Benchmark values of Shannon entropy for spherically confined hydrogen atom

The information‐theoretic measure of confined hydrogen atom has been investigated extensively in the literature. However, most of them were focused on the ground state and accurate values of information entropies, such as Shannon entropy, for confined hydrogen are still not determined. In this work, we establish the benchmark results of the Shannon entropy for confined hydrogen atom in a spherical impenetrable sphere, in both position and momentum spaces. This is done by examining the bound state energies, the normalization of wave functions, and the scaling property with respect to isoelectronic hydrogenic ions. The angular and radial parts of Shannon entropy in two conjugate spaces are provided in detail for both free and confined hydrogen atom in ground and several excited states. The entropies in position space decrease logarithmically with decreasing the size of confinement, while those in momentum space increase logarithmically. The Shannon entropy sum, however, approaches to finite values when the confinement radius closes to zero. It is also found that the Shannon entropy sum shares same trend for states with similar density distributions. Variations of entropy for nodeless bound states are significantly distinct form those owning nodes when changing the confinement radius.     

Shannon-information entropy sum in the confined hydrogenic atom

The appearance of critical points in the Shannon entropy sum as a function of confinement radius, in ground and excited state confined hydrogenic systems, is discussed. We illustrate that the Coulomb potential in tandem with the hard sphere confinement are responsible for these points. The positions of these points are observed to vary with the intensity of the potential. The effects of the Coulomb potential on the system are further probed, by examining the differences between the densities of the confined atom and those of the particle confined in a spherical box, for the same confinement radius. These differences are quantified by using Kullback-Leibler and cumulative residual Kullback-Leibler distance measures from information theory. These measures detect that the effects of the Coulomb potential are squeezed out of the system as the confinement radius decreases. That is, the confined atom densities resemble the particle in a box ones, for smaller confinement radii. Furthermore, the critical points in the entropy sum lie in the same regions where there are changes in the distance measures, as the atom behaves more particle in a spherical box-like. The analysis is further complemented by examination of the derivative of the entropy sum with respect to confinement radius. This study illustrates the inhomogeneity in the magnitudes of the derivatives of the entropy sum components and their dependence on the Coulomb potential. A link between the derivative and the entropic force is also illustrated and discussed. Similar behaviors are observed when the virial ratio is compared to the entropic power one, as a function of confinement radius.     

内含式化合物X@Al12P12的结构与稳定性研究

采用B3LYP／6—31G*方法,对内含式化合物X@Al12P12(X=Li^0/ ,Na^0/ ,K^0/2 ,Be^0/2 ,Mg^0/2 ,Ca^0/2 ,H和He)的不同对称性构型进行计算,讨论其最稳定构型的几何参数、布居分析、偶极矩、电离势、包含能、频率、HOMO—LUMO能隙和自旋密度．发现X@Al12P12化合物中,客体X=Na^0/ ,K^0/ ,Mg和He几乎处在笼的中心,Be和Ca^0/2 处在中心附近0．033nm的半径内,Li^0/ ,Be^2 ,Mg^2 和H很大程度上偏离笼的中心位置．大部分金属内含式化合物的C3对称性构型稳定．Li^0/ 。,Be^0/2 ,Mg^2 ,Ca^2 和H与其它离子相比更易嵌入笼内形成稳定的内含式化合物．     

Ab initio quantum dynamics with very weak van der Waals interactions: Structure and stability of small Li2(1Sigmag+)-(He)n clusters

The potential energy surface (PES) for the interaction between Li2(1Sigmag+) and 4He has been computed using an accurate, post-Hartree-Fock quantum calculation for its ground electronic state. The orientational anisotropy of the forces and the interplay between repulsive and attractive effects within the PES are analyzed to extract information on the possible existence of bound states in the triatomic system. The structures of a few of the Li2(He)n small clusters are examined by comparing a classical approach with a full quantum one to generate bound configurations and to extract information on the possible spatial arrangements of the smaller clusters via à vis the location of the Li2 dopant. Some significant consequences on the Li2 behavior in larger clusters and droplets are drawn from the above findings.     

The energetics of shooting ions into the dodecahedrane cage

The activation barriers and energy profiles along the inclusion coordinate for the penetration of H+, He, Li+, Be+, Be2+, and Mg2+ into dodecahedrane 1 vary considerably with the nature of the projectile. Using Hartree-Fock and MP2 derived structures and energies, the overall process of creating endohedral X n+@1 complexes is examined in detail.     

