The almost bottleable triplet carbene: 2,6-dibromo-4-tert-butyl-2',6'-bis(trifluoromethyl)-4'-isopropyldiphenylcarbene.

Computations on 2,6-dibromo-4-tert-butyl-2',6'-bis(trifluoromethyl)-4'-isopropyldiphenylcarbene (1) using ab initio and density functional theory methods underscore the unusual stability of the triplet over the singlet state. At the B3LYP/6-311G(d,p) level, the triplet state had a slightly bent central C-C-C bond angle of 167 degrees, whereas this angle in the singlet was 134 degrees. The B3LYP singlet-triplet splitting (12.2 kcal/mol) was larger than that of the parent molecule (5.8 kcal/mol), diphenylcarbene (2), which also has a triplet ground state. The energy of a suitable isodesmic reaction showed the triplet and singlet states of (1) to be destabilized, by 6.3 and 12.5 kcal/mol, respectively, due to the combined effects of the CF3, Br, and alkyl substituents. The linear-coplanar form of (3)(1), which might facilitate dimerization or electrophilic attack at the more exposed diradical center, was prohibitively (35.9 kcal/mol) higher in energy. Our results confirm Tomioka's conclusion that the triplet diarylcarbene, ortho-substituted with bulky CF3 and Br substituents, is persistent due to steric protection of the diradical center. Dimerization and other possible reaction pathways are inhibited, not only by the bulky ortho substituents but also by the para alkyl groups. The increase in stability of the triplet ((3)(1)) state relative to the singlet ((1)(1)) state does not influence the reactivity directly.     

The nature and extent of pi-stabilization within foiled carbenes

B3LYP/6-311+G(d,p) computations of the stabilization energies, singlet-triplet energy gaps, and lowest transition states for a set of cyclic alkenylidenes were performed in order to find the strongest interactions between the C-C double bond and the carbene center. The results suggest that among the alkenylidenes investigated in this study, those with a norbornenylidene structure represent strongly stabilized carbenes with a reduced reactivity toward intermolecular reactions. Further stabilization is found when the double bond is electron-rich or pyramidalized. Thus, for the rearrangement of syn-34 to take place, an activation barrier of about 22 kcal/mol needs to be overcome. The inclination to undergo a retro-Skatteb?l rearrangement, which to our knowledge has never been observed experimentally, is characteristic for highly stabilized foiled carbenes.     

Carbene stabilization by aryl substituents. Is bigger better?

The geometries and relative stabilities of the singlet and triplet states of phenyl- (Cs), diphenyl- (C2), 1-naphthyl- (Cs), di(1-naphthyl)- (C2), and 9-anthryl-substituted (Cs) carbenes were investigated at the B3LYP/6-311+G(d,p) + ZPVE level of density functional theory. The singlet-triplet energy separations (DeltaEST), 2.7, 2.9, 3.4, 3.7, and 5.7 kcal/mol, respectively, after including an empirical correction (2.8 kcal/mol) based on the error in the computed singlet-triplet gap for methylene versus experiment, are in good agreement with available experimental values. Consistent with literature reports, triplet di(9-anthryl)carbene has a linear, D2d symmetrical, allene structure with 1.336 A C=C bond lengths and considerable biradical character. B3LYP favors such cumulene biradical structures and triplet spin states and predicts a large (>15 kcal/mol) "di(9-anthryl)carbene" singlet-triplet (biradical) energy gap. The resonance stabilization of both singlet and triplet carbenes increases modestly with the size of the arene substituent and overall, (di)arylcarbenes, both singlet and triplet, are better stabilized by bigger substituents. For example, methylene is stabilized more by a naphthyl than a phenyl group (singlets, 26.6 versus 24.4; and triplets, 20.9 versus 18.1 kcal/mol, respectively). The carbene geometries are affected by both steric effects and arene-carbene orbital interactions (sigma-p and p-pi). For instance, the central angles at the carbene are widened by a second arene group, which leads to increased s-character and shorter carbene bond lengths (i.e., C-C, C-H). In general, the aromaticity of the substituted rings in triplet carbenes is most affected by the presence of the unpaired electrons.     

Carbene Rearrangements Unsurpassed: Details of the C(7)H(6) Potential Energy Surface Revealed

The rearrangement of phenylcarbene (1) to 1,2,4,6-cycloheptatetraene (3) has been studied theoretically, using SCF, CASSCF, CASPT2N, DFT (B3LYP), CISD, CCSD, and CCSD(T) methods in conjunction with the 6-31G, 6-311+G, 6-311G(2d,p), cc-pVDZ, and DZd basis sets. Stationary points were characterized by vibrational frequency analyses at CASSCF(8,8)/6-31G and B3LYP/6-31G. Phenylcarbene (1) has a triplet ground state ((3)A") with a singlet-triplet separation (DeltaE(ST)) of 3-5 kcal mol(-)(1). In agreement with experiment, chiral 3 is the lowest lying structure on this part of the C(7)H(6) potential energy surface. Bicyclo[4.1.0]hepta-2,4,6-triene (2) is an intermediate in the rearrangement of 1 into 3, but it is unlikely to be observable experimentally due to a barrier height of only 1-2 kcal mol(-)(1). The enantiomers of 3 interconvert via the (1)A(2) state of cycloheptatrienylidene (4) with an activation energy of 20 kcal mol(-)(1). The "aromatic" (1)A(1) state, previously believed to be the lowest singlet state of 4, is roughly 10 kcal mol(-)(1) higher in energy than the (1)A(2) state, and, in violation of Hund's rule, (3)A(2) is also calculated to lie above (1)A(2) in energy. Thus, even if (3)A(2) were populated, it is likely to undergo rapid intersystem crossing to (1)A(2). We suggest (3)B(1)-4 is the metastable triplet observed by EPR.     

Homoaromaticity in carbene intermediates

Analyses of isodesmic reactions for singlet 7-carbenanorbornene (4S), 8-carbena-endo-tricyclo[3.2.1.0(2,4)]octane (5S), 3-carbenabicyclo[3.1.0]hexane (3S), 2-carbenanorbornene 6S, and 2-carbenabicyclooctadiene 7S at the B3LYP/6-311+G(3df, 2p)//B3LYP/6-31G level provide stabilization energies of 13.83, 13. 50, 3.00, -2.22, and -3.01 kcal/mol, respectively. The C7 carbene in 4S and the C8 carbene center in 5S are strongly bent toward the double bond and cyclopropane ring, respectively, in contrast to their related triplets, 4T and 5T and parent hydrocarbons. The geometric change for 3S compared to 3T or to parent bicyclo[3.1. 0]hexane is minimal. Comparison of the stability of 6S with 2-carbenanorbornane and the geometry of 6S with that of 6T and also with the singlet and triplet 2-carbenanorbornane suggests very modest bridging. The stabilization energy and geometry of 2-carbenabicyclooctadiene 7 resemble antihomoaromatic bicyclooctadienyl cation 9 rather than the related homoaromatic bicyclooctadienyl anion 8. The diamagnetic susceptibility exhaltations (Deltachi) of 3, 4, 5, and 7, calculated at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G level, are -0.7, 22.7, 26.0, and -10.3 cgs-ppm, respectively. The singlet-triplet energy differences, DeltaE(TS), for carbenacyclohexane, carbenacyclopentane, 3, 4, 5, 6, 7, and 2-carbenabicyclo[3.2.1]oct-3-ene at the B3LYP/6-311+G(3df, 2p)//B3LYP/6-31G level are 3.4, 10.3, 8.8, 27.1, 25.9, 12.7, -4.0, and -0.9 kcal/mol, respectively.     

Corannulene as a Lewis base: computational modeling of protonation and lithium cation binding.

A computational modeling of the protonation of corannulene at B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p) and of the binding of lithium cations to corannulene at B3LYP/6-311G(d,p)//B3LYP/6-31G(d,p) has been performed. A proton attaches preferentially to one carbon atom, forming a sigma-complex. The isomer protonated at the innermost (hub) carbon has the best total energy. Protonation at the outermost (rim) carbon and at the intermediate (bridgehead rim) carbon is less favorable by ca. 2 and 14 kcal mol(-)(1), respectively. Hydrogen-bridged isomers are transition states between the sigma-complexes; the corresponding activation energies vary from 10 to 26 kcal mol(-)(1). With an empirical correction obtained from calculations on benzene, naphthalene, and azulene, the best estimate for the proton affinity of corannulene is 203 kcal mol(-)(1). The lithium cation positions itself preferentially over a ring. There is a small energetic preference for the 6-ring over the 5-ring binding (up to 2 kcal mol(-)(1)) and of the convex face over the concave face (3-5 kcal mol(-)(1)). The Li-bridged complexes are transition states between the pi-face complexes. Movement of the Li(+) cation over either face is facile, and the activation energy does not exceed 6 kcal mol(-)(1) on the convex face and 2.2 kcal mol(-)(1) on the concave face. In contrast, the transition of Li(+) around the corannulene edge involves a high activation barrier (24 kcal mol(-)(1) with respect to the lowest energy pi-face complex). An easier concave/convex transformation and vice versa is the bowl-to-bowl inversion with an activation energy of 7-12 kcal mol(-)(1). The computed binding energy of Li(+) to corannulene is 44 kcal mol(-)(1). Calculations of the (7)Li NMR chemical shifts and nuclear independent chemical shifts (NICS) have been performed to analyze the aromaticity of the corannulene rings and its changes upon protonation.     

