Natural orbitals renormalization group approach to a Kondo singlet

A magnetic impurity embedded in a Fermi sea is collectively screened by a cloud of conduction electrons to form a Kondo singlet below a characteristic energy scale TK,the Kondo temperature,through the mechanism of the Kondo effect.We have reinvestigated the Kondo singlet by means of the newly developed natural orbitals renormalization group(NORG)method.We find that,in the framework of natural orbitals formalism,the Kondo screening mechanism becomes transparent and simple,while the intrinsic structure of a Kondo singlet is clearly resolved.For a single impurity Kondo system in whichever case of either finite size or thermodynamic limit,there exists a single active natural orbital that screens the magnetic impurity dominantly.In the perspective of entanglement,the magnetic impurity is entangled dominantly with the active natural orbital,i.e.,the subsystem formed by the active natural orbital and the magnetic impurity basically disentangles from the remaining system.We have also studied the structures of the active natural orbital respectively projected into real space and momentum space.Moreover,the dynamical properties,represented by one-particle Green’s functions defined at the active natural orbital,are obtained by the correction vector method.Meanwhile,the well-known Kondo resonance is clearly observed in the spectral function at the active natural orbital.To realize the thermodynamic limit,the Wilson chains with the numerical renormalization group approach are employed.

Synthesis,Structure,Fluorescent Property and Natural Bond Orbital(NBO) Analysis of a One-dimensional Cobalt(III) Complex Containing 1,3-Benzenedicarboxylate and 2-Methyldipyrido[3,2-f:2',3'-h]quinoxaline Ligand

A novel metal-organic coordination polymer [Co（m-BDC）（Medpq）·2H2O]n（m-H2BDC = benzene-1,3-dicarboxyalic acid,Medpq = 2-methyldipyrido[3,2-f：2＇,3＇-h]quinoxaline） has been hydrothermally synthesized and structurally characterized by elemental analysis,IR spectrum and single-crystal X-ray diffraction.The title compound crystallizes in monoclinic,space group C2/c with a = 19.986（4）,b = 15.789（3）,c = 16.292（3）（A°）,β = 126.54（3）°,V = 4130.3（14）（A°）^3,C23H18N4O6Co,Mr = 505.34,Dc = 1.625 g·cm^-3,Z = 8,μ = 0.883 mm^-1,F（000） = 2072,the final R = 0.0772 and wR = 0.1428.The crystal structure of complex 1 is an infinite zigzag-like chain of hexacoordinate Co^3＋ ions,in which the Co^3＋ ions are bridged in two coordination modes by m-BDC^2＋ ligands and decorated by Medpq ligands,showing a slightly distorted octahedral geometry.Additionally,the compound shows strong fluorescence in the solid state at room temperature.Natural bond orbital（NBO） analysis is performed by using the NBO method built in Gaussian 03 Program.The calculation results show a covalent interaction between the coordinated atoms and Co^3＋ ions.

Natural Bond Orbital(NBO)Population Analysis,First Order Hyperpolarizabilities and Thermodynamic Properties of Cyclohexanone

The molecular structure of cyclohexanone was calculated by the B3LYP density functional model with 6-31G(d,p)and 6-311++G(d,p)basis set by Gaussian program.The results from natural bond orbital(NBO)analysis have been analyzed in terms of the hybridization of atoms and the electronic structure of the title molecule.The electron density based local reactivity descriptors such as Fukui functions were calculated.The dipole moment(μ)and polarizability(α),anisotropy polarizability(Δα)and first order hyperpolarizability(βtot)of the molecule have been reported.Thermodynamic properties of the title compound were calculated at different temperatures.

The present status and prospects in the research of orbital dynamics and control near small celestial bodies

Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the modeling of dynamics environment and the orbital dynamics mechanism. This paper introduced state-ofthe-art researches, major challenges, and future trends in this field. Three topics are mainly discussed： the gravitational field modeling of irregular-shaped small celestial bodies, natural orbital dynamics and control, and controlled orbital dynamics. Finally, constructive suggestions are made for China’s future space exploration missions.

