Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix.

As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.

Impact of conformation and intramolecular interactions on vibrational circular dichroism spectra identified with machine learning.

Vibrational Circular Dichroism (VCD) spectra often differ strongly from one conformer to another, even within the same absolute configuration of a molecule. Simulated molecular VCD spectra typically require expensive quantum chemical calculations for all conformers to generate a Boltzmann averaged total spectrum. This paper reports whether machine learning (ML) can partly replace these quantum chemical calculations by capturing the intricate connection between a conformer geometry and its VCD spectrum. Three hypotheses concerning the added value of ML are tested. First, it is shown that for a single stereoisomer, ML can predict the VCD spectrum of a conformer from solely the conformer geometry. Second, it is found that the ML approach results in important time savings. Third, the ML model produced is unfortunately hardly transferable from one stereoisomer to another.

Uncovering phase transitions that underpin the flat-planes in the tilted Hubbard model using subsystems and entanglement measures.

The failure of many approximate electronic structure methods can be traced to their erroneous description of fractional charge and spin redistributions in the asymptotic limit toward infinity, where violations of the flat-plane conditions lead to delocalization and static correlation errors. Although the energetic consequences of the flat-planes are known, the underlying quantum phase transitions that occur when (spin)charge is redistributed have not been characterized. In this study, we use open subsystems to redistribute (spin)charges in the tilted Hubbard model by imposing suitable Lagrange constraints on the Hamiltonian. We computationally recover the flat-plane conditions and quantify the underlying quantum phase transitions using quantum entanglement measures. The resulting entanglement patterns quantify the phase transition that gives rise to the flat-plane conditions and quantify the complexity required to accurately describe charge redistributions in strongly correlated systems. Our study indicates that entanglement patterns can uncover those phase transitions that have to be modeled accurately if the delocalization and static correlation errors of approximate methods are to be reduced.

Analyzing the Behavior of Spin Phases in External Magnetic Fields by Means of Spin-Constrained States.

During molecular dissociation in the presence of an external uniform magnetic field, electrons flip their spin antiparallel to the magnetic field because of the stabilizing influence of the spin Zeeman operator. Although generalized Hartree-Fock descriptions furnish the optimal mean-field energetic description of such bond-breaking processes, they are allowed to break Sz symmetry, leading to intricate and unexpected spin phases and phase transitions. In this work, we show that the behavior of these molecular spin phases can be interpreted in terms of spin phase diagrams constructed by constraining states to target expectation values of projected spin. The underlying constrained states offer a complete electronic characterization of the spin phases and spin phase transitions, as they can be analyzed using standard quantum chemical tools. Because the constrained states effectively span the entire phase space, they could provide an excellent starting point for post-Hartree-Fock methods aimed at gaining more electron correlation or regaining spin symmetry.

Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?

Several fully π-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules, an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel's 4n + 2 rule for each macrocyclic path, yet their π-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic π-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial π-electron delocalization, they cannot be classified as true 3D-aromatics.

Constrained iterative Hirshfeld charges: A variational approach.

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.

Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field.

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.

Uncovering Clar's aromatic π -sextet rule in the Hubbard model using Maximum Probability Domain Partitions.

Clar's aromatic π -sextet rule is a widely used qualitative method for assessing the electronic structure of polycyclic benzenoid hydrocarbons. Unfortunately, many of the quantum chemical concordances for this rule have a limited range of applicability. Here, we show that the fundamental probabilities associated with a distribution of electrons over domain partitions support Clar's rule in both mean-field and static correlation regimes. In particular, domain partitions that maximize those probabilities reflect the dominance of Clar structures in the electronic structure of these molecules. These findings suggest that extending methods that aim to maximize probabilities by deforming domain partitions could lead to novel quantum chemical underpinnings for many chemical concepts.

Quantifying Delocalization and Static Correlation Errors by Imposing (Spin)Population Redistributions through Constraints on Atomic Domains.

The failure of many density functional approximations can be traced to their behavior under fractional (spin)population redistributions in the asymptotic limit toward infinite bonding distances, which should obey the flat-plane conditions. However, such errors can only be characterized sufficiently in terms of those redistributions if exact energies are available for many possible (spin)population redistributions at different bonding distances. In this study, we propose to model such redistributions by imposing (spin)populations on atomic domains by constraining full configuration interaction wave functions. The resulting N-representable descriptions of small hydrogen chains at different bonding distances allow us to computationally illustrate the effects of the flat-plane conditions in the limit to infinite bond distances, leading to more chemical insight into those flat-plane conditions. As the proposed methodology is able to capture the effects of the flat plane conditions, it could be used to generate the reference data that is required to measure the extent to which approximate methods violate the requirements of the exact functional, leading to a quantification of the delocalization and static correlation error of such methods.

Exploring machine learning methods for absolute configuration determination with vibrational circular dichroism.

