Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators

We report the first implementation of the calculation of electronic g-tensors by density functional methods with hybrid functionals. Spin-orbit coupling is treated by the atomic meanfield approximation. g-Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3-type (B3PW91) and BH-type (BHPW91) hybrid functionals. For main group radicals, the effect of exact-exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient-corrected functionals tend to underestimate the "paramagnetic" contributions to the g-tensors in these cases and thereby recover only about 40-50% of the range of experimental g-tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half-and-half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g-tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g-tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin-orbit contributions to the g-tensor are discussed.     

The role of range-separated Hartree-Fock exchange in the calculation of magnetic exchange couplings in transition metal complexes

We assess the dependence of magnetic exchange couplings on the variation of Hartree-Fock exchange (HFX) admixture in global hybrid functionals and the range-separation parameter ω in range-separated hybrid functionals in a set of 12 spin-1/2 binuclear transition metal complexes. The global hybrid PBEh (hybrid Perdew-Burke-Ernzerhof) and range-separated hybrids HSE (Heyd-Scuseria-Ernzerhof) and LC-ωPBE (long-range corrected hybrid PBE) are employed for this assessment, and exchange couplings are calculated from energy differences within the framework of the spin-projected approach. It is found that these functionals perform optimally for magnetic exchange couplings with 35% HFX admixture for PBEh, ω = 0.50 a.u.(-1) for LC-ωPBE, and ω at or near 0.0 a.u.(-1) for HSE (which corresponds to PBEh). We find that in their standard respective forms, LC-ωPBE slightly outperforms PBEh, while PBEh with 35% HFX yields exchange couplings closer to experiment than those of LC-ωPBE with ω = 0.50 a.u.(-1). Additionally, we show that the profile of exchange couplings with respect to ω in HSE is appreciably flat from 0 to 0.2 a.u.(-1). This combined with the fact that HSE is computationally more tractable than global hybrids makes HSE an attractive alternative for the evaluation of exchange couplings in extended systems. These results are rationalized with respect to how varying the parameters within these functionals affects the delocalization of the magnetic orbitals, and conclusions are made regarding the relative importance of range separation versus global mixing of HFX for the calculation of exchange couplings.     

Hybrid density functional theory band structure engineering in hematite

We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.     

A simple model for the Slater exchange potential and its performance for solids

A simple local model for the Slater exchange potential is determined by least square fit procedure from Hartree–Fock (HF) atomic data. Since the Slater potential is the exact exchange potential yielding HF electron density from Levy‐Perdew‐Sahni density functional formalism (Levy et al., Phys. Rev. A 1984, 30, 2745), the derived local potential is significantly more negative than the conventional local density approximation. On the set of 22 ionic, covalent and van der Waals solids including strongly correlated transition metal oxides, it has been demonstrated, that this simple model potential is capable of reproducing the band gaps nearly as good as popular meta GGA potentials in close agreement with experimental values.     

Theoretical study of CeO2 and Ce2O3 using a screened hybrid density functional

The predicted structures and electronic properties of CeO(2) and Ce(2)O(3) have been studied using conventional and hybrid density functional theory. The lattice constant and bulk modulus for CeO(2) from local (LSDA) functionals are in good agreement with experiment, while the lattice parameter from a generalized gradient approximation (GGA) is too long. This situation is reversed for Ce(2)O(3), where the LSDA lattice constant is much too short, while the GGA result is in reasonable agreement with experiment. Significantly, the screened hybrid HSE functional gives excellent agreement with experimental lattice constants for both CeO(2) and Ce(2)O(3). All methods give insulating ground states for CeO(2) with gaps for the 4f band lying between 1.7 eV (LSDA) and 3.3 eV (HSE) and 6-8 eV for the conduction band. For Ce(2)O(3) the local and GGA functionals predict a semimetallic ground state with small (0-0.3 eV) band gap but weak ferromagnetic coupling between the Ce(+3) centers. By contrast, the HSE functional gives an insulating ground state with a band gap of 3.2 eV and antiferromagnetic coupling. Overall, the hybrid HSE functional gives a consistent picture of both the structural and electronic properties of CeO(2) and Ce(2)O(3) while treating the 4f band consistently in both oxides.     

Structural and electronic properties of ZrX2)and HfX2 (X=S and Se) from first principles calculations

Early transition metal dichalcogenides (TMDC), characterized by their quasi-two-dimensional layered structure, have attracted intensive interest due to their versatile chemical and physical properties, but a comprehensive understanding of their structural and electronic properties from a first-principles point of view is still lacking. In this work, four simple TMDC materials, MX(2) (M = Zr and Hf, X = S and Se), are investigated by the Kohn-Sham density functional theory (KS-DFT) with different local or semilocal exchange-correlation (xc) functionals and many-body perturbation theory in the GW approximation. Although the widely used Perdew-Burke-Ernzelhof (PBE) generalized gradient approximation (GGA) xc functional overestimates the interlayer distance dramatically, two newly developed GGA functionals, PBE-for-solids (PBEsol) and Wu-Cohen 2006 (WC06), can reproduce experimental crystal structures of these TMDC materials very well. The GW method, currently the most accurate first-principles approach for electronic band structures of extended systems, gives the fundamental band gaps of all these materials in good agreement with the experimental values obtained from optical absorption. The minimal direct gaps from GW are systematically larger than those measured from thermoreflectance by about 0.1-0.3 eV, implying that excitonic effects may be stronger than previously estimated. The calculated density of states from GW quasi-particle band energies agrees very well with photo-emission spectroscopy data. Ionization potentials of these materials are also computed by combining PBE calculations based on the slab model and GW quasi-particle corrections. The calculated absolute band energies with respect to the vacuum level indicate that that ZrS(2) and HfS(2), although having suitable band gaps for visible light absorption, cannot be used for overall water splitting as a result of mismatch of the conduction band minimum with the redox potential of H(+)/H(2).     

