Espen Sagvolden

Choice of basic variables in current-density-functional theory

The selection of basic variables in current-density-functional theory and formal properties of the resulting formulations are critically examined. Focus is placed on the extent to which the Hohenberg-Kohn theorem, constrained-search approach, and Lieb’s formulation (in terms of convex and concave conjugation) of standard density-functional theory can be generalized to provide foundations for current-density-functional theory. For the well-known case with the gauge-dependent paramagnetic current density as a basic variable, we find that the resulting total energy functional is not concave. It is shown that a simple redefinition of the scalar potential restores concavity and enables the application of convex analysis and convex (or concave) conjugation. As a result, the solution sets arising in potential-optimization problems can be given a simple characterization. We also review attempts to establish theories with the physical current density as a basic variable. Despite the appealing physical motivation behind this choice of basic variables, we find that the mathematical foundations of the theories proposed to date are unsatisfactory. Moreover, the analogy to standard density-functional theory is substantially weaker as neither the constrained-search approach nor the convex analysis framework carry over to a theory making use of the physical current density.

Förster Energy Transfer and Davydov Splittings in Time-Dependent Density Functional Theory: Lessons from 2-Pyridone Dimer.

The Davydov or exciton splitting of vertical excitation energies is commonly used to estimate the excitation energy transfer rate between chromophores. Here we investigate the S1-S2 Davydov splitting in 2-pyridone dimer as a function of the monomer separation, R. We assess the ability of various functionals to reproduce the Davydov splitting at finite R predicted by the approximate coupled cluster singles doubles method CC2. While semilocal functionals fail qualitatively because of spurious charge-transfer intruder states, global hybrids with a large fraction of exact exchange, such as BHandH-LYP, reproduce the CC2 splittings within few wavenumbers. We analyze our results by comparison to lowest-order intermolecular perturbation theory in the spirit of Förster and Dexter. At equilibrium hydrogen bond distance, the Förster-Dexter splittings are too small by up to a factor of 2.

Is there symmetry breaking in the first excited singlet state of 2-pyridone dimer?

We investigate the S(1) state potential energy surface of 2-pyridone dimer (2PY)(2) using time-dependent density functional and coupled cluster theory. Although the ground and S(2) excited states of (2PY)(2) have C(2h) symmetry, the S(1) state shows symmetry breaking and localization of the excitation on one of the two monomers upon relaxation of the geometry. This localization is rationalized using a simple diabatic curve crossing model. As a consequence of the symmetry breaking, S(1) to S(0) transitions become optically allowed. We hypothesize that the band at 30,776 cm(-1) observed in the excitation spectrum of (2PY)(2) might be attributed to the S(1) state rather than the S(2) state; the S(2) state origin is predicted 3000-4000 cm(-1) above the S(1) state by hybrid density functional and coupled cluster methods. Asymmetric transfer of one hydrogen atom leads to a second S(1) state minimum that can rapidly decay to the ground state. This suggests that photoinduced tautomerization of (2PY)(2) occurs in a stepwise fashion, with only one hydrogen transfer taking place on the S(1) surface.

Prediction of solute diffusivity in Al assisted by first-principles molecular dynamics

Ab initio calculations of the solid-state diffusivity of solute atoms in bulk aluminium have previously been based on transition state theory (TST), employing transition state searches and systematic assessments of single jumps together with appropriate models of jump frequencies and correlation factors like the five-frequency model. This work compared TST benchmark predictions of diffusivities with first-principles molecular dynamics (FPMD). The TST calculations were performed at unprecedented high precision, including the temperature dependent entropy of vacancy formation which has not been included in previous studies of diffusion in Al; this led to improved agreement with experimental data. It was furthermore demonstrated that FPMD can yield sufficient statistics to predict the frequency of single jumps, and FPMD was used to successfully predict the macroscopic diffusivity of Si in Al. The latter is not possible in systems with higher activation energies, but it was demonstrated that FPMD in such cases can identify which jumps are prevalent for a given defect configuration. Thus, information from FPMD can be used to simplify the calculation of correlation terms, prefactors and effective transition barriers with TST significantly. This can be particularly important for the study of more complicated defect configurations, where the number of distinct jumps rapidly increases to be intractable by systematic methods.

Isoorbital indicators for current density functional theory

Exchange-correlation density functionals at the meta-generalised gradient approximation level typically use the Kohn–Sham orbitals as an ingredient to create the isoorbital indicator , where is the von Weizsäcker kinetic energy density and is the kinetic energy density of the Kohn–Sham orbitals. When a magnetic field is included in the treatment, the Kohn–Sham orbitals vary with the vector-potential gauge, as does and implicitly the exchange-correlation energy. However, it is a known result in current density functional theory that the exact exchange-correlation energy is gauge independent. Three different gauge-independent replacements for have been proposed by other authors. Only one of these is, however, known to stay between 0 and 1. We modify one of the others, the Maximoff–Scuseria isoorbital indicator, so that it also stays between 0 and 1. We investigate the ability of the isoorbital indicators evaluated in a system with density and paramagnetic current density to reproduce the value of in a system having no paramagnetic current, but the same density . We provide the first example known to us where the Tao–Perdew isoorbital indicator goes outside of the interval from 0 to 1.

Discovering Thermoelectric Materials Using Machine Learning: Insights and Challenges

This work involves the use of combined forces of data-driven machine learning models and high fidelity density functional theory for the identification of new potential thermoelectric materials. The traditional method of thermoelectric material discovery from an almost limitless search space of chemical compounds involves expensive and time consuming experiments. In the current work, the density functional theory (DFT) simulations are used to compute the descriptors (features) and thermoelectric characteristics (labels) of a set of compounds. The DFT simulations are computationally very expensive and hence the database is not very exhaustive. With an anticipation that the important features can be learned by machine learning (ML) from the limited database and the knowledge could be used to predict the behavior of any new compound, the current work adds knowledge related to (a) understanding the impact of selection of influence of training/test data, (b) influence of complexity of ML algorithms, and (c) computational efficiency of combined DFT-ML methodology.