Fragment Orbitals Research Articles

Electric fields imbue enzyme reactivity by aligning active site fragment orbitals

It is broadly recognized that intramolecular electric fields, produced by the protein scaffold and acting on the active site, facilitate enzymatic catalysis. This field effect can be described by several theoretical models, each of which is intuitive to varying degrees. In this contribution, we show that a fundamental effect of electric fields is to generate electrostatic potentials that facilitate the energetic alignment of reactant frontier orbitals. We apply this model to demystify the impact of electric fields on high-valent iron-oxo heme proteins: catalases, peroxidases, and peroxygenases/monooxygenases. Specifically, we show that this model easily accounts for the observed field-induced changes to the spin distribution within peroxidase active sites and explains the transition between epoxidation and hydroxylation pathways seen in Cytochrome P450 active site models. Thus, for the intuitive interpretation of the chemical effect of the field, the strategy involves analyzing the response of the orbitals of active site fragments, and their energetic alignment. We note that the energy difference between fragment orbitals involved in charge redistribution acts as a measure for the chemical hardness/softness of the reactive complex. This measure, and its sensitivity to electric fields, offers a single parameter model from which to quantitatively assess the effects of electric fields on reactivity and selectivity. Thus, the model provides an additional perspective to describe electrostatic preorganization and offers ways for its manipulation.

Quantification of the Donor-Acceptor Character of Ligands by the Effective Fragment Orbitals.

Metal-ligand interactions are at the heart of transition metal complexes. The Dewar-Chat-Duncanson model is often invoked, whereby the metal-ligand bonding is decomposed into the simultaneous ligand→metal electron donation and the metal→ligand back-donation. The separate quantification of both effects is not a trivial task, neither from experimental nor computational exercises. In this work we present the effective fragment orbitals (EFOs) and their occupations as a general procedure beyond the Kohn-Sham density functional theory (KS-DFT) framework for the identification and quantification of donor-acceptor interactions, using solely the wavefunction of the complex. Using a common Fe(II) octahedral complex framework, we quantify the σ-donor, π-donor, and π-acceptor character for a large and chemically diverse set of ligands, by introducing the respective descriptors σd, πd, and πa. We also explore the effect of the metal size, coordination number, and spin state on the donor/acceptor features. The spin-state is shown to be the most critical effect, inducing a systematic decrease of the sigma donation and π-backdonation going from low spin to high spin. Finally, we illustrate the ability of the EFOs to rationalize the Tolman electronic parameter and the trans influence in planar square complexes in terms of these new descriptors.

Fragment Orbitals Extracted from First-Principles Plane-Wave Calculations.

Decomposing extended structures into smaller, molecular, even functional groups or simple fragments has a long tradition in chemistry because it allows for understanding certain electronic peculiarities in truly chemical terms. By doing so, invaluable property information is chemically accessible, for example, needed to rationalize catalytic or magnetic or optical nature. In order to also follow that train of thought for periodic materials, we have developed a tool which in a straightforward manner derives fragment molecular orbitals from plane-wave electronic-structure data of whatever kind of solid-state material. We here report on the mathematical apparatus of the method dubbed linear combination of fragment orbitals (LCFO) used for that purpose, implemented within the LOBSTER code. The method is illustrated from various sorts of molecular entities contained in such crystalline materials, together with an assessment of both accuracy and robustness of the new tool.

