Grid-free DFT implementation of local and gradient-corrected XC functionals

Following an approach to density functional theory calculations based on the matrix representation of operators, we implemented a scheme as an alternative to traditional grid-based methods. These techniques allow integrals over exchange-correlation operators to be evaluated through matrix manipulations. Both local and gradient-corrected functionals can be treated in a similar way. After deriving all the required expressions, selected examples with various functionals are given. Received: 7 March 1998 / Accepted: 21 May 1998 / Published on line: 6 August 1998     

Comparison study of several numerical integration schemes used in calculations of density functional theory

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.     

对含重元素体系的接合二分量-标量相对论密度泛函计算方法

在相对论密度泛函ZORA方法的基础上,提出一种用于含重元素体系的接合二分量-标量相对论密度泛函计算方法.对于只含少数几个重元素的较大体系,仅对其中旋轨耦合作用强的重元素作二分量相对论计算,而对体系的其余部分则作标量相对论计算,通过对动能矩阵元的近似处理实现两种计算的接合.对一系列含6p区重元素分子进行计算的结果表明,当非重元素是第三周期以前的元素时,此方法与二分量ZO-RA方法的计算结果吻合得很好.当非重元素为第四周期元素时,计算结果有一定偏差,表明在后一种情况下旋轨耦合作用已比较显著,但误差仍在目前近似密度泛函计算的精度范围内.此方法可以有效地节省计算量,而且避免了Dyall方法的缺点.     

元素电负性和硬度的密度泛函理论研究

应用密度泛函理论的DFT LDA、DFT LDA/NL和改进的Slater过渡态方法,把元素的电离能和电子亲合能的计算扩展到周期表的103种元素.并用有限差分方法计算了这103种元素的电负性和硬度.计算中考虑了相对论效应.计算结果比以前Robles等用密度泛函理论的XGL和Xα近似的交换相关泛函的计算结果有所改进,更接近实验值.     

Towards an order-N DFT method

One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (the “Fock” matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential. Received: 30 March 1998 / Accepted: 6 July 1998 / Published online: 15 September 1998     

First-principles study of the phonon vibrational spectra and thermal properties of hexagonal MoS2

The phonon spectra and thermal properties of the hexagonal MoS₂ are investigated by using first-principles calculations within the density functional theory (DFT). Finite displacement method is used to calculate the phonon vibrational spectra and phonon density of states. The vibrational modes at the Gamma point are analyzed by using group theory. The temperature and pressure dependence of its thermal quantities such as the thermal expansion, the heat capacity at constant volume, the Gibbs energy and entropy are obtained based on the quasi-harmonic approximation (QHA). Our results show that both the thermal expansion coefficient α and the heat capacity C_V increase with T³ at low temperatures and gradually turn almost linear as the temperature increases. It is found that the entropy is sensitive to the temperature while the Gibbs free energy is more sensitive to the pressure change.     

KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set?

KSSOLV (Kohn-Sham Solver) is a MATLAB (Matrix Laboratory) toolbox for solving the Kohn-Sham density functional theory (KS-DFT) with the plane-wave basis set. In the KS-DFT calculations, the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field (SCF) scheme. To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms, we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox. We compare the performance of KSSOLV-GPU on three types of GPU, including RTX3090, V100, and A100, with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.     

Bringing about matrix sparsity in linear-scaling electronic structure calculations

The performance of linear-scaling electronic structure calculations depends critically on matrix sparsity. This article gives an overview of different strategies for removal of small matrix elements, with emphasis on schemes that allow for rigorous control of errors. In particular, a novel scheme is proposed that has significantly smaller computational overhead compared with the Euclidean norm-based truncation scheme of Rubensson et al. (J Comput Chem 2009, 30, 974) while still achieving the desired asymptotic behavior required for linear scaling. Small matrix elements are removed while ensuring that the Euclidean norm of the error matrix stays below a desired value, so that the resulting error in the occupied subspace can be controlled. The efficiency of the new scheme is investigated in benchmark calculations for water clusters including up to 6523 water molecules. Furthermore, the foundation of matrix sparsity is investigated. This includes a study of the decay of matrix element magnitude with distance between basis function centers for different molecular systems and different methods. The studied methods include Hartree–Fock and density functional theory using both pure and hybrid functionals. The relation between band gap and decay properties of the density matrix is also discussed.     

基于密度泛函理论研究二元排斥Yukawa流体的表面结构性质

基于自由能密度泛函理论(DFT)考察了二元排斥Yukawa (HCRY)流体在不同外场下的密度分布. 基于微扰理论, 体系的Helmholtz自由能泛函采用硬球排斥部分和长程色散部分贡献之和, 其中Kierlik和Rosinberg的加权密度近似(WDA)被用来计算硬球排斥部分, 而色散部分采用平均场理论(MFT)进行描述. 为了验证DFT计算结果的合理性, 研究中采用巨正则Monte Carlo(GCMC)模拟计算了在不同主体相密度、硬核直径和位能参数比的条件下二元HCRY混合流体的密度分布. 结果表明, 该DFT计算结果与GCMC模拟值吻合良好.     

