Solving the electron-nuclear Schrodinger equation of helium atom and its isoelectronic ions with the free iterative-complement-interaction method

Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrodinger equation in the fixed-nucleus approximation could be very accurately solved for helium atom and its isoelectronic ions (Z=1-10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained -2.903 304 557 729 580 294 733 816 943 892 697 752 659 273 965 a.u. for helium atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary atom called "eneon," [e(-)e(10+)e(-)](8+), in which both of the quantum effect of nuclear motion and the three-particle collisions are differently important from the helium and its isoelectronic ions. This revealed the accurate physics automatically generated by the free ICI formalism.     

Solving the electron and electron-nuclear Schrodinger equations for the excited states of helium atom with the free iterative-complement-interaction method

Very accurate variational calculations with the free iterative-complement-interaction (ICI) method for solving the Schrodinger equation were performed for the 1sNs singlet and triplet excited states of helium atom up to N=24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schrodinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. The small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry.     

Relativistic free complement method for correctly solving the Dirac equation with the applications to hydrogen isoelectronic atoms

The accuracy of the relativistic free complement (FC) method, which was previously reported for solving the Dirac?CCoulomb equations of atoms and molecules, has been strictly examined with the applications to hydrogen isoelectronic atoms. The FC wave function grown up by the Hamiltonian automatically takes care of the correct relationship between large and small components, i.e., FC or ICI balance. Combining the FC method with the inverse Hamiltonian method can help to obtain correct solutions safely against to several obstacles characteristic to the Dirac?CCoulomb equation. To ensure the exactness of the obtained wave function, we examined the total square deviation from the exact wave function, local energy constancy, H-square error, and energy upper and lower bounds for hydrogen-like atoms.     

Variational calculations in a halfspace for the interaction of a ground and excited state helium atom with its mirror image

Correlated trial wave-functions (depending explicitly upon the inter-electronic separation in the helium atom) subjected to boundary conditions excluding the helium electrons from the solid surface are used in half space, to evaluate in a variational approach the holding potential between an helium atom in its ground and metastable³S state with a perfectly imaging metallic conductor limited by a plane surface. Inter-electronic correlation effects are pointed out, and are seen to be non negligible. The holding potential for the helium³S displays a well of nearly an order of magnitude deeper than for the ground state. These results could be useful to determine the distance of closest approach of thermal atoms, and an approximate wave function for an helium atom interacting with a surface.     

The eigenenergies for ~3S excited states of the helium atom with CFPHGLF method

The matrix elements of the correlation function between symmetric potential harmonics were first simplified into the analytical summation of the grand angular momentum. The correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF) proposed by us recently was then applied to directly solve the Schrodinger equation for n3S(n=2-5) excited states of the helium atom. With only 12 PHs, the convergent eigenenergies of 23S, 33S, 43S and 53S states were 2.17427, 2.06849, 2.03644, 2.02257 Eh, respectively. The errors only were 0.00096, 0.00020, 0.00007, 0.00005 Eh, when compared with the exact Hylleraas variational results respectively.     

A Schiff-base cross-linked supramolecular polymer containing diiminophenol compartments and its interaction with copper(II) ions

We report here the preparation of a Schiff-base linked organic polymer 1 based on linkages containing the potent supramolecular aggregator benzene-1,3,5-tricarboxamide, connected through 2,6-diiminophenol metal binding pockets into a cross-linked polymer. The morphological and physical properties of this material are studied using electron microscopy techniques, thermal analysis, NMR, fluorescence spectroscopy and gas adsorption studies. The interaction of the polymer 1 with Cu^II ions is then investigated by soaking the material with methanolic copper acetate solution, and studying the resulting aggregates using EDX microscopy and FTIR spectroscopy. A small-molecule model compound 2 is also prepared and crystallographically characterised to act as a spectroscopic comparison, providing strong evidence that 1 interacts with copper ions through a nucleation/seeding mechanism for the growth of microcrystalline copper acetate deposits, rather than via chemisorption of the copper ions within the diiminophenol binding pockets. Preliminary results suggest a similar mechanism for Co^II adsorption, while Zn^II ions exhibit a separate interaction mode.     

The interaction of silver ions with the isothiocyanatopenta-amminechromium(III) cation

The reaction of the isothiocyanatochromium(III) ion with silver ions produces adducts of the type [Cr(NH₃)₅NCSAg_n]X_n+2. For X = ClO₄, n = 1 and for NO₃, n = 2.     

