Why Are Addition Reactions to N₂ Thermodynamically Unfavorable?

Thermochemical data are used to show that, of the 89.9 kcal/mol difference between the endothermicity of H₂ addition to N₂ (<i>Δ<i>H</i></i> = 47.9 kcal/mol) and the exothermicity of H₂ addition to acetylene (<i>Δ<i>H</i></i> = −42.0 kcal/mol), less than half is due to a stronger π bond in N₂ than in acetylene. The other major contributor to the difference of 89.9 kcal/mol between the enthalpies of hydrogenation of N₂ and acetylene is that the pair of N–H bonds that are created in the addition of H₂ to N₂ are significantly weaker than the pair of C–H bonds that are created in the addition of H₂ to acetylene. The reasons for this large difference between the strengths of the N–H bonds in <i>E</i>-HNNH and the C–H bonds in H₂CCH₂ are analyzed and discussed

Calculations of the Effects of Methyl Groups on the Energy Differences between Cyclooctatetraene and Bicyclo[4.2.0]octa-2,4,7-triene and between Their Iron Tricarbonyl Complexes

In accord with experiment, DFT calculations find that cyclooctatetraene (COT, <b>1a</b>) is lower in energy than its valence isomer, bicyclo[4.2.0]­octa-2,4,7-triene (BCOT, <b>3a</b>) and that the iron tricarbonyl complex of COT [COT-Fe­(CO)₃, <b>2a</b>] is lower in energy than the iron tricarbonyl complex of BCOT [BCOT-Fe­(CO)₃, <b>4a</b>]. Also in agreement with experiment are the DFT findings that 1,3,5,7-tetramethylCOT (TMCOT, <b>1b</b>) is lower in energy than 1,3,5,7-tetramethylBCOT (TMBCOT, <b>3b</b>), but that the iron tricarbonyl complex of TMCOT [TMCOT-Fe­(CO)₃, <b>2b</b>] is higher in energy than the iron tricarbonyl complex of TMBCOT [TMBCOT-Fe­(CO)₃, <b>4b</b>]. Calculations of the energies of isodesmic reactions allow the effect of each of the four methyl groups in <b>1b</b>–<b>4b</b> to be analyzed in terms of its additive contribution to the relative energies of TMCOT (<b>1b</b>) and TMBCOT (<b>3b</b>) and to the Fe­(CO)₃ binding energies in TMCOT-Fe­(CO)₃ (<b>2b</b>) and TMBCOT-Fe­(CO)₃ (<b>4b</b>). Our calculations also predict that the eight methyl groups in octamethylCOT-Fe­(CO)₃ [OMCOT-Fe­(CO)₃, <b>2c</b>] should have much more than twice the effect of the four methyl groups in TMCOT-Fe­(CO)₃ (<b>2b</b>) on raising the energy of OMCOT-Fe­(CO)₃ (<b>2c</b>), relative to that of OMBCOT-Fe­(CO)₃ (<b>4c</b>). The effects of the interactions between the methyl groups in OMCOT-Fe­(CO)₃ (<b>2c</b>) and OMBCOT-Fe­(CO)₃ (<b>4c</b>) are dissected and discussed

Dioxygen: What Makes This Triplet Diradical Kinetically Persistent?

Experimental heats of formation and enthalpies obtained from G4 calculations both find that the resonance stabilization of the two unpaired electrons in triplet O₂, relative to the unpaired electrons in two hydroxyl radicals, amounts to 100 kcal/mol. The origin of this huge stabilization energy is described within the contexts of both molecular orbital (MO) and valence-bond (VB) theory. Although O₂ is a triplet diradical, the thermodynamic unfavorability of both its hydrogen atom abstraction and oligomerization reactions can be attributed to its very large resonance stabilization energy. The unreactivity of O₂ toward both these modes of self-destruction maintains its abundance in the ecosphere and thus its availability to support aerobic life. However, despite the resonance stabilization of the π system of triplet O₂, the weakness of the O–O σ bond makes reactions of O₂, which eventually lead to cleavage of this bond, very favorable thermodynamically

Variations in Rotational Barriers of Allyl and Benzyl Cations, Anions, and Radicals

High accuracy quantum chemical calculations show that the barriers to rotation of a CH₂ group in the allyl cation, radical, and anion are 33, 14, and 21 kcal/mol, respectively. The benzyl cation, radical, and anion have barriers of 45, 11, and 24 kcal/mol, respectively. These barrier heights are related to the magnitude of the delocalization stabilization of each fully conjugated system. This paper addresses the question of why these rotational barriers, which at the Hückel level of theory are independent of the number of nonbonding electrons in allyl and benzyl, are in fact calculated to be factors that are of 2.4 and 4.1 higher in the cations and 1.5 and 1.9 higher in the anions than in the radicals. We also investigate why the barrier to rotation is higher for benzyl than for allyl in the cations and in the anions. Only in the radicals is the barrier for benzyl lower than that for allyl, as Hückel theory predicts should be the case. These fundamental questions in electronic structure theory, which have not been addressed previously, are related to differences in electron–electron repulsions in the conjugated and nonconjugated systems, which depend on the number of nonbonding electrons

