Interatomic and intraatomic analysis of the density matrix: applications to chlorobenzenes

Bond orders and valence indices have been evaluated employing Mayer’s definitions with orthogonalized atomic orbitals (OAO) obtained from L?wdin orthogonalization over an STO-3G basis set in anab initio formalism. It has been observed that the eigenvalues of the submatrices associated with bond order orbitals. natural hybrid orbitals and natural bond orbitals also reproduce the same values of the bond orders and the valence indices which in turn are quite close to the classical values. Bond orders obtained by a similarity transformation of theab initio density matrix differ appreciably in numerical magnitude.     

Coherent superposition of resonance wave function in terms of weighted orthogonalized natural localized configurations

In this research, the projection technique has been applied in order to decompose the electronic wave function into its weighted orthogonalized resonance components. These components have been constructed by determinants whose orbitals are selected among natural bond orbitals. However, the procedure is general and any other localized orbitals can be used as well. Both σ and π delocalize systems have been considered in order to check the reliability of the calculated resonance weights. For π‐systems, the presented procedure could predict significant decrease of weight of certain resonance structures when the molecular planarity was destroyed. Water cyclic clusters were also tested and the results confirmed the existence of strong σ‐delocalization in the clusters. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The nature of the rotational barriers in simple carbonyl compounds

The rotational barriers around the CO and CC bonds are investigated in formic acid, ethanedial and glycolaldedyde molecules on the basis of DFT-B3LYP/aug-cc-pVDZ calculations. Natural bond orbitals analysis is applied to enhance physical understanding of rotational barriers. In the case of attractive barriers in formic acid and Gc-glycolaldehyde, the barrier originates from the loss of hyperconjugation that determines the equilibrium structures while for the repulsive barriers in ethanedial and Go-glycolaldehyde, both Lewis and hyperconjugation terms contribute.     

KNaY-zeolite catalyzed dehydration of methyl lactate

A promising catalyst,KNaY was prepared by an ion exchange method with aqueous potassium chloride solution.Comparedwith NaY,KNaY was an effective catalyst for the dehydration of methyl lactate to methyl acrylate.Under the optimized conditions,an improved yield of 37.9 mol%was achieved.     

Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

Ab initio study of the methyl internal rotation and aldehyde hydrogen wagging of thioacetaldehyde in the X1A′ and a3A″ states

Ab initio SCF calculations have been performed for the methyl internal rotation and for aldehyde hydrogen wagging of thioacetaldehyde in the first triplet excited state, a³A, as well as in the singlet ground state, X¹A. The preferred conformations for these states are the anti-eclipsed and the eclipsed ones, respectively. The calculated barrier heights to methyl rotation (118.3 and 455.6 cm^–1 for a³A and X¹A, respectively) are in good agreement with the available experimental data. The singlet ground state and the triplet excited state exhibit a planar and pyramidal configuration, respectively. The inversion barrier of the pyramidal configuration is found to be very low 67.4 cm^–1. Finally, the change of conformation and structure with the transition is explained by a change of hydridization of the aldehyde carbon atom due to an n ^* excitation.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

The Bond Order of C2 from a Strictly N‐Representable Natural Orbital Energy Functional Perspective

The bond order of the ground electronic state of the carbon dimer has been analyzed in the light of natural orbital functional theory calculations carried out with an approximate, albeit strictly N‐representable, energy functional. Three distinct solutions have been found from the Euler equations of the minimization of the energy functional with respect to the natural orbitals and their occupation numbers, which expand upon increasing values of the internuclear coordinate. In the close vicinity of the minimum energy region, two of the solutions compete around a discontinuity point. The former, corresponding to the absolute minimum energy, features two valence natural orbitals of each of the following symmetries, σ, σ*, π and π*, and has three bonding interactions and one antibonding interaction, which is very suggestive of a bond order large than two but smaller than three. The latter, features one σ–σ* linked pair of natural orbitals and three degenerate pseudo‐bonding like orbitals, paired each with one triply degenerate pseudo‐antibonding orbital, which points to a bond order larger than three. When correlation effects, other than Hartree–Fock for example, between the paired natural orbitals are accounted for, this second solution vanishes yielding a smooth continuous dissociation curve. Comparison of the vibrational energies and electron ionization energies, calculated on this curve, with their corresponding experimental marks, lend further support to a bond order for C ₂ intermediate between acetylene and ethylene.     

Unique reactivity of a 1,4-dilithiobutadiene with methyl iodide

Reactions of 1,4-dilithiobutadiene 5 with MeI in THF gave predominantly methyl iododiene 6. Monolithio monoiodo intermediate 8 was shown not to be involved in the formation of 6, but the results were consistent with the involvement of monolithio monomethyl intermediate 11, which could lead to 6 by metal-halogen exchange. Several other lithioalkenes also reacted with MeI to give alkenyl iodides.     

