Definition and benchmarking of ab initio fragment methods for accurate excimer potential energy surfaces

Abstract

While Coupled-Cluster methods have been proven to provide an accurate description of excited electronic states, the scaling of the computational costs with the system size limits their applicability. In this study a fragment-based approach is presented which can be applied to non-covalently bound molecules with interacting chromophores localized on the fragments (so called Frankel pairs), such as $\pi$-stacked nucleobases. The interaction of the fragments is considered at two distinct points. First, the states localized on the fragments are described in the presence of the other fragment(s), for which we test two approaches. A QM/MM type method that only includes the electrostatic interaction between the fragments in the electronic structure calculations, while Pauli repulsion and dispersion effects are added separately. The other model, a Projection-based Embedding (PbE) using the Huzinaga equation includes both electrostatic and Pauli repulsion and only needs to be augmented by dispersion interactions. In both schemes the extended Effective Fragment Potential (EFP2) method of Gordon et al.~was found to provide an accurate correction for the missing terms. In the second step, the interaction of the localized chromophores is modeled for a proper description of the excitonic coupling. Here the inclusion of purely electrostatic contributions appears to be sufficient: it is found that the Coulomb part of the coupling, as evaluated using the Transition Density Cube method, provides accurate splitting of the energy of interacting chromophores above 4 \AA\ intermolecular separations.

Projected Atomic Orbitals As Optimal Virtual Space for Excited State Projection-Based Embedding Calculations

“…Conventional MObased localization, such as Pipek−Mezey 17 and SPADE, 19 can also be applied to the virtual space, and by assigning orbitals to the subsystems based on some selection criteria, those of the environment can be discarded. 25 Using the original SPADE algorithm 19 for the virtual orbitals we observed, 16 however, that without any further adjustments, the resulting virtual space can be severely distorted compared to that of an isolated monomer. As suggested in ref 16, the distortion can be reduced by extending the space by some environment orbitals that show the largest overlap with the atomic orbitals centered on the active subsystem (called the "extended SPADE" approach hereafter).…”

“…The investigated excited states are selected such that, for simplicity, the two-state model is valid for them except for very short intermolecular distances in certain cases. The same states have been studied a recent work, 16 and the PbE technique using the SPADE-based localization of virtual orbitals was found to give unphysical potential energy surfaces in most cases. As reference, we use Coupled Cluster with Singles and Doubles (CCSD) 29 and Equation-of-Motion Coupled Cluster with Singles and Doubles (EOM-CCSD) 30,31 calculations for the ground and excited states, respectively, corrected for the basis set superposition error (BSSE).…”

“…While for noncovalently interacting systems the nonadditive terms are less crucial, for higher accuracy and for generalizability, topdown projection-based embedding (PbE) 4 methods seem more suited for the description of multichromophore systems. 16 In the top-down models, a low-level calculation (usually at the DFT level) is performed first on the entire system, followed by a localization of the occupied orbitals on a priori defined sets of atoms (subsystems). This latter step is usually accomplished by using Pipek−Mezey localization, 17 intrinsic bond orbitals, 18 or the SPADE (Subsystem Projected AO DEcomposition) 19 technique, and the orbital space belonging to the different fragments, which is then used to set up the embedding potential from the fragments' density, is defined by the position of the resulting localized orbitals.…”

“…Nevertheless, the original formulations of PbE supersystem, which poses serious limitations on the applicability of the higher-level ab initio methods due to the unfavorable scaling of the computational cost with the size of the virtual space. 21 In addition, the untruncated virtual space tendentially leads to the appearance of artifactual low-lying charge transfer (CT) states, 16 often rendering the identification of local excited states impossible. Several approaches have been investigated to deal with this problem by truncating the virtual space in a reasonable way, including the absolutely localized embedding schemes of Chulhai and Goodpaster 6,9 that avoid the issue entirely by using monomer basis sets, or the basis set truncation method for PbE by Bennie et al 22 which relies on net Mulliken population criteria.…”

“…Nevertheless, the effective construction of appropriate virtual orbitals, especially if diffuse basis functions are present, remains a challenge in PbE applications. Improper virtual spaces can cause a drastic overestimation of the energy and result in nonphysically repulsive intermolecular potentials, 16 calling for a compelling remedy for this issue. In this Letter, the use of projected atomic orbitals (PAOs) is suggested as an alternative for creating virtual orbitals localized on the active subsystem.…”