Peter Koval

Donostia International Physics Center, San Sebastián, Basque Country, Spain

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Publications (21)51.8 Total impact

  • [Show abstract] [Hide abstract] ABSTRACT: The correlation between transport properties across sub-nanometric metallic gaps and the optical response of the system is a complex effect which is determined by the fine atomic-scale details of the junction structure. As experimental advances are progressively accessing transport and optical characterization of smaller nanojunctions, a clear connection between the structural, electronic and optical properties in these nanocavities is needed. Using ab initio calculations, we present here a study of the simultaneous evolution of the structure and the optical response of a plasmonic junction as the particles forming the cavity, two Na380 clusters, approach and retract. Atomic reorganizations are responsible for a large hysteresis of the plasmonic response of the system, that shows a jump-to-contact instability during the approach process and the formation of an atom-sized neck across the junction during retraction. Our calculations demonstrate that, due to the quantization of the conductance in metal nanocontacts, atomic-scale reconfigurations play a crucial role in determining the optical response of the whole system. We observe abrupt changes in the intensities and spectral positions of the dominating plasmon resonances, and find a one-to-one correspondence between these jumps and those of the quantized transport as the neck cross-section diminishes. These results reveal an important connection between transport and optics at the atomic scale, which is at the frontier of current optoelectronics and can drive new options in optical engineering of signals driven by the motion and manipulation of single atoms.
    No preview · Article · Jan 2016
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    [Show abstract] [Hide abstract] ABSTRACT: We present a study of the optical response of compact and hollow icosahedral clusters containing up to 868 silver atoms by means of time-dependent density functional theory. We have studied the dependence on size and morphology of both the sharp plasmonic resonance at 3--4 eV (originated mainly from $sp$-electrons), and the less studied broader feature appearing in the 6--7 eV range (interband transitions). An analysis of the effect of structural relaxations, as well as the choice of exchange correlation functional (local density versus generalized gradient approximations) both in the ground state and optical response calculations is also presented. We have further analysed the role of the different atom layers (surface versus inner layers) and the different orbital symmetries on the absorption cross-section for energies up to 8 eV. We have also studied the dependence on the number of atom layers in hollow structures. Shells formed by a single layer of atoms show a pronounced red shift of the main plasmon resonances that, however, rapidly converge to those of the compact structures as the number of layers is increased. The methods used to obtain these results are also carefully discussed. Our methodology is based on the use of localized basis (atomic orbitals, and atom-centered- and dominant- product functions), which bring several computational advantages related to their relatively small size and the sparsity of the resulting matrices. Furthermore, the use of basis set of atomic orbitals also brings the possibility to extend some of the standard population analysis tools (e.g., Mulliken population analysis) to the realm of optical excitations. Some examples of these analyses are described in the present work.
    Full-text · Article · Dec 2015 · Journal of Physics Condensed Matter
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    Full-text · Article · Dec 2015
  • [Show abstract] [Hide abstract] ABSTRACT: The correlation between transport properties across sub-nanometric metallic gaps and the optical response of the system is a complex effect which is determined by the fine atomic-scale details of the junction structure. As experimental advances are progressively accessing transport and optical characterization of smaller nanojunctions, a clear connection between the structural, electronic and optical properties in these nanocavities is needed. Using ab initio calculations, we present here a study of the simultaneous evolution of the structure and the optical response of a plasmonic junction as the particles forming the cavity, two Na$_{380}$ clusters, approach and retract. Atomic reorganizations are responsible for a large hysteresis of the plasmonic response of the system, that shows a jump-to-contact instability during the approach process and the formation of an atom-sized neck across the junction during retraction. Our calculations demonstrate that, due to the quantization of the conductance in metal nanocontacts, atomic-scale reconfigurations play a crucial role in determining the optical response of the whole system. We observe abrupt changes in the intensities and spectral positions of the dominating plasmon resonances, and find a one-to-one correspondence between these jumps and those of the quantized transport as the neck cross-section diminishes. These results point out to an unforeseen connection between transport and optics at the atomic scale, which is at the frontier of current optoelectronics and can drive new options in optical engineering of signals driven by the motion and manipulation of single atoms.
    No preview · Article · Sep 2015
  • [Show abstract] [Hide abstract] ABSTRACT: A method is presented to compute the dielectric function for extended systems using linear response time-dependent density functional theory. Localized basis functions with finite support are used to expand both eigenstates and response functions. The electron-energy loss function is directly obtained by an iterative Krylov-subspace method. We apply our method to graphene and silicon and compare it to plane-wave based approaches. Finally, we compute electron-energy loss spectrum of C60 crystal to demonstrate the merits of the method for molecular crystals, where it will be most competitive.