Theoretical Analysis of the Fragmentation of (CO)₅: A Symmetry-Allowed Highly Exothermic Reaction that Follows a Stepwise Pathway

B3LYP and CCSD­(T) calculations, using an aug-cc-pVTZ basis set, have been carried out on the fragmentation of 1,2,3,4,5-cyclopentanepentone, (CO)₅, to five molecules of CO. Although this reaction is calculated to be highly exothermic and is allowed to be concerted by the Woodward–Hoffmann rules, our calculations find that the <i>D</i>_5<i>h</i> energy maximum is a multidimensional hilltop on the potential energy surface. This <i>D</i>_5<i>h</i> hilltop is 16–20 kcal/mol higher in energy than a <i>C</i>₂ transition structure for the endothermic cleavage of (CO)₅ to (CO)₄ + CO and 11–15 kcal/mol higher than a <i>C</i>_s transition structure for the loss of two CO molecules. The reasons for the very high energy of the <i>D</i>_5<i>h</i> hilltop are discussed, and the geometries of the two lower energy transition structures are rationalized on the basis of mixing of the e₂′ HOMO and the a₂″ LUMO of the hilltop

Negative Ion Photoelectron Spectroscopy Confirms the Prediction that (CO)₅ and (CO)₆ Each Has a Singlet Ground State

Cyclobutane-1,2,3,4-tetraone has been both predicted and found to have a triplet ground state, in which a b_2g σ molecular orbital (MO) and an a_2u π MO are each singly occupied. In contrast, (CO)₅ and (CO)₆ have each been predicted to have a singlet ground state. These predictions have been tested by generating the (CO)₅^•– and (CO)₆^•– radical anions in the gas phase, using electrospray vaporization of solutions of, respectively, the croconate (CO)₅^2– and rhodizonate (CO)₆^2– dianions. The negative ion photoelectron (NIPE) spectrum of the (CO)₅^•– radical anion gives an electron affinity of EA = 3.830 eV for formation of the singlet ground state of (CO)₅. The triplet is found to be higher in energy by 0.850 eV (19.6 kcal/mol). The NIPE spectrum of the (CO)₆^•– radical anion gives EA = 3.785 eV for forming the singlet ground state of (CO)₆, with the triplet state higher in energy by 0.915 eV (21.1 kcal/mol). (RO)­CCSD­(T)/aug-cc-pVTZ//(U)­B3LYP/6-311+G­(2df) calculations give EA values that are only approximately 1 kcal/mol lower than those measured and Δ<i><i>E</i></i>_ST values that are 2–3 kcal/mol higher than those obtained from the NIPE spectra. Calculations of the Franck–Condon factors for transitions from the ground state of each radical anion, (CO)_<i>n</i>^•– to the lowest singlet and triplet states of the <i>n</i> = 4–6 neutrals, nicely reproduce all of the observed vibrational features in the low-binding energy regions of all three NIPE spectra. Thus, the calculations of both the energies and vibrational structures of the two lowest energy bands in each of the NIPE spectra support the interpretation of the spectra in terms of a singlet ground state for (CO)₅ and (CO)₆ but a triplet ground state for (CO)₄

Experimental and Theoretical Studies of the F^• + H–F Transition-State Region by Photodetachment of [F–H–F]⁻

The transition-state (TS) region of the simplest heavy-light-heavy type of reaction, F^• + H–F → F–H + F^•, is investigated in this work by a joint experimental and theoretical approach. Photodetaching the bifluoride anion, [F···H···F]⁻, generates a negative ion photoelectron (NIPE) spectrum with three partially resolved bands in the electron binding energy (<i>eBE</i>) range of 5.4–7.0 eV. These bands correspond to the transition from the ground state of the anion to the electronic ground state of [F–H–F]^• neutral, with associated vibrational excitations. The significant increase of <i>eBE</i> of the bifluoride anion, relative to that of F^–, reflects a hydrogen bond energy between F^– and HF of ∼46 kcal/mol. Theoretical modeling reveals that the antisymmetric motion of H between the two F atoms, near the TS on the neutral [F–H–F]^• surface, dominates the observed three bands, while the F–H–F bending, F–F symmetric stretching modes, and the couplings between them are calculated to account for the breadth of the observed spectrum. From the NIPE spectrum, a lower limit on the activation enthalpy for F^• + H–F → F–H + F^• can be estimated to be <i>Δ<i>H</i></i>^‡ = 12 ± 2 kcal/mol, a value below that of <i>Δ<i>H</i></i>^‡ = 14.9 kcal/mol, given by our G4 calculations

