SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES

In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.

QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

Ultra-deep Removal of Metal Ions from Coal Tar by Complexation:Experimental Studies and Density Functional Theory Simulations

As one of the important aspects of upgrading coal tar,the ultra-deep removal of metal ions via the complexation method was investigated by screening four complexing agents and performing density functional theory(DFT)simulations.Analysis of the compositions and contents of the metallic compounds in the coal tar revealed that the main components were iron and calcium naphthenates.Direct filtration reduced the mechanical impurity content from 0.24%to 0.0752%,indicating that most of the large particles could be easily removed.Among the four complexing agents,namely,acetic acid,oxalic acid,citric acid,and ethylenediaminetetraacetic acid,oxalic acid exhibited the best demetallization performance.The DFT simulations suggested that the high performance of oxalic acid originated from its 1:1 coordination mode,rigid dicarboxyl structure,and greater binding energy.

SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.

Effect of radiolysis of TODGA on the extraction of TODGA/n-dodecane toward Eu(Ⅲ):an experimental and DFT study

N,N,N′,N′-Tetraoctyl diglycolamide(TODGA)is one of the most promising extractants tailored for high-level liquid radioactive waste treatment during nuclear fuel reprocessing.Theγ-radiolysis of TODGA(0.2 mol/L)in n-dodecane(n DD)solution with and without pre-equilibrated 3.0 mol/L HNO_(3)was investigated using HPLC and UPLC-QTOF-MS and compared with theγ-radiolysis of neat TODGA in this study.With increased absorbed doses,the concentration of TODGA decreased exponentially for the studied systems.Moreover,pre-equilibration with HNO_(3)(3.0 mol/L)slightly influenced theγ-radiolysis of TODGA in n DD.Seven radiolytic products generated from the rupture of the C–C,C–O,and C–N bonds in TODGA were identified in the studied extraction system.The influence ofγ-radiation on TODGA/n DD for the extraction of Eu(Ⅲ)was evaluated using the first combination of extraction experiments and density functional theory(DFT)calculations,in which the complexations of Eu(Ⅲ)with TODGA and its radiolytic products were systematically compared.Based on the radiolysis kinetic model of TODGA,the slope curve of the distribution ratio of Eu(Ⅲ)(D_(Eu))and the absorbed dose,and fluorescence titration analysis,the empirical equation of the absorbed dose and D_(Eu)was obtained successfully.Below 300 kGy,the experimental D_(Eu)agreed well with the obtained empirical equation for TODGA/n DD.Conversely,at a high absorbed dose,the experimental D_(Eu)was higher than the theoretical D_(Eu)based on the empirical equation because the radiolytic products of TODGA with similar coordination structures still possessed partial complexation toward Eu(Ⅲ),which was confirmed by DFT calculations.This work provides a method to predict the extraction distribution ratio of an irradiated extractant system and to understand the complex extraction process.

Study of engineering electronic structure modulated non-noble metal oxides for scaled-up alkaline blend seawater splitting

Scaled-up industrial water electrolysis equipment that can be used with abundant seawater is key for affordable hydrogen production.The search for highly stable,dynamic,and economical electrocatalysts could have a significant impact on hydrogen commercialization.Herein,we prepared energy-efficient,scalable,and engineering electronic structure modulated Mn-Ni bimetal oxides(Mn_(0.25)Ni_(0.75)O)through simple hydrothermal followed by calcination method.As-optimized Mn_(0.25)Ni_(0.75)O displayed enhanced oxygen and hydrogen evolution reaction(OER and HER)performance with overpotentials of 266 and115 mV at current densities of 10 mA cm^(-2)in alkaline KOH added seawater electrolyte solution.Additionally,Mn-Ni oxide catalytic benefits were attributed to the calculated electronic configurations and Gibbs free energy for OER,and HER values were estimated using first principles calculations.In real-time practical application,we mimicked industrial operating conditions with modified seawater electrolysis using Mn_(0.25)Ni_(0.75)O‖Mn_(0.25)Ni_(0.75)O under various temperature conditions,which performs superior to the commercial IrO_(2)‖Pt-C couple.These findings demonstrate an inexpensive and facile technique for feasible large-scale hydrogen production.

