Is there a generalized anomeric effect? Analyses from energy components and information-theoretic quantities from density functional reactivity theory

Some Recent Advances in Density-Based Reactivity Theory

Establishing a chemical reactivity theory in density functional theory (DFT) language has been our intense research interest in the past two decades, exemplified by the determination of steric effect and stereoselectivity, evaluation of electrophilicity and nucleophilicity, identification of strong and weak interactions, and formulation of cooperativity, frustration, and principle of chirality hierarchy. In this Featured Article, we first overview the four density-based frameworks in DFT to appreciate chemical understanding, including conceptual DFT, use of density associated quantities, information-theoretic approach, and orbital-free DFT, and then present a few recent advances of these frameworks as well as new applications from our studies. To that end, we will introduce the relationship among these frameworks, determining the entire spectrum of interactions with Pauli energy derivatives, performing topological analyses with information-theoretic quantities, and extending the density-based frameworks to excited states. Applications to examine physiochemical properties in external electric fields and to evaluate polarizability for proteins and crystals are discussed. A few possible directions for future development are followed, with the special emphasis on its merger with machine learning.

Simple, Efficient, and Universal Energy Decomposition Analysis Method Based on Dispersion-Corrected Density Functional Theory

Energy decomposition analysis (EDA) is an important class of methods to explore the nature of interaction between fragments in a chemical system. It can decompose the interaction energy into different physical components to understand the factors that play key roles in the interaction. This work proposes an EDA strategy based on dispersion-corrected density functional theory (DFT), called sobEDA. This method is fairly easy to implement and very universal. It can be used to study weak interactions, chemical bond interactions, open-shell systems, and interactions between multiple fragments. The total time consumption of sobEDA is only about twice that of conventional DFT single-point calculation for the entire system. This work also proposes a variant of the sobEDA method named sobEDAw, which is designed specifically for decomposing weak interaction energies. Through a proper combination of DFT correlation energy and dispersion correction term, sobEDAw gives a ratio between dispersion energy and electrostatic energy that is highly consistent with the symmetry-adapted perturbation theory, which is quite popular and robust in studying weak interactions but expensive. We present a shell script sobEDA.sh to implement the methods proposed in this work based on the very popular Gaussian quantum chemistry program and Multiwfn wavefunction analysis code. Via the script, theoretical chemists can use the sobEDA and sobEDAw methods very conveniently in their study. Through a series of examples, the rationality of the new methods and their implementation are verified, and their great practical values in the study of various chemical systems are demonstrated.

Impacts of external fields on aromaticity and acidity of benzoic acid: a density functional theory, conceptual density functional theory and information-theoretic approach study

The impact of external fields on the molecular structure and reactivity properties has been of considerable interest in the recent literature. Benzoic acid as one of the most widely used compounds in medicinal and materials sciences is known for its dual propensity in aromaticity and acidity. In this work, we systematically investigate the impact of a uniform external electric field on these properties. We apply density functional theory, conceptual density functional theory, and an information-theoretic approach to appreciate the change pattern of aromaticity and acidity properties in external fields with different strengths. Our results show that they possess different change patterns under external fields, which can be satisfactorily rationalized by variations in reactivity descriptors and partial charges. The surprising yet novel results from this study should enrich the body of our knowledge about the impact of external fields for different kinds of electronic properties and provide guidance and foundation for future studies of this phenomenon in other molecular systems.

Explaining the High Catalytic Activity in Bis(indenyl)methyl Zirconium Cation Using Combined EDA-NOCV/QTAIM Approach

The main purpose of this study is to elucidate some discrepancies already observed in the catalytic activity values of some zirconocene methyl cations. The EDA-NOCV scheme was employed for a theoretical description of the interactions between an ethylene molecule and five catalysts of zirconocene methyl cation. The nature of the chemical interactions has been elucidated through the QTAIM topological analysis. The steric hindrance due to the ligands was evaluated qualitatively by means of an IRI-based analysis and quantitively through Fisher information. The findings prove that the indenyl ligand seems to favor the orbital interaction between the ethylene molecule and the metal centre of zirconocene methyl cation. Both electrostatic and orbital contributions play a crucial role in stabilising the studied complexes. Based on the NOCV deformation density contributions, the strongest orbital interaction is reached with the bis(indenyl)methyl zirconium cation, which is the only one exhibiting covalent interactions. Especially, the strong contribution of π-back donation (occurring from the occupied orbitals of the zirconium atom to the π* anti-bonding orbital of ethylene) may be a key to understand why this catalyst has a higher polymerisation yield than the other studied catalysts. This work suggests a perspective for predicting values of catalytic activity when theoretically designing novel catalysts of zirconocene type.

