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Andrea Ferretti

Publications and source records attributed to Andrea Ferretti.

50 records · Page 3Linked to original sources
arXiv2014

Photoemission Spectroscopy and Orbital Imaging from Koopmans-Compliant Functionals

The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches, such as density-functional theory. We show here that Koopmans-compliant functionals, constructed to enforce piecewise linearity in energy functionals with respect to fractional occupations - i.e. with respect to charged excitations - provide molecular photoemission spectra and momentum maps of Dyson orbitals that are in excellent agreement with experimental ultraviolet photoemission spectroscopy and orbital tomography data. These results highlight the role of Koopmans-compliant functionals as accurate and inexpensive quasiparticle approximations to the spectral potential.

cond-mat.mtrl-sci↗
arXiv2014

Koopmans-compliant functionals and their performance against reference molecular data

Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional functionals can then be constructed that modify the potential energy surface, including e.g. Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G$_0$W$_0$ and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations (Note: Supplemental Material is included in the source).

cond-mat.mtrl-sci↗
arXiv2013

Effective and accurate representation of extended Bloch states on finite Hilbert spaces

We present a straightforward, noniterative projection scheme that can represent the electronic ground state of a periodic system on a finite atomic-orbital-like basis, up to a predictable number of electronic states and with controllable accuracy. By co-filtering the projections of plane-wave Bloch states with high-kinetic-energy components, the richness of the finite space and thus the number of exactly-reproduced bands can be selectively increased at a negligible computational cost, an essential requirement for the design of efficient algorithms for electronic structure simulations of realistic material systems and massive high-throughput investigations.

cond-mat.mes-hall↗
arXiv2013

Relative Prym varieties associated to the double cover of an Enriques surface

Given an Enriques surface $T$, its universal K3 cover $f: S\to T$, and a genus $g$ linear system $|C|$ on $T$, we construct the relative Prym variety $P_H=\Prym_{v, H}(\D/\CC)$, where $\CC\to |C|$ and $\D\to |f^*C|$ are the universal families, $v$ is the Mukai vector $(0,[D], 2-2g)$ and $H$ is a polarization on $S$. The relative Prym variety is a $(2g-2)$-dimensional possibly singular variety, whose smooth locus is endowed with a hyperkähler structure. This variety is constructed as the closure of the fixed locus of a symplectic birational involution defined on the moduli space $M_{v,H}(S)$. There is a natural Lagrangian fibration $η: P_H \to |C|$, that makes the regular locus of $P_H$ into an integrable system whose general fiber is a $(g-1)$-dimensional (principally polarized) Prym variety, which in most cases is not the Jacobian of a curve. We prove that if $|C|$ is a hyperelliptic linear system, then $P_H$ admits a symplectic resolution which is birational to a hyperkähler manifold of K3$^{[g-1]}$-type, while if $|C|$ is not hyperelliptic, then $P_H$ admits no symplectic resolution. We also prove that any resolution of $P_H$ is simply connected and, when $g$ is odd, any resolution of $P_H$ has $h^{2,0}$-Hodge number equal to one.

math.AG↗
arXiv2012

Donor and acceptor levels of organic photovoltaic compounds from first principles

Accurate and efficient approaches to predict the optical properties of organic semiconducting compounds could accelerate the search for efficient organic photovoltaic materials. Nevertheless, predicting the optical properties of organic semiconductors has been plagued by the inaccuracy or computational cost of conventional first-principles calculations. In this work, we demonstrate that orbital-dependent density-functional theory based upon Koopmans' condition [Phys. Rev. B 82, 115121 (2010)] is apt at describing donor and acceptor levels for a wide variety of organic molecules, clusters, and oligomers within a few tenths of an electron-volt relative to experiment, which is comparable to the predictive performance of many-body perturbation theory methods at a fraction of the computational cost.

cond-mat.mtrl-sci↗
arXiv2012

Ab initio complex band structure of conjugated polymers: Effects of hydrid DFT and GW schemes

The non-resonant tunneling regime for charge transfer across nanojunctions is critically dependent on the so-called β parameter, governing the exponential decay of the current as the length of the junction increases. For periodic materials, this parameter can be theoretically evaluated by computing the complex band structure (CBS) -- or evanescent states -- of the material forming the tunneling junction. In this work we present the calculation of the CBS for organic polymers using a variety of computational schemes, including standard local, semilocal, and hybrid-exchange density functionals, and many-body perturbation theory within the GW approximation. We compare the description of localization and β parameters among the adopted methods and with experimental data. We show that local and semilocal density functionals systematically underestimate the β parameter, while hybrid-exchange schemes partially correct for this discrepancy, resulting in a much better agreement with GW calculations and experiments. Self-consistency effects and self-energy representation issues of the GW corrections are discussed together with the use of Wannier functions to interpolate the electronic band-structure.

