Accelerating inverse crystal structure prediction by machine learning: A case study of carbon allotropes

Based on structure prediction method, the machine learning method is used instead of the density functional theory (DFT) method to predict the material properties, thereby accelerating the material search process. In this paper, we established a data set of carbon materials by high-throughput calculation with available carbon structures obtained from the Samara Carbon Allotrope Database. We then trained a machine learning (ML) model that specifically predicts the elastic modulus (bulk modulus, shear modulus, and the Young’s modulus) and confirmed that the accuracy is better than that of AFLOW–ML in predicting the elastic modulus of a carbon allotrope. We further combined our ML model with the CALYPSO code to search for new carbon structures with a high Young’s modulus. A new carbon allotrope not included in the Samara Carbon Allotrope Database, named Cmcm–C24, which exhibits a hardness greater than 80 GPa, was firstly revealed. The Cmcm–C24 phase was identified as a semiconductor with a direct bandgap. The structural stability, elastic modulus, and electronic properties of the new carbon allotrope were systematically studied, and the obtained results demonstrate the feasibility of ML methods accelerating the material search process.     

Erratum to: Superconductivity and spin fluctuations

Based on structure prediction method, the machine learning method is used instead of the density functional theory (DFT) method to predict the material properties, thereby accelerating the material search process. In this paper, we established a data set of carbon materials by high-throughput calculation with available carbon structures obtained from the Samara Carbon Allotrope Database. We then trained a machine learning (ML) model that specifically predicts the elastic modulus (bulk modulus, shear modulus, and the Young’s modulus) and confirmed that the accuracy is better than that of AFLOW-ML in predicting the elastic modulus of a carbon allotrope. We further combined our ML model with the CALYPSO code to search for new carbon structures with a high Young’s modulus. A new carbon allotrope not included in the Samara Carbon Allotrope Database, named Cmcm-C24, which exhibits a hardness greater than 80 GPa, was firstly revealed. The Cmcm-C24 phase was identified as a semiconductor with a direct bandgap. The structural stability, elastic modulus, and electronic properties of the new carbon allotrope were systematically studied, and the obtained results demonstrate the feasibility of ML methods accelerating the material search process.

     

Self-energy correction to momentum-density distribution of positron-electron pairs

Positron two-dimensional angular correlation of annihilation radiation (2D ACAR), i.e., the 2D projection of the electron momentum densities sampled by positron, in Si is employed to verify the prediction of the density functional theory within the local-density approximation (LDA). Carefully conducted test shows that the LDA introduces small but definite discrepancies to the 2D-ACAR anisotropies. Self-energy calculation using the GW method indicates that density-fluctuation contributes anisotropic momentum-density correction and thus improves the agreement between theory and experiment. These results provide valuable annotations to the arguments concerning the accuracy and validity of the LDA and GW schemes.     

氧、硫掺杂六方氮化硼单层的第一性原理计算

采用基于密度泛函理论和投影缀加平面波的第一性原理计算方法, 研究了六方氮化硼单层(h-BN)中的氮原子缺陷(V_N)、氧原子取代氮原子(O_N)和硫原子取代氮原子(S_N)时的几何结构、磁性性质和电子结构.研究发现, V_N和O_N体系形变较小, 而S_N体系形变较大; h-BN本身无磁矩, 但具有N缺陷或者掺杂后总磁矩都是1 μ_B; 同时给出了态密度和能带结构.利用掺杂体系的局域对称性和分子轨道理论解释了相关结果, 尤其是杂质能级和磁矩的产生. 关键词： 六方BN单层 第一性原理计算 密度泛函理论 分子轨道理论     

Optical Properties of Neutral and Charged Low Band Gap Alternating Copolyfluorenes: TD-DFT Investigation

