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Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold

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A special issue of Molecules (ISSN 1420-3049). This special issue belongs to the section "Inorganic Chemistry".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 26793

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Prof. Dr. Eric Glendening

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Department of Chemistry and Physics, Indiana State University, Terre Haute, IN 47809, USA
Interests: electronic structure theory; natural bond orbital methods; delocalization and resonance theory; molecular interactions and energy decomposition analysis; organic reaction mechanisms

Special Issue Information

Dear Colleagues,

This Special Issue of Molecules celebrates the 80th birthday of Prof. Dr. Frank Weinhold, Professor Emeritus of Chemistry at the University of Wisconsin-Madison. We invite you to submit a manuscript for this issue in recognition of Prof. Weinhold’s contributions to chemical bonding theory, interpretation, and calculation.

Frank Albert Weinhold was born in Scottsbluff, Nebraska (1941) and received his chemistry BA degree from the University of Colorado, Boulder (1962). He was awarded a Fulbright Scholarship for study at the University of Freiburg, Germany, in 1962–1963 and thereafter began his graduate studies in physical chemistry at Harvard University as a Woodrow Wilson National Fellow (1963). He completed his Ph.D. degree in 1967 under the direction of Prof. E. Bright Wilson, Jr. Postdoctoral studies took Weinhold first to Oxford University as a National Science Foundation Fellow with Prof. C. A. Coulson (1967–1968), and then to the University of California, Berkeley, as a Miller Research Fellow (1968–1969). In 1969, he became Assistant Professor of Chemistry at Stanford University, where he received the Alfred P. Sloan Award (1970–1972) and the Camille and Henry Dreyfus Foundation Fellowship (1972–1976). In 1976, he moved to the Theoretical Chemistry Institute and Chemistry Department at the University of Wisconsin, Madison, becoming Associate Professor (1977) and Full Professor (1979). In 1983–1985, he served as Acting Director, and in 1986–1991 as Director of the Theoretical Chemistry Institute. Weinhold became Emeritus Professor of Chemistry in 2007 but continues writing and research at UW-Madison, including the ongoing development of the Natural Bond Orbital (NBO) computer program.

Prof. Weinhold’s earlier (1965–1980) research interests centered on N-representability conditions for reduced density matrices, upper and lower bounds for quantum-mechanical properties, the metric geometry of equilibrium thermodynamics, and complex-coordinate rotation theory of autoionizing resonances. His more recent research has primarily focused on the development of the NBO method and its application to torsional barriers, hydrogen bonding, hypervalent, and other stereoelectronic and bonding phenomena. Related studies also led to the development of the Quantum Cluster Equilibrium (QCE) theory for liquid water and other supramolecular species. His influence is indicated by the widespread adoption of NBO methodology in modern electronic structure programs (including ADF, deMon, Firefly, GAMESS, Gaussian, Jaguar, Molpro, NWChem, Orca, PQS, Q-Chem, Spartan, and TeraChem), frequent citation by Wikipedia on chemical bonding topics (>60 entries), and numerous NBO applications in the chemical literature (>20,000, increasing by about 2000 per year). His research monographs include Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective (Cambridge University Press, 2005; with C. R. Landis), Classical and Geometrical Theory of Chemical and Phase Thermodynamics (Wiley, 2009), and Discovering Chemistry with Natural Bond Orbitals (Wiley, 2012; with C. R. Landis). Total citations of his works currently exceed 60,000 (h-index = 74; e-index > 200).

It is our pleasure to invite you to submit a manuscript for this Special Issue honoring Prof. Frank Weinhold. The issue focuses on chemical bonding and valency, and we especially encourage submissions reporting the application of NBO or complementary methods of analysis to interpret molecular properties and chemical bonding phenomena. Manuscripts describing original work as well as review articles are welcome. Manuscripts related to Prof. Weinhold’s other areas of research interest will also be considered.