Structural Properties and Stereochemically Distinct Folding Preferences of 4,5‐cis and trans‐Methano‐L‐Proline Oligomers: The Shortest Crystalline PPII‐Type Helical Proline‐Derived Tetramer

The synthesis, structural properties, and folding patterns of a series of L ‐proline methanologues represented by cis‐ and trans‐4,5‐methano‐L ‐proline amides and their oligomers are reported as revealed by X‐ray crystallography, circular dichroism measurements, and DFT calculations. We disclose the first example of a crystalline tetrameric proline congener to exhibit a polyproline II helical conformation. Experimental evidence of PPII‐type helical arrangement (both in solution and in the solid state) of cis‐4,5‐methano‐L ‐proline oligomers is supported by theoretical calculations reflecting the extent of n→π* stabilization of the trans‐amide conformation.     

键能的分子轨道理论研究2: 键能与Mulliken布居对键强度的 判断的比较

用键能E~A~B和Mulliken布居对化学键强度的判别进行了分析比较。结果表明,键能判据比Mulliken布居判据所得结论更符合实际情况。作为衡量原子间化学键强度的尺度,不仅应考虑原子轨道间的布居因素,还应考虑分子轨道(或原子轨道)的能量因素。     

Ab initio study of the rotational energy barrier in carbonylylide

The rotational energy barrier in carbonylylide CH₂OCH₂ is studied using RHF CI calculations. Depending on the size of the CI and the basis set (STO-3G and 4–31G), values in the range 13–17 $\text{kcal}\text{mol}$ are found. At this level of calculation, the mid-point of the isomerization process can be mainly described by the diradical rather than the zwitterion.     

Chemical interpretation of molecular electron density distributions

In this study, the two small molecules HS(CH)(CH(2)), 1, and F(CH)(4)F, 2, are presented, which yield different chemical interpretations when one and the same density is interpreted either by means of Natural Bond Orbital and subsequent Natural Resonance Theory application or by the Quantum Theory of Atoms In Molecules. The first exhibits a S-C bond in the orbital based approach, whereas the density based Quantum Theory of Atoms In Molecules detects no corresponding bond. In F(CH)(4)F a F...F bond is detected in the density based approach, whereas in the orbital based approach no corresponding bond is found. Geometrical reasons for the presence of unexpected and the absence of expected bond critical points are discussed.     

Theoretical and Structural Analysis of Long CC Bonds in the Adducts of Polycyanoethylene and Anthracene Derivatives and Their Connection to the Reversibility of Diels–Alder Reactions

X‐ray structure determinations on four Diels–Alder adducts derived from the reactions of cyano‐ and ester‐substituted alkenes with anthracene and 9,10‐dimethylanthracene have shown the bonds formed in the adduction to be particularly long. Their lengths range from 1.58 to 1.62 Å, some of the longest known for Diels–Alder adducts. Formation of the four adducts is detectably reversible at ambient temperature and is associated with free energies of reaction ranging from ?2.5 to ?40.6 kJ mol^?1. The solution equilibria have been experimentally characterised by NMR spectroscopy. Density‐functional‐theory calculations at the MPW1K/6‐31+G(d,p) level with PCM solvation agree with experiment with average errors of 6 kJ mol^?1 in free energies of reaction and structural agreement in adduct bond lengths of 0.013 Å. To understand more fully the cause of the reversibility and its relationship to the long adduct bond lengths, natural‐bond‐orbital (NBO) analysis was applied to quantify donor–acceptor interactions within the molecules. Both electron donation into the σ*‐anti‐bonding orbital of the adduct bond and electron withdrawal from the σ‐bonding orbital are found to be responsible for this bond elongation.     

Theoretical model of internal rotation in monosubstituted derivatives of furfural

The present work explores the effect of substitution in all free positions of furfural on conformational preferences of formyl group by using ab-initio calculations at the MP2/6-31G(p,d) level of theory. Theoretical modeling was made in vacuo. The selected substituents were -CH(3), NH(2), NO(2) and F groups in 3, 4, 5 and ipso carbonyl positions. Geometries of all derivatives were analyzed and it is ascertained that substitution has not important consequences on furan ring geometry. Differences of energy between OO-cis and trans conformers and energy barriers between them are described and extreme cases are explained. Interesting features appear in the cases of -NH(2) and -NO(2) groups, and particularly when the 3 and ipso carbonyl positions are substituted. Variations in energy barriers are correlated with variations in C2-C6 distances for the transition states and planar forms. Substitution effect on Mülliken charges are analyzed and related with internal rotation energy barriers and differences between conformers.     

