Alberto Ambrosetti

Long-range correlation energy calculated from coupled atomic response functions

An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

Wavelike charge density fluctuations and van der Waals interactions at the nanoscale

Describing dispersion forces Dispersion or van der Waals interactions are attractive forces that arise from induced dipoles. They are not seen just in atoms and molecules but also in larger nanostructures and even macroscopic objects. Ambrosetti et al. created a qualitatively correct description of van der Waals interactions between polarizable nanostructures over a wide range of finite distances. This required delocalized electrons that have wavelike electron density fluctuations, unlike the more common approaches with dipoles fixed on atoms. Furthermore, the authors observed an enhancement in the nonlocality of the charge density response on the scale of 10 to 20 nm. Science, this issue p. 1171 The description of van der Waals interactions in nanostructures must include delocalized electron density fluctuations. Recent experiments on noncovalent interactions at the nanoscale have challenged the basic assumptions of commonly used particle- or fragment-based models for describing van der Waals (vdW) or dispersion forces. We demonstrate that a qualitatively correct description of the vdW interactions between polarizable nanostructures over a wide range of finite distances can only be attained by accounting for the wavelike nature of charge density fluctuations. By considering a diverse set of materials and biological systems with markedly different dimensionalities, topologies, and polarizabilities, we find a visible enhancement in the nonlocality of the charge density response in the range of 10 to 20 nanometers. These collective wavelike fluctuations are responsible for the emergence of nontrivial modifications of the power laws that govern noncovalent interactions at the nanoscale.

Including screening in van der Waals corrected density functional theory calculations: The case of atoms and small molecules physisorbed on graphene

The Density Functional Theory (DFT)/van der Waals-Quantum Harmonic Oscillator-Wannier function (vdW-QHO-WF) method, recently developed to include the vdW interactions in approximated DFT by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique, is applied to the cases of atoms and small molecules (X=Ar, CO, H2, H2O) weakly interacting with benzene and with the ideal planar graphene surface. Comparison is also presented with the results obtained by other DFT vdW-corrected schemes, including PBE+D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal generalized gradient approximation approaches. While for the X-benzene systems all the considered vdW-corrected schemes perform reasonably well, it turns out that an accurate description of the X-graphene interaction requires a proper treatment of many-body contributions and of short-range screening effects, as demonstrated by adopting an improved version of the DFT/vdW-QHO-WF method. We also comment on the widespread attitude of relying on LDA to get a rough description of weakly interacting systems.

Adsorption of rare-gas atoms on Cu(111) and Pb(111) surfaces by van der Waals corrected density functional theory

The DFT/vdW-WF method, recently developed to include the Van der Waals interactions in Density Functional Theory (DFT) using the maximally localized Wannier functions, is applied to the study of the adsorption of rare-gas atoms (Ne, Ar, Kr, and Xe) on the Cu(111) and Pb(111) surfaces at three high-symmetry sites. We evaluate the equilibrium binding energies and distances and the induced work-function changes and dipole moments. We find that for Ne, Ar, and Kr on the Cu(111) surface the different adsorption configurations are characterized by very similar binding energies while the favored adsorption site for Xe on Cu(111) is on top of a Cu atom, in agreement with previous theoretical calculations and experimental findings and in common with other close-packed metal surfaces. Instead, the favored site is always the hollow one on the Pb(111) surface, which therefore represents an interesting system where the investigation of high-coordination sites is possible. Moreover, the Pb(111) substrate is subject, upon rare-gas adsorption, to a significantly smaller change in the work function (and to a correspondingly smaller induced dipole moment) than Cu(111). The roles of the chosen reference DFT functional and of different van der Waals corrections as well as their dependence on different rare-gas adatoms are also discussed.

van der Waals corrected DFT simulation of adsorption processes on transition-metal surfaces: Xe and graphene on Ni(111)

The DFT/vdW-WF2s1 method, recently developed to include the van der Waals interactions in the Density Functional Theory and describe adsorption processes on metal surfaces by taking metal-screening effects into account, is applied to the case of the interaction of Xe and graphene with a transition-metal surface, namely Ni(111). In general the adsorption of rare-gas atoms on metal surfaces is important because is prototypical for physisorption processes. Moreover, the interaction of graphene with Ni(111) is of particular interest for practical applications (efficient and large-scale production of high-quality graphene) and, from a theoretical point of view, is particularly challenging, since it can be described by a delicate interplay between chemisorption and physisorption processes. The first-principles simulation of transition metals require particular care also because they can be viewed as intermediate systems between simple metals and insulating crystals. Even in these cases the method performs well as demonstrated by comparing our results with available experimental data and other theoretical investigations. We confirm that the rare gas Xe atom is preferentially adsorbed on the top-site configuration on the Ni(111) surface too. Our approach based on the use of the Maximally Localized Wannier Functions also allow us to well characterize the bonds between graphene and Ni(111).

Spin-orbit interactions in electronic structure quantum Monte Carlo methods

We develop generalization of the fixed-phase diffusion Monte Carlo method for Hamiltonians which explicitly depend on particle spins such as for spin-orbit interactions. The method is formulated in zero variance manner and is similar to treatment of nonlocal operators in commonly used static- spin calculations. Tests on atomic and molecular systems show that it is very accurate, on par with the fixed-node method. This opens electronic structure quantum Monte Carlo methods to a vast research area of quantum phenomena in which spin-related interactions play an important role.

Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated carbon and lead atoms. In the case of the carbon atom, we investigate the differences between the inclusion of spin-orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for a systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.

Cohesive properties of noble metals by van der Waals-corrected density functional theory: Au, Ag, and Cu as case studies

The cohesive energy, equilibrium lattice constant, and bulk modulus of noble metals are computed by different van der Waals-corrected Density Functional Theory methods, including vdW-DF, vdW-DF2, vdW-DF-cx, rVV10 and PBE-D. Two specifically-designed methods are also developed in order to effectively include dynamical screening effects: the DFT/vdW-WF2p method, based on the generation of Maximally Localized Wannier Functions, and the RPAp scheme (in two variants), based on a single-oscillator model of the localized electron response. Comparison with results obtained without explicit inclusion of van der Waals effects, such as with the LDA, PBE, PBEsol, or the hybrid PBE0 functional, elucidates the importance of a suitable description of screened van der Waals interactions even in the case of strong metal bonding. Many-body effects are also quantitatively evaluated within the RPAp approach.

Polarization of a quasi-two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling: A variational study

Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wavefunction, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: 1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional 2D Stoner instability. 2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e. it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.