arXiv subjects

Nektarios N. Lathiotakis

Publications and source records attributed to Nektarios N. Lathiotakis.

At least 19 recordsLinked to original sources

arXiv2025

First-principles derived force field for h-BN monolayer nanostructures: Applications to sheets, nanotubes and nanotori

In this work, we present an empirical force field for hexagonal boron nitride (hBN) monolayers, derived via a bottom-up strategy from first principles calculations. We aim to deliver a simple analytical force field for boron nitride which is efficient and applicable to large-scale simulations, without compromising its accuracy. The force field is developed with the goal to analytically reproducing the potential energy contributions arising from planar bond-stretching and bond-angle-bending deformations, as well as from out-of-plane torsional deformations, as obtained from periodic density functional theory calculations. Analytical anharmonic potential energy functions were employed to describe and parameterize the force field through a fitting process. The potential is applied for estimating in-plane (stiffness matrix and elastic constants) and out-of-plane (bending and Gaussian rigidity) mechanical properties of monolayer hBNs using both molecular mechanics calculations and analytical formulas. Additionally, we determined the elastic properties of more complex nanostructures, including hBN nanotubes and nanotori. By combining a continuum model for bent hollow beams with the definition of bending rigidity, we validate the model predictions against an analytical expression for the bending rigidity of large-diameter hBN nanotubes, expressed as a function of their radius and the in-plane Young modulus.

cond-mat.mes-hall↗

arXiv2024

Porous carbon nitride fullerenes: a novel family of porous cage molecules

We propose and study theoretically a novel family of cage molecules, the porous carbon nitride fullerenes (PCNFs), which can be considered the zero-dimensional counterparts of the two-dimensional porous graphitic carbon nitrides, in accordance with icosahedral fullerenes, representing the zero-dimensional counterpart of graphene. We focus on two representative members of the PCNF family, the icosahedral C$_{60}$N$_{60}$ and C$_{120}$N$_{60}$ which are the first members of the two main sub-families of these structures derived from the class I and II Goldberg polyhedra, respectively. Taking into account that the two-dimensional graphitic carbon nitrides are considered the next-generation materials for several interesting applications, the interest in their zero-dimension counterparts is obvious. In the present study, we utilize Density Functional Theory to find their structural, vibrational, and electronic properties. The stability of the proposed cages was demonstrated through vibrational analysis and molecular dynamics simulations with ReaxFF potentials. Regarding thermal stability, we found that C$_{60}$N$_{60}$ could be stable well above 1000 K and C$_{120}$N$_{60}$ well above 2000 K. Finally, we discuss several ideas regarding precursors that could be possibly used for their bottom-up synthesis.

cond-mat.mtrl-sci↗

arXiv2023

Effective local potentials for density and density-matrix functional approximations with non-negative screening density

A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. {\bf 136}, 224109 (2012)]. As illustrated, a convenient variational quantity in that approach is the ``screening'' or ``electron repulsion'' density, $ρ_{\rm rep}$, corresponding to the local, KS Hartree, exchange and correlation potential through Poisson's equation. Two constraints, applied to this minimization, largely remove self-interaction errors from the effective potential: (i) $ρ_{\rm rep}$ integrates to $N-1$, where $N$ is the number of electrons, and (ii) $ρ_{\rm rep}\geq 0$ everywhere. In the present work, we introduce an effective ``screening'' amplitude, $f$, as the variational quantity, with the screening density being $ρ_{\rm rep}=f^2$. In this way, the positivity condition for $ρ_{\rm rep}$ is automatically satisfied and the minimization problem becomes more efficient and robust. We apply this technique to molecular calculations employing several approximations in DFT and in reduced density matrix functional theory. We find that the proposed development is an accurate, yet robust, variant of the constrained effective potential method.

physics.chem-ph↗

arXiv2021

Generalised Kohn-Sham equations with accurate total energy and single-particle eigenvalue spectrum

