Dataset of noncovalent intermolecular interaction energy curves for 24 small high-spin open-shell dimers.

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets.

The nature of three-body interactions in DFT: Exchange and polarization effects.

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar2-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Tuned range-separated hybrid functionals in the symmetry-adapted perturbation theory.

The aim of this study is to present a performance test of optimally tuned long-range corrected (LRC) functionals applied to the symmetry-adapted perturbation theory (SAPT). In the present variant, the second-order energy components are evaluated at the coupled level of theory. We demonstrate that the generalized Kohn-Sham (GKS) description of monomers with optimally tuned LRC functionals may be essential for the quality of SAPT interaction energy components. This is connected to the minimization of a many-electron self-interaction error and exemplified by two model systems: polyacetylenes of increasing length and stretching of He 3 (+). Next we provide a comparison of SAPT approaches based on Kohn-Sham and GKS description of the monomers. We show that LRC leads to results better or comparable with the hitherto prevailing asymptotically corrected functionals. Finally, we discuss the advantages and possible limitations of SAPT based on LRC functionals.

Density-dependent onset of the long-range exchange: a key to donor-acceptor properties.

Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band gap materials. This promise is contingent upon the ability of DFT to predict one-particle states accurately. Unfortunately, approximate functionals fail to align the orbital energies with ionization potentials. We describe a new paradigm for achieving this alignment. In the proposed model, an average electron-exchange hole separation controls the onset of the orbital-dependent exchange in approximate range-separated functionals. The correct description of one-particle states is thus achieved without explicit electron removal or attachment. Extensive numerical tests show that the proposed method provides physically sound orbital gaps and leads to excellent predictions of charge-transfer excitations and other properties critically depending on the tail of the electron density.

A first-principles-based correlation functional for harmonious connection of short-range correlation and long-range dispersion.

We present a physically motivated correlation functional belonging to the meta-generalized gradient approximation (meta-GGA) rung, which can be supplemented with long-range dispersion corrections without introducing double-counting of correlation contributions. The functional is derived by the method of constraint satisfaction, starting from an analytical expression for a real-space spin-resolved correlation hole. The model contains a position-dependent function that controls the range of the interelectronic correlations described by the semilocal functional. With minimal empiricism, this function may be adjusted so that the correlation model blends with a specific dispersion correction describing long-range contributions. For a preliminary assessment, our functional has been combined with an atom-pairwise dispersion correction and full Hartree-Fock (HF)-like exchange. Despite the HF-exchange approximation, its predictions compare favorably with reference interaction energies in an extensive set of non-covalently bound dimers.

Dispersion-free component of non-covalent interaction via mutual polarization of fragment densities.

Comprehensive tests within a diverse set of noncovalently bonded systems are carried out to assess the performance of the recently-developed dispersion-free approach in the framework of density functional theory [L. Rajchel, P. Zuchowski, M. Szczesniak, and G. Chalasinski, Phys. Rev. Lett. 104, 163001 (2010)]. A numerical algorithm which cures the convergence problems of the previous implementation is presented.

A density functional theory approach to noncovalent interactions via interacting monomer densities.

A recently proposed "DFT + dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists of the self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli blockade technique. Within the monomers a complete exchange-correlation potential should be used, but between them only the exact exchange operates. The application to a wide range of molecular complexes from rare-gas dimers to hydrogen-bonds to π-electron interactions shows good agreement with benchmark values.

Density functional theory approach to noncovalent interactions via monomer polarization and Pauli blockade.

We propose a "DFT+dispersion" treatment which avoids double counting of dispersion terms by deriving the dispersion-free density functional theory (DFT) interaction energy and combining it with DFT-based dispersion. The formalism involves self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli-blockade technique. Any exchange-correlation potential can be used within monomers, but only the exchange operates between them. The applications to rare-gas dimers, ion-rare-gas interactions, and hydrogen bonds demonstrate that the interaction energies agree with benchmark values.

Nonadditive interactions in ns2 and spin-polarized ns metal atom trimers.

