Accurate finite element method for atomic calculations based on density functional theory and Hartree–Fock method

An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and Hartree–Fock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for , and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchange–correlation potentials to the same cubic Hermite spline functions using a set of recurrence formulas. The total energy of atoms systematically converges from above, and the error algebraically decays as the mesh spacing decreases. When the mesh spacing d is taken to be , the total energy for an atom of atomic number Z can be calculated within error of ¹⁰−7 hartree for both the LDA and HF methods. The equal applicability of the method to DFT and the HF method with a similar degree of high accuracy enables the method to be a reliable platform for development of new functionals in DFT such as hybrid functionals.     

A numerical method for exact diagonalization of semiconductor quantum dot model

An approach to the exact diagonalization of many-electron Hamiltonian in semiconductor quantum dot (QD) structures is proposed. The QD model is based on 3D finite hard-wall confinement potential and nonparabolic effective-mass approximation (EMA) that render analytical basis functions such as Laguerre polynomials inaccessible for the numerical treatment of this kind of models. In this approach, the many-electron wave function is expanded in a basis of Slater determinants constructed from numerical wave functions of the single-electron Hamiltonian with the nonparabolic EMA which results in a cubic eigenvalue problem from a finite difference discretization. The nonlinear eigenvalue problem is solved by using the Jacobi-Davidson method. The Coulomb matrix elements in the many-electron Hamiltonian are obtained by solving Poisson's problems via GMRES. Numerical results reveal that a good convergence can be achieved by means of a few single-electron basis states.     

乙炔基双二茂铁丙烷衍生物的密度泛函理论研究

为揭示取代基对金属有机化合物乙炔基双二茂铁丙烷电子结构的影响,采用密度泛函理论方法模拟计算了乙炔基双二茂铁丙烷及其2个衍生物苯炔基双二茂铁丙烷及二茂铁炔基双二茂铁丙烷的电子结构、前线轨道、电离能(IP)以及电子亲和势(EA),并讨论了取代基对化合物能级和能隙的影响。计算结果表明,电子在基态与激发态间的跃迁,主要是发生在双二茂铁丙烷和乙炔基苯或乙炔基二茂铁之间。取代基为苯基时化合物最高占据轨道(HOMO)能级降低量小于最低空轨道(LUMO)能级降低量,因此二者之间的能隙总体降低。取代基为二茂铁基时化合物HOMO能级增加,LUMO能级降低,从而使HOMO-LUMO能隙降低。结合化合物6-苯炔基双二茂铁丙烷电子亲和势最大以及化合物6-二茂铁炔基双二茂铁丙烷电离能最小,可见苯基取代使炔基双二茂铁丙烷类化合物电子传输能力增强,而二茂铁基取代则可以使该类化合物的空穴传输能力增强,这使炔基双二茂铁丙烷类化合物在功能导电材料方面具有较好的应用前景。     

新型咔唑衍生物密度泛函理论的研究

运用量子化学中的密度泛函和含时密度泛函理论法,计算1种新型咔唑衍生物,以探讨其几何构型、电子结构、前线分子轨道和电子光谱性质。计算结果表明当2-(4-吡啶基)乙烯基的反式构型与咔唑环作用时比顺式稳定,引入取代基后使化合物的HOMO和LUMO之间的能隙降低,吸收光谱红移。电子被激发时,电子从咔唑环向吡啶环转移,说明新型咔唑类化合物具有很好的光学性能,可以作为空穴传输材料。     

8-羟基喹啉衍生物密度泛函理论的研究

运用量子化学中的密度泛函理论(TD-DFT)法,在B3LYP/6-31G(d,p)水平上,理论计算两种新型的8-羟基喹啉衍生物,5-[(4-E-苯乙烯基)-苯甲亚胺基]-8-羟基喹啉(1)和5-[(4-溴-2-氟)苯甲亚胺基]-8-羟基喹啉(2).探讨化合物(1)和(2)的几何构型、电子结构、前线分子轨道和电子光谱性质.结果表明由于引入取代基使体系的HOMO与LUMO之间的能隙降低,增强了与金属铝配位的能力;电子吸收光谱与实验数据基本吻合.     

