Vibrational computations beyond the harmonic approximation: performances of the B3LYP density functional for semirigid molecules

The performances of the B3LYP density functional in the computation of harmonic and anharmonic frequencies were tested using 14 standard basis sets of double and triple zeta quality for a set of semirigid molecules containing from 4 to 12 atoms. The quality of the results is assessed by comparison with the most reliable computations available in the literature. The study reveals that the relatively cheap 6-31+G(d,p) basis set performs a very good job for harmonic frequency calculations and that B3LYP anharmonicities are in close agreement with the reference values irrespective of the basis set used. On these grounds "hybrid force fields" are proposed to achieve the best compromise between computer time and quality of the results.     

Benchmarking approximate density functional theory for s/d excitation energies in 3d transition metal cations

Holthausen has recently provided a comprehensive study of density functional theory for calculating the s/d excitation energies of the 3d transition metal cations. This study did not include the effects of scalar relativistic effects, and we show here that the inclusion of scalar relativistic effects significantly alters the conclusions of the study. We find, contrary to the previous study, that local functionals are more accurate for the excitation energies of 3d transition method cations than hybrid functionals. The most accurate functionals, of the 38 tested, are SLYP, PBE, BP86, PBELYP, and PW91.     

B3LYP,BLYP and PBE DFT band structures of the nucleotide base stacks

DFT crystal orbital (band structure) calculations have been performed for the nucleotide base stacks of cytosine, thymine, adenine, and guanine arranged in DNA B geometry. The band structures obtained with PBE, BLYP, and B3LYP functionals are presented and compared to other related experimental and theoretical results. The influence of the quality of the basis set on the fundamental gap values was also investigated using Clementi's double ζ, 6‐31G and 6‐31G* basis sets. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Accurate heats of formation of polycyclic saturated hydrocarbons predicted by using the XYG3 type of doubly hybrid functionals

Polycyclic saturated hydrocarbons (PSHs) are attractive candidates as hydrocarbon propellants. To assess their potential values, one of the key factors is to determine their energy contents, such as to calculate their heats of formation (HOF). In this work, we have calculated HOFs for a set of 36 PSHs including exo-Tricyclo[5.2.1.0^(2,6)] decane, the principal component of the high-energy density hydrocarbon fuel commonly identified as JP-10. The results from B3LYP, B3LYP-D3BJ, M06-2X, B2PLYP, B2PLYP-D3BJ, and the XYG3 type of doubly hybrid (xDH) functionals are presented. It is demonstrated here that the xDH functionals yield accurate HOFs in good agreement with those from experiments or the G4 theory. In particular, XYGJ-OS, a low scaling xDH functional, is shown to hold the promise for accurate prediction of HOFs for PSHs of larger sizes. © 2018 Wiley Periodicals, Inc.     

Spin quenching of transition metals deposited on MgO insulator and CdO semiconductor density functional calculations

We have analyzed spin quenching of first row transition metals deposited on (001) defect‐free and defect‐containing surfaces of MgO insulator and CdO semiconductor by means of density functional calculations and embedded cluster model. Clusters of moderate sizes were embedded in the simulated Coulomb fields that closely approximate the Madelung fields of the host surfaces, and relaxation of ions that surround the defect sites was taken into account. Spin states of metals deposited on the defect free surfaces were maintained as in the isolated metals except for Ti, V, and Co on MgO, and Ti, V, and Cr on CdO. On the defect containing surfaces, spin states were maintained too except for Fe on MgO, and V and Cr on CdO. The metal‐support interactions stabilize the low spin state of the adsorbed metal with respect to the isolated metal, but the effect was not in general enough to quench the spin. Spin polarization effects tend to preserve the spin states of the adsorbed metals relative to those of the isolated metals. Although charge transfer took place from the adsorbed metal to the insulator surface, it took place the other way round from the semiconductor surface to the adsorbed metal. The encountered variations in magnetic properties were attributed to the smaller band gap of the semiconductor, and the behavior of a single metal atom adsorbed on a particular surface was a result of a competition between Hund's rule for the adsorbed metal and the formation of a chemical bond at the interface. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Enthalpies of formation from B3LYP calculations

We have calculated the geometries, energies, and normal vibrations of 845 compounds containing the elements H, C, N, O, F, Al, Si, P, S, and Cl using hybrid density functional theory in order to investigate the accuracy of atom-additive schemes for predicting enthalpies of formation at 298 K. The results give a more realistic estimate of the accuracy of density functional calculations than some overoptimistic earlier correlations. We have also calculated atom-additive schemes for the zero-point energies and enthalpic corrections to the energies. Remarkably, it is not important to include the vibrational or rotational contributions, which can be estimated well within a purely Born-Oppenheimer regression model.     

