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Paola Gori-Giorgi

Publications and source records attributed to Paola Gori-Giorgi.

At least 37 records · Page 2Linked to original sources
arXiv2020

London dispersion forces without density distortion: a path to first principles inclusion in density functional theory

We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a constrained search formalism for a supramolecular wavefunction that is forced to leave the diagonal of the many-body density matrix of each fragment unchanged, and is exact for the interaction between one-electron densities. We discuss several aspects: the needed features a density functional approximation for the exchange-correlation holes of the monomers should have, the optimal choice of the one-electron basis needed (named "dispersals"), and the functional derivative with respect to monomer density variations.

physics.chem-ph↗
arXiv2020

Kohn-Sham equations with functionals from the strictly-correlated regime: Investigation with a spectral renormalization method

We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory (DFT), with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so-called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation (ISI) functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential.

cond-mat.str-el↗
arXiv2020

MAP: an MP2 accuracy predictor for weak interactions from adiabatic connection theory

Second order Møller-Plesset perturbation theory (MP2) approximates the exact Hartree-Fock (HF) adiabatic connection (AC) curve by a straight line. Thus by using the deviation of the exact curve from the linear behaviour, we construct an indicator for the accuracy of MP2. We then use an interpolation along the HF AC to transform the exact form of our indicator into a highly practical MP2 accuracy predictor (MAP) that comes at negligible additional computational cost. We show that this indicator is already applicable to systems that dissociate into fragments with a non-degenerate ground state, and we illustrate its usefulness by applying it to the S22 and S66 datasets.

physics.chem-ph↗
arXiv2019

Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory

We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy--Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.

physics.chem-ph↗
arXiv2019

A variational approach to London dispersion interactions without density distortion

We introduce a class of variational wavefunctions that capture the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy optimization yields explicit expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated systems, providing a clean theoretical framework to build new approximations in several contexts. As the individual monomer densities are kept fixed, we can also unambiguously assess the effect of the density distortion on van der Waals interactions: for example, we obtain virtually exact dispersion coefficients between two hydrogen atoms up to $C_{10}$, and relative errors below $0.2\%$ in other simple cases.

physics.chem-ph↗
arXiv2018

Strong-interaction limit of an adiabatic connection in Hartree-Fock theory

We show that the leading term in the strong-interaction limit of the adiabatic connection that has as weak-interaction expansion the Moeller-Plesset perturbation theory can be fully determined from a functional of the Hartree-Fock density. We analyze this functional and highlight similarities and differences with the strong-interaction limit of the density-fixed adiabatic connection case of Kohn-Sham density functional theory.

physics.chem-ph↗
arXiv2018

Sum-rules of the response potential in the strongly-interacting limit of DFT

The response part of the exchange-correlation potential of Kohn-Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.

physics.chem-ph↗
arXiv2018

Response potential in the strong-interaction limit of DFT: Analysis and comparison with the coupling-constant average

Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analysing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.

physics.chem-ph↗
arXiv2018

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

It is known that the asymptotic decay of the electron density outside a molecule is informative about its first ionization potential. It has recently become clear that the special circumstance that the Kohn-Sham (KS) highest-occupied molecular orbital (HOMO) has a nodal plane that extends to infinity may give rise to different cases for the asymptotic behavior of the exact density and of the exact KS potential [Mol. Phys. 114 (2016) 1086]. Here we investigate the consequences of such a HOMO nodal plane for the effective potential in the Schrödinger-like equation for the square root of the density, showing that for atoms and molecules it will usually diverge asymptotically on the plane, either exponentially or polynomially, depending on the coupling between Dyson orbitals. We also analyze the issue in the etxernal harmonic potential, reporting an example of an exact analytic density for a fully interacting system that exhibits a different asymptotic behavior on the nodal plane.

physics.chem-ph↗
arXiv2017

Fermionic statistics in the strongly correlated limit of Density Functional Theory

Exact pieces of information on the adiabatic connection integrand $W_λ[ρ]$, which allows to evaluate the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit ($λ\to\infty$, where $λ$ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the fermionic statistics at large coupling $λ$, both numerical and theoretical, confirming that spin effects enter at orders $\sim e^{-\sqrtλ}$.

cond-mat.str-el↗
arXiv2017

Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT

The augmented potential introduced by Levy and Zahariev [Phys. Rev. Lett. 113, 113002 (2014)] is shifted with respect to the standard exchange-correlation potential of Kohn-Sham density functional theory by a density-dependent constant that makes the total energy become equal to the sum of the occupied orbital energies. In this work we analyze several features of this approach, focusing on the limit of infinite coupling strength, and studying the shift and the corresponding energy density at different correlation regimes. We also study other definitions of the energy density in relation to local interpolations along the adiabatic connection, present and discuss coordinate scaling properties, and use the shift to analyze the classical jellium and uniform gas models.

physics.chem-ph↗
arXiv2017

Simple fully non-local density functionals for the electronic repulsion energy

From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully non-local. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard DFT functionals, are captured by the highly nonlocal structure, which goes beyond the Jacob's ladder framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.

physics.chem-ph↗
arXiv2017

Interpolated energy densities, correlation indicators and lower bounds from approximations to the strong coupling limit of DFT

We investigate the construction of approximated exchange-correlation functionals by interpolating locally along the adiabatic connection between the weak- and the strong-coupling regimes, focussing on the effect of using approximate functionals for the strong-coupling energy densities. The gauge problem is avoided by dealing with quantities that are all locally defined in the same way. Using exact ingredients at weak coupling we are able to isolate the error coming from the approximations at strong coupling only. We find that the nonlocal radius model, which retains some of the non-locality of the exact strong-coupling regime, yields very satisfactory results. We also use interpolation models and quantities from the weak- and strong-coupling regimes to define a correlation-type indicator and a lower bound to the exact exchange-correlation energy. Open problems, related to the nature of the local and global slope of the adiabatic connection at weak coupling, are also discussed.

physics.chem-ph↗
arXiv2017

The strictly-correlated electron functional for spherically symmetric systems revisited

The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to yield strictly-correlated particle positions, related to each other by co-motion functions (or optimal maps), but the existence of such a deterministic solution in the general three-dimensional case is still an open question. A conjecture for the co-motion functions for radially symmetric densities was presented in Phys.~Rev.~A {\bf 75}, 042511 (2007), and later used to build approximate exchange-correlation functionals for electrons confined in low-density quantum dots. Colombo and Stra [Math.~Models Methods Appl.~Sci., {\bf 26} 1025 (2016)] have recently shown that these conjectured maps are not always optimal. Here we revisit the whole issue both from the formal and numerical point of view, finding that even if the conjectured maps are not always optimal, they still yield an interaction energy (cost) that is numerically very close to the true minimum. We also prove that the functional built from the conjectured maps has the expected functional derivative also when they are not optimal.

cond-mat.str-el↗
arXiv2016

Exchange-correlation functionals via local interpolation along the adiabatic connection

The construction of density-functional approximations is explored by modeling the adiabatic connection em locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of range of local interpolation models against accurate exchange-correlation energy densities. The importance of the strictly-correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models and prospects for future approximations based on the local adiabatic connection are discussed.

physics.chem-ph↗
arXiv2016

The adiabatic strictly-correlated-electrons functional: kernel and exact properties

We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.

cond-mat.str-el↗
arXiv2015

Challenging the Lieb-Oxford Bound in a systematic way

The Lieb-Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the wavefunction for strictly-correlated electrons of a given density, we turn the search over wavefunctions appearing in the original bound into a more manageable search over electron densities. This allows us to challenge the bound in a systematic way. We find that a maximizing density for the bound, if it exists, must have compact support. We also find that, at least for particle numbers $N\le 60$, a uniform density profile is not the most challenging for the bound. With our construction we improve the bound for $N=2$ electrons that was originally found by Lieb and Oxford, we give a new lower bound to the constant appearing in the Lieb-Oxford inequality valid for any $N$, and we provide an improved upper bound for the low-density uniform electron gas indirect energy.

physics.chem-ph↗