Multistate QM/QM Extrapolation of UV/Vis Absorption Spectra with Point Charge Embedding

Abstract

The simulation of UV/vis absorption spectra of large chromophores is prohibitively expensive with accurate quantum mechanical (QM) methods. Thus, hybrid methods, which treat the core chromophoric region at a high level of theory while the substituent effects are treated with a more computationally efficient method, may provide the best compromise between cost and accuracy. The ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics) method has proved successful at describing ground-state processes. However, for excited states, it suffers from difficulties in matching the correct excited states among the different levels of theory. We devised an approach, based on the ONIOM extrapolation formula, to combine two QM levels of theory to extrapolate entire excitation bands rather than individual states. In this contribution, we extend the same QM/QM hybrid scheme to include polarization effects on the core region through point charge embedding. The charges are computed to reproduce the electrostatic potential of the entire chromophore at the low level of theory, with proper constraints to avoid overpolarization issues at the boundary between layers. We test this approach on a variety of model compounds that show how the multistate QM/QM-embedding scheme is able to accurately reproduce the spectrum of the entire system at the high level of theory better than (i) the bare QM/QM hybrid scheme, (ii) the low-level calculation on the entire system, and (iii) the high-level calculation on the core region.

Multilevel Density Functional Theory

“…The inactive density matrix is kept frozen during the SCF cycles and enters the active Fock matrix as a one-electron term. The MLDFT shares many similarities with FDE methods; − ,,, however, some relevant differences are present, some of which are mentioned in the previous section. First, due to the partitioning performed on the density matrix instead of the density function as in FDE, we avoid the problems arising in the definition of the nonadditive kinetic potential terms that enforce Pauli exclusion between the electrons of the various subsystems in FDE.…”

“…The environment is instead described classically, by means of either continuous descriptions, such as the polarizable continuum model, , or by retaining its atomistic nature in the so-called QM/molecular mechanics (QM/MM) approaches. − In all these methods, however, the interaction between the two parts of the whole system is usually described by classical electrostatics ,− and very rarely by including the interactions of the quantum nature, such as Pauli repulsion and dispersion. − Also, QM/classical methods allow for the treatment of very large systems; however, their accuracy crucially depends on the quality of the parametrization of the classical fragments. In order to avoid such a variability, quantum embedding methods can be exploited. − In these approaches, the whole system is treated by resorting to a QM description; thus, Pauli repulsion effects are introduced in the modeling. The reduction in the computational cost is then achieved by partitioning the system in at least one active and one inactive part.…”

Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions

“…In order to overcome such limitations, quantum embedding approaches can be used. [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] The latter are usually based on partitioning the density of the investigated system into two parts: an active, which leads the property, and an inactive part, which perturbs the active moiety.…”

Energy-Based Molecular Orbital Localization in a Specific Spatial Region

“…Such a partitioning defines the so-called focused models . Most focused models are formulated in terms of quantum mechanical (QM)/classical approaches in which the active–inactive interaction is usually limited to electrostatics. − In addition, several fragmentation approaches have been proposed in the last years, demonstrating their capability to treat large molecular systems. − However, such approaches are commonly limited to the ground-state energy, although some of them have been extended to treat excitation energies, − and the interaction between the monomers is usually treated at the electrostatic level. , Such shortcomings can be overcome using quantum-embedding approaches, such as frozen density embedding and projected-based methods. − ,,,− …”