arXiv subjects

Julien Toulouse

Publications and source records attributed to Julien Toulouse.

At least 37 records · Page 2Linked to original sources

arXiv2022

Basis-set correction for coupled-cluster estimation of dipole moments

The present work proposes an approach to obtain a basis-set correction based on density-functional theory (DFT) for the computation of molecular properties in wave-function theory (WFT). This approach allows one to accelerate the basis-set convergence of any energy derivative of a non-variational WFT method, generalizing previous works on the DFT-based basis-set correction where either only ground-state energies could be computed with non-variational wave functions [J. Phys. Chem. Lett. 10, 2931 (2019)] or properties where computed as expectation values over variational wave functions [J. Chem. Phys. 155, 044109 (2021)]. This work focuses on the basis-set correction of dipole moments in coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)), which is numerically tested on a set of fourteen molecules with dipole moments covering two orders of magnitude. As the basis-set correction relies only on Hartree-Fock densities, its computational cost is marginal with respect to the one of the CCSD(T) calculations. Statistical analysis of the numerical results shows a clear improvement of the basis convergence of the dipole moment with respect to the usual CCSD(T) calculations.

physics.chem-ph↗

arXiv2022

Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model

We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional model Hamiltonian with delta-potential interactions which has the advantage of making easier to perform a more systematic analysis than for three-dimensional Coulombic systems while keeping the essence of the slow basis convergence problem of wave-function methods. We provide some mathematical details about the theory and propose a new variant of basis-set correction which has the advantage of being suited to the development of an adapted local-density approximation. We show indeed how to develop a local-density approximation for the basis-set correction functional which is automatically adapted to the basis set employed, without resorting to range-separated density-functional theory as in previous works, but using instead a finite uniform electron gas whose electron-electron interaction is projected on the basis set. The work puts the basis-set correction theory on firmer grounds and provides an interesting strategy for the improvement of this approach.

physics.chem-ph↗

arXiv2021

Accurate energies of transition metal atoms, ions, and monoxides using selected configuration interaction and density-based basis-set corrections

The semistochastic heat-bath configuration interaction (SHCI) method is a selected configuration interaction plus perturbation theory method that has provided near-full configuration interaction (FCI) levels of accuracy for many systems with both single- and multi-reference character. However, obtaining accurate energies in the complete basis set limit is hindered by the slow convergence of the FCI energy with respect to basis size. Here we show that the recently developed basis-set correction method based on range-separated density-functional theory can be used to significantly speed up basis-set convergence in SHCI calculations. In particular, we study two such schemes that differ in the functional used, and apply them to transition metal atoms and monoxides to obtain total, ionization, and dissociation energies well converged to the complete-basis-set limit within chemical accuracy.

physics.chem-ph↗

arXiv2021

Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments?

This work provides a self-consistent extension of the recently proposed density-based basis-set correction method for wave-function electronic-structure calculations [J. Chem. Phys. 149, 194301 (2018)]. In contrast to the previously used approximation where the basis-set correction density functional was a posteriori added to the energy from a wave-function calculation, here the energy minimization is performed including the basis-set correction. Compared to the non-self-consistent approximation, this allows one to lower the total energy and change the wave function under the effect of the basis-set correction. This work addresses two main questions: i) What is the change in total energy compared to the non-self-consistent approximation, and ii) can we obtain better properties, namely dipole moments, with the basis-set corrected wave functions? We implement the present formalism with two different basis-set correction functionals and test it on different molecular systems. The main results of the study are that i) the total energy lowering obtained by the self-consistent approach is extremely small, which justifies the use of the non-self-consistent approximation, and ii) the dipole moments obtained from the basis-set corrected wave functions are improved, being already close to their complete-basis-set values with triple-zeta basis sets. Thus, the present study further confirms the soundness of the density-based basis-set correction scheme.

physics.class-ph↗

arXiv2021

Short-range correlation energy of the relativistic homogeneous electron gas

We construct the complementary short-range correlation relativistic local-density-approximation functional to be used in relativistic range-separated density-functional theory based on a Dirac-Coulomb Hamiltonian in the no-pair approximation. For this, we perform relativistic random-phase-approximation calculations of the correlation energy of the relativistic homogeneous electron gas with a modified electron-electron interaction, we study the high-density behavior, and fit the results to a parametrized expression. The obtained functional should eventually be useful for electronic-structure calculations of strongly correlated systems containing heavy elements.

physics.chem-ph↗

arXiv2021

Relativistic density-functional theory based on effective quantum electrodynamics

A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.

