Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study

In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.

Geminal-Based Strategies for Modeling Large Building Blocks of Organic Electronic Materials

We elaborate on unconventional electronic structure methods based on geminals and their potential to advance the rapidly developing field of organic photovoltaics (OPVs). Specifically, we focus on the computational advantages of geminal-based methods over standard approaches and identify the critical aspects of OPV development. Examples are reliable and efficient computations of orbital energies, electronic spectra, and van der Waals interactions. Geminal-based models can also be combined with quantum embedding techniques and a quantum information analysis of orbital interactions to gain a fundamental understanding of the electronic structures and properties of realistic OPV building blocks. Furthermore, other organic components present in, for instance, dye-sensitized solar cells (DSSCs) represent another promising scope of application. Finally, we provide numerical examples predicting the properties of a small building block of OPV components and two carbazole-based dyes proposed as possible DSSC sensitizers.

Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry

In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.

Resolving the π-assisted U-N σf-bond formation using quantum information theory

We model the potential energy profiles of the UO₂ (NCO)Cl₂^- → NUOCl₂^- + CO₂ reaction pathway [Y. Gong, V. Vallet, M. del Carmen Michelini, D. Rios and J. K. Gibson, J. Phys. Chem. A, 2014, 118, 325-330] using different pair coupled-cluster doubles (pCCD) methods. Specifically, we focus on pCCD and pCCD-tailored coupled cluster models in predicting relative energies for the various intermediates and transition states along the reaction coordinate. Furthermore, we augment our study on energetics with an orbital-pair correlation analysis of the complete reaction pathway that features two distinct paths. Our analysis of orbital correlations sheds new light on the formation and breaking of respective bonds between the uranium, oxygen, and nitrogen atoms along the reaction coordinates where the "yl" bond is broken and a nitrido compound formed. Specifically, the strengthening of the U-N σ_f-bond is assisted by a π-type interaction that is delocalized over the C-N-U backbone of the UO₂ (NCO)Cl₂^- complex.

Concept of Orbital Entanglement and Correlation in Quantum Chemistry

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements in numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement seen previously. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.

Elucidating the multi-configurational character of the firefly dioxetanone anion and its prototypes in the biradical region using full valence active spaces

We analyzed the near-degenerate states of the firefly dioxetanone anion (FDO-) and its prototypes, especially in the biradical region, using multi-configurational approaches. The importance of utilizing full valence active spaces by means of density-matrix renormalization group self-consistent field (DMRG-SCF) calculations was described. Our results revealed that the neglect of some valence orbitals can affect the quantitative accuracy in later multi-reference calculations or the qualitative conclusion when optimizing conical intersections. Using all of the relevant valence orbitals of FDO-, we confirmed that there were two conical intersections, as reported in previous work, and that the intersecting states were changed when the active space was enlarged. Beyond these, we found that there were strong interactions between states in the biradical regions, in which the changes in entanglements can be used to visualize the interacting state evolution.

Quantum information-based analysis of electron-deficient bonds

Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here, for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely, diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe the bonding situation in more exotic molecules which have been synthesized and characterized only recently, in particular, the diborane molecule with four hydrogen atoms [diborane(4)] and a neutral zerovalent s-block beryllium complex, whose surprising stability was attributed to a strong three-center two-electron π bond stretching across the C-Be-C core. Our approach is of high importance especially in the light of a constant chase after novel compounds with extraordinary properties where the bonding is expected to be unusual.

Elucidating cation–cation interactions in neptunyl dications using multi-reference ab initio theory

Understanding the binding mechanism in neptunyl clusters formed due to cation–cation interactions is of crucial importance in nuclear waste reprocessing and related areas of research.

Polarization propagator theory and the entanglement between MO excitations

Entanglement is at the core of quantum physics and so, one may conjecture that it should have some influence on atomic and molecular response properties. The usual way of treating entanglement is by applying information theory via the von Newman entropy. Given that the principal propagator is the operator that contains the physical information that arises due to the transmission of the effects of two external perturbations through the electronic framework of a quantum system, it should have in it the information necessary to quantify the likely entanglement among molecular orbital excitations. In this article we first propose a proper density matrix and from it, the way to quantify entangled excitations by using information theory. The NMR J-couplings are among the best candidates to learn about the potentialities of this formalism. We applied this new tool to analyze the famous Karplus rule and found a relationship between the dihedral angular dependence and the entanglement. We also found that the entangled excitations are related to electron correlation. The new formalism can be applied to all other response properties.