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 A for HSE vs 0.047 A for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0-1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.     

Interaction of atomic hydrogen with single-walled carbon nanotubes: a density functional theory study

We have studied the interaction of atomic hydrogen with (5,5) and (10,0) single-walled carbon nanotubes (SWNT) using density functional theory. These calculations use Gaussian orbitals and periodic boundary conditions. We compare results from the local spin density approximation, generalized gradient approximation (GGA), and hybrid density functionals. We have first kept the SWNT geometric structure fixed while a single H atom approaches the tube on top of a carbon atom. In that case, a weakly bound state with binding energies from -0.8 to -0.4 eV was found. Full geometry relaxation leads to a strong SWNT deformation, weakening the nearest C-C bonds and increasing the binding energy by about 1 eV. Full hydrogen coverage of the (5,5) SWNT converts this metallic nanotube into an insulator with a band gap of 3.4 eV for the GGA functional and 4.8 eV for the hybrid functional. Hybrid functionals perform similar to pure density functional theory functionals for the calculation of binding energies while band gaps critically depend on the functional choice.     

Databases for transition element bonding: metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations

We propose a data set of bond lengths for 8 selected transition metal dimers (Ag(2), Cr(2), Cu(2), CuAg, Mo(2), Ni(2), V(2), and Zr(2)) and another data set containing their atomization energies and the atomization energy of ZrV, and we use these for testing density functional theory. The molecules chosen for the test sets were selected on the basis of the expected reliability of the data and their ability to constitute a diverse and representative set of transition element bond types while the data sets are kept small enough to allow for efficient testing of a large number of computational methods against a very reliable subset of experimental data. In this paper we test 42 different functionals: 2 local spin density approximation (LSDA) functionals, 12 generalized gradient approximation (GGA) methods, 13 hybrid GGAs, 7 meta GGA methods, and 8 hybrid meta GGAs. We find that GGA density functionals are more accurate for the atomization energies of pure transition metal systems than are their meta, hybrid, or hybrid meta analogues. We find that the errors for atomization energies and bond lengths are not as large if we limit ourselves to dimers with small amounts of multireference character. We also demonstrate the effects of increasing the fraction of Hartree-Fock exchange in multireference systems by computing the potential energy curve for Cr(2) and Mo(2) with several functionals. We also find that BLYP is the most accurate functional for bond energies and is reasonably accurate for bond lengths. The methods that work well for transition metal bonds are found to be quite different from those that work well for organic and other main group chemistry.     

Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space

The Heyd-Scuseria-Ernzerhof (HSE) density functionals are popular for their ability to improve upon the accuracy of standard semilocal functionals such as Perdew-Burke-Ernzerhof (PBE), particularly for semiconductor band gaps. They also have a reduced computational cost compared to hybrid functionals, which results from the restriction of Fock exchange calculations to small inter-electron separations. These functionals are defined by an overall fraction of Fock exchange and a length scale for exchange screening. We systematically examine this two-parameter space to assess the performance of hybrid screened exchange (sX) functionals and to determine a balance between improving accuracy and reducing the screening length, which can further reduce computational costs. Three parameter choices emerge as useful: "sX-PBE" is an approximation to the sX-LDA screened exchange density functionals based on the local density approximation (LDA); "HSE12" minimizes the overall error over all tests performed; and "HSE12s" is a range-minimized functional that matches the overall accuracy of the existing HSE06 parameterization but reduces the Fock exchange length scale by half. Analysis of the error trends over parameter space produces useful guidance for future improvement of density functionals.     

Electronic and magnetic properties of substituted BN sheets: a density functional theory study

Using density functional calculations, we investigate the geometries, electronic structures and magnetic properties of hexagonal BN sheets with 3d transition metal (TM) and nonmetal atoms embedded in three types of vacancies: V(B), V(N), and V(B+N). We show that some embedded configurations, except TM atoms in V(N) vacancy, are stable in BN sheets and yield interesting phenomena. For instance, the band gaps and magnetic moments of BN sheets can be tuned depending on the embedded dopant species and vacancy type. In particular, embedment such as Cr in V(B+N), Co in V(B), and Ni in V(B) leads to half-metallic BN sheets interesting for spin filter applications. From the investigation of Mn-chain (C(Mn)) embedments, a regular 1D structure can be formed in BN sheets as an electron waveguide, a metal nanometre wire with a single atom thickness.     

