We analyze with DFT calculations the charge effects on the reactivity of the polycationic Compound I (Cpd I) and Compound II (Cpd II) mimics experimentally investigated by Bell and Groves (Bell, S. R.; Groves, J. T. J. Am. Chem. Soc. 2009, 131, 9640). Specifically, we consider the Cpd I model [(4-THPyP)•+(H2O)FeIV═O]5+ (THPyP = 5,10,15,20-tetrakis(N-hydro-4-pyridinium) porphyrinate), 1H2O, and its Cpd II counterparts [(4-THPyP)FeIV═O]4+, 2, and [(4-THPyP)(H2O)FeIV═O]4+, 2H2O. In gas phase simulations it is found that all positive charges enhance the reactivity. According to a detailed electronic structure analysis in the gas phase of the reactant complexes en route to the transition state, the positive charges stabilize the electron acceptor orbital (EAO) of the catalyst more than the electron donor orbital (EDO) of the substrate, thereby reducing the energy gap between these orbitals and, hence, the H-abstraction barrier. The effect of the peripheral charges residing on the pyridinium groups is dampened in water solution by screening effects of the solvent. However, the effect of the positive charge residing on the porphyrin ring of the Cpd I mimic is not much diminished by the solvent. The well-known stronger oxidizing capability of Cpd I mimics relative to their Cpd II counterparts is ascribed to the effect on the frontier orbitals of the positive charge on the ring, rather than to the presence of a hole per se.Keywords: cationic oxoiron(IV) porphyrins; charge effects on reactivity; Cpd I and Cpd II mimics; C−H bond activation; density functional calculations; heme iron enzymes; oxidation catalysis

The electronic structure explanation of H abstraction from aliphatic CH bonds by the ferryl ion, FeIVO2+, has received a great deal of attention. We review the insights that have been gained, in particular into the effect of the spin state. However, we emphasize that the spin state is dictated by the field of the ligands coordinated to the Fe ion and is but one of the effects of the ligand field. Using the model systems [FeO(H2O)5]2+, representative of the weak field situation, and [FeO(H2O)ax(NH3)4]2+, representative of a strong (equatorial) field, we distinguish the effect of spin state (high spin (quintet) versus low spin (triplet)) from other effects, notably the orbital interaction (pushing up) effect of the ligand donor orbitals and the electron-donating ability of the ligands, directly affecting the charge on the FeO group. We describe the changes in electronic structure during the reaction with the help of elementary orbital interaction diagrams involving the frontier orbitals. These give a straightforward electronic structure picture of the reaction but do not provide support for the description of the reactivity of FeO2+ as starting with oxyl radical formation.Keywords: DFT calculations; H abstraction; high-spin low-spin; ligand field effects; nonheme iron−oxo complexes; oxidation catalysis

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn–Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn–Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn–Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn–Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree–Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the “band gap” in molecules: the HOMO–LUMO gap is close to the first excitation energy (the optical gap).

The basis set superposition effect (BSSE) is a simple concept, and its validity is almost universally accepted. So is the counterpoise method to correct for it. The idea is that the basis set is biased toward the dimer because each monomer in the dimer can “use” the basis functions on the other monomer, which it cannot in a simple monomer calculation. This hypothesis can only be tested if basis set free benchmark numbers are available for monomers and dimer. We are testing the hypothesis on a few systems (in this paper Be2) that are small enough that sufficiently accurate benchmark numbers (basis set free, or close to basis set limit; full CI or close to full CI) are available or can be obtained. We find that the answer to the title question is negative: the standard basis sets of quantum chemistry appear to be biased toward the atom in the sense that basis set errors are larger for the dimer than the monomer. Applying the counterpoise correction increases the imbalance by reducing the already smaller basis set error of the monomer even further. Counterpoise corrected bond energies then deviate more from the basis set limit numbers than uncorrected bond energies. These conclusions hold both at the Hartree–Fock level and (much stronger) at the correlated (CCSD(T), full CI) levels. So the answer to the title question is No.

Enantiomeric excess (ee) in asymmetric catalysis may be strongly dependent on the solvent. The reaction product may range from an almost racemic mixture to an ee of over 90% for different solvents. We study this phenomenon for the C–C coupling reaction between nitromethane and benzaldehyde (the Henry reaction) with cinchona thiourea as the catalyst, where solvents that are strong Lewis bases induce a high ee. We show that the effect of the solvent does not consist of a change in the reaction mechanism. Instead, the solvation “prepares” the molecule, which is very flexible, in a specific conformation. The reaction barriers in this conformer are not lower than for other conformers, but are sufficiently differentiated between the enantiomers to give rise to a large ee. It is the strong Lewis basicity of the solvent that leads to the clear preference in solution for the “asymmetric” conformer. Although general rules or predictions for how solvent effects could be harnessed to produce a desired ee in general would be hard to formulate, this study does show that it is in this case (and presumably in many other cases as well) specific solute–solvent interactions rather than effects of the dielectric continuum of the solvent that are the root cause of the solvent effect. This is in agreement with experiment for the Henry reaction.

Solvation effects on chemical reactivity are often rationalized using electrostatic considerations: the reduced stabilization of the transition state results in higher reaction barriers and lower reactivity in solution. We demonstrate that the effect of solvation on the relative energies of the frontier orbitals is equally important and may even reverse the trend expected from purely electrostatic arguments. We consider the H abstraction reaction from methane by quintet [EDTAHn·FeO](n−2)+, (n = 0–4) complexes in the gas phase and in aqueous solution, which we examine using ab initio thermodynamic integration. The variation of the charge of the complex with the protonation of the EDTA ligand reveals that the free energy barrier in gas phase increases with the negative charge, varying from 16 kJ mol–1 for [EDTAH4·FeO]2+ to 57 kJ mol–1 for [EDTAHn·FeO]2–. In aqueous solution, the barrier for the +2 complex (38 kJ mol–1) is higher than in gas phase, as predicted by purely electrostatic arguments. For the negative complexes, however, the barrier is lower than in gas phase (e.g., 45 kJ mol–1 for the −2 complex). We explain this increase in reactivity in terms of a stabilization of the virtual 3σ* orbital of FeO2+, which acts as the dominant electron acceptor in the H-atom transfer from CH4. This stabilization originates from the dielectric screening caused by the reorientation of the water dipoles in the first solvation shell of the charged solute, which stabilizes the acceptor orbital energy for the −2 complex sufficiently to outweigh the unfavorable electrostatic destabilization of the transition-state relative to the reactants in solution.

A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual orbitals, they often describe excited states much more closely as simple orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO orbital energy difference (in Koopmans' frozen orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual orbitals.

Hydroxylation of aliphatic C–H bonds is a chemically and biologically important reaction, which is catalyzed by the oxidoiron group FeO2+ in both mononuclear (heme and nonheme) and dinuclear complexes. We investigate the similarities and dissimilarities of the action of the FeO2+ group in these two configurations, using the Fenton-type reagent [FeO2+ in a water solution, FeO(H2O)52+] and a model system for the methane monooxygenase (MMO) enzyme as representatives. The high-valent iron oxo intermediate MMOHQ (compound Q) is regarded as the active species in methane oxidation. We show that the electronic structure of compound Q can be understood as a dimer of two FeIVO2+ units. This implies that the insights from the past years in the oxidative action of this ubiquitous moiety in oxidation catalysis can be applied immediately to MMOHQ. Electronically the dinuclear system is not fundamentally different from the mononuclear system. However, there is an important difference of MMOHQ from FeO(H2O)52+: the largest contribution to the transition state (TS) barrier in the case of MMOHQ is not the activation strain (which is in this case the energy for the C–H bond lengthening to the TS value), but it is the steric hindrance of the incoming CH4 with the ligands representing glutamate residues. The importance of the steric factor in the dinuclear system suggests that it may be exploited, through variation in the ligand framework, to build a synthetic oxidation catalyst with the desired selectivity for the methane substrate.

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an “achiral” alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.

We present a combined experimental and computational investigation of the vibrational absorption (VA) and vibrational circular dichroism (VCD) spectra of [1,1′-binaphthalene]-2,2′-diol. First, the sensitive dependence of the experimental VA and VCD spectra on the solvent is demonstrated by comparing the experimental spectra measured in CH2Cl2, CD3CN, and DMSO-d6 solvents. Then, by comparing calculations performed for the isolated solute molecule to calculations performed for molecular complexes formed between solute and solvent molecules, we identify three main types of perturbations that affect the shape of the VA and VCD spectra when going from one solvent to another. These sources of perturbations are (1) perturbation of the Boltzmann populations, (2) perturbation of the electronic structure, and (3) perturbation of the normal modes.

In the oxidation of alcohols with TEMPO as catalyst, the substrate has alternatively been postulated to be oxidized but uncoordinated TEMPO+ (Semmelhack) or Cu-coordinated TEMPO• radical (Sheldon). The reaction with the Cu(bipy)2+/TEMPO cocatalyst system has recently been claimed, on the basis of DFT calculations, to not be a radical reaction but to be best viewed as electrophilic attack on the alcohol C–Hα bond by coordinated TEMPO+. This mechanism combines elements of the Semmelhack mechanism (oxidation of TEMPO to TEMPO+) and the Sheldon proposal (“in the coordination sphere of Cu”). The recent proposal has been challenged on the basis of DFT calculations with a different functional, which were reported to lead to a radical mechanism. We carefully examine the results for the two functionals and conclude from both the calculated energetics and from an electronic structure analysis that the results of the two DFT functionals are consistent and that both lead to the proposed mechanism with TEMPO not acting as radical but as (coordinated) positive ion.

The concept of robustness of rotational strengths of vibrational modes in a VCD spectrum has been introduced as an aid in assignment of the absolute configuration with the help of the VCD spectrum. The criteria for robustness have been based on the distribution around 90° of the angles ξ(i) between electric and magnetic transition dipoles of all the modes i of a molecule. The angles ξ(i) (not, of course, the rotational strengths) are, however, dependent on the choice of origin. The derived criteria are for the center of mass chosen as the origin of the coordinate system. We stress in this note that application of the derived criteria assumes that excessive translation of the coordinate origin is not applied. Although the ξ(i) angles are not very sensitive to the position of the origin, very small displacements (a few Å) are not a problem, excessive translation of the origin does have considerable effect on the ξ(i) angles. In this note we quantify this effect and demonstrate how the distribution of ξ(i) angles is affected. Although it is possible to recalibrate the robustness criteria for the angles for a specific (large) displacement, we recommend that such displacement simply be avoided. It is to be noted that some modeling software does yield output with excessively displaced coordinate origin; this should be checked and corrected.

We study the generation of a dinuclear Fe(IV)oxo species, [EDTAH·FeO·OFe·EDTAH]2−, in aqueous solution at room temperature using Density Functional Theory (DFT) and Ab Initio Molecular Dynamics (AIMD). This species has been postulated as an intermediate in the multi-step mechanism of autoxidation of Fe(II) to Fe(III) in the presence of atmospheric O2 and EDTA ligand in water. We examine the formation of [EDTAH·FeO·OFe·EDTAH]2− by direct cleavage of O2, and the effects of solvation on the spin state and O–O cleavage barrier. We also study the reactivity of the resulting dinuclear Fe(IV)oxo system in CH4 hydroxylation, and its tendency to decompose to mononuclear Fe(IV)oxo species. The presence of the solvent is shown to play a crucial role, determining important changes in all these processes compared to the gas phase. We show that, in water solution, [EDTAH·FeO·OFe·EDTAH]2− (as well as its precursor [EDTAH·Fe·O2·Fe·EDTAH]2−) exists as stable species in a S = 4 ground spin state when hydrogen-bonded to a single water molecule. Its structure comprises two facing Fe(IV)oxo groups, in an arrangement similar to the one evinced for the active centre of intermediate Q of soluble Methane Monooxygenase (sMMO). The inclusion of the water molecule in the complex decreases the overall symmetry of the system, and brings about important changes in the energy and spatial distribution of orbitals of the Fe(IV)oxo groups relative to the gas phase. In particular, the virtual 3σ* orbital of one of the Fe(IV)oxo groups experiences much reduced repulsive orbital interactions from ligand orbitals, and its consequent stabilisation dramatically enhances the electrophilic character of the complex, compared to the symmetrical non-hydrated species, and its ability to act as an acceptor of a H atom from the CH4 substrate. The computed free energy barrier for H abstraction is 28.2 kJ mol−1 (at the BLYP level of DFT), considerably below the gas phase value for monomeric [FeO·EDTAH]−, and much below the solution value for the prototype hydrated ferryl ion [FeO(H2O)5]2+.

We study the effect of counter-ion complexation on the example of Cl− ions interacting with the [Co(en)3]3+ complex. The H-bonding of the N–H groups of the ethylenediamine (en) ligands with the Cl− ions may lead to giant enhancement of the VCD intensity for the N–H stretches, but may also lead to VCD sign changes in the finger print region of N–H wagging, twisting and scissoring motions. Such sign changes should not be mistaken for signatures of the presence of the other enantiomer. We elucidate the mechanism for the sign changes and give a recommendation on how to deal with this problem. We also show that the experimental spectrum is only in good accord with the calculations if complexation of 5 Cl− ions (two axial, three equatorial) is assumed, but not with two (axial) or three (equatorial) Cl− ions, thus showing the potential of VCD to be used as an experimental probe for complexation.

