Extended Hartree—Fock (EHF) theory of chemical reactions VI: hybrid DFT and post-Hartree—Fock approaches for concerted and non-concerted transition structures of the Diels—Alder reaction

Halide Abstraction Competes with Oxidative Addition in the Reactions of Aryl Halides with [Ni(PMen Ph(3-n) )4 ]

Density functional theory (DFT) calculations have been used to study the oxidative addition of aryl halides to complexes of the type [Ni(PMen Ph(3-n) )4 ], revealing the crucial role of an open-shell singlet transition state for halide abstraction. The formation of NiI versus NiII has been rationalised through the study of three different pathways: (i) halide abstraction by [Ni(PMen Ph(3-n) )3 ], via an open-shell singlet transition state; (ii) SN 2-type oxidative addition to [Ni(PMen Ph(3-n) )3 ], followed by phosphine dissociation; and (iii) oxidative addition to [Ni(PMen Ph(3-n) )2 ]. For the overall reaction between [Ni(PMe3 )4 ], PhCl, and PhI, a microkinetic model was used to show that our results are consistent with the experimentally observed ratios of NiI and NiII when the PEt3 complex is used. Importantly, [Ni(PMen Ph(3-n) )2 ] complexes often have little, if any, role in oxidative addition reactions because they are relatively high in energy. The behaviour of [Ni(PR3 )4 ] complexes in catalysis is therefore likely to differ considerably from those based on diphosphine ligands in which two coordinate Ni0 complexes are the key species undergoing oxidative addition.

Anomalous effect of non-alternant hydrocarbons on carbocation and carbanion electronic configurations

Carbocations are widely viewed to be closed-shell singlet electrophiles. Here, computations show that azulenyl-substituted carbocations have triplet ground states. This triplet ground state for azulenyl carbocations stands in striking contrast to the isomeric naphthenyl carbocation, which is a normal closed-shell singlet with a large singlet-triplet gap. Furthermore, substitution of the azulenyl carbocation can substantially alter the energy gap between the different electronic configurations and can manipulate the ground state towards either the singlet or the triplet state depending on the nature and location of the substituent. A detailed investigation into the origin of this spin state reversal, including NICS calculations, structural effects, substitution patterns, orbital analysis, and detailed linear free-energy relationships allowed us to distill a set of principles that caused these azulenyl carbocations to have such low-lying diradical states. The fundamental origin of this effect mostly centers on singlet state destabilization from increasing antiaromatic character, in combination with a smaller, but important, Baird triplet state aromatic stabilization. We find that azulene is not unique, as extension of these principles allowed us to generate simple rules to predict an entire class of analogous non-alternant carbocation and carbanion structures with low-energy or ground state diradical states, including a purely hydrocarbon triplet cation with a large singlet-triplet gap of 8 kcal mol-1. Although these ions have innocuous-looking Lewis structures, these triplet diradical ions are likely to have substantially different reactivity and properties than typical closed-shell singlet ions.

Electrophilic substitution reactions of metallabenzynes

The electrophilic substitution reactions of metallabenzynes Os(≡CC(R)═C(CH(3))C(R)═CH)Cl(2)(PPh(3))(2) (R = SiMe(3), H) were studied. These metallabenzynes react with electrophilic reagents, including Br(2), NO(2)BF(4), NOBF(4), HCl/H(2)O(2), and AlCl(3)/H(2)O(2) to afford the corresponding bromination, nitration, nitrosation, and chlorination products. The reactions usually occur at the C2 and C4 positions of the metallacycle. These observations support the notion that metallabenzynes exhibit aromatic properties.

Geometric and electronic structure differences between the type 3 copper sites of the multicopper oxidases and hemocyanin/tyrosinase

