Compressed intramolecular dispersion interactions

Abstract

The feasibility of the compression of localized virtual orbitals is explored in the context of intramolecular long-range dispersion interactions. Singular value decomposition (SVD) of coupled cluster doubles amplitudes associated with the dispersion interactions is analyzed for a number of long-chain systems, including saturated and unsaturated hydrocarbons and a silane chain. Further decomposition of the most important amplitudes obtained from these SVDs allows for the analysis of the dispersion-specific virtual orbitals that are naturally localized. Consistent with previous work on intermolecular dispersion interactions in dimers, it is found that three important geminals arise and account for the majority of dispersion interactions at the long range, even in the many body intramolecular case. Furthermore, it is shown that as few as three localized virtual orbitals per occupied orbital can be enough to capture all pairwise long-range dispersion interactions within a molecule.

Double hybrid DFT calculations with Slater type orbitals

“…The fact that semi‐local and hybrid‐functionals do not reproduce the correct 1/ r 6 ‐behaviour of the London‐dispersion interaction [ 310–312 ] has often been used as an argument for the importance of explicit electron correlation to accurately describe NCIs. [ 48,132,134,135,144 ] Indeed, Engel et al could show [ 313 ] that the exchange‐correlation functional from second order Levy–Görling perturbation theory (LG‐PT2) contains the leading contribution to the van der Waals interaction which might have served as the main motivation for the construction of an early DH which includes an MP2 term in the long‐range regime only.…”

Local Second-Order Møller–Plesset Theory with a Single Threshold Using Orthogonal Virtual Orbitals: Theory, Implementation, and Assessment

“…This could be estimated by the dipole–dipole interaction in the multipole expansion. We choose to use dipole uFERF orbitals to estimate the pair correlation energy, because the compressed form of dispersion interactions look like uFERF orbitals. , Because the uFERF estimation undershoots the real pair correlation energy (Figure S3 in the Supporting Information) and the error is also accumulative, we choose a tight threshold of 10 –2 ε here. i → a : determined by the 1s-Slater-orbital-approximation of the integral ∫ i 2 a 2 d r with threshold 10 –3 . …”

“…We choose to use dipole uFERF orbitals to estimate the pair correlation energy, because the compressed form of dispersion interactions look like uFERF orbitals. 29,89 Because the uFERF estimation undershoots the real pair correlation energy (Figure S3 in the Supporting Information) and the error is also accumulative, we choose a tight threshold of 10 −2 ε here.…”

“…Nevertheless, since correlation amplitudes depend on matrix elements over occupied ( i , j ) and virtual ( a , b ) orbitals, such as ( ia | jb ), it is clear that there are only a linear number of significant ia products. Since each such product has zero charge due to strong orthogonality, the magnitude of ( ia | jb ) behaves at long-range like a dipole–dipole interaction: − i.e., false( i a false| j b false) ∝ | bold-italicr − bold-italicr ′ | − 3 . So with an appropriate set of localized occupied and virtual orbitals, the number of numerically significant ( ia | jb ) exhibits only linear growth, scriptO ( A 1 ) , for a large enough molecule.…”