Hedin's scheme is solved with the inclusion of the vertex function ($GW\Gamma$) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the self-energy. A diagrammatic analysis shows that the self-energy formed with this four-point vertex does not lead to double counting of diagrams, that can be classified as direct bubbles and exchange diagrams. By removing the exchange diagrams from the self-energy, a simpler approximation is obtained, called $GW^{\rm{tc-tc}}$. Very good agreement with expensive wavefunction-based methods is obtained for both approximations.
The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of Second Order Screened Exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as $\mathcal O(N^5)$ or $\mathcal O(N^4)$ in orbital space or real space, respectively. Its memory requirement scales as $\mathcal O(N^2)$.
We have carried out first principles calculations to examine the adsorption and dissociation of oxygen on the Cu (110) surface. At low coverage, our results indicate two absorption species: a peroxo- and a superoxo-like species which have direct implications to the dissociation process. In agreement with experimental studies, the most favourable absorption site for O2 is found to be the 4-fold hollow site. The dissociation barrier at this site is only 150 meV, which is consistent with experimental findings. Static calculations also reveal other possible dissociation pathways with significantly different energy barriers. First principles MD simulations are used to probe the dynamics of the dissociation process. We find only selected pathways are likely to be utilised because of interaction with the surface.
We present the results of a density functional theory (generalized gradient approximation) study of the hydrogenated C(100) surfaces. We have analyzed the formation energy of phases with different hydrogen coverages $(\ensuremath{\theta}=1.0,$ 1.2, 1.33, 1.5, and 2.0) as a function of the hydrogen chemical potential. As the hydrogen chemical potential increases, the stable phase changes from the bare surface through all the hydrides considered, in order of increasing coverage. The value of the hydrogen chemical potential beyond which dihydride units are stabilized on the surface nearly coincides with the potential at which the the formation energy of methane is zero. However, since the desorption of hydrocarbons is an activated process, dihydride units can appear in metastable surface phases. To investigate this possibility, we have calculated vibrational frequencies for the $(2\ifmmode\times\else\texttimes\fi{}1):\mathrm{H},$ $(5\ifmmode\times\else\texttimes\fi{}1):1.2\mathrm{H},$ and $(3\ifmmode\times\else\texttimes\fi{}1):1.33\mathrm{H}$ phases of the H/C(100) surface. The presence of a dihydride unit on the surface leads to a H-C-H bending mode with a frequency near $1475{\mathrm{cm}}^{\ensuremath{-}1}.$ Because there is no vibrational mode with a frequency in this region of the spectrum for the monohydride surface, this peak may be viewed as evidence that dihydride units are present on the surface.
We develop a strategy that integrates machine learning and first-principles calculations to achieve technical accurate predictions of infrared spectra. Specifically, the methodology allows to predict infrared spectra for complex systems at finite temperatures. The method's effectiveness is demonstrated in challenging scenarios, such as the analysis of water and the organic-inorganic halide perovskite MAPbI$_{3}$, where our results consistently align with experimental data. A distinctive feature of the methodology is the incorporation of derivative learning, which proves indispensable for obtaining accurate polarization data in bulk materials and facilitates the training of a machine learning surrogate model of the polarization adapted to rotational and translational symmetries. We achieve polarisation prediction accuracies of about 1 % by training only on the predicted Born effective charges.
We introduce the hybrid functional HSEsol. It is based on PBEsol, a revised Perdew–Burke–Ernzerhof functional, designed to yield accurate equilibrium properties for solids and their surfaces. We present lattice constants, bulk moduli, atomization energies, heats of formation, and band gaps for extended systems, as well as atomization energies for the molecular G2-1 test set. Compared to HSE, significant improvements are found for lattice constants and atomization energies of solids, but atomization energies of molecules are slightly worse than for HSE. Additionally, we present zero-point anharmonic expansion corrections to the lattice constants and bulk moduli, evaluated from ab initio phonon calculations.
No abstract is provided for this article.
