CateCom: A Practical Data-Centric Approach to Categorization of Computational Models.

The advent of data-driven science in the 21st century brought about the need for well-organized structured data and associated infrastructure able to facilitate the applications of artificial intelligence and machine learning. We present an effort aimed at organizing the diverse landscape of physics-based and data-driven computational models in order to facilitate the storage of associated information as structured data. We apply object-oriented design concepts and outline the foundations of an open-source collaborative framework that is (1) capable of uniquely describing the approaches in structured data, (2) flexible enough to cover the majority of widely used models, and (3) utilizes collective intelligence through community contributions. We present example database schemas and corresponding data structures and explain how these are deployed in software at the time of this writing.

Dissociation of HCl in water nanoclusters: an energy decomposition analysis perspective.

As known, small HCl-water nanoclusters display a particular dissociation behaviour, whereby at least four water molecules are required for the ionic dissociation of HCl. In this work, we examine how intermolecular interactions promote the ionic dissociation of such nanoclusters. To this end, a set of 45 HCl-water nanoclusters with up to four water molecules is introduced. Energy decomposition analysis based on absolutely localized molecular orbitals (ALMO-EDA) is employed in order to study the importance of frozen interaction, dispersion, polarization, and charge-transfer for the dissociation. The vertical ALMO-EDA scheme is applied to HCl-water clusters along a proton-transfer coordinate varying the amount of spectator water molecules. The corresponding ALMO-EDA results show a clear preference for the dissociated cluster only in the presence of four water molecules. Our analysis of adiabatic ALMO-EDA results reveals a push-pull mechanism for the destabilization of the HCl bond based on the synergy between forward and backward charge-transfer.

Effective Two-Body Interactions.

Cooperative or nonadditive effects contribute to the pairwise noncovalent interaction of two molecules in a cluster or the condensed phase in ways that depend on the specific arrangements and interactions of the other surrounding molecules that constitute their environment. General expressions for an effective two-body interaction are presented, which are correct to increasing orders in the many-body expansion. The simplest result, correct through third order, requires only seven individual calculations, in contrast to a linear number of three-body contributions. Two applications are presented. First, an error analysis is performed on a model (H2O)8 cluster which completes the first solvation shell of a central water-water hydrogen bond. Energy decomposition analysis is performed to show that the largest effects of cooperativity on the central hydrogen bond arise from electrical polarization. Second, the nature of cooperative effects on proton transfer in an HCl + (H2O)4 cluster is characterized.

Benchmark of the Extension of Frozen-Density Embedding Theory to Nonvariational Correlated Methods: The Embedded-MP2 Case.

The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput. 2020, 16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao-Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller-Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys. 2019, 150, 121101]. Local density approximation is used for ExcTnad[ρA,ρB] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for ExcTnad[ρA,ρB] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for ExcTnad[ρA,ρB] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3-30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.

Extension of frozen-density embedding theory for non-variational embedded wavefunctions.

In the original formulation, frozen-density embedding theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050-8053 (1993); T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] concerns multi-level simulation methods in which variational methods are used to obtain the embedded NA-electron wavefunction. In this work, an implicit density functional for the total energy is constructed and used to derive a general expression for the total energy in methods in which the embedded NA electrons are treated non-variationally. The formula is exact within linear expansion in density perturbations. Illustrative numerical examples are provided.

Explicit vs. implicit electronic polarisation of environment of an embedded chromophore in frozen-density embedding theory.

Frozen-Density Embedding Theory (FDET) provides a system-independent formal framework for multi-level computational methods. Despite apparent similarity, the interaction energy components commonly used in QM/MM methods do not have their corresponding counterparts in FDET. We show how the effect of the polarisation on the electron distribution in the environment can be (or is) accounted for either explicitly or implicitly within the FDET framework. Numerical examples are provided for vertical excitation energies in four representative cases of embedded chromophores.

Benchmark of Excitation Energy Shifts from Frozen-Density Embedding Theory: Introduction of a Density-Overlap-Based Applicability Threshold.

We present a thorough investigation of the errors in results obtained with the combination of frozen-density embedding theory and the algebraic diagrammatic construction scheme for the polarization propagator of second order (FDE-ADC(2)). The study was carried out on a set of 52 intermolecular complexes with varying interaction strength, each consisting of a chromophore of fundamental interest and a few small molecules in its environment. The errors emerging in frozen-density embedding theory-based methods originate from (a) the solver of the quantum many-body problem used to obtain the embedded wave function (ΨAemb), (b) the approximation for the explicit density functional for the embedding potential, and (c) the choice of the density representing the environment (ρB( r⃗)). The present work provides a comprehensive analysis of the errors in the excitation energies based on the last two factors. Furthermore, a density-overlap-based parameter is proposed to be used as an a priori criterion of applicability.

Implementation and Application of the Frozen Density Embedding Theory with the Algebraic Diagrammatic Construction Scheme for the Polarization Propagator up to Third Order.

Implementation, benchmarking, and representative applications of the new FDE-ADC(3) method for describing environmental effects on excited states as a combination of frozen density embedding (FDE) and the algebraic-diagrammatic construction scheme for the polarization propagator of third order (ADC(3)) are presented. Results of FDE-ADC(3) calculations are validated with respect to supersystem calculations on test systems with varying molecule-environment interaction strengths from dispersion up to multiple hydrogen bonds. The overall deviation compared to the supersystem calculations is as small as 0.029 eV for excitation energies, which is even smaller than the intrinsic error of ADC(3). The dependence of the accuracy on the choice of method and functional for the calculation of the environment and the nonelectrostatic part of the system-environment interaction is evaluated. In three representative examples, the FDE-ADC method is applied to investigate larger systems and to analyze excited state properties using visualization of embedded densities and orbitals.

First time combination of frozen density embedding theory with the algebraic diagrammatic construction scheme for the polarization propagator of second order.

The combination of Frozen Density Embedding Theory (FDET) and the Algebraic Diagrammatic Construction (ADC) scheme for the polarization propagator for describing environmental effects on electronically excited states is presented. Two different ways of interfacing and expressing the so-called embedding operator are introduced. The resulting excited states are compared with supermolecular calculations of the total system at the ADC(2) level of theory. Molecular test systems were chosen to investigate molecule-environment interactions of varying strength from dispersion interaction up to multiple hydrogen bonds. The overall difference between the supermolecular and the FDE-ADC calculations in excitation energies is lower than 0.09 eV (max) and 0.032 eV in average, which is well below the intrinsic error of the ADC(2) method itself.

Orthogonality of embedded wave functions for different states in frozen-density embedding theory.

Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles--embedded wave functions are only auxiliary objects used to obtain stationary densities--working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.