The coupled binuclear "type 3" Cu sites are found in hemocyanin (Hc), tyrosinase (Tyr), and the multicopper oxidases (MCOs), such as laccase (Lc), and play vital roles in O(2) respiration. Although all type 3 Cu sites share the same ground state features, those of Hc/Tyr have very different ligand-binding properties relative to those of the MCOs. In particular, the type 3 Cu site in the MCOs (Lc(T3)) is a part of the trinuclear Cu cluster, and if the third (i.e., type 2) Cu is removed, the Lc(T3) site does not react with O(2). Density functional theory calculations indicate that O(2) binding in Hc is approximately 9 kcal mol(-1) more favorable than for Lc(T3). The difference is mostly found in the total energy difference of the deoxy states (approximately 7 kcal mol(-1)), where the stabilization of deoxy Lc(T3) derives from its long equilibrium Cu-Cu distance of approximately 5.5-6.5 A, relative to approximately 4.2 A in deoxy Hc/Tyr. The O(2) binding in Hc is driven by the electrostatic destabilization of the deoxy Hc site, in which the two Cu(I) centers are kept close together by the protein for facile 2-electron reduction of O(2). Alternatively, the lack of O(2) reactivity in Lc(T3) reflects the flexibility of the active site, capable of minimizing the electrostatic repulsion of the 2 Cu(I)s. Thus, the O(2) reactivity of the MCOs is intrinsic to the trinuclear Cu cluster, leading to different O(2) intermediates as required by its function of irreversible reduction of O(2) to H(2)O.

Generating Cu(II)-oxyl/Cu(III)-oxo species from Cu(I)-alpha-ketocarboxylate complexes and O2: in silico studies on ligand effects and C-H-activation reactivity

A mechanism for the oxygenation of Cu(I) complexes with alpha-ketocarboxylate ligands that is based on a combination of density functional theory and multireference second-order perturbation theory (CASSCF/CASPT2) calculations is elaborated. The reaction proceeds in a manner largely analogous to those of similar Fe(II)-alpha-ketocarboxylate systems, that is, by initial attack of a coordinated oxygen molecule on a ketocarboxylate ligand with concomitant decarboxylation. Subsequently, two reactive intermediates may be generated, a Cu-peracid structure and a [CuO](+) species, both of which are capable of oxidizing a phenyl ring component of the supporting ligand. Hydroxylation by the [CuO](+) species is predicted to proceed with a smaller activation free energy. The effects of electronic and steric variations on the oxygenation mechanisms were studied by introducing substituents at several positions of the ligand backbone and by investigating various N-donor ligands. In general, more electron donation by the N-donor ligand leads to increased stabilization of the more Cu(II)/Cu(III)-like intermediates (oxygen adducts and [CuO](+) species) relative to the more Cu(I)-like peracid intermediate. For all ligands investigated, the [CuO](+) intermediates are best described as Cu(II)-O(*-) species with triplet ground states. The reactivity of these compounds in C-H abstraction reactions decreases with more electron-donating N-donor ligands, which also increase the Cu-O bond strength, although the Cu-O bond is generally predicted to be rather weak (with a bond order of about 0.5). A comparison of several methods to obtain singlet energies for the reaction intermediates indicates that multireference second-order perturbation theory is likely more accurate for the initial oxygen adducts, but not necessarily for subsequent reaction intermediates.

Isotopic probing of molecular oxygen activation at copper(I) sites

Copper-dioxygen (CuO2) adducts are frequently proposed as intermediates in enzymes, yet their electronic and vibrational structures have not always been understood. [Cu(eta1-O2)TMG3tren]+ (TMG3tren = 1,1,1-tris{2-[N2-(1,1,3,3-tetramethylguanidino)]ethyl}amine) features end-on (eta1) O2 coordination in the solid state. Described here is an investigation of the compound's solution properties by nuclear magnetic resonance spectroscopy, density functional calculations, and oxygen isotope effects. The study yields two major findings. First, [Cu(eta1-O2)TMG3tren]+ is paramagnetic due to a triplet electronic structure; this is in contrast to other copper compounds where O2 is bound in a side-on manner. Second, the oxygen equilibrium isotope effect upon O2 binding to copper(I) (18O EIE [triple bond] K(16O16O)/K(16O18O) = 1.0148 +/- 0.0012) is significantly larger than those determined for iron and cobalt eta1-O2 adducts. This result is suggested to reflect greater ionic (CuII-O2-I) character within the valence bond description. A revised interpretation of the physical origins of the 18O EIEs upon O2 binding to redox metals is also advanced along with experimental data that should be used as benchmarks for interpreting 18O kinetic isotope effects upon enzyme reactions.

Validation of density functional modeling protocols on experimental bis(μ-oxo)/μ-η2:η2-peroxo dicopper equilibria

The bis(mu-oxo)/mu-eta(2):eta(2)-peroxo equilibria for seven supported Cu(2)O(2) cores were studied with different hybrid and nonhybrid density functional theory models, namely, BLYP, mPWPW, TPSS, TPSSh, B3LYP, mPW1PW, and MPW1K. Supporting ligands 3,3'-iminobis(N,N-dimethylpropylamine), N,N,N',N',N''-pentamethyldipropylenetriamine, N-[2-(pyridin-2-yl)ethyl]-N,N,N'-trimethylpropane-1,3-diamine, bis[2-(2-pyridin-2-yl)ethyl]methylamine, bis[2-(4-methoxy-2-pyridin-2-yl)ethyl]methylamine, bis[2-(4-N,N-dimethylamino-2-pyridin-2-yl)ethyl]methylamine, and 1,4,7-triisopropyl-1,4,7-triazacyclononane were chosen on the basis of the availability of experimental data for comparison. Density functionals were examined with respect to their ability accurately to reproduce experimental properties, including, in particular, geometries and relative energies for the bis(mu-oxo) and side-on peroxo forms. While geometries from both hybrid and nonhybrid functionals were in good agreement with experiment, the incorporation of Hartree-Fock (HF) exchange in hybrid density functionals was found to have a large, degrading effect on predicted relative isomer energies. Specifically, hybrid functionals predicted the mu-eta(2):eta(2)-peroxo isomer to be too stable by roughly 5-10 kcal mol(-1) for each 10% of HF exchange incorporated into the model. Continuum solvation calculations predict electrostatic effects to favor bis(mu-oxo) isomers by 1-4 kcal mol(-1) depending on ligand size, with larger ligands having smaller differential solvation effects. Analysis of computed molecular partition functions suggests that nonzero measured entropies of isomerization are likely to be primarily associated with interactions between molecular solutes and their first solvation shell.

Benzylic Cations with Triplet Ground States: Computational Studies of Aryl Carbenium Ions, Silylenium Ions, Nitrenium Ions, and Oxenium Ions Substituted with Meta π Donors

Density functional theory (B3LYP/6-31G(d,p)) was used to predict the effect of meta substitution on aryl cationic (Ar-X+) species, including aryloxenium ions, arylsilylenium ions, arylnitrenium ions, and arylcarbenium ions. Multireference second-order perturbation theory (CASPT2) calculations were used to benchmark the quantitative accuracy of the DFT calculations for representative systems. Substituting the meta positions on these species with pi donors stabilizes a pi,pi* diradical state analogous to the well-known m-xylylene diradical. Notably, the 3,5-bis(N,N-dimethylamino)benzyl cation is predicted to have a triplet ground state by 1.9 kcal/mol by DFT and to have essentially degenerate singlet-triplet states at the CASPT2(10,9) level of theory. Adding electron-withdrawing CF3 groups to the exocyclic carbon of this meta-disubstituted benzyl cation further increases the predicted singlet-triplet gap in favor of the triplet. Other aryl cationic species substituted with strong pi electron-donating groups in the meta positions are predicted to have low-energy or ground-state triplet states. Systems analogous to the naphthaquinodimethane diradicals are also reported.

Singlet-triplet gaps in large multireference systems: Spin-flip-driven alternatives for bioinorganic modeling

The proper description of low-spin states of open-shell systems, which are commonly encountered in the field of bioinorganic chemistry, rigorously requires using multireference ab initio methodologies. Such approaches are unfortunately very CPU-time consuming as dynamic correlation effects also have to be taken into account. The broken-symmetry unrestricted (spin-polarized) density functional theory (DFT) technique has been widely employed up to now to bypass that drawback, but despite a number of relative successes in the determination of singlet-triplet gaps, this framework cannot be considered as entirely satisfactory. In this contribution, we investigate some alternative ways relying on the spin-flip time-dependent DFT approach [Y. Shao et al. J. Chem. Phys. 118, 4807 (2003)]. Taking a few well-documented copper-dioxygen adducts as examples, we show that spin-flip (SF)-DFT computed singlet-triplet gaps compare very favorably to either experimental results or large-scale CASMP2 computations. Moreover, it is shown that this approach can be used to optimize geometries at a DFT level including some multireference effects. Finally, a clear-cut added value of the SF-DFT computations is drawn: if pure ab initio data are required, then the electronic excitations revealed by SF-DFT can be considered in designing dramatically reduced zeroth-order variational spaces to be used in subsequent multireference configuration interaction or multireference perturbation treatments.