Effective Ion Charges in Ion Exchangers and Electrolyte Solutions

Structures, effective numbers of charges and molecular orbitals of ion pairs and representative fragments of a sulfocation exchanger in various ionic forms were calculated by the non-empirical quantum chemical method of LCAO MO. The effective charges of ions in accordance with the principles of the molecular orbital method were fractional values. For contact ion pairs, where the effective ion charges were experimentally measured by X-ray absorption spectroscopy, we obtained full agreement with the calculated values. The charge numbers of cations and anions differed in both hydrate-separated and ion-exchange systems due to the fact that the oxygen atoms of hydrated water molecules influenced the formation of molecular orbitals. According to the obtained values of the numbers of charges and interionic distances, the energies of the electrostatic interaction of ions were calculated using the integral form of Coulomb's law. Experimental values of the energies of chemical bonds of counterions and fixed ions were obtained using the conductometric contact-difference method when measuring the specific electrical conductivity of MK-40 cation exchange membranes in the range of 20-50oC and according to the Arrhenius equation. The coordination of experimental and calculated chemical bond energies in the ion exchanger was achieved after the addition of hydrogen bond energy to the electrostatic interaction energy. In order to be able to completely nonempirically calculate the energies of chemical bonds in an ion exchanger, we took the value of the hydrogen bond energy as the excitation energy of the first energy level of deformation vibrations of water molecules having a value of 19.4 kJ/mol. A comparison of the contribution of the electrostatic interaction to the total binding energy of alkali metal cations with a fixed ion showed its small role in ion exchange and membrane transport, so that in the first approximation we can say that the transfer of alkali metal cations is determined by the breaking of the hydrogen bond. For cations of a larger charge (calcium), the electrostatic energy already makes a significant contribution, and for trivalent ions, the energies of the Coulomb interaction and hydrogen bonding are close to each other. The soliton mechanism of translation of the energy of deformation vibrations along a chain of water molecules is considered, which allows explaining the decrease in energy when several hydrogen bonds are broken.

Metal-metal bonds with unusual oxidation states in early s-block elements: A computational perspective

This review article features recent progress in the field of metal-metal bonding chemistry, with a focus on Li−Li, Be−Be, and Mg−Mg bonds via computational means. The use of advanced and sophisticated computational methods has allowed us to gain deeper insights into the nature of metal-metal and metal-ligand bonding which showed that the valence s and p orbitals of these metal atoms play a significant role. Computational methods such as density functional theory (DFT) and post-Hartree-Fock approaches have enabled researchers to explore the electronic structure and thermodynamic properties of metal-metal bonded systems. The computational tools such as natural bond orbital (NBO) analysis, energy decomposition analysis (EDA), and atoms-in-molecules (AIM) have been useful in predicting key electronic properties such as localized bond orbitals, interacting fragment orbitals, electron density-based descriptors, etc., which can be used to design new materials. This summarized study of metal-metal bonding will provide significant implications for the development of new materials with desirable properties for a wide range of applications.

Open shell versus closed shell bonding interaction in cyclopropane derivatives: EDA-NOCV analyses.

Cyclopropane ring is a very common motif in organic/bio-organic compounds. The chemical bonding of this strained ring is taught to all chemistry students. This three-membered cyclic, C3 ring is quite reactive which has attracted both, synthetic and theoretical chemists to rationalize/correlate its stability and bonding with its reactivity and physical properties over a century. There are a few bonding models (mainly the Bent-Bond model and Walsh model) of this C3 ring that are debated to date. Herein, we have carried out energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV) to study the two most reactive bonds of cyclopropane rings of 49 different organic compounds containing different functional groups to obtain a much deeper bonding insight toward a more general bonding model of this class of compounds. The EDA-NOCV analyses of fragment orbitals and susequent bond formation revealed that the nature of the CC bond of the cyclopropane (splitting two bonds at a time out of three CC bonds) ring is preferred to form two dative covalent CC bonds (between a singlet olefin-fragment and an excited singlet carbene-fragment with a vacant sp2 orbital and a filled p-orbital) for the majority (37/49) of compounds over two covalent electron sharing bonds in some (7/49) compounds (between an excited triplet olefin and triplet carbene), while a few (5/49) compounds show flexibility to adopt either the electron sharing or dative covalent bond as both are equally possible. The effects of functional groups on the nature of chemical bond in cyclopropane rings have been studied in detail. Our bonding analyses are in line with the QTAIM analyses which produce small negative values of the Laplacian, significantly positive values of bond ellipticity, and accumulation of electron densities around the ring critical point of C3 -rings. These corresponding QTAIM parameters of C3 -rings are quite different for CC single bonds of normal hydrocarbons as expected. The chemical bonding in the majority of cyclopropane rings can be very similar to those of metal-olefin systems.

