Publications (58)137.84 Total impact
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ABSTRACT: We present a rangeseparated linearresponse timedependent densityfunctional theory (TDDFT) which combines a densityfunctional approximation for the shortrange response kernel and a frequencydependent secondorder BetheSalpeter approximation for the longrange response kernel. This approach goes beyond the adiabatic approximation usually used in linearresponse TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequencydependent secondorder BetheSalpeter correlation kernel is given using manybody Greenfunction theory. Preliminary tests of this rangeseparated TDDFT method are presented for the calculation of excitation energies of four small molecules: N2, CO2, H2CO, and C2H4. The results suggest that the addition of the longrange secondorder BetheSalpeter correlation kernel overall slightly improves the excitation energies.  [Show abstract] [Hide abstract]
ABSTRACT: We provide a pedagogical introduction to the two main variants of realspace quantum Monte Carlo methods for electronicstructure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the MetropolisHastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixednode approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the groundstate wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.  [Show abstract] [Hide abstract]
ABSTRACT: Quantum chemistry methods exploiting densityfunctional approximations for shortrange electronelectron interactions and secondorder M{{\o}}llerPlesset (MP2) perturbation theory for longrange electronelectron interactions have been implemented for periodic systems using Gaussiantype basis functions and the local correlation framework. The performance of these rangeseparated double hybrids has been benchmarked on a significant set of systems including raregas, molecular, ionic, and covalent crystals. The use of spincomponentscaled MP2 for the longrange part has been tested as well. The results show that the value of $\mu$ = 0.5 bohr^{1} for the rangeseparation parameter usually used for molecular systems is also a reasonable choice for solids. Overall, these rangeseparated double hybrids provide a good accuracy for binding energies using basis sets of moderate sizes such as ccpVDZ and augccpVDZ.The Journal of Chemical Physics 06/2015; 143(10). DOI:10.1063/1.4922996 · 2.95 Impact Factor 
 The Journal of Chemical Physics 06/2015; 142(21):219901. DOI:10.1063/1.4921987 · 2.95 Impact Factor
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ABSTRACT: In this paper, an alternative method to rangeseparated linearresponse timedependent densityfunctional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the rangeseparated or linear adiabatic connection where either the electronelectron interaction is scaled or only the longrange part of the Coulomb interaction is included. The extrapolation scheme is first applied to the rangeseparated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the rangeseparation parameter. The rangeseparated extrapolation scheme is compared with a similar approach for the linear adiabatic connection, highlighting the relative strengths and weaknesses of each approach.Physical Review A 03/2015; 91(3). DOI:10.1103/PhysRevA.91.032519 · 2.81 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We explore the possibility of calculating electronic excited states by using perturbation theory along a rangeseparated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a firstorder correction is defined with two variants of perturbation theory: a straightforward perturbation theory, and an extension of the G{\"o}rlingLevy one that has the advantage of keeping the groundstate density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the dihydrogene molecule. The firstorder correction within this perturbation theory improves significantly the total groundand excitedstate energies of the different systems. However, the excitation energies are mostly deteriorated with respect to the zerothorder ones, which may be explained by the fact that the ionization energy is no longer correct for all interaction strengths. The second variant of the perturbation theory should improve these results but has not been tested yet along the rangeseparated adiabatic connection.Molecular Physics 12/2014; 113(13). DOI:10.1080/00268976.2015.1011248 · 1.72 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Rangeseparated densityfunctional theory (DFT) is an alternative approach to KohnSham densityfunctional theory. The strategy of rangeseparated densityfunctional theory consists in separating the Coulomb electronelectron interaction into longrange and shortrange components and treating the longrange part by an explicit manybody wavefunction method and the shortrange part by a densityfunctional approximation. Among the advantages of using manybody methods for the longrange part of the electronelectron interaction is that they are much less sensitive to the oneelectron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of rangeseparated densityfunctional theory. We study the convergence of the partialwave expansion of the longrange wave function near the electronelectron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the longrange wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the longrange secondorder MøllerPlesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a threepoint completebasisset extrapolation scheme for rangeseparated densityfunctional theory based on an exponential formula.The Journal of Chemical Physics 12/2014; 142(7). DOI:10.1063/1.4907920 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We test the performance of a number of two and oneparameter doublehybrid approximations, combining semilocal exchangecorrelation density functionals with periodic local secondorder M{\o}llerPlesset (LMP2) perturbation theory, for calculating lattice energies of a set of molecular crystals: urea, formamide, ammonia, and carbon dioxide. All doublehybrid methods perform better on average than the corresponding KohnSham calculations with the same