关于偶泛函临界点理论中的空间可分性假设

凭借本文中证明的一个引理,在关于偶泛函临界点的某些定理中,可以去掉空间可分性的假设.

一类拟椭圆边值问题的无穷多个广义解

利用偶泛函的临界点理论，在一定条件下证明了二阶偏微分方程在空间中具有无穷多个广义解．

Ligand Size Effect on PdLn Oxidative Addition with Aryl Bromide： A DFT Study

The process and mechanism of the ligand volume controlled Pd（PR3）2 （PR3=PH3, PMe3, and PtBu3） oxidative addition with aryl bromide were investigated, using density functional theory method with the conductor-like screening model. Association pathway and dissocia-tion pathway were investigated by the comparison of several energies. The cleavage energy of Pd（PR3）2 complex was calculated, as well as the oxidative addition reaction barrier energy of Pd（PR3）n （n=1,2） with aryl bromide in N,N-dimethylformamide solvent. This study proved that the ligands volume possessed a great impact on the mechanism of oxidative addition： less bulky ligand palladium associated with aryl bromide via two donor ligands,but larger bulky ligand palladium coordinated via monoligand.

Infinitely many periodic solutions for second-order Hamiltonian systems

The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.

Mechanistic Study of Palladium-Catalyzed Oxidative C-H/C-H Coupling of Polyfluoroarenes with Simple Arenes

Pd-catalyzed oxidative C-H/C-H coupling reaction is an emerging type of C-H acti- vation reaction, which attracts great interests because both reaction partners do not re- quire pre-functionalization. In the present study, we employed DFT methods to investigate the mechanism of Pd（OAc）2-catalyzed oxidative C-H/C-H coupling of pentafluoroben-zene with benzene. Four possible pathways were examined in the C-H activation part： path A benzene-pentafluorobenzene mechanism （C-H activation of benzene occurs before the C-H activation of pentafluorobenzene）, path B pentafluorobenzene-benzene mechanism （C-H activation of benzene occurs after the C-H activation of pentafluorobenzene）, path C benzene-pentafluorophenylsilver mechanism （C-H activation of benzene and subsequent transmetalation with pentafiuorophenyl silver complex）, path D pentafiuorophenylsilver- benzene mechanism （transmetalation with pentafluorophenyl silver complex and subsequent C-H activation of benzene）. Based on the calculations, the sequences of two C-H activation steps are found to be different in the oxidative couplings of same substrates （i. e. pentafiu- orobenzene and benzene） in different catalytic systems, where the additive Ag salts played a determinant role. In the absence of Ag salts, the energetically favored pathway is path B （i.e. the C-H activation of pentafluorobenzene takes place before the C-H cleavage of benzene）. In contrast, with the aid of Ag salts, the coordination of pentafluorophenylsilver to Pd center could occur easily with a subsequent C-H activation of benzene in the second step, and the second step significantly raises the whole reaction barrier. Alternatively, in the presence of Ag salts, the kinetically preferred mechanism is path C （i. e. the C-H activation of benzene takes place in the first step followed by transmetalation with pentafluorophenyl- silver complex）, which is similar to path A. The calculations are consistent with the H/D exchange experiment and kinetic isotope effects. Thus the present study not only offers a deeper understanding of oxidative C-H/C-H coupling reaction, but also provides helpful insights to further development of more efficient and selective oxidative C-H/C-H coupling reactions.

Reaction mechanism of methyl nitrite dissociation during co catalytic coupling to dimethyl oxalate:A density functional theory study

Dissociation of methyl nitrite is the first step during CO catalytic coupling to dimethyl oxalate followed by hydrogenation to ethyl glycol in a typical coal to liquid process. In this work, the first-principle calculations based on density functional theory were performed to explore the reaction mechanism for the non-catalytic dissociation of methyl nitrite in the gas phase and the catalytic dissociation of methyl nitrite on Pd(111) surface since palladium supported on alpha-alumina is the most effective catalyst for the coupling. For the non-catalytic case, the calculated results show that the CH_3O–NO bond will break with a bond energy of 1.91 eV, and the produced CH_3O radicals easily decompose to formaldehyde, while the further dissociation of formaldehyde in the gas phase is difficult due to the strong C–H bond. On the other hand, the catalytic dissociation of methyl nitrite on Pd(111) to the adsorbed CH_3O and NO takes place with a small energy barrier of 0.03 eV. The calculated activation energies along the proposed reaction pathways indicate that(i) at low coverage, a successive dehydrogenation of the adsorbed CH_3O to CO and H is favored while(ii) at high coverage, hydrogenation of CH_3O to methanol and carbonylation of CH_3O to methyl formate are more preferred. On the basis of the proposed reaction mechanism,two meaningful ways are proposed to suppress the dissociation of methyl nitrate during the CO catalytic coupling to dimethyl oxalate.