2-氨基-3H-吩噁嗪-3-酮的溶剂热法合成、晶体结构及密度泛函理论研究

采用溶剂热法合成了2-氨基-3H-吩噁嗪-3-酮,并通过红外光谱、元素分析、x射线单晶衍射进行了结构表征。结构解析表明,该晶体属于单斜晶系,P2₁/c空间群,晶胞参数为a=1.29322（10）nm,b=0.50832（4）nm,c=1.47609（11）nm,β=99.323（1）°,V=957.52（13） A³,Z=4,Dc=1.472 Mg/m³,F（000）=440,μ=0.10 mm^-1,Mr=212.20,最终偏差因子（对I>2σ（I）的衍射点）R₁[F²>2σ（F²）]=0.037,wR₂（F²）=0.097（对全部衍射点）,权重方案w^-1=1/[σ²（Fo²）+（0.0402P）²+0.2667P],P=（Fo²+2Fc²）/3。该化合物分子由3个共轭环形成几乎共平面的结构。应用密度泛函理论DFT方法,结合6-31*基组优化了几何构型,通过同一水平的振荡分析和单点能分析得出热力学参数、净电荷分布和原子轨道对分子轨道的贡献。     

用密度泛函理论研究三价铁掺杂锐钛矿二氧化钛

采用密度泛函理论(DFT)的全势PLAPW方法,通过构造超晶胞模型,按GGA-PW91水平计算,研究Fe(Ⅲ)掺杂锐钛矿TiO_2的电子态密度、化学键性质。结果表明,Fe(Ⅲ)掺杂TiO_2后,Ti-O键长及重叠布居数发生了变化;在费米能级附近,Fe (Ⅲ)周围的O2p轨道发生分裂,并与Fe(Ⅲ)的3d轨道有较明显的重叠,导致Fe(Ⅲ)/TiO_2晶体禁带变窄。     

萘类衍生物荧光发射光谱的密度泛函理论研究

运用密度泛函（DFT）及含时密度泛函（TDDFT）方法对萘类衍生物的荧光发射光谱进行了探讨，发现荧光发射波数υ↑-emit与分子基态能隙△ε以及单电子第一激发能△E成线性关系，运用所得回归方程的预测结果与实验结果符合得较好。对训练样本以外的6种分子的预测结果表明，该回归模型可以用于对萘类衍生物的荧光发射波数υ↑-emit进行预测。     

CO在贵金属Pt(111)表面吸附的密度泛函理论研究

采用密度泛函理论研究CO在Pt(111)表面的吸附位和活化机理。研究采用三维周期结构取代以往的团簇模型,消除金属表面结构选择对计算结果的影响。结果表明,CO在不同的表面活性位吸附后C-O键有不同程度的增长,即C-O键均不同程度地削弱,从而活化CO分子。经比较吸附能、化学键参数和CO重叠布居数,发现在顶位、桥位、hcp空穴位和fcc空穴位4个吸附位中,fcc空穴位是CO的最佳活性位。通过考察原子轨道电子变化,分析CO在Pt(111)表面的吸附活化机理,得到了CO分子在Pt(111)表面吸附的σ／π键作用机理。     

The effects of fluorine substitution on the chemical properties and inhibitory capacity of Donepezil anti-Alzheimer drug; density functional theory and molecular docking calculations

Drug fluorination has the potential to reproduce useful drugs with decreasing the side effect of them. Identifying the effect of this improvement on the chemical properties and biological interactions of drug symbolizes a meaningful progress in drug design. Here the fluorination of Donepezil as an anti-Alzheimer drug, including 7 fluorinated derivatives of it, was investigated computationally. In the first part of our calculations, the most important chemical properties of drug that affects the drug efficiency were investigated by applying the M06/6–31 g (d, p) and M062X/6–31 g (d, p) levels of theories. Findings showed that the fluorine substitution changed the drug stability as altered the solubility and molecular polarity. Furthermore, the intramolecular hydrogen bonding, charge distribution and electron delocalization of the drug were affected by this replacement. In the second section, the effect of fluorination on the drug⋯enzyme interactions was evaluated by using two effective methods Based on the molecular docking and density functional theory (DFT) calculations fluorine substitution influenced the Donepezil⋯Acetylcholinesterase interactions. Calculated binding energies by two computational methods displayed that the fluorine replacement changed the binding affinity of drug. Finally, the most significant non-bonded interactions between drugs and involved residues were investigated by bond length data analysis.     

Block spin density matrix of the inhomogeneous AKLT model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.      

利用多目标量子粒子群算法求解背包问题

提出一种基于博弈论的多目标量子粒子群算法。算法中将每个目标函数看成是一个智能体,智能体控制种群往自己最有利的方向进行搜索,然后将它看成是参与博弈的一个参与人。采用存在一个博弈序列的重复博弈模型,在重复博弈中,并不是每次博弈都产生最大效益,而是要总的效益最大化。将算法用于求解多目标0/1背包问题。仿真实验结果表明,该算法能够找到接近Pareto最优前端的更好的解,同时维持解分布的均匀性。     

脂肪族聚酰胺振动光谱的密度泛函理论研究

采用密度泛函理论DFT-B3LYP方法,在6-31G基组水平上对3种脂肪族聚酰胺尼龙2(PA2),尼龙4(PA4)和尼龙6 (PA6)的低聚物OA2,OA4和OA6构型进行优化,得到基态稳定构型;在优化构型基础上计算了分子振动谐性力场,并对理论谐性力场进行了简正坐标分析,得到了低聚物红外光谱及拉曼光谱,用标度因子0.96对计算频率校正。对照实验值,根据振动模式对其特征峰进行了指认。并讨论了由不同长度亚甲基链组成的聚酰胺对振动光谱的影响。     

