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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes.

Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way that clarifies the enormous freedom one has within the information-theoretic ansatz.

Method for making 2-electron response reduced density matrices approximately N-representable.

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.

Direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions: The influence of three-index N-representability conditions.

This work proposes the variational determination of two-electron reduced density matrices corresponding to the ground state of N-electron systems within the doubly occupied-configuration-interaction methodology. The P, Q, and G two-index N-representability conditions have been extended to the T1 and T2 (T2') three-index ones and the resulting optimization problem has been addressed using a standard semidefinite program. We report results obtained from the doubly occupied-configuration-interaction method, from the two-index constraint variational procedure and from the two- and three-index constraint variational treatment. The discussion of these results along with a study of the computational cost demanded shows the usefulness of our proposal.

Model-averaging of ab initio spectra for the absolute configuration assignment via vibrational circular dichroism.

Vibrational absorption and vibrational circular dichroism spectra (VA and VCD) have been recorded for two hybrid isoindolinone-phtalide stereoisomers dissolved in CDCl3. Density-functional calculations have been performed to determine their absolute configuration. A comparison of calculated and measured values has been made using several goodness-of-fit indicators, and also introducing a model-averaging technique, taking into account the variation of calculated spectra with the details of the computational method. The model-averaging technique, preliminarily tested on two VCD spectra already assigned to two diastereomers of tadalafil, gives higher credibility to the ab initio calculations, and should be useful for other molecules with high flexibility and/or more than one stereogenic center.

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach.

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.

Exploring the role of the 3-center-4-electron bond in hypervalent λ(3)-iodanes using the methodology of domain averaged Fermi holes.

Hypervalent iodine compounds, in particular λ(3)-iodanes, have become important reagents in organic synthesis for the electrophilic transfer of substituents to arenes and other nucleophiles. The structure and reactivity of these compounds are usually described based on a 3-center-4-electron bond model, involving the iodine central atom and its two trans substituents. The goal of this computational study is to explore Fermi correlation in view of a more advanced description of bonding in these compounds. For that matter, we apply the analysis of Domain Averaged Fermi Holes (DAFH). The DAFH analysis reveals a relationship between the occurrence of multicenter bonding and structural parameters which cannot be easily observed based on simple MO theory. Whereas for λ(3)-iodanes carrying electron-rich ligands pairing of electrons over three centers is indeed observed, compounds with electron-withdrawing substituents fall into a different category: the pairing of electrons is restricted to extend over two centers only, thus challenging the multicenter bonding picture in this case. Accordingly, a drastic reduction of the DAFH three center bond index is observed. The establishment of the multicenter bond in λ(3)-iodanes is driven by a pseudo Jahn-Teller (PJT) effect, whose extent is tightly coupled to the reactivity of the corresponding compound. The PJT stabilization scales with the degree of s-p hybridization of the central atom, which, in return, depends on the electron-withdrawing power of the ligands in the trans position. The response of the multicenter bond to the iodine "ligand field" can be expressed quantitatively in terms of DAFH bond indices. These show, for example, that the activation of the reacting hypervalent species by means of protonation results in a weaker 3-center-4-electron bond, thus making the reagent more reactive. In this work we explain a number of experimentally known facts concerning the reactivity of these compounds. We also show that the DAFH analysis offers a more complete understanding of hypervalency in λ(3)-iodanes, and that it is a tool to assist the search for novel reagents.