Prof. Dr. Eric Glendening
Guest Editor

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Published Papers (13 papers)

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Research

15 pages, 7036 KiB

Open AccessArticle

Analysis of Conformational Preferences in Caffeine

by Sara Gómez, Natalia Rojas-Valencia and Albeiro Restrepo

Molecules 2022, 27(6), 1937; https://doi.org/10.3390/molecules27061937 - 17 Mar 2022

Cited by 1 | Viewed by 2049

Abstract

High level DLPNO–CCSD(T) electronic structure calculations with extended basis sets over B3LYP–D3 optimized geometries indicate that the three methyl groups in caffeine overcome steric hindrance to adopt uncommon conformations, each one placing a C–H bond on the same plane of the aromatic system, leading to the C–H bonds eclipsing one carbonyl group, one heavily delocalized C–N bond constituent of the fused double ring aromatic system, and one C–H bond from the imidazole ring. Deletion of indiscriminate and selective non-Lewis orbitals unequivocally show that hyperconjugation in the form of a bidirectional –CH

_{3} ⇆

aromatic system charge transfer is responsible for these puzzling conformations. The structural preferences in caffeine are exclusively determined by orbital interactions, ruling out electrostatics, induction, bond critical points, and density redistribution because the steric effect, the allylic effect, the Quantum Theory of Atoms in Molecules (QTAIM), and the non-covalent interactions (NCI), all predict wrong energetic orderings. Tiny rotational barriers, not exceeding 1.3 kcal/mol suggest that at room conditions, each methyl group either acts as a free rotor or adopts fluxional behavior, thus preventing accurate determination of their conformations. In this context, our results supersede current experimental ambiguity in the assignation of methyl conformation in caffeine and, more generally, in methylated xanthines and their derivatives. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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15 pages, 3104 KiB

Open AccessArticle

The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium

by Barbara Kirchner, Johannes Ingenmey, Michael von Domaros and Eva Perlt

Molecules 2022, 27(4), 1286; https://doi.org/10.3390/molecules27041286 - 14 Feb 2022

Cited by 6 | Viewed by 2488

Abstract

The theoretical description of water properties continues to be a challenge. Using quantum cluster equilibrium (QCE) theory, we combine state-of-the-art quantum chemistry and statistical thermodynamic methods with the almost historical Clausius–Clapeyron relation to study water self-dissociation and the thermodynamics of vaporization. We pay particular attention to the treatment of internal rotations and their impact on the investigated properties by employing the modified rigid-rotor–harmonic-oscillator (mRRHO) approach. We also study a novel QCE parameter-optimization procedure. Both the ionic product and the vaporization enthalpy yield an astonishing agreement with experimental reference data. A significant influence of the mRRHO approach is observed for cluster populations and, consequently, for the ionic product. Thermodynamic properties are less affected by the treatment of these low-frequency modes. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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23 pages, 8275 KiB

Open AccessArticle

Theoretical Study of the Geometry of Dibenzoazepine Analogues

by Małgorzata Szymańska and Irena Majerz

Molecules 2022, 27(3), 790; https://doi.org/10.3390/molecules27030790 - 25 Jan 2022

Viewed by 2407

Abstract

The geometry of dibenzoazepine analogues—typical multifunctional drugs—was investigated to find the geometrical parameters sensitive to the substitution of the central seven-membered ring. Exploration of the crystal structure database (CSD) shows that the geometrical parameter sensitive to the substitution of the carbon atom distance of the central ring not included in the aromatic rings to the plane through the carbon atoms common for the central ring and the aromatic side rings. Presence of the double bond in the central ring was reflected in its partial aromaticity expressed by the HOMED parameter. Some derivatives of 5H-dibenzo[b,f]azepine with flat conformation of the central ring are characterized by mobility of the electron density comparable to the mobility in the aromatic side rings. Influence of the surrounding on the investigated compounds was confirmed by comparison of the optimized molecules and the molecules in the crystal state where the packing forces can influence the molecular geometry. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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11 pages, 1105 KiB

