On the formulation of a density matrix functional for Van der Waals interaction of like- and opposite-spin electrons in the helium dimer

Exploring the potential of natural orbital functionals

In recent years, Natural Orbital Functional (NOF) theory has gained increasing significance in quantum chemistry, successfully addressing one of the field's most challenging problems: providing an accurate and balanced description of systems with strong electronic correlation. The quest for NOFs that strike the delicate balance between computational tractability and predictive accuracy represents a holy grail for researchers. Today, NOFs provide an alternative formalism to both density functional and wavefunction-based methods, with their appeal rooted in a wonderfully simple conceptual framework. This perspective outlines the basic concepts, strengths and weaknesses, and current status of NOFs, while offering suggestions for their future development.

Compact two-electron wave function for bond dissociation and Van der Waals interactions: a natural amplitude assessment

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r12) depending on the interelectronic distance r12. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r12) needs to diverge for large r12 at large internuclear distances while for shorter bond distances it increases as a function of r12 to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

Can the Counterpoise Correction for Basis Set Superposition Effect Be Justified?

The basis set superposition effect (BSSE) is a simple concept, and its validity is almost universally accepted. So is the counterpoise method to correct for it. The idea is that the basis set is biased toward the dimer because each monomer in the dimer can "use" the basis functions on the other monomer, which it cannot in a simple monomer calculation. This hypothesis can only be tested if basis set free benchmark numbers are available for monomers and dimer. We are testing the hypothesis on a few systems (in this paper Be2) that are small enough that sufficiently accurate benchmark numbers (basis set free, or close to basis set limit; full CI or close to full CI) are available or can be obtained. We find that the answer to the title question is negative: the standard basis sets of quantum chemistry appear to be biased toward the atom in the sense that basis set errors are larger for the dimer than the monomer. Applying the counterpoise correction increases the imbalance by reducing the already smaller basis set error of the monomer even further. Counterpoise corrected bond energies then deviate more from the basis set limit numbers than uncorrected bond energies. These conclusions hold both at the Hartree-Fock level and (much stronger) at the correlated (CCSD(T), full CI) levels. So the answer to the title question is No.

A natural orbital analysis of the long range behavior of chemical bonding and van der Waals interaction in singlet H2: the issue of zero natural orbital occupation numbers

This paper gives a natural orbital (NO) based analysis of the van der Waals interaction in (singlet) H2 at long distance. The van der Waals interaction, even if not leading to a distinct van der Waals well, affects the shape of the interaction potential in the van der Waals distance range of 5-9 bohrs and can be clearly distinguished from chemical bonding effects. In the NO basis the van der Waals interaction can be quantitatively covered with, apart from the ground state configurations (1σ(g))(2) and (1σ(u))(2), just the 4 configurations (2σ(g))(2) and (2σ(u))(2), and (1π(u))(2) and (1π(g))(2). The physics of the dispersion interaction requires and explains the peculiar relatively large positive CI coefficients of the doubly excited electron configurations (2σ(u))(2) and (1π(g))(2) (the occupancy amplitudes of the 2σ(u) and 1π(gx, y) NOs) in the distance range 5-9 bohrs, which have been observed before by Cioslowski and Pernal [Chem. Phys. Lett. 430, 188 (2006)]. We show that such positive occupancy amplitudes do not necessarily lead to the existence of zero occupation numbers at some H-H distances.