On the multi-reference nature of plutonium oxides: PuO22+, PuO2, PuO3 and PuO2(OH)2

Actinide-containing complexes present formidable challenges for electronic structure methods due to the large number of degenerate or quasi-degenerate electronic states arising from partially occupied 5f and 6d shells. Conventional multi-reference methods can treat active spaces that are often at the upper limit of what is required for a proper treatment of species with complex electronic structures, leaving no room for verifying their suitability. In this work we address the issue of properly defining the active spaces in such calculations, and introduce a protocol to determine optimal active spaces based on the use of the Density Matrix Renormalization Group algorithm and concepts of quantum information theory. We apply the protocol to elucidate the electronic structure and bonding mechanism of volatile plutonium oxides (PuO₃ and PuO₂(OH)₂), species associated with nuclear safety issues for which little is known about the electronic structure and energetics. We show how, within a scalar relativistic framework, orbital-pair correlations can be used to guide the definition of optimal active spaces which provide an accurate description of static/non-dynamic electron correlation, as well as to analyse the chemical bonding beyond a simple orbital model. From this bonding analysis we are able to show that the addition of oxo- or hydroxo-groups to the plutonium dioxide species considerably changes the π-bonding mechanism with respect to the bare triatomics, resulting in bent structures with a considerable multi-reference character.

The correlation theory of the chemical bond

The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.

Hückel-Hubbard-Ohno modeling of π-bonds in ethene and ethyne with application to trans-polyacetylene

Quantum chemistry calculations provide the potential energy between two carbon atoms in ethane (H3C-CH3), ethene (H2C[double bond, length as m-dash]CH2), and ethyne (HC[triple bond, length as m-dash]CH) as a function of the atomic distance. Based on the energy function for the σ-bond in ethane, Vσ(r), we use the Hückel model with Hubbard-Ohno interaction for the π electrons to describe the energies Vσπ(r) and Vσππ(r) for the σπ double bond in ethene and the σππ triple bond in ethyne, respectively. The fit of the force functions shows that the electron transfer matrix element and the Peierls coupling can be estimated with some precision whereas the Hubbard-Ohno parameters are insignificant at the distances under consideration. We apply the Hückel-Hubbard-Ohno model to describe the bond lengths and the energies of elementary electronic excitations of trans-polyacetylene, (CH)n, whereby we adjust the σ-bond potential for conjugated polymers.

Quantum Entanglement and Chemical Reactivity

The water molecule and a hydrogenic abstraction reaction are used to explore in detail some quantum entanglement features of chemical interest. We illustrate that the energetic and quantum-information approaches are necessary for a full understanding of both the geometry of the quantum probability density of molecular systems and the evolution of a chemical reaction. The energy and entanglement hypersurfaces and contour maps of these two models show different phenomena. The energy ones reveal the well-known stable geometry of the models, whereas the entanglement ones grasp the chemical capability to transform from one state system to a new one. In the water molecule the chemical reactivity is witnessed through quantum entanglement as a local minimum indicating the bond cleavage in the dissociation process of the molecule. Finally, quantum entanglement is also useful as a chemical reactivity descriptor by detecting the transition state along the intrinsic reaction path in the hypersurface of the hydrogenic abstraction reaction corresponding to a maximally entangled state.

Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex

Multiconfigurational wavefunction analysis and entanglement measures based on von Neumann entropy shed light on the electronic structure of a Ru nitrosyl complex, in particular on the Ru–NO bond.

Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru–NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru–NO π bonds show static and dynamic correlation, while other Ru–ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru–NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru–NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru^II and Ru^III configurations, with the Ru^III configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

Singlet ground state actinide chemistry with geminals

We present the first application of the variationally orbital optimized antisymmetric product of 1-reference orbital geminals (vOO-AP1roG) method to singlet-state actinide chemistry.