    No preview · Article · Jul 2015 · Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms
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    [Show abstract] [Hide abstract] ABSTRACT: The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present difficulties for simpler approaches. We present a local basis set formulation of the BSE for molecules where the optical spectrum is computed with the iterative Haydock recursion scheme, leading to a low computational complexity and memory footprint. Using a variant of the algorithm we can go beyond the Tamm-Dancoff approximation (TDA). We rederive the recursion relations for general matrix elements of a resolvent, show how they translate into continued fractions, and study the convergence of the method with the number of recursion coefficients and the role of different terminators. Due to the locality of the basis functions the computational cost of each iteration scales asymptotically as $O(N^3)$ with the number of atoms, while the number of iterations is typically much lower than the size of the underlying electron-hole basis. In practice we see that , even for systems with thousands of orbitals, the runtime will be dominated by the $O(N^2)$ operation of applying the Coulomb kernel in the atomic orbital representation
    Full-text · Article · May 2015 · Physical Review B
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    [Show abstract] [Hide abstract] ABSTRACT: Atomistic Near-Field Nanoplasmonics: Reaching Atomic-Scale Resolution in Nanooptics Additional details on the computational parameters used in our calculations, and how they influence the results, on the structures of the different systems studied here, as well as a more detailed discussion of the data regarding the optical absorption versus dsep in Figure 2, together with the study of the corresponding currents established across the gap.
    No preview · Dataset · May 2015
  • [Show abstract] [Hide abstract] ABSTRACT: Electromagnetic field localization in nanoantennas is one of the leitmotivs that drives the development of plasmonics. The near-fields in these plasmonic nanoantennas are commonly addressed theoretically within classical frameworks that neglect atomic-scale features. This approach is often appropriate since the irregularities produced at the atomic scale are typically hidden in far-field optical spectroscopies. However, a variety of physical and chemical processes rely on the fine distribution of the local fields at this ultraconfined scale. We use time-dependent density functional theory and perform atomistic quantum mechanical calculations of the optical response of plasmonic nanoparticles, and their dimers, characterized by the presence of crystallographic planes, facets, vertices, and steps. Using sodium clusters as an example, we show that the atomistic details of the nanoparticles morphologies determine the presence of subnanometric near-field hot spots that are further enhanced by the action of the underlying nanometric plasmonic fields. This situation is analogue to a self-similar nanoantenna cascade effect, scaled down to atomic dimensions, and it provides new insights into the limits of field enhancement and confinement, with dramatic implications in the optical resolution of field-enhanced spectroscopies and microscopies.
    No preview · Article · Apr 2015 · Nano Letters
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    [Show abstract] [Hide abstract] ABSTRACT: Two self-consistent schemes involving Hedin's $GW$ approximation are studied for a set of sixteen different atoms and small molecules. We compare results from the fully self-consistent $GW$ approximation (SC$GW$) and the quasi-particle self-consistent $GW$ approximation (QS$GW$) within the same numerical framework. Core and valence electrons are treated on an equal footing in all the steps of the calculation. We use basis sets of localized functions to handle the space dependence of quantities and spectral functions to deal with their frequency dependence. We compare SC$GW$ and QS$GW$ on a qualitative level by comparing the computed densities of states (DOS). To judge their relative merit on a quantitative level, we compare their vertical ionization potentials (IPs) with those obtained from coupled-cluster calculations CCSD(T). Our results are futher compared with "one-shot" $G_0W_0$ calculations starting from Hartree-Fock solutions ($G_0W_0$-HF). Both self-consistent $GW$ approaches behave quite similarly. Averaging over all the studied molecules, both methods show only a small improvement (somewhat larger for SC$GW$) of the calculated IPs with respect to $G_0W_0$-HF results. Interestingly, SC$GW$ and QS$GW$ calculations tend to deviate in opposite directions with respect to CCSD(T) results. SC$GW$ systematically underestimates the IPs, while QS$GW$ tends to overestimate them. $G_0W_0$-HF produces results which are surprisingly close to QS$GW$ calculations both for the DOS and for the numerical values of the IPs.