用含时的密度泛函(TD-DFT)方法研究了低带隙的中性和带电的交替共聚芴(Green 1),该化合物是由烷基取代芴和(1,2,5-噻吩基-3,4-硫重氮基)喹喔啉噻吩(T-TDQ-T)单元交替重复组成,对他们的激发态特性用二维(2D)和三维(3D)实空间分析方法做了进一步分析．对于中性的Green 1,分别得到其带隙、键能、激子结合能和核驰豫能．用3D跃迁密度方法对中性和带电的Green 1的跃迁偶极矩进行比较可显示出跃迁偶极矩的取向和强度;用3D电荷差异密度方法显示出激发后的中性和带电的Green 1电荷重新分布和比较,用2D实空间分析方法(跃迁密度矩阵)来研究中性和带电的Green1处于激发态时的电子空穴相干性．中性Green 1的激发态特性分别用TD-DFT和ZINDO两种方法进行了计算,比较得出电子-电子相互作用(在TD-DFT中)对激发态性质的重要影响．     

TiN分子基态(X2Σ)结构和势能函数

应用群论及原子分子反应静力学方法推导了TiN分子基态(X²Σ)的离解极限. 采用不同的密度泛函方法,包括BP86, B3P86, B3LYP, B3PW91, 分别选用不同的基组对TiN分子基态进行结构优化计算.通过比较得出使用BP86方法, 对N原子使用D95V++(d,P)基组和Ti原子使用6-311++G^**基组时,计算得到的平衡几何结构、分子离解能和谐振频率与实验值符合得最好. 并采用最小二乘法拟合改进的Murrell-Sorbie函数得到了相应电子态的完整势能函数. 计算得到的光谱常数与实验光谱数据符合得很好. 关键词： BP86 TiN分子基态 势能函数 光谱常数     

Differentiable programming and density matrix based Hartree–Fock method

Differentiable programming is an emerging programming paradigm that allows people to take derivative of an output of arbitrary code snippet with respect to its input. It is the workhorse behind several well known deep learning frameworks,and has attracted significant attention in scientific machine learning community. In this paper, we introduce and implement a density matrix based Hartree–Fock method that naturally fits into the demands of this paradigm, and demonstrate it by performing fully variational ground state calculation on several representative chemical molecules.     

Interpretation of the electronic spectra of phthalocyanines with transition metals from quantum-chemical calculations by the density functional method

Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of some metal phthalocyanines of transition metals and of their anionic forms with different electron localization are studied quantum chemically. It is shown that, in all the cases studied, calculations using the B3LYP functional with even a comparatively narrow basis set (6–31G) are quite consistent with the previous calculations of the same objects by the ZINDO/S-CI semiempirical method taking into account double excitations. For a number of particular examples, it is shown that a lack of consideration of doubly excited configurations in the calculation of excited states by the TDDFT method can be compensated by the contribution from single excitations, which proves to be more significant due to the presence of the correlation component of the exchange-correlation functional.     

金属铜的晶格结构与热力学性质的第一性原理计算

基于第一性原理,利用密度泛函理论(DFT)和密度泛函的微扰理论(DFPT),以及广义梯度近似(GGA),研究了过渡金属Cu的晶体结构、能量、电子能带和态密度、声子的能带结构和态密度,以及其在298.15K下的热容,体积模量,格林艾森参数和体胀系数等热力学函数并与实验值作了对比.通过分析Cu的晶格几何与能量之间的关系,讨论了金属Cu的固-液相变与晶格声子振动能量之间可能的内在联系,首次提出直接得到Cu熔化温度Tm的静力学方法,研究了熔化温度与压强的关系.计算结果与实验值符合较好,明显优于分子动力学模拟的结果.     

金属铜的晶体结构与热力学性质的第一性原理计算

基于第一性原理,利用密度泛函理论(DFT)和密度泛函的微扰理论(DFPT),以及广义梯度近似(GGA),研究了过渡金属Cu的晶体结构、能量、电子能带和态密度、声子的能带结构和态密度,以及其在298.15 K下的热容,体积模量,格林艾森参数和体胀系数等热力学函数并与实验值作了对比.通过分析Cu的晶格几何与能量之间的关系,讨论了金属Cu的固-液相变与晶格声子振动能量之间可能的内在联系,首次提出直接得到Cu熔化温度T_m的静力学方法,研究了熔化温度与压强的关系.计算结果与实验值符合较好,明显优于分子动力学模拟的结果.     