A joint experimental and theoretical study of cation-pi interactions: multiple-decker sandwich complexes of ferrocene with alkali metal ions (Li+, Na+, K+, Rb+, Cs+)

A systematic study of cation-pi interactions between alkali metal ions and the cyclopentadienyl ring of ferrocene is presented. The alkali metal (Li+, Na+, K+, Rb+, Cs+) salts of the ditopic mono(pyrazol-1-yl)borate ligand [1,1'-fc(BMe2pz)2]2- crystallize from dimethoxyethane as multiple-decker sandwich complexes with the M+ ions bound to the pi faces of the ferrocene cyclopentadienyl rings in an eta5 manner (fc = (C5H4)2Fe; pz = pyrazolyl). X-ray crystallography of the lithium complex reveals discrete trimetallic entities with each lithium ion being coordinated by only one cyclopentadienyl ring. The sodium salt forms polyanionic zigzag chains where each Na+ ion bridges the cyclopentadienyl rings of two ferrocene moieties. Linear columns [-CpR-Fe-CpR-M+-CpR-Fe-CpR-M+-](infinity) (R = [-BMe2pz]-) are established by the K+, Rb+, and Cs+ derivatives in the solid state. According to DFT calculations, the binding enthalpies of M+-eta5(ferrocene) model complexes are about 20% higher as compared to the corresponding M+-eta6(benzene) aggregates when M+ = Li+ or Na+. For K+ and Rb+, the degree of cation-pi interaction with both aromatics is about the same. The binding sequence along the M+-eta5(ferrocene) series follows a classical electrostatic trend with the smaller ions being more tightly bound.     

Ligand-stabilized aromatic three-membered gold rings and their sandwichlike complexes

Electronic structure calculations (DFT) suggest that ligand-stabilized three-membered gold(I) rings constituting the core structure in a series of cyclo-Au3L(n)H(3-n) (L = CH3, NH2, OH and Cl; n = 1, 2, 3) molecules exhibit aromaticity, which is primarily due to 6s and 5d cyclic electron delocalization over the triangular Au3 framework (s- and d-orbital aromaticity). The aromaticity of the novel triangular gold(I) isocycles was verified by a number of established criteria of aromaticity. In particular, the nucleus-independent chemical shift, NICS(0), the upfield changes in the chemical shifts for Li+, Ag+, and Tl+ cations over the Au3 ring plane, and their interaction with electrophiles (e.g., H+, Li+, Ag+, and Tl+) are indicative for the aromaticity of the three-membered gold(I) rings. Interestingly, unlike the respective substituted derivatives of cyclopropenium cation and the bora-cyclopropene carbacyclic analogues, the aromatic Au3 rings, although exhibit comparable diatropicity, react with electrophiles in a different way affording 1:1 and 2:1 sandwichlike complexes. The bonding in the three-membered gold(I) rings is characterized by a common ring-shaped electron density, more commonly seen in aromatic organic molecules and in "all-metal" aromatics, such as the cyclo-[Hg3]4- tetraanion. Moreover, the cation-pi interactions in the 1:1 and 1:2 sandwichlike complexes formed upon reacting the Au3 rings with electrophiles, depending on the nature of the cation, are predicted to be predominantly electrostatic (Li+, Tl+) or covalent (H+, Ag+). The 1:2 complexes constitute a new class of sandwichlike complexes, which are expected to have novel properties and applications.     

Interaction of low-energy ions and atoms of light elements with a fluorinated carbon molecular lattice

The mechanism of interaction of low-energy atoms and ions of light elements (H, H+, He, Li, the kinetic energy of the particles 2-40 eV) with C6H6, C6F12, C60, and C60F48 molecules was studied by ab initio MD simulations and quantum-chemical calculations. It was shown that starting from 6 A from the carbon skeleton for the "C6H6 + proton" and "C60 + proton" systems, the electronic charge transfer from the aromatic molecule to H+ occurs with a probability close to 1. The process transforms the H+ to a hydrogen atom and the neutral C6H6 and C60 molecules to cation radicals. The mechanism of interaction of low-energy protons with C6F12 and C60F48 molecules has a substantially different character and can be considered qualitatively as the interaction between a neutral molecule and a point charge. The Coulomb perturbation of the system arising from the interaction of the uncompensated proton charge with the Mulliken charges of fluorine atoms results in an inversion of the energies of the electronic states localized on the proton and on the C6F12 and C60F48 molecules and makes the electronic charge transfer energetically unfavorable. On the different levels of theory, the barriers of the proton penetration for the C6F12 and C60F48 molecules are from two to four times lower than those for the corresponding parent systems (C6H6 and C60). The penetration barriers of the He atom and Li+ ion depend mainly on the effective radii of the bombarding particles. The theoretical penetration and escaped barriers for the "Li+ + C60" process qualitatively explain the experimental conditions of synthesis of the Li@C60 complex.     