Structure and Vibrational Spectroscopy of 2-Methylallyl Alcohol

The intramolecular O−H…πhydrogen bond has garnered significant research interest in recent decades.In this work,we utilized the infrared(IR)-vacuum-ultraviolet(VUV)nonresonant ionization detected IR spectroscopy(NRID-IR)method to study the molecular structure of neutral and cationic 2-methylallyl alcohol(MAA,CH_(2)=C(CH_(3))−CH_(2)−OH).Density functional theory calculations revealed five stable neutral and three stable cationic MAA conformers,respectively.Two neutral MAA conformers are expected to have an O−H…πintramolecular hydrogen bond interaction,based on the structural characterization that the OH group is directed toward the C=C double bond.The IR spectra of both neutral(2700−3700 cm^(−1))and cationic MAA(2500−7200 cm^(−1))were measured,and the anharmonic IR spectra were calculated at the B3LYP-D3(BJ)/def2-TZVPP level.The OH stretching vibration frequency of neutral MAA was observed at 3656 cm−1,slightly lower than those of methanol and ethanol.In contrast,the OH stretching vibration of cationic MAA was red-shifted by about 140 cm^(−1)compared to neutral MAA.The interaction region indicator and natural bond orbital analysis suggest that the O−H…πinteraction in neutral MAA is weak,and may not play a major role in stabilizing the neutral MAA.

Non-additivity of Methyl Group in the Single-electron Lithium Bond of H3C… Li-H Complex

The non-additivity of the methyl groups in the single-electron lithium bond was investigated using ab initio calculations at the B3LYP/6-311＋＋G＊＊ and UMP2/6-311＋＋G＊＊ levels. The strength of the interaction in the H3C… LiH, H3CH2C… LiH, （H3C）2HC… LiH, and u v （H3C）3C… LiH complexes was analyzed in term of the geometries, energies, frequency shifts, stabilization energies, charges, and topological parameters. It is shown that （H3C）3C radical with LiH forms the strongest single-electron lithium bond, followed by （H3C）2HC radical, then H3CH2C radical, and H3C radical forms the weakest single-electron lithium bond. A positive non-additivity is present among methyl groups. Natural bond orbital and atoms in molecules analyses were used to estimate such conclusions. Furthermore, there are few linear/nonlinear relationships in the system and the interaction mode of single-electron Li- bond is different from the single-electron H-bond and single-electron halogen bond.

Ab initio Study on Ionization Energies of 3-Amino-1-propanol

Fourteen conformers of 3-amino-1-propanol as the minima on the potential energy surface are examined at the MP2/6-311＋＋G＊＊ level. Their relative energies calculated at B3LYP, MP3 and MP4 levels of theory indicated that two most stable conformers display the intramolecular OH - N hydrogen bonds. The vertical ionization energies of these conformers calculated with ab initio electron propagator theory in the P3/aug-cc-pVTZ approximation are in agreement with experimental data from photoelectron spectroscopy. Natural bond orbital analyses were used to explain the differences of IEs of the highest occupied molecular ortibal of conformers. Combined with statistical mechanics principles, conformational distributions at various temperatures are obtained and the temperature dependence of photoelectron spectra is interpreted.

Ab initio Study of Hyperconjugative Effect on Electronic Wavefunctions of 2-chloroethanol

The electronic structure of five conformers of 2-chloroethanol was studied by ab initio calculations at B3LYP and MP2 levels of theory with aug-cc-pVTZ basis set. The existing hydrogen bond and hyperconjugation effects on the stability of 2-chloroethanol conformers were discussed on the base of natural bond orbital analyses. The result exhibits that hyperconjugation is the main factor to determine the stability of conformers. Such effects on the electron wavefunctions of the highest-occupied molecular orbital （HOMO） of different conformers are demonstrated with electron momentum spectroscopy, exhibiting the obviously different symmetries of the HOMO wavefunctions in momentum space.