基于滑动势能面的二维材料原子尺度摩擦行为的量化计算

近年来,二维材料优异的摩擦特性成为人们关注的焦点,然而目前缺乏理论上对其摩擦力进行快速、有效、精确的计算预测方法.本文提出采用密度泛函理论计算真实体系的滑动势能面,利用得到的"数值型势能面"替代传统的解析势函数,并结合Prandtl-Tomlinson模型,量化求解具有复杂形状势能面的真实二维材料体系的摩擦行为.基于该方法,揭示了原子力显微镜实验中观察到的石墨烯Moire纹超晶格结构的双周期"黏-滑"摩擦现象;理论预测了二维材料异质结构的层间超低摩擦现象,相对于同质材料,其静摩擦力和滑动摩擦力均成数量级降低,发现势能面起伏和驱动弹簧刚度均会影响层间相对滑动路径,进而对层间的摩擦行为产生影响.该方法同样可拓展到其他van der Waals作用主导的界面摩擦体系.     

Computational study on the kinetics of OH initiated oxidation of methyl difluoroacetate (CF2HCOOCH3)

The kinetics of hydrogen atom abstraction reactions of methyl difluoroacetate (CF₂HCOOCH₃) by OH radical has been studied by quantum mechanical method. The geometry optimisation and frequency calculation of the titled compound was performed with density functional theory using hybrid meta density functional MPWB1K with 6-31+G(d,p) basis set. Transition states have been determined and intrinsic reaction coordinate (IRC) calculation has been performed to ascertain that the transition from reactants to products was smooth through the corresponding transition state. Energy values are refined by making single point energy calculation at G3B3 level of theory and an energy level diagram is constructed. The standard enthalpies of formation of reactants and other species formed during the reaction were calculated using isodesmic method. The rate constants are calculated using canonical transition state theory and the overall rate constant is determined to be 1.35×10^?13 cm³ molecule^?1 s^?1 at 298 K and 1 atmospheric pressure. Tunnelling has been taken into account in the determination of the rate constant because it plays a critical role at low temperature especially when transfer of hydrogen takes place. The calculated value is found to be in good agreement with the experimentally determined value of 1.48×10^?13 cm³ molecule^?1 s^?1.     

First-principles theory of the EPR g tensor in solids: defects in quartz

A theory for the reliable prediction of the EPR g tensor for paramagnetic defects in solids is presented. It is based on density functional theory and on the gauge including projector augmented wave approach to the calculation of all-electron magnetic response. The method is validated by comparison with existing quantum chemical and experimental data for a selection of diatomic radicals. We then perform the first prediction of EPR g tensors in the solid state and find the results to be in excellent agreement with experiment for the E(1)(prime) and substitutional phosphorus defect centers in quartz.     

DFT study on magnetic interaction in an orbitally degenerate Ti3+ dimer complex

The magnetic interaction in an orbitally degenerate transition metal dimer complex is investigated using a typical example of a d(1)-d(1) dimer complex, the Ti2Cl9(3-) cluster. The local orbital functions are defined by linear combinations of the molecular orbital functions which are calculated by density functional theory (DFT). In the DFT calculation, the Perdew-Burke-Ernzerhof (PBE) functional and hybrid PBE0 functional are utilized. The matrix elements of the effective Hamiltonian of the d-electrons are evaluated by the DFT calculation except for one parameter which is determined by comparing the zero-temperature magnetic susceptibility in the direction along the c axis χ(∥) with the experimental result. By the calculation with the PBE0 functional, the zero-temperature magnetic susceptibility in the perpendicular direction χ(⊥) and the temperature dependence of the susceptibilities in both directions agree with the experiment. On the other hand, by the calculation with the PBE functional, χ(⊥) is smaller than the experimental values because the on-site potential is underestimated.     