Kinetics and mechanism of the interaction of hexaaquochromium(III) with octacyanomolybdate(IV) ions

The kinetics of the interaction of hexaaquochromium(III) ion with potassium octacyanomolybdate(IV) have been studied using conductance and spectrophotometric data. The mechanism of the reaction is discussed and the effect of H⁺ ion and the ionic strength on the rate of the reaction determined. The reaction is found to be pseudo-first order with respect to potassium octacyanomolybdate(IV) and inverse first order with [H₃O⁺]. The rate of the reaction increases with increase in ionic strength and temperature. Activation parameters have been calculated using the Arrhenius equation and have the values ΔE^* = 1.3 × 10² kJ mol^?1, ΔH^* = 129 kJ mol^?1, ΔS^* = ?315 e.u., ΔF^* = 2.3 × 10² kJ and A = 1.5 × 10^?3. The mechanism proposed is based on ion-pair formation and the rate equation obtained is given by: k_obs=$\text{[}{}_{\mathrm{kK}}{}_{\mathrm{<mtext>E</mtext>}}\text{[H}{}_3\text{O}{}^{\mathrm{+}}\text{]+}\text{k′K′k}{}_{\mathrm{E}}\text{k}{}_{\mathrm{h}}\text{][Mo(CN)}{}_8{}^{\mathrm{4?}}\text{]}\text{[H}{}_3\text{O}{}^{\mathrm{+}}\text{]+}\text{k}{}_{\mathrm{<mtext>h</mtext>}}\text{+[}\text{K}{}_{\mathrm{<mtext>E</mtext>}}\text{[H}{}_3\text{O}{}^{\mathrm{+}}\text{]+}\text{K′}{}_{\mathrm{E}}\text{k}{}_{\mathrm{h}}\text{][Mo(CN)}{}_8{}^{\mathrm{4?}}\text{]}$     

Chemometric and statistical analysis of polyoxometalate interaction with lanthanide(III) ions

Application of CAT (computer-assisted target factor analysis) for quality assessment and quality control in spectroscopy is demonstrated. As a working example, interaction of polyoxometalates (POM) with neodymium in aqueous solutions is followed by UV-Vis spectroscopy. CAT is combined with Monte Carlo and resampling techniques (i.e. threshold bootstrap methods) in order to capture the complete distribution of suitable interpretations of the systems under study. Decisions during the evaluation process are based on statistical criteria conditional on the empirical distributions obtained from CAT. Single component spectra of the Nd-POM solution species are extracted and species concentrations in the experimental samples are obtained together with their respective confidence limits.     

Voltammetric and spectroscopic studies of the interaction between copper (II) ions with the pesticide carbendazim and its effect in the soil

Journal of Solid State Electrochemistry - The pesticide carbendazim (MBC) has nitrogen and oxygen in their structure which can interact with metal ions. This work evaluated the interaction between...     

Cluster models of interaction of a fluorine atom with the (111) face of silicon

The AMI method has been used in calculating activation energies of desorption of surface complexes from the (111) face of silicon. For the desorption of a surface Si atom, the desorption of an FSi radical containing this Si atom when a fluorine atom implanted in the surface layer is present, and the desorption of the FSi radical when such a fluorine atom is not present, the values found for the activation energy are 8.0, 0.9, and 6.4 eV, respectively.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 2, pp. 144–147, March–April, 1992.     

Accurately solving the electronic Schrodinger equation of atoms and molecules using explicitly correlated (r12-) multireference configuration interaction. VII. The hydrogen fluoride molecule

We compute the potential-energy curve of the hydrogen fluoride molecule (HF) using a novel variant of the explicitly correlated multireference averaged coupled-pair functional method with a carefully selected basis set and reference space. After correcting for scalar relativistic effects and spin-orbit coupling, the potential is used to compute the dissociation energy, the equilibrium bond distance, the harmonic frequency, the anharmonicity, and the vibrational levels up to the dissociation limit. The errors in the equilibrium geometry constants compare favorably with the most elaborate (single reference) calculations of the literature. Starting at the region of RA/angstroms approximately 2,...,3, where the covalent HF bond begins to break and where single-reference methods become impractical, our potential begins to slightly underestimate the atomic interaction, which is reflected in an estimated error in the well depth of -0.2 kcal/mol.     

Helium atom scattering study of the interaction of water with the BaF2(111) surface

The interaction of water with the BaF2(111) single crystal surface is investigated using the helium atom scattering technique. It is found that H2O forms a long-range ordered two-dimensional (2D) phase with (1 x 1) translational symmetry already after an exposure of 3 L (1 L=10(-6) Torr s) at temperatures below 150 K. The activation energy for desorption of the saturated 2D phase, which is assigned to a bilayer, is estimated to be 46+/-2 kJ mol(-1), corresponding to a desorption temperature of 165 K. The desorption of multilayers was observed at 150 K, consistent with a binding energy of 42+/-2 kJ mol(-1). Before completion and after desorption of the saturated 2D phase, a superstructure consistent with a disordered (square root of 3 x square root of 3)R30 degrees lattice has been observed, which is attributed to the first layer of water with a coverage of one molecule per surface unit cell, in accordance with recent theoretical studies. Desorption of this phase is observed at temperatures above 200 K, consistent with an unexpectedly strong bonding of the molecules to the substrate.     