Open AccessArticle

On the Nature of the Bonding in Coinage Metal Halides

by Slađana Đorđević, Slavko Radenković, Sason Shaik and Benoît Braïda

Molecules 2022, 27(2), 490; https://doi.org/10.3390/molecules27020490 - 13 Jan 2022

Cited by 7 | Viewed by 2299

Abstract

This article analyzes the nature of the chemical bond in coinage metal halides using high-level ab initio Valence Bond (VB) theory. It is shown that these bonds display a large Charge-Shift Bonding character, which is traced back to the large Pauli pressure arising from the interaction between the bond pair with the filled semicore d shell of the metal. The gold-halide bonds turn out to be pure Charge-Shift Bonds (CSBs), while the copper halides are polar-covalent bonds and silver halides borderline cases. Among the different halogens, the largest CSB character is found for fluorine, which experiences the largest Pauli pressure from its σ lone pair. Additionally, all these bonds display a secondary but non-negligible π bonding character, which is also quantified in the VB calculations. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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18 pages, 8067 KiB

Open AccessArticle

Ring Vibrations to Sense Anionic Ibuprofen in Aqueous Solution as Revealed by Resonance Raman

by Sara Gómez, Natalia Rojas-Valencia, Tommaso Giovannini, Albeiro Restrepo and Chiara Cappelli

Molecules 2022, 27(2), 442; https://doi.org/10.3390/molecules27020442 - 10 Jan 2022

Cited by 14 | Viewed by 2241

Abstract

We unravel the potentialities of resonance Raman spectroscopy to detect ibuprofen in diluted aqueous solutions. In particular, we exploit a fully polarizable quantum mechanics/molecular mechanics (QM/MM) methodology based on fluctuating charges coupled to molecular dynamics (MD) in order to take into account the dynamical aspects of the solvation phenomenon. Our findings, which are discussed in light of a natural bond orbital (NBO) analysis, reveal that a selective enhancement of the Raman signal due to the normal mode associated with the C–C stretching in the ring,

ν_{C = C}

, can be achieved by properly tuning the incident wavelength, thus facilitating the recognition of ibuprofen in water samples. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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13 pages, 7105 KiB

Open AccessArticle

Scaled in Cartesian Coordinates Ab Initio Molecular Force Fields of DNA Bases: Application to Canonical Pairs

by Igor Kochikov, Anna Stepanova and Gulnara Kuramshina

Molecules 2022, 27(2), 427; https://doi.org/10.3390/molecules27020427 - 10 Jan 2022

Viewed by 1260

Abstract

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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8 pages, 584 KiB

Open AccessArticle

Computational Estimation of the Acidities of Pyrimidines and Related Compounds

by Rachael A. Holt and Paul G. Seybold

Molecules 2022, 27(2), 385; https://doi.org/10.3390/molecules27020385 - 07 Jan 2022

Cited by 4 | Viewed by 1666

Abstract

Pyrimidines are key components in the genetic code of living organisms and the pyrimidine scaffold is also found in many bioactive and medicinal compounds. The acidities of these compounds, as represented by their pK_as, are of special interest since they determine the species that will prevail under different pH conditions. Here, a quantum chemical quantitative structure–activity relationship (QSAR) approach was employed to estimate these acidities. Density-functional theory calculations at the B3LYP/6-31+G(d,p) level and the SM8 aqueous solvent model were employed, and the energy difference ∆E_H2O between the parent compound and its dissociation product was used as a variation parameter. Excellent estimates for both the cation → neutral (pK_a1, R² = 0.965) and neutral → anion (pK_a2, R² = 0.962) dissociations were obtained. A commercial package from Advanced Chemical Design also yielded excellent results for these acidities. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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22 pages, 3702 KiB

