Abstract
The calculation of accurate excitation energies using ab initio electronic structure methods such as standard equation of motion coupled cluster singles and doubles (EOM-CCSD) has been cost prohibitive for large systems. In this work, we use a simple projector-based embedding scheme to calculate the EOM-CCSD excitation energies of acrolein solvated in water molecules modeled using density functional theory (DFT). We demonstrate the accuracy of this approach gives excitation energies within 0.01 eV of full EOM-CCSD, but with significantly reduced computational cost. This approach is also shown to be relatively invariant to the choice of functional used in the environment and allows for the description of systems with large numbers of basis functions (>1000) to be treated using state-of-the-art wave function methods. The flexibility of embedding to select orbitals to add to the excited-state method provides insights into the origins of the excitations and can reduce artifacts that could arise in traditional linear response time-dependent DFT (LR-TDDFT).
Highlights
The main disadvantage of LR-TDDFT arises from the wide choice of functionals, each of which may have certain failure cases depending on the systems and physical process under study
EOM-CCSD has a worse formal scaling compared to LR-TDDFT
Various approaches have been developed to improve the scaling and cost of EOM-CCSD, such as local orbital methods,[17−21] restricted virtual spaces and highly efficient implementations.[22,23]. Methods with such high scaling often require a multiscale approach such as the quantum mechanical molecular mechanical (QM/MM) type partitioning[24−27] or other multilevel techniques.[28−30] The aim of multiscale modeling is to treat different regions of a system with methods matched to the required accuracy, e.g., important regions are treated with higher accuracy methods, and less important regions with lower accuracy methods
Summary
Letter focused on a noncovalent system for embedding to show it is possible to obtain solvent effects cheaply and avoid artifacts that are known to occur in such systems;[35] we show that it is possible to partition covalently bound systems by selecting important orbitals on the water to improve accuracy. Such weak dependence is clearly not observed with LR-TDDFT (and TDHF) when using the same set of functionals, as shown in the right part of Figure 3 These results further show that the most important factor in the embedding is the selection of environment orbitals in the active region to be treated at the high-level. The approach to determine which orbitals of the environment to be included was as follows: (i) HF on the whole system; (ii) select the atoms of the photoactive molecule (or part of the molecule); (iii) run CIS (or LR-TDDFT, CC2, etc.) for subsystem A; (iv) increase the number of orbitals in the embedding region by 1 and check if the difference in the excitation energy is larger than some threshold value (e.g 0.01 eV); (v) add all those orbitals whose inclusion causes the difference in CIS (or LR-TDDFT, CC2, etc.) excitation energy to change by more than the specified threshold and rerun with eEOM-CCSD.
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