Coulomb interactions between dipolar quantum fluctuations in van der Waals bound molecules and materials

Abstract

Mutual Coulomb interactions between electrons lead to a plethora of interesting physical and chemical effects, especially if those interactions involve many fluctuating electrons over large spatial scales. Here, we identify and study in detail the Coulomb interaction between dipolar quantum fluctuations in the context of van der Waals complexes and materials. Up to now, the interaction arising from the modification of the electron density due to quantum van der Waals interactions was considered to be vanishingly small. We demonstrate that in supramolecular systems and for molecules embedded in nanostructures, such contributions can amount to up to 6 kJ/mol and can even lead to qualitative changes in the long-range van der Waals interaction. Taking into account these broad implications, we advocate for the systematic assessment of so-called Dipole-Correlated Coulomb Singles in large molecular systems and discuss their relevance for explaining several recent puzzling experimental observations of collective behavior in nanostructured materials.

Fig. 1. Schematic representation of dipole-correlated Coulomb singles (DCS).

a Green arrows represent dipole coupling between electronic fragments. First-order perturbation theory (PT) on top of the many-body dispersion formalism (MBD) captures the interaction energy, E_DCS, between δρ_A and δρ_B, depicted by field lines. b E_DCS vanishes in 3D isotropic vacuum because of symmetry. c Under rotational symmetry-breaking confinement, electric field lines between electronic fragments deform, which leads to E_DCS ≠ 0. d Further inclusion of higher-order terms leads to full Coulomb-coupled vdW interaction.

Fig. 2. Binding energies and dispersion–polarization of a C₇₀ fullerene different host molecules.

Host molecules: 6-CPPA (left), “buckyball-catcher” (right). PBE0+MBD results (orange), diffusion quantum Monte-Carlo reference (DQMC, blue line; error bars shown as boxes), PBE0+MBD including dipole-correlated Coulomb singles (DCS, black line). DQMC reference data were taken from ref. . The depiction of the complexes includes iso-surfaces at ±0.003 (a.u.) of the change in the density of electronic fluctuations with respect to the isolated monomers (red: decrease, blue: increase).

Fig. 3. Dipole-correlated Coulomb singles (DCS) contributions to binding energies of ring–C₇₀ complexes and correlation to structural features.

A Binding energies for four ring–C₇₀ host–guest complexes (R1–R4): PBE0+MBD results (orange), diffusion quantum Monte-Carlo reference (DQMC, blue line; error bars as boxes), PBE0+MBD including DCS (black line). DQMC reference data taken from ref. . The hosts for R1–R4 are 8-CPPA rings. B Measure of axial–radial asymmetry (f_a), proximity measure (f_d), and DCS contribution (f_e) to binding energy (all values normalized to results for R4). Definition of axial and radial phenyl units of 8-CPPA via P_v plane shown in C.

Fig. 4. MBD and dipole-correlated Coulomb singles (DCS) contributions to the Xe–Xe interaction inside carbon nanotubes (CNTs).

A Comparing the MBD and DCS contributions inside a (6, 6)-CNT and in gas-phase as a function of the Xe–Xe separation, R. B Effect of the different confinements of a (5, 5)- and (6, 6)-CNT on E_MBD and E_DCS. C Two Xe atoms (violet) encapsulated in a CNT. Total van der Waals interaction energy given as sum of E_MBD and E_DCS including the results when increasing the Xe polarizability by 50% (black). The inset shows the variation of the absolute value of the ratio of E_DCS and E_MBD.