Hydride affinity scale of various substituted arylcarbeniums in acetonitrile

Combined with the integral equation formalism polarized continuum model (IEFPCM), the hydride affinities of 96 various acylcarbenium ions in the gas phase and CH(3)CN were estimated by using the B3LYP/6-31+G(d)//B3LYP/6-31+G(d), B3LYP/6-311++G(2df,2p)//B3LYP/6-31+G(d), and BLYP/6-311++G(2df,2p)//B3LYP/6-31+G(d) methods for the first time. The results show that the combination of the BLYP/6-311++G(2df,2p)//B3LYP/6-31+G(d) method and IEFPCM could successfully predict the hydride affinities of arylcarbeniums in MeCN with a precision of about 3 kcal/mol. On the basis of the calculated results from the BLYP method, it can be found that the hydride affinity scale of the 96 arylcarbeniums in MeCN ranges from -130.76 kcal/mol for NO(2)-PhCH(+)-CN to -63.02 kcal/mol for p-(Me)(2)N-PhCH(+)-N(Me)(2), suggesting most of the arylcarbeniums are good hydride acceptors. Examination of the effect of the number of phenyl rings attached to the carbeniums on the hydride affinities shows that the increase of the hydride affinities takes place linearly with increasing number of benzene rings in the arylcarbeniums. Analyzing the effect of the substituents on the hydride affinities of arylcarbeniums indicates that electron-donating groups decrease the hydride affinities and electron-withdrawing groups show the opposite effect. The hydride affinities of arylcarbeniums are linearly dependent on the sum of the Hammett substituent parameters σ(p)(+). Inspection of the correlation of the solution-phase hydride affinities with gas-phase hydride affinities and aqueous-phase pK(R)(+) values reveals a remarkably good correspondence of ΔG(H(-)A)(R(+)) with both the gas-phase relative hydride affinities only if the α substituents X have no large electron-donating or -withdrawing properties and the pK(R)(+) values even though the media are dramatically different. The solution-phase hydride affinities also have a linear relationship with the electrophilicity parameter E, and this dependence can certainly serve as one of the most effective ways to estimate the new E values from ΔG(H(-)A)(R(+)) or vice versa. Combining the hydride affinities and the reduction potentials of the arylcarbeniums, we obtained the bond homolytic dissociation Gibbs free energy changes of the C-H bonds in the corresponding hydride adducts in acetonitrile, ΔG(HD)(RH), and found that the effects of the substituent on ΔG(HD)(RH) are very small. Simple thermodynamic analytic platforms for the three C-H cleavage modes were constructed. It is evident that the present work would be helpful in understanding the nature of the stabilities of the carbeniums and mechanisms of the hydride transfers between carbeniums and other hydride donors.     

Substituent effects on singlet-triplet gaps and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidenes to 1,3-oxazoles

