Viktor N. Staroverov

Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes

A comprehensive study is undertaken to assess the nonempirical meta-generalized gradient approximation (MGGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) against 14 common exchange-correlation energy functionals. Principal results are presented in the form of statistical summaries of deviations from experiment for the G3/99 test set (223 enthalpies of formation, 86 ionization potentials, 58 electron affinities, 8 proton affinities) and three additional test sets involving 96 bond lengths, 82 harmonic vibrational frequencies, and 10 hydrogen-bonded complexes, all computed using the 6-311++G(3df,3pd) basis. The TPSS functional matches, or exceeds in accuracy all prior nonempirical constructions and, unlike semiempirical functionals, consistently provides a high-quality description of diverse systems and properties. The computational cost of self-consistent MGGA is comparable to that of ordinary GGA, and exact exchange (unavailable in some codes) is not required. A one-parameter global hybrid version of ...

Meta-generalized gradient approximation: Explanation of a realistic nonempirical density functional

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.

Optimized effective potentials yielding Hartree–Fock energies and densities

It is commonly believed that the exchange-only optimized effective potential (OEP) method must yield total energies that are above corresponding ground-state Hartree-Fock (HF) energies except for one- and two-electron systems. We present a simple procedure for constructing local (multiplicative) exchange potentials that reproduce exactly the HF energy and density in any finite basis set for any number of electrons. For any finite basis set, no matter how large, there exist infinitely many such OEPs, which questions their suitability for practical applications.

A Cryptand-Encapsulated Germanium(II) Dication

Unlike cations of metals such as sodium or calcium, oxidized silicon and germanium centers generally require strongly bound covalent ligands. We report the synthesis and characterization of a germanium(II) dication in the form of the salt (Ge·cryptand[2.2.2])(O3SCF3)2. The salt is isolated in 88% yield from the reaction of cryptand [2.2.2] and an N-heterocyclic carbene complex of GeCl(O3SCF3) as an air-sensitive, white solid. The crystal structure of the salt shows minimal interaction between the cryptand-encapsulated germanium(II) ion and the two –O3SCF3 counterions. These results suggest a widely expanded role of cryptands and related molecules in stabilizing nonmetallic cations.

Progress in the development of exchange-correlation functionals

Publisher Summary This chapter discusses progress in constructing practical exchange-correlation approximations of Kohn–Sham density functional theory. The emphasis is on the general techniques of density functional design that have been particularly successful in quantum chemistry. Back in the 1960s, hopes for future progress in electronic structure theory were associated with correlated wave function techniques and the tantalizing possibility of variational calculations based on the two-electron reduced density matrix. Density functional theory (DFT) was not on the quantum chemistry agenda at that time. Meanwhile, approximate DFT has become the most widely used method of quantum chemistry, offering an unprecedented accuracy-to-cost ratio. Nearly all density functionals embraced nowadays by computational chemists are discussed. Persistent misconceptions about several widely used functionals are clarified.

Exchange and correlation in open systems of fluctuating electron number

While the exact total energy of a separated open system varies linearly as a function of average electron number between adjacent integers, the energy predicted by semilocal density-functional approximations is concave up and the exact-exchange-only or Hartree-Fock energy is concave down. As a result, semilocal density functionals fail for separated open systems of fluctuating electron number, as in stretched molecular ions A{sub 2}{sup +} and in solid transition-metal oxides. We develop an exact-exchange theory and an exchange-hole sum rule that explain these failures and we propose a way to correct them via a local hybrid functional.

Effective local potentials for orbital-dependent density functionals

Practicality of the Kohn-Sham density functional scheme for orbital-dependent functionals hinges on the availability of an efficient procedure for constructing local exchange-correlation potentials in finite basis sets. We have shown recently that the optimized effective potential (OEP) method, commonly used for this purpose, is not free from difficulties. Here we propose a robust alternative to OEPs, termed effective local potentials (ELPs), based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart. The ELP method is applied to the exact-exchange-only problem and shown to be promising for overcoming troubles with OEPs.

Assessment of simple exchange-correlation energy functionals of the one-particle density matrix

An improved density matrix functional (DMF) combining the properties of the “corrected Hartree” (CH) and “corrected Hartree–Fock” (CHF) approximations is proposed. Functionals of the CH/CHF type and the closely related natural orbital functional of Goedecker and Umrigar (GU) are tested in fully variational finite basis set calculations of light atoms, the lowest energy singlet methylene, and, for the first time, potential energy curves of diatomic molecules. Although CH/CHF-style DMFs may give reasonable energies for atoms and molecules near equilibrium geometries, they predict unrealistically shallow minima in the potential energy curves for diatomic molecules with more than two electrons. The calculated CH and CHF molecular dissociation curves exhibit the same patterns of over- and under-correlations as the corresponding correlation energy plots for the homogeneous electron gas undergoing a transition from high to low densities. In contrast, the GU functional yields not only accurate atomic and molecula...

Exact-exchange energy density in the gauge of a semilocal density-functional approximation

Exact-exchange energy density and energy density of a semilocal density functional approximation are two key ingredients for modeling the static correlation, a strongly nonlocal functional of the density, through a local hybrid functional. Because energy densities are not uniquely defined, the conventional (Slater) exact-exchange energy density

Optimization of density matrix functionals by the Hartree–Fock–Bogoliubov method

e_\mathrm{x}^\mathrm{ex(conv)}