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

The projected atomic orbital (PAO) technique is presented for the construction of virtual orbital spaces in projection-based embedding (PbE) applications. The proposed straightforward procedure produces a set of virtual orbitals that are used in the final, high-level calculation of the embedded active subsystem. The PAO scheme is demonstrated on intermolecular potentials of bimolecular complexes in ground and excited states, including Rydberg excitations. The results show the outstanding performance of the PbE method when used with PAO virtual orbitals compared with those produced using common orbital localization techniques. The good agreement of the resulting PbE potential curves with those from high-level ab initio dimer calculations, also in diffuse basis sets, confirms that the PAO technique can be suggested for future applications using top-down embedding methods.

Development of analytic gradients for the Huzinaga quantum embedding method and its applications to large-scale hybrid and double hybrid DFT forces.

The theory of analytic gradients is presented for the projector-based density functional theory (DFT) embedding approach utilizing the Huzinaga-equation. The advantages of the Huzinaga-equation-based formulation are demonstrated. In particular, it is shown that the projector employed does not appear in the Lagrangian, and the potential risk of numerical problems is avoided at the evaluation of the gradients. The efficient implementation of the analytic gradient theory is presented for approaches where hybrid DFT, second-order Møller-Plesset perturbation theory, or double hybrid DFT are embedded in lower-level DFT environments. To demonstrate the applicability of the method and to gain insight into its accuracy, it is applied to equilibrium geometry optimizations, transition state searches, and potential energy surface scans. Our results show that bond lengths and angles converge rapidly with the size of the embedded system. While providing structural parameters close to high-level quality for the embedded atoms, the embedding approach has the potential to relax the coordinates of the environment as well. Our demonstrations on a 171-atom zeolite and a 570-atom protein system show that the Huzinaga-equation-based embedding can accelerate (double) hybrid gradient computations by an order of magnitude with sufficient active regions and enables affordable force evaluations or geometry optimizations for molecules of hundreds of atoms.

Performance of Multilevel Methods for Excited States.

The performance of multilevel quantum chemical approaches, which utilize an atom-based system partitioning scheme to model various electronic excited states, is studied. The considered techniques include the mechanical-embedding (ME) of "our own N-layered integrated molecular orbital and molecular mechanics" (ONIOM) method, the point charge embedding (PCE), the electronic-embedding (EE) of ONIOM, the frozen density-embedding (FDE), the projector-based embedding (PbE), and our local domain-based correlation method. For the investigated multilevel approaches, the second-order algebraic-diagrammatic construction [ADC(2)] approach was utilized as the high-level method, which was embedded in either Hartree-Fock or a density functional environment. The XH-27 test set of Zech et al. [ J. Chem. Theory Comput., 2018, 14, 4028] was used for the assessment, where organic dyes interact with several solvent molecules. With the selection of the chromophores as active subsystems, we conclude that the most reliable approach is local domain-based ADC(2) [L-ADC(2)], and the least robust schemes are ONIOM-ME and ONIOM-EE. The PbE, FDE, and PCE techniques often approach the accuracy of the L-ADC(2) scheme, but their precision is far behind. The results suggest that a more conservative subsystem selection algorithm or the inclusion of subsystem charge-transfers is required for the atom-based cost-efficient methods to produce high-accuracy excitation energies.

The MRCC program system: Accurate quantum chemistry from water to proteins.

MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller-Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes.

A dual basis (DB) approach is proposed which is suitable for the reduction of the computational expenses of the Hartree-Fock, Kohn-Sham, and wave function-based correlation methods. The approach is closely related to the DB approximation of Head-Gordon and co-workers [ J. Chem. Phys. 2006 , 125 , 074108 ] but specifically designed for embedding calculations. The new approach is applied to our variant of the projector-based embedding theory utilizing the Huzinaga-equation, multilevel local correlation methods, and combined density functional-multilevel local correlation approximations. The performance of the resulting DB density functional and wave function embedding methods is evaluated in extensive benchmark calculations and also compared to that of the corresponding embedding schemes exploiting the mixed-basis approximation. Our results show that, with an appropriate combination of basis sets, the DB approach significantly speeds up the embedding calculations, and, for chemical processes where the electronic structure considerably changes, it is clearly superior to the mixed-basis approximation. The results also demonstrate that the DB approach, if integrated with the mixed-basis approximation, efficiently eliminates the major weakness of the latter, and the combination of the DB and mixed-basis schemes is the most efficient strategy to accelerate embedding calculations.

Solvation and protonation of coumarin 102 in aqueous media: a fluorescence spectroscopic and theoretical study.

The ground- and excited-state protonation of Coumarin 102 (C102), a fluorescent probe applied frequently in heterogeneous systems with an aqueous phase, has been studied in aqueous solutions by spectroscopic experiments and theoretical calculations. For the dissociation constant of the protonated form in the ground state, pKa = 1.61 was obtained from the absorption spectra; for the excited-state dissociation constant, pKa* = 2.19 was obtained from the fluorescence spectra. These values were closely reproduced by theoretical calculations via a thermodynamic cycle (the value of pKa* also by calculations via the Förster cycle) using an implicit­explicit solvation model (polarized continuum model + addition of a solvent molecule). The theoretical calculations indicated that (i) in the ground state, C102 occurs primarily as a hydrogen-bonded water complex, with the oxo group as the binding site, (ii) this hydrogen bond becomes stronger upon excitation, and (iii) in the ground state, the amino nitrogen atom is the protonation site, and in the excited state, the carboxy oxygen atom is the protonation site. A comprehensive analysis of fluorescence decay data yielded the values kpr = 3.27 × 10(10) M(­1) s(­1) for the rate constant of the excited-state protonation and kdpr = 2.78 × 10(8) s(­1) for the rate constant of the reverse process (kpr and kdpr were treated as independent parameters). This, considering the relatively long fluorescence lifetimes of neutral C102 (6.02 ns) and its protonated form (3.06 ns) in aqueous media, means that a quasi-equilibrium state of excited-state proton transfer is reached in strongly acidic solutions.