functionals, but generally not better than standard LMP2. The oneparameter doublehybrid approximations based on the PBEsol density functional gives lattice energies per molecule with an accuracy of about 6 kJ/mol, which is similar to the accuracy of LMP2. This conclusion is further verified on molecular dimers and on the hydrogen cyanide crystal.The Journal of Chemical Physics 07/2014; 141(4):044105. DOI:10.1063/1.4890439 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a study of the variation of total energies and excitation energies along a rangeseparated adiabatic connection. This connection links the noninteracting KohnSham electronic system to the physical interacting system by progressively switching on the electronelectron interactions whilst simultaneously adjusting a oneelectron effective potential so as to keep the groundstate density constant. The interactions are introduced in a rangedependent manner, first introducing predominantly longrange, and then allrange, interactions as the physical system is approached, as opposed to the conventional adiabatic connection where the interactions are introduced by globally scaling the standard Coulomb interaction. Reference data are reported for the He and Be atoms and the H2 molecule, obtained by calculating the shortrange effective potential at the full configurationinteraction level using Lieb's Legendretransform approach. As the strength of the electronelectron interactions increases, the excitation energies, calculated for the partially interacting systems along the adiabatic connection, offer increasingly accurate approximations to the exact excitation energies. Importantly, the excitation energies calculated at an intermediate point of the adiabatic connection are much better approximations to the exact excitation energies than are the corresponding KohnSham excitation energies. This is particularly evident in situations involving strong static correlation effects and states with multiple excitation character, such as the dissociating H2 molecule. These results highlight the utility of longrange interacting reference systems as a starting point for the calculation of excitation energies and are of interest for developing and analyzing practical approximate rangeseparated densityfunctional methodologies.The Journal of Chemical Physics 07/2014; 141(4):044123. DOI:10.1063/1.4890652 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Within exact electron densityfunctional theory, we investigate KohnSham (KS) potentials, orbital energies, and noninteracting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which are then fitted, interpolated at noninteger electron numbers $N$, and inverted to produce accurate KS potentials $v_s^N(r)$. We study the dependence of the KS potential on $N$, and in particular we numerically confirm the existence of the theoretically predicted spatially constant discontinuity of $v_s^N(r)$ as $N$ passes through an integer. We further show that, for all the cases considered, the inner orbital energies and the noninteracting kinetic energy are nearly piecewise linear functions of $N$. This leads us to propose a simple approximation of the KS potential $v_s^N(r)$ at any fractional electron number $N$ which uses only quantities of the systems with the adjacent integer electron numbers.Physical Review A 07/2014; 90(5). DOI:10.1103/PhysRevA.90.050502 · 2.81 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We explore several random phase approximation (RPA) correlation energy variants within the adiabaticconnection fluctuationdissipation theorem approach. These variants differ in the way the exchange interactions are treated. One of these variants, named dRPAII, is original to this work and closely resembles the secondorder screened exchange (SOSEX) method. We discuss and clarify the connections among different RPA formulations. We derive the spinadapted forms of all the variants for closedshell systems, and test them on a few atomic and molecular systems with and without range separation of the electronelectron interaction.Journal of Chemical Theory and Computation 04/2014; 7(1010). DOI:10.1021/ct200501r · 5.50 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We extend the previously proposed oneparameter doublehybrid densityfunctional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to metageneralizedgradientapproximation (metaGGA) exchangecorrelation density functionals. We construct several variants of oneparameter doublehybrid approximations using the TaoPerdewStaroverovScuseria (TPSS) metaGGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard KohnSham TPSS and secondorder MøllerPlesset calculations.The Journal of Chemical Physics 02/2014; 140(8):084107. DOI:10.1063/1.4865963 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The alternative separation of exchange and correlation energies proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] is explored in the context of multiconfiguration rangeseparated densityfunctional theory. The new decomposition of the shortrange exchangecorrelation energy relies on the auxiliary longrange interacting wavefunction rather than the KohnSham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using shortrange optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the HartreeFock (HF) and multiconfiguration selfconsistentfield (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the shortrange local density approximation on H2, N2, Li2, and H2O. Significant improvements in binding energies are obtained with the new decomposition of the shortrange energy. The importance of optimizing the shortrange OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finitedifference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.The Journal of Chemical Physics 10/2013; 139(13):134113. DOI:10.1063/1.4822135 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study linearresponse timedependent densityfunctional theory (DFT) based on the singledeterminant rangeseparated hybrid (RSH) scheme, i.e. combining a longrange HartreeFock exchange kernel with a shortrange DFT exchangecorrelation kernel, for calculating electronic excitation energies of molecular systems. It is an alternative to the longrange correction (LC) scheme which has a standard fullrange DFT correlation kernel instead of only a shortrange one. We discuss the localdensity approximation (LDA) to the shortrange exchangecorrelation kernel, and assess the performance of the linearresponse RSH scheme for singletsinglet and singlettriplet valence and Rydberg excitations in the N2, CO, H2CO, C2H4, and C6H6 molecules, and for the first chargetransfer excitation in the C2H4C2F4 dimer. The introduction of longrange HF exchange corrects the underestimation of chargetransfer and highlying Rydberg excitation energies obtained with standard (semi)local densityfunctional approximations, but also leads to underestimated excitation energies to lowlying spintriplet valence states which can be cured by the TammDancoff approximation. This work thus suggests that the present linearresponse RSH scheme is a reasonable starting approximation for describing electronic excitation energies, even before adding an explicit treatment of longrange correlation.Molecular Physics 07/2013; 111(911):12191234. DOI:10.1080/00268976.2013.794313 · 1.72 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We assess a variant of linearresponse rangeseparated timedependent densityfunctional theory (TDDFT), combining a longrange HartreeFock (HF) exchange kernel with a shortrange adiabatic exchangecorrelation kernel in the localdensity approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closedshell atoms and small molecules. This rangeseparated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to timedependent HartreeFock which has a mean absolute percentage error of about 6%. These results thus show that introduction of longrange HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of rangeseparated TDDFT is a reasonably accurate method even using only a LDAtype density functional and without adding an explicit treatment of longrange correlation.The Journal of Chemical Physics 05/2013; 138(19):194106. DOI:10.1063/1.4804981 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We review the BetheSalpeter equation (BSE) approach to the calculation of electronic excitation energies of molecular systems. We recall the general Green's function manytheory formalism and give the working equations of the BSE approach within the static GW approximation with and without spin adaptation in an orbital basis. We apply the method to the pedagogical example of the H2 molecule in a minimal basis, testing the effects of the choice of the starting oneparticle Green's function. Using the noninteracting oneparticle Green's function leads to incorrect energy curves for the first singlet and triplet excited states in the dissociation limit. Starting from the exact oneparticle Green's function leads to a qualitatively correct energy curve for the first singlet excited state, but still an incorrect energy curve for the triplet excited state. Using the exact oneparticle Green's function in the BSE approach within the static GW approximation also leads to a number of additional excitations, all of them being spurious except for one which can be identified as a double excitation corresponding to the second singlet excited state.  [Show abstract] [Hide abstract]
ABSTRACT: We propose a multiconfigurational hybrid densityfunctional theory which rigorously combines a multiconfiguration selfconsistentfield calculation with a densityfunctional approximation based on a linear decomposition of the electronelectron interaction. This gives a straightforward extension of the usual hybrid approximations by essentially adding a fraction λ of exact static correlation in addition to the fraction λ of exact exchange. Test calculations on the cycloaddition reactions of ozone with ethylene or acetylene and the dissociation of diatomic molecules with the PerdewBurkeErnzerhof and BeckeLeeYangParr density functionals show that a good value of λ is 0.25, as in the usual hybrid approximations. The results suggest that the proposed multiconfigurational hybrid approximations can improve over usual densityfunctional calculations for situations with strong static correlation effects.The Journal of Chemical Physics 07/2012; 137(4):044104. DOI:10.1063/1.4733672 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant SlaterJastrow trial wavefunction formed from HartreeFock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant SlaterJastrow trial wavefunction, diffusion Monte Carlo with a small complete active space SlaterJastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.The Journal of Chemical Physics 03/2012; 136(12):124116. DOI:10.1063/1.3697846 · 2.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We provide a rationale for a new class of doublehybrid approximations introduced by Br\'emond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchangecorrelation density functional with HartreeFock exchange weighted by $\l$ and secondorder M{\o}llerPlesset (MP2) correlation weighted by $\l^3$. We show that this doublehybrid model can be understood in the context of the densityscaled doublehybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the densityscaled correlation functional $E_c[n_{1/\l}]$ by a linear function of $\l$, interpolating between MP2 at $\l=0$ and a densityfunctional approximation at $\l=1$. Numerical results obtained with the PerdewBurkeErnzerhof density functional confirms the relevance of this doublehybrid model.The Journal of Chemical Physics 09/2011; 135(10):101102. DOI:10.1063/1.3640019 · 2.95 Impact Factor
Publication Stats
2k  Citations  
137.84  Total Impact Points  
Top Journals
Institutions

20092015

French National Centre for Scientific Research
Lutetia Parisorum, ÎledeFrance, France


2014

Université ParisSorbonne  Paris IV
Lutetia Parisorum, ÎledeFrance, France


20042014

Pierre and Marie Curie University  Paris 6
 Laboratoire de Chimie Théorique (LCT  UMR 7616)
Lutetia Parisorum, ÎledeFrance, France


2007

Cornell University
 Laboratory of Atomic and Solid State Physics
Ithaca, NY, United States