The origins of nonadditivity in the following groups of metal trimers are examined: alkali earth metals of the IIA group (Be, Mg, and Ca), Zn as a transition metal analog of this group, spin-polarized alkali metals from IA group (Li, Na, K), and the spin-polarized Cu as its transition metal analog. The nonadditive interactions in these trimers are analyzed using the following hierarchy of approximations: the Heitler-London, self-consistent field (SCF), and correlated levels of theory. The exchange nonadditivity, which is included at the Heitler-London level, constitutes a bulk of nonadditive interactions in these systems in their equilibrium structures. The SCF treatment reveals some unphysical characteristics. At the post-SCF levels of theory the multireference character of the wave function increases from atom to dimer to trimer. The role of configurations involving excitations ns-np increases in this sequence and it is the genuine nonadditive effect. There is also a dramatic change in the characteristics of the excited states upon formation of clusters. We use the parameters of these excited states to predict which complexes are bound by the unusually strong nonadditive interactions and which are not.

Interactions of transition metal atoms in high-spin states: Cr2, Sc-Cr, and Sc-Kr.

The high-spin van der Waals states are examined for the following dimers: Cr(2) ((13)Sigma(g)(+)), Sc-Cr ((8)Sigma(+), (8)Pi, (8)Delta), and Sc-Kr ((2)Sigma(+), (2)Pi, (2)Delta). These three systems offer a wide range of van der Waals interactions: anomalously strong, intermediate, and typically weak. The single-reference [coupled cluster with single, double, and noniterative triple excitations, RCCSD(T)] method is used in the calculations for all three systems. In addition, a range of configuration-interaction based methods is applied in Cr(2) and Sc-Cr. The three dimers are shown to be bound by the dispersion interaction of varying strength. In a related effort, the dispersion energy and its exchange counterpart are calculated using the newly developed open-shell variant of the symmetry-adapted perturbation theory (SAPT). The restricted open-shell time-dependent Hartree-Fock linear response function is used in the calculations of the dispersion energy in Sc-Cr and Sc-Kr calculations, while the restricted open-shell time-dependent density functional linear response function is used for Cr(2). A hybrid method combining the repulsive restricted open-shell Hartree-Fock (or complete active space self-consistent field) interaction energy with the dispersion and exchange-dispersion terms is tested against the RCCSD(T) results for the three complexes. The Cr(2) ((13)Sigma(g)(+)) complex has the well depth of 807.8 cm(-1) at the equilibrium distance of 6.18a(0) and the dissociation energy of 776.8 cm(-1). The octet-state Sc-Cr is about four times more strongly bound with the order of well depths of (8)Delta>(8)Pi>(8)Sigma(+) and a considerable anisotropy. The enhanced bonding is attributed to the unusually strong dispersion interaction. Sc-Kr ((2)Sigma(+), (2)Pi, (2)Delta) is a typical van der Waals dimer with well depths in the range of 81 cm(-1) ((2)Delta), 84 cm(-1) ((2)Sigma(+)), and 86 cm(-1) ((2)Pi). The hybrid model based on SAPT leads to results which are in excellent qualitative agreement with RCCSD(T) for all three interactions.

Interactions in open-shell clusters: ab initio study of pre-reactive complex O(3P) + HCl.

Van der Waals interactions between the ground-state triplet O(3P) atom and the closed-shell HCl molecule are investigated in the pre-reactive region. Three adiabatic (two of A'' symmetry and one of A' symmetry) and four non-relativistic diabatic potential energy surfaces are obtained by combining a restricted open-shell coupled cluster approach with the multireference configuration interaction method. The lower A'' adiabatic potential surface has a single minimum (D(e) = 589 cm(-1)) for a linear O...HCl configuration. The upper A'' potential has a weak (D(e) = 65 cm(-1)) minimum for a linear HCl...O configuration. The A' adiabatic potential has a weak (124 cm(-1)) T-shaped minimum. Adiabatic potentials intersect once in the O...HCl linear configuration and twice in the linear HCl...O geometry. The role of electrostatic interactions in shaping these potentials is discussed. The effects of spin-orbit coupling on this interaction are also investigated assuming a constant value of the SO parameter.