Photoinduced Intramolecular Charge Transfer in Donor-acceptor Dyad and Donor-bridge-acceptor Triad

在fullerene-PBTDP-TPA三体体系中的光诱导的分子内电荷转移的实验基础上,分别利用密度泛函理论和含时密度泛函理论以及结合二维、三维实空分析方法对fullerene、PBTDP-TPA二体以及fullerene-PBTDP-TPA三体的基态和激发态的性质进行了理论研究．二维定点表象揭示了激发情况下电子和空穴的相干情况．三维跃迁矩阵展示了跃迁偶极矩的方向和强度,而且三维电荷差密度给出了光诱导的分子内电荷转移的方向和结果．同时,用二维和三维表象的方法对fullerene-PBTDP-TPA三体中光诱导的分子内电荷转移过程进行了验证,揭示了在给予者-桥-接收者三体分子体系中分子内激发时电荷转移的机制．除此之外,还发现直接从给予者到接收者超交换的分子内电荷转移极大地促进了给予者-桥-接收者三体分子体系内的电荷转移．     

钙钛矿(C6H5CH2NH3)2PbBr4拉曼光谱研究

运用激光拉曼光谱实验和密度泛函理论计算研究了450～1 700 cm-1光谱范围内有机-无机杂化钙钛矿材料(C₆H₅CH₂NH₃)₂PbBr₄的振动模式特性。对比实验所得拉曼光谱和理论计算所得拉曼光谱,发现密度泛函理论计算可以很好的模拟(C₆H₅CH₂NH₃)₂PbBr₄有机部分的分子振动模式。同时通过比较分析密度泛函理论计算和参考文献,对450～1 700 cm-1光谱范围内的拉曼峰的分子振动模式进行了初步的归属,并发现该光谱范围内的拉曼峰主要是由(C₆H₅CH₂NH₃)₂PbBr₄分子中有机部分振动所产生的。     

Neural Estimator of Information for Time-Series Data with Dependency

Novel approaches to estimate information measures using neural networks are well-celebrated in recent years both in the information theory and machine learning communities. These neural-based estimators are shown to converge to the true values when estimating mutual information and conditional mutual information using independent samples. However, if the samples in the dataset are not independent, the consistency of these estimators requires further investigation. This is of particular interest for a more complex measure such as the directed information, which is pivotal in characterizing causality and is meaningful over time-dependent variables. The extension of the convergence proof for such cases is not trivial and demands further assumptions on the data. In this paper, we show that our neural estimator for conditional mutual information is consistent when the dataset is generated with samples of a stationary and ergodic source. In other words, we show that our information estimator using neural networks converges asymptotically to the true value with probability one. Besides universal functional approximation of neural networks, a core lemma to show the convergence is Birkhoff’s ergodic theorem. Additionally, we use the technique to estimate directed information and demonstrate the effectiveness of our approach in simulations.     

YH,YD,YT分子基态的结构与势能函数

在Y的有效核势近似下, 对H分别选6-311++G(3df,2pd), AUG-cc-PVTZ, AUG-cc-PVQZ基组, 应用密度泛函理论的B3LYP方法, 优化计算了YH(D,T)分子基态的能量, 平衡结构, 和谐振频率.根据原子分子反应静力学原理, 导出了YH(D,T)分子基态的合理离解极限. 通过优化计算结果和已有的实验和理论数据对比, 得出LANL2TZ/AUG-cc-PVQZ混合基组为对体系进行计算的最优基组. 基于此, 在B3LYP/LANL2TZ/AUG-cc-PVQZ水平对YH(D,T)分子基态的势能面进行了单点能扫描. 并采用最小二乘法拟合得到了相应的Murrell-Sorbie势能函数. 计算出了这些分子的力常数(f₂, f₃, f₄)和光谱常数(B_e, α_e, ω_e, ω_eχ_e, D_e).结果与已有的实验数据符合得很好.