Covalent intermolecular interaction of the nitric oxide dimer (NO)_2

Covalent bonds arise from the overlap of the electronic clouds in the internucleus region, which is a pure quantum effect and cannot be obtained in any classical way. If the intermolecular interaction is of covalent character, the result from direct applications of classical simulation methods to the molecular system would be questionable. Here, we analyze the special intermolecular interaction between two NO molecules based on quantum chemical calculation. This weak intermolecular interaction, which is of covalent character, is responsible for the formation of the NO dimer,（NO）2, in its most stable conformation, a cis conformation. The natural bond orbital（NBO） analysis gives an intuitive illustration of the formation of the dimer bonding and antibonding orbitals concomitant with the breaking of the πbonds with bond order 0.5of the monomers. The dimer bonding is counteracted by partially filling the antibonding dimer orbital and the repulsion between those fully or nearly fully occupied nonbonding dimer orbitals that make the dimer binding rather weak. The direct molecular mechanics（MM） calculation with the UFF force fields predicts a trans conformation as the most stable state, which contradicts the result of quantum mechanics（QM）. The lesson from the investigation of this special system is that for the case where intermolecular interaction is of covalent character, a specific modification of the force fields of the molecular simulation method is necessary.

Halogen Bonding or Hydrogen Bonding between 2,2,6,6-Tetramethyl- piperidine-noxyl Radical and Trihalomethanes CHX3 （X=CI, Br, I）

The halogen and hydrogen bonding complexes and trihalomethanes （CHX3, X=C1, Br, I） are between 2,2,6,6-tetramethylpiperidine-noxyl simulated by computational quantum chem- istry. The molecular electrostatic potentials, geometrical parameters and interaction energy of halogen and hydrogen bonding complexes combined with natural bond orbital analysis are obtained. The results indicate that both halogen and hydrogen bonding interactions obey the order CI〈Br〈I, and hydrogen bonding is stronger than the corresponding halogen bond- ing. So, hydrogen bonding complexes should be dominant in trihalomethanes. However, it is possible that halogen bonding complex is competitive, even preponderant, in triiodomethane due to the similar interaction energy. This work might provide useful information on specific solvent effects as well as for understanding the mechanism of nitroxide radicals as a bioprobe to interact with the halogenated compounds in biological and biochemical fields.

Synthesis, Crystal Structure and Theoretical Calculations of a New Co(Ⅱ) Coordination Polymer Based on 5-Nitroisophthalic Acid and Bis(imidazol) Ligands

A new complex[Co（NIPH）（mbix）]n（1,H2NIPH = 5-nitroisophthalic acid,mbix =l,3-bis（imidazol-l-ylmethyl）benzene） has been hydrothermally synthesized and structurally characterized by elemental analysis,IR spectrum,UV spectrum,TG and single-crystal X-ray diffraction.Pink crystals crystallize in the triclinic system,space group P1 with a = 8.3797（8）,b= 10.2522（10）,c= 13.4244（13） A,α=94.820（2）,β=108.105（2）,γ=104.816（2）°,V=1042.84（17） A^3,C（22）H（17）CoN5O6,Mr = 506.34,Dc = 1.613 g/cm^3,F（000） = 518,Z = 2,μ（MoKα） =0.876 mm^（-1）,the final R = 0.0505 and wR = 0.1254 for 3267 observed reflections（I〉2σ（I））.The structure of 1 exhibits a two-dimensional network structure and is extended into a three-dimensional supramolecule through hydrogen bonds and n-n interactions.In addition,Natural Bond Orbital（NBO） analysis was performed by using the PBE0/LANL2 DZ method built in Gaussian 09 Program.The calculation results showed obvious covalent interactions between the coordinated atoms and Co（Ⅱ） ion.

