Interoperable workflows by exchanging grid-based data between quantum-chemical program packages.

Quantum-chemical subsystem and embedding methods require complex workflows that may involve multiple quantum-chemical program packages. Moreover, such workflows require the exchange of voluminous data that go beyond simple quantities, such as molecular structures and energies. Here, we describe our approach for addressing this interoperability challenge by exchanging electron densities and embedding potentials as grid-based data. We describe the approach that we have implemented to this end in a dedicated code, PyEmbed, currently part of a Python scripting framework. We discuss how it has facilitated the development of quantum-chemical subsystem and embedding methods and highlight several applications that have been enabled by PyEmbed, including wave-function theory (WFT) in density-functional theory (DFT) embedding schemes mixing non-relativistic and relativistic electronic structure methods, real-time time-dependent DFT-in-DFT approaches, the density-based many-body expansion, and workflows including real-space data analysis and visualization. Our approach demonstrates, in particular, the merits of exchanging (complex) grid-based data and, in general, the potential of modular software development in quantum chemistry, which hinges upon libraries that facilitate interoperability.

A simple and consistent quantum-chemical fragmentation scheme for proteins that includes two-body contributions.

The Molecular Fractionation with Conjugate Caps (MFCC) method is a popular fragmentation method for the quantum-chemical treatment of proteins. However, it does not account for interactions between the amino acid fragments, such as intramolecular hydrogen bonding. Here, we present a combination of the MFCC fragmentation scheme with a second-order many-body expansion (MBE) that consistently accounts for all fragment-fragment, fragment-cap, and cap-cap interactions, while retaining the overall simplicity of the MFCC scheme with its chemically meaningful fragments. We show that with the resulting MFCC-MBE(2) scheme, the errors in the total energies of selected polypeptides and proteins can be reduced by up to one order of magnitude and relative energies of different protein conformers can be predicted accurately.

Protein network centralities as descriptor for QM region construction in QM/MM simulations of enzymes.

The construction of a suitable QM region is the most crucial step in setting up hybrid quantum mechanics/molecular mechanics (QM/MM) simulations for enzymatic reactions. The QM region should ideally include all important amino acids residues, while being as small as possible to save computational effort. Most available methods for systematic QM region construction are based either on the distance of single amino acids to the active site or on their electrostatic effect. Such approaches might miss non-electrostatic and long-range allosteric interactions. Here, we present a proof of concept study for the application of protein network analysis to tackle this problem. Specifically, we explore the use of the protein network centralities as descriptor for QM region construction. We find that protein network centralities, in particular the betweenness centrality, can be a useful descriptor for systematic QM region construction. We show that in combination with our previously developed point charge variation analysis, they can be used to identify important residues that are missed in purely electrostatic approaches.

Efficient automatic construction of atom-economical QM regions with point-charge variation analysis.

The setup of QM/MM calculations is not trivial since many decisions have to be made by the simulation scientist to achieve reasonable and consistent results. The main challenge to be tackled is the construction of the QM region to make sure to take into account all important parts of the adjacent environment and exclude less important ones. In our previous work [F. Brandt and Ch. R. Jacob, Systematic QM Region Construction in QM/MM Calculations Based on Uncertainty Quantification, J. Chem. Theory Comput., 2022, 18, 2584-2596.], we introduced the point charge variation analysis (PCVA) as a simple and reliable tool to systematically construct QM regions based on the sensitivity of the reaction energy with respect to variations of the MM point charges. Here, we assess several simplified variants of this PCVA approach for the example of catechol O-methyltransferase and apply PCVA for another system, the triosephosphate isomerase. Furthermore, we extend its scope by applying it to a DNA system. Our results indicate that PCVA offers an efficient and versatile approach of the automatic construction of atom-economical QM regions, but also identify possible pitfalls and limitations.

Coupled-Cluster Density-Based Many-Body Expansion.

