Bond electron pair: Its relevance and analysis from the quantum chemistry point of view

Dinitrogen Activation Mediated by the (P2PPh)Fe Complex: Electronic Structure, Dimerization Mechanism, and Magnetic Coupling

Herein, we report the estimation of the extent of dinitrogen activation by different charged and structural forms of (P2PPh)Fe biomimetic catalysts, which, in the presence of light, exhibit significant yield in the N2-to-NH3 conversion. Complete active space self-consistent field (CASSCF) calculations have been used to determine the electronic structure of different reduced forms of the mononuclear complexes: the neutral (P2PPh)Fe(N2)2 adduct and the anionic [(P2PPh)Fe(N2)]- and [(P2PPh)Fe(N2)]2- complexes. These calculations also revealed that the extent of reduction of a dinitrogen molecule reaches up to one electron (N21-) due to the back-bonding from the Fe center, in agreement with the changes observed in the vibration frequency of the N-N bond in these complexes. In addition, the energy profile of the dimerization of the mononuclear (P2PPh)Fe(N2)2 complex to the dinuclear mono-N2-bridged [(P2PPh)Fe]2(μ-N2) complex has been determined by means of density functional theory (DFT) calculations. A three-step mechanism has been proposed for the dimerization, favored by both kinetics and thermodynamics criteria. Finally, the magnetic coupling constant in the diiron (μ-N2) complex is estimated from CASSCF/NEVPT2 calculations. Such a dinuclear complex presents a strong antiferromagnetic coupling resulting from the interaction between two S = 1 d6 Fe2+ ions, bridged by a highly activated dinitrogen molecule (N22-) with two electrons on the π* orbitals.

Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations

In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.

How reduced are nucleophilic gold complexes?

Nucleophilic formal gold(-I) and gold(I) complexes are investigated via Intrinsic Bond Orbital analysis and Energy Decomposition Analysis, based on density functional theory calculations. The results indicate gold(0) centres engaging in electron-sharing bonding with Al- and B- based ligands. Multiconfigurational (CASSCF) calculations corroborate the findings, highlighting the gap between the electonic structures and the oxidation state formalism.

Spin polarization as an electronic cooperative effect

Taking as an example the simple CH₃ radical, this work demonstrates the cooperative character of the spin-polarization phenomenon of the closed-shell core in free radicals. Spin polarization of CH σ bonds is not additive here, as spin polarization of one bond enhances that of the next bond. This cooperativity is demonstrated by a series of configuration interaction calculations converging to the full valence limit and is rationalized by analytic developments. The same phenomenon is shown to take place in those diradicals where spin polarization plays a major role, as illustrated in square planar carbo-cyclobutadiene C₁₂H₄. The treatment of cooperativity represents a challenge for usual post-Hatree-Fock methods.

The maximum occupancy condition for the localized property-optimized orbitals

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

Nonclassical Single-State Reactivity of an Oxo-Iron(IV) Complex Confined to Triplet Pathways

C-H bond activation mediated by oxo-iron (IV) species represents the key step of many heme and nonheme O₂-activating enzymes. Of crucial interest is the effect of spin state of the Fe^IV(O) unit. Here we report the C-H activation kinetics and corresponding theoretical investigations of an exclusive tetracarbene ligated oxo-iron(IV) complex, [L^NHCFe^IV(O)(MeCN)]²⁺ (1). Kinetic traces using substrates with bond dissociation energies (BDEs) up to 80 kcal mol^-1 show pseudo-first-order behavior and large but temperature-dependent kinetic isotope effects (KIE 32 at -40 °C). When compared with a topologically related oxo-iron(IV) complex bearing an equatorial N-donor ligand, [L^TMCFe^IV(O) (MeCN)]²⁺ (A), the tetracarbene complex 1 is significantly more reactive with second order rate constants k'₂ that are 2-3 orders of magnitude higher. UV-vis experiments in tandem with cryospray mass spectrometry evidence that the reaction occurs via formation of a hydroxo-iron(III) complex (4) after the initial H atom transfer (HAT). An extensive computational study using a wave function based multireference approach, viz. complete active space self-consistent field (CASSCF) followed by N-electron valence perturbation theory up to second order (NEVPT2), provided insight into the HAT trajectories of 1 and A. Calculated free energy barriers for 1 reasonably agree with experimental values. Because the strongly donating equatorial tetracarbene pushes the Fe-d_x²-y² orbital above d_z², 1 features a dramatically large quintet-triplet gap of ∼18 kcal/mol compared to ∼2-3 kcal/mol computed for A. Consequently, the HAT process performed by 1 occurs on the triplet surface only, in contrast to complex A reported to feature two-state-reactivity with contributions from both triplet and quintet states. Despite this, the reactive Fe^IV(O) units in 1 and A undergo the same electronic-structure changes during HAT. Thus, the unique complex 1 represents a pure "triplet-only" ferryl model.

Magnetic Circular Dichroism Evidence for an Unusual Electronic Structure of a Tetracarbene-Oxoiron(IV) Complex

In biology, high valent oxo-iron(IV) species have been shown to be pivotal intermediates for functionalization of C-H bonds in the catalytic cycles of a range of O₂-activating iron enzymes. This work details an electronic-structure investigation of [Fe^IV(O)(L^NHC)(NCMe)]²⁺ (L^NHC = 3,9,14,20-tetraaza-1,6,12,17-tetraazoniapenta-cyclohexacosane-1(23),4,6(26),10,12(25),15,17(24),21-octaene, complex 1) using helium tagging infrared photodissociation (IRPD), absorption, and magnetic circular dichroism (MCD) spectroscopy, coupled with DFT and highly correlated wave function based multireference calculations. The IRPD spectrum of complex 1 reveals the Fe-O stretching vibration at 832 ± 3 cm^-1. By analyzing the Franck-Condon progression, we can determine the same vibration occurring at 616 ± 10 cm^-1 in the E(d_xy → d_xz,yz) excited state. Both values are similar to those measured for [Fe^IV(O)(TMC)(NCMe)]²⁺ (TMC = 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane). The low-temperature MCD spectra of complex 1 exhibit three pseudo A-term signals around 12 500, 17 000, and 24 300 cm^-1. We can unequivocally assign them to the ligand field transitions of d_xy → d_xz,yz, d_xz,yz → d_z2, and d_xz,yz → d_x2-y2, respectively, through direct calculations of MCD spectra and independent determination of the MCD C-term signs from the corresponding electron donating and accepting orbitals. In comparison with the corresponding transitions observed for [Fe^IV(O) (SR-TPA)(NCMe)]²⁺ (SR-TPA = tris(3,5-dimethyl-4-methoxypyridyl-2-methy)amine), the excitations within the (FeO)²⁺ core of complex 1 have similar transition energies, whereas the excitation energy for d_xz,yz → d_x2-y2 is significantly higher (∼12 000 cm^-1 for [Fe^IV(O)(SR-TPA)(NCMe)]²⁺). Our results thus substantiate that the tetracarbene ligand (L^NHC) of complex 1 does not significantly affect the bonding in the (FeO)²⁺ unit but strongly destabilizes the d_x2-y2 orbital to eventually lift it above d_z2. As a consequence, this unusual electron configuration leads to an unprecedentedly larger quintet-triplet energy separation for complex 1, which largely rules out the possibility that the H atom transfer reaction may take place on the quintet surface and hence quenches two-state reactivity. The resulting mechanistic implications are discussed.

Highly efficient perturbative + variational strategy based on orthogonal valence bond theory for the evaluation of magnetic coupling constants. Application to the trinuclear Cu(ii) site of multicopper oxidases

A new perturbative + variational strategy: a low-cost, quantitative and rational evaluation of the magnetic coupling constant in complex systems.

Magnetic circular dichroism and computational study of mononuclear and dinuclear iron(IV) complexes

High-valent iron(IV)-oxo species are key intermediates in the catalytic cycles of a range of O2-activating iron enzymes. This work presents a detailed study of the electronic structures of mononuclear ([FeIV(O)(L)(NCMe)]2+, 1, L = tris(3,5-dimethyl-4-methoxylpyridyl-2-methyl)amine) and dinuclear ([(L)FeIV(O)(μ-O)FeIV(OH)(L)]3+, 2) iron(IV) complexes using absorption (ABS), magnetic circular dichroism (MCD) spectroscopy and wave-function-based quantum chemical calculations. For complex 1, the experimental MCD spectra at 2-10 K are dominated by a broad positive C-term band between 12000 and 18000 cm-1. As the temperature increases up to ~20 K, this feature is gradually replaced by a derivative-shaped signal. The computed MCD spectra are in excellent agreement with experiment, which reproduce not only the excitation energies and the MCD signs of key transitions but also their temperature-dependent intensity variations. To further corroborate the assignments suggested by the calculations, the individual MCD sign for each transition is independently determined from the corresponding electron donating and accepting orbitals. Thus, unambiguous assignments can be made for the observed transitions in 1. The ABS/MCD data of complex 2 exhibit ten features that are assigned as ligand-field transitions or oxo- or hydroxo-to-metal charge transfer bands, based on MCD/ABS intensity ratios, calculated excitation energies, polarizations, and MCD signs. In comparison with complex 1, the electronic structure of the FeIV=O site is not significantly perturbed by the binding to another iron(IV) center. This may explain the experimental finding that complexes 1 and 2 have similar reactivities toward C-H bond activation and O-atom transfer.

Chemical bonding: the orthogonal valence-bond view

Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbitals (MO) used to construct the wave functions. The transformation of such wave functions into valence bond (VB) wave functions, which are based on localized orbitals, reveals the hidden information; this transformation is called a VB reading of MCSCF wave functions. The two-electron VB wave functions describing the Lewis electron pair that connects two atoms are frequently called covalent or neutral, suggesting that these wave functions describe an electronic situation where two electrons are never located at the same atom; such electronic situations and the wave functions describing them are called ionic. When the distance between two atoms decreases, however, every covalent VB wave function composed of non-orthogonal atomic orbitals changes its character from neutral to ionic. However, this change in the character of conventional VB wave functions is hidden by its mathematical form. Orthogonal VB wave functions composed of orthonormalized orbitals never change their character. When localized fragment orbitals are used instead of atomic orbitals, one can decide which local information is revealed and which remains hidden. In this paper, we analyze four chemical reactions by transforming the MCSCF wave functions into orthogonal VB wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry. Using orthogonal instead of non-orthogonal orbitals is not just a technical issue; it also changes the interpretation, revealing the properties of wave functions that remain otherwise undetected.

Electronic structure aspects of the complete O2 transfer reaction between Ni(II) and Mn(II) complexes with cyclam ligands

This work explores the electronic structure aspects involving the complete intermolecular O2 transfer between Ni(ii) and Mn(ii) complexes, both containing N-tetramethylated cyclams (TMC). The energy of the low-lying states of reactants, intermediates and products is established at the CASSCF level and also the DDCI level when possible. The orthogonal valence bond analysis of the wave functions obtained from CASSCF and DDCI calculations indicates the dominant superoxide nature of all the adducts participating in the reaction, and consequently that the whole reaction can be described as the transfer of the superoxide O2(-) between Ni(ii) and Mn(ii) complexes, without any additional change in the electronic structure of the fragments.

Case of a strong antiferromagnetic exchange coupling induced by spin polarization of a Mn-Mn partial single bond

The large antiferromagnetic coupling in the Mn(IV)-Mn(IV) bond in the Li(6)Ca(2)[Mn(2)N(6)] and Li(6)Sr(2)[Mn(2)N(6)] crystals (J = -739 and -478 cm(-1), respectively, with H = -JS(A)·S(B)) is studied using different theoretical methods: solid-state density functional theory calculations, molecular density functional theory, and post-Hartree-Fock calculations with large embeddings. This magnetic coupling is a challenge for theoretical methods because both correlation and polarization effects are crucial for the correct description of the bond. All methods predict a large antiferromagnetic coupling, but none of the considered methods give a quantitative agreement with the experimental values. The molecular methods, except B3LYP and CASPT2, underestimate the coupling for the calcium compound, while they overestimate it in the strontium compound, within 30%. These methods, on the other hand, strongly underestimate the decrease of the coupling between the two compounds, with the most correlated one predicting the same value for both compounds. The solid-state method overestimates the coupling within 60% but reproduces better their ratio. Analysis of the calculations shows that the magnetic coupling between the local π orbitals is not caused by a direct interaction but by the spin-polarized σ bond.

Energy decomposition analysis based on a block-localized wavefunction and multistate density functional theory

An interaction energy decomposition analysis method based on the block-localized wavefunction (BLW-ED) approach is described. The first main feature of the BLW-ED method is that it combines concepts of valence bond and molecular orbital theories such that the intermediate and physically intuitive electron-localized states are variationally optimized by self-consistent field calculations. Furthermore, the block-localization scheme can be used both in wave function theory and in density functional theory, providing a useful tool to gain insights on intermolecular interactions that would otherwise be difficult to obtain using the delocalized Kohn-Sham DFT. These features allow broad applications of the BLW method to energy decomposition (BLW-ED) analysis for intermolecular interactions. In this perspective, we outline theoretical aspects of the BLW-ED method, and illustrate its applications in hydrogen-bonding and π-cation intermolecular interactions as well as metal-carbonyl complexes. Future prospects on the development of a multistate density functional theory (MSDFT) are presented, making use of block-localized electronic states as the basis configurations.

Role of charge transfer configurations in LaMnO3, CaMnO3, and CaFeO3

A simple scheme is proposed to analyze the N-electron wave function obtained in embedded cluster calculations in valence bond terms such as ligand-to-metal charge transfer and non-charge-transfer determinants. The analysis is based on a unitary transformation of pairs of natural orbitals to optimal atomiclike orbitals. The procedure is applied to compare the degree of ionicity in NiO and MnO and to explain the existence or absence of Jahn-Teller distortions in LaMnO3, CaMnO3, and CaFeO3. The authors find that the ground state of LaMnO3 is dominated by non-charge-transfer configurations, whereas the charge transfer configurations dominate the ground state wave function in the other two perovskites.