and experimental data found in the literature.Even considering that our sets are relatively compact,they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell.The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated and the results are also discussed.

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

In real space density functional theory calculations,the effective potential depends on the electron density,requiring self-consistent iterations,and numerous integrals at each step,making the process time-consuming.In our research,we propose an optimization method to expedite density functional theory(DFT)calculations for systems with large aspect ratios,such as metallic nanorods,nanowires,or scanning tunneling microscope tips.This method focuses on employing basis set to expand the electron density,Coulomb potential,and exchange-correlation potential.By precomputing integrals and caching redundant results,this expansion streamlines the integration process,significantly accelerating DFT computations.As a case study,we have applied this optimization to metallic nanorod systems of various radii and lengths,obtaining corresponding ground-state electron densities and potentials.

Accurate equilibrium inversion barrier of ammonia by extrapolation to the one-electron basis set limit

A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite one-electron basis-set limit. The dual-level method is tested on the extrapolation of the full correlation in coupled-cluster singles and doubles and in the case also a noniterative perturbative correction for connected triple energies for the C3v and D3h structures of ammonia, with correlation-consistent basis sets of the type cc-pVXZ （X = D, T, Q, 5, 6） and aug-cc-pVXZ （X = D, T, Q, 5）. For testing and comparison purposes, the energies reported by Klopper [J. Comput. Chem. 22 1306 （2001）] have been taken. From a corresponding extrapolation of CCSD（T）/AVXZ energies for X = 4, 5, we obtain total inversion barriers of 1833.87 cm-1/1832.33 cm^-1 for the two/three-parameter extrapolation rules, which are in good agreement with other theoretical extrapolation and empirical values in the literature.

Basis Sets Dependency in Constructing Spectroscopy-Accuracy Ab Initio Global Electric Dipole Moment Functions

Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do.In this letter,using Ar…He as an example,we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods.We especially focused on the basis set dependency in this scenario,i.e.,the convergence of DMF with the sizes of basis sets,basis set superposition error,and mid-bond functions.We also tested the explicitly correlated method,which converges with smaller basis sets than the conventional methods do.This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.

Basis Set Extrapolation for the High Resolution Spectroscopy

Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the levels of MP2, RI-MP2, and CCSD （T） with Dunnings sequential correlation consistent basis sets. A two point basis set extrapolation scheme for correlation energies to the complete basis set limit based on only DZ （double-zeta） and TZ （triple-zeta） results is presented and analyzed. We show that this basis set extrapolation scheme reduces the computational cost by two to three orders of magnitude to obtain the same accuracy as simpler extrapolations from higher order basis set computations.

Structural Investigation of Technetium-Diphosphonate Complex 99mTc-MDP

Density functional theory method has been employed to investigate the structures of the prototypical technetium-labeled diphosphonate complex 99mTc-MDP, where MDP represents methylenediphosphonic acid. A total of 14 trial structures were generated by allowing for the geometric, conformational, charge, and spin isomerism. Based on the optimized structures and calculated energies at the B3LYP/LANL2DZ level, two stable isomers were determined for the title complex. And they were further studied systematically in comparison with the experimental structure. The basis sets 6-31G＊（LANL2DZ for Tc）, 6-31G＊（cc-pVDZ-pp for Tc）, and DGDZVP have also been employed in combination with the B3LYP functional to study the basis set effect on the geometries of isomers. The optimized structures agree well with the available experimental data, and the bond lengths are more sensitive to the basis set than the bond angles. The charge distributions were studied by the Mulliken population analysis and natural bond orbital analysis. The results reflect a significant ligand-to-metal electron donation.

Structure,stability,catalytic activity,and polarizabilities of small iridium clusters

At the second order Douglas–Kroll–Hess（DKH2） level, the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths, dissociation energies, vertical ionization potentials, and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters（Irn, n≤8）. These results are compared with the experimental and theoretical data available in the literature. Our results confirm the theoretical predictions made by Feng et al. about the catalytic activities of the Ir4 and Ir6 clusters. From the optimized geometries, DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out. It is the first time that the polarizabilities of small iridium clusters have been studied. For n≤4, the mean dipole polarizabilities per atom present an odd–even oscillatory behavior,whereas from Ir5 to Ir8, they decrease with the cluster size increasing. The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.