We present ab initio calculations of the structural, cohesive, and electronic properties of various polymorphic forms of carbon and boron nitride. Our calculations are based on ultrasoft pseudopotentials and a variational approach to the solution of the Kohn-Sham equations. Optimization of the atomic geometries is performed using total energy calculations and by minimizing the energy via a quasi-Newton quench using the Hellmann-Feynman forces. Special attention is devoted to the convergence of the results with respect to the plane-wave basis. The entire set of structural energy differences calculated in our work is in good agreement with the most accurate results obtained using a variety of different techniques---our results represent a consistent set of data based all on the same potential. We show that the use of ultrasoft potentials allows one to achieve accurate results with low cutoff energies (and hence small basis sets).
The radial dependency of the vibrational frequencies of single-wall carbon nanotubes in the G band (1500-1600 cm(-1)) is studied by density functional theory. In metallic nanotubes, a mode with A1 symmetry is found to be significantly softer than the corresponding mode in insulating tubes or graphite. The mechanism that leads to the mode softening is explored. It is reminiscent of the driving force inducing Peierls distortions. At ambient temperature, the energy gained by opening the gap is, however, not sufficient for a static lattice distortion. Instead the corresponding vibrational frequency is lowered.
This study presents a long-range descriptor for machine learning force fields that maintains translational and rotational symmetry, similar to short-range descriptors while being able to incorporate long-range electrostatic interactions. The proposed descriptor is based on an atomic density representation and is structurally similar to classical short-range atom-centered descriptors, making it straightforward to integrate into machine learning schemes. The effectiveness of our model is demonstrated through comparative analysis with the long-distance equivariant (LODE) [Grisafi and Ceriotti, J. Chem. Phys. 151, 204105 (2019)] descriptor. In a toy model with purely electrostatic interactions, our model achieves errors below 0.1%, worse than LODE but still very good. For real materials, we perform tests for liquid NaCl, rock salt NaCl, and solid zirconia. For NaCl, the present descriptors improve on short-range density descriptors, reducing errors by a factor of two to three and coming close to message-passing networks. However, for solid zirconia, no improvements are observed with the present approach, while message-passing networks reduce the error by almost a factor of two to three. Possible shortcomings of the present model are briefly discussed.
Ab initio electronic structure calculations, based upon density functional theory within the generalised gradient approximation using ultrasoft non-norm-conserving Vanderbilt pseudopotentials, have been used to predict the structure and properties of crystalline and liquid iron and solid FeSi at conditions found in the Earth's core. The quality of the pseudopotentials used was assessed by calculating well documented properties of the solid phase: we have accurately modelled the equation of state of bcc and hcp Fe and FeSi, the bcc→hcp phase transition, the magnetic moment of bcc Fe, the elastic constants of bcc Fe, the bcc→bct distortive phase transition and the phonon frequencies for fcc Fe; the results show good agreement with both theory and experiment. Simulations were also performed on liquid iron and we present the first abinitio quantum molecular dynamics calculations on the structure and transport properties of liquid iron under core conditions. Our calculations show that the structure of liquid iron at the conditions to be found in the outer core is highly compressed with a first-neighbour coordination number inferred from the radial distribution function of ca. 12. We have also predicted a diffusion coefficient of 0.5×10-4 cm2 s-1 indicative of a core viscosity of ca. 0.026 Pa s, in line with current estimates.
The adsorption of atomic hydrogen on the (100) surfaces of face-centered-cubic rhodium, palladium and silver has been studied using ab-initio density-functional calculations (including generalized gradient corrections). At the example of Rh(100) we present detailed investigations of the influence of the nonlocal corrections to the exchange-correlation functional on the stable geometries and the energies of adsorption. We also study the influence of the adsorbate on the relaxation of the substrate. Chemical trends are studied along the series Rh–Pd–Ag.
Received 8 November 2001DOI:https://doi.org/10.1103/PhysRevB.66.146401©2002 American Physical Society
On 30 September 2010, Jürgen Hafner, one of the most prominent and influential members within the solid state community, retired. His remarkably broad scientific oeuvre has made him one of the founding fathers of modern computational materials science: more than 600 scientific publications, numerous contributions to books, and a highly cited monograph, which has become a standard reference in the theory of metals, witness not only the remarkable productivity of Jürgen Hafner but also his impact in theoretical solid state physics.
