具有N-各向异性拉普拉斯算子的超线性问题的先验界

通过改进Brezis和Merle的方法,结合Moser-Trudinger不等式,移动平面方法及比较原理,得到了方程-Q_Nu=f(u),u∈W_0~(1,N)(Ω)的正解的先验界,其中Ω是R~N中的一个有界光滑区域,非线性项f至多具有指数型增长.     

Laplace Transform Method for the Ulam Stability of Linear Fractional Differential Equations with Constant Coefficients

Using the Laplace transform method, this paper deals with the Ulam stability of linear fractional differential equations with constant coefficients.     

Prediction of stable BC3N2 monolayer from first-principles calculations: Stoichiometry,crystal structure,electronic and adsorption properties

In this paper, a novel BC₃N₂ monolayer has been found with a graphene-like structure using the developed particle swarm optimization algorithm in combination with ab initio calculations. The predicted structure meets the thermodynamical, dynamical, and mechanical stability requirements. Interestingly, the BC₃N₂ plane shows a metallic character. Importantly, BC₃N₂ has an in-plane stiffness comparable to that of graphene. We have also investigated the adsorption characteristics of CO₂ on pristine monolayer and Mo functionalized monolayer using density functional theory. Subsequently, electronic structures of the interacting systems (CO₂ molecule and substrates) have been preliminarily explored. The results show that Mo/BC₃N₂ has a stronger adsorption capacity towards CO₂ comparing with the pristine one, which can provide a reference for the further study of the CO₂ reduction mechanism on the transition metal-functionalized surface as well as the new catalyst’s design.     

Computational Screening of 3 d Transition Metal Atoms Anchored on Defective Graphene for Efficient Electrocatalytic N2 Fixation

The synthesis of ammonia (NH₃) through the electrochemical reduction of molecular nitrogen (N₂) is a promising strategy for significantly reducing energy consumption compared to traditional industrial processes. Herein, we report the design of a series of monovacancy and divacancy defective graphenes decorated with single 3d transition metal atoms (TM@MVG and TM@DVG; TM=Sc−Zn) as electrocatalysts for the nitrogen-reduction reaction (NRR) aided by density functional theory (DFT) calculations. By comparing energies for N₂ adsorption as well as the free energies associated with *N₂ activation and *N₂H formation, we successfully identified V@MVG, with the lowest potential of −0.63 V, to be an effective catalytic substrate for the NRR in an enzymatic mechanism. Electronic properties, including Bader charges, charge density differences, partial densities of states, and crystal orbital Hamilton populations, are further analyzed in detail. We believe that these results help to explain recent observations in this field and provide guidance for the exploration of efficient electrocatalysts for the NRR.     

Theoretical prediction of the host–guest interactions between novel photoresponsive nanorings and C60: A strategy for facile encapsulation and release of fullerene

A series of photoresponsive‐group‐containing nanorings hosts with 12～14 Å in diameter is designed by introducing different number of azo groups as the structural composition units. And the host–guest interactions between fullerene C₆₀ and those nanoring hosts were investigated theoretically at M06‐2X/6‐31G(d)//M06‐L/MIDI! and wB97X‐D/6‐31G(d) levels. Analysis on geometrical characteristics and host–guest binding energies revealed that the designed nanoring molecule (labeled as 7 ) which is composed by seven azo groups and seven phenyls is the most feasible host for encapsulation of C₆₀ guest among all candidates. Moreover, inferring from the simulated UV‐vis‐NIR spectroscopy, the C₆₀ guest could be facilely released from the cavity of the host 7 via configuration transformation between trans‐form and cis‐form of the host under the 563 nm photoirradiation. Additionally, the frontier orbital features, weak interaction regions, infrared, and NMR spectra of the C₆₀@7 host–guest complex have also been investigated theoretically. © 2015 Wiley Periodicals, Inc.     

4类图完美匹配数目的递推求法

本文研究了4类特殊图完美匹配数目的显式表达式.利用划分,求和,再递推的方法分别给出了图3-n Z4,2-n(2-C6),2-n(2-K4)和3-n(C4-C6)的完美匹配数目的计算公式.     