Open AccessArticle

Thermodynamically Stable Cationic Dimers in Carboxyl-Functionalized Ionic Liquids: The Paradoxical Case of “Anti-Electrostatic” Hydrogen Bonding

by Loai Al-Sheakh, Sebastian Fritsch, Andreas Appelhagen, Alexander Villinger and Ralf Ludwig

Molecules 2022, 27(2), 366; https://doi.org/10.3390/molecules27020366 - 07 Jan 2022

Viewed by 1569

Abstract

We show that carboxyl-functionalized ionic liquids (ILs) form doubly hydrogen-bonded cationic dimers (c⁺=c⁺) despite the repulsive forces between ions of like charge and competing hydrogen bonds between cation and anion (c⁺–a⁻). This structural motif as known for formic acid, the archetype of double hydrogen bridges, is present in the solid state of the IL 1−(carboxymethyl)pyridinium bis(trifluoromethylsulfonyl)imide [HOOC−CH₂−py][NTf₂]. By means of quantum chemical calculations, we explored different hydrogen-bonded isomers of neutral (HOOC–(CH₂)_n–py⁺)₂(NTf₂⁻)₂, single-charged (HOOC–(CH₂)_n–py⁺)₂(NTf₂⁻), and double-charged (HOOC– (CH₂)_n−py⁺)₂ complexes for demonstrating the paradoxical case of “anti-electrostatic” hydrogen bonding (AEHB) between ions of like charge. For the pure doubly hydrogen-bonded cationic dimers (HOOC– (CH₂)_n−py⁺)₂, we report robust kinetic stability for n = 1–4. At n = 5, hydrogen bonding and dispersion fully compensate for the repulsive Coulomb forces between the cations, allowing for the quantification of the two equivalent hydrogen bonds and dispersion interaction in the order of 58.5 and 11 kJmol⁻¹, respectively. For n = 6–8, we calculated negative free energies for temperatures below 47, 80, and 114 K, respectively. Quantum cluster equilibrium (QCE) theory predicts the equilibria between cationic monomers and dimers by considering the intermolecular interaction between the species, leading to thermodynamic stability at even higher temperatures. We rationalize the H-bond characteristics of the cationic dimers by the natural bond orbital (NBO) approach, emphasizing the strong correlation between NBO-based and spectroscopic descriptors, such as NMR chemical shifts and vibrational frequencies. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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13 pages, 2439 KiB

Open AccessArticle

Computational Studies of Coinage Metal Anion M⁻ + CH₃X (X = F, Cl, Br, I) Reactions in Gas Phase

by Fan Wang, Xiaoyan Ji, Fei Ying, Jiatao Zhang, Chongyang Zhao and Jing Xie

Molecules 2022, 27(1), 307; https://doi.org/10.3390/molecules27010307 - 04 Jan 2022

Cited by 3 | Viewed by 1983

Abstract

We characterized the stationary points along the nucleophilic substitution (S_N2), oxidative insertion (OI), halogen abstraction (XA), and proton transfer (PT) product channels of M⁻ + CH₃X (M = Cu, Ag, Au; X = F, Cl, Br, I) reactions using the CCSD(T)/aug-cc-pVTZ level of theory. In general, the reaction energies follow the order of PT > XA > S_N2 > OI. The OI channel that results in oxidative insertion complex [CH₃–M–X]⁻ is most exothermic, and can be formed through a front-side attack of M on the C-X bond via a high transition state OxTS or through a S_N2-mediated halogen rearrangement path via a much lower transition state invTS. The order of OxTS > invTS is inverted when changing M⁻ to Pd, a d¹⁰ metal, because the symmetry of their HOMO orbital is different. The back-side attack S_N2 pathway proceeds via typical Walden-inversion transition state that connects to pre- and post-reaction complexes. For X = Cl/Br/I, the invS_N2-TS’s are, in general, submerged. The shape of this M⁻ + CH₃X S_N2 PES is flatter as compared to that of a main-group base like F⁻ + CH₃X, whose PES has a double-well shape. When X = Br/I, a linear halogen-bonded complex [CH₃−X∙··M]⁻ can be formed as an intermediate upon the front-side attachment of M on the halogen atom X, and it either dissociates to CH₃ + MX⁻ through halogen abstraction or bends the C-X-M angle to continue the back-side S_N2 path. Natural bond orbital analysis shows a polar covalent M−X bond is formed within oxidative insertion complex [CH₃–M–X]⁻, whereas a noncovalent M–X halogen-bond interaction exists for the [CH₃–X∙··M]⁻ complex. This work explores competing channels of the M⁻ + CH₃X reaction in the gas phase and the potential energy surface is useful in understanding the dynamic behavior of the title and analogous reactions. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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20 pages, 1642 KiB