Fukui Functions for the Temporary Anion Resonance States of Be^-, Mg^-, and Ca^-

In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction with the complex rotation of the Hamiltonian,were used to determine their wave functions.The electron densities,Fukui functions,and values of the hyper-radius<r^2>were computed from these wave functions.The Fukui functions have negative regions in the valence shell in addition to the inner shell regions,indicating screening effects of the outer temporary electron.Selected configuration interactions with up to quadruple excitations were used along the trajectories and for computing the final wave function.Based on this data,the densities,Fukui functions,and<r^2>were calculated.

Control of the Electronic Structure of Manganese Nitrido Complexes by Para Ring Substituents：a Theoretical Study

The relationship between the electronic structures of manganese nitrido complexes and the substituted ligands is investigated by using density functional theory.By designing a series of manganese nitrido complexes [Mn（SalenR）N]＋ with different para ring substituents（R = H,CH_3,NH_2,OCH_3,NMeF,etc） of the ancillary ligand,the properties of manganese-nitrogen bonds were compared for two kinds of electronic structures,of which the radical resides on metal center or the coordinated ring ligand.Our calculation shows that for R = H,CH_3 and NH_2,the [Mn（SalenR）N]＋ complexes have a high-valent Mn（VI） center,and for R = OCH_3 and NMeF,the complexes represent a configuration where the radical delocalizes on the ligand.It is found that the relative energies of these two species depend on electronic properties of the substituent,originating from the intrinsic property of HOMO-LUMO gaps.

UV-Vis Spectrum and the Third-order Nonlinear Optical Properties of the Chiral Camphorderived β-diketonate Platinum Complexes

UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G＊ level. The results showed that the introduction of electron-drawing group -CF3 and -C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of -OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the -C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.

Theoretical Investigation on the Geometries and Properties of Guanine-BX_3 (X = F, Cl) Complex

Geometries and binding energies were predicted at the B3LYP/6-311＋G＊ level for the guanine-BX3 （X = F, Cl） systems and four isomers with no imaginary frequencies have been obtained for both guanine-BF3 and guanine-BCl3, respectively. Single energy calculations using much larger basis sets （6-311＋G（2df, p） and aug-cc-pVDZ were carded out as well. It was found that the most stable isomer of guanine-BF3 is BF3 connected to N3 of guanine with the stabilization energy of-19.93 kcal/mol （BSSE corrected）, while that of guanine-BC13 is BC13 connected to O10 of guanine having stabilization energy of -15.02 kcal/mol at the same level. The analyses for the combining interaction between BX3 and guanine with the atom-in-molecules theory （AIM） and natural bond orbital （NBO） methods have been performed. The results indicated that all the isomers are formed with σ-p type interactions between guanine and BX3, in which pyridine-type nitrogen or carbonyl oxygen or nitrogen atom of amino group offers its lone pair electrons to the empty p orbital of boron atom and the concomitance of charge transfer from guanine to BX3 has occurred. Still, one or two hydrogen bonds exist in some isomers of guanine-BX3 system and contribute to the stability of complex systems. Frequency analysis suggested that the stretching vibration of BX3 undergoes a red shift in complexes. Guanine-BF3 complex is more stable than guanine-BC13 although the B-Y （Y=N, O） bond distance in the latter is shorter.

Ligand Effects in Dinitrogen Hydrogenation of Binuclear Zirconium Complexes

In this work, we report a theoretical exploration of the ground-state electronic structures and molecular vibrational properties of a series of binuclear zirconium complexes in the framework of density functional theory （DFT） employing the B3LYP hybrid functional. The calculated results reveal that the electronic structure of the complex [（η^5-C5Me5）2Zr]2（μ^2, η^2, η^2-N2） is unfavorable for hydrogenation due to the exclusion of side-on dinitrogen in the LUMO＋ 1 molecular orbital as compared with the reactant 1 [（η^5-C5Me4H）2Zr]2（μ2,η^2,η^2-N2）. Besides, the structural feature of the hypothetical intermediate 1′, [（η^5C5Me4H）2Zr]2（μ2,η^2, η^2-N2）-n2, clearly implies the possibility of further hydrogenation. In addition, the distinguishing of vibrational modes of experimental intermediate 2, [（η^5-C5Me4H）2ZrH]2（μ2,η^2,η^2-N2H2）, indicates that the asymmetric stretching of Zr-N and Zr-H leads to dissociation. Moreover, the vibrational intensity of Zr-H is stronger than that of Zr-N. Therefore, it can be predicted that excess hydrogen atmosphere is necessary to ensure the dissociation of Zr-N bonds.