Theoretical Characterization of End-On and Side-On Peroxide Coordination in Ligated Cu2O2 Models

The relative energetics of mu-eta1:eta1 (trans end-on) and mu-eta2:eta2 (side-on) peroxo isomers of Cu2O2 fragments supported by 0, 2, 4, and 6 ammonia ligands have been computed with various density functional, coupled-cluster, and multiconfigurational protocols. There is substantial disagreement between the different levels for most cases, although completely renormalized coupled-cluster methods appear to offer the most reliable predictions. The significant biradical character of the end-on peroxo isomer proves problematic for the density functionals, while the demands on active space size and the need to account for interactions between different states in second-order perturbation theory prove challenging for the multireference treatments. In the latter case, it proved impossible to achieve any convincing convergence.

Theoretical Models on the Cu2O2 Torture Track: Mechanistic Implications for Oxytyrosinase and Small-Molecule Analogues

Accurately describing the relative energetics of alternative bis(mu-oxo) and mu-eta2:eta2 peroxo isomers of Cu2O2 cores supported by 0, 2, 4, and 6 ammonia ligands is remarkably challenging for a wide variety of theoretical models, primarily owing to the difficulty of maintaining a balanced description of rapidly changing dynamical and nondynamical electron correlation effects and a varying degree of biradical character along the isomerization coordinate. The completely renormalized coupled-cluster level of theory including triple excitations and extremely efficient pure density functional levels of theory quantitatively agree with one another and also agree qualitatively with experimental results for Cu2O2 cores supported by analogous but larger ligands. Standard coupled-cluster methods, such as CCSD(T), are in most cases considerably less accurate and exhibit poor convergence in predicted relative energies. Hybrid density functionals significantly underestimate the stability of the bis(mu-oxo) form, with the magnitude of the error being directly proportional to the percentage Hartree-Fock exchange in the functional. Single-root CASPT2 multireference second-order perturbation theory, by contrast, significantly overestimates the stability of bis(mu-oxo) isomers. Implications of these results for modeling the mechanism of C-H bond activation by supported Cu2O2 cores, like that found in the active site of oxytyrosinase, are discussed.

How useful are vibrational frequencies of isotopomeric O2 fragments for assessing local symmetry? Some simple systems and the vexing case of a galactose oxidase model

The tendency for mixed-isotope O2 fragments to exhibit different stretching frequencies in asymmetric environments is examined with various levels of electronic structure theory for simple peroxides and peroxyl radicals, as well as for a variety of monocopper-O2 complexes. The study of the monocopper species is motivated by their relevance to the active site of galactose oxidase. Extensive theoretical work with an experimental model characterized by Jazdzewski et al. (J. Biol. Inorg. Chem. 8:381-393, 2003) suggests that the failure to observe a splitting between 16O18O and 18O16O isotopomers cannot be taken as evidence against end-on O2 coordination. Conformational analysis on an energetic basis, however, is complicated by biradical character inherent in all of the copper-O2 singlet structures.

Mechanistic insights in charge-transfer-induced luminescence of 1,2-dioxetanones with a substituent of low oxidation potential

We have investigated the decomposition pathway of dioxetanones 1c with a phenoxide anion group by the B3LYP/6-31+G(d) method together with the second-order multireference Møller-Plesset perturbation (MRMP) theory and propose charge-transfer-induced luminescence (CTIL) with polarization-induced branching excitation processes. In the gas phase, the thermal decomposition of 1c occurs by an asynchronous two-stage pathway without a discrete intermediate; that is, the initial O-O bond breaking to generate a charge-transfer (CT) diradical species is immediately followed by the subsequent C-C bond breaking with simultaneous back CT, which is responsible for the surface crossing at the avoided crossing. The activation energy is dramatically reduced from 19.4 to 3.8 kcal mol(-)(1) by the deprotonation of phenol meta-1d to its anion meta-1c, showing an important role of the endothermic CT. The odd/even selection rule for the chemiluminescence efficiency can be explained by the orbital interaction for the back CT between the carbonyl pi orbital and either a HOMO or a LUMO of the generated light emitters. To examine the accessibility of the chemically initiated electron exchange luminescence (CIEEL) route, we considered the solvent effects on the free-energy change of meta-1c by using continuum solvent models. The bending vibration mode of the CO(2) fragment is specifically considered. Borderline features emerges from the solution-phase CT reaction of meta-1c, which depends on the solvent polarity: one is a nonadiabatic or adiabatic back CT process (polarization-induced concerted CTIL), and the other is a radical dissociation, i.e., complete one-electron-transfer process (CIEEL).