Intramolecular Natural Energy Decomposition Analysis: Applications to the Rational Design of Foldamers

We describe an intramolecular version of the natural energy decomposition analysis (NEDA), with the aim of evaluating interactions between molecular fragments across covalent bonds. The electronic energy in intramolecular natural energy decomposition analysis (INEDA) is divided into electrical, core, and charge transfer components. The INEDA method describes the fragments using the nonfragmented electronic density, and, therefore, there are no limitations in how to choose the boundary orbital. We used INEDA to evaluate the interaction energies that give origin to barriers of rotation around C_amide C_aromatic (C_am C_ar) and N_amide C_aromtaic (N_am C_ar) bonds in arylamide‐foldamer building blocks. We found that differences of barrier height between models with different ortho‐aryl substituents stem from charge transfer and core interactions. In three‐center hydrogen‐bond (H‐bond) models with an NH proton donor H‐bound to two electronegative ortho‐aryl substituents, the interaction energy of the three‐center system is larger than in either of the two‐center H‐bond subsystem alone, indicating an increase of overall rigidity. The combination of INEDA and NEDA allows the evaluation of intermolecular and intramolecular interactions using a consistent theoretical framework. © 2018 Wiley Periodicals, Inc.     

Sulfur Tetrahydride and Allied Superhydride Clusters: When Resonance Takes Precedence

Sulfur offers a variety of bonding surprises compared to the parent oxygen atom of the chalcogen family. In the present work, we employ standard quantum chemistry methods to characterize formation of previously unrecognized sulfur tetrahydride (C_4v-symmetric SH₄) from hydrogen sulfide (H₂S) and molecular hydrogen (H₂) on the ground state potential energy surface. The unusual intramolecular interactions of SH₄ defy Lewis-like bonding conceptions, exhibiting the dominance of resonance-type donor-acceptor delocalizations well beyond those of SF₄ (C_2v sawhorse geometry) and other known tetrahalides. The distressed character of SH₄ bonding also leads to exotic intermolecular structural motifs in clusters of pure (SH₄)_n and mixed (SH₄⋅⋅⋅H₂S)_n composition. We evaluate structural, spectroscopic, and electronic properties for various 2D/3D coordination patterns and discuss how (SH₄⋅⋅⋅H₂S)_n-type building blocks may relate to recent experimental studies of superconductivity in high-pressure materials of “SH₃” stoichiometry.     

Theoretical Insights into the Mechanism of Carbon Monoxide (CO) Release from CO‐Releasing Molecules

We used density functional theory to investigate the capacity for carbon monoxide (CO) release of five newly synthesized manganese‐containing CO‐releasing molecules (CO‐RMs), namely CORM‐368 ( 1 ), CORM‐401 ( 2 ), CORM‐371 ( 3 ), CORM‐409 ( 4 ), and CORM‐313 ( 5 ). The results correctly discriminated good CO releasers ( 1 and 2 ) from a compound unable to release CO ( 5 ). The predicted Mn? CO bond dissociation energies were well correlated (R²≈0.9) with myoglobin (Mb) assay experiments, which quantified the formation of MbCO, and thus the amount of CO released by the CO‐RMs. The nature of the Mn? CO bond was characterized by natural bond orbital (NBO) analysis. This allowed us to identify the key donor–acceptor interactions in the CO‐RMs, and to evaluate the Mn? CO bond stabilization energies. According to the NBO calculations, the charge transfer is the major source of Mn? CO bond stabilization for this series. On the basis of the nature of the experimental buffers, we then analyzed the nucleophilic attack of putative ligands (L′=HPO₄^2?, H₂PO₄^?, H₂O, and Cl^?) at the metal vacant site through the ligand‐exchange reaction energies. The analysis revealed that different L′‐exchange reactions were spontaneous in all the CO‐RMs. Finally, the calculated second dissociation energies could explain the stoichiometry obtained with the Mb assay experiments.     

A method to calculate the weights of nbo electronic structures from Moffitt's theorem

A method is presented allowing the calculation of the weights of Natural Bond Orbital (NBO) electronic structures, providing the probabilities to find simultaneously electrons and electron pairs in various types of bond orbitals. The MO wave function is assumed to be known, and can be of any type (e.g., uncorrelated or correlated). The used transformation process of the initial MO wave function and Moffitt's theorem are combined so that the calculation of the weights does not involve any approximation. The method is general, holding for any system and for any type of NBOs, but the chemical interpretation is more conveniant for systems having one dominant Lewis structure. The methylamine molecule in minimal, double zeta, and double zeta plus polarization basis sets is considered as an example to illustrate the method. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 306–315, 2001     

Lagrange function method for energy optimization directly in the space of natural orbitals

We propose a Lagrange method to obtain the electronic energy directly in the space of natural orbitals. The Lagrange function contains constraints to force the off‐diagonal elements of the one‐particle density matrix to zero, so the molecular orbitals converge to the natural orbitals simultaneously while the energy minimizes. The recently discovered “generalized Pauli conditions” for the occupation numbers are invoked to generate an initial approximation. As a demonstration of this approach, we study the system of three electrons in six orbitals which has become a paradigm for investigating multi‐particle entanglement.