Spectral features of the ferrous-CO complex in cytochrome P450: a revisit using TDDFT calculations.

There are different views in the literature regarding how to interpret the observed spectral features of the ferrous-CO complexes in cytochrome P450 enzymes (P450s). In this work, we applied density functional theory (DFT) and time-dependent DFT (TDDFT) calculations at the B3LYP-D3BJ/def2-TZVP level with a CPCM correction to the ferrous-CO models of P450s as well as of proteins that contain a histidine-ligated heme. Our results support the notion derived from a previously reported iterative extended Hückel calculation that the involvement of the sulfur lone-pair orbital (S(nz)) of the axial cysteine ligand in the electronic excitations gives rise to a spectral anomaly. The Q and the shorter-wavelength Soret (B') peaks are primarily due to the electronic transitions from the a2u- and S(nz)-type molecular orbitals (MOs), generated via an orbital interaction of fragment orbitals, to the near-degenerate eg-type π* MOs, respectively. The transitions from the a1u-type MO to the eg-type MOs contribute most to the longer wavelength Soret (B) peaks. Both a2u- and S(nz)-type MOs contribute to the B peaks, but the contribution of the latter is greater. When the axial ligand is histidine, the Q and Soret peaks originate essentially from the excitations from the a2u- and a1u-type MOs to the eg-type MOs. The transitions from the b2u-type MOs to the eg-type MOs play the most significant role in the N peaks of such ferrous-CO complexes. Here, the b2u-type MOs have a large contribution from the imidazole π orbital.

Colorimetric probing and fluorescent chemosensor features of functionalized sulphonamide-azomethine derivatives

In this work, we have experimentally synthesized bromosulfonamide-based azomethine compounds through the reaction of 4-bromobenzenesulfonamide with 2-hydroxy-5-iodobenzaldehyde, 2-hydroxy-5-nitrobenzaldehyde, and 2-hydroxy-1-naphthaldehyde. We have also characterized the molecular structure of the investigated compounds with MS, 1H NMR, FTIR and UV–vis spectra. Theoretically, using DFT and TD-DFT methods, we computed frontier molecular orbitals (FMOs) energies and UV–vis spectra as well. We have also obtained the electron localization function (ELF) maps to identify electrophilic substitution sites in the molecules and density of states (DOS) diagrams to show the composition of the fragment orbitals that contribute to the molecular orbitals. We have investigatedsteady-state absorption, emission features, and excited state dynamics to better understand the photophysical process of bromosulfonamide-based azomethines. It has been demonstrated that by adding a naphthalene unit, the absorption properties of azomethine into two branches. Besides, azomethine, including heavy iodo atoms, presents a slight decrement in the fluorescence intensity. According to thorough calculations of charge transfer dynamics using femtosecond transient absorption spectra, the bromosulfonamide-based azomethines with iodo atoms and incorporating naphthalene units exhibit an intersystem crossing mechanism following photoexcitation. The colorimetric response of the compounds in DMSO to the addition of the equivalent amount of anions (F−, Br−, I−, CN−, SCN−, ClO4−, HSO4−, AcO−, H2PO4−, N3− and OH−) was investigated. In this regard, while the addition of F−, CN−, AcO−, H2PO4− and OH− anions into the solution containing the compounds resulted in a significant color change, the addition of Br−, I−, SCN−, ClO4−, HSO4− and N3−anions resulted in no color change.