Component spectroscopic properties of light-harvesting complexes with DFT calculations

Photosynthesis is a fundamental process in biosciences and biotechnology that influences profoundly the research in other disciplines.In this paper,we focus on the characterization of fundamental components,present in pigment-protein complexes,in terms of their spectroscopic properties such as infrared spectra,nuclear magnetic resonance,as well as nuclear quadrupole resonance,which are of critical importance for many applications.Such components include chlorophylls and bacteriochlorophylls.Based on the density functional theory method,we calculate the main spectroscopic characteristics of these components for the Fenna-Matthews-Olson light-harvesting complex,analyze them and compare them with available experimental results.Future outlook is discussed in the context of current and potential applications of the presented results.

Theoretical Study on the Structures and Magnetic Properties of Metal String Complexes Containing Rigid Equatorial Ligands [Ni3(L)4(NCS)2] (L = dzp-, mpmpa-, mppda-, mptpa-)

Density functional theory at the BP86 level was used to investigate the influence of equatorial ligands on the Ni–Ni interactions and magnetic coupling properties of metal string complexes [Ni3（L）4（NCS）2] （L represents the rigid equatorial ligands; L = dzp- （1）, mpmpa- （2）, mppda- （3）, mptpa- （4））. The following conclusions can be drawn. （1） With increasing the radius of the connecting atom in the cental ring in equatorial ligands, the two pyridine rings bend down, resulting in the decreasing distance between the two pyridine-nitrogen atoms and the Ni–Ni distance. Therefore, the strength order of the Ni–Ni interaction is 4 〉 2 〉 3 〉 1. The Ni–Ni interactions in 2 and 4 are stronger than those in Ni3（dpa）4（NCS）2 containing no-rigid equatorial ligands. （2） The calculated -Jab is 4 〉 2 〉 3 〉 1. There are two types of magnetic exchange pathways in these complexes： the σ-type pathway through the Ni36＋ chains and the δ-type pathway through the equatorial ligands. The magnetic coupling through the metals is the dominant part. Hence, the magnetic coupling strength increases with increasing the Ni–Ni interaction. Modifying the radius of the connecting atom may be one of the means to fine tuning of magnetic coupling strength of this kind of metal string complexes.

A Density Functional Theory Study of the Hydrates of 2NH_3:H_2SO_4 and Its Implications for the Formation of Atmosphere Particles

Density functional theory was used at the B3LYP/6-311＋＋G（d,p） level of theory to study the hydrates of 2NH3：H2SO4：nH2O for n = 0～4. Neutrals of the most stable clusters, when n = 0 and 1, spontaneously formed and were determined to be hydrogen-bonded molecular complexes of monomeric species. Double ions （clusters containing a NH4＋ cation and a HSO4- anion） or even ternary ions （clusters with two NH4＋ cations and one SO42- anion） spontaneously formed in the most stable clusters of 2NH3：H2SO4：nH2O （n = 2, 3, 4）. The energetics of binding and incremental association was also calculated. Double ions are not energetically favorable until 2NH3：H2SO4：2H2O because of the about equal free energies for forming the neutral （the most stable） and double ion （the second stable） isomers. The free energy of incremental association from free H2O and 2NH3：H2SO4：nH2O has a maximum at n = 2 at room temperature with ΔG ≈ –2 kcal/mol. The comparison of incremental association energies between 2NH3：H2SO4：nH2O, NH3：H2SO4：nH2O and H2SO4：nH2O clusters revealed that NH3 plays an important role in the atmospheric particle nucleation.

