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.

Crosstalk between glucocorticoid and mineralocorticoid receptors boosts glucocorticoid-induced killing of multiple myeloma cells.

The glucocorticoid receptor (GR) is a crucial drug target in multiple myeloma as its activation with glucocorticoids effectively triggers myeloma cell death. However, as high-dose glucocorticoids are also associated with deleterious side effects, novel approaches are urgently needed to improve GR action in myeloma. Here, we reveal a functional crosstalk between GR and the mineralocorticoid receptor (MR) that plays a role in improved myeloma cell killing. We show that the GR agonist dexamethasone (Dex) downregulates MR levels in a GR-dependent way in myeloma cells. Co-treatment of Dex with the MR antagonist spironolactone (Spi) enhances Dex-induced cell killing in primary, newly diagnosed GC-sensitive myeloma cells. In a relapsed GC-resistant setting, Spi alone induces distinct myeloma cell killing. On a mechanistic level, we find that a GR-MR crosstalk likely arises from an endogenous interaction between GR and MR in myeloma cells. Quantitative dimerization assays show that Spi reduces Dex-induced GR-MR heterodimerization and completely abolishes Dex-induced MR-MR homodimerization, while leaving GR-GR homodimerization intact. Unbiased transcriptomics analyses reveal that c-myc and many of its target genes are downregulated most by combined Dex-Spi treatment. Proteomics analyses further identify that several metabolic hallmarks are modulated most by this combination treatment. Finally, we identified a subset of Dex-Spi downregulated genes and proteins that may predict prognosis in the CoMMpass myeloma patient cohort. Our study demonstrates that GR-MR crosstalk is therapeutically relevant in myeloma as it provides novel strategies for glucocorticoid-based dose-reduction.

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.

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.

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.

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.

Interpreting the behavior of the NICSzz by resolving in orbitals, sign, and positions.

The zz component of the nucleus independent chemical shift or the NICSzz is commonly used as a quantifier of the (anti)aromatic character of a (sub)system. One of the underlying assumptions is that a position can be found where the "aromatic" ring currents are adequately reflected in the corresponding NICSzz value. However, as the NICSzz is the result of an integration over the entire space, it no longer explicitly contains the information needed to quantify the separate contributions arising from underlying current density patterns. In this study, we will show that these contributions can be revealed by resolving the NICSzz into orbitals, sign, and positions. Our analysis of benzene in terms of these resolutions shows that the same underlying current density can lead to highly complex shielding patterns that vary greatly depending on the position of the NICSzz-probe. As such, our results indicate that any analysis solely based on NICSzz-values can lead to results that are difficult to interpret, even if the system under study is considered to be well-known. © 2017 Wiley Periodicals, Inc.

Can the current density map topology be extracted from the nucleus independent chemical shifts?

Aromatic compounds are characterised by the presence of a ring current when in a magnetic field. As a consequence, current density maps are used to assess (the degree of) aromaticity of a compound. However, often a more discrete set of so-called Nucleus Independent Chemical Shift (NICS) values is used that is derived from the current density. It is shown here that there is no simple one-to-one relationship that allows reconstructing current density maps from only NICS-values. NICS values should therefore not be used as aromaticity indices without analysis of the ab initio computed current density map.

Performance of DFT Methods in Momentum Space: Quantum Similarity Measures versus Moments of Momentum.

The quality of momentum space electron densities obtained from a large array of density functionals is investigated through careful numerical comparison with the density obtained using reference CCSD calculations. Using a test set of 68 closed-shell molecules in their ground state and 77 different computational methods, including coupled cluster, MP2 perturbation theory, Hartree-Fock, and a total of 74 DFT functionals, including long-range corrected functionals, we confirm that DFT momentum densities generally show poorer agreement with the reference than MP2 densities. The performance of DFT functionals varies significantly with only 8 DFT functionals outperforming Hartree-Fock with respect to electron momentum densities and their spherically averaged counterparts.

Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods.

The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.