Fragment-orbital-dependent spin fluctuations in the single-component molecular conductor [Ni(dmdt)2]

Motivated by recent nuclear magnetic resonance experiments, we calculated the spin susceptibility, Knight shift, and spin-lattice relaxation rate ($1/T_{1}T$) of the single-component molecular conductor [Ni(dmdt)$_2$] using the random phase approximation in a multi-orbital Hubbard model describing the Dirac nodal line electronic system in this compound. This Hubbard model is composed of three fragment orbitals and on-site repulsive interactions obtained using ab initio many-body perturbation theory calculations. We found fragment-orbital-dependent spin fluctuations with the momentum $\textbf{q}$=$\textbf{0}$ and an incommensurate value of the wavenumber $\textbf{q}$=$\textbf{Q}$ at which a diagonal element of the spin susceptibility is maximum. The $\textbf{q}$=$\textbf{0}$ and $\textbf{Q}$ responses become dominant at low and high temperatures, respectively, with the Fermi-pocket energy scale as the boundary. We show that $1/T_{1}T$ decreases with decreasing temperature but starts to increase at low temperature owing to the $\textbf{q}$=$\textbf{0}$ spin fluctuations, while the Knight shift keeps monotonically decreasing. These properties are due to the intra-molecular antiferromagnetic fluctuations caused by the characteristic wave functions of this Dirac nodal line system, which is described by an $n$-band ($n\geq 3$) model. We show that the fragment orbitals play important roles in the magnetic properties of [Ni(dmdt)$_2$].

An Unprecedented Interconversion Between Non-covalent and Covalent Interactions Driven by Halogen Bonding.

The spontaneous interconversion between covalent forces and noncovalent counterparts remains an unexplained mystery to date. Here we have discovered a marvelous transformation between them through halogen bonding using NI3 as a prototype. Our results show that the interaction strength of the NI3 dimer is 7.01 kcal mol-1 , demonstrating that it is a quite strong halogen bond. Molecular orbital analyses indicate that the frontier molecular orbitals result from strong mixing of the fragment orbitals, which may be the electronic structure basis for interconversion. Further studies on a series of NI3 oligomers (5-, 10-, 15-, 20-, 26-, 30-mer) show that the interconversion occurs approximately at 26-mer on the basis on bond distance, ELF, etc.; the interconversion is a gradual transformation and not a sudden one. This study provides more insights into the halogen bonding and the high explosivity of NI3 containing species.

Comparing the nature of quantum plasmonic excitations for closely spaced silver and gold dimers.

In the new field of quantum plasmonics, plasmonic excitations of silver and gold nanoparticles are utilized to manipulate and control light-matter interactions at the nanoscale. While quantum plasmons can be described with atomistic detail using Time-Dependent Density Functional Theory (DFT), such studies are computationally challenging due to the size of the nanoparticles. An efficient alternative is to employ DFT without approximations only for the relatively fast ground state calculations and use tight-binding approximations in the demanding linear response calculations. In this work, we use this approach to investigate the nature of plasmonic excitations under the variation of the separation distance between two nanoparticles. We thereby provide complementary characterizations of these excitations in terms of Kohn-Sham single-orbital transitions, intrinsic localized molecular fragment orbitals, scaling of the electron-electron interactions, and probability of electron tunneling between monomers.

Unveiling the Electronic Structure of the Bi(+1)/Bi(+3) Redox Couple on NCN and NNN Pincer Complexes.