    Full-text · Article · Apr 2014
  • [Show abstract] [Hide abstract] ABSTRACT: Two self-consistent schemes involving Hedin's GW approximation are studied for a set of sixteen different atoms and small molecules. We compare results from the fully self-consistent GW approximation (SCGW) and the quasiparticle self-consistent GW approximation (QSGW) within the same numerical framework. Core and valence electrons are treated on an equal footing in all the steps of the calculation. We use basis sets of localized functions to handle the space dependence of quantities and spectral functions to deal with their frequency dependence. We compare SCGW and QSGW on a qualitative level by comparing the computed densities of states (DOS). To judge their relative merit on a quantitative level, we compare their vertical ionization potentials (IPs) with those obtained from coupled-cluster calculations CCSD(T). Our results are futher compared with "one-shot" G0W0 calculations starting from Hartree-Fock solutions (G0W0-HF). Both self-consistent GW approaches behave quite similarly. Averaging over all the studied molecules, both methods show only a small improvement (somewhat larger for SCGW) of the calculated IPs with respect to G0W0-HF results. Interestingly, SCGW and QSGW calculations tend to deviate in opposite directions with respect to CCSD(T) results. SCGW systematically underestimates the IPs, while QSGW tends to overestimate them. G0W0-HF produces results which are surprisingly close to QSGW calculations both for the DOS and for the numerical values of the IPs.
    No preview · Article · Mar 2014 · Physical Review B
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    [Show abstract] [Hide abstract] ABSTRACT: We show that chemically synthesized polycyclic aromatic hydrocarbons (PAHs) exhibit molecular plasmon resonances that are remarkably sensitive to the net charge state of the molecule and the atomic structure of the edges. These molecules can be regarded as nanometer-sized forms of graphene, from which they inherit their high electrical tunability. Specifically, the addition or removal of a single electron switches on/off these molecular plasmons. Our first-principles time-dependent density-functional theory (TDDFT) calculations are in good agreement with a simpler tight-binding approach that can be easily extended to much larger systems. These fundamental insights enable the development of novel plasmonic devices based upon chemically available molecules, which, unlike colloidal or lithographic nanostructures, are free from structural imperfections. We further show a strong interaction between plasmons in neighboring molecules, quantified in significant energy shifts and field enhancement, and enabling molecular-based plasmonic designs. Our findings suggest new paradigms for electro-optical modulation and switching, single-electron detection, and sensing using individual molecules.
    Full-text · Article · Mar 2013 · ACS Nano
  • [Show abstract] [Hide abstract] ABSTRACT: Many-body perturbation theory of bulk systems is often realized within reciprocal space, using plane-wave (PW) basis sets. PW basis is advantageous because of its elementary basis functions and simple convergence control. However, the number of functions in PW basis grows with third power of unit cell size, irrespective of actual number of atoms present in the unit cell. Moreover, PW basis gives rise to full matrices in tensor algebra due to space-filling nature of PW. An alternative to PW would be usage of localized basis functions. In this contribution, we show how a basis of dominant products (DP) can be used to describe excitations in finite and bulk systems. We present calculations of absorption spectra and electron-energy loss spectra within time-dependent density functional theory, realized within DP basis. The usage of localized functions and iterative techniques allow to keep the complexity of the calculations rather low: the overall number of operations grows with third power of number of atoms in the unit cell.Moreover, we have recently shown that Hedin's GW calculations can also be performed using DP basis with an order-N^3 scaling for finite systems. We are currently extending this GW methodology to bulk systems.
    No preview · Article · Mar 2013
  • [Show abstract] [Hide abstract] ABSTRACT: Hedin's GW approximation (GWA) is a well known method to study charged excitations in electronic systems with a moderate computational cost [1]. Already one-shot GWA delivers a considerable improvement if compared with Green's functions from density-functional theory (DFT). However, the one-shot results are dependent on the used starting point. This unphysical dependence can be eliminated by iterating a GW calculation to self-consistency. We implemented self-consistent GWA for molecules [2], within our original framework of dominant products basis. We use the DFT calculation by SIESTA code as starting point. The framework allowed to calculate Green's functions on a fine frequency mesh for such small molecules as benzene. We demonstrate the level of independence on starting point achievable within pseudo-potential framework, validating the implementation. Effects of the self-consistency on the interacting Green's function will be discussed along with different levels of self-consistency and mixing schemes. Finally, we compare the self-consistency with so-called quasi-particle self-consistent GW [3]. [0pt] [1] F.Aryasetiawan, O.Gunnarsson, Rep. Prog. Phys. 61, 237 (1998).[0pt] [2] D.Foerster, P.Koval, D.Sanchez Portal, J. Chem. Phys. 135, 074105 (2011).[0pt] [3] T.Kotani, M.van Schilfgaarde, S.V.Falleev, Phys. Rev. B 76, 165106 (2007).
