Using the ONIOM hybrid method to apply equation of motion CCSD to larger systems: Benchmarking and comparison with time-dependent density functional theory, configuration interaction singles, and time-dependent Hartree–Fock

Core Binding Energy Calculations: A Scalable Approach with the Quantum Embedding-Based Equation-of-Motion Coupled-Cluster Method

We investigated the use of density matrix embedding theory to facilitate the computation of core ionization energies (IPs) of large molecules at the equation-of-motion coupled-cluster singles doubles with perturbative triples (EOM-CCSD*) level in combination with the core-valence separation (CVS) approximation. The unembedded IP-CVS-EOM-CCSD* method with a triple-ζ basis set produced ionization energies within 1 eV of experiment with a standard deviation of ∼0.2 eV for the core65 data set. The embedded variant contributed very little systematic error relative to the unembedded method, with a mean unsigned error of 0.07 eV and a standard deviation of ∼0.1 eV, in exchange for accelerating the calculations by many orders of magnitude. By employing embedded EOM-CC methods, we computed the core ionization energies of the uracil hexamer, doped fullerene, and chlorophyll molecule, utilizing up to ∼4000 basis functions within 1 eV from experimental values. Such calculations are not currently possible with the unembedded EOM-CC method.

ONIOM Method with Charge Transfer Corrections (ONIOM-CT): Analytic Gradients and Benchmarking

Hybrid methods such as ONIOM that treat different regions of a large molecule using different methods are widely used to investigate chemical reactions in a variety of materials and biological systems. However, there are inherent sources of significant errors due to the standard treatment of the boundary between the regions using hydrogen link atoms. In particular, an unbalanced charge distribution in the chemically important model region is a potential source of such problems. We have previously suggested ONIOM-CT (ONIOM with charge transfer corrections) which addresses this issue by applying a potential in the form of point charges to obtain a desired charge redistribution. The metric for charge redistribution relies on the type of population analysis used to obtain the charges. ONIOM-CT has been implemented using Mulliken and Löwdin population analyses and has been shown to improve computed reaction energies for illustrative chemical reactions. In this work, we derive and implement the analytic gradients for ONIOM-CT that requires solving two sets of coupled-perturbed self-consistent equations, one each for the model system and the full system. However, both are needed only at the low level of theory, allowing for an efficient formulation and implementation for both Mulliken and Löwdin population analyses. Benchmarking and illustrative geometry optimizations have been carried out for a previously studied set of reactions involving a single link atom between regions. Additionally, we have generalized our method for the treatment of model systems involving multiple link atoms to enable applications for a broader set of problems. The generalized methods are illustrated for both charge models. Furthermore, we have studied a set of three proton transfer reactions and demonstrate that significant improvement is achieved by ONIOM-CT over ONIOM using both Mulliken and Löwdin population analyses.

Point charge embedding for ONIOM excited states calculations

Hybrid quantum mechanical methods can assist in the interpretation and prediction of the electronic spectra of large molecular structures. In this work, we study the performance of the ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics) hybrid method for the calculation of transition energies and oscillator strengths by embedding the core region in a field of fixed point charges. These charges introduce polarization effects from the substituent groups to the core region. We test various charge definitions, with particular attention to the issue of overpolarization near the boundary between layers. To minimize this issue, we fit the charges on the electrostatic potential of the entire structure in the presence of the link atoms used to cap dangling bonds. We propose two constrained fitting strategies: one that produces an average set of charges common to both model system calculations, EE(L1), and one that produces two separate sets of embedding charges, EE(L2). The results from our tests show that indeed electronic embedding with constrained-fitted charges tends to improve the performance of ONIOM compared to non-embedded calculations. However, the EE(L2) charges work best for transition energies, and the EE(L1) charges work best for oscillator strengths. This may be an indication that fixed point charges do not have enough flexibility to adapt to each system, and other effects (e.g., polarization of the embedding field) may be necessary.

Multi-state extrapolation of UV/Vis absorption spectra with QM/QM hybrid methods

In this work, we present a simple approach to simulate absorption spectra from hybrid QM/QM calculations. The goal is to obtain reliable spectra for compounds that are too large to be treated efficiently at a high level of theory. The present approach is based on the extrapolation of the entire absorption spectrum obtained by individual subcalculations. Our program locates the main spectral features in each subcalculation, e.g., band peaks and shoulders, and fits them to Gaussian functions. Each Gaussian is then extrapolated with a formula similar to that of ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics). However, information about individual excitations is not necessary so that difficult state-matching across subcalculations is avoided. This multi-state extrapolation thus requires relatively low implementation effort while affording maximum flexibility in the choice of methods to be combined in the hybrid approach. The test calculations show the efficacy and robustness of this methodology in reproducing the spectrum computed for the entire molecule at a high level of theory.

A benchmark study of electronic excitation energies, transition moments, and excited-state energy gradients on the nicotine molecule

In this work, we report a comparative study of computed excitation energies, oscillator strengths, and excited-state energy gradients of (S)-nicotine, chosen as a test case, using multireference methods, coupled cluster singles and doubles, and methods based on time-dependent density functional theory. This system was chosen because its apparent simplicity hides a complex electronic structure, as several different types of valence excitations are possible, including n-π(*), π-π(*), and charge-transfer states, and in order to simulate its spectrum it is necessary to describe all of them consistently well by the chosen method.

Excited-state calculations with TD-DFT: from benchmarks to simulations in complex environments

In this perspective, we present an overview of recent progress on Time-Dependent Density Functional Theory (TD-DFT) with a specific focus on its accuracy and on models able to take into account environmental effects, including complex media. To this end, we first summarise recent benchmarks and define an average TD-DFT accuracy in reproducing excitation energies when a conventional approach is used. Next, coupling of TD-DFT with models able to account for different kinds of interactions between a central chromophore and nearby chemical objects (solvent, organic cage, metal as well as semi-conducting surface) is investigated. Examples of application to excitation properties are presented, allowing to briefly describe several recent computational strategies. In addition, an extension of TD-DFT to describe a phenomenon involving interacting chromophores, e.g. the electronic energy transfer (EET), is presented to illustrate that this methodology can be applied to processes beyond the vertical excitation. This perspective therefore aims to provide to non-specialists a flavour of recent trends in the field of simulations of excited states in "realistic" situations.