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Register a new userThe Diamine Cation Is Not a Chemical Example Where Density Functional Theory Fails
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In a recent communication, Weber and co-workers presented a surprising study on charge-localization effects in the N,N-dimethylpiperazine (DMP+) diamine cation to provide a stringent test of density functional theory (DFT) methods. Within their study, the authors examined various DFT methods and concluded that all DFT functionals commonly used today, including hybrid functionals with exact exchange, fail to predict a stable charge-localized state. This surprising conclusion is based on the authors use of a self-interaction correction (namely, complex-valued Perdew-Zunger Self-Interaction Correction (PZ-SIC)) to DFT, which appears to give excellent agreement with experiment and other wavefunction-based benchmarks. Since the publication of this recent communication, the same DMP+ molecule has been cited in numerous subsequent studies as a prototypical example of the importance of self-interaction corrections for accurately calculating other chemical systems. In this correspondence, we have carried out new high-level CCSD(T) analyses on the DMP+ cation to show that DFT actually performs quite well for this system (in contrast to their conclusion that all DFT functionals fail), whereas the PZ-SIC approach used by Weber et al. is the outlier that is inconsistent with the high-level CCSD(T) (coupled-cluster with single and double excitations and perturbative triples) calculations. Our new findings and analysis for this system are briefly discussed in this correspondence.
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Semi-local approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.
We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional Density Functional Theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term LDFT, the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre--Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogues in LDFT. We prove results concerning $N$-representability, Hohenberg--Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analogue to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (i) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (ii) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.
Standard flavors of density-functional theory (DFT) calculations are known to fail in describing anions, due to large self-interaction errors. The problem may be circumvented by using localized basis sets of reduced size, leaving no variational flexibility for the extra electron to delocalize. Alternatively, a recent approach exploiting DFT evaluations of total energies on electronic densities optimized at the Hartree-Fock (HF) level has been reported, showing that the self-interaction-free HF densities are able to lead to an improved description of the additional electron, returning affinities in close agreement with the experiments. Nonetheless, such an approach can fail when the HF densities are too inaccurate. Here, an alternative approach is presented, in which an embedding environment is used to stabilize the anion in a bound configuration. Similarly to the HF case, when computing total energies at the DFT level on these corrected densities, electron affinities in very good agreement with experiments can be recovered. The effect of the environment can be evaluated and removed by an extrapolation of the results to the limit of vanishing embedding. Moreover, the approach can be easily applied to DFT calculations with delocalized basis sets, e.g. plane-waves, for which alternative approaches are either not viable or more computationally demanding. The proposed extrapolation strategy can be thus applied also to extended systems, as often studied in condensed-matter physics and materials science, and we illustrate how the embedding environment can be exploited to determine the energy of an adsorbing anion - here a chloride ion on a metal surface - whose charge configuration would be incorrectly predicted by standard density functionals.
We present a time-dependent density-functional method able to describe the photoelectron spectrum of atoms and molecules when excited by laser pulses. This computationally feasible scheme is based on a geometrical partitioning that efficiently gives access to photoelectron spectroscopy in time-dependent density-functional calculations. By using a geometrical approach, we provide a simple description of momentum-resolved photoe- mission including multi-photon effects. The approach is validated by comparison with results in the literature and exact calculations. Furthermore, we present numerical photoelectron angular distributions for randomly oriented nitrogen molecules in a short near infrared intense laser pulse and helium-(I) angular spectra for aligned carbon monoxide and benzene.
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