    No preview · Article · Feb 2012
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    [Show abstract] [Hide abstract] ABSTRACT: We describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N(3)) with the number of atoms. Our method is guided by two strategies: (i) to respect the locality of the underlying electronic interactions and (ii) to avoid the singularities of Green's functions by manipulating, instead, their spectral functions using fast Fourier transform methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors.
    Full-text · Article · Aug 2011 · The Journal of Chemical Physics
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    [Show abstract] [Hide abstract] ABSTRACT: Organic electronics is a rapidly developing technology. Typically, the molecules involved in organic electronics are made up of hundreds of atoms, prohibiting a theoretical description by wavefunction-based ab-initio methods. Density-functional and Green's function type of methods scale less steeply with the number of atoms. Therefore, they provide a suitable framework for the theory of such large systems. In this contribution, we describe an implementation, for molecules, of Hedin's GW approximation. The latter is the lowest order solution of a set of coupled integral equations for electronic Green's and vertex functions that was found by Lars Hedin half a century ago. Our implementation of Hedin's GW approximation has two distinctive features: i) it uses sets of localized functions to describe the spatial dependence of correlation functions, and ii) it uses spectral functions to treat their frequency dependence. Using these features, we were able to achieve a favorable computational complexity of this approximation. In our implementation, the number of operations grows as N^3 with the number of atoms N.
    Full-text · Article · May 2011
  • No preview · Article · Aug 2010 · physica status solidi (b)
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    [Show abstract] [Hide abstract] ABSTRACT: The use of the LCAO (Linear Combination of Atomic Orbitals) method for excited states involves products of orbitals that are known to be linearly dependent. We identify a basis in the space of orbital products that is local for orbitals of finite support and with a residual error that vanishes exponentially with its dimension. As an application of our previously reported technique we compute the Kohn--Sham density response function $\chi_{0}$ for a molecule consisting of $N$ atoms in $N^{2}N_{\omega}$ operations, with $N_{\omega}$ the number of frequency points. We test our construction of $\chi_{0}$ by computing molecular spectra directly from the equations of Petersilka--Gossmann--Gross in $N^{2}N_{\omega}$ operations rather than from Casida's equations which takes $N^{3}$ operations. We consider the good agreement with previously calculated molecular spectra as a validation of our construction of $\chi_{0}$. Ongoing work indicates that our method is well suited for the computation of the GW self-energy $\Sigma=\mathrm{i}GW$ and we expect it to be useful in the analysis of exitonic effects in molecules.
    Full-text · Article · Aug 2010 · physica status solidi (b)
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    [Show abstract] [Hide abstract] ABSTRACT: We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.
    Full-text · Article · May 2010 · Journal of Chemical Theory and Computation
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    Peter Koval · Dietrich Foerster
    [Show abstract] [Hide abstract] ABSTRACT: We extend the LCAO (Linear Combination of Atomic Orbitals) method to excited states by constructing a particularly simple basis in the space of orbital products. The residual error of our procedure vanishes exponentially with the number of products and our procedure avoids auxiliary sets of fitting functions and their intrinsic ambiguities. As an application of our technique, we compute the Kohn--Sham density response function $\chi_{0}$ for a molecule consisting of $N$ atoms in $O(N^{2}N_{\omega })$ operations, with $N_{\omega }$ the number of frequency points. Our construction of $\chi_{0}$ allows us to compute molecular spectra directly from the equations of Petersilka--Gossmann--Gross in $O(N^{2}N_{\omega })$ operations rather than from Casida's equations which takes $O(N^{3})$ operations. Ongoing work indicates that our method is well suited to a computation of the GW self-energy $\Sigma=\mathrm{i}GW$ and we expect a similar situation for the Bethe--Salpeter equation.
    Full-text · Article · Sep 2009
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    Dietrich Foerster · Peter Koval
    [Show abstract] [Hide abstract] ABSTRACT: We construct the Kohn-Sham density response function chi(0) in a previously described basis of the space of orbital products. The calculational complexity of our construction is O(N(2)N(omega)) for a molecule of N atoms and in a spectroscopic window of N(omega) frequency points. As a first application, we use chi(0) to calculate the molecular spectra from the Petersilka-Gossmann-Gross equation. With chi(0) as input, we obtain the correct spectra with an extra computational effort that grows also as O(N(2)N(omega)) and, therefore, less steeply in N than the O(N(3)) complexity of solving Casida's equations. Our construction should be useful for the study of excitons in molecular physics and in related areas where chi(0) is a crucial ingredient.
    Full-text · Article · Aug 2009 · The Journal of Chemical Physics