A Computational Study of the Cycloaddition of Thiobenzophenone S-Methylide to Thiobenzophenone

The cycloaddition of thiobenzophenone S-methylide to thiobenzophenone, an experimentally well-known reaction, was studied, using (U)HF/3-21G* for finding stationary points and (U)B3LYP/6-31G*//(U)HF/3-21G* single-point calculations for energies. Some optimizations were performed by (U)B3LYP/ 6-31G* to check the reliability of the calculations. The comparison of the concerted pathways and stepwise reactions via C,C-biradicals and C,S-zwitterions showed that the formation of a tetraphenyl-substituted C,C-biradical and its ring closure to 4,4,5,5-tetraphenyl-1,3-dithiolane constitutes the energetically most probable pathway of product formation, despite the fact that the regioisomeric 2,2,4,4-tetraphenyl-substituted product is more favorable by 17 kcal mol(-1). Model calculations on bond dissociation energies showed that (U)B3LYP with various basis sets overestimates radical stabilization, whereas CBS-QB3 closely reproduced experimental values. Results with the BLYP functional are similar to those with B3LYP. The consequences of the overestimation of radical stability for the cycloaddition mechanism involving biradicals are discussed. Thiobenzophenone S-methylide, if not captured by a dipolarophile, dimerizes to 2,2,3,3-tetraphenyl-1,4-dithiane. Calculation disclosed likewise a tetraphenyl-substituted C,C-biradical as intermediate.

On the formation of cyclobutane pyrimidine dimers in UV-irradiated DNA: why are thymines more reactive?

The reaction pathways for thermal and photochemical formation of cyclobutane pyrimidine dimers in DNA are explored using density functional theory techniques. Although it is found that the thermal [2 + 2] cycloadditions of thymine + thymine (T + T --> T x T), cytosine + cytosine (C + C --> C x C) and cytosine + thymine (C + T --> C x T) all are similarly unfavorable in terms of energy barriers and reaction energies, the excited-state energy curves associated with the corresponding photochemical cycloadditions display differences that--in line with experimental findings--unanimously point to the predominance of T x T in UV-irradiated DNA. It is shown that the photocycloaddition of thymines is facilitated by the fact that the S1 state of the corresponding reactant complex lies comparatively high in energy. Moreover, at a nuclear configuration coinciding with the ground-state transition structure, the excited-state energy curve displays an absolute minimum only for the T + T system. Finally, the T + T system is also associated with the most favorable excited-state energy barriers and has the smallest S2-S0 energy gap at the ground-state transition structure.

Hybrid density functional theory studies on the magnetic interactions and the weak covalent bonding for the phenalenyl radical dimeric pair

The phenalenyl radical (1) is a prototype of the hydrocarbon radical. Recently, the single crystal of 2,5,8-tri-tert-butylphenalenyl (2) was isolated and showed that the two phenalenyl radicals form a staggered dimeric pair, giving rise to strong antiferromagnetic interactions. The origin of the antiferromagnetic interactions and the nature of the chemical bond for the dimeric pair are challenging issues for chemists. First, spin-polarized hybrid DFT (Becke's half and half LYP (UB2LYP)) and CASSCF calculations were performed for 2 and its simplified model, the staggered-stacking phenalenyl radical dimeric pair (3a), to elucidate the origin of the strong antiferromagnetic coupling and the characteristics of the chemical bond. The calculated results showed that a SOMO-SOMO overlap effect was responsible for the strong antiferromagnetic interactions and weak or intermediate covalent bonding between phenalenyl radicals. The tert-butyl groups introduced at three beta-positions hardly affected the magnetic coupling, mainly causing steric hindrances in the crystalline state. Next, to obtain insight into ferromagnetic stacking, we investigated the stacking effect of staggered (3a)- and eclipsed (3b)-stacking phenalenyl radical dimeric pairs with a change of the SOMO-SOMO overlap on the basis of the extended McConnell model. We found that the stacking mode of the dimeric pair with both a small SOMO-SOMO overlap and a ferromagnetic spin polarization effect provided a ferromagnetic coupling.