physics.chem-ph↗

arXiv2020

Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method

The recently developed semistochastic heat-bath configuration interaction (SHCI) method is a systematically improvable selected configuration interaction plus perturbation theory method capable of giving essentially exact energies for larger systems than is possible with other such methods. We compute SHCI atomization energies for 55 molecules which have been used as a test set in prior studies because their atomization energies are known from experiment. Basis sets from cc-pVDZ to cc-pV5Z are used, totaling up to 500 orbitals and a Hilbert space of $10^{32}$ Slater determinants for the largest molecules. For each basis, an extrapolated energy well within chemical accuracy (1 kcal/mol or 1.6 mHa/mol) of the exact energy for that basis is computed using only a tiny fraction of the entire Hilbert space. We also use our almost exact energies to benchmark coupled-cluster [CCSD(T)] energies. The energies are extrapolated to the complete basis set limit and compared to the experimental atomization energies. The extrapolations are done both without and with a basis-set correction based on density-functional theory. The mean absolute deviations from experiment for these extrapolations are 0.46 kcal/mol and 0.51 kcal/mol, respectively. Orbital optimization methods used to obtain improved convergence of the SHCI energies are also discussed.

physics.chem-ph↗

arXiv2020

Relativistic short-range exchange energy functionals beyond the local-density approximation

We develop relativistic short-range exchange energy functionals for four-component relativistic range-separated density-functional theory using a Dirac-Coulomb Hamiltonian in the no-pair approximation. We show how to improve the short-range local-density approximation exchange functional for large range-separation parameters by using the on-top exchange pair density as a new variable. We also develop a relativistic short-range generalized-gradient approximation exchange functional which further increases the accuracy for small range-separation parameters. Tests on the helium, beryllium, neon, and argon isoelectronic series up to high nuclear charges show that this latter functional gives exchange energies with a maximal relative percentage error of 3 %. The development of this exchange functional represents a step forward for the application of four-component relativistic range-separated density-functional theory to chemical compounds with heavy elements.

physics.chem-ph↗

arXiv2020

A basis-set error correction based on density-functional theory for strongly correlated molecular systems

We extend to strongly correlated molecular systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner et al., J. Chem. Phys. 149, 194301 (2018)]. This basis-set correction relies on a mapping between wave-function calculations in a finite basis set and range-separated DFT (RSDFT) through the definition of an effective non-divergent interaction corresponding to the electron-electron Coulomb interaction projected in the finite basis set. This enables the use of RSDFT-type complementary density functionals to recover the dominant part of the short-range correlation effects missing in this finite basis set. To study both weak and strong correlation regimes we consider the potential energy curves of the H10, N2, O2, and F2 molecules up to the dissociation limit, and we explore various approximations of complementary functionals fulfilling two key properties: spin-multiplet degeneracy (i.e., independence of the energy with respect to the spin projection Sz) and size consistency. Specifically, we investigate the dependence of the functional on different types of on-top pair densities and spin polarizations. The key result of this study is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin polarization without any significant loss of accuracy. Quantitatively, we show that the basis-set correction reaches chemical accuracy on atomization energies with triple-zeta quality basis sets for most of the systems studied here. Also, the present basis-set incompleteness correction provides smooth potential energy curves along the whole range of internuclear distances.

physics.chem-ph↗

arXiv2020

A Density-Based Basis-Set Incompleteness Correction for GW Methods

Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. This displeasing feature is due to lack of explicit electron-electron terms modeling the infamous Kato electron-electron cusp and the correlation Coulomb hole around it. Here, we propose a computationally efficient density-based basis set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics towards the complete basis set limit. The performance of this density-based correction is illustrated by computing the ionization potentials of the twenty smallest atoms and molecules of the GW100 test set at the perturbative $GW$ (or $G_0W_0$) level using increasingly large basis sets. We also compute the ionization potentials of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained.

physics.chem-ph↗

arXiv2019

Self-consistent range-separated density-functional theory with second-order perturbative correction via the optimized-effective-potential method

We extend the range-separated double-hybrid RSH+MP2 method [J. G. Angyan et al., Phys. Rev. A 72, 012510 (2005)], combining long-range HF exchange and MP2 correlation with a short-range density functional, to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter $μ=0.5$ bohr$^{-1}$, we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.

physics.chem-ph↗

arXiv2019

Chemically Accurate Excitation Energies With Small Basis Sets

By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [Giner et al.,J. Chem. Phys. 2018, 149, 194301], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-$ζ$ basis sets. We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene). The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.

physics.chem-ph↗

arXiv2019

Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs

\textsc{Quantum Package} is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven framework allows the programmer to include any arbitrary set of determinants in the reference space, hence providing greater methodological freedoms. The sCI method implemented in \textsc{Quantum Package} is based on the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm which complements the variational sCI energy with a PT2 correction. Additional external plugins have been recently added to perform calculations with multireference coupled cluster theory and range-separated density-functional theory. All the programs are developed with the IRPF90 code generator, which simplifies collaborative work and the development of new features. \textsc{Quantum Package} strives to allow easy implementation and experimentation of new methods, while making parallel computation as simple and efficient as possible on modern supercomputer architectures. Currently, the code enables, routinely, to realize runs on roughly 2\,000 CPU cores, with tens of millions of determinants in the reference space. Moreover, we have been able to push up to 12\,288 cores in order to test its parallel efficiency. In the present manuscript, we also introduce some key new developments: i) a renormalized second-order perturbative correction for efficient extrapolation to the full CI limit, and ii) a stochastic version of the CIPSI selection performed simultaneously to the PT2 calculation at no extra cost.

physics.comp-ph↗

arXiv2019

A Density-Based Basis-Set Correction For Wave Function Theory

We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. The present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $μ$, the key ingredient here is a range-separation \textit{function} $μ(\bf{r})$ that automatically adapts to the spatial non-homogeneity of the basis-set incompleteness error. As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets.

physics.chem-ph↗

arXiv2019

Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations

We construct range-separated double-hybrid schemes which combine coupled-cluster or random-phase approximations with a density functional based on a two-parameter Coulomb-attenuating-method-like decomposition of the electron-electron interaction. We find that the addition of a fraction of short-range electron-electron interaction in the wave-function part of the calculation is globally beneficial for the range-separated double-hybrid scheme involving a variant of the random-phase approximation with exchange terms. Even though the latter scheme is globally as accurate as the corresponding scheme employing only second-order M{ø}ller-Plesset perturbation theory for atomization energies, reaction barrier heights, and weak intermolecular interactions of small molecules, it is more accurate for the more complicated case of the benzene dimer in the stacked configuration. The present range-separated double-hybrid scheme employing a random-phase approximation thus represents a new member in the family of double hybrids with minimal empiricism which could be useful for general chemical applications.

physics.chem-ph↗

arXiv2019

Linear-response range-separated density-functional theory for atomic photoexcitation and photoionization spectra

We investigate the performance of the range-separated hybrid (RSH) scheme, which combines long-range Hartree-Fock (HF) and a short-range density-functional approximation (DFA), for calculating photoexcitation/photoionization spectra of the H and He atoms, using a B-spline basis set in order to correctly describe the continuum part of the spectra. The study of these simple systems allows us to quantify the influence on the spectra of the errors coming from the short-range exchange-correlation DFA and from the missing long-range correlation in the RSH scheme. We study the differences between using the long-range HF exchange (nonlocal) potential and the long-range exact exchange (local) potential. Contrary to the former, the latter supports a series of Rydberg states and gives reasonable photoexcitation/photoionization spectra, even without applying linear-response theory. The most accurate spectra are obtained with the linear-response time-dependent range-separated hybrid (TDRSH) scheme. In particular, for the He atom at the optimal value of the range-separation parameter, TDRSH gives slightly more accurate photoexcitation and photoioniza-tion spectra than standard linear-response time-dependent HF. More generally, the present work shows the potential of range-separated density-functional theory for calculating linear and nonlinear optical properties involving continuum states.

physics.chem-ph↗

arXiv2019

A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW +BSE and self-consistent RPA

A formally exact Bethe-Salpeter-like equation for the linear-response function is introduced with a kernel which depends only on the one frequency of the applied field. This is in contrast with the standard Bethe-Salpeter equation (BSE) which involves multiple-frequency integrals over the kernel and response functions. From the one-frequency kernel, known approximations are straightforwardly recovered. However, the present formalism lends itself to more powerful approximations. This is demonstrated with the exact analytical solution of the Hubbard molecule. Similarities and differences of the $GW$+BSE approach with the self-consistent random-phase approximation (RPA) is also discussed.

physics.chem-ph↗

arXiv2019

Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density

We introduce an approximation to the short-range correlation energy functional with multide-terminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density, the density gradient, and the on-top pair density, which locally interpolates between the standard Perdew-Burke-Ernzerhof correlation functional at vanishing range-separation parameter and the known exact asymptotic expansion at large range-separation parameter. When combined with (selected) configuration-interaction calculations for the long-range wave function, this approximation gives accurate dissociation energy curves of the H2, Li2, and Be2 molecules, and thus appears as a promising way to accurately account for static correlation in range-separated density-functional theory.

physics.chem-ph↗