The versatility of pentalene coordination to transition metals: a density functional theory investigation

DFT calculations with full geometry optimization have been carried out on a series of real and hypothetical compounds of the type [CpM(C8H6)], [(CO)3M(C8H6)], [M(C8H6)2], [(CpM)2(C8H6)], [[(CO)3M]2(C8H6)], and [M2(C8H6)2] (M = transition metal). The bonding in all the currently known compounds is rationalized, as well as in the (so far) hypothetical stable complexes. Depending on the electron count and the nature of the metal(s), eta2 (predicted), eta3, eta5, eta8, or intermediate coordination modes can be adopted. In the case of the mononuclear species, the most favored closed-shell electron counts are 18 and 16 metal valence electrons (MVE). In the case of the dinuclear species, an electron count of 34 MVEs is most favored. However, other electron counts can be stabilized, especially in the case of dinuclear complexes. Coordinated pentalene should most often be considered as formally being a dianion, but sometimes as a neutral ligand. In the former case it can behave as an aromatic species made of two equivalent fused rings, as a C5 aromatic ring connected to an allylic anion, or even as two allylic anions bridged by a C7=C8 double bond. In the latter case, it can behave as a bond-alternating cyclic polyene or as a C5 aromatic ring connected to an allylic cation.     

结合神经网络方法和扩大训练基组构建新B3LYP泛函

神经网络方法成功地应用于修正密度泛函理论B3LYP方法中的三个参数(a0、ax和ac)以构建新B3LYP交换相关泛函.本文采用包含输入层、隐藏层和输出层的三层式神经网络结构.总电子数、多重度、偶极矩、动能、四极矩和零点能被选为物理描述符.296个能量数据被随机地分成两组,246个能量数据作为训练集以确定神经网络的最优结构和最优突触权重,50个能量数据作为测试集以测试神经网络的预测能力.修正后的三个参数觔0、觔x、觔c从输出层处得到,并用于计算体系的热化学性质如原子化能(AE)、电离势(IP)、质子亲合能(PA)、总原子能(TAE)和标准生成热(ΔfH苓).修正后的计算结果优于传统B3LYP/6-311+G(3df,2p)方法的计算结果.经过神经网络修正后,296个物种的总体均方根偏差从41.0 kJ.mol-1减少到14.2 kJ.mol-1.     

Standard grids for high‐precision integration of modern density functionals: SG‐2 and SG‐3

Density‐functional approximations developed in the past decade necessitate the use of quadrature grids that are far more dense than those required to integrate older generations of functionals. This category of difficult‐to‐integrate functionals includes meta‐generalized gradient approximations, which depend on orbital gradients and/or the Laplacian of the density, as well as functionals based on B97 and the popular “Minnesota” class of functionals, each of which contain complicated and/or oscillatory expressions for the exchange inhomogeneity factor. Following a strategy introduced previously by Gill and co‐workers to develop the relatively sparse “SG‐0” and “SG‐1” standard quadrature grids, we introduce two higher‐quality grids that we designate SG‐2 and SG‐3, obtained by systematically “pruning” medium‐ and high‐quality atom‐centered grids. The pruning procedure affords computational speedups approaching a factor of two for hybrid functionals applied to systems of atoms, without significant loss of accuracy. The grid dependence of several popular density functionals is characterized for various properties. © 2017 Wiley Periodicals, Inc.     

Density functionals in the presence of magnetic field

In this article, density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density ρ and paramagnetic current density j^p. This approach is motivated by an adapted version of the Vignale and Rasolt formulation of current density functional theory, which establishes a one‐to‐one correspondence between the nondegenerate ground‐state and the particle and paramagnetic current density. Definition of N‐representable density pairs (ρ,j^p) is given and it is proven that the set of v‐representable densities constitutes a proper subset of the set of N‐representable densities. For a Levy–Lieb‐type functional Q(ρ,j^p), it is demonstrated that (i) it is a proper extension of the universal Hohenberg–Kohn functional to N‐representable densities, (ii) there exists a wavefunction ψ₀ such that , where H₀ is the Hamiltonian without external potential terms, and (iii) it is not convex. Furthermore, a convex and universal functional F(ρ,j^p) is studied and proven to be equal the convex envelope of Q(ρ,j^p). For both Q and F, we give upper and lower bounds. © 2014 Wiley Periodicals, Inc.     

