Warming Up Density Functional Theory

Density functional theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. Last year, at least 30,000 papers used DFT to make useful predictions or give insight into an enormous diversity of scientific problems, ranging from battery development to solar cell efficiency and far beyond. The success of this field has been driven by usefully accurate approximations based on known exact conditions and careful testing and validation. In the last decade, applications of DFT in a new area, warm dense matter, have exploded. DFT is revolutionizing simulations of warm dense matter including applications in controlled fusion, planetary interiors, and other areas of high energy density physics. Over the past decade or so, molecular dynamics calculations driven by modern density functional theory have played a crucial role in bringing chemical realism to these applications, often (but not always) with excellent agreement with experiment. This chapter summarizes recent work from our group on density functional theory at non-zero temperatures, which we call thermal DFT. We explain the relevance of this work in the context of warm dense matter, and the importance of quantum chemistry to this regime. We illustrate many basic concepts on a simple model system, the asymmetric Hubbard dimer

Controlling the yield and structure of carbon nanofibers grown on a nickel/activated carbon catalyst

Carbon nanofibers (CNFs) were grown via the chemical vapor deposition of C2H4 on an activated carbon (AC)-supported Ni catalyst. The texture of the CNF/AC composites can be tuned by varying the growth temperature and by treatment in reducing atmosphere prior to C2H4/H2 exposure. The Ni-catalyzed gasification of the AC support increases the microporosity of the composite and shown to be dominant throughout the composite synthesis especially during reduction, subsequent treatment in reducing atmosphere, and CNF growth at low temperatures. N2 isotherm and scanning electron microscope were used to characterize the texture and morphology of the composites. Subsequent treatment in reducing atmosphere were shown to increase the Ni catalyst activity to grow CNFs. High resolution transmission electron microscope however did not reveal any microstructural difference for Ni catalyst with and without the subsequent reduction treatment. We propose in this paper that the carbon dissolutions during treatment of the catalyst might have an implication on the CNF growth

Correlation energies of inhomogeneous many-electron systems

We generalize the uniform-gas correlation energy formalism of Singwi, Tosi, Land and Sjolander to the case of an arbitrary inhomogeneous many-particle system. For jellium slabs of finite thickness with a self-consistent LDA groundstate Kohn-Sham potential as input, our numerical results for the correlation energy agree well with diffusion Monte Carlo results. For a helium atom we also obtain a good correlation energy.Comment: 4 pages,1 figur

Symmetry breaking and the random-phase approximation in small quantum dots

The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration and the role of the spurious modes within the random-phase approximation. A systematics with the Coulombic interaction strength is presented for the 2-electron dot, while for the 6- and 12-electron dots selected cases are discussed. The validity of the random-phase approximation is assessed by comparison with available exact results.Comment: 9 pages, 4 embedded + 6 gif Figs. Published versio

Synthesis and reductive chemistry of bimetallic and trimetallic rare-earth metallocene hydrides with (C5H4SiMe3)1− ligands

The reductive chemistry of [Cp\u272Ln(μ–H)(THF)x]y [Ln = Y, Dy, Tb; Cp\u27 = (C5H4SiMe3)1−; x = 2, 0 and y = 2, 3] was examined to determine if these hydrides would be viable precursors for 4fn5d1 Ln2+ ions that could form 5d1-5d1 metal–metal bonded complexes. The hydrides were prepared by reaction of the chlorides, [Cp\u272Ln(μ–Cl)]2, 1-Ln, with allylmagnesium chloride to form the allyl complexes, [Cp\u272Y(η3–C3H5)(THF)], 2-Ln, which were hydrogenolyzed. The solvent-free reaction of solid 2-Ln with 60 psi of H2 gas in a Fischer-Porter apparatus produced, in the Y case, the trimetallic species, [Cp\u272Y(μ–H)]3, 3-Y, and in the Dy and Tb cases, the bimetallic complexes [Cp\u272Ln(μ–H)(THF)]2, 4-Ln (Ln = Dy, Tb). The latter complexes could be converted to 3-Dy and 3-Tb by heating under vacuum. Isopiestic data indicate that 3-Y solvates to 4-Y in THF. Reductions of 4-Y, 4-Dy, and 4-Tb with KC8 in the presence of a chelate such as 2.2.2-cryptand or 18-crown-6 all gave reaction products with intense dark colors characteristic of Ln2+ ions. In the yttrium case, with either chelating agent, the dark green product gives a rhombic EPR spectrum (g1 = 2.01, g2 = 1.99, g3 = 1.98, A = 24.1 G) at 77 K. However, the only crystallographically-characterizable products obtainable from these solutions were Ln3+polyhydride anion complexes of composition, [K(chelate)]{[Cp\u272Ln(μ–H)]3(μ–H)}

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation

doi:10.1063/1.1756865Time-dependent density-functional theory in the adiabatic approximation has been very successful for calculating excitation energies in molecular systems. This paper studies nonadiabatic effects for excitation energies, using the current-density functional of Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. We derive a general analytic expression for nonadiabatic corrections to excitation energies of finite systems and calculate singlet s→s and s→p excitations of closed-shell atoms. The approach works well for s→s excitations, giving a small improvement over the adiabatic local-density approximation, but tends to overcorrect s→p excitations. We find that the observed problems with the nonadiabatic correction have two main sources: (1) the currents associated with the s→p excitations are highly nonuniform and, in particular, change direction between atomic shells, (2) the so-called exchange-correlation kernels of the homogeneous electron gas, fxcL and fxcT, are incompletely known, in particular in the high-density atomic core regions.C.A.U. acknowledges support by the donors of the Petroleum Research Fund, administered by the ACS, and by the University of Missouri Research Board. K.B. was supported by DOE under Grant No. DE-FG02-01ER45928