We propose a new generalised Kohn-Sham or constrained hybrid method, where the exchange potential is the (equally weighted) average of the nonlocal Fock exchange term and the self-interaction-corrected exchange potential, as obtained from our constrained minimisation method of semi-local approximations. The new method gives an accurate single-particle eigenvalue spectrum with an average deviation between (the negative of) the valence orbital eigenvalues and the experimental ionisation potentials of about 0.5eV, while the deviation of core orbitals is within 2eV. The improvement in the eigenvalue spectrum is achieved with a minimal increase in the total energy.

physics.chem-ph↗

arXiv2021

Improving the exchange and correlation potential in density functional approximations through constraints

We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a previously imposed positivity constraint, which increased the computational cost and we find that it is safe to do so, except in systems with very few electrons. The constrained minimisation leads invariably to the solution of an optimised effective potential (OEP) equation in order to determine the KS potential. We review briefly our previous work on this problem and demonstrate with numerous examples that despite well-known mathematical issues of the OEP with finite basis sets, our OEP equations are well behaved. We demonstrate that constraining the screening charge of the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlation potential to exhibit nonzero derivative discontinuity, a feature of the exact KS potential that is necessary for the accurate prediction of band-gaps in solids but very hard to capture with semi-local approximations.

physics.chem-ph↗

arXiv2020

Density-inversion method for the Kohn-Sham potential: role of the screening density

We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) which shares that density. Our method employs the concept of screening density, which is naturally constrained by the inversion procedure and thus ensures the density being inverted leads to a smooth KS potential with correct asymptotic behaviour. We demonstrate the applicability of our method by inverting both local (LDA) and non-local (Hartree-Fock and Coupled Cluster) densities; we also show how the method can be used to mitigate the effects of self-interactions in common DFT potentials with appropriate constraints on the screening density.

physics.chem-ph↗

arXiv2018

Performance of the Constrained Minimization of the Total Energy in Density Functional Approximations: the Electron Repulsion Density and Potential

In the constrained minimization method of Gidopoulos and Lathiotakis (J. Chem. Phys. 136, 224109), the Hartree exchange and correlation Kohn-Sham potential of a finite $N$-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of $N-1$ electrons. The optimal effective charge density (electron repulsion density, $ρ_{\rm rep}$) and the corresponding optimal effective potential (electron repulsion potential $v_{\rm rep}$) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from $v_{\rm rep}$, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE, and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39%, and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.

physics.chem-ph↗

arXiv2017

Atomistic potential for graphene and other sp$^2$ carbon systems

We introduce a torsional force field for sp$^2$ carbon to augment an in-plane atomistic potential of a previous work (Kalosakas et al, J. Appl. Phys. {\bf 113}, 134307 (2013)) so that it is applicable to out-of-plane deformations of graphene and related carbon materials. The introduced force field is fit to reproduce DFT calculation data of appropriately chosen structures. The aim is to create a force field that is as simple as possible so it can be efficient for large scale atomistic simulations of various sp$^2$ carbon structures without significant loss of accuracy. We show that the complete proposed potential reproduces characteristic properties of fullerenes and carbon nanotubes. In addition, it reproduces very accurately the out-of-plane ZA and ZO modes of graphene's phonon dispersion as well as all phonons with frequencies up to 1000~cm$^{-1}$.

cond-mat.mtrl-sci↗

arXiv2017

A Torsional potential for graphene derived from fitting to DFT results

We present a simple torsional potential for graphene to accurately describe its out-of-plane deformations. The parameters of the potential are derived through appropriate fitting with suitable DFT calculations regarding the deformation energy of graphene sheets folded around two different folding axes, along an armchair or along a zig-zag direction. Removing the energetic contribution of bending angles, using a previously introduced angle bending potential, we isolate the purely torsional deformation energy, which is then fitted to simple torsional force fields. The presented out-of-plane torsional potential can accurately fit the deformation energy for relatively large torsional angles up to 0.5 rad. To test our proposed potential, we apply it to the problem of the vertical displacement of a single carbon atom out of the graphene plane and compare the obtained deformation energy with corresponding DFT calculations. The dependence of the deformation energy on the vertical displacement of the pulled carbon atom is indistinguishable in these two cases, for displacements up to about 0.5 $Å$. The presented potential is applicable to other sp$^2$ carbon structures.