Open AccessArticle

Interaction Energy Analysis of Monovalent Inorganic Anions in Bulk Water Versus Air/Water Interface

by John M. Herbert and Suranjan K. Paul

Molecules 2021, 26(21), 6719; https://doi.org/10.3390/molecules26216719 - 06 Nov 2021

Cited by 6 | Viewed by 2002

Abstract

Soft anions exhibit surface activity at the air/water interface that can be probed using surface-sensitive vibrational spectroscopy, but the structural implications of this surface activity remain a matter of debate. Here, we examine the nature of anion–water interactions at the air/water interface using a combination of molecular dynamics simulations and quantum-mechanical energy decomposition analysis based on symmetry-adapted perturbation theory. Results are presented for a set of monovalent anions, including Cl⁻, Br⁻, I⁻, CN⁻, OCN⁻, SCN⁻,

{NO}_{2}^{-}

{NO}_{3}^{-}

, and

{ClO}_{n}^{-}

(

n = 1, 2, 3, 4

), several of which are archetypal examples of surface-active species. In all cases, we find that average anion–water interaction energies are systematically larger in bulk water although the difference (with respect to the same quantity computed in the interfacial environment) is well within the magnitude of the instantaneous fluctuations. Specifically for the surface-active species Br⁻(aq), I⁻(aq),

{ClO}_{4}^{-}

(aq), and SCN⁻(aq), and also for ClO⁻(aq), the charge-transfer (CT) energy is found to be larger at the interface than it is in bulk water, by an amount that is greater than the standard deviation of the fluctuations. The Cl⁻(aq) ion has a slightly larger CT energy at the interface, but

{NO}_{3}^{-}

(aq) does not; these two species are borderline cases where consensus is lacking regarding their surface activity. However, CT stabilization amounts to <20% of the total induction energy for each of the ions considered here, and CT-free polarization energies are systematically larger in bulk water in all cases. As such, the role of these effects in the surface activity of soft anions remains unclear. This analysis complements our recent work suggesting that the short-range solvation structure around these ions is scarcely different at the air/water interface from what it is in bulk water. Together, these observations suggest that changes in first-shell hydration structure around soft anions cannot explain observed surface activities. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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9 pages, 1393 KiB

Open AccessArticle

In Search of the Perfect Triple BB Bond: Mechanical Tuning of the Host Molecular Trap for the Triple Bond B≡B Fragment

by Shmuel Zilberg and Michael Zinigrad

Molecules 2021, 26(21), 6428; https://doi.org/10.3390/molecules26216428 - 25 Oct 2021

