Absolutely Localized Projection-Based Embedding for Excited States

Abstract

We present a quantum embedding method that allows for the calculation of local excited states embedded in a Kohn-Sham density functional theory (DFT) environment. Projection-based quantum embedding methodologies provide a rigorous framework for performing DFT-in-DFT and wave function in DFT (WF-in-DFT) calculations. The use of absolute localization, where the density of each subsystem is expanded in only the basis functions associated with the atoms of that subsystem, provide improved computationally efficiency for WF-in-DFT calculations by reducing the number of orbitals in the WF calculation. In this work, we extend absolutely localized projection-based quantum embedding to study localized excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding results are highly accurate compared to the corresponding canonical EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently more accurate than canonical TDDFT. The 1 arXiv:1909.12423v1 [physics.chem-ph] 26 Sep 2019 absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge transfer states and prevent over delocalization of excited states.Additionally, we attempt to recover the environment response caused by the electronic excitations in the high-level subsystem using different schemes and compare their accuracy. Finally, we apply this method to the calculation of the excited state energy of green fluorescent protein and show that we systematically converge to the full system results. Here we demonstrate how this method can be useful in understanding excited states, specifically which chemical moieties polarize to the excitation. This work shows absolutely localized projection-based quantum embedding can treat local electronic excitations accurately, and make computationally expensive WF methods applicable to systems beyond current computational limits. many systems. 16 However, the computational cost of EOM-CCSD (scaling as O(N 6 )) restricts its usage to about 50 or fewer atoms in a moderate basis. Methods that extend the applicability of EOM-CCSD to larger systems include the use of local orbitals, [17][18][19][20][21] restricted virtual spaces, 22,23 and multiscale approaches. [24][25][26][27] Multiscale approaches treat different regions of the molecule with methods of varying cost and accuracy to reflect their importance. 28,29 For example, one may use EOM-CCSD to describe the important region of the molecule while using molecular mechanics (MM), in EOM-CCSD-in-MM methods, [30][31][32] or DFT, in EOM-CCSD-in-DFT methods, 33 to describe the remainder of the molecule. Such approaches take advantage of the high accuracy of EOM-CCSD and the low scaling of MM or DFT to go beyond the size/accuracy limits of any one method alone.Density functional theory embedding provides a formally exact framework for performing multiscale calculations. This approach has been shown to be accurate for combining density functional theory with wave function theory. The key choice in density function theory embedd...

Quantum Mechanics / Extremely Localized Molecular Orbital Embedding Strategy for Excited-States. 1. Coupling to Time-Dependent Density Functional Theory

“…Finally, it is worth noting that the TDDFT/ELMO computations performed on the 161-atom model of the Green Fluorescent Protein also allowed us to roughly determine the relative importance of the different residues/moieties to the global excitation energy. In fact, in analogy with the PBE-based TDDFT approach for excited-states proposed by Goodpaster and coworkers, 54 in Figures 9A and 9C we can observe that also the TDDFT/ELMO calculations are quite stable, independently of the order with which the fragments are included in the QM region. For example, for the computations with the 6-311G(d,p) basis-set (see Figure 9A), the inclusion of the single water molecule in the QM subsystem according to the direct order (first subunit added to the chromophore) entails a reduction of the excitation energy of 0.030 eV.…”

“…These calculations also allowed us to test the performances of the proposed method when the frontier between the QM and ELMO regions is represented by a covalent bond. recently proved this for their PBE-TDDFT approach for excited-states, 54 which is particularly suitable to solve the above-mentioned problem due the absolute localization of the electron density on each subsystem. For the sake of completeness, it is worth noting that, as side effect, these strategies unfortunately lead to also neglect global and real charge-transfer excited-states.…”

“…To conclude our validations, we finally decided to test our TDDFT/ELMO approach on a 161-atom model for the Aform of the Green Fluorescent Protein (GFP), which was previously extracted from a crystal structure (PDB code: 1EMB) by Kaila et al 73 and which was also used by Afterwards, following Goodpaster and coworkers, 54 we performed embedded TDDFT/ELMO computations on the 161-atom model of the Green Fluorescent Protein by gradually increasing the chemically active region (i.e., the chromophore pHBDI) in two different ways: i) sequentially including the H2O, Ser205, Arg96,…”

“…[45][46][47][48][49][50] The projection-based embedding (PBE) technique 37,38 has also been taken into account. The first attempt in this direction was the one by Chulhai and Jensen, 51 followed by the works conducted by the Neugebauer group 52,53 and recently by Goodpaster and collaborators 54 , who exploited their absolutely localized variant of PBE 40,41 to further reduce the TDDFT computational cost. For the sake of completeness, here it is also worth mentioning that the projection-based embedding strategy has not only been interfaced to TDDFT, but also to other and more computationally expensive methods for excited-states, particularly the CASSCF 55 (Complete Active Space Self-Consistent Field) and EOM-CCSD 54,56 (Equation-of-Motion Coupled Cluster with single and double substitutions) techniques.…”

“…and the remaining part through frozen extremely localized molecular orbitals [59][60][61] (ELMOs) that are exported from suitable databanks [62][63][64] or tailor-made model molecules. In fact, being orbitals strictly localized on small molecular subunits (e.g., atoms, bonds or functional groups), ELMOs are reliably transferable from a molecule to another [62][63][64][65][66][67][68][69] As already stated above, here the focus will be on the TDDFT/ELMO technique, which underwent most of the validation tests that were conceived to assess performances and capabilities of the LR-TD-EMFT method 43 and of the absolutely localized PBE strategy for excited-states 54 . We wanted to prove that the new approach is able i) to describe local excited-states in large systems also when the partition between the QM and ELMO subunits occurs across covalent bonds, ii) to eliminate the typical spurious low-lying charge-transfer states of TDDFT, iii) to provide accurate results when sufficiently large parts of biological systems are considered as chemically active regions in the calculations.…”