While CCSD(T) is often considered the "gold standard" of computational chemistry, the scaling of its computational cost as N7 limits its applicability for large and complex molecular systems. In this work, we apply the density-based many-body expansion [ Int. J. Quantum Chem. 2020, 120, e26228] in combination with CCSD(T). The accuracy of this approach is assessed for neutral, protonated, and deprotonated water hexamers, as well as (H2O)16 and (H2O)17 clusters. For the neutral water clusters, we find that already with a density-based two-body expansion, we are able to approximate the supermolecular CCSD(T) energies within chemical accuracy (4 kJ/mol). This surpasses the accuracy that is achieved with a conventional, energy-based three-body expansion. We show that this accuracy can be maintained even when approximating the electron densities using Hartree-Fock instead of using coupled-cluster densities. The density-based many-body expansion thus offers a simple, resource-efficient, and highly parallelizable approach that makes CCSD(T)-quality calculations feasible where they would otherwise be prohibitively expensive.

A new ultrafast energy funneling material harvests three times more diffusive solar energy for GaInP photovoltaics.

There is no theoretical limit in using molecular networks to harvest diffusive sun photons on large areas and funnel them onto much smaller areas of highly efficient but also precious energy-converting materials. The most effective concept reported so far is based on a pool of randomly oriented, light-harvesting donor molecules that funnel all excitation quanta by ultrafast energy transfer to individual light-redirecting acceptor molecules oriented parallel to the energy converters. However, the best practical light-harvesting system could only be discovered by empirical screening of molecules that either align or not within stretched polymers and the maximum absorption wavelength of the empirical system was far away from the solar maximum. No molecular property was known explaining why certain molecules would align very effectively whereas similar molecules did not. Here, we first explore what molecular properties are responsible for a molecule to be aligned. We found a parameter derived directly from the molecular structure with a high predictive power for the alignability. In addition, we found a set of ultrafast funneling molecules that harvest three times more energy in the solar's spectrum peak for GaInP photovoltaics. A detailed study on the ultrafast dipole moment reorientation dynamics demonstrates that refocusing of the diffusive light is based on ∼15-ps initial dipole moment depolarization followed by ∼50-ps repolarization into desired directions. This provides a detailed understanding of the molecular depolarization/repolarization processes responsible for refocusing diffusively scattered photons without violating the second law of thermodynamics.

Biased Borate Esterification during Nucleoside Phosphorylase-Catalyzed Reactions: Apparent Equilibrium Shifts and Kinetic Implications.

Biocatalytic nucleoside (trans-)glycosylations catalyzed by nucleoside phosphorylases have evolved into a practical and convenient approach to the preparation of modified nucleosides, which are important pharmaceuticals for the treatment of various cancers and viral infections. However, the obtained yields in these reactions are generally determined exclusively by the innate thermodynamic properties of the nucleosides involved, hampering the biocatalytic access to many sought-after target nucleosides. We herein report an additional means for reaction engineering of these systems. We show how apparent equilibrium shifts in phosphorolysis and glycosylation reactions can be effected through entropically driven, biased esterification of nucleosides and ribosyl phosphates with inorganic borate. Our multifaceted analysis further describes the kinetic implications of this in situ reactant esterification for a model phosphorylase.

Accurate quantum-chemical fragmentation calculations for ion-water clusters with the density-based many-body expansion.

The many-body expansion (MBE) provides an attractive fragmentation method for the efficient quantum-chemical treatment of molecular clusters. However, its convergence with the many-body order is generally slow for molecular clusters that exhibit large intermolecular polarization effects. Ion-water clusters are thus a particularly challenging test case for quantum-chemical fragmentation methods based on the MBE. Here, we assess the accuracy of both the conventional, energy-based MBE and the recently developed density-based MBE [Schmitt-Monreal and Jacob, Int. J. Quantum Chem., 2020, 120, e26228] for ion-water clusters. As test cases, we consider hydrated Ca2+, F-, OH-, and H3O+, and compare both total interaction energies and the relative interaction energies of different structural isomers. We show that an embedded density-based two-body expansion yields highly accurate results compared to supermolecular calculations. Already at the two-body level, the density-based MBE clearly outperforms a conventional, energy-based embedded three-body expansion. We compare different embedding schemes and find that a relaxed frozen-density embedding potential yields the most accurate results. This opens the door to accurate and efficient quantum-chemical calculations for large ion-water clusters as well as condensed-phase systems.

Quantum-chemical calculation of two-dimensional infrared spectra using localized-mode VSCF/VCI.

Computational protocols for the simulation of two-dimensional infrared (2D IR) spectroscopy usually rely on vibrational exciton models which require an empirical parameterization. Here, we present an efficient quantum-chemical protocol for predicting static 2D IR spectra that does not require any empirical parameters. For the calculation of anharmonic vibrational energy levels and transition dipole moments, we employ the localized-mode vibrational self-consistent field (L-VSCF)/vibrational configuration interaction (L-VCI) approach previously established for (linear) anharmonic theoretical vibrational spectroscopy [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365-3377 (2014)]. We demonstrate that with an efficient expansion of the potential energy surface using anharmonic one-mode potentials and harmonic two-mode potentials, 2D IR spectra of metal carbonyl complexes and dipeptides can be predicted reliably. We further show how the close connection between L-VCI and vibrational exciton models can be exploited to extract the parameters of such models from those calculations. This provides a novel route to the fully quantum-chemical parameterization of vibrational exciton models for predicting 2D IR spectra.

Electrocatalytic Activation of Donor-Acceptor Cyclopropanes and Cyclobutanes: An Alternative C(sp3 )-C(sp3 ) Cleavage Mode.

We describe the first electrochemical activation of D-A cyclopropanes and D-A cyclobutanes leading after C(sp3 )-C(sp3 ) cleavage to the formation of highly reactive radical cations. This concept is utilized to formally insert molecular oxygen after direct or DDQ-assisted anodic oxidation of the strained carbocycles, delivering ß- and γ-hydroxy ketones and 1,2-dioxanes electrocatalytically. Furthermore, insights into the mechanism of the oxidative process, obtained experimentally and by additional quantum-chemical calculations are presented. The synthetic potential of the reaction products is demonstrated by diverse derivatizations.

Spin-state dependence of exchange-correlation holes.

Applications of density-functional theory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations feature such an explicit spin-state dependence [C. R. Jacob and M. Reiher, Int. J. Quantum Chem., 2012, 112, 3661-3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.

Electronic Structure of the Hieber Anion [Fe(CO)3(NO)]- Revisited by X-ray Emission and Absorption Spectroscopy.

While the Hieber anion [Fe(CO)3(NO)]- has been reincarnated in the last years as an active catalyst in organic synthesis, there is still a debate about the oxidation state of the central Fe atom and the resulting charge of the NO ligand. To shed new light on this question and to understand the Fe-NO interaction in the Hieber anion, it is investigated in comparison to the formal 3d8 reference Fe(CO)5 and the formal 3d10 reference [Fe(CO)4]2- by the combination of valence-to-core X-ray emission spectroscopy (VtC-XES), X-ray absorption near-edge structure spectroscopy (XANES), and high-energy-resolution fluorescence-detected XANES. In order to extract information about the electronic structure, time-dependent density functional theory and ground-state density functional theory calculations are applied. This combination of experimental and computational methods reveals that the electron density at the Fe center of the Hieber resembles that of the isoelectronic [Fe(CO)4]2-. These observations challenge recent descriptions of the Hieber anion and reopen the debate about the experimentally and computationally determined Fe oxidation state and charge on the NO ligand.

The DIRAC code for relativistic molecular calculations.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

QMflows: A Tool Kit for Interoperable Parallel Workflows in Quantum Chemistry.

We present the QMflows Python package for quantum chemistry workflow automatization. QMflows allows users to write complex workflows in terms of simple Python scripts. It supports the development of interoperable workflows involving multiple quantum chemistry codes and executes them efficiently on large scale parallel computers. This open source library provides standardized interfaces to a number of quantum chemistry packages and can be easily extended to accommodate additional codes. QMflows features are described and illustrated with a number of representative applications.

Description of intermolecular charge transfer with subsystem density-functional theory.

Efficient quantum-chemical methods that are able to describe intermolecular charge transfer are crucial for modeling organic semiconductors. However, the correct description of intermolecular charge transfer with density-functional theory (DFT) is hampered by the fractional charge error of approximate exchange-correlation (xc) functionals. Here, we investigate the charge transfer induced by an external electric field in a tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) complex as a test case. For this seemingly simple model system, a supermolecular DFT treatment fails with most conventional xc functionals. Here, we present an extension of subsystem DFT to subsystems with a fractional number of electrons. We show that within such a framework, it becomes possible to overcome the fractional charge error by enforcing the correct dependence of each subsystem's total energy on the subsystem's fractional charge. Such a subsystem DFT approach allows for a correct description of the intermolecular charge transfer in the TTF-TCNQ model complex. The approach presented here can be generalized to larger molecular aggregates and will thus allow for modeling organic semiconductor materials accurately and efficiently.

On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction.

By a suitable choice of coordinates, the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation of the conventionally used normal-mode coordinates, anharmonic couplings between modes can be significantly reduced. However, such a transformation introduces harmonic couplings between the localized modes. To elucidate the role of these harmonic couplings, we consider the vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) calculations for both few-mode model systems and for ethene as a molecular test case. We show that large harmonic couplings can result in significant errors in localized-mode L-VSCF/L-VCI calculations and study the convergence with respect to the size of the VCI excitation space. To further elucidate the errors introduced by harmonic couplings, we discuss the connection between L-VSCF/L-VCI and vibrational exciton models. With the help of our results, we propose an algorithm for the localization of normal modes in suitable subsets that are chosen to strictly limit the errors introduced by the harmonic couplings while still leading to maximally localized modes.

Revisiting the Dependence of Cu K-Edge X-ray Absorption Spectra on Oxidation State and Coordination Environment.

X-ray absorption spectroscopy (XAS) at the Cu K-edge is an important tool for probing the properties of copper centers in transition-metal chemistry and catalysis. However, the interpretation of experimental XAS spectra requires a detailed understanding of the dependence of spectroscopic features on the local geometric and electronic structure, which can be established by theoretical X-ray spectroscopy. Here, we present a systematic computational study of the Cu K-edge XAS spectra of selected Cu complexes based on time-dependent density-functional theory in combination with a molecular orbital analysis of the relevant transitions. For a series of Cu ammine model complexes as well as a comprehensive test set of 12 Cu(I) and 5 Cu(II) complexes, we revisit the dependence of the pre-edge region in Cu K-edge XAS spectra on oxidation state and coordination geometry. While our calculations confirm earlier experimental assignments, we can also reveal additional signatures of the ligand orbitals and identify the underlying orbital interactions. The comprehensive picture revealed by this study will provide a reliable basis for the interpretation of in situ Cu K-edge XAS spectra of catalytic intermediates.

Simulation of FRET dyes allows quantitative comparison against experimental data.

Fully understanding biomolecular function requires detailed insight into the systems' structural dynamics. Powerful experimental techniques such as single molecule Förster Resonance Energy Transfer (FRET) provide access to such dynamic information yet have to be carefully interpreted. Molecular simulations can complement these experiments but typically face limits in accessing slow time scales and large or unstructured systems. Here, we introduce a coarse-grained simulation technique that tackles these challenges. While requiring only few parameters, we maintain full protein flexibility and include all heavy atoms of proteins, linkers, and dyes. We are able to sufficiently reduce computational demands to simulate large or heterogeneous structural dynamics and ensembles on slow time scales found in, e.g., protein folding. The simulations allow for calculating FRET efficiencies which quantitatively agree with experimentally determined values. By providing atomically resolved trajectories, this work supports the planning and microscopic interpretation of experiments. Overall, these results highlight how simulations and experiments can complement each other leading to new insights into biomolecular dynamics and function.

Analytical gradients for subsystem density functional theory within the slater-function-based amsterdam density functional program.

We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc.

No need for external orthogonality in subsystem density-functional theory.

Recent reports on the necessity of using externally orthogonal orbitals in subsystem density-functional theory (SDFT) [Annu. Rep. Comput. Chem., 8, 2012, 53; J. Phys. Chem. A, 118, 2014, 9182] are re-investigated. We show that in the basis-set limit, supermolecular Kohn-Sham-DFT (KS-DFT) densities can exactly be represented as a sum of subsystem densities, even if the subsystem orbitals are not externally orthogonal. This is illustrated using both an analytical example and in basis-set free numerical calculations for an atomic test case. We further show that even with finite basis sets, SDFT calculations using accurate reconstructed potentials can closely approach the supermolecular KS-DFT density, and that the deviations between SDFT and KS-DFT decrease as the basis-set limit is approached. Our results demonstrate that formally, there is no need to enforce external orthogonality in SDFT, even though this might be a useful strategy when developing projection-based DFT embedding schemes.