First-principles calculation of effective onsite Coulomb interactions of 3d transition metals: Constrained local density functional approach with maximally localized Wannier functions (original) (raw)
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This Ph.D. thesis has been carried out in the period from 1999 till 2002. The work is organized as follows. After an introduction, concerning the goals and key ideas of this work, we review the density functional theory. This is followed by a look at how the electronic structure calculations are performed, in particular the LMTO method and the tetrahedron method. Next, a chapter is devoted to the calculation of maximally localized Wannier functions using a method proposed by Marzari and Vanderbilt. We then focus on the second quantized Hamiltonian, its matrix elements in Wannier representation and their evaluation within the atomic sphere approximation. By then, we will have all the pieces to perform many-particle calculations using this second quantized Hamiltonian with its matrix elements from first-principle, which will be dealt with in chapter 6. Finally, we present results for the 3d transition metals iron, cobalt, nickel and copper.
Density functional theory for transition metals and transition metal chemistry
We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids. *E-mails: cramer@umn.edu, truhlar@umn.edu used to describe not only the quasiparticle energies as a function of momentum ! hk but also the independent-particle approximation to those curves.
Screening of Coulomb interactions in transition metals
Physical Review B, 2005
We discuss different methods of calculation of the screened Coulomb interaction U in transition metals and compare the so-called constraint local-density approximation (LDA) with the GW approach. We clarify that they offer complementary methods of treating the screening and therefore should serve for different purposes. The analysis is illustrated by calculations for the ferromagnetic Ni. In the ab initio GW method, the renormalization of bare on-site Coulomb interactions between 3d electrons (being of the order of 20-30 eV) occurs mainly through the screening by the same 3d electrons, treated in the random-phase approximation (RPA). The basic difference of the constraint-LDA method from the GW method is that it deals with the neutral processes, where the Coulomb interactions are additionally screened by the "excited" electron, since it continues to stay in the system. This is the main channel of screening by the itinerant ͑4sp͒ electrons, which is especially strong in the case of transition metals and missing in the GW approach, although the details of this screening may be affected by additional approximations, which typically supplement these two methods. The major drawback of the conventional constraint-LDA method is that it does not allow us to treat the energy dependence of U, while the full GW calculations require heavy computations. We propose a promising approximation based on the combination of these two methods. First, we take into account the screening of Coulomb interactions in the 3d-electron-like bands located near the Fermi level by the states from the orthogonal subspace, using the constraint-LDA methods. The obtained interactions are further renormalized within the bands near the Fermi level in RPA. This allows the energy-dependent screening by electrons located near the Fermi level, including the same 3d electrons.
Journal of Physics: …, 2006
We propose a computational method that simplifies drastically the inclusion of spin-orbit interaction in density functional theory when implemented over localised atomic orbital basis sets. Our method is based on a well-known procedure for obtaining pseudopotentials from atomic relativistic ab initio calculations and on an on-site approximation for the spin-orbit matrix elements. We have implemented the technique in the SIESTA[34] code, and show that it provides accurate results for the overall band structure and splittings of group IV and III-IV semiconductors as well as for 5d metals.
Grid-based density functional calculations of many-electron systems
International Journal of Quantum Chemistry, 2008
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set, electronic density and the two-body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange-correlation potential, while Hay-Wadt-type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom-centered grid as well as the grid-free calculation. Results for 3 atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many-electron systems.
Grid-based density functional calculation of many-electron systems
2010
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set, electronic density and the two-body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange-correlation potential, while Hay-Wadt-type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom-centered grid as well as the grid-free calculation. Results for 3 atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many-electron systems.
Journal of Computational Chemistry, 2005
The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.
Journal of Chemical Theory and Computation, 2014
The 3d-series transition metals (also called the fourth-period transition metals), Sc to Zn, are very important in industry and biology, but they provide unique challenges to computing the electronic structure of their compounds. In order to successfully describe the compounds by theory, one must be able to describe their components, in particular the constituent atoms and cations. In order to understand the ingredients required for successful computations with density functional theory, it is useful to examine the performance of various exchange−correlation functionals; we do this here for 4s N 3d N ′ transition-metal atoms and their cations. We analyze the results using three ways to compute the energy of the open-shell states: the direct variational method, the weighted-averaged broken symmetry (WABS) method, and a new broken-symmetry method called the reinterpreted broken symmetry (RBS) method. We find the RBS method to be comparable in accuracy with the WABS method. By examining the overall accuracy in treating 18 multiplicity-changing excitations and 10 ionization potentials with the RBS method, 10 functionals are found to have a mean-unsigned error of <5 kcal/mol, with ωB97X-D topping the list. For local density functionals, which are more practical for extended systems, the M06-L functional is the most accurate. And by combining the results with our previous studies of p-block and 4d-series elements as well as databases for alkyl bond dissociation, main-group atomization energies, and π−π noncovalent interactions, we find five functionals, namely, PW6B95, MPW1B95, M08-SO, SOGGA11-X, and MPWB1K, to be highly recommended. We also studied the performance of PW86 and C09 exchange functionals, which have drawn wide interest in recent studies due to their claimed ability to reproduce Hartree−Fock exchange at long distance. By combining them with four correlation functionals, we find the performance of the resulting functionals disappointing both for 3d transition-metal chemistry and in broader tests, and thus we do not recommend PW86 and C09 as components of generalized gradient approximations for general application. a GS − electronic state of neutral ground state; ES − electronic state of neutral excited state; ΔE − excitation energy of neutral atom, kcal/mol; GS + − electronic state of cation ground state; ES + − electronic state of cation excited state; ΔE + − excitation energy of cation, kcal/mol; IP − ionization potential, kcal/mol Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400712k | J. Chem. Theory Comput. 2014, 10, 102−121 Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400712k | J. Chem. Theory Comput. 2014, 10, 102−121 a MUE is in kcal/mol. The functionals are arranged in order of increasing MUE for the RBS method. When the MUE for RBS is the same (rounded to the nearest tenth of a kcal/mol), the order is the sum of the MUs for the variational, WABS, and RBS methods.
The Journal of Chemical Physics, 2007
Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.
Journal of Computational Chemistry, 2001
We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second-row transition metals, platinum, and gold. The outermost s-d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second-and third-row transition metal atoms. Compared with the first-row transition metal dimer calculations (J Chem Phys 2000, 112, 545-553), the binding energies calculated using the combination of the Becke 1988 exchange and the one-parameter progressive correlation (BOP) functional and Becke's three-parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high-angular-momentum open-shell orbitals. Analysis of the s-d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long-range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree-Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions.