Understanding glycine conformation through molecular orbitals

The four most stable C(s) conformers of glycine have been investigated using a variety of quantum-mechanical methods based on Hartree-Fock theory, density-functional theory (B3LYP and statistical average of orbital potential), and electron propagation (OVGF) treatments. Information obtained from these models were analyzed in coordinate and momentum spaces using dual space analysis to provide insight based on orbitals into the bonding mechanisms of glycine conformers, which are generated by rotation of C-O(H) (II), C-C (III), and C-N (IV) bonds from the global minimum structure (I). Wave functions generated from the B3LYP/TZVP model revealed that each rotation produced a unique set of fingerprint orbitals that correspond to a specific group of outer valence orbitals, generally of a' symmetry. Orbitals 14a', 13a', 12a', and 11a' are identified as the fingerprint orbitals for the C-O(H) (II) rotation, whereas fingerprint orbitals for the C-C (III) bond rotation are located as 16a' [highest occupied molecular orbital (HOMO)], 15a' [next highest molecular occupied molecular orbital (NHOMO)], 14a', and 12a' orbitals. Fingerprint orbitals for IV generated by the combined rotations around the C-C, C-O(H), and C-N bonds are found as 16a', 15a', 14a', 13a', and 11a', as well as in orbitals 2a" and 1a". Orbital 14a' is identified as the fingerprint orbital for all three conformational processes, as it is the only orbital in the outer valence region which is significantly affected by the conformational processes regardless rotation of which bond. Binding energies, molecular geometries, and other molecular properties such as dipole moments calculated based on the specified treatments agree well with available experimental measurements and with previous theoretical calculation.     

6‐31G* basis set for third‐row atoms

Medium basis sets based upon contractions of Gaussian primitives are developed for the third‐row elements Ga through Kr. The basis functions generalize the 6‐31G and 6‐31G* sets commonly used for atoms up to Ar. A reexamination of the 6‐31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6‐31G basis for the whole third‐row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split‐valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third‐row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d‐type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor‐phase metal complexes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 976–984, 2001     

Metalmetal bonding trends in mixed-group,face-shared d3d3 bioctahedral dimer systems,M′M″Cl9 n−

The results of density functional theory (DFT) calculations on a set of binuclear nonachloride complexes M′M″Cl₉ ⁴⁻ (M′=V, Nb, Ta; M″=Cr, Mo, W) and M′M″Cl₉ ²⁻ (M′=Cr, Mo, W; M″=Mn, Tc, Re), in which each metal possesses a nominal d³ valence electronic configuration, are reported. When compared with previous studies on same-group dimers (typified by the M′M″Cl₉ ³⁻ complexes of the chromium triad), the present results display an increased tendency for electron donation from M′ to M″. Structural trends evident for the M′M″Cl₉ ⁴⁻ and M′M″Cl₉ ²⁻ series of dimers are remarkably consistent: weak ferromagnetic coupling between M′ and M″ is the most favorable intermetallic interaction when M″ is a first-row transition metal, antiferromagnetic coupling dominates when M′ is first-row but M″ is second- or third-row, and metalmetal triple bond formation generally yields the lowest-energy structure when neither metal is first-row. These structural trends, and other characteristics of the dimers described here, can be satisfactorily rationalized in terms of the tendency for electron transfer from M′ to M″, coupled with effects due to spin polarization and ligand field splitting of the valence d orbitals on M′ and M″.     

A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.     

Nature of the water/aromatic parallel alignment interactions

The water/aromatic parallel alignment interactions are interactions where the water molecule or one of its O? H bonds is parallel to the aromatic ring plane. The calculated energies of the interactions are significant, up to ΔE_{CCSD(T)(limit)} = ?2.45 kcal mol^?1 at large horizontal displacement, out of benzene ring and CH bond region. These interactions are stronger than CH···O water/benzene interactions, but weaker than OH···π interactions. To investigate the nature of water/aromatic parallel alignment interactions, energy decomposition methods, symmetry‐adapted perturbation theory, and extended transition state‐natural orbitals for chemical valence (NOCV), were used. The calculations have shown that, for the complexes at large horizontal displacements, major contribution to interaction energy comes from electrostatic interactions between monomers, and for the complexes at small horizontal displacements, dispersion interactions are dominant binding force. The NOCV‐based analysis has shown that in structures with strong interaction energies charge transfer of the type π → σ*(O? H) between the monomers also exists. © 2014 Wiley Periodicals, Inc.     

