Benchmark CCSD-SAPT study of rare gas dimers with comparison to MP-SAPT and DFT-SAPT

Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

Long-range interactions of aromatic molecules with alkali-metal and alkaline-earth-metal atoms

The isotropic and anisotropic coefficients C_n ^l,m of the long-range spherical expansion ∼1/Rⁿ (R-the intermolecular distance) of the dispersion and induction intermolecular energies are calculated using the first principles for the complexes containing an aromatic molecule (benzene, pyridine, furan, and pyrrole) and alkali-metal (Li, Na, K, Rb, and Cs) or alkaline-earth-metal (Be, Mg, Ca, Sr, and Ba) atoms in their electronic ground states. The values of the first- and second-order properties of the aromatic molecules are calculated using the response theory with the asymptotically corrected LPBE0 functional. The second-order properties of the closed-shell alkaline-earth-metal atoms are obtained using the expectation-value coupled cluster theory and of the open-shell alkali-metal atoms using analytical wavefunctions. These properties are used for the calculation of the dispersion C_n,disp ^l,m and induction C_n,ind ^l,m coefficients (C_n ^l,m=C_n,disp ^l,m+C_n,ind ^l,m) with n up to 12 using the available implemented analytical formulas. It is shown that the inclusion of the coefficients with n > 6 is important for reproducing the interaction energy in the van der Waals region at R ≈ 6 Å. The reported long-range potentials should be useful for constructing the analytical potentials valid for the whole intermolecular interaction range, which are needed for spectroscopic and scattering studies.

The development of a full range analytical interatomic potential

A chronological account is given to the development of a full range interatomic potential. Starting with a simple phenomenological model, the terms in the model are gradually modified, so that they can carry some definite physical meaning. To gain insight, a systematic, order by order interaction potential theory is developed. Conversely, this theory suggests the functional form for the potential model. At present, we have a simple interaction model that is capable of describing the van der Waals potentials of many systems from R = 0 to R→∞.

ZMP-SAPT: DFT-SAPT using ab initio densities

Symmetry Adapted Perturbation Theory (SAPT) has become an important tool when predicting and analyzing intermolecular interactions. Unfortunately, Density Functional Theory (DFT)-SAPT, which uses DFT for the underlying monomers, has some arbitrariness concerning the exchange-correlation potential and the exchange-correlation kernel involved. By using ab initio Brueckner Doubles densities and constructing Kohn-Sham orbitals via the Zhao-Morrison-Parr (ZMP) method, we are able to lift the dependence of DFT-SAPT on DFT exchange-correlation potential models in first order. This way, we can compute the monomers at the coupled-cluster level of theory and utilize SAPT for the intermolecular interaction energy. The resulting ZMP-SAPT approach is tested for small dimer systems involving rare gas atoms, cations, and anions and shown to compare well with the Tang-Toennies model and coupled cluster results.

Theoretical study of the complexes of dichlorobenzene isomers with argon. II. SAPT analysis of the intermolecular interaction

The interaction of argon with dichlorobenzene isomers (DCB-Ar) has been analyzed with the help of the symmetry-adapted perturbation theory based on the density functional description of monomer properties (DFT-SAPT). The global potential energy surface (PES) of these complexes determined from the DFT-SAPT interaction energy (E_int) values has been compared to the CCSD(T) (coupled cluster method including single and double excitations with perturbative triple excitations) PES reported in the companion Paper I [J. Makarewicz and L. Shirkov, J. Chem. Phys. 150, 074301 (2019)]. The equilibrium structures and the binding energies found using DFT-SAPT and CCSD(T) methods combined with adequate basis sets are in good agreement. Besides DCB-Ar, we confirmed that DFT-SAPT gives accurate values of these quantities for other complexes containing an aromatic molecule and Ar. However, DFT-SAPT PES of DCB-Ar is flatter than the corresponding CCSD(T) one. As a result, the intermolecular vibrational energies are systematically underestimated. The analytical form of the important interrelations between SAPT components of E_int, established previously by us [J. Makarewicz and L. Shirkov, J. Chem. Phys. 144, 204115 (2016)], has been approved for the DCB-Ar complexes. Simplified SAPT models based on these relations have been employed to explain physical reasons for differences in the structures and the binding energies of DCB-Ar isomers. It is shown that the equilibrium distance of Ar to DCB plane and the binding energy are determined mainly by dispersion energy. The shift of Ar toward Cl is caused by both exchange and dispersion terms.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Quantum-Mechanical Relation between Atomic Dipole Polarizability and the van der Waals Radius

The atomic dipole polarizability α and the van der Waals (vdW) radius R_{vdW} are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently and separately from each other. Here, we derive the quantum-mechanical relation R_{vdW}=const×α^{1/7}, which is markedly different from the common assumption R_{vdW}∝α^{1/3} based on a classical picture of hard-sphere atoms. As shown for 72 chemical elements between hydrogen and uranium, the obtained formula can be used as a unified definition of the vdW radius solely in terms of the atomic polarizability. For vdW-bonded heteronuclear dimers consisting of atoms A and B, the combination rule α=(α_{A}+α_{B})/2 provides a remarkably accurate way to calculate their equilibrium interatomic distance. The revealed scaling law allows us to reduce the empiricism and improve the accuracy of interatomic vdW potentials, at the same time suggesting the existence of a nontrivial relation between length and volume in quantum systems.