arXiv subjects

Julien Toulouse

Publications and source records attributed to Julien Toulouse.

At least 73 records · Page 4Linked to original sources

arXiv2015

Calculating excitation energies by extrapolation along adiabatic connections

In this paper, an alternative method to range-separated linear-response time-dependent density-functional 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 range-separated or linear adiabatic connection where either the electron--electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated 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 range-separation parameter. The range-separated extrapolation scheme is compared with a similar approach for the linear adiabatic connection, highlighting the relative strengths and weaknesses of each approach.

physics.chem-ph↗

arXiv2015

Basis convergence of range-separated density-functional theory

Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order M{ø}ller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

physics.chem-ph↗

arXiv2014

Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straight-forward perturbation theory, and an extension of the G{ö}rling--Levy one that has the advantage of keeping the ground-state 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 first-order correction within this perturbation theory improves significantly the total ground-and excited-state energies of the different systems. However, the excitation energies are mostly deterio-rated with respect to the zeroth-order 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 range-separated adiabatic connection.

physics.chem-ph↗

arXiv2014

Excitation energies along a range-separated adiabatic connection

We present a study of the variation of total energies and excitationenergies along a range-separated adiabatic connection. This connectionlinks the non-interacting Kohn-Sham electronic system to the physicalinteracting system by progressively switching on theelectron-electron interactions whilst simultaneously adjusting aone-electron effective potential so as to keep the ground-statedensity constant. The interactions are introduced in arange-dependent manner, first introducing predominantly long-range,and then all-range, interactions as the physical system is approached,as opposed to the conventional adiabatic connection where theinteractions are introduced by globally scaling the standard Coulomb interaction.Reference data are reported for the He and Be atoms and the H2molecule, obtained by calculating the short-range effective potentialat the full configuration-interaction level using Lieb'sLegendre-transform approach. As the strength of the electron-electroninteractions increases, the excitation energies, calculated for thepartially interacting systems along the adiabatic connection, offerincreasingly accurate approximations to the exact excitation energies.Importantly, the excitation energies calculated at an intermediatepoint of the adiabatic connection are much better approximations tothe exact excitation energies than are the corresponding Kohn-Shamexcitation energies. This is particularly evident in situationsinvolving strong static correlation effects and states with multipleexcitation character, such as the dissociating H2 molecule. Theseresults highlight the utility of long-range interacting referencesystems as a starting point for the calculation of excitation energiesand are of interest for developing and analyzing practical approximaterange-separated density-functional methodologies.

physics.chem-ph↗

arXiv2014

Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers

Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting 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 non-integer 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 reproduce 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 non-interacting 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.

physics.chem-ph↗

arXiv2014

Double-hybrid density-functional theory applied to molecular crystals

We test the performance of a number of two- and one-parameter double-hybrid approximations, combining semilocal exchange-correlation density functionals with periodic local second-order Møller-Plesset (LMP2) perturbation theory, for calculating lattice energies of a set of molecular crystals: urea, formamide, ammonia, and carbon dioxide. All double-hybrid methods perform better on average than the corresponding Kohn-Sham calculations with the same functionals, but generally not better than standard LMP2. The one-parameter double-hybrid 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.

physics.chem-ph↗

arXiv2014

Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions

Range-separated methods combining a short-range density functional with long-range random phase approximations RPAs with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006 )] . The methods are also compared to full-range RPA approaches. Both range separation and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermolecular interaction energies. The best results are obtained with the method called RSH+RPAx, which yields interaction energies for the S22 set with an estimated mean absolute error of about 0.5-0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7%-9% depending on the reference interaction energies used. In particular, the RSH+RPAx method is found to be overall more accurate than the range-separated method based on long-range second-order Møller-Plesset MP2 perturbation theory RSH+MP2 .

physics.chem-ph↗

arXiv2014

Correlation energy expressions from the adiabatic-connection fluctuation-dissipation theorem approach

We explore several random phase approximation (RPA) correlation energy variants within the adiabatic-connection fluctuation-dissipation theorem approach. These variants differ in the way the exchange interactions are treated. One of these variants, named dRPA-II, is original to this work and closely resembles the second-order screened exchange (SOSEX) method. We discuss and clarify the connections among different RPA formulations. We derive the spin-adapted forms of all the variants for closed-shell systems, and test them on a few atomic and molecular systems with and without range separation of the electron-electron interaction.

physics.chem-ph↗

arXiv2014

Double-hybrid density-functional theory with meta-generalized-gradient approximations