Revisiting the trapping of noble gases (He-Kr) by the triatomic H3+ and Li3+ species: a density functional reactivity theory study

Small atomic clusters with exotic stability, bonding, aromaticity, and reactivity properties can be made use of for various purposes. In this work, we revisit the trapping of noble gas atoms (He-Kr) by the triatomic H₃⁺ and Li₃⁺ species by using some analytical tools from density functional theory, conceptual density functional theory, and the information-theoretic approach. Our results showcase that though similar in geometry, H₃⁺ and Li₃⁺ exhibit markedly different behavior in bonding, aromaticity, and reactivity properties after the addition of noble gas atoms. Moreover, the exchange-correlation interaction and steric effect are key energy components in stabilizing the clusters. This study also finds that the origin of the molecular stability of these species is due to the spatial delocalization of the electron density distribution. Our work provides an additional arsenal towards a better understanding of small atomic clusters capturing noble gases.

Principle of Chirality Hierarchy in Three-Blade Propeller Systems

There are different kinds of molecular chirality, such as zero-dimensional point chirality, one-dimensional axial chirality, 2D planar chirality, and 3D chirality. When they coexist in one system, such as in helical structures of proteins and DNA, they form a chirality hierarchy. Earlier, we showed that the chirality propensity of a lower level in a hierarchy is dictated by that of a higher level and henceforth proposed the Principle of Chirality Hierarchy. In this work, we confirm the validity of this principle in the three-blade propeller molecular system. Our results show that the preference of the 0D chirality of a functional group in the propeller system is determined by the 1D chirality, and homochirality is also a remarkable feature for this system. The establishment and confirmation of the Principle of Chirality Hierarchy from this work should find important applications in asymmetric synthesis, macromolecular assembly, and many others.

Quantifications and Applications of Relative Fisher Information in Density Functional Theory

Though density functional theory is widely accepted as one of the most successful developments in theoretical chemistry in the past few decades, the knowledge of how to apply this new electronic structure theory, to help us better understand chemical processes and transformations, is still an unaccomplished task. The information-theoretic approach is emerging as a viable option for that purpose in the recent literature, providing new insights about steric effect, cooperativity, electrophilicity, nucleophilicity, stereoselectivity, homochirality, etc. In this work, based on the result from a recent paper by one of us [ J. Chem. Phys, 2019, 151, 141103], we present two quantifications of the relative Fisher information and discuss their physiochemical properties and possible applications. To that end, their analytical properties have been elucidated. They have also been applied to six categories of systems to illustrate their applicability. A better descriptor to quantify the single bond rotation barrier has been obtained. The relative Fisher information can also simultaneously determine electrophilicity and nucleophilicity, and effectively describe helical structures with different homochiral and heterochiral propensities. As integral parts of the information-theoretic approach, these newly introduced quantities will provide us with more analytical tools toward the long-term goal of crafting a chemical reactivity theory in the density-based language.

Density Functional Theory and Information-Theoretic Approach Study on the Origin of Homochirality in Helical Structures

Homochirality of macromolecules such as proteins and DNA is one of the most striking features in nature; yet, there is still no convincing theory to explain its origin. In a recent work by one of the present authors (J. Phys. Chem. Lett. 2020, 11, 8690-8696), a general proposal from the viewpoint of thermodynamics has been put forward. It proposes that it is the handedness of helices ubiquitous in biological macromolecules that plays the decisive role. It also unveiled that there exist strong cooperativity effects dominated by favorable electrostatic interactions in the homochiral conformer. In this work, making use of analytical tools, we recently developed a density functional theory and an information-theoretic approach and through four sets of helical structures we designed for the present study, we examine these systems to provide new insights about these properties. We found that the 3₁₀-helix and the α-helix are markedly different in cooperativity from the viewpoint of both the total energy and its three components. The electrostatic dominance of homochiral species is manifested by both the electron charge distribution and information gain. At the atomic level, different elements behave significantly differently because they play different roles in the systems. Our results from this work validate that these analytical tools can be applied to homochiral systems, which can be further extended to others with potential interest in asymmetric synthesis and macromolecular assembly where the Principle of Homochirality Hierarchy comes into play.