A novel single‐electron sodium bond system of H3C···Na?Y (YH,OH, F,CCH, CN,and NC)

A novel single‐electron sodium bond system of H₃C···Na? H (I), H₃C···Na? OH(II), H₃C···Na? F(III), H₃C···Na‐CCH(IV), H₃C···Na? CN (V) and H₃C···Na? NC (VI) complexes has been studied by using MP2/6‐311++G** and MP2/aug‐cc‐pVTZ methods for the first time. We demonstrated that the single‐electron sodium bond H₃C···Na? Y formed between H₃C and Na? Y (Y?H, OH, F, CCH, CN, and NC) could induce the Na? Y increased and stretching frequencies of I–IV and VI are red‐shifted, including the Na? N bond in complex V is blue‐shifted abnormally. The interaction energies are calculated at two levels of theory [MP2, CCSD(T)] with different basis. The results shows that the strength of binding bond in group 2 (IV–VI) with π electrons are stronger than that of group 1 (I–III) without π electrons. For all complexes, the main orbital interactions between moieties H₃C and Na? Y are LP₁(C)→LP*₁(Na). By comparisons with some related systems, it is concluded that the strength of single‐electron bond is increased in the order: hydrogen bond < bromine bond < sodium bond < lithium bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On the catalytic mechanism of Pt 4+/? in the oxygen transport activation of N2O by CO

The two-state reaction mechanism of the Pt₄^+/− with N₂O (CO) on the quartet and doublet potential energy surfaces has been investigated at the B3LYP level. The effect of Pt₄ ⁻ anion assistance is analyzed using the activation strain model in which the activation energy (ΔΕ ^≠) is decomposed into the distortion energies (\Updelta E ¹ _\textdist ) (\Updelta E^{ \ne }_{\text{dist}} ) and the stabilizing transition state (TS) interaction energies (\Updelta E ¹ _\textint ) (\Updelta E^{ \ne }_{\text{int}} ) , namely \Updelta E ¹ = \Updelta E ¹ _\textdist + \Updelta E ¹ _\textint \Updelta E^{ \ne } = \Updelta E^{ \ne }_{\text{dist}} + \Updelta E^{ \ne }_{\text{int}} . The lowering of activation barriers through Pt₄ ⁻ anion assistance is caused by the TS interaction \Updelta E ¹ _\textint \Updelta E^{ \ne }_{\text{int}} (−90.7 to −95.6 kcal/mol) becoming more stabilizing. This is attributed to the N₂O π*-LUMO and Pt d HOMO back-donation interactions. However, the strength of the back-donation interactions has significantly impact on the reaction mechanism. For the Pt₄ ⁻ anion system, it has very significant back-bonding interaction (N₂O negative charge of 0.79e), HOMO has 81.5% π* LUMO(N₂O) character, with 3d orbital contributions of 10.7% from Pt₍₃₎ and 7.7% from Pt₍₇₎ near the ⁴TS4 transition state. This facilitates the bending of the N₂O molecule, the N–O bond weakening, and an O⁻(²P) dissociation without surface crossing. For the Pt₄ ⁺ cation system, the strength of the charge transfer is weaker, which leads to the diabatic (spin conserving) dissociation of N₂O: N₂O(¹∑⁺) → N₂(¹∑_g⁺) + O(¹D). The quartet to doublet state transition should occur efficiently near the ⁴TS1 due to the larger SOC value calculated of 677.9 cm⁻¹. Not only will the reaction overcome spin-change-induced barrier (ca. 7 kcal/mol) but also overcome adiabatic barrier (ca. 40.1 kcal/mol).Therefore, the lack of a thermodynamic driving force is an important factor contributing to the low efficiency of the reaction system.     

Inverse hydrogen bonds between SiH_4 and hydrides of Na,Mg and Be

The optimized geometries of the three complexes between MeHn (Me=Na,Mg,Be;n=1 or 2) and SiH4 have been calculated at the B3LYP/6-311++g**,MP2/6-311++g(3df,3pd) and MP2/aug-cc-pvtz levels,respectively.The red-shift inverse hydrogen bonds (IHBs) based on Si-H,an electron donor,were reported.The calculated binding energies with basis set super-position error (BSSE) correction of the three complexes are-5.98,-8.65 and-3.96 kJ mol-1 (MP2/6-311++g(3df,3pd)),respectively,which agree with the results obtained via M...     

乙炔与H2O分子之间的氢键结构与性质

采用B3LYP方法,在6-311++G水平上优化得到了H2O…C2H2氢键复合物的σ-n和H-π型两种稳定构型,并进行频率分析,讨论了相关自然键红外振动光谱的红移现象.采用NBO理论对σ-n和H-π氢键复合物形成过程中的电荷转移的类型进行了分析讨论.分子间的氢键相互作用能结果表明,σ-n型比H-π型氢键复合物更稳定.