Low-valent group 15 compounds stabilized by pincer ligands have gained particular interest, given their direct access to fine-tune their reactivity by the coordination pattern. Recently, bismuth has been employed in a variety of catalytic transformations by taking advantage of the (+1/+3) redox couple. In this work, we present a detailed quantum–chemical study on the electronic structure of bismuth pincer complexes from two different families, namely, bis(ketimine)phenyl (NCN) and triamide bismuthinidene (NNN). The use of the so-called effective oxidation state analysis allows the unambiguous assignation of the bismuth oxidation state. In contrast to previous studies, our calculations suggest a Bi(+1) assignation for NCN pincer ligands, while Bi(+3) character is found for NNN pincer complexes. Notably, regardless of its oxidation state, the central bismuth atom disposes of up to two lone pairs for coordinating Lewis acids, as indicated by very high first and second proton affinity values. Besides, the Bi–NNN systems can also accommodate two Lewis base ligands, indicating also ambiphilic behavior. The effective fragment orbital analysis of Bi and the ligand allows monitoring of the intricate electron flow of these processes, revealing the noninnocent nature of the NNN ligand, in contrast with the NCN one. By the dissection of the electron density into effective fragment orbitals, we are able to quantify and rationalize the Lewis base/acid character.

Complex Featuring Two Double Dative Bonds Between Carbon(0) and Uranium

Complex Featuring Two Double Dative Bonds Between Carbon(0) and Uranium

Rare-Earth Metal Boroxide with Formal Triple Metal–Oxygen Orbital Interaction: Synthesis from B(C 6 F 5 ) 3 ·H 2 O and Radical-Anion Ligated Rare-Earth Metal Amides

Rare-earth metal boroxides are not only rare and of great synthetic challenge but also important theoretically due to their unrevealed bonding characteristics. In this paper, we report the synthesi...

Characterization of bonding modes in metal complexes through electron density cross-sections.

Qualitative inspection of molecular orbitals (MOs) remains one of the most popular analysis tools used to describe the electronic structure and bonding properties of transition metal complexes. In symmetric coordination complexes, the use of group theory and the symmetry-adapted linear combination (SALC) of fragment orbitals allows for a very accurate and informative interpretation of MOs, but the same procedure cannot be performed for asymmetric complexes, such as Schrock and Fischer carbenes. In this work, we present a straight-forward approach for classifying and quantifying MO contributions to a particular metal-ligand interaction. Our approach utilizes the topology of MO density contributions to a cross-section of an inter-nuclear region, and is computationally inexpensive and applicable to symmetric and asymmetric complexes alike. We also apply the same approach with similar decompositions using Natural Bond Orbitals (NBO) and the recently developed Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) density decomposition scheme. In particular, FALDI analysis provides additional insights regarding the multi-centric nature of metal-carbene bonds without resorting to expensive multi-reference calculations.

Stabilization of Plutonium(V) Within a Crown Ether Inclusion Complex

Crystalline coordination complexes of actinides, especially in atypical oxidation states, are not only fundamentally important for expanding the notably limited knowledge on the bonding nature of a...

Computationally Guided Molecular Design to Minimize the LE/CT Gap in D-π-A Fluorinated Triarylboranes for Efficient TADF via D and π-Bridge Tuning.

In this combined experimental and theoretical study, a computational protocol is reported to predict the excited states in D‐π‐A compounds containing the B(FXyl)2 (FXyl = 2,6‐bis(trifluoromethyl)phenyl) acceptor group for the design of new thermally activated delayed fluorescence (TADF) emitters. To this end, the effect of different donor and π‐bridge moieties on the energy gaps between local and charge‐transfer singlet and triplet states is examined. To prove this computationally aided design concept, the D‐π‐B(FXyl)2 compounds 1–5 were synthesized and fully characterized. The photophysical properties of these compounds in various solvents, polymeric film, and in a frozen matrix were investigated in detail and show excellent agreement with the computationally obtained data. Furthermore, a simple structure–property relationship is presented on the basis of the molecular fragment orbitals of the donor and the π‐bridge, which minimize the relevant singlet–triplet gaps to achieve efficient TADF emitters.