Study on the interaction of platinum(IV), gold(III) and silver(I) ions with DNA

Fluorescence, absorption spectra have been produced by the interaction of platinum(IV), silver(I) and gold(III) ions with the berberine–DNA system (berberine, Scheme 1). Platinum(IV) and gold(III) ions show different effects from that of silver(I) ion on the spectral characteristics of the berberine–DNA system. Quenching fluorescence is seen with platinum(IV) and gold(III) ions addition, whereas increasing fluorescence is observed for silver(I) ions. The addition of gold(III) and silver(I) ions cause an increase in absorption of the berberine–DNA system. The above results suggest that different metal ions exhibit different affinities when binding to DNA correlates well with the ions’ charge, structure and the coordination ability.     

Formation of free radicals during the oxidation of N-methylhydroxyurea with dioxovanadium(V) ions

Unlike the oxidation of hydroxyurea with dioxovanadium(V) ions, which proceeds through the formation of a single free radical, oxidation of N-methylhydroxyurea is characterized by consecutive formation of two oxygen-based free radicals, as recorded by EPR spectroscopy. Although the consumption of overall five V(V) ions per N-methylhydroxyurea molecule has been determined, the formation of NO, or was not observed. These results are in accordance with a previous suggestion that nitric oxide transfer requires an unsubstituted acylhydroxylamine group.     

Study on the interaction of copper-zinc superoxide dismutase with aluminum ions by electrochemical and fluorescent method

The interaction of superoxide dismutase (SOD) with aluminum (Al) ions was investigated by cyclic voltammetry, fluorescence spectroscopy and synchronous fluorescence spectroscopy. The electrochemical activity of the SOD enzyme electrode was inhibited irreversibly by the addition of Al. Meanwhile, the static fluorescence quenching mechanism further revealed the existing of molecular complex of SOD with Al(3+). The association constant was obtained from Lineweaver-Burk plot. The experimental results of voltammetry and fluorescence spectroscopy indicated that the conformation of SOD molecule was altered by the formation of Al-SOD complex. It may influence the activity of SOD enzyme since the optimum action of SOD depends upon a particular configuration of electrostatic charges in the enzyme molecule.     

Valence isoelectronic substitution in the B8(-) and B9(-) molecular wheels by an Al dopant atom: umbrella-like structures of AlB7(-) and AlB8(-)

The structures and the electronic properties of two aluminum-doped boron clusters, AlB(7)(-) and AlB(8)(-), were investigated using photoelectron spectroscopy and ab initio calculations. The photoelectron spectra of AlB(7)(-) and AlB(8)(-) are both broad, suggesting significant geometry changes between the ground states of the anions and the neutrals. Unbiased global minimum searches were carried out and the calculated vertical electron detachment energies were used to compare with the experimental data. We found that the Al atom does not simply replace a B atom in the parent B(8)(-) and B(9)(-) planar clusters in AlB(7)(-) and AlB(8)(-). Instead, the global minima of the two doped-clusters are of umbrella shapes, featuring an Al atom interacting ionically with a hexagonal and heptagonal pyramidal B(7) (C(6v)) and B(8) (C(7v)) fragment, respectively. These unique umbrella-type structures are understood on the basis of the special stability of the quasi-planar B(7)(3-) and planar B(8)(2-) molecular wheels derived from double aromaticity.     

Calculating the energies for Ag(001) twist boundaries utilizing the modified analytical embedded atom method

The unrelaxed energies for Ag(001) twist grain boundaries (GBs) have been calculated using the modified analytical embedded atom method (MAEAM). The results show that, besides zero energy in a perfect crystal (corresponding to the twist angle 0°), the second smallest GB energy corresponds to the twist angle 36.87°. This is consistent with the experimental results. For other twist angles, the GB energies remain nearly constant even for a twist angle as small as 1.94°. Translation parallel to the boundary plane could result in a periodic change in GB energy. Copyright © 2004 John Wiley & Sons, Ltd.     

H-point standard addition method for simultaneous determination of cobalt(II) and zinc(II) ions

The H-point standard addition method (HPSAM) was applied to the simultaneous determination of zinc(II) and cobalt(II). This method is based on the difference in the absorbance of methylthymol blue complexes of Zn(II) and Co(II) at pH 6 using different wavelength pairs. The results showed that Zn(II) and Co(II) can be determined simultaneously with concentration ratios of 20:1 and 1:7.5. Under working conditions, the proposed method was successfully applied to the simultaneous determination of zinc and cobalt in synthetic, drinking water and vitamin samples.