This paper considers the p-Laplacian PDE for p = 1,∞ and some interesting new game theoretic interpretations, due to Kohn–Serfaty [K-S] and to Peres–Schramm–Sheffield–Wilson [P-S-S-W].

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the ...

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn– Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order pertu...

Localized representation of the Kohn-Sham subspace plays an important role in quantum chemistry and materials science. The recently developed selected columns of the density matrix (SCDM) method [J. Chem. Theory Comput. 11, 1463, 2015] is a simple and robust procedure for finding a localized representation of a set of Kohn-Sham orbitals from an insulating system. The SCDM method allows the dire...

The accuracy of excited states calculated with Kohn-Sham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for open-shell singlet excited states. The computed Kohn-Sham adiabatic excitation energies are improved significantl...

Multiplier ideal sheaves are constructed as obstructions to the convergence of the Kähler-Ricci flow on Fano manifolds, following earlier constructions of Kohn, Siu, and Nadel, and using the recent estimates of Kolodziej and Perelman.

Using the Kohn–Sham density functional theory, we numerically study four-wave mixing response of a carbon atom model system exposed to train femtosecond two color ?–3? random phase coheren...

Multiplier ideal sheaves are constructed as obstructions to the convergence of the Kähler-Ricci flow on Fano manifolds, following earlier constructions of Kohn, Siu, and Nadel, and using the recent estimates of Kolodziej and Perelman.

We study the standard and extended Kohn-Shammodels for quasirelativistic N -electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator