arXiv subjects

Julien Toulouse

Publications and source records attributed to Julien Toulouse.

At least 91 records · Page 5Linked to original sources

arXiv2011

Quantum Monte Carlo with Jastrow-valence-bond wave functions

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 self-consistent-field (VBSCF) and breathing-orbital valence bond (BOVB) wave functions. Complemented by a Jastrow factor, these Jastrow-Valence-Bond 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 (VMC) and diffusion Monte Carlo (DMC). 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 correlation. These wave functions can be systematically improved by inclusion of valence bond structures corresponding to additional bonding patterns.

physics.chem-ph↗

arXiv2011

Double-hybrid density-functional theory made rigorous

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Moller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.

physics.chem-ph↗

arXiv2011

Basis set construction for molecular electronic structure theory: Natural orbital and Gauss-Slater basis for smooth pseudpotentials

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 multi-configurational self-consistent 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 Burkatzki-Filippi-Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss-Slater functions are the appropriate primitives. Double- and triple-zeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg 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.

cond-mat.mtrl-sci↗

arXiv2010

Quantum Monte Carlo calculations of electronic excitation energies: the case of the singlet $n \to π^*$ (CO) transition in acrolein

We report state-of-the-art quantum Monte Carlo calculations of the singlet $n \to π^*$ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouabça {\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 state-average versus state-specific complete-active-space (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 state-average and state-specific 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.

physics.chem-ph↗

arXiv2010

Combining Density Functional Theory and Density Matrix Functional Theory

We combine density-functional theory with density-matrix functional theory to get the best of both worlds. This is achieved by range separation of the electronic interaction which permits to rigorously combine a short-range density functional with a long-range density-matrix functional. The short-range density functional is approximated by the short-range version of the Perdew-Burke-Ernzerhof functional (srPBE). The long-range density-matrix functional is approximated by the long-range version of the Buijse-Baerends functional (lrBB). The obtained srPBE+lrBB method accurately describes both static and dynamic electron correlation at a computational cost similar to that of standard density-functional approximations. This is shown for the dissociation curves of the H$_{2}$, LiH, BH and HF molecules.

physics.chem-ph↗

arXiv2010

Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications

Using Green-function many-body theory, we present the details of a formally exact adiabatic-connection fluctuation-dissipation density-functional theory based on range separation, which was sketched in Toulouse, Gerber, Jansen, Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated density-functional theory approaches combining short-range density functional approximations with long-range random phase approximations (RPA) are then obtained as well-identified approximations on the long-range Green-function self-energy. Range-separated RPA-type schemes with or without long-range Hartree-Fock exchange response kernel are assessed on rare-gas and alkaline-earth dimers, and compared to range-separated second-order perturbation theory and range-separated coupled-cluster theory.

physics.chem-ph↗

arXiv2010

Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations

Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within quantum Monte Carlo yields more compact basis sets for a given accuracy. Particularly large gains are achieved for highly excited states. For calculations requiring non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that behave as Gaussians at short distances and Slaters at long distances. These basis functions further improve the energy and fluctuations of the local energy for a given basis size. Gains achieved by exponent optimization and Gauss-Slater basis use are exemplified by calculations for the ground state of carbon, the lowest lying excited states of carbon with $^5S^o$, $^3P^o$, $^1D^o$, $^3F^o$ symmetries, carbon dimer, and naphthalene. Basis size reduction enables quantum Monte Carlo treatment of larger molecules at high accuracy.

physics.chem-ph↗

arXiv2009

Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation

An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly-bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be$_2$ and Ne$_2$.

cond-mat.mtrl-sci↗

arXiv2008

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently-introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely the Jastrow, configuration state function and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C_2 molecule up to the dissociation limit, and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations of the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.

physics.comp-ph↗

arXiv2007

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically- and system-averaged electron pair density (i.e. the probability density of finding two electrons separated by a relative distance u), also known as the spherically-averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth non-local operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.

physics.chem-ph↗

arXiv2007

Optimization of quantum Monte Carlo wave functions by energy minimization

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a non-symmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C$_2$ molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C$_2$ molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.

physics.chem-ph↗

arXiv2006

Short-range exchange-correlation energy of a uniform electron gas with modified electron-electron interaction

We calculate the short-range exchange-correlation energy of the uniform electron gas with two modified electron-electron interactions. While the short-range exchange functionals are calculated analytically, Coupled-Cluster and Fermi-hypernetted chain calculations are carried out for the correlation energy and the results are fitted to an analytical parametrization. These data enable to construct the local density approximation corresponding to these modified interactions.

cond-mat.mtrl-sci↗

arXiv2006

A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn-Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron-electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.

physics.chem-ph↗

arXiv2006

Alleviation of the Fermion-sign problem by optimization of many-body wave functions

We present a simple, robust and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wav e function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging C$_2$ molecule to the experimental accuracy of 0.02 eV.

cond-mat.other↗

arXiv2006

Model hamiltonians in density functional theory

The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this hamiltonian is unique. In principle, this density can be chosen as that of the real, interacting system. To obtain the energy, or other properties of the real system, approximations are needed. Working with non interacting fermions is an important simplification, but it may be easier to produce approximations with different choices of the model hamiltonian. The feature that the exact density is (ideally) reproduced can be kept in the newly defined fictitious systems. Using model hamiltonians having the same form as the physical one, that is, being built of one- and two-body operators, allows to approach the physical hamiltonian arbitrarily close, and thus a systematic reduction of the approximations.

cond-mat.mtrl-sci↗

arXiv2006

Local density approximation for long-range or for short-range energy functionals?

Density functional methods were developed, in which the Coulomb electron-electron interaction is split into a long- and a short-range part. In such methods, one term is calculated using traditional density functional approximations, like the local density approximation. The present paper tries to shed some light upon the best way to do it by comparing the accuracy of the local density approximation with accurate results for the He atom.

physics.chem-ph↗

arXiv2006

Scaling relations, virial theorem and energy densities for long-range and short-range density functionals

We analyze a decomposition of the Coulomb electron-electron interaction into a long-range and a short-range part in the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high-density limit for the long-range and the short-range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long-range only electron-electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples.

physics.chem-ph↗

arXiv2005

Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction

A simple approximate expression in real and reciprocal spaces is given for the static exchange-correlation kernel of a uniform electron gas interacting with the long-range part only of the Coulomb interaction. This expression interpolates between the exact asymptotic behaviors of this kernel at small and large wave vectors which in turn requires, among other thing, information from the momentum distribution of the uniform electron gas with the same interaction that have been calculated in the G0W0 approximation. This exchange-correlation kernel as well as its complement analogue associated to the short-range part of the Coulomb interaction are more local than the Coulombic exchange-correlation kernel and constitute potential ingredients in approximations for recent adiabatic connection fluctuation-dissipation and/or density functional theory approaches of the electronic correlation problem based on a separate treatment of long-range and short-range interaction effects.

cond-mat.mtrl-sci↗