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We follow the evolution of the Ionization Potential (IP) for the paradigmatic quasi-one-dimensional trans-acetylene family of conjugated molecules, from short to long oligomers and to the infinite polymer trans-poly-acetylene (TPA). Our results for short oligomers are very close to experimental available data. We find that the IP varies with oligomer length and converges to the given value for TPA with a smooth, coupled inverse-length-exponential behavior. Our prediction is based on an internally-consistent scheme to adjust the exchange mixing parameter $alpha$ of the PBEh hybrid density functional, so as to obtain a description of the electronic structure consistent with the quasiparticle approximation for the IP. This is achieved by demanding that the corresponding quasiparticle correction, in the GW@PBEh approximation, vanishes for the IP when evaluated at PBEh($alpha^{ic}$). We find that $alpha^{ic}$ is also system-dependent and converges with increasing oligomer length, allowing to capture the dependence of IP and other electronic properties.
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The $GW$ approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically-defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree-Fock reference, ionization potentials predicted by the $GW$ approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an increased mean absolute error of 0.5 eV. This result suggests that vertex corrections in the self-energy cannot be neglected, at least for molecules. We also assess the behavior of eigenvalue self-consistency in vertex-corrected $GW$ calculations, finding a further worsening of the predicted ionization potentials.
We implement the GW space-time method at finite temperatures, in which the Greens function G and the screened Coulomb interaction W are represented in the real space on a suitable mesh and in imaginary time in terms of Chebyshev polynomials, paying particular attention to controlling systematic errors of the representation. Having validated the technique by the canonical application to silicon and germanium, we apply it to calculation of band gaps in hexagonal solid hydrogen with the bare Greens function obtained from density functional approximation and the interaction screened within the random phase approximation (RPA). The results, obtained from the asymptotic decay of the full Greens function without resorting to analytic continuation, suggest that the solid hydrogen above 250 GPa can not adopt the hexagonal-closed-pack (hcp) structure. The demonstrated ability of the method to store the full G and W functions in memory with sufficient accuracy is crucial for its subsequent extensions to include higher orders of the diagrammatic series by means of diagrammatic Monte Carlo algorithms.
Graphite is the most widely used and among the most widely-studied anode materials for lithium-ion batteries. With increasing demands on lithium batteries to operate at lower temperatures and higher currents, it is crucial to understand lithium intercalation in graphite due to issues associated with lithium plating. Lithium intercalation into graphite has been extensively studied theoretically using density functional theory (DFT) calculations, complemented by experimental studies through X-ray diffraction, spectroscopy, optical imaging and other techniques. In this work, we present a first principles based model using DFT calculations, employing the BEEF-vdW as the exchange correlation functional, and Ising model to determine the phase transformations and subsequently, the thermodynamic intercalation potential diagram. We explore a configurational phase space of about 1 billion structures by accurately determining the important interactions for the Ising model. The BEEF-vdW exchange correlation functional employed accurately captures a range of interactions including vdW, covalent and ionic interactions. We incorporate phonon contributions at finite temperatures and configurational entropy to get high accuracy in free energy and potentials. We utilize the built-in error estimation capabilities of the BEEF-vdW exchange correlation functional and to develop a methodological framework for determining the uncertainty associated with DFT calculated phase diagrams and intercalation potentials. The framework also determines the confidence of each predicted stable phase. The confidence value of a phase can help us to identify regions of solid solutions and phase transformations accurately.
The computation of excited electronic states with commonly employed (approximate) methods is challenging, typically yielding states of lower quality than the corresponding ground state for a higher computational cost. In this work, we present a mean field method that extends the previously proposed eXcited Constrained DFT (XCDFT) from single Slater determinants to ensemble 1-RDMs for computing low-lying excited states. The method still retains an associated computational complexity comparable to a semilocal DFT calculation while at the same time is capable of approaching states with multireference character. We benchmark the quality of this method on well-established test sets, finding good descriptions of the electronic structure of multireference states and maintaining an overall accuracy for the predicted excitation energies comparable to semilocal TDDFT.
Kohn-Sham density functional theory (DFT) has become established as an indispensable tool for investigating aqueous systems of all kinds, including those important in chemistry, surface science, biology and the earth sciences. Nevertheless, many widely used approximations for the exchange-correlation (XC) functional describe the properties of pure water systems with an accuracy that is not fully satisfactory. The explicit inclusion of dispersion interactions generally improves the description, but there remain large disagreements between the predictions of different dispersion-inclusive methods. We present here a review of DFT work on water clusters, ice structures and liquid water, with the aim of elucidating how the strengths and weaknesses of different XC approximations manifest themselves across this variety of water systems. Our review highlights the crucial role of dispersion in describing the delicate balance between compact and extended structures of many different water systems, including the liquid. By referring to a wide range of published work, we argue that the correct description of exchange-overlap interactions is also extremely important, so that the choice of semi-local or hybrid functional employed in dispersion-inclusive methods is crucial. The origins and consequences of beyond-2-body errors of approximate XC functionals are noted, and we also discuss the substantial differences between different representations of dispersion. We propose a simple numerical scoring system that rates the performance of different XC functionals in describing water systems, and we suggest possible future developments.
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