Shannon entropy as a predictor of avoided crossing in confined atoms

Avoided crossing is one of the unique spectroscopic features of a confined atomic system. Shannon information entropy of the ground state and some of the excited states of confined H atom as a predictor of avoided crossing is studied in this work. This is accomplished by varying the strength of the confinement and examining structure properties like ionization energy and Shannon information entropy. Along with the energy level repulsion at the avoided crossing, Shannon information entropy is also exchanged between the involved states. This work also addresses a question: In addition to that regarding localization, what other property of the system can be extracted from Shannon entropy? Insightful connection is discovered between Shannon entropy and the average value of confinement potential, Coulomb potential, and kinetic energy.     

High-enthalpy hydrogen adsorption in cation-exchanged variants of the microporous metal-organic framework Mn3[(Mn4Cl)3(BTT)8(CH3OH)10]2

Exchange of the guest Mn2+ ions in Mn3[(Mn4Cl)3(BTT)8(CH3OH)10]2 (1-Mn2+; BTT=1,3,5-benzenetristetrazolate) with selected cations results in the formation of isostructural framework compounds 1-M (M=Li+, Cu+, Fe2+, Co2+, Ni2+, Cu2+, Zn2+). Similar to the parent compound, the new microporous materials are stable to desolvation and exhibit a high H2 storage capacity, ranging from 2.00 to 2.29 wt % at 77 K and 900 torr. Measurements of the isosteric heat of adsorption at zero coverage reveal a difference of 2 kJ/mol between the weakest and strongest H2-binding materials, which is attributed to variations in the strength of interaction between H2 molecules and unsaturated metal centers within each framework. The Co2+-exchanged compound, 1-Co2+, exhibits an initial enthalpy of adsorption of 10.5 kJ/mol, the highest yet observed for a microporous metal-organic framework.     

Potentiometric sensor array for the determination of lysine in feed samples using multivariate calibration methods

A potentiometric sensor array has been developed for the determination of lysine in feed samples. The sensor array consists of a lysine biosensor and seven ion-selective electrodes for NH4+, K+, Na+, Ca2+, Mg2+, Li+, and H+, all based on all-solid-state technology. The potentiometric lysine biosensor comprises a lysine oxidase membrane assembled on an NH4+ electrode. Because the selectivity of the lysine biosensor towards other cation species is not sufficient, there is severe interference with the potentiometric response. This poor selectivity can be circumvented mathematically by analysis of the richer information contained in the multi-sensor data. The sensor array takes advantage of the cross-selectivity of lysine for each electrode, which differs from the other species and quantification of lysine in complex feed sample extracts is accomplished with multivariate calibration methods, such as partial least-squares regression. The results obtained are in a reasonable agreement with those given by the standard method for amino acid analysis.     

邻甲氧基羰基苄氧基取代杯[4]芳烃衍生物的合成及其性？…

杯芳烃是继冠醚、环糊精之后的第三代主体分子 [1] .据文献 [2 ,3]报道 ,在杯 [4]芳烃下沿酚氧原子上连接乙酸酯得到的四取代衍生物对 Na+ 有很高的选择性 ,核磁与晶体结构研究均证实这是由于羧酸酯的羰基和酚氧基参与了对 Na+ 的配位 ,而且配位基团所形成的包络空间大小与钠离子相匹配 .一般认为 ,随着包络空间改变 ,对金属离子的识别作用会有所变化[4] .但目前对这方面的工作并没有给予更多的重视 .我们发现 ,用 2 -溴甲基苯甲酸甲酯与杯 [4 ]芳烃反应 ,得到了一种新的四取代杯 [4]芳烃衍生物 2 ,萃取研究结果表明 ,该化合物对钾离子有较…     