基于平均影响值的反向传播神经网络方法用于提高密度泛函理论计算Y—NO键均裂能精度

将基于平均影响值(Mean impact value,MIV)的反向传播神经网络(Back propagation neural netowrk,BPNN)(MIV-BPNN)方法用于提高密度泛函理论(Density functional theory,DFT)计算Y—NO(Y=N,S,O及C)键均裂能的精度.利用量子化学计算和MIV-BPNN联合方法计算92个含Y—NO键的有机分子体系的均裂能.结果表明,相对于单一的密度泛函理论B3LYP/6-31G(d)方法,利用全参数下的BPNN方法计算92个有机分子均裂能的均方根误差从22.25 kJ/mol减少到1.84 kJ/mol,而MIV-BPNN方法使均方根误差减少到1.36 kJ/mol,可见B3LYP/6-31G(d)和MIV-BPNN联合方法可以提高均裂能的量子化学计算精度,并可预测实验上无法获取的均裂能值.     

Molecular conformations and harmonic force field of 1,3,5-benzenetriol molecule from ab initio and density functional theory investigations

The molecular conformers of the molecule 1,3,5-benzenetriol have been studied by ab initio and density functional methods to determine optimized equilibrium geometries, harmonic vibrational frequencies and relative stability. The results of the quantum-chemical calculations have been used to investigate the functional theory-infrared (FT-IR) spectrum of the 1,3,5-benzenetriol vapors trapped in Ar matrix at 12 K.     

Ab initio studies on the zero-field splitting parameters of manganese porphyrin complexes

The magnetic property of a one-dimensional magnetic chain, 5,10,15,20-tetrakis(4-bromophenyl)porphyrinatomanganese(III) tetracyanoethenide ([MnTBrPP]⁺[TCNE]⁻), is investigated by using model complexes and ab initio calculations. In these models, MnTBrPP is reduced to a manganese porphyrin complex (MnP). The spin-polarized density functional theory (UDFT) and the hybrid UDFT were used to calculate the complexes, and Pederson’s scheme was used to calculate their zero-field splitting (ZFS) parameters. We found from the model calculations that the TCNE coordination hardly affects the magnetic anisotropy of MnP.     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

萤火虫氧化荧光素及其衍生物的电子结构和光物理性质

通过密度泛函理论(DFT)的MPW3PBE泛函, 对萤火虫生物发光底物氧化荧光素及其衍生物进行了结构全优化. 计算了其电离能、 电子亲和势、 空穴抽取能、 电子抽取能、 空穴和电子重组能, 并评估了其空穴和电子传输能力. 采用含时密度泛函理论(TD-DFT)//MPW3PBE/6-31+G(d)方法计算了吸收光谱, 优化了最低单重态S₁, 研究了其荧光光谱, 进而考察了具有较高发光效率的氧化荧光素作为有机发光二极管(OLED)材料的可能性. 计算结果表明, 氧化荧光素及其衍生物可以同时作为电子传输层和发光层材料.     

A combined electrochemical and DFT study of the lattice strain effect on the surface reactivity of Pd

We report a combined study of electrochemical experiments and ab initio calculations on tuning the surface reactivity of Pd via a compressive lattice strain achieved by employing nanoparticles of Pd-Cu alloys with a Pd-rich surface.Surface oxygen-containing species were used as the probing molecule for revealing the surface reactivity.Both density functional theory (DFT) calculations and experiments showed linear relationships,with very close slopes,between the adsorption strength of OH_(ads) and the Pd lattice constant.Not only is this work a successful realization of controllable modulation in the surface reactivity,but it also provides valuable information for the rational design of Pd-based catalysts for fuel cell applications.     

H2S2的构型及其异构化反应的密度泛函理论研究

B3LYP calculations of density functional theory with the 6-311 + G（3df,2p）basis set level are used to investigate the equilibrium structures and intramolecular rearrangement reaction between the linear HSSH and branched H2SS isomers. The predicted geometrical parameters and scaled harmonic vibrational frequencies for HSSH are in good agreement with the available values experimentally. The predicted S-S and S-H bond lengths in the thiosulfoxide structure H2SS are 0.1986 and 0.1366 nm respectively and the values of 5SSH and 5HSH bond angles are 108. 3o and 89. 5o respectively. The transition-state for the unimolecular isomerization is suitably characterized by diagonalizing the matrix of energy second derivatives to determine the unique imaginary vibrational frequency and confirmed by the IRC calculation. The calculated results show that the linear structure is stable with respect to the branched form（lower 109.8 kJ/mol corrected with zero point vibrational energy）energetically. The calculated energy barrier for the direct intramolecular hydrogen atom transfer isomerization process is 190.3 kJ/mol. The kinetic results demonstrate that the isomerization is a unimolecular process,but the reaction rate is pretty slow. This agrees with the thermodynamical results. So the isomerization process should proceed via the other likely processes.     

A general,recursive, and open‐ended response code

We present a new implementation of a recent open‐ended response theory formulation for time‐ and perturbation‐dependent basis sets (Thorvaldsen et al., J. Chem. Phys. 2008, 129, 214108) at the Hartree–Fock and density functional levels of theory. A novel feature of the new implementation is the use of recursive programming techniques, making it possible to write highly compact code for the analytic calculation of any response property at any valid choice of rule for the order of perturbation at which to include perturbed density matrices. The formalism is expressed in terms of the density matrix in the atomic orbital basis, allowing the recursive scheme presented here to be used in linear‐scaling formulations of response theory as well as with two‐ and four‐component relativistic wave functions. To demonstrate the new code, we present calculations of the third geometrical derivatives of the frequency‐dependent second hyperpolarizability for HSOH at the Hartree–Fock level of theory, a seventh‐order energy derivative involving basis sets that are both time and perturbation dependent. © 2014 Wiley Periodicals, Inc.