THE THEORETICAL STUDY OF ADSORPTION OF METAL IONS ON CHITOSAN

The interactions between metal ions such as Zn2+, Pb2+, Mn2+, Hg2+, Cd2+, Ni2+ and chitosan have been investigated using the model cluster model method and density functional method. Full optimization and frequency analysis of all cluster models have been performed employing B3LYP hybrid method at 3-21G basis set level except metal ions which were invoked to use effective core potential (ECP) method. The energy changes, and the main structural parameters have been obtained during the theoretical study of the adsorption of metal ions on the chitosan. The calculations showed that the coordination modes of metal ions with chitosan models were different, the geometries of Mn2+, Zn2+, Cd2+, Hg2+, Pb2+ ions coordinated with two nitrogen atoms and two oxygen atoms were distorted tetrahedral, while the square planar structure of Ni2+ coordinated two nitrogen atoms and two oxygen atoms was observed. The heat of reaction between six metal ions and chitosan models showed the order: Mn2+ >Ni2+ >Zn2+ >Pb2+ >Hg2+ >Cd2+, this suggested that the coordination strength of Mn2+ >Ni2+ >Zn2+ >Pb2+ >Hg2+ >Cd2+.

Ground state energy of He isoelectronic sequence treated variationally via Hylleraas-like wavefunction

In this study, the energy for the ground state of helium and a few helium-like ions （Z=1-6） is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.

Ab Initio Molecular Orbital Calculation on Dinuclear Gold(Ⅰ) Complexes──Metal-Metal Interaction and Electronic Structure of Binuclear Gold(Ⅰ) Complexes with Bridging Bidentate Ligands

The electronic structure and electronic absorption spectra of binuclear Au(Ⅰ) complexes with bidentate phophines and a bidentate ylid ligand have been studied using quasirelativistic pseudopotential ab initio calculations at the HF and MP2 levels by the LANL2DZ basis sets. The electronic properties of the spectral transition and Au(Ⅰ)—Au(Ⅰ) interaction were also discussed.

Dipole (hyper)polarizabilities of neutral silver clusters

At the Douglas-Kroll-Hess （DKI4） level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters （Agn, n ≤ 7）. The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.

Efficient Mapping of High Order Basis Sets for Unbounded Domains

Many physical problems involve unbounded domains where the physical quantities vanish at infinities.Numerically,this has been handled using different techniques such as domain truncation,approximations using infinitely extended and vanishing basis sets,and mapping bounded basis sets using some coordinate transformations.Each technique has its own advantages and disadvantages.Yet,approximating simultaneously and efficiently a wide range of decaying rates has persisted as major challenge.Also,coordinate transformation,if not carefully implemented,can result in non-orthogonal mapped basis sets.In this work,we revisited this issue with an emphasize on designing appropriate transformations using sine series as basis set.The transformations maintain both the orthogonality and the efficiency.Furthermore,using simple basis set(sine function)help avoid the expensive numerical integrations.In the calculations,four types of physically recurring decaying behaviors are considered,which are:non-oscillating and oscillating exponential decays,and non-oscillating and oscillating algebraic decays.The results and the analyses show that properly designed high-order mapped basis sets can be efficient tools to handle challenging physical problems on unbounded domains.Decay rate ranges as large of 6 orders of magnitudes can be approximated efficiently and concurrently.

Density Functional Theory Study of the Interaction between Thymine and Luteolin

The density function B3LYP method has been used to optimize the geometries of the luteolin, thymine and lute- olin-thymine complexes at 6-31＋G＊ basis. The vibrational frequencies have been studied at the same level to ana- lyze these seventeen complexes, respectively. Theories of atoms in molecules （AIM） and natural bond orbital （NBO） have been utilized to investigate the hydrogen bonds involved in all the systems. The interaction energies of the complexes corrected by basis set superposition error are between -93.00-76.69 kJ/mol. The calculating results indicate that strong hydrogen bonding interactions have been found in the luteolin-thymine complexes.

Solutions of the 1D Coupled Nonlinear Schrodinger Equations by the CIP-BS Method

In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis set,by which physical quantities are approximated with their values and derivatives associated with grid points.Nonlinear operations on functions are carried out in the framework of differential algebra.Then,by introducing scalar products and requiring the residue to be orthogonal to the basis,the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives.The method gives stable,less diffusive,and accurate results for the CNLS equations.