Electronic structures, partial atomic charges, singlet-triplet gaps (Delta E ST), substituent effects, and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidene ( 5) and 4,5-dimethyl- ( 6), 4,5-difluoro- ( 7), 4,5-dichloro- ( 8), 4,5-dibromo- ( 9), and 3-methyl-1,3-oxazol-2-ylidene ( 10) to the corresponding 1,3-oxazoles have been studied using complete-basis-set methods (CBS-QB3, CBS-Q, CBS-4M), second-order M?ller-Plesset perturbation method (MP2), hybrid density functionals (B3LYP, B3PW91), coupled-cluster theory with single and double excitations (CCSD) and CCSD plus perturbative triple excitations [CCSD(T)], and the quadratic configuration interaction method including single and double excitations (QCISD) and QCISD plus perturbative triple excitations [QCISD(T)]. The 6-311G(d,p), 6-31+G(d,p), 6-311+G(d,p), and correlation-consistent polarized valence double-xi (cc-pVDZ) basis sets were employed. The carbenes have singlet ground states, and the CBS-QB3 and CBS-Q methods predict Delta E ST values for 5- 8 and 10 of 79.9, 79.8, 74.7, 77.0, and 82.0 kcal/mol, respectively. CCSD(T), QCISD(T), B3LYP, and B3PW91 predict smaller Delta E ST values than CBS-QB3 and CBS-Q, with the hybrid density functionals predicting the smallest values. The concerted unimolecular exothermic out-of-plane 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes to their respective 1,3-oxazoles proceed via cyclic three-center transition states. The CBS-predicted barriers to the 1,2-rearrangements of singlet carbenes 5- 9 to their respective 1,3-oxazoles are 41.4, 40.4, 37.8, 40.4, and 40.5 kcal/mol, respectively. During the 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes 5- 9, there is a decrease in electron density at oxygen, N3 (the migration origin), and C5 and an increase in electron density at C2 (the migration terminus), C4, and the partially positive migrating hydrogen.     

Computational study of the electronic structure of substituted phenylcarbene in the gas phase

Gas-phase calculations for ortho-, meta-, and para-substituted phenylcarbenes demonstrate that aromatic ring substituents can have a large effect on the singlet-triplet splitting in these molecules. For example, p-aminophenylcarbene is predicted to have a singlet-triplet splitting (DeltaE(ST)) of 0.7 kcal/mol, which is 4.7 kcal/mol smaller than that of the parent phenylcarbene. However, when the mesomeric effect of pi-donation is removed, as in the meta-substituted molecules, this affect is greatly attenuated. m-Amino substitution lowers the DeltaE(ST) to 5.2 kcal/mol, a change of only 0.2 kcal/mol from the parent phenylcarbene. The sensitivity of phenylcarbene to substitution is judged by the slope of the line correlating the singlet-triplet gaps to linear free energy (LFE) parameters. In this study, the best linear correlation for DeltaE(ST) in the para-substituted phenycarbenes is observed when plotted against sigma(p)(+). The resultant slope (rho) is 5.0. The origin of this effect is preferential interaction of aryl substituents with the singlet rather than the triplet species as demonstrated by electron density analyses.     

A computational study of conformational interconversions in 1,4-dithiacyclohexane (1,4-dithiane)

Ab initio molecular orbital theory with the 6-31G(d), 6-31G(d,p), 6-31+G(d), 6-31+G(d,p), 6-31+G(2d,p), 6-311G(d), 6-311G(d,p), and 6-311+G(2d,p) basis sets and density functional theory (BLYP, B3LYP, B3P86, B3PW91) have been used to locate transition states involved in the conformational interconversions of 1,4-dithiacyclohexane (1,4-dithiane) and to calculate the geometry optimized structures, relative energies, enthalpies, entropies, and free energies of the chair and twist conformers. In the chair and 1,4-twist conformers the C-Hax and C-Heq bond lengths are equal at each carbon, which suggest an absence of stereoelectronic hyperconjugative interactions involving carbon-hydrogen bonds. The 1,4-boat transition state structure was 9.53 to 10.5 kcal/mol higher in energy than the chair conformer and 4.75 to 5.82 kcal/mol higher in energy than the 1,4-twist conformer. Intrinsic reaction coordinate (IRC) calculations showed that the 1,4-boat transition state structure was the energy maximum in the interconversion of the enantiomers of the 1,4-twist conformer. The energy difference between the chair conformer and the 1,4-twist conformer was 4.85 kcal/mol and the chair-1,4-twist free energy difference (deltaG degrees (c-t)) was 4.93 kcal/mol at 298.15 K. Intrinsic reaction coordinate (IRC) calculations connected the transition state between the chair conformer and the 1,4-twist conformer. This transition state is 11.7 kcal/mol higher in energy than the chair conformer. The effects of basis sets on the 1,4-dithiane calculations and the relative energies of saturated and unsaturated six-membered dithianes and dioxanes are also discussed.     