Cited by 1 | Viewed by 1273

Abstract

The coordination of the B₂ fragment by two σ-donor ligands L: could lead to a diboryne compound with a formal triple bond L:→B≡B←:L. σ-Type coordination L:→B leads to an excess of electrons around the B₂ central fragment, whereas π-back-donation from the B≡B moiety to ligand L has a compensation effect. Coordination of the σ-donor and π-acceptor ligand is accompanied by the lowering of the BB bond order. Here, we propose a new approach to obtain the perfect triple BB bond through the incorporation of the BB unit into a rigid molecular capsule. The idea is the replacement of π-back-donation, as the principal stabilization factor in the linear NBBN structure, with the mechanical stabilization of the BB fragment in the inert molecular capsule, thus preserving the perfect B≡B triple bond. Quantum-chemical calculations show that the rigid molecular capsule provided a linear NBBN structure and an unusually short BB bond of 1.36 Å. Quantum-chemical calculations of the proposed diboryne adducts show a perfect triple bond B≡B without π-back-donation from the B₂ unit to the host molecule. Two mechanisms were tested for the molecular design of a diboryne adduct with a perfect B≡B triple bond: the elimination of π-back-donation and the construction of a suitable molecular trap for the encapsulation of the B₂ unit. The second factor that could lead to the strengthening or stretching of a selected chemical bond is molecular strain produced by the rigid molecular host capsule, as was shown for B≡B and for C≡C triple bonds. Different derivatives of icosane host molecules exhibited variation in BB bond length and the corresponding frequency of the BB stretch. On the other hand, this group of molecules shows a perfect triple BB bond character and they all possess a similar level of HOMO. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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15 pages, 6028 KiB

Open AccessArticle

Two Sides of Quantum-Based Modeling of Enzyme-Catalyzed Reactions: Mechanistic and Electronic Structure Aspects of the Hydrolysis by Glutamate Carboxypeptidase

by Alexandra V. Krivitskaya, Maria G. Khrenova and Alexander V. Nemukhin

Molecules 2021, 26(20), 6280; https://doi.org/10.3390/molecules26206280 - 17 Oct 2021

Cited by 4 | Viewed by 1908

Abstract

We report the results of a computational study of the hydrolysis reaction mechanism of N-acetyl-l-aspartyl-l-glutamate (NAAG) catalyzed by glutamate carboxypeptidase II. Analysis of both mechanistic and electronic structure aspects of this multistep reaction is in the focus of this work. In these simulations, model systems are constructed using the relevant crystal structure of the mutated inactive enzyme. After selection of reaction coordinates, the Gibbs energy profiles of elementary steps of the reaction are computed using molecular dynamics simulations with ab initio type QM/MM potentials (QM/MM MD). Energies and forces in the large QM subsystem are estimated in the DFT(PBE0-D3/6-31G**) approximation. The established mechanism includes four elementary steps with the activation energy barriers not exceeding 7 kcal/mol. The models explain the role of point mutations in the enzyme observed in the experimental kinetic studies; namely, the Tyr552Ile substitution disturbs the “oxyanion hole”, and the Glu424Gln replacement increases the distance of the nucleophilic attack. Both issues diminish the substrate activation in the enzyme active site. To quantify the substrate activation, we apply the QTAIM-based approaches and the NBO analysis of dynamic features of the corresponding enzyme-substrate complexes. Analysis of the 2D Laplacian of electron density maps allows one to define structures with the electron density deconcentration on the substrate carbon atom, i.e., at the electrophilic site of reactants. The similar electronic structure element in the NBO approach is a lone vacancy on the carbonyl carbon atom in the reactive species. The electronic structure patterns revealed in the NBO and QTAIM-based analyses consistently clarify the reactivity issues in this system. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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14 pages, 629 KiB

Open AccessArticle

Variational Solutions for Resonances by a Finite-Difference Grid Method

by Roie Dann, Guy Elbaz, Jonathan Berkheim, Alan Muhafra, Omri Nitecki, Daniel Wilczynski and Nimrod Moiseyev

Molecules 2021, 26(17), 5248; https://doi.org/10.3390/molecules26175248 - 30 Aug 2021

Viewed by 2141

Abstract

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes. Full article

(This article belongs to the Special Issue Chemical Bonding and Valency: A Special Issue Celebrating the 80th Birthday of Prof. Frank Weinhold)

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