A new hybrid DFT approach to electronic excitation and first hyperpolarizabilities of transition metal complexes

The electronic excitations and the static first hyperpolarizability of three typical transition metal (TM) aromatic carbonyl complexes, two tungsten pentacarbonyl derivatives (W(CO)₅L, L = Py and PyCHO) and one chromium tricarbonyl arene derivative (Cr(CO)₃Bz, Bz = benzene), have been theoretically studied by a variety of density functional methods. The assessments reveal that most of the conventional DFT methods including local density approximation, generalized gradient approximation (GGA), and the various kinds of hybrid exchange‐correlation (xc) methods present the first hyperpolarizabilities of these TM‐containing molecules with large deviations from the experiments. A one‐parameter hybrid xc functional is introduced by using the Perdew‐Wang 1991 gradient‐corrected correlation functional (PW91) and the Barone's‐modified PW91 exchange functional (mPW). The ratio between the exact and the density functional exchange is determined to be 0.40 by the adiabatic connection method. The application of the new hybrid functional to the three organometallic carbonyl molecules results in the satisfactory agreement between the calculated first hyperpolarizabilities and the experimental ones. The second‐order nonlinear optical properties of the three organometallic complexes are addressed to the metal‐to‐ligand charge transfers, and the extended π‐delocalization ligands benefit the enhancement of the first hyperpolarizability. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Ge_nEu(n=1-13)团簇的结构、电子及磁性质(英文)

利用密度泛函理论在广义梯度近似下研究了GenEu(n=1-13)团簇的生长模式和磁性.结果表明:对于GenEu(n=1-13)团簇的基态结构而言,没有Eu原子陷入笼中.这和SinEu以及其它过渡金属掺杂半导体团簇的生长模式不同.除GeEu团簇外,GenEu(n=2-13)团簇的磁矩均为7μB.团簇的总磁矩与Eu原子的4f轨道磁矩基本相等.Ge、Eu原子间的电荷转移以及Eu原子的5d、6p和6s间的轨道杂化可以增强Eu原子的局域磁矩,却不能增强团簇总磁矩.     

Efficient hybrid density functional calculations in solids: assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional

The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree-Fock (HF) exchange used in the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2-4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.     

LSDA+U方法研究Ni掺杂CuO和Cu掺杂NiO的电子结构和反铁磁学性质

光催化分解水制H2和光催化还原CO2是解决能源危机和全球变暖的有效途径.但是,由于粉末光催化剂存在回收效率低的问题,因而光催化成本很高.而磁性光催化剂便于回收和重复利用,因此人们把目光转向具有磁性的非光催化剂材料,试图通过改性使得磁性材料具有合适的水分解或者还原CO2的氧化还原电位.同时,对具有光催化活性但是没有磁性的材料进行磁化改性可以得到新型的磁性光催化剂.本文通过对本身具有磁性的NiO材料进行Cu掺杂能带调整,使调整后的NiO具有合适的氧化还原电位;对本身具有良好光催化氧化还原电位的CuO材料进行Ni掺杂磁化调整,使磁化后的CuO既有良好的氧化还原电位又有磁性.最终两种材料经过掺杂变成磁性光催化材料,既有较好的光催化性能,又可高效回收,因此有望在光催化领域具有潜在的应用前景.LSDA(局域自旋密度近似)+U(有效库仑相关能)计算方法能够很好地给出磁矩和禁带宽度等电子结构性质.本文通过LSDA+U计算方法对具有磁性的宽禁带半导体材料NiO进行电子结构改性研究,希望通过降低其禁带宽度、调整其氧化还原电位使之对太阳光有响应.因其同时具有磁性便于回收,使得光催化分解水制H2和光催化还原CO2成本高的问题得到解决.对NiO的磁胞进行了Cu掺杂计算,结果发现Cu的掺杂几乎没有引起NiO空间结构的变化,这是因为Cu和Ni的离子半径相近.通过对电子结构的计算发现掺杂体系的禁带变窄,并且在禁带中间出现了两条杂质能级,该杂质能级是由掺杂原子Cu 3d态组成.杂质能级的出现能够降低光生载流子在带隙中的复合,从而提高光催化效率.计算结果同时表明,Cu掺杂的NiO系统具有一个1μB的净磁矩,即Cu的掺杂使得NiO显示出磁性,而Ni的磁矩在掺杂前后几乎保持不变,由纯相的1.67μB增加到掺杂体系中的1.70μB.由于CuO本身低指数(111)面和(011)面具有合适的分解水制H2和还原CO2的氧化还原电位,如果对CuO进行磁化改性,可以使光催化剂CuO同时带有磁性,便于回收再利用.本文对CuO磁胞进行了Ni的掺杂计算.结果表明,由于离子半径相近,Ni掺杂几乎没有引起CuO空间结构的变化.掺杂后的体系具有一个1.66μB的净磁矩,同时Ni的掺杂引起多个杂质能级出现,靠近价带的杂质能级由Cu 3d态组成,而在导带底位置出现的杂质能级主要由Ni 3d态组成.整个能带向高能级方向平移.