Enantiomeric excess (ee) in asymmetric catalysis may be strongly dependent on the solvent. The reaction product may range from an almost racemic mixture to an ee of over 90% for different solvents. We study this phenomenon for the C–C coupling reaction between nitromethane and benzaldehyde (the Henry reaction) with cinchona thiourea as the catalyst, where solvents that are strong Lewis bases induce a high ee. We show that the effect of the solvent does not consist of a change in the reaction mechanism. Instead, the solvation “prepares” the molecule, which is very flexible, in a specific conformation. The reaction barriers in this conformer are not lower than for other conformers, but are sufficiently differentiated between the enantiomers to give rise to a large ee. It is the strong Lewis basicity of the solvent that leads to the clear preference in solution for the “asymmetric” conformer. Although general rules or predictions for how solvent effects could be harnessed to produce a desired ee in general would be hard to formulate, this study does show that it is in this case (and presumably in many other cases as well) specific solute–solvent interactions rather than effects of the dielectric continuum of the solvent that are the root cause of the solvent effect. This is in agreement with experiment for the Henry reaction.

We study the effect of counter-ion complexation on the example of Cl− ions interacting with the [Co(en)3]3+ complex. The H-bonding of the N–H groups of the ethylenediamine (en) ligands with the Cl− ions may lead to giant enhancement of the VCD intensity for the N–H stretches, but may also lead to VCD sign changes in the finger print region of N–H wagging, twisting and scissoring motions. Such sign changes should not be mistaken for signatures of the presence of the other enantiomer. We elucidate the mechanism for the sign changes and give a recommendation on how to deal with this problem. We also show that the experimental spectrum is only in good accord with the calculations if complexation of 5 Cl− ions (two axial, three equatorial) is assumed, but not with two (axial) or three (equatorial) Cl− ions, thus showing the potential of VCD to be used as an experimental probe for complexation.

We study the generation of a dinuclear Fe(IV)oxo species, [EDTAH·FeO·OFe·EDTAH]2−, in aqueous solution at room temperature using Density Functional Theory (DFT) and Ab Initio Molecular Dynamics (AIMD). This species has been postulated as an intermediate in the multi-step mechanism of autoxidation of Fe(II) to Fe(III) in the presence of atmospheric O2 and EDTA ligand in water. We examine the formation of [EDTAH·FeO·OFe·EDTAH]2− by direct cleavage of O2, and the effects of solvation on the spin state and O–O cleavage barrier. We also study the reactivity of the resulting dinuclear Fe(IV)oxo system in CH4 hydroxylation, and its tendency to decompose to mononuclear Fe(IV)oxo species. The presence of the solvent is shown to play a crucial role, determining important changes in all these processes compared to the gas phase. We show that, in water solution, [EDTAH·FeO·OFe·EDTAH]2− (as well as its precursor [EDTAH·Fe·O2·Fe·EDTAH]2−) exists as stable species in a S = 4 ground spin state when hydrogen-bonded to a single water molecule. Its structure comprises two facing Fe(IV)oxo groups, in an arrangement similar to the one evinced for the active centre of intermediate Q of soluble Methane Monooxygenase (sMMO). The inclusion of the water molecule in the complex decreases the overall symmetry of the system, and brings about important changes in the energy and spatial distribution of orbitals of the Fe(IV)oxo groups relative to the gas phase. In particular, the virtual 3σ* orbital of one of the Fe(IV)oxo groups experiences much reduced repulsive orbital interactions from ligand orbitals, and its consequent stabilisation dramatically enhances the electrophilic character of the complex, compared to the symmetrical non-hydrated species, and its ability to act as an acceptor of a H atom from the CH4 substrate. The computed free energy barrier for H abstraction is 28.2 kJ mol−1 (at the BLYP level of DFT), considerably below the gas phase value for monomeric [FeO·EDTAH]−, and much below the solution value for the prototype hydrated ferryl ion [FeO(H2O)5]2+.

The concept of robustness of rotational strengths of vibrational modes in a VCD spectrum has been introduced as an aid in assignment of the absolute configuration with the help of the VCD spectrum. The criteria for robustness have been based on the distribution around 90° of the angles ξ(i) between electric and magnetic transition dipoles of all the modes i of a molecule. The angles ξ(i) (not, of course, the rotational strengths) are, however, dependent on the choice of origin. The derived criteria are for the center of mass chosen as the origin of the coordinate system. We stress in this note that application of the derived criteria assumes that excessive translation of the coordinate origin is not applied. Although the ξ(i) angles are not very sensitive to the position of the origin, very small displacements (a few Å) are not a problem, excessive translation of the origin does have considerable effect on the ξ(i) angles. In this note we quantify this effect and demonstrate how the distribution of ξ(i) angles is affected. Although it is possible to recalibrate the robustness criteria for the angles for a specific (large) displacement, we recommend that such displacement simply be avoided. It is to be noted that some modeling software does yield output with excessively displaced coordinate origin; this should be checked and corrected.

A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual orbitals, they often describe excited states much more closely as simple orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO orbital energy difference (in Koopmans' frozen orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual orbitals.