Quadricyclane radical cation rearrangements: a computational study of the transformations to 1,3,5-cycloheptatriene and norbornadiene

An alternative skeletal rearrangement of the quadricyclane radical cation (Q*+) explains the side products formed in the one-electron oxidation to norbornadiene. First, the bicyclo[2.2.1]hepta-2-ene-5-yl-7-ylium radical cation, with an activation energy of 14.9 kcal mol(-1), is formed. Second, this species can further rearrange to 1,3,5-cycloheptatriene through two plausible paths, that is, a multistep mechanism with two shallow intermediates and a stepwise path in which the bicyclo[3.2.0]hepta-2,6-diene radical cation is an intermediate. The multistep rearrangement has a rate-limiting step with an estimated activation energy of 16.5 kcal mol(-1), which is 2.8 kcal mol(-1) lower in energy than the stepwise mechanism. However, the lowest activation energy is found for the Q*+ cycloreversion to norbornadiene that has a transition structure, in close correspondence with earlier studies, and an activation energy of 10.1 kcal mol(-1), which agrees well with the experimental estimate of 9.3 kcal mol(-1). The computational estimates of activation energies were done using the CCSD(T)/6-311+G(d,p) method with geometries optimized on the B3LYP/6-311+G(d,p) level, combined with B3LYP/6-311+G(d,p) frequencies.     

13C NMR, infrared, solvation and theoretical investigation of the conformational isomerism in 1-haloacetones (X = Cl, Br and I)

The solvent dependence of the 13C NMR spectra of chloroacetone (CA), bromoacetone (BA) and iodoacetone (IA) are reported and the 3J(CH) couplings analysed using ab initio calculations and solvation theory. In CA the energy difference (E(cis) - E(gauche)) between the cis (Cl-C-C=O 0 degrees) and gauche (Cl-C-C=O 155 degrees) conformers is 1.7 kcal mol(-1) in the vapour, decreasing to 0.8 kcal mol(-1) in CCl4 solution and to -1.0 kcal mol(-1) in the pure liquid. The conformational equilibrium, in BA, is between the more polar cis (Br-C-C=O 0 degrees) and gauche (Br-C-C=O 132 degrees) conformations. The energy difference (E(cis) - E(gauche)) is 1.8 kcal mol(-1) in the vapour, decreasing to 0.9 kcal mol(-1) in CCl4 solution and to -0.4 kcal mol(-1) in the pure liquid. The energy difference (E(cis) - E(gauche)), in IA, between the cis (I-C-C=O 0 degrees) and gauche (I-C-C=O 104 degrees) conformers is 1.1 kcal mol(-1) in the vapour phase, decreasing to 0.5 kcal mol(-1) in CCl4 solution and to -0.5 kcal mol(-1) in the pure liquid. The vapour state energy difference for BA [1.4 kcal mol(-1) at B3LYP/6-311++G(d,p)] and for IA [1.6 kcal mol(-1) at B3LYP/6-311++G(d,p)/LANL2DZ)] are in very good agreement with the above values. For CA the agreement is also satisfactory [1.4 kcal mol(-1) at B3LYP/6-311++G(d,p)].     

A new scheme for determining the intramolecular seven-membered ring N-H...O=C hydrogen-bonding energies of glycine and alanine peptides

In this paper a new scheme was proposed to calculate the intramolecular hydrogen-bonding energies in peptides and was applied to calculate the intramolecular seven-membered ring N-H...O=C hydrogen-bonding energies of the glycine and alanine peptides. The density-functional theory B3LYP6-31G(d) and B3LYP6-311G(d,p) methods and the second-order Moller-Plesset perturbation theory MP26-31G(d) method were used to calculate the optimal geometries and frequencies of glycine and alanine peptides and related structures. MP26-311++G(d,p), MP26-311++G(3df,2p), and MP2/aug-cc-pVTZ methods were then used to evaluate the single-point energies. It was found that the B3LYP6-31G(d), MP26-31G(d), and B3LYP6-311G(d,p) methods yield almost similar structural parameters for the conformers of the glycine and alanine dipeptides. MP2/aug-cc-pVTZ predicts that the intramolecular seven-membered ring N-H...O=C hydrogen-bonding strength has a value of 5.54 kcal/mol in glycine dipeptide and 5.73 and 5.19 kcal/mol in alanine dipeptides, while the steric repulsive interactions of the seven-membered ring conformers are 4.13 kcal/mol in glycine dipeptide and 6.62 and 3.71 kcal/mol in alanine dipeptides. It was also found that MP26-311++G(3df,2p) gives as accurate intramolecular N-H...O=C hydrogen-bonding energies and steric repulsive interactions as the much more costly MP2/aug-cc-pVTZ does.     

