Van der Waals coefficients beyond the classical shell model

Van der Waals (vdW) coefficients can be accurately generated and understood by modelling the dynamic multipole polarizability of each interacting object. Accurate static polarizabilities are the key to accurate dynamic polarizabilities and vdW coefficients. In this work, we present and study in detail a hollow-sphere model for the dynamic multipole polarizability proposed recently by two of the present authors (JT and JPP) to simulate the vdW coefficients for inhomogeneous systems that allow for a cavity. The inputs to this model are the accurate static multipole polarizabilities and the electron density. A simplification of the full hollow-sphere model, the single-frequency approximation (SFA), circumvents the need for a detailed electron density and for a double numerical integration over space. We find that the hollow-sphere model in SFA is not only accurate for nanoclusters and cage molecules (e.g., fullerenes) but also yields vdW coefficients among atoms, fullerenes, and small clusters in good agreement with expensive time-dependent density functional calculations. However, the classical shell model (CSM), which inputs the static dipole polarizabilities and estimates the static higher-order multipole polarizabilities therefrom, is accurate for the higher-order vdW coefficients only when the interacting objects are large. For the lowest-order vdW coefficient C6, SFA and CSM are exactly the same. The higher-order (C8 and C10) terms of the vdW expansion can be almost as important as the C6 term in molecular crystals. Application to a variety of clusters shows that there is strong non-additivity of the long-range vdW interactions between nanoclusters

Carbon clusters near the crossover to fullerene stability

The thermodynamic stability of structural isomers of $\mathrm{C}_{24}$, $\mathrm{C}_{26}$, $\mathrm{C}_{28}$ and $\mathrm{C}_{32}$, including fullerenes, is studied using density functional and quantum Monte Carlo methods. The energetic ordering of the different isomers depends sensitively on the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo calculations predict that a $\mathrm{C}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the $\mathrm{C}_{26}$ and $\mathrm{C}_{28}$ clusters with $\mathrm{C}_{2v}$ and $\mathrm{T}_{d}$ symmetry, respectively. These results support proposals that a $\mathrm{C}_{28}$ solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper and related information see http://www.tcm.phy.cam.ac.uk/~prck

Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian

International audienceBackground: While coupled-cluster theory accurately models weakly correlated quantum systems, it often fails in the presence of strong correlations where the standard mean-field picture is qualitatively incorrect. In many cases, these failures can be largely ameliorated by permitting the mean-field reference to break physical symmetries. Symmetry-broken coupled-cluster, e.g., Bogoliubov-coupled-cluster, theory can indeed provide reasonably accurate energetic predictions, but the broken symmetry can compromise the quality of the resulting wave function and predictions of observables other than the energy. Purpose: Merging symmetry projection and coupled-cluster theory is therefore an appealing way to describe strongly correlated systems. One indeed expects to inherit and further improve the energetic accuracy of broken-symmetry coupled cluster while retaining proper symmetries. Methods: Independently, two different but related formalisms have been recently proposed to achieve this goal. The two formalisms are contrasted in this manuscript, with results tested on the Richardson pairing Hamiltonian. While the present paper focuses on the breaking and restoration of U(1) global-gauge symmetry associated with particle-number conservation, the symmetry-projected coupled-cluster formalism is applicable to other symmetries such as rotational (i.e., spin) symmetry. Results: Both formalisms are based on the disentangled cluster representation of the symmetry-rotated coupled-cluster wave function. However, they differ in the way that the disentangled clusters are solved. One approach sets up angle-dependent coupled-cluster equations, while the other involves first-order ordinary differential equations. The latter approach yields energies and occupation probabilities significantly better than those of number-projected Bardeen-Cooper-Schrieffer (BCS) and BCS coupled cluster and, when the disentangled clusters are truncated at low excitation levels, has a computational cost not too much larger than that of BCS coupled cluster. Conclusions: The high quality of results presented in this manuscript indicates that symmetry-projected coupled cluster is a promising method that can accurately describe both weakly and strongly correlated finite many-fermion systems

Tensor-decomposition techniques for ab initio nuclear structure calculations. From chiral nuclear potentials to ground-state energies

International audienceBackground: The computational resources needed to generate the ab initio solution of the nuclear many-body problem for increasing mass number and/or accuracy necessitates innovative developments to improve upon (i) the storage of many-body operators and (ii) the scaling of many-body methods used to evaluate nuclear observables. The storing and efficient handling of many-body operators with high particle ranks is currently one of the major bottlenecks limiting the applicability range of ab initio studies with respect to mass number and accuracy. Recently, the application of tensor decomposition techniques to many-body tensors has proven highly beneficial to reduce the computational cost of ab initio calculations in quantum chemistry and solid-state physics. Purpose: The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked. Methods: The first proof-of-principles application of tensor-decomposition techniques to the nuclear Hamiltonian is performed. Two different tensor formats are investigated by systematically benchmarking the approximation error on matrix elements stored in various bases of interest. The analysis is achieved while including normal-ordered three-nucleon interactions that are nowadays used as input to the most advanced ab initio calculations in medium-mass nuclei. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed. Results: The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated tensor hypercontraction scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum J for which one performs the decomposition, which is itself directly related to the sparsity of the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in He4,O16, and Ca40. Conclusions: It is presently demonstrated that tensor-decomposition techniques can be efficiently applied to systematically approximate the nuclear many-body Hamiltonian in terms of lower-rank tensors. Beyond the input Hamiltonian, tensor-decomposition techniques can be envisioned to scale down the cost of state-of-the-art nonperturbative many-body methods in order to extend ab initio studies to (i) higher precisions, (ii) larger masses, and (iii) nuclei of doubly open-shell character

Role of nonlocal exchange in molecular crystals: The case of two proton-ordered phases of ice

cited By 14International audienceWe present a periodic density functional theory investigation of twoproton-ordered phases of ice. Their equilibrium lattice parameters,relative stabilities, formation energies, and densities of states havebeen evaluated. Nine exchange-correlation functionals, representativeof the generalized gradient approximation (GGA), global hybrids,range-separated hybrids, meta-GGA, and hybrid meta-GGA families havebeen taken into account, considering two oxygen basis sets. Althoughthe hydrogen-bond network of ice is well reproduced at the B3LYP,M06-L, or LC- wPBE levels, formation energies are only correctlyevaluated with the two former functionals. Band gaps on the other handare only quantitatively reproduced at the B3LYP level. These resultsindicate that this last functional, a de facto reference formolecular calculations, gives in average the most accurate results forthe considered ice properties. © 2011 Wiley Periodicals, Inc

Nitrogen quadrupole coupling constants for HCN and H2CN +: Explanation of the absence of fine structure in the microwave spectrum of interstellar H2CN+

Nitrogen 14 quadrupole coupling constants for H2CN+ and HCN are predicted via ab initio self-consistent-field and configuration interaction theory. Effects of electron correlation, basis set completeness, and geometrical structure on the predicted electric field gradients are analyzed. The quadrupole coupling constant obtained for H2CN+ is one order of magnitude less than in HCN, providing an explanation for the experimental fact that the fine structure of the microwave spectrum of H 2CN+ has not been resolved. This research also allows a reliable prediction of the nuclear quadrupole moment of 14N, namely Q(14N)=2.00×10-26 cm2. © 1986 American Institute of Physics.Fil:Scuseria, G.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Relativistic calculation of indirect NMR spin-spin couplings using the Douglas-Kroll-Hess approximation

We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides C H4, Si H4, Ge H4, and Sn H4. Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data. © 2005 American Institute of Physics.Fil:Melo, J.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Peralta, J.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Scuseria, G.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina