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.

Nucleoside Phosphorylases make N7-xanthosine.

Modern, highly evolved nucleoside-processing enzymes are known to exhibit perfect regioselectivity over the glycosylation of purine nucleobases at N9. We herein report an exception to this paradigm. Wild-type nucleoside phosphorylases also furnish N7-xanthosine, a "non-native" ribosylation regioisomer of xanthosine. This unusual nucleoside possesses several atypical physicochemical properties such as redshifted absorption spectra, a high equilibrium constant of phosphorolysis and low acidity. Ultimately, the biosynthesis of this previously unknown natural product illustrates how even highly evolved, essential enzymes from primary metabolism are imperfect catalysts.

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.

Structural Dependence of Extended Amide III Vibrations in Two-Dimensional Infrared Spectra.

Two-dimensional infrared (2D-IR) spectroscopy is a powerful experimental method for probing the structure and dynamics of proteins in aqueous solution. So far, most experimental studies have focused on the amide I vibrations, for which empirical vibrational exciton models provide a means of interpreting such experiments. However, such models are largely lacking for other regions of the vibrational spectrum. To close this gap, we employ an efficient quantum-chemical methodology for the calculation of 2D-IR spectra, which is based on anharmonic theoretical vibrational spectroscopy with localized modes. We apply this approach to explore the potential of 2D-IR spectroscopy in the extended amide III region. Using calculations for a dipeptide model as well as alanine polypeptides, we show that distinct 2D-IR cross-peaks in the extended amide III region can potentially be used to distinguish α-helix and ß-strand structures. We propose that the extended amide III region could be a promising target for future 2D-IR experiments.

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.

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.

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.

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.

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.

Systematic QM Region Construction in QM/MM Calculations Based on Uncertainty Quantification.

While QM/MM studies of enzymatic reactions are widely used in computational chemistry, the results of such studies are subject to numerous sources of uncertainty, and the effect of different choices by the simulation scientist that are required when setting up QM/MM calculations is often unclear. In particular, the selection of the QM region is crucial for obtaining accurate and reliable results. Simply including amino acids by their distance to the active site is mostly not sufficient as necessary residues are missing or unimportant residues are included without evidence. Here, we take a first step toward quantifying uncertainties in QM/MM calculations by assessing the sensitivity of QM/MM reaction energies with respect to variations of the MM point charges. We show that such a point charge variation analysis (PCVA) can be employed to judge the accuracy of QM/MM reaction energies obtained with a selected QM region and devise a protocol to systematically construct QM regions that minimize this uncertainty. We apply such a PCVA to the example of catechol O-methyltransferase and demonstrate that it provides a simple and reliable approach for the construction of the QM region. Our PCVA-based scheme is computationally efficient and requires only calculations for a system with a minimal QM region. Our work highlights the promise of applying methods of uncertainty quantification in computational chemistry.

Density-Based Many-Body Expansion as an Efficient and Accurate Quantum-Chemical Fragmentation Method: Application to Water Clusters.

Fragmentation methods based on the many-body expansion offer an attractive approach for the quantum-chemical treatment of large molecular systems, such as molecular clusters and crystals. Conventionally, the many-body expansion is performed for the total energy, but such an energy-based many-body expansion often suffers from a slow convergence with respect to the expansion order. For systems that show strong polarization effects such as water clusters, this can render the energy-based many-body expansion infeasible. Here, we establish a density-based many-body expansion as a promising alternative approach. By performing the many-body expansion for the electron density instead of the total energy and inserting the resulting total electron density into the total energy functional of density functional theory, one can derive a density-based energy correction, which in principle accounts for all higher-order polarization effects. Here, we systematically assess the accuracy of such a density-based many-body expansion for test sets of water clusters. We show that already a density-based two-body expansion is able to reproduce interaction energies per fragment within chemical accuracy and is able to accurately predict the energetic ordering as well as the relative interaction energies of different isomers of water clusters.

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.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms.

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naïve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naïve approach.

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.

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.

Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions.

Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem, and in the limit of the weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear-response TDDFT. The method is found to give stable numerical results also in the presence of a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.

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.