Comparison of HF,HF + MP2, LDA,BLYP, and B3LYP band structures of the homopolypeptides

Ab initio HF, HF + MP2, LDA DFT, BLYP DFT, and B3LYP DFT calculations are compared in the case of 19 homopolypeptides in their β pleated sheet conformation. The results show that the B3LYP method provides good results for the fundamental gaps, as compared with the values estimated on the basis of available UV spectra and intermediate exciton calculations for PolyGly and PolyAla. The HF method gives the best agreement, using Koopman's theorem for the ionization potential, taking the calculated VB_max values in the HF case if one compares them with the experimental ionization potentials of the 19 amino acids measured by mass spectroscopy. Finally, how these methods might be improved to determine the most stable conformations of the homopolypeptides is outlined. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

统计方法校正O3LYP方法计算的生成热

由于引入各种内在近似, 密度泛函理论存在固有误差. 本文采用O3LYP/6-311+G(3df, 2p)//O3LYP/6-31G(d)计算了220个中小型有机分子的生成热(Δ_fH_calc^Θ), 随后应用神经网络(ANN)和多元线性回归(MLR)方法对Δ_fH_calc^Θ进行校正. 采用计算得到的生成热、零点能、分子中原子总数、氢原子个数、双中心成键电子数、双中心反键电子数、单中心价层孤对电子数、单中心内层电子数作为ANN和MLR的描述符. 以180个分子作为训练集构造ANN或MLR模型, 并对40 个独立测试集分子的Δ_fH_calc^Θ进行了预测. 结果表明: 经过ANN和MLR校正后,训练集分子生成热的理论计算值和实验值间的均方根偏差(RMSD)从24.7 kJ·mol^-1分别降低到11.8、13.0 kJ·mol^-1; 独立测试集分子的RMSD从21.3 kJ·mol^-1分别降低到10.4、12.1 kJ·mol^-1. 因此ANN模型的拟合和预测能力要明显优于MLR模型.     

A theoretical study on the structures and energetics of hypothetical TiM(NCN)3 compounds of the 3d transition metals

Quasi-ternary cyanamides and carbodiimides of general formula AB(NCN)(3) with A not equal B have neither been predicted nor synthesized. Thus, hypothetical compounds of that kind containing 3d transition metals were considered (A = Ti, B = Mn, Fe, Co, Ni, Cu) by means of density-functional calculations on 34 structural models, most of which were derived from chemically related phases. After performing structure optimizations based on the local-density approximation, the relative energetic orderings are rationalized in terms of geometrical factors such as molar volumes and polyhedral connections. Total-energy generalized-gradient calculations evidence that the most stable models are enthalpically favored with respect to the elements. Even at ambient temperatures, the ternary phases are predicted as being thermodynamically stable in terms of their Gibbs free formation energies, especially if energetically competing and low-lying binaries (TiC, TiN) can be excluded by a kinetic reaction control. The best models are characterized by low-spin magnetic transition metals found in octahedral coordination, and the TiN(6) and MN(6) polyhedra either share faces or edges.     

Development of new pseudopotential methods: improved model core potentials for the first-row transition metals

We have recently developed new nonrelativistic and scalar-relativistic pseudopotentials for the first-row transition metal and several main-group elements. These improved Model Core Potentials were tested on a variety of transition metal complexes to determine their accuracy in reproducing electronic structures, bond lengths, and harmonic vibrational frequencies with respect to both all-electron reference data as well as experimental data. The new potentials are also compared with the previous model core potentials available for the first-row transition metals. The new potentials do a superior job at reproducing atomic data, reproduce molecular data as well as the previous version, and in conjunction with new main-group pseudopotentials that have L-shell structure of the valence basis set, they are slightly faster.     

On the NH3+HCO3H→HCOOH+H3NO mechanism: a density functional theory study

The B1LYP, B3LYP and MPW1PW91 density functional theory methods combined with the 6-311G(2d, 2p) basis set were used to carry out a density functional theory study of the NH₃+HCO₃H→HCOOH+H₃NO reaction. The purpose of this work is to study the reaction mechanism from the viewpoint of bond order transformations throughout the course of the reaction, and propose the reasons for the apparent differences in activation barriers.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Fitting elephants in the density functionals zoo: Statistical criteria for the evaluation of density functional theory methods as a suitable replacement for counting parameters

Counting parameters has become customary in the density functional theory community as a way to infer the transferability of popular approximations to the exchange‐correlation functionals. Recent work in data science, however, has demonstrated that the number of parameters of a fitted model is not related to the complexity of the model itself, nor to its eventual overfitting. Using similar arguments, here, we show that it is possible to represent every modern exchange‐correlation functional approximations using just one single parameter. This procedure proves the futility of the number of parameters as a measure of transferability. To counteract this shortcoming, we introduce and analyze the performance of three statistical criteria for the evaluation of the transferability of exchange‐correlation functionals. The three criteria are called Akaike information criterion, Vapnik‐Chervonenkis criterion, and cross‐validation criterion and are used in a preliminary assessment to rank 60 exchange‐correlation functional approximations using the ASCDB database of chemical data.