密度泛函方法研究辣椒碱分子的结构和性质

辣椒碱(Capsaicin)在医药、农业和反恐装备方面具有广泛的应用前景.本文用密度泛函理论DFT/B3LYP方法,在6-31+G(d,p)基组水平上对其进行了计算.密度泛函理论方法既考虑了电子相关,又较其他组态相互作用或微扰方法节省机时,其计算结果可靠,被广泛应用于研究各类化合物结构性质.本文获得了辣椒碱分子稳定的几何构象和电荷分布,确定O(12)、N(16)、O(19)、C(37)和C(38)原子,可以作为氢键受体;C(18)与O(19)原子形成一对偶极,它们均是关键药效团的活性部位.通过进行分子轨道特征分析,确定苯环区是参加化学反应时的活性部位.进行的自然键轨道分析结果与分子轨道特征分析结论一致.在振动分析的基础上获得分子的振动频率、IR光谱与实验结论一致;在振动分析的基础上,同时获得不同温度下的热力学性质以及温度对热力学性能影响的关系式,其中,当T＞2 542 K时,热容Cp,mθ会随温度的升高而减小,各表达式和热力学量对深入研究辣椒碱分子的其它热力学性质有帮助.探讨了辣椒碱热分解机理,获得该分子热分解时C-N键的断裂能为306.6 kJ·mol-1.本文为研究辣椒碱类化合物的定量构效关系研究提供理论依据.     

Van der Waals density functional calculations of binding in molecular crystals

A recent paper [J. Chem. Phys. 132 (2010) 134705] illustrated the potential of the van der Waals density functional (vdW-DF) method [Phys. Rev. Lett. 92 (2004) 246401] for efficient first-principle accounts of structure and cohesion in molecular crystals. Since then, modifications of the original vdW-DF version (identified as vdW-DF1) have been proposed, and there is also a new version called vdW-DF2 [Phys. Rev. B 82 (2010) 081101(R)], within the vdW-DF framework. Here we investigate the performance and nature of the modifications and the new version for the binding of a set of simple molecular crystals: hexamine, dodecahedrane, C60, and graphite. These extended systems provide benchmarks for computational methods dealing with sparse matter. We show that a previously documented enhancement of non-local correlations of vdW-DF1 over an asymptotic atom-based account close to and a few Å beyond binding separation persists in vdW-DF2. The calculation and analysis of the binding in molecular crystals require appropriate computational tools. In this paper, we also present details on our real-space parallel implementation of the vdW-DF correlation and on the method used to generate asymptotic atom-based pair potentials based on vdW-DF.     

吡嗪类硝基衍生物结构与爆轰性能的DFT研究

采用B3LYP/6-311++G**方法对26种硝基吡嗪类衍生物体系进行了全优化,几何优化结果表明所有优化后的化合物结构均无虚频,为势能面上的稳定结构;采用Monte-Carlo方法理论估算了26种化合物的密度,随着硝基数目的增加,密度增加;并设计等键等电子反应计算了其生成焓及其热力学性质,硝基数目逐渐增加时,Cp、S...     

noloco: An efficient implementation of van der Waals density functionals based on a Monte-Carlo integration technique

The treatment of van der Waals interactions in density functional theory is an important field of ongoing research. Among different approaches developed recently to capture these non-local interactions, the van der Waals density functional (vdW-DF) developed in the groups of Langreth and Lundqvist is becoming increasingly popular. It does not rely on empirical parameters, and has been successfully applied to molecules, surface systems, and weakly-bound solids. As the vdW-DF requires the evaluation of a six-dimensional integral, it scales, however, unfavorably with system size. In this work, we present a numerically efficient implementation based on the Monte-Carlo technique for multi-dimensional integration. It can handle different versions of vdW-DF. Applications range from simple dimers to complex structures such as molecular crystals and organic molecules physisorbed on metal surfaces.     

卟吩结构的HARTREE-FORCK和密度泛函研究比较

采用传统的Hartree-Fock(HF)从头算和密度泛函中的B3LYP和B3PW91方法,选择了不同基组水平(STO-3G,3-21G和6-31G~*)对卟吩结构进行了全几何优化,并对得到的结果相互进行了比较,同时与实验数据进行了对照。结果表明,对于H_2P以及具有类似结构的卟啉衍生物,传统的HF方法得到的几何构型以及相关性质(核磁共振谱,NMR)并不可靠。这种体系中电子相关能是不可忽略的。在B3LYP水平上选用较小的基组3-21G得到的结果与中等基组6-31G~*差别不大,但是最小基组STO-3G得到的优化构型却是一个鞍点结构。