The added value of supervised Machine Learning (ML) methods to determine the Absolute Configuration (AC) of compounds from their Vibrational Circular Dichroism (VCD) spectra was explored. Among all ML methods considered, Random Forest (RF) and Feedforward Neural Network (FNN) yield the best performance for identification of the AC. At its best, FNN allows near-perfect AC determination, with accuracy of prediction up to 0.995, while RF combines good predictive accuracy (up to 0.940) with the ability to identify the spectral areas important for the identification of the AC. No loss in performance of either model is observed as long as the spectral sampling interval used does not exceed the spectral bandwidth. Increasing the sampling interval proves to be the best method to lower the dimensionality of the input data, thereby decreasing the computational cost associated with the training of the models.

GQCP: The Ghent Quantum Chemistry Package.

The Ghent Quantum Chemistry Package (GQCP) is an open-source electronic structure software package that aims to provide an intuitive and expressive software framework for electronic structure software development. Its high-level interfaces (accessible through C++ and Python) have been specifically designed to correspond to theoretical concepts, while retaining access to lower-level intermediates and allowing structural run-time modifications of quantum chemical solvers. GQCP focuses on providing quantum chemical method developers with the computational "building blocks" that allow them to flexibly develop proof of principle implementations for new methods and applications up to the level of two-component spinor bases.

CFA-18: a homochiral metal-organic framework (MOF) constructed from rigid enantiopure bistriazolate linker molecules.

In this work, we introduce the first enantiopure bistriazolate-based metal-organic framework, CFA-18 (Coordination Framework Augsburg-18), built from the R-enantiomer of 7,7,7',7'-tetramethyl-6,6',7,7'-tetrahydro-3H,3'H-5,5'-spirobi[indeno[5,6-d]-[1,2,3]triazole] (H2-spirta). The enantiopurity and absolute configuration of the new linker were confirmed by several chiroselective methods. Reacting H2-spirta in hot N,N-dimethylformamide (DMF) with manganese(ii) chloride gave CFA-18 as colorless crystals. The crystal structure with the composition [Mn2Cl2(spirta)(DMF)2] was solved using synchrotron single-crystal X-ray diffraction. CFA-18 shows a framework topology that is closely related to previously reported metal-azolate framework (MAF) structures in which the octahedrally coordinated manganese(ii) ions are triazolate moieties, and the chloride anions form crosslinked one-dimensional helical chains, giving rise to hexagonal channels. In contrast to MAFs crystallizing in the centrosymmetric space group R3[combining macron], the handedness of the helices found in CFA-18 is strictly uniform, leading to a homochiral framework that crystallizes in the trigonal crystal system within the chiral space group P3121 (no. 152).

Richardson-Gaudin mean-field for strong correlation in quantum chemistry.

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly correlated electrons.

A combined Raman optical activity and vibrational circular dichroism study on artemisinin-type products.

Artemisinin and two of its derivatives, dihydroartemisinin and artesunate, which are front line drugs against malaria, were investigated using Raman optical activity (ROA) and vibrational circular dichroism (VCD) experiments, both supported by density functional theory (DFT) level calculations. The experimental techniques combined with DFT calculations could show that dihydroartemisinin was present as an epimeric mixture in solution. In addition, an approximation of the epimeric ratio could be extracted which was in agreement with the ratio obtained by 1H-NMR spectroscopy. The current study also demonstrates that both ROA and VCD are able to assign the correct absolute configuration (AC) of artemisinin and artesunate out of all their possible diastereomers without any explicit knowledge on their correct stereochemistry and accentuates the synergetic effect between ROA and VCD in AC determination.

Comparative Study of the Vibrational Optical Activity Techniques in Structure Elucidation: The Case of Galantamine.

The absolute configuration of the alkaloid galantamine was studied using a range of solution-state techniques; nuclear magnetic resonance (NMR), vibrational circular dichroism (VCD), and Raman optical activity (ROA). While the combined use of NMR and VCD does provide a fast, high-resolution methodology for determining the absolute configuration of galantamine, both techniques were needed in concert to achieve this goal. ROA, on the other hand, proved to be sensitive enough to assign the full absolute configuration without relying on other techniques. In both cases, statistical validation was applied to aid the determination of absolute configuration. In the case of galantamine, ROA combined with statistical validation is shown to be a powerful stand-alone tool for absolute configuration determination.

The effect of protein backbone hydration on the amide vibrations in Raman and Raman optical activity spectra.

Raman and specifically Raman optical activity (ROA) spectroscopy are very sensitive to the solution structure and conformation of biomolecules. Because of this strong conformational sensitivity, density functional theory (DFT) calculations are often used to get a better understanding of the experimentally observed spectral patterns. While e.g. for carbohydrate structure the water molecules that surround the solute have been demonstrated to be of vital importance to get accurate modelled ROA spectra, the effect of explicit water molecules on the calculated ROA patterns of peptides and proteins is less well studied. Here, the effect of protein backbone hydration was studied using DFT calculations of HCO-(l-Ala)5-NH2 in specific secondary structure conformations with different treatments of the solvation. The effect of the explicit water molecules on the calculated spectra mainly arises from the formation of hydrogen bonds with the amide C[double bond, length as m-dash]O and N-H groups. Hydrogen bonding of water with the C[double bond, length as m-dash]O group determines the shape and position of the amide I band. The C[double bond, length as m-dash]O bond length increases upon formation of C[double bond, length as m-dash]OH2O hydrogen bonds. The effect of the explicit water molecules on the amide III vibrations arises from hydrogen bonding of the solvent with both the C[double bond, length as m-dash]O and N-H group, but their contributions to this spectral region differ: geometrically, the formation of a C[double bond, length as m-dash]OH2O bond decreases the C-N bond length, while upon forming a N-HH2O hydrogen bond, the N-H bond length increases.