Synthesis,Crystal Structure and Theoretical Calculations of a Nickel(Ⅱ) Coordination Polymer Assembled by 4,4'-Oxydibenzoic Acid and 1,3-Bis(imidazol-1-ylmethyl)-benzene Ligands

A new metal-organic coordination polymer [Ni（oba）（mbix）（H2O）]n·n H2O（H2oba = 4,4‘-oxydibenzoic acid,mbix = 1,3-bis（imidazol-1-ylmethyl）-benzene） 1 has been hydrothermally synthesized and structurally characterized by elemental analysis,IR,TG,UV and single-crystal X-ray diffraction.Green crystals crystallize in the triclinic system,space group P1 with a = 10.1915（18）,b = 11.415（2）,c = 12.314（2）A,α = 74.263（3）,β = 84.545（2）,γ = 74.369（3）o,V = 1327.6（4） A,C28H26N4 Ni O7,Mr = 589.24,Dc = 1.474 g/cm3,F（000） = 612,Z = 2,μ（Mo Kα） = 0.786 mm-1,the final R = 0.0332 and w R = 0.0869 for 4622 observed reflections（I 〉 2σ（I））.The structure of 1 exhibits a one-dimensional chain-like structure.In addition,natural bond orbital（NBO） analysis was performed by the PBE0/LANL2 DZ method in Gaussian 03 Program.The calculation results show obvious covalent interaction between the coordinated atoms and Ni（Ⅱ） ion.

Hydrogen-bonding Interaction of 1,2,3-triazine-waters Complexes

Density functional theory B3LYP method with 6-31＋＋G＊＊ basis was used to optimize the geometries of the ground states for 1,2,3-triazine-（H2O）n（n=1,2,3） complexes. All calculations indicate that the 1,2,3- triazine-water complexes in the ground states have strong hydrogen-bonding interaction, and the complex having a N… .H-O hydrogen bond and a chain of water molecules which is terminated by a O. … .H-C hydrogen bond is the most stable. The H-O stretching modes of complexes are red-shifted relative to that of the monomer. In addition, the Natural bond orbit （NBO） analysis indicates that the intermolecular charge transfer between 1,2,3-triazine and water is 0.0222e, 0.0261e and 0.0273e for the most stable 1：1, 1：2 and 1：3 complexes, respectively. The first singlet （n, π＊） vertical excitation energy of the monomer 1,2,3-triazine and the hydrogen-bonding complexes of 1,2,3-triazine-（H2O）n were investigated by time-dependent density functional theory.

Synthesis,Crystal Structure and Theoretical Calculations of a Manganese(Ⅱ) Coordination Polymer Assembled by 2,5-Thiophenedicarboxylic Acid and 3-(2-Pyridyl)pyrazole Ligands

A new Mn（Ⅱ） complex, [Mn_（0.5）（tdc）0.5（L）]2n（1, H2 tdc = 2,5-thiophenedicarboxylic acid, L = 3-（2-pyridyl）pyrazole）, has been successfully synthesized under hydrothermal conditions. Its structure has been determined by single-crystal X-ray diffraction analysis, elemental analyses, IR, TG and UV spectrum. Single-crystal X-ray diffraction analysis reveals that complex 1 belongs to the orthorhombic system, space group Pnna with a = 11.5184（6）, b = 16.8399（8）, c = 11.7249（5） A^°, V = 2274.26（19） A^°^3, Z = 4, D3c = 1.505 g/cm^3, μ = 0.715 mm^-1, Mr = 515.41, F（000） = 1052, the final R = 0.0336 and w R = 0.0802 with I 〉 2σ（I）. It exhibits a one-dimensional zigzag-chain structure, which was stabilized through intermolecular C–H…O and intramolecular N–H…O hydrogen bonding interactions. Moreover, we analyzed Natural Bond Orbital（NBO） by using the PBE0/LANL2 DZ method built in Gaussian 09 Program. The calculation results showed obvious covalent interaction between the coordinated atoms and Mn（Ⅱ） ion.