Molecular states of atoms. I. Orbital energy parameters

Atomic valence state energies are analyzed to obtain values of orbital energy parameters that may be used in semiempirical molecular orbital calculations. Difficulty in defining the interaction between orbitals with non-integer electron populations is systematically avoided by distinguishing between a valence state and a molecular state of an atom, only the latter state having non-integer spin paired orbital occupancy. Application of the virial theorem to the molecular state enables a value for the orbital kinetic energy to be obtained from the valence state orbital energy parameters once an arbitrary configuration is defined as reference. The orbitals then are eigenfunctions of the atomic Fock operator for that reference molecular state and, with their energy parameters, may be employed as a fixed basis set for molecular orbital calculations.     

Electronic Structure Trends in N‐Heterocyclic Carbenes (NHCs) with Varying Number of Nitrogen Atoms and NHC?Transition‐Metal Bond Properties

Carbenes derived from five‐membered heterocycles with different numbers of nitrogen atoms ranging from two to four lead formally either to normal N‐heterocyclic or mesoionic carbenes with, in some cases, the same skeletal structure. The electronic structures of fourteen of these compounds were examined by means of DFT calculations at the B3LYP/aug‐cc‐pVTZ level. The examined parameters include the energies of the σ‐lone pair at C_carbene and the π‐HOMO of the protonated form, which are correlated to the first and second proton affinities. The singlet–triplet energy gap was used as a measure of the stability of the N‐heterocyclic carbene (NHC) towards dimerisation. Natural population analysis provided insight into the variation of the p_π population and the natural charge at C_carbene with NHC structure. Additionally, the transition metal? NHC bond in L‐AuCl and L‐TiCl₄ and the nature of the orbital interactions between the NHC and the transition‐metal fragment were analysed in detail by the extended transition state–natural orbitals for chemical valence (ETS–NOCV) approach at the BP86/TZ2P level. Similarities and differences between the NHC? gold and the NHC? titanium bond are discussed, and trends in key bonding properties can be traced back to the variation of the electronic parameters of the NHC.     

Symmetry and bonding in metalloporphyrins. A modern implementation for the bonding analyses of five- and six-coordinate high-spin iron(III)-porphyrin complexes through density functional calculation and NMR spectroscopy

Bonding interactions between the iron and the porphyrin macrocycle of five- and six-coordinate high-spin iron(III)-porphyrin complexes are analyzed within the framework of approximate density functional theory with the use of the quantitative energy decomposition scheme in combination with removal of the vacant pi orbitals of the porphyrin from the valence space. Although the relative extent of the iron-porphyrin interactions can be evaluated qualitatively through the spin population and orbital contribution analyses, the bond strengths corresponding to different symmetry representations can be only approximated quantitatively by the orbital interaction energies. In contrast to previous suggestions, there are only limited Fe --> P pi back-bonding interactions in high-spin iron(III)-porphyrin complexes. It is the symmetry-allowed bonding interaction between d(z)2 and a(2u) orbitals that is responsible for the positive pi spin densities at the meso-carbons of five-coordinate iron(III)-porphyrin complexes. Both five- and six-coordinate complexes show significant P --> Fe pi donation, which is further enhanced by the movement of the metal toward the in-plane position for six-coordinate complexes. These bonding characteristics correlate very well with the NMR data reported experimentally. The extraordinary bonding interaction between d(z)2 and a(2u) orbitals in five-coordinate iron(III)-porphyrin complexes offers a novel symmetry-controlled mechanism for spin transfer between the axial ligand sigma system and the porphyrin pi system and may be critical to the electron transfer pathways mediated by hemoproteins.     

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.     

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.     