cond-mat.mtrl-sci↗

arXiv2017

Towards a formal definition of static and dynamic electronic correlations

Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress on the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.

physics.chem-ph↗

arXiv2017

Relating correlation measures: the importance of the energy gap

The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched H$_2$ to illustrate this connection and to show how the corresponding measures of correlation compare.

quant-ph↗

arXiv2017

Structural deformations of two-dimensional planar structures under uniaxial strain: The case of graphene

In the present work, a method for the study of the structural deformations of two dimensional planar structures under uniaxial strain is presented. The method is based on molecular mechanics using the original stick and spiral model and a modified one which includes second nearest neighbor interactions for bond stretching. As we show, the method allows an accurate prediction of the structural deformations of any two dimensional planar structure as a function of strain, along any strain direction in the elastic regime, if structural deformations are known along specific strain directions, which are used to calculate the stick and spiral model parameters. Our method can be generalized including other strain conditions and not only uniaxial strain. We apply this method to graphene and we test its validity, using results obtained from {\it ab initio} Density Functional Theory calculations. What we find is that the original stick and spiral model is not appropriate to describe accurately the structural deformations of graphene in the elastic regime. However, the introduction of second nearest neighbor interactions provides a very accurate description.

cond-mat.mtrl-sci↗

arXiv2016

Conditions for describing triplet states in reduced density matrix functional theory

We consider necessary conditions for the one-body-reduced density matrix (1RDM) to correspond to a triplet wave-function of a two electron system. The conditions concern the occupation numbers and are different for the high spin projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used to test if an approximate 1RDM functional yields the same energies for both projections. We employ these conditions in reduced density matrix functional theory calculations for the triplet excitations of two-electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space. We assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied.

physics.chem-ph↗

arXiv2015

Orbitals from local RDMFT: Are they Kohn-Sham or Natural Orbitals?

Recently, an approximate theoretical framework was introduced, called local reduced density matrix functional theory (local-RDMFT), where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional condition that the optimal orbitals satisfy a single electron Schrödinger equation with a local potential. In the present work, we focus on the character of these optimal orbitals. In particular, we compare orbitals obtained by local-RDMFT with those obtained with the full minimization (without the extra condition) by contrasting them against the exact NOs and orbitals from a density functional calculation using the local density approximation (LDA). We find that the orbitals from local-RMDFT are very close to LDA orbitals, contrary to those of the full minimization that resemble the exact NOs. Since local RDMFT preserves the good quality of the description of strong static correlation, this finding opens the way to a mixed density/density matrix scheme, where Kohn-Sham orbitals obtain fractional occupations from a minimization of the occupation numbers using 1-RDM functionals. This will allow for a description of strong correlation at a cost only minimally higher than a density functional calculation.

physics.chem-ph↗

arXiv2015

Generalized Pauli constraints in reduced density matrix functional theory

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman's ensemble $N$-representability conditions. Recently, the topic of pure-state $N$-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble $N$-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.

physics.chem-ph↗

arXiv2014

Quasi-particle energy spectra in local reduced density matrix functional theory

Recently, we introduced (e-print arXiv:1407.7128) {\em local reduced density matrix functional theory} (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C$_{20}$ isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solids.

physics.chem-ph↗

arXiv2014

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.

physics.chem-ph↗

arXiv2012

Constraining density functional approximations to yield self-interaction free potentials

Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local potential, under constraints for the effective potential that guarantee it is free from SI errors and consequently asymptotically correct. More specifically, we constrain the Hartree, exchange and correlation potential to be the electrostatic potential of a non-negative effective repulsive density of $N-1$ electrons. In this way, the optimal effective potentials exhibit the correct asymptotic decay, resulting in significantly improved one-electron properties.

cond-mat.other↗