Principal interacting orbital: A chemically intuitive method for deciphering bonding interaction

AbstractModular bonding picture is a central part of chemical understanding as exemplified by the wide usage of Lewis structure as a chemical language to describe molecular electronic structures. A chemically intuitive bonding picture requires the descriptors to be localized and transferable. Molecular orbitals directly derived from quantum calculations are too delocalized to interpret in this regard, hence many efforts have been devoted to the development of bonding analysis methods. After a brief overview of various bonding analysis methods, this review outlines the framework of principal interacting orbital (PIO) analysis and presents its role in recovering intuitive chemical concepts and producing modular bonding pictures. The PIO analysis identifies the most important fragment orbitals that are involved in fragment interactions and characterizes a one‐to‐one orbital interaction pattern that underlies a unique set of bonding and anti‐bonding orbitals derived from pairwise orbital interactions between two fragments. By making use of the principal component analysis (PCA), PIO analysis can effectively combine complex delocalized interaction patterns involved in numerous molecular orbitals into a handful of localized PIOs to provide easily interpretable results with intimate connection to localized chemical concepts, while maintaining necessary delocalized features when dealing with systems that involve mutlicentered interactions such as cluster compounds and various reactions. Such adaptability guarantees the robustness of PIO analysis with respect to change of substituents and the transferability of obtained PIOs across different systems.This article is categorized under: Structure and Mechanism > Molecular Structures

GronOR: Massively parallel and GPU-accelerated non-orthogonal configuration interaction for large molecular systems.

GronOR is a program package for non-orthogonal configuration interaction calculations for an electronic wave function built in terms of anti-symmetrized products of multi-configuration molecular fragment wave functions. The two-electron integrals that have to be processed may be expressed in terms of atomic orbitals or in terms of an orbital basis determined from the molecular orbitals of the fragments. The code has been specifically designed for execution on distributed memory massively parallel and Graphics Processing Unit (GPU)-accelerated computer architectures, using an MPI+OpenACC/OpenMP programming approach. The task-based execution model used in the implementation allows for linear scaling with the number of nodes on the largest pre-exascale architectures available, provides hardware fault resiliency, and enables effective execution on systems with distinct central processing unit-only and GPU-accelerated partitions. The code interfaces with existing multi-configuration electronic structure codes that provide optimized molecular fragment orbitals, configuration interaction coefficients, and the required integrals. Algorithm and implementation details, parallel and accelerated performance benchmarks, and an analysis of the sensitivity of the accuracy of results and computational performance to thresholds used in the calculations are presented.

Synthesis, spectroscopic and DFT studies of Schiff based (E)-N′-(Benzo[d][1, 3]Dioxol-5-ylmethylene)nicotinohydrazide monohydrate single crystal: a promising organic nonlinear optical material

(E)-N′-(benzo[d][1, 3]dioxol-5-ylmethylene)nicotinohydrazide monohydrate (BDMNH) material was synthesized by Schiff based method. The BDMNH material crystalizes in monoclinic crystal system with a space group of P21/n. The molecular structure was confirmed by 1H-NMR and 13C-NMR spectrum. The BDMNH compound has two rings namely piperonal and pyridine. The carbon-carbon stretching vibrations of piperonal ring have been observed at 1567 cm−1 in FT-IR and 1590 cm−1 in FT-Raman. The H…H (34.6%) interaction occupies the highest portion in the total area of Hirshfeld surface. The peak is observed at 376 nm in the electronic spectrum of the title compound reveals that the transition is π-π*. The EHOMO and ELUMO values are found to be −5.27 eV and −1.57 eV, respectively. The oxygen atom O3 possess high negative charge (−0.3573) comparing with the other oxygen atoms like O5, O9 and O32. From the partial density of states (PDOS) spectrum, fragment orbitals (H, C, N, and O) are contributing to the molecular orbitals composition. The molecular orbital interactions σ (N8–C14) → σ*(C7–C15) and σ (C10–H22) → σ*(C14–C18) have the stabilization energy values of 22.87 and 26.48 kJ mol−1, respectively. The third order nonlinear absorption coefficient value β = 6.246 × 10−5 cm/W.