The nonadditive, noninteracting kinetic energy (NAKE) is calculated numerically for fragments of H2, Li2, Be2, C2, N2, F2, and Na2 within partition density functional theory (PDFT). The resulting fragments are uniquely determined, and their sum reproduces the Kohn–Sham molecular density of the corresponding XC functional. We present the NAKE of these unique fragments as a function of internuclear separation and compare the use of fractional orbital occupation to the usual PDFT ensemble method for treating the fragment energies and densities. We also compare Thomas–Fermi and von Weizsäcker approximate kinetic energy functionals to the numerically exact solutions and find significant regions where the von Weizsäcker functional is nearly exact. In addition, we find that the von Weizsäcker approximation can provide accurate NAKE in stretched covalent bonds, especially in the cases of Li2 and Na2.

We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn–Sham equations and to systems in higher dimensions.

Most approximations to the exchange-correlation functional of Kohn–Sham density functional theory lead to delocalization errors that undermine the description of charge-transfer phenomena. We explore how various approximate functionals and charge-distribution schemes describe ground-state atomic-charge distributions in the lithium–benzene complex, a model system of relevance to carbon-based supercapacitors. To understand the trends, we compare Hartree–Fock (HF) and correlated post-HF calculations, confirming that the HOMO–LUMO gap is narrower in semilocal functionals but widened by hybrid functionals with large fractions of HF exchange. For semilocal functionals, natural bond orbital (NBO) and Mulliken schemes yield opposite pictures of how charge transfer occurs. In PBE, for example, when lithium and benzene are <1.5 Å apart, NBO yields a positive charge on the lithium atom, but the Mulliken scheme yields a negative charge. Furthermore, the partial charges in conjugated materials depend on the interplay between the charge-distribution scheme employed and the underlying exchange-correlation functional, being critically sensitive to the admixture of HF exchange. We analyze and explain why this happens, discuss implications, and conclude that hybrid functionals with an admixture of about one-fourth of HF exchange are particularly useful in describing charge transfer in the lithium–benzene model.

Conceiving a molecule as being composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient algorithms can be proposed to address problems in the description of chemical bond formation and breaking. We present a formally exact time-dependent density functional theory for the electronic dynamics of molecular fragments with a variable number of electrons. This new formalism is an extension of previous work [Phys. Rev. Lett. 111, 023001 (2013)]. We also introduce a stable density-inversion method that is applicable to time-dependent and ground-state density functional theories and their extensions, including those discussed in this work.

With the growing complexity of systems that can be treated with modern electronic-structure methods, it is critical to develop accurate and efficient strategies to partition the systems into smaller, more tractable fragments. We review some of the various recent formalisms that have been proposed to achieve this goal using fragment (ground-state) electron densities as the main variables, with an emphasis on partition density-functional theory (PDFT), which the authors have been developing. To expose the subtle but important differences between alternative approaches and to highlight the challenges involved with density partitioning, we focus on the simplest possible systems where the various methods can be transparently compared. We provide benchmark PDFT calculations on homonuclear diatomic molecules and analyze the associated partition potentials. We derive a new exact condition determining the strength of the singularities of the partition potentials at the nuclei, establish the connection between charge-transfer and electronegativity equalization between fragments, test different ways of dealing with fractional fragment charges and spins, and finally outline a general strategy for overcoming delocalization and static-correlation errors in density-functional calculations.

High harmonic spectra of N2N2 are calculated using time-dependent density functional theory. The adiabatic local density approximation (A-LDA) and the adiabatic van Leeuwen–Baerends (A-LB94) approximations are used to study effects of differing spatial asymptotics. The LB94 potential corrects the LDA potential to the exact -1/r-1/r decay, but does not satisfy the zero-force condition. The A-LB94 makes a significant change in ionization probabilities but not in the relevant orbital contributions to ionization. This leads to qualitatively similar spectra, the exception being harmonic intensities. We also discuss why spurious dipoles induced by the A-LB94 do not affect significantly the structure of the N2N2 harmonic spectrum.Graphical abstractHighlights► High Harmonic Generation from N2N2 is studied via adiabatic TDDFT. ► Harmonic spectra obtained via adiabatic LDA and LB94 are compared and contrasted. ► We assess the importance of the asymptotic behavior of the ground-state XC-potential.

We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn–Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials, and wave functions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li, and Be) as well as the H2 molecule. Extensions are briefly discussed.Keywords: complex scaling; excitations; lasers; open quantum systems; resonances; spectroscopy; tunneling;

The ab initio calculation of resonance lifetimes of metastable anions challenges modern quantum chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex “density” that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density.Keywords (keywords): anion; complex scaling; density functional theory; lifetime; metastable negative ion; resonance;

We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn–Sham equations and to systems in higher dimensions.