Theoretical Study on the Photodegradation Mechanism of Pyrethroid Insecticide Fenvalerate in Water

The photodegradation mechanism of fenvalerate in water has been investigated by density functional theory（DFT）.The geometries of reactants,transition states,intermediates and products are optimized at the B3LYP/6-31G＊ level.The calculated results indicate that the reaction process mainly includes the nucleophilic attack and the substitution reaction by hydroxyl radical to the carbonyl group.By vibrational frequency analysis and intrinsic reaction coordinate（IRC） method,the transition state and its reaction pathway are confirmed.Moreover,the changes of natural population analysis（NPA）,calculated using the Natural bond orbital（NBO） method,are analyzed along with the degradation reaction which can explain the variation of chemical bonds.Additionally,the solvent effect is also investigated and the results show that the reaction preferably takes place in water.

Theoretical Study on the Intermolecular Interactions of Tetrazole Dimers

Tetrazole monomers （Ⅰ, Ⅱ） and all of their possible stable dimers （1, 2, 3, 4, 5, 6, 7 and 8） were fully optimized by DFT method at the B3LYP/6-311＋＋G^＊＊ level. Among the eight dimers, there were two 1H-tetrazole dimers, three 2H-tetrazole dimers and three hetero dimers of 1H-tetrazole and 2H-tetrazole. Vibrational frequencies were calculated to ascertain that each structure was stable （no imaginary frequencies）. The basis set superposition errors （BSSE） are 2.78, 2.28, 2.97, 2.75, 2.74, 2.18, 1.23 and 3.10 kJ/mol, and the zero point energy （ZPE） corrections for the interaction energies are 4.88, 4.18, 3.87, 3.65, 3.54, 3.22, 2.87 and 4.34 kJ/mol for 1, 2, 3, 4, 5, 6, 7 and 8, respectively. After BSSE and ZPE corrections, the greatest corrected intermolecular interaction energy of the dimers is -43.71 kJ/mol. The charge redistribution mainly occurs on the adjacent N-H…N atoms between submolecules. The charge transfer between two subsystems is very small. Natural bond orbital （NBO） analysis was performed to reveal the origin of the interaction. Based on the statistical thermodynamic method, the standard thermodynamic functions, heat capacities （C^0P）, entropies （S^0T） and thermal corrections to enthalpy （H^0T）, and the changes of thermodynamic properties from monomer to dimer in the temperature range of 200.00 K to 700 K have been obtained. 1H-tetrazole monomer can spontaneously turn into two stable dimers at 298.15 K.

A New Cd(Ⅱ) Coordination Polymer Constructed by 3-(2-Pyridyl)pyrazole and 5-Nitroisophthalic Acid：Synthesis, Crystal Structure and Theoretical Calculations

A new coordination polymer, [Cd2（NIPH）（L）2（H2O）]n（1, HL = 3-（2-pyridyl）pyrazole and H2NIPH = 5-nitroisophthalic acid）, has been synthesized. The structure of complex 1 has been characterized by X-ray single-crystal diffraction, elemental analysis, IR spectrum analysis, thermogravimetric analysis and fluorescence spectrum analysis. Complex 1 belongs to the triclinic system, space group P1 with a = 8.9539（6）, b = 11.6252（8）, c = 12.2472（8） A^°, α = 80.011（2）, β = 80.3850（10）, γ = 86.773（2）°, V = 1237.37（14） A^°3, Z = 2, Dc = 1.987 g/cm^3, μ = 1.780 mm^-1, Mr = 740.25, F（000） = 724, the final R = 0.0295 and wR = 0.1015 with I 〉 2σ（I）. Two H2NIPH as monodentate and bidentate ligands and two L ligands link four Cd（Ⅱ） ions to form a tetranuclear subunit. Each pair of the tetranuclear subunits is bridged by NIPH ligands to yield a one-dimensional double-chain structure. Furthermore, the 1D chains are linked into a 3D supramolecular framework with hydrogen bonds and π-π interactions. In addition, we analyzed Natural Bond Orbital（NBO） in using the PBE0/LANL2DZ method built in Gaussian 03 Program. The calculation results indicated the obvious covalent interaction between the coordinated atoms and Cd（Ⅱ） ion.

Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole

The aim of this paper is to understand the common characteristics of the generalized flyby trajectory around natural elongated bodies. Such flyby trajectories provide a short-term mechanism to clear away vicinal objects or temporally capture ejecta into circling orbits. The gravitational potential of elongated bodies is described by a unified approximate model, i.e., the rotating mass dipole which is two point masses connected with a constant massless rod The energy power is used to illustrate the flyby effect in terms of the instantaneous orbital energy. The essential of the single flyby trajectory is studied analytically, and the relationship between the flyby trajectory and its Jacobi integral is also illustrated. Sample trajectories are given to show the variational trend of the energy increment with respect to differen orbital periapsides. The distribution of natural ejecting orbits is presented by varying the parameters of the approximate model.

Hydrothermal Processing,Characterization and Theoretical Calculations of a Copper(Ⅱ) Compound with 1,10-Phenanthroline Derivative Ligand:2-(4-Methoxyphenyl)-1H-imidazo[4,5-f][1,10] Phenanthroline

The metal-organic compound [Cu（MOPIP）2（OH）2] 1（MOPIP = 2-（4-methoxy-phenyl）-1H-imidazo[4,5-f][1,10] phenanthroline） was hydrothermally synthesized and structurally characterized by elemental analysis,Fourier-transformed infrared spectroscopy,thermogravimetric analysis,single-crystal X-ray diffraction and theoretical calculations in Gaussian 03.In the crystal structure,the copper（Cu） atoms are tetra-coordinated with four different nitrogen atoms from two different MOPIP ligands,and the Cu atom is one of the five vertexes of the tetrahedron.Presumably due to the steric bulk of the phenyl ligands,compound 1 adopts a slightly distorted tetrahedral configuration.Moreover,it exhibits a zero-dimensional structure with Cu-MOPIP as the building units.Natural Bond Orbital（NBO） analysis was performed by using the NBO method built in Gaussian 03 Program.The calculation results showed a covalent interaction between the coordinated atoms and Cu（Ⅱ） ion.

Synthesis,Crystal Structure and Theoretical Calculations of a Cadmium Complex Containing 3-Hydroxybenzoic Acid and 1,4-Bis(imidazol-1-yl)-butane

A new complex [Cd（hba）2（bib）]n·nH2O（1,Hhba = 3-hydroxybenzoic acid,bib = 1,4-bis（imidazol-1-yl）-butane） has been hydrothermally synthesized and characterized by elemental analysis,IR spectrum,thermogravimetric analysis,fluorescence spectrum,and singlecrystal X-ray diffraction.Yellow crystal crystallizes in the orthorhombic system,space group Pbca with a = 16.220（5）,b = 14.980（5）,c = 20.521（5） ？,V = 4986（3） ？~3,C（24）H（26）CdN4O7,Mr = 594.89,Dc = 1.585 g/cm^3,μ（Mo Kα） = 0.927 mm^（-1）,F（000） = 2416,Z = 8,the final R = 0.0242 and w R = 0.0589 for 4076 observed reflections（I 〉 2s（I））.In 1,the Cd（Ⅱ） ion takes a six-coordination mode,and bib ligand bridges adjacent Cd（Ⅱ） ions to generate 1D zigzag chains; these neighboring chains are connected by O–H···O hydrogen bonding interactions,producing a 2D folded layered structure.Furthermore,by O–H···O hydrogen bonding between layers and layers,a 3D supramolecular architecture is formed.In addition,we analyzed Natural Bond Orbital（NBO） in using the PBE0/LANL2 DZ method built in Gaussian 03 Program.The calculation results indicated obvious covalent interaction between the coordinated atoms and Cd（Ⅱ） ion.