Quantifying the conceptual problems associated with the isotropic NICS through analyses of its underlying density.

The isotropic Nucleus Independent Chemical Shift (NICSiso) is widely considered to be a suitable descriptor for aromaticity based on the correlations it exhibits with other aromaticity descriptors. To gain more insight into the origin of these correlations, we establish causal relations between the NICSiso and the underlying current density patterns by resolving the NICSiso into its underlying density. Our results indicate that the origin of the behavior of the NICSiso can be radically different from what is generally assumed. Not only does this bring into question the robustness of applying the NICSiso beyond the realms of where good correlations with other measures of aromaticity have been established, it also points to an inherent weakness in all interpretations of NICSiso values that are not based on additional data.

Absolute configuration and biological profile of pyrazoline enantiomers as MAO inhibitory activity.

A new racemic pyrazoline derivative was synthesized and resolved to its enantiomers using analytic and semipreparative high-pressure liquid chromatography. The absolute configuration of both fractions was established using vibrational circular dichroism. The in vitro monoamine oxidase (MAO) inhibitory profiles were evaluated for the racemate and both enantiomers separately for the two isoforms of the enzyme. The racemic compound and both enantiomers were found to inhibit hMAO-A selectively and competitively. In particular, the R enantiomer was detected as an exceptionally potent and a selective MAO-A inhibitor (Ki  = 0.85 × 10-3  ± 0.05 × 10-3  µM and SI: 2.35 × 10-5 ), whereas S was determined as poorer compound than R in terms of Ki and SI (0.184 ± 0.007 and 0.001). The selectivity of the enantiomers was explained by molecular modeling docking studies based on the PDB enzymatic models of MAO isoforms.

The influence of correlation on (de)localization indices from a valence bond perspective.

When going beyond the Hartree-Fock level to correlated methods, one observes a significant reduction in the delocalization index. This is commonly interpreted as a weakening of electron sharing due to electron correlation, although this is rather counter-intuitive to the concomitant energy lowering. In this study, we use an analytical valence bond model and full CI calculations to show that this reduction in the delocalization index actually goes hand in hand with increased covalent contributions at the expense of ionic contributions. This suggests that we should be careful in formulating interpretations of these results in (de)localization indices. Graphical Abstract Variation of the localization Δ(ΩA, ΩA) and delocalization index Δ(ΩA, ΩB) as a function of the parameter ω. By adjusting this parameter ω from [Formula: see text] to 0, we can gradually change the underlying wave function from a Hartree-Fock to a Heitler-London description.

Covalency and Ionicity Do Not Oppose Each Other-Relationship Between Si-O Bond Character and Basicity of Siloxanes.

Covalency and ionicity are orthogonal rather than antipodal concepts. We demonstrate for the case of siloxane systems [R3 Si-(O-SiR2 )n -O-SiR3 ] that both covalency and ionicity of the Si-O bonds impact on the basicity of the Si-O-Si linkage. The relationship between the siloxane basicity and the Si-O bond character has been under debate since previous studies have presented conflicting explanations. It has been shown with natural bond orbital methods that increased hyperconjugative interactions of LP(O)→σ*(Si-R) type, that is, increased orbital overlap and hence covalency, are responsible for the low siloxane basicity at large Si-O-Si angles. On the other hand, increased ionicity towards larger Si-O-Si angles has been revealed with real-space bonding indicators. To resolve this ostensible contradiction, we perform a complementary bonding analysis, which combines orbital-space, real-space, and bond-index considerations. We analyze the isolated disiloxane molecule H3 SiOSiH3 with varying Si-O-Si angles, and n-membered cyclic siloxane systems Si2 H4 O(CH2 )n-3 . All methods from quite different realms show that both covalent and ionic interactions increase simultaneously towards larger Si-O-Si angles. In addition, we present highly accurate absolute hydrogen-bond interaction energies of the investigated siloxane molecules with water and silanol as donors. It is found that intermolecular hydrogen bonding is significant at small Si-O-Si angles and weakens as the Si-O-Si angle increases until no stable hydrogen-bond complexes are obtained beyond φSiOSi =168°, angles typically displayed by minerals or polymers. The maximum hydrogen-bond interaction energy, which is obtained at an angle of 105°, is 11.05 kJ mol-1 for the siloxane-water complex and 18.40 kJ mol-1 for the siloxane-silanol complex.