Publications (49)103.69 Total impact
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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.12/2014;  [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.  [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 MøllerPlesset (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 give 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.  [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.07/2014;  [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.J. Chem. Theory Comput. 04/2014; 7(10).  [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. · 3.12 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. · 3.12 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. · 1.67 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. · 3.12 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.04/2013;  [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. · 3.12 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. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We provide a rationale for a new class of doublehybrid approximations introduced by Brémond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchangecorrelation density functional with HartreeFock exchange weighted by λ and secondorder MøllerPlesset (MP2) correlation weighted by λ(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/λ)] by a linear function of λ, interpolating between MP2 at λ = 0 and a densityfunctional approximation at λ = 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. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We explore different variants of the random phase approximation to the correlation energy derived from closedshell ringdiagram approximations to coupled cluster doubles theory. We implement these variants in rangeseparated densityfunctional theory, i.e., by combining the longrange random phase approximations with shortrange densityfunctional approximations. We perform tests on the raregas dimers He(2), Ne(2), and Ar(2), and on the weakly interacting molecular complexes of the S22 set of Jurečka et al. [P. Jurečka, J. Šponer, J. Černý, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones originally proposed by Szabo and Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)]. With range separation, they reach mean absolute errors on the equilibrium interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to mean absolute percentage errors of about 4%, with the augccpVDZ basis set.The Journal of Chemical Physics 08/2011; 135(8):084119. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: When using HartreeFock (HF) trial wave functions in quantum Monte Carlo calculations, one faces, in case of HF instabilities, the HF symmetry dilemma in choosing between the symmetryadapted solution of higher HF energy and symmetrybroken solutions of lower HF energies. In this work, we have examined the HF symmetry dilemma in hydrogen rings which present singlet instabilities for sufficiently large rings. We have found that the symmetryadapted HF wave function gives a lower energy both in variational Monte Carlo and in fixednode diffusion Monte Carlo. This indicates that the symmetryadapted wave function has more accurate nodes than the symmetrybroken wave functions, and thus suggests that spatial symmetry is an important criterion for selecting good trial wave functions.07/2011;  [Show abstract] [Hide abstract]
ABSTRACT: A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multiconfigurational selfconsistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the BurkatzkiFilippiDolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed GaussSlater functions are the appropriate primitives. Double and triplezeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding BurkatzkiFilippiDolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.The Journal of Chemical Physics 02/2011; 134(6):064104. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the use in quantum Monte Carlo calculations of two types of valence bond wave functions based on strictly localized active orbitals, namely valence bond selfconsistentfield and breathingorbital valence bond wave functions. Complemented by a Jastrow factor, these Jastrowvalencebond wave functions are tested by computing the equilibrium well depths of the four diatomic molecules C(2), N(2), O(2), and F(2) in both variational Monte Carlo and diffusion Monte Carlo. We show that it is possible to design compact wave functions based on chemical grounds that are capable of describing both static and dynamic electron correlations. These wave functions can be systematically improved by inclusion of valence bond structures corresponding to additional bonding patterns.The Journal of Chemical Physics 02/2011; 134(8):084108. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We provide a rigorous derivation of a class of doublehybrid approximations, combining HartreeFock exchange and secondorder MøllerPlesset correlation with a semilocal exchangecorrelation density functional. These doublehybrid approximations contain only one empirical parameter and use a densityscaled correlation energy functional. Neglecting density scaling leads to a oneparameter version of the standard doublehybrid approximations. We assess the performance of these doublehybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including rangeseparated hybrids. Our best oneparameter doublehybrid approximation, called 1DHBLYP, roughly reproduces the two parameters of the standard B2PLYP or B2GPPLYP doublehybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.The Journal of Chemical Physics 02/2011; 134(6):064113. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We report stateoftheart quantum Monte Carlo calculations of the singlet $n \to \pi^*$ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouab\c{c}a {\it et al.} [J. Chem. Phys. {\bf 130}, 114107 (2009)]. We investigate the effect of using a Slater basis set instead of a Gaussian basis set, and of using stateaverage versus statespecific completeactivespace (CAS) wave functions, with or without reoptimization of the coefficients of the configuration state functions (CSFs) and of the orbitals in variational Monte Carlo (VMC). It is found that, with the Slater basis set used here, both stateaverage and statespecific CAS(6,5) wave functions give an accurate excitation energy in diffusion Monte Carlo (DMC), with or without reoptimization of the CSF and orbital coefficients in the presence of the Jastrow factor. In contrast, the CAS(2,2) wave functions require reoptimization of the CSF and orbital coefficients to give a good DMC excitation energy. Our best estimates of the vertical excitation energy are between 3.86 and 3.89 eV. Comment: 6 pages, 1 figure, 2 tables, to appear in Progress in Theoretical Chemistry and Physics12/2010;  [Show abstract] [Hide abstract]
ABSTRACT: We combine densityfunctional theory with densitymatrixfunctional theory to draw the best from both worlds. This is achieved by range separation of the electronic interaction which permits one to rigorously combine a shortrange density functional with a longrange densitymatrix functional. The shortrange density functional is approximated by the shortrange version of the PerdewBurkeErnzerhof functional (srPBE). The longrange densitymatrix functional is approximated by the longrange version of the BuijseBaerends functional (lrBB). The obtained srPBE+lrBB method accurately describes both the static and dynamic electron correlation at a computational cost similar to that of standard densityfunctional approximations. This is shown for the dissociation curves of the H2, LiH, BH, and HF molecules.Physical Review A 11/2010; 82(5). · 3.04 Impact Factor
Publication Stats
858  Citations  
103.69  Total Impact Points  
Top Journals
Institutions

2009–2014

Polytech ParisUPMC
Lutetia Parisorum, ÎledeFrance, France 
Stanford University
 Department of Chemical Engineering
Stanford, CA, United States


2005–2013

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


2007–2012

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


2010

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