cond-mat.mtrl-sci↗
arXiv2011

Variational Minimization of Orbital-dependent Density Functionals

Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density dependent, and provide a very promising avenue to go beyond density-functional theory, especially when studying electronic, optical and dielectric properties, charge-transfer excitations, and molecular dissociations. Unlike conventional density functionals, these functionals are not invariant under unitary transformations of occupied electronic states, which leave the total charge density intact, and this added complexity has greatly inhibited both their development and their practical applicability. Here, we first recast the minimization problem for non-unitary invariant energy functionals into the language of ensemble density-functional theory, decoupling the variational search into an inner loop of unitary transformations that minimize the energy at fixed orbital subspace, and an outer-loop evolution of the orbitals in the space orthogonal to the occupied manifold. Then, we show that the potential energy surface in the inner loop is far from convex parabolic in the early stages of the minimization and hence minimization schemes based on these assumptions are unstable, and present an approach to overcome such difficulty. The overall formulation allows for a stable, robust, and efficient variational minimization of non-unitary-invariant functionals, essential to study complex materials and molecules, and to investigate the bulk thermodynamic limit, where orbitals converge typically to localized Wannier functions. In particular, using maximally localized Wannier functions as an initial guess can greatly reduce the computational costs needed to reach the energy minimum while not affecting or improving the convergence efficiency.

cond-mat.mtrl-sci↗
arXiv2010

Koopmans' condition for density-functional theory

In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans' condition -- that identifies orbital energies as opposite total electron removal energies -- to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data -- with an accuracy comparable to that of GW many-body perturbation theory -- while providing an explicit total energy functional that preserves or improves on the description of established structural properties.

cond-mat.mtrl-sci↗
arXiv2009

The Chow ring of double EPW sextics

A conjecture of Beauville and Voisin states that for an irreducible symplectic variety X, any polynomial relation between classes of divisors and the Chern classes of X which holds in cohomology already holds in the Chow groups. We verify the conjecture for a very general double EPW sextic.

math.AG↗
arXiv2007

Ab initio correlation effects on the electronic and transport properties of metal(II)-phthalocyanine based devices

Using first principles calculations in the framework of Density Functional Theory, we investigated the electronic and transport properties of metal(II)-phthalocyanine (M(II)Pc) systems, both in a single molecule configuration and in a model-device geometry. In particular, using the Copper(II)- and Manganese(II)-Pc as prototypical examples, we studied how electronic correlations on the central metal-ion influence the analysis of the electronic structure of the system and we demonstrated that the choice of the exchange-correlation functional, also beyond the standard local or gradient corrected level, is of crucial importance for a correct interpretation of the data. Finally, our electronic transport simulations have shown that M(II)Pc-based devices can act selectively as molecular conductors, as in the case of Copper, or as spin valves, as in the case of Manganese, demonstrating once more the great potential of these systems for molecular nanoelectronics applications.

cond-mat.soft↗
arXiv2007

Equations in the Hadamard ring of rational functions

Let k be a number field. It is well known that the set of sequences composed by Taylor coefficients of rational functions over k is closed under component-wise operations, and so it can be equipped with a ring structure. A conjecture due to Pisot asks if (after enlarging the field) one can take d-th roots in this ring, provided d-th roots of coefficients can be taken in k. This was proved true in a preceding paper of the second author; in this article we generalize this result to more general equations, monic in Y, where the former case can be recovered for g(X,Y)=X^d-Y=0. Combining this with the Hadamard quotient theorem by Pourchet and Van der Poorten, we are able to get rid of the monic restriction, and have a theorem that generalizes both results.

math.NT↗
arXiv2006

Ab initio GW electron-electron interaction effects in Quantum Transport

We present an ab initio approach to electronic transport in nanoscale systems which includes electronic correlations through the GW approximation. With respect to Landauer approaches based on density-functional theory (DFT), we introduce a physical quasiparticle electronic-structure into a non-equilibrium Green's function theory framework. We use an equilibrium non-selfconsistent $G^0W^0$ self-energy considering both full non-hermiticity and dynamical effects. The method is applied to a real system, a gold mono-atomic chain. With respect to DFT results, the conductance profile is modified and reduced by to the introduction of diffusion and loss-of-coherence effects. The linear response conductance characteristic appear to be in agreement with experimental results.

cond-mat.mes-hall↗
arXiv2006

Maximally localized Wannier functions from PAW or ultrasoft pseudopotentials

We report a theoretical scheme that enables the calculation of maximally localized Wannier functions in the formalism of projector-augmented-waves (PAW) which also includes the ultrasoft-pseudopotential (USPP) approach. We give a description of the basic underlying formalism and explicitly write all the required matrix elements from the common ingredients of the PAW/USPP theory. We report an implementation of the method in a form suitable to accept the input electronic structure from USPP plane-wave DFT simulations. We apply the method to the calculation of Wannier functions, dipole moments and spontaneous polarizations in a range of test cases. Comparison with norm-conserving pseudopotentials is reported as a benchmark.

cond-mat.soft↗