Tuning of inter- versus intrachain magnetic interactions in cyano-bridged Ni(II)/M(III) (M = Cr, Fe, Co) chain complexes

The reaction of [M(CN)6]3- (M = Cr3+, Fe3+, Co3+) with the nickel(II) complex of 2,4-diamino-1,3,5-triazin-6-yl-{3-(1,3,5,8,12-pentaazacyclotetradecane)} ([NiL]2+) in excess of ANO3 or ACl (A = Li+, Na+, K+, Rb+, Cs+, NH4+) leads to the cyano-bridged dinuclear assemblies A{[NiL][M(CN)6]}.xH2O (x = 2-5). X-ray structures of Li{[NiL][Cr(CN)6]}.5H2O, NH4{[NiL][Cr(CN)6]}.3.5H2O, K{[NiL][Cr(CN)6]}.4H2O, K{[NiL][Fe(CN)6]}.4H2O, Rb{[NiL][Fe(CN)6]}.3.5H2O, and Cs{[NiL][Fe(CN)6]}.3.5H2O, as well as the powder diffractometry of the entire Fe(III) series, are reported. The magnetic properties of the assemblies are dependent on the monocation A and discussed in detail. New efficient pathways for ferromagnetic exchange between Ni(II) and Fe(III) or Cr(III) are demonstrated. Field dependencies of the magnetization for the Fe(III) samples at low temperature and low magnetic field indicate a weak interchain antiferromagnetic coupling, which is switched to ferromagnetic coupling at increasing magnetic field (metamagnetic behavior). The interchain magnetic coupling can be tuned by the size of the A cations.     

Polarized basis sets of Slater-type orbitals: H to Ne atoms

We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.     

Effect of metal ions (Li+, Na+, K+, Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+) and water coordination on the structure of glycine and zwitterionic glycine

Interactions between metal ions and amino acids are common both in solution and in the gas phase. Here, the effect of metal ions and water on the structure of glycine is examined. The effect of metal ions (Li+, Na+, K+, Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+) and water on structures of Gly.Mn+(H2O)m and GlyZwitt.Mn+(H2O)m (m = 0, 2, 5) complexes have been determined theoretically by employing the hybrid B3LYP exchange-correlation functional and using extended basis sets. Selected calculations were carried out also by means of CBS-QB3 model chemistry. The interaction enthalpies, entropies, and Gibbs energies of eight complexes Gly.Mn+ (Mn+ = Li+, Na+, K+, Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+) were determined at the B3LYP density functional level of theory. The computed Gibbs energies DeltaG degrees are negative and span a rather broad energy interval (from -90 to -1100 kJ mol(-1)), meaning that the ions studied form strong complexes. The largest interaction Gibbs energy (-1076 kJ mol(-1)) was computed for the NiGly2+ complex. Calculations of the molecular structure and relative stability of the Gly.Mn+(H2O)m and GlyZwitt.Mn+(H2O)m (Mn+ = Li+, Na+, K+, Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+; m = 0, 2, and 5) systems indicate that in the complexes with monovalent metal cations the most stable species are the NO coordinated metal cations in non-zwitterionic glycine. Divalent cations Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+ prefer coordination via the OO bifurcated bonds of the zwitterionic glycine. Stepwise addition of two and five water molecules leads to considerable changes in the relative stability of the hydrated species. Addition of two water molecules at the metal ion in both Gly.Mn+ and GlyZwitt.Mn+ complexes reduces the relative stability of metallic complexes of glycine. For Mn+ = Li+ or Na+, the addition of five water molecules does not change the relative order of stability. In the Gly.K+ complex, the solvation shell of water molecules around K+ ion has, because of the larger size of the potassium cation, a different structure with a reduced number of hydrogen-bonded contacts. This results in a net preference (by 10.3 kJ mol(-1)) of the GlyZwitt.K+H2O5 system. Addition of five water molecules to the glycine complexes containing divalent cations Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+ results in a net preference for non-zwitterionic glycine species. The computed relative Gibbs energies are quite high (-10 to -38 kJ mol(-1)), and the NO coordination is preferred in the Gly.Mn+(H2O)5 (Mn+ = Mg2+, Ca2+, Ni2+, Cu2+, and Zn2+) complexes over the OO coordination.     

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.     

