Peter Koval

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

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Publications (13)19.77 Total impact

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    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.
    04/2014;
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    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.
    03/2014; 89(15).
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    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.
    ACS Nano 03/2013; · 12.03 Impact Factor
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    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.
    03/2013;
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    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).
    02/2012;
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    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.
    The Journal of Chemical Physics 08/2011; 135(7):074105. · 3.12 Impact Factor
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    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.
    05/2011;
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    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.
    Journal of Chemical Theory and Computation - J CHEM THEORY COMPUT. 05/2010;
  • Physica Status Solidi B-basic Solid State Physics - PHYS STATUS SOLIDI B-BASIC SO. 01/2010; 247(8).
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    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.
    physica status solidi (b) 10/2009; · 1.49 Impact Factor
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    Dietrich Foerster, Peter Koval
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    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.
    The Journal of Chemical Physics 08/2009; 131(4):044103. · 3.12 Impact Factor
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    Peter Koval, Dietrich Foerster
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    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.

Publication Stats

16 Citations
19.77 Total Impact Points

Institutions

  • 2011
    • Donostia International Physics Center
      San Sebastián, Basque Country, Spain
    • Center of Materials Physics
      San Sebastián, Basque Country, Spain
  • 2009
    • Université Bordeaux 1
      Talence, Aquitaine, France
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France