Homochirality Originates from the Handedness of Helices

Homochirality is a common feature of amino acids and carbohydrates, and its origin is still unknown. Meanwhile, right-handed helices are ubiquitous in nature. Are these two phenomena intrinsically correlated? Here, we propose that homochirality of amino acids and nucleotide sugars originated from the handedness of helices. We show that right-handed 3₁₀-helix and α-helix favor the l-chiral form for amino acids, but for deoxyribose sugars, right-handed helices prefer the d-chiral form instead. Our analyses unveil strong cooperativity effects dominated by electrostatic interactions. This work not only resolves the mystery of homochirality by providing a unified explanation for the origin of homochirality in proteins and DNA using helical secondary structures as the root cause but also ratifies the Principle of Chirality Hierarchy, in which the chirality of a higher hierarchy dictates that of lower ones. Possible applications of this work to asymmetric synthesis and macromolecular assembly are discussed.

On Silylated Oxonium and Sulfonium Ions and Their Interaction with Weakly Coordinating Borate Anions

Attempts have been made to prepare salts with the labile tris(trimethylsilyl)chalconium ions, [(Me3 Si)3 E]+ (E=O, S), by reacting [Me3 Si-H-SiMe3 ][B(C6 F5 )4 ] and Me3 Si[CB] (CB- =carborate=[CHB11 H5 Cl6 ]- , [CHB11 Cl11 ]- ) with Me3 Si-E-SiMe3 . In the reaction of Me3 Si-O-SiMe3 with [Me3 Si-H-SiMe3 ][B(C6 F5 )4 ], a ligand exchange was observed in the [Me3 Si-H-SiMe3 ]+ cation leading to the surprising formation of the persilylated [(Me3 Si)2 (Me2 (H)Si)O]+ oxonium ion in a formal [Me2 (H)Si]+ instead of the desired [Me3 Si]+ transfer reaction. In contrast, the expected homoleptic persilylated [(Me3 Si)3 S]+ ion was formed and isolated as [B(C6 F5 )4 ]- and [CB]- salt, when Me3 Si-S-SiMe3 was treated with either [Me3 Si-H-SiMe3 ][B(C6 F5 )4 ] or Me3 Si[CB]. However, the addition of Me3 Si[CB] to Me3 Si-O-SiMe3 unexpectedly led to the release of Me4 Si with simultaneous formation of a cyclic dioxonium dication of the type [Me3 Si-μO-SiMe2 ]2 [CB]2 in an anion-mediated reaction. DFT studies on structure, bonding and thermodynamics of the [(Me3 Si)3 E]+ and [(Me3 Si)2 (Me2 (H)Si)E]+ ion formation are presented as well as mechanistic investigations on the template-driven transformation of the [(Me3 Si)3 E]+ ion into a cyclic dichalconium dication [Me3 Si-μE-SiMe2 ]2 2+ .

Identity for Kullback-Leibler divergence in density functional reactivity theory

Density functional reactivity theory (DFRT) makes use of simple electron density functionals to appreciate chemical reactivity. The Kullback-Leibler divergence, also called information gain or relative Shannon entropy, as a key component of the DFRT framework has entertained a few fascinating applications in the recent literature. For instance, it was employed to rationalize the Hirshfeld stockholder partition of atoms in molecules. It has also been applied to both determine regioselectivity and simultaneously quantify molecular electrophilicity and nucleophilicity, the capability of atoms in molecules to accept and donate electrons. In this work, we examine the local behavior of the Kullback-Leibler divergence and present a novel identity for it. The validity of the identity is subsequently verified by the numerical results of neutral atoms from He to Kr with different choices of the reference density. Analytical properties and local behaviors of the three new functions introduced in the identity are discussed. These new local functions, together with the identity unveiled in this work, should provide new perspectives for us to further develop the DFRT framework with added insights about the local behavior of molecular physiochemical properties.

SCI: a robust and reliable density-based descriptor to determine multiple covalent bond orders

Very recently [J. Phys. Chem. A 2018, 122 (11), 3087-3095], we proposed to employ the Pauli energy to identify and determine strong covalent interactions (SCI), whose bond order are equal to or larger than two. This is done through the signature isosurface shape between the two bonding atoms. We discovered that the signature shape for a double, triple, and quadruple covalent bond is like a dumbbell, donut (torus), and four-beats, respectively. Systems with even higher bond orders were examined and confirmed. This work is a follow-up study of our previous work. The dependence of the signature isosurface shape on the choice of methodologies and basis sets is systematically investigated. Its effectiveness and robustness in determining bond orders are highlighted again with more examples. In addition, using the molybdenum dimer in different environments, e.g., in vacuum, sandwiched between molecules, and encapsulated in the C₈₀ cage, as illustrative examples, we show that, generally speaking, bond strength and bond order are two different chemical concepts. For systems containing transition metals, it is not always true that a short metal-metal bond length corresponds to a larger bond order. Put together, these results should provide additional pieces of convincing evidence showing that the SCI index is a robust and reliable density-based descriptor to accurately determine multiple covalent bond orders.