arXiv subjects

Julien Toulouse

Publications and source records attributed to Julien Toulouse.

At least 55 records · Page 3Linked to original sources

arXiv2018

Four-component relativistic range-separated density-functional theory: Short-range exchange local-density approximation

We lay out the extension of range-separated density-functional theory to a four-component relativistic frame-work using a Dirac-Coulomb-Breit Hamiltonian in the no-pair approximation. This formalism combines a wave-function method for the long-range part of the electron-electron interaction with a density(-current) functionalfor the short-range part of the interaction. We construct for this formalism a short-range exchange local-densityapproximation based on calculations on a relativistic homogeneous electron gas with a modified Coulomb-Breitelectron-electron interaction. More specifically, we provide the relativistic short-range Coulomb and Breit ex-change energies per particle of the relativistic homogeneous electron gas in the form of Pad e approximantswhich are systematically improvable to arbitrary accuracy. These quantities, as well as the associated effectiveCoulomb-Breit exchange hole, show the important impact of relativity on short-range exchange effects for highdensities.

physics.chem-ph↗

arXiv2018

Range-separated density-functional theory applied to the beryllium dimer and trimer

The beryllium dimer and trimer are, despite their small number of electrons, excellent systems for assessing electronic-structure computational methods. With reference data provided by multi-reference averaged coupled-pair functional calculations, we assess several variants of range-separated density-functional theory, combining long-range second-order perturbation theory or coupled-cluster theory with a short-range density functional. The results show that i) long-range second-order perturbation theory is not sufficient, ii) long-range coupled-cluster theory gives reasonably accurate potential energy curves, but iii) provided a relatively large value of $μ=1$ bohr$^{-1}$ for the range-separationparameter is used. The article is dedicated to the memory of János G. Ángyán.

physics.chem-ph↗

arXiv2018

On the optimal basis set for electron dynamics in strong laser fields: The case of molecular ion H$^{+}_2$

A clear understanding of the mechanisms that control the electron dynamics in strong laser field is still a challenge that requires to be interpreted by advanced theory. Development of accurate theoretical and computational methods, able to provide a precise treatment of the fundamental processes generated in the strong field regime, is therefore crucial. A central aspect is the choice of the basis for the wave-function expansion. Accuracy in describing multiphoton processes is strictly related to the intrinsic properties of the basis, such as numerical convergence, computational cost, and representation of the continuum. By explicitly solving the 1D and 3D time-dependent Schrödinger equation for H$^{+}_{2}$ in presence of an intense electric field, we explore the numerical performance of using a real-space grid, a B-spline basis, and a Gaussian basis (improved by optimal Gaussian functions for the continuum). We analyze the performance of the three bases for high-harmonic generation and above-threshold ionization for H$^{+}_{2}$. In particular, for high-harmonic generation, the capability of the basis to reproduce the two-center interference and the hyper-Raman phenomena is investigated.

physics.chem-ph↗

arXiv2018

Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach

The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a real-space representation of the electron-electron Coulomb operator projected in a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both full-configuration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level.

physics.chem-ph↗

arXiv2018

Multiconfigurational Short-Range Density-Functional Theory for Open-Shell Systems

Many chemical systems cannot be described by quantum chemistry methods based on a singlereference wave function. Accurate predictions of energetic and spectroscopic properties require a delicate balance between describing the most important configurations (static correlation) and obtaining dynamical correlation efficiently. The former is most naturally done through a multiconfigurational (MC) wave function, whereas the latter can be done by, e.g., perturbation theory. We have employed a different strategy, namely, a hybrid between multiconfigurational wave functions and density-functional theory (DFT) based on range separation. The method is denoted by MC short-range (sr) DFT and is more efficient than perturbative approaches as it capitalizes on the efficient treatment of the (short-range) dynamical correlation by DFT approximations. In turn, the method also improves DFT with standard approximations through the ability of multiconfigurational wave functions to recover large parts of the static correlation. Until now, our implementation was restricted to closed-shell systems, and to lift this restriction, we present here the generalization of MC-srDFT to open-shell cases. The additional terms required to treat open-shell systems are derived and implemented in the DALTON program. This new method for open-shell systems is illustrated on dioxygen and [Fe(H2O)6]3+.

physics.chem-ph↗

arXiv2018

A general range-separated double-hybrid density-functional theory

A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order M{ø}ller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.

physics.chem-ph↗

arXiv2017

Excitation energies from G{ö}rling-Levy perturbation theory along the range-separated adiabatic connection

A G{ö}rling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schr{ö}dinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113, 1740 (2015)], this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionization energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

physics.chem-ph↗

arXiv2017

Casimir-Polder size consistency -- a constraint violated by some dispersion theories

A key goal in quantum chemistry methods, whether ab initio or otherwise, is to achieve size consistency. In this manuscript we formulate the related idea of "Casimir-Polder size consistency" that manifests in long-range dispersion energetics. We show that local approximations in time-dependent density functional theory dispersion energy calculations violate the consistency condition because of incorrect treatment of highly non-local "xc kernel" physics, by up to 10% in our tests on closed-shell atoms.

physics.chem-ph↗

arXiv2017

Ab initio lifetime correction to scattering states for time-dependent electronic-structure calculations with incomplete basis sets

We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schr{ö}dinger equation. It gives lifetimes adapted to any given basis set without using any empirical parameters. The method can be considered as an ab initio version of the heuristic lifetime model of Klinkusch et al. [J. Chem. Phys. 131, 114304 (2009)]. The method is validated on the H and He atoms using Gaussian-type basis sets for calculation of high-harmonic-generation spectra.