Negative Ion Photoelectron Spectroscopy Confirms the Prediction that 1,2,4,5-Tetraoxatetramethylenebenzene Has a Singlet Ground State

The negative ion photoelectron (NIPE) spectrum of 1,2,4,5-tetraoxatetramethylenebenzene radical anion (<b>TOTMB</b>^•–) shows that, like the hydrocarbon, 1,2,4,5-tetramethylenebenzene (<b>TMB</b>), the <b>TOTMB</b> diradical has a singlet ground state and thus violates Hund’s rule. The NIPE spectrum of <b>TOTMB</b>^•– gives a value of −Δ<i>E</i>_ST = 3.5 ± 0.2 kcal/mol for the energy difference between the singlet and triplet states of <b>TOTMB</b> and a value of <i>EA</i> = 4.025 ± 0.010 eV for the electron affinity of <b>TOTMB</b>. (10/10)­CASPT2 calculations are successful in predicting the singlet–triplet energy difference in <b>TOTMB</b> almost exactly, giving a computed value of −Δ<i>E</i>_ST = 3.6 kcal/mol. The same type of calculations predict −Δ<i>E</i>_ST = 6.1–6.3 kcal/mol in <b>TMB</b>. Thus, the calculated effect of the substitution of the four oxygens in <b>TOTMB</b> for the four methylene groups in <b>TMB</b> is very unusual, since the singlet state is selectively destabilized relative to the triplet state. The reason why <b>TMB</b> → <b>TOTMB</b> is predicted to result in a decrease in the size of −Δ<i>E</i>_ST is discussed

How to Make the σ⁰π² Singlet the Ground State of Carbenes

Successful strategies have previously been developed to stabilize the σ²π⁰ singlet states of carbenes, relative to σ¹π¹ triplet states. However, little or no attention has been paid to the stabilization of the σ⁰π² singlet states. We present two simple strategies to stabilize the σ⁰π² singlet states of carbenes, relative to both the σ²π⁰ singlet and σ¹π¹ triplet states. These strategies consist of destabilization of the carbene σ orbital by two, adjacent, sp² nitrogen lone pairs of electrons and stabilization of the carbene 2p−π orbital by incorporating it into a five-membered ring, containing two double bonds, or into a six-membered ring, containing two double bonds and a sixth atom that has a low-lying empty π orbital. B3LYP, CASPT2, and CCSD­(T) calculations have been performed in order to assess the success of these strategies in creating derivatives of cyclopenta-2,4-dienylidene and cyclohexa-2,5-dienylidene with σ⁰π⁶ singlet ground states. Differences between the calculated geometries and binding energies of the Xe complexes of the σ⁰π⁶ singlet ground state of 2,5-diazacyclopentadienylidene (<b>5</b>) and the σ²π⁰ singlet states of CH₂ and CF₂ are discussed

Negative Ion Photoelectron Spectroscopy Confirms the Prediction of the Relative Energies of the Low-Lying Electronic States of 2,7-Naphthoquinone

Cryogenic negative ion photoelectron (NIPE) spectra of the radical anion of 2,7-naphthoquinone (<b>NQ</b>^{<b>•–</b>}<b>)</b> have been taken at 20 K, using 193, 240, 266, 300, and 355 nm lasers for electron detachment. The electron affinity of the <b>NQ</b> diradical is determined from the first resolved peak in the NIPE spectrum to be 2.880 ± 0.010 eV. CASPT2/aug-cc-pVDZ calculations predict with reasonable accuracy the positions of the 0–0 bands in the three lowest electronic states of <b>NQ</b>. In addition, the Franck–Condon factors calculated from the CASPT2/aug-cc-pVDZ optimized geometries, vibrational frequencies, and normal modes successfully simulate the vibrational structures in these bands. The NIPE spectrum of <b>NQ</b>^{<b>•–</b>} confirms that, as predicted, ³B₂ is the ground state, and the ¹B₂ and ¹A₁ states are, respectively, 12.7 and 16.4 kcal/mol higher in energy than the triplet ground state. The experimental value of <i>Δ<i>E</i></i>_ST = 12.7 kcal/mol in <b>NQ</b> and the finding that ¹B₂ is the lower energy of the two singlet states confirm the results of the previous calculations on <b>NQ</b>. These calculations predicted an <i>increase</i> in Δ<i>E</i>_ST on the substitution of both methylene groups in 2,7-naphthoquinodimethane (<b>NQDM</b>) by oxygens in <b>NQ</b>, thus providing a dramatic contrast to the decrease of 17.5 kcal/mol in Δ<i>E</i>_ST found for substitution of one methylene group by one oxygen on going from trimethylenemethane (<b>TMM</b>) to oxyallyl (<b>OXA</b>)