We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA 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 Kohn-Sham TPSS and second-order Moller-Plesset calculations.

physics.chem-ph↗

arXiv2013

Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory

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 multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange-correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn-Sham (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 short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2 and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.

physics.chem-ph↗

arXiv2013

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated 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 time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

physics.chem-ph↗

arXiv2013

Electronic excitation energies of molecular systems from the Bethe-Salpeter equation: Example of the H2 molecule

We review the Bethe-Salpeter equation (BSE) approach to the calculation of electronic excitation energies of molecular systems. We recall the general Green's function many-theory 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 one-particle Green's function. Using the non-interacting one-particle Green's function leads to incorrect energy curves for the first singlet and triplet excited states in the dissociation limit. Starting from the exact one-particle 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 one-particle 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.

physics.chem-ph↗

arXiv2013

Electronic excitations from a linear-response range-separated hybrid scheme

We study linear-response time-dependent density-functional theory (DFT) based on the single-determinant range-separated hybrid (RSH) scheme, i.e. combining a long-range Hartree-Fock exchange kernel with a short-range DFT exchange-correlation kernel, for calculating electronic excitation energies of molecular systems. It is an alternative to the long-range correction (LC) scheme which has a standard full-range DFT correlation kernel instead of only a short-range one. We discuss the local-density approximation (LDA) to the short-range exchange-correlation kernel, and assess the performance of the linear-response RSH scheme for singlet-singlet and singlet-triplet valence and Rydberg excitations in the N2, CO, H2CO, C2H4, and C6H6 molecules, and for the first charge-transfer excitation in the C2H4-C2F4 dimer. The introduction of long-range HF exchange corrects the underestimation of charge-transfer and high-lying Rydberg excitation energies obtained with standard (semi)local density-functional approximations, but also leads to underestimated excitation energies to low-lying spin-triplet valence states which can be cured by the Tamm-Dancoff approximation. This work thus suggests that the present linear-response RSH scheme is a reasonable starting approximation for describing electronic excitation energies, even before adding an explicit treatment of long-range correlation.

physics.chem-ph↗

arXiv2012

A multiconfigurational hybrid density-functional theory

We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension of the usual hybrid approximations by essentially adding a fraction λof exact static correlation in addition to the fraction λof exact exchange. Test calculations on the cycloaddition reactions of ozone with ethylene or acetylene and the dissociation of diatomic molecules with the Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) density functionals show that a good value of λis 0.25, as in the usual hybrid approximations. The results suggest that the proposed multiconfigurational hybrid approximations can improve over usual density-functional calculations for situations with strong static correlation effects.

physics.chem-ph↗

arXiv2012

Approaching Chemical Accuracy with Quantum Monte Carlo

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 Slater-Jastrow trial wavefunction formed from Hartree-Fock 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 Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow 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.

physics.chem-ph↗

arXiv2011

Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions

We explore different variants of the random phase approximation (RPA) to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated density-functional theory, i.e. by combining the long-range random phase approximations with short-range density-functional approximations. We perform tests on the rare-gas dimers He_2, Ne_2, and Ar_2, and on the weakly interacting molecular complexes of the S22 set of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones originally proposed by Szabo and 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 aug-cc-pVDZ basis set.

physics.chem-ph↗

arXiv2011

Rationale for a new class of double-hybrid approximations in density-functional theory

We provide a rationale for a new class of double-hybrid approximations introduced by Brémond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by $ł$ and second-order Møller-Plesset (MP2) correlation weighted by $ł^3$. We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional $E_c[n_{1/ł}]$ by a linear function of $ł$, interpolating between MP2 at $ł=0$ and a density-functional approximation at $ł=1$. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.

physics.chem-ph↗

arXiv2011

Quantum Monte Carlo facing the Hartree-Fock symmetry dilemma: The case of hydrogen rings

When using Hartree-Fock (HF) trial wave functions in quantum Monte Carlo calculations, one faces, in case of HF instabilities, the HF symmetry dilemma in choosing between the symmetry-adapted solution of higher HF energy and symmetry-broken 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 symmetry-adapted HF wave function gives a lower energy both in variational Monte Carlo and in fixed-node diffusion Monte Carlo. This indicates that the symmetry-adapted wave function has more accurate nodes than the symmetry-broken wave functions, and thus suggests that spatial symmetry is an important criterion for selecting good trial wave functions.

physics.chem-ph↗