Two-dimensional confined hydrogen: An entropy and complexity approach

The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the confinement radius for the 1s, 2s, 2p, and 3d quantum states by means of the main entropy and complexity information-theoretical measures. First, the Shannon entropy and the Fisher information, as well as the associated uncertainty relations, are computed and discussed. Then, the Fisher-Shannon, lopezruiz-mancini-alvet, and LMC-Rényi complexity measures are examined and mutually compared. We have found that these entropy and complexity quantities reflect the rich properties of the electron confinement extent in the two conjugated spaces.     

五元交互体系Li+,Na+,K+//CO32-,Cl--H2O在298.15K的相平衡研究

针对西藏扎布耶盐湖卤水组成,采用等温溶解平衡法研究了五元交互体系Li+,Na+,K+//CO32-,Cl--H2O于298.15K时的相平衡,并绘制了相图(空间立体图和Li2CO3饱和的投影图).结果表明,该五元体系相图含有7个结晶区、13条单变量线和4个无变量点.7个结晶区由6个单盐结晶区和1个复盐结晶区组成,分别为LiCl·H2O,NaCl,KCl,Li2CO3,K2CO3·3/2H2O,Na2CO3·10H2O和NaKCO3·6H2O,没有形成固溶体和天然碱(Na2CO3·NaHCO3·2H2O).4个无变量点标记成K1,K2,K3和K4,所对应的平衡固相盐分别是:Li2CO3+NaKCO3·6H2O+Na2CO3·10H2O+KCl,Li2CO3+NaKCO3·6H2O+K2CO3·3/2H2O+KCl,Li2CO3+NaCl+KCl+LiCl·H2O和Li2CO3+NaCl+Na2CO3·10H2O+KCl.     

Theoretical and experimental study of weakly bound CO2-(pH2)2 trimers

The infrared spectrum of CO(2)-(pH(2))(2) trimers is predicted by performing exact basis-set calculations on a global potential energy surface defined as the sum of accurately known two-body pH(2)-CO(2) (J. Chem. Phys. 2010, 132, 214309) and pH(2)-pH(2) potentials (J. Chem. Phys. 2008, 129, 094304). These results are compared with new spectroscopic measurements for this species, for which 13 transitions are now assigned. A reduced-dimension treatment of the pH(2) rotation has been employed by applying the hindered-rotor averaging technique of Li, Roy, and Le Roy (J. Chem. Phys. 2010, 133, 104305). Three-body effects and the quality of the potential are discussed. A new technique for displaying the three-dimensional pH(2) density in the body-fixed frame is used, and shows that in the ground state the two pH(2) molecules are localized much more closely together than is the case for the two He atoms in the analogous CO(2)-(He)(2) species. A clear tunneling splitting is evident for the torsional motion of the two pH(2) molecules on a ring about the CO(2) molecular axis, in contrast to the case of CO(2)-(He)(2) where a more regular progression of vibrational levels reflects the much lower torsional barrier.     

Ionization potentials of small lithium clusters (Lin) and hydrogenated lithium clusters (LinH)

We present accurate ionization potentials (IPs) for small lithium clusters and hydrogenated lithium clusters (n=1-4), computed using coupled-cluster singles and doubles theory augmented with a perturbative correction for connected triple excitations [CCSD(T)] with the correlation-consistent weighted core-valence quadruple-zeta basis set (cc-pwCVQZ). In some cases the full CCSDT method has been used. Comparison of computed binding energies with experiment for the pure cationic lithium clusters reveals excellent agreement, demonstrating that previous discrepancies between computed and experimentally derived atomization energies for the corresponding neutral clusters are due to the use of an inaccurate experimental IP for Li(4). The experimental IP for Li(4) falls 0.43 eV below our theoretical adiabatic value of 4.74 eV, which should be a lower bound to the measured IP. Our recommended zero-point corrected adiabatic IPs for Li, Li(2), Li(3), Li(4), LiH, Li(2)H, Li(3)H, and Li(4)H are 5.39, 5.14, 4.11, 4.74, 7.69, 3.98, 4.69, and 4.05 eV, respectively. Zero-point vibrationally corrected CCSD(T) atomization energies per atom for Li(2) (+), Li(3) (+), Li(4) (+), LiH(+), Li(2)H(+), Li(3)H(+), and Li(4)H(+) are 0.64, 0.96, 0.90, 0.056, 1.62, 1.40, and 1.40 eV, respectively.