physics.comp-ph↗

arXiv2017

Time-dependent linear-response variational Monte Carlo

We present the extension of variational Monte Carlo (VMC) to the calculation of electronic excitation energies and oscillator strengths using time-dependent linear-response theory. By exploiting the analogy existing between the linear method for wave-function optimisation and the generalised eigenvalue equation of linear-response theory, we formulate the equations of linear-response VMC (LR-VMC). This LR-VMC approach involves the first-and second-order derivatives of the wave function with respect to the parameters. We perform first tests of the LR-VMC method within the Tamm-Dancoff approximation using single-determinant Jastrow-Slater wave functions with different Slater basis sets on some singlet and triplet excitations of the beryllium atom. Comparison with reference experimental data and with configuration-interaction-singles (CIS) results shows that LR-VMC generally outperforms CIS for excitation energies and is thus a promising approach for calculating electronic excited-state properties of atoms and molecules.

physics.chem-ph↗

arXiv2016

Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method

We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order M{ø}ller-Plesset (MP2) correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules. While the OEP-based self-consistency does not provide any improvement for the calculations of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities.

physics.chem-ph↗

arXiv2016

Fractional-charge and fractional-spin errors in range-separated density-functional theory

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory. Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation density functional, and the RSH+MP2 method which adds long-range second-order M{ø}ller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corresponding contributions for the full-range exchange and correlation density-functional approximations, RSH gives fractional-spin errors that are larger than in the standard KS scheme and only slightly smaller than in standard HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-separated density-functional theory approaches for eliminating self-interaction and static-correlation errors.

physics.chem-ph↗

arXiv2016

Gaussian continuum basis functions for calculating high-harmonic generation spectra

We explore the computation of high-harmonic generation spectra by means of Gaussian basis sets in approaches propagating the time-dependent Schr{ö}dinger equation. We investigate the efficiency of Gaussian functions specifically designed for the description of the continuum proposed by Kaufmann et al. [J. Phys. B 22, 2223 (1989)]. We assess the range of applicability of this approach by studying the hydrogen atom, i.e. the simplest atom for which "exact" calculations on a grid can be performed. We notably study the effect of increasing the basis set cardinal number, the number of diffuse basis functions, and the number of Gaussian pseudo-continuum basis functions for various laser parameters. Our results show that the latter significantly improve the description of the low-lying continuum states, and provide a satisfactory agreement with grid calculationsfor laser wavelengths $λ$0 = 800 and 1064 nm. The Kaufmann continuum functions therefore appear as a promising way of constructing Gaussian basis sets for studying molecular electron dynamics in strong laser fields using time-dependent quantum-chemistry approaches.

physics.comp-ph↗

arXiv2016

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

We consider several spin-unrestricted random-phase approximation (RPA) variants for calculating correlation energies, with and without range separation, and test them on datasets of atomization energies and reaction barrier heights. We show that range separation greatly improves the accuracy of all RPA variants for these properties. Moreover, we show that a RPA variant with exchange, hereafter referred to as RPAx-SO2, first proposed by Sz-abo and Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)] in a spin-restricted closed-shell formalism, and extended here to a spin-unrestricted formalism , provides on average the most accurate range-separated RPA variant for atomization energies and reaction barrier heights. Since this range-separated RPAx-SO2 method had already been shown to be among the most accurate range-separated RPA variants for weak intermolecular interactions [J. Toulouse, W. Zhu, A. Savin, G. Jansen, and J. G. {Á}ngy{á}n, J. Chem. Phys. 135, 084119 (2011)], this works confirms range-separated RPAx-SO2 as a promising method for general chemical applications.

physics.chem-ph↗

arXiv2016

Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel

We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H2, N2, CO2, H2CO, and C2H4). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.

physics.chem-ph↗

arXiv2016

Quantum Monte Carlo with reoptimized perturbatively selected configuration-interaction wave functions

We explore the use in quantum Monte Carlo (QMC) of trial wave functions consisting of a Jastrow factor multiplied by a truncated configuration-interaction (CI) expansion in Slater determinants obtained from a CI perturbatively selected iteratively (CIPSI) calculation. In the CIPSI algorithm, the CI expansion is iteratively enlarged by selecting the best determinants using perturbation theory, which provides an optimal and automatic way of constructing truncated CI expansions approaching the full CI limit. We perform a systematic study of variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) total energies of first-row atoms from B to Ne with different levels of optimization of the parameters (Jastrow parameters, coefficients of the determinants, and orbital parameters) in these trial wave functions. The results show that the reoptimization of the coefficients of the determinants in VMC (together with the Jastrow factor) leads to an important lowering of both VMC and DMC total energies, and to their monotonic convergence with the number of determinants. In addition, we show that the reoptimization of the orbitals is also important in both VMC and DMC for the Be atom when using a large basis set. These reoptimized Jastrow-CIPSI wave functions appear as promising, systematically improvable trial wave functions for QMC calculations.

physics.chem-ph↗

arXiv2015

Introduction to the variational and diffusion Monte Carlo methods

We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings 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 fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state 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.

physics.chem-ph↗

arXiv2015

Range-separated double-hybrid density-functional theory applied to periodic systems

Quantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order M{ø}ller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been implemented for periodic systems using Gaussian-type basis functions and the local correlation framework. The performance of these range-separated double hybrids has been benchmarked on a significant set of systems including rare-gas, molecular, ionic, and covalent crystals. The use of spin-component-scaled MP2 for the long-range part has been tested as well. The results show that the value of $μ$ = 0.5 bohr^{--1} for the range-separation parameter usually used for molecular systems is also a reasonable choice for solids. Overall, these range-separated double hybrids provide a good accuracy for binding energies using basis sets of moderate sizes such as cc-pVDZ and aug-cc-pVDZ.

physics.chem-ph↗