Isomerization pathways from the norbornadiene to the cycloheptatriene radical cation by opening a bridgehead-methylene bond: a theoretical investigation

Three skeletal rearrangement channels for the norbornadiene (N*+) to the 1,3,5-cycloheptatriene (CHT*+) radical cation conversion, initialized by opening a bridgehead-methylene bond in N*+, are investigated using the quantum chemical B3LYP, MP2 and CCSD(T) methods in conjunction with the 6-311 +G(d,p) basis set. Two of the isomerizations proceed through the norcaradiene radical cation (NCD*+), either through a concerted path (N*+ - NCD*+), or by a stepwise mechanism via a stable intermediate (N*+ - I1 - NCD*+). At the CCSD(T)/6-311 +G(d,p)//B3LYP/6-311 +G(d,p) level, the lowest activation energy, 28.9 kcal mol(-1), is found for the concerted path whereas the stepwise path is found to be 2.3 kcal mol(-1) higher. On both pathways, NCD*+ rearranges further to CHT*+ with significantly less activation energy. The third channel proceeds from N*+ through I1 and then directly to CHT*+, with an activation energy of 37.1 kcal mol(-1). The multi-step channel reported earlier by our group, which proceeds from N*+ to CHT*+ via the quadricyclane and the bicyclo[2.2.1]hepta-2-ene-5-yl-7-ylium radical cations, is 4.6 kcal mol(-1) lower than the most favorable path of the present study. If the methylene group is substituted with C(CH3)2, however, the concerted path is estimated to be 5.6 kcal mol(-1) lower than the corresponding substituted multi-step path at the B3LYP/6-311+(d,p) level. This shows that substitution of particular positions can have dramatic effects on altering reaction barriers in the studied rearrangements. We also note that identical energies are computed for CHT*+ and NCD*+ whereas, in earlier theoretical investigations, the former was reported to be 6-17 kcal mol(-1) more stable than the latter. Finally, a bent geometry is obtained for CHT*+ with MP2/6-311 +G(d,p) in contradiction with the planar conformation reported for this cation in earlier computational studies.     

Effects of ethynyl substitution on cyclobutadiene

The effects of ethynyl substitution on cyclobutadiene are explored via density functional theory and coupled-cluster calculations. The computed singlet-triplet gaps indicate a monotonic dependence on the degree of ethynyl substitution, which differentially stabilizes the triplet relative to the singlet ground state and reduces the gap. A series of isodesmic, homodesmotic, and hyperhomodesmotic equations are employed to quantify the stabilization upon ethynyl substitution. Analyses that rely on a simple isodesmic equation and/or B3LYP/6-31G(d) values are found to be problematic. Analyses that rely on homodesmotic or hyperhomodesmotic equations, in conjunction with CCSD/cc-pVDZ values, are more robust. Using a hyperhomodesmotic equation to assess the stabilization enthalpies of tetra-substituted singlet cyclobutadienes, our analysis predicts tetramethylcyclobutadiene (ΔH(0)(rxn) = -17.3 kcal/mol) to be more stable than tetraethynylcyclobutadiene (ΔH(0)(rxn) = -11.7 kcal/mol), which, in turn, is substantially more stable than tetracyanocyclobutadiene (ΔH(0)(rxn) = +12.7 kcal/mol).     

Density functional theory calculations of the lowest energy quintet and triplet states of model hemes: role of functional, basis set, and zero-point energy corrections

We investigated the effect of several computational variables, including the choice of the basis set, application of symmetry constraints, and zero-point energy (ZPE) corrections, on the structural parameters and predicted ground electronic state of model 5-coordinate hemes (iron(II) porphines axially coordinated by a single imidazole or 2-methylimidazole). We studied the performance of B3LYP and B3PW91 with eight Pople-style basis sets (up to 6-311+G*) and B97-1, OLYP, and TPSS functionals with 6-31G and 6-31G* basis sets. Only hybrid functionals B3LYP, B3PW91, and B97-1 reproduced the quintet ground state of the model hemes. With a given functional, the choice of the basis set caused up to 2.7 kcal/mol variation of the quintet-triplet electronic energy gap (DeltaEel), in several cases, resulting in the inversion of the sign of DeltaEel. Single-point energy calculations with triple-zeta basis sets of the Pople (up to 6-311G++(2d,2p)), Ahlrichs (TZVP and TZVPP), and Dunning (cc-pVTZ) families showed the same trend. The zero-point energy of the quintet state was approximately 1 kcal/mol lower than that of the triplet, and accounting for ZPE corrections was crucial for establishing the ground state if the electronic energy of the triplet state was approximately 1 kcal/mol less than that of the quintet. Within a given model chemistry, effects of symmetry constraints and of a "tense" structure of the iron porphine fragment coordinated to 2-methylimidazole on DeltaEel were limited to 0.3 kcal/mol. For both model hemes the best agreement with crystallographic structural data was achieved with small 6-31G and 6-31G* basis sets. Deviation of the computed frequency of the Fe-Im stretching mode from the experimental value with the basis set decreased in the order: nonaugmented basis sets, basis sets with polarization functions, and basis sets with polarization and diffuse functions. Contraction of Pople-style basis sets (double-zeta or triple-zeta) affected the results insignificantly for iron(II) porphyrin coordinated with imidazole. Poor performance of a "locally dense" basis set with a large number of basis functions on the Fe center was observed in calculation of quintet-triplet gaps. Our results lead to a series of suggestions for density functional theory calculations of quintet-triplet energy gaps in ferrohemes with a single axial imidazole; these suggestions are potentially applicable for other transition-metal complexes.     

Novel substituent effects on the mechanism of the thermal denitrogenation of 2,3-diazabicyclo[2.2.1]hept-2-ene derivatives, stepwise versus concerted

The substituent effect on the thermal denitrogenation mechanism of 7,7-disubstituted 2,3-diazabicyclo[2.2.1]hept-2-enes, concerted versus stepwise, has been investigated in detail. Unrestricted DFT calculations at the B3LYP/6-31G(d) level of theory suggest that azoalkanes that possess electron-withdrawing substituents at C(7) prefer to expel the nitrogen molecule in a stepwise manner. The activation energy is calculated to be ca. 36 kcal/mol for the dihydroxy-substituted azoalkane. In contrast, the preferred mechanism of the concerted denitrogenation is predicted for azoalkanes that possess electron-donating substituents at C(7). The activation energy is computed to be ca. 28 kcal/mol for the silyl-substituted azoalkane. The theoretical prediction of the substituent effects on the mechanistic change is supported by analyzing the activation parameters of the azoalkane decompositions. The activation enthalpy for the decomposition of the 7,7-diethoxy-substituted azoalkane is determined to be 39.1 kcal/mol, which is 13.1 kcal/mol higher in energy for the denitrogenation of the 7-silyl-substituted azoalkane. These dramatic substituent effects can be reasonably explained by the preferred electronic configuration of the lowest singlet state of the cyclopentane-1,3-diyls produced during the denitrogenation of the azoalkanes.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Transition state structure and energetics of the N(2)O + X (X = Cl,Br) reactions

The structural and vibrational properties of the transition state of the N(2)O + X (X = Cl,Br) reactions have been characterized by ab initio methods using density functional theory. We have employed Becke's hybrid functional (B3LYP), and transition state optimizations were performed with 6-31G(d), 6-311G(2d,2p), 6-311+G(3d,2p), and 6-311+G(3df,2p) basis sets. For the chlorine atom reaction the coupled-cluster method (CCSD(T)) with 6-31G(d) basis set was also used. All calculations resulted in transition state structures with a planar cis arrangement of atoms for both reactions. The geometrical parameters of transition states at B3LYP are very similar, and the reaction coordinates involve mainly the breaking of the N-O bond. At CCSD(T)/6-31G(d) level a contribution of the O-Cl forming bond is also observed in the reaction coordinate. In addition, several highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction energetics. All model chemistries predict exothermic reactions. The G3 and G2 methods result in the smallest deviations from experiment, 1.8 and 0 kcal mol(-1), for the enthalpies of reaction for N(2)O reaction with chlorine and bromine, respectively. The G3//B3LYP and G1 methods perform best among the composite methods in predicting energies of the transition state, with a deviation of 1.9 and 3.0 kcal mol(-1), respectively, in the activation energies for the above processes. However, the B3LYP/6-311+G(3df,2p) method gives smaller deviations of 0.4 and -1.0 kcal mol(-1), respectively. The performance of the methodologies applied in predicting transition state energies was analyzed.