Anion Photoelectron Spectroscopy and Density Functional Theory Studies of AuC_(n)^(-/0)(n=3-8):Odd-Even Alternation in Electron Binding Energies and Structures

We measured the photoelectron spectra of AuC_(n)^(-)(n=3-8)and conducted theoretical study on the structures and properties of AuC_(n)^(-/0)(n=3-8).It is found that the photoelectron spectra of AuC_(n)^(-)exhibit odd-even alternation.The spectral features of AuC_(3)^(-),AuC_(5)^(-),and AuC_(7)^(-)are much broader than those of AuC_(4)^(-),AuC_(6)^(-),and AuC_(5)^(-).The vertical detachment energies of AuC_(3)^(-),AuC_(5)^(-),and AuC_(7)^(-)are lower than those of AuC_(4)^(-),AuC_(6)^(-),and AuCs_(8)^(-).The most stable structures of AuC_(n)^(-)(n=3-8)are chain structures.The most stable structures of neutral AuC_(n)(n=3-8)are linear structures except that those of AuC_(3) and AuC_(5) are slightly bent.The calculated∠AuCC angles,Au-C bond lengths,and the charges on Au atom also show odd-even alternations,consistent with the experimental observations.

Theoretical Study of Mechanism and Regioselectivity of 1,3-dipolar Cycloaddition of N-[methyl]-C-[5-nitro-2-furyl] Nitrilimine with Dimethyl 7-oxabicyclo[2,2,1]hepta-2,5-diene-2,3-dicarboxylate

The mechanism and regioselectivity of 1,3-dipolar cycloaddition of N-[methyl]-C-[5-nitro-2-furyl] nitrilimine with dimethyl 7-oxabicyclo[2,2,1]hepta-2,5-diene-2,3-dicarboxylate were investigated using activation energy calculations and density functional theory-based reactivity indexes. The reaction proceeds by an asynchronous concerted mechanism. The calculations are performed at the B3LYP/6-31G（d） level of theory and the obtained results are in agreement with experimental outcome.

Hydrogen-Assisted C-C Coupling on Reaction of CuC3H-Cluster Anion with CO

A fundamental study on C-C coupling,that is the crucial step in the Fischer-Tropsch synthesis(FTS)process to obtain multi-carbon products,is of great importance to tailor catalysts and then guide a more promising pathway.It has been demonstrated that the coupling of CO with the metal carbide can represent the early stage in the FTS process,while the related mechanism is elusive.Herein,the reactions of the CuC3H-and CuC3-cluster anions with CO have been studied by using mass spectrometry and theoretical calculations.The experimental results showed that the coupling of CO with the C3H-moiety of CuC3H can generate the exclusive ion product COC3H-.The reactivity and selectivity of this reaction of CuC3H-with CO are greatly higher than that of the reaction of CuC3-with CO,and this H-assisted C-C coupling process was rationalized by theoretical calculations.

Computational Insights into the Mechanism of the Mo-Catalyzed Deoxygenative Coupling of Aromatic Aldehydes

Mo/o-quinone complexes have shown great capability in promoting deoxygenation of carbonyl groups in the presence of appropriate reducing agents,which yields key Mo-carbene complexes and subsequently undergoes further transformations.However,the detailed mechanistic pathways for the deoxygenation of carbonyl groups with the assistance of additive remain unclear.Herein,a comprehensive density functional theory(DFT)study was performed to gain mechanistic insights into the Mo-catalyzed deoxygenative coupling of aromatic aldehydes to produce diaryl alkenes with the assistance of triphenylphosphine(PPh_(3))as a reductant.Computational results suggest that the Mo(IV)complex(with two o-quinone ligands)is more efficient than the commonly proposed Mo(Ⅱ)complex(with one o-quinone ligand)in mediating the deoxygenation of aromatic aldehyde to yield a critical Mo-carbene intermediate.An outer-sphere stepwise mechanistic pathway is suggested for the PPh3 assisted deoxygenation of aromatic aldehyde,which proceeds through the generation of an adduct with aldehyde via P—O bond formation followed by the breaking of C—O bond of aldehyde to give the key Mo(IV)-carbene intermediate.The commonly proposed oxidative addition of carbonyl group onto Mo(Ⅱ)to form an oxo-Mo-carbene intermediate might not be feasible.After the formation of the Schrock-type Mo(IV)carbene intermediate,a metathesis mechanistic pathway via a[2+2]cycloaddition adduct is reasonable to afford the final product.The factors accounting for the formation of Mo(IV)carbene and the stereo-selectivity of the product are discussed.