On the nature of spin- and orbital-resolved Cu+–NO charge transfer in the gas phase and at Cu(I) sites in zeolites

Electronic factors essential for NO activation by Cu(I) sites in zeolites are investigated within spin-resolved analysis of electron transfer channels (natural orbitals for chemical valence). NOCV analysis is performed for three DFT-optimized models of Cu(I)?CNO site in ZSM-5: [CuNO]⁺, (T1)CuNO, and (M7)CuNO. NO as a non-innocent, open-shell ligand reveals significant differences between independent deformation density components for ?? and ?? spins. Four distinct components are identified: (i) unpaired electron donation from NO ??_??* antibonding orbital to Cu_s,d; (ii) backdonation from copper d _yz to ??_??* antibonding orbital; (iii) donation from occupied ??_?? and Cu d _xz to bonding region, and (iv) donation from nitrogen lone-pair to Cu_s,d. Channel (i), corresponding to one-electron bond, shows-up solely for spin majority and is effective only in the interaction of NO with naked Cu⁺. Channel (ii) dominates for models b and c: it strongly activates NO bond by populating antibonding ??* orbital and weakens the N?CO bond in contrast to channel (i), depopulating the antibonding orbital and strengthening N?CO bond. This picture perfectly agrees with IR experiment: interaction with naked Cu⁺ imposes small blue-shift of NO stretching frequency while it becomes strongly red-shifted for Cu(I) site in ZSM-5 due to enhanced backdonation.     

Carbodicarbene: geminal-Bimetallic Coordination in Selective Manner

The reaction of Pd(OAc)₂ with free carbodicarbene (CDC) generates a Pd acetate trinuclear complex 1 via intramolecular C(sp³)−H bond activation at one of the CDC methyl side arms. The solid structure of 1 reveals the capability of CDC to facilitate a double dative bond with two palladium centers in geminal fashion. This is attributed to the chelating mode of CDC, which can frustrate π-conjugation within the CDC framework. Such effect maybe also amplified by ligand-ligand interaction. The formation of other gem-bimetallic Pd−Pd, Pd−Au, and Ni−Au provides further structural evidence for this proof-of-concept in selective installation. Structural analysis is supported by computational calculations based on state-of-the-art energy decomposition analysis (EDA) in conjunction with natural orbitals for chemical valence (NOCV) method.     

Bond orders between molecular fragments

An extension of the Mayer bond order for the interaction between molecular fragments is presented. This approach allows the classical chemical concepts of bond order and valence to be utilised for fragments and the interactions between the fragments and symmetry-adapted linear combinations to be analysed. For high-symmetry systems, the approach allows the contribution from each irreducible representation to be assessed and provides a semiquantitative measure of the role of each bonding mode to interfragment interactions. The utility of this tool has been examined by a study of the bonding in symmetrical sandwich complexes. The validity of the frontier-orbital approach and the contributions from each frontier-orbital interaction can also be assessed within this model. As demonstrated by a study of a number of mixed-sandwich complexes, the model proves to be especially useful for low-symmetry systems in which separation of the sigma, pi and delta roles in bonding of the ligand is difficult to assess. The fragment bond order describes the interaction between preoptimized fragment orbitals and is independent of the charges that are placed on these fragments. Although the method allows the chemist to define fragments in any way they choose, most insight is gained by using the same frontier orbitals employed so successfully in perturbational molecular-orbital approaches. The results are free from the influence of the electron-counting method used to describe fragments, such as the rings and metals in sandwich complexes.     

The nature of the chemical bond in UO2

The nature of the chemical bond in UO₂ was analyzed taking into account the X-ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO₈ (D_4h) cluster, reflecting uranium's close environment in UO₂, and the U₁₃O₅₆ and U₆₃O₂₁₆ clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO₂ single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO₂ are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO₂ was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO₈ and by 25% in U₆₃O₂₁₆.     

Ab initio study of the singlet-triplet splitting in reduced polyoxometalates

A valence bond analysis of the wave function of doubly reduced polyoxometales is presented, using the M₆O₁₉ Lindqvist structure as test case. By a unitary transformation of the delocalised valence orbitals to localised metal centred orbitals, the multiconfigurational wave function is mapped onto a valence bond function with three different types of configurations: the two electrons are on the same site, on neighbouring sites, or on next-nearest neighbour sites. The inspection of the relative weights of these configurations for triplet and singlet state shows that the triplet-coupled electrons are confined to a smaller volume, and hence have a higher energy than the singlet-coupled electrons. This is in line with the experimental observation that the doubly reduced polyoxometalates show non-mangetic behaviour.     

The generalized Slater–Condon rules

By relating the blocking structure of the relevant matrix of overlap-integrals to its cofactors, the Slater–Condon rules for the evaluation of an element of a matrix representation of an electronic Hamiltonian in a Slater determinant basis are generalized to the case where not all orbitals are orthogonal. This yields a set of 33 rules, which allows for an efficient implementation of the valence bond theory.