Insight of the Structures and Properties on 2-Thioxanthine Complexes with One Hg^(2+)and Two Cl^-Ions:a Theoretical Investigation

The molecular structures of fifteen possible 2-thioxanthine（2TX） complexes with one Hg^2＋ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311＋＋G^＊＊ method. The effective pseudo potential LANL2DZ basis set was used for metal Hg^2＋ion. The vibrational analysis was also carried out at the same level. The bond lengths, bond angles, zero point energies, Gibbs free energies, thermodynamic energies and relative energies of all the complexes were obtained. The NBO analysis for natural charge and the second order perturbation energy values was carried out for three stable complexes and the IR spectroscopy of the two complexes was assigned to the experimental data. The results show that the 2-thioxanthine complexes with one Hg^2＋ and two Cl^-ions were formed and the complexes resulting from the thione tautomer are more stable than that of the thiol ones. The order of three complexes with relative lower energy is 2TX（1,3,7）-Hg^2＋-2, 2 TX（1,3,7）-Hg^2＋-1 and 2 TX（1,3,9）-Hg^2＋. The calculated IR spectroscopy of the two complexes agreed with the experimental data.

Theoretical Studies on the Structure and Spectrum of Imidazole-Chloranil Charge Transfer Complex

分子的建筑群的紫外力的吸收系列由咪唑(Im ) 形成了， chloranil (CA ) 在氯仿被测量。imidazole-chloranil (Im-CA ) 的 stoichiometry 建筑群被使用 Benesi Hildebrand 的方程和工作的连续变化方法作为 1:1 决定。密度功能理论(DFT ) 和 MP2 计算被执行学习结构和 Im-CA 建筑群的有约束力的精力。计算定位了四符合构造(作为 S1 表示了 S4 ) 为 Im-CA，建筑群，连接的二边(Im )-to-face(CA) 和二个边(Im )-to-edge(CA) 连接了。edge-to-face 反对前者比 edge-to-edge 更稳定，这被发现。这些反对前者的结合的特征与自然人口被调查分析(NPA ) ，电子密度的拓扑的分析，和天赋结合轨道(NBO ) 分析。而 edge-to-edge 反对前者是氢契约建筑群， edge-to-face 反对前者是费用转移(CT ) 建筑群，这被揭示。为 Im-CA 建筑群( S1 )的最稳定的符合构造，咪唑 n ( N15 )的费用转移相互作用与 chloranil &#960; 轨道的孤独的对*( C1 = O7 )轨道的戏在 Im-CA 绑定的一个关键角色，并且绑定被 O7 进一步加强... H20 氢债券。建筑群(S1 ) 的电子刺激精力与时间依赖者 DFT (TDDFT ) 被计算，并且建筑群的观察紫外可见的光谱基于计算结果被分析。

Investigation of Structural and Electronic Properties of [Tris(Benzene-1,2-Dithiolato)M]^3-(M = V, Cr, Mn, Fe and Co) Complexes: A Spectroscopic and Density Functional Theoretical Study

In this study, the first raw transition metals from V to Co complexes with benzene-1,2-dithiolate (L2-) ligand have been studied theoretically to elucidate the geometry, electronic structure and spectroscopic properties of the complexes. Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TD-DFT) methods have been used. The ground state geometries, binding energies, spectral properties (UV-vis), frontier molecular orbitals (FMOs) analysis, charge analysis and natural bond orbital (NBO) have been investigated. The geometrical parameters are in good agreement with the available experimental data. The metal-ligand binding energies are 1 order of magnitude larger than the physisorption energy of a benzene-1, 2-dthiolate molecule on a metallic surface. The electronic structures of the first raw transition metal series from V to Co have been elucidated by UV-vis spectroscopic using DFT calculations. In accordance with experiment the calculated electronic spectra of these tris complexes show bands at 522, 565, 559, 546 and 863 nm for V3+, Cr3+, Mn3+, Fe3+ and Co3+ respectively which are mainly attributed to ligand to metal charge transfer (LMCT) transitions. The electronic properties analysis shows that the highest occupied molecular orbital (HOMO) is mainly centered on metal coordinated sulfur atoms whereas the lowest unoccupied molecular orbital (LUMO) is mainly located on the metal surface. From calculation of intramolecular interactions and electron delocalization by natural bond orbital (NBO) analysis, the stability of the complexes was estimated. The NBO results showed significant charge transfer from sulfur to central metal ions in the complexes, as well as to the benzene. The calculated charges on metal ions are also reported at various charge schemes. The calculations show encouraging agreement with the available experimental data.

The Growth Order of Solutions of Systems Complex Difference Equations

In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended.