Singlet hydrocarbon carbenes with high barriers toward isomerization: a computational investigation

A prerequisite for a stable singlet hydrocarbon carbene is the existence of high barriers toward isomerization. Four derivatives of cyclopentylidene (1-4) with rigid and varying carbon cages are examined computationally at the B3LYP/6-311+G(d,p) level of theory. Singlet ground states are predicted for carbenes 1-4, with DeltaE(ST)'s = 7-22 kcal/mol. The rearrangement paths considered are 1,3-hydrogen shift, 1,2-carbon shift and beta-CC bond-cleavage. Carbenes 3 and 4 lie in relatively shallow potential-energy wells (around 4 and 6 kcal/mol, respectively) and are expected to rearrange via 1,3-hydrogen shifts to cyclopropane derivatives. For 1 and 2, the lowest energy rearrangement path is beta-CC bond-cleavage requiring about 12 and 20 kcal/mol, respectively, placing 2 in the deepest potential-energy well among the four carbenes.     

An ab initio study of the photochemical decomposition of 3, 3-dimethyldiazirine

Photochemical decomposition of 3,3-dimethyldiazirine (DMD) has been computationally investigated by using high-level ab initio calculations in conjunction with the 6-31G and cc-pvdz basis sets. The geometries of minima and transition states, as well as conical intersection points in the seam of crossing of two surfaces, have been optimized with the complete active space self-consistent field (CAS-SCF) method, and their energies, recalculated with second-order multireference perturbation (CAS/MP2) theory. The reaction path starting at the excited n-pi state of DMD is predicted to occur via a nonadiabatic mechanism, giving carbene and molecular dinitrogen (both in their singlet ground states) as the main products; the computed barrier height (1.0 kcal mol(-)(1)) agrees well with the experimental estimate of the activation energy in the singlet excited state (0.0-1.5 kcal mol(-)(1)). Ground state of dimethylcarbene is the only species where a 1,2-hydrogen shift takes place, being the only source of propene. The calculated potential energy barrier height for dimethylcarbene to propene isomerization (2.6 kcal mol(-)(1)) agrees well with the observed activation energy (2.56 kcal mol(-)(1)). No evidence for rearrangement in the first singlet excited state of DMD has been found; such a process would lead to a higher activation energy than the observed one. Consequently, 1,2-hydrogen migration concurrent with N(2) extrusion in the excited state has been ruled out.     

New insight into the gas-phase bimolecular self-reaction of the HOO radical

The singlet and triplet potential energy surfaces (PESs) for the gas-phase bimolecular self-reaction of HOO*, a key reaction in atmospheric environments, have been investigated by means of quantum-mechanical electronic structure methods (CASSCF and CASPT2). All the reaction pathways on both PESs consist of a first step involving the barrierless formation of a prereactive doubly hydrogen-bonded complex, which is a diradical species lying about 8 kcal/mol below the energy of the reactants at 0 K. The lowest energy reaction pathway on both PESs is the degenerate double hydrogen exchange between the HOO* moieties of the prereactive complex via a double proton transfer mechanism involving an energy barrier of only 1.1 kcal/mol for the singlet and 3.3 kcal/mol for the triplet at 0 K. The single H-atom transfer between the two HOO* moieties of the prereactive complex (yielding HOOH + O2) through a pathway keeping a planar arrangement of the six atoms involves a conical intersection between either two singlet or two triplet states of A' and A" symmetries. Thus, the lowest energy reaction pathway occurs via a nonplanar cisoid transition structure with an energy barrier of 5.8 kcal/mol for the triplet and 17.5 kcal/mol for the singlet at 0 K. The simple addition between the terminal oxygen atoms of the two HOO* moieties of the prereactive complex, leading to the straight chain H2O4 intermediate on the singlet PES, involves an energy barrier of 7.3 kcal/mol at 0 K. Because the decomposition of such an intermediate into HOOH + O2 entails an energy barrier of 45.2 kcal/mol at 0 K, it is concluded that the single H-atom transfer on the triplet PES is the dominant pathway leading to HOOH + O2. Finally, the strong negative temperature dependence of the rate constant observed for this reaction is attributed to the reversible formation of the prereactive complex in the entrance channel rather than to a short-lived tetraoxide intermediate.     

Singlet-triplet energy separation of cyclobutylidene

Ab initio (MP2, CCSD(T)) and density functional theory (BLYP, B3LYP) calculations provide insight concerning novel aspects of structure and bonding in cyclobutylidene (1). Singlet cyclobutylidene ((1)1) adopts a bicyclobutane-like structure (C(s) symmetry) that includes a weak, transannular bonding interaction between the carbene carbon and the opposing CH(2) group. Conformational ring inversion in (1)1 occurs through a transition state of C(2)(v)() symmetry (TS(1)1) with an enthalpy barrier of approximately 3 kcal/mol. Stabilization afforded the singlet state by the transannular interaction appears to be largely offset by a loss of hyperconjugative stabilization from the adjacent C-H bonds. Triplet cyclobutylidene ((3)1) exhibits a C(2)(v)() structure and conventional bonding. The triplet state lies 5.9 kcal/mol above the singlet ground state at the CCSD(T)/TZP//CCSD(T)/DZP level of theory. The singlet-triplet energy gap of cyclobutylidene (-5.9 kcal/mol) lies between that of an acyclic analogue, dimethylcarbene (-1.6 kcal/mol), and a highly strained analogue, cyclopropylidene (-13.8 kcal/mol). The magnitude of the energy gap suggests that triplet cyclobutylidene ((3)1) will be thermally accessible under a variety of experimental conditions.     

Formation of a Criegee intermediate in the low-temperature oxidation of dimethyl sulfoxide

Dimethyl sulfoxide (DMSO) is the major sulfur-containing constituent of the Marine Boundary Layer. It is a significant source of H2SO4 aerosol/particles and methane sulfonic acid via atmospheric oxidation processes, where the mechanism is not established. In this study, several new, low-temperature pathways are revealed in the oxidation of DMSO using CBS-QB3 and G3MP2 multilevel and B3LYP hybrid density functional quantum chemical methods. Unlike analogous hydrocarbon peroxy radicals the chemically activated DMSO peroxy radical, [CH3S(=O)CH2OO*]*, predominantly undergoes simple dissociation to a methylsulfinyl radical CH3S*(=O) and a Criegee intermediate, CH2OO, with the barrier to dissociation 11.3 kcal mol(-1) below the energy of the CH3S(=O)CH2* + O2 reactants. The well depth for addition of O2 to the CH3S(=O)CH2 precursor radical is 29.6 kcal mol(-1) at the CBS-QB3 level of theory. We believe that this reaction may serve an important role in atmospheric photochemical and irradiated biological (oxygen-rich) media where formation of initial radicals is facilitated even at lower temperatures. The Criegee intermediate (carbonyl oxide, peroxymethylene) and sulfinyl radical can further decompose, resulting in additional chain branching. A second reaction channel important for oxidation processes includes formation (via intramolecular H atom transfer) and further decomposition of hydroperoxide methylsulfoxide radical, *CH2S(=O)CH2OOH over a low barrier of activation. The initial H-transfer reaction is similar and common in analogous hydrocarbon radical + O2 reactions; but the subsequent very low (3-6 kcal mol(-1)) barrier (14 kcal mol(-1) below the initial reagents) to beta-scission products is not common in HC systems. The low energy reaction of the hydroperoxide radical is a beta-scission elimination of *CH2S(=O)CH2OOH into the CH2=S=O + CH2O + *OH product set. This beta-scission barrier is low, because of the delocalization of the *CH2 radical center through the -S(=O) group, to the -CH2OOH fragment in the transition state structure. The hydroperoxide methylsulfoxide radical can also decompose via a second reaction channel of intramolecular OH migration, yielding formaldehyde and a sulfur-centered hydroxymethylsulfinyl radical HOCH2S*(=O). The barrier of activation relative to initial reagents is 4.2 kcal mol(-1). Heats of formation for DMSO, DMSO carbon-centered radical and Criegee intermediate are evaluated at 298 K as -35.97 +/- 0.05, 13.0 +/- 0.2 and 25.3 +/- 0.7 kcal mol(-1) respectively using isodesmic reaction analysis. The [CH3S*(=O) + CH2OO] product set is shown to form a van der Waals complex that results in O-atom transfer reaction and the formation of new products CH3SO2* radical and CH2O. Proper orientation of the Criegee intermediate and methylsulfinyl radical, as a pre-stabilized pre-reaction complex, assist the process. The DMSO radical reaction is also compared to that of acetonyl radical.     

A semiempirical study of the optimized ground and excited state potential energy surfaces of retinal and its protonated Schiff base.

The electronic ground and first excited states of retinal and its Schiff base are optimized for the first time using the semiempirical AM1 Hamiltonian. The barrier for rotation about the C(11)-C(12) double bond is characterized by variation of both the twist angle delta(C(10)-C(11)-C(12)-C(13)) and the bond length d(C(11)-C(12)). The potential energy surface is obtained by varying these two parameters. The calculated ground state rotational barrier is equal to 15.6 kcal/mol for retinal and 20.5 kcal/mol for its Schiff base. The all-trans conformation is more stable by 3.7 kcal/mol than the 11-cis geometry. For the first excited state, S(1,) the 90 degrees twisted geometry represents a saddle point for retinal with the rotational barrier of 14.6 kcal/mol. In contrast, this conformation is an energy minimum for the Schiff base. It can be easily reached at room temperature from the planar minima since it is separated from them by a barrier of only 0.6 kcal/mol. The 90 degrees minimum conformation is more stable than the all-trans by 8.6 kcal/mol. We are thus able to present a reaction path on the S(1) surface of the retinal Schiff base with an almost barrier-less geometrical relaxation into a twisted minimum geometry, as observed experimentally. The character of the ground and first excited singlet states underscores the need for the inclusion of double excitations in the calculations.     

Theoretical studies on the photochemical reaction mechanisms of o-xylylene. Effects of phenyl group for electrocyclic reaction mechanism

The potential energy surfaces (PESs) of the electrocyclic reactions of o-xylylene at the ground and the lowest excited states are calculated by CASSCF molecular orbital and MRMP2 methods. The lowest excited state geometry of o-xylylene has C(2v) symmetry and is about 65 kcal mol(-1) in energy above the ground state. The PESs in the vicinity of the conical intersection are different from those of the electrocyclic reaction of cis-butadiene. In the vicinity of the conical intersection, the transition state at the ground state relating to methylene-cycloheptadienyl carbene is located. The transition state is only 4.3 kcal mol(-1) lower in energy than the conical intersection at the CASSCF(10,10)/6-31G(d) level and 0.5 kcal mol(-1) lower at the MRMP2/6-311+G(d,p) level. The transition state corresponding to benzocyclobutene does not locate in the vicinity of the conical intersection because of the resonance energy between benzene ring and methylene group.     

On the mechanism of the cis-trans isomerization in the lowest electronic states of azobenzene: S0, S1, and T1

In this paper, we identify the most efficient decay and isomerization route of the S(1), T(1), and S(0) states of azobenzene. By use of quantum chemical methods, we have searched for the transition states (TS) on the S(1) potential energy surface and for the S(0)/S(1) conical intersections (CIs) that are closer to the minimum energy path on the S(1). We found only one TS, at 60 degrees of CNNC torsion from the E isomer, which requires an activation energy of only 2 kcal/mol. The lowest energy CIs, lying also 2 kcal/mol above the S(1) minimum, were found on the torsion pathway for CNNC angles in the range 95-90 degrees. The lowest CI along the inversion path was found ca. 25 kcal/mol higher than the S(1) minimum and was characterized by a highly asymmetric molecular structure with one NNC angle of 174 degrees. These results indicate that the S(1) state decay involves mainly the torsion route and that the inversion mechanism may play a role only if the molecule is excited with an excess energy of at least 25 kcal/mol with respect to the S(1) minimum of the E isomer. We have calculated the spin-orbit couplings between S(0) and T(1) at several geometries along the CNNC torsion coordinate. These spin-orbit couplings were about 20-30 cm(-)(1) for all the geometries considered. Since the potential energy curves of S(0) and T(1) cross in the region of twisted CNNC angle, these couplings are large enough to ensure that the T(1) lifetime is very short ( approximately 10 ps) and that thermal isomerization can proceed via the nonadiabatic torsion route involving the S(0)-T(1)-S(0) crossing with preexponential factor and activation energy in agreement with the values obtained from kinetic measures.     

Synthesis of the arachno-4-CB(8)H(12)(2)(-) monocarbaborane dianion and NMR/computational studies of the fluxional processes observed in the isoelectronic nine-vertex arachno anions: arachno-4-CB(8)H(12)(2)(-), arachno-4-CB(8)H(13)(-), and arachno-4-SB(8)H(11)(-)

The new monocarbaborane dianion, arachno-4-CB(8)H(12)(2)(-) has been synthesized from the reaction of arachno-4-CB(8)H(14) with 2 equiv of NaH in polar solvents. DFT/GIAO computations at the B3LYP/6-311G//B3LYP/6-311G level, in conjunction with 1D and 2D NMR spectroscopic studies, have confirmed that the dianion results from deprotonation of both the endo-CH and one bridging hydrogen of the parent arachno-4-CB(8)H(14). While the DFT calculations indicate that a C(1) symmetric structure is lowest in energy, the experimental solution NMR data are consistent with the dianion having a C(s)() symmetric structure, thus suggesting that it is fluxional in solution. Transition state calculations located a low-energy pathway with an activation energy of only 2.7 kcal/mol that allows the migration of the bridging hydrogen between the two enantiomeric forms of the dianion. The process can occur by a single-step, simple rotation through a transition state structure containing a -BH(2) group at the B7 boron. Averaging the calculated (11)B NMR chemical shifts of the resonances for those atoms in the static enantiomeric structures that become equivalent by this fluxional process then gives excellent agreement with the solution NMR data. Transition state calculations of the fluxional behavior previously observed for the isoelectronic arachno-4-CB(8)H(13)(-) and arachno-4-SB(8)H(11)(-) monoanions have likewise revealed related low-energy (0.3 and 5.0 kcal/mol, respectively) rearrangement mechanisms involving the simultaneous rotation of three hydrogens (two bridging and one -BH(2)) through a C(s)() symmetry transition state containing three -BH(2) groups.     

Ab initio kinetics of the reaction of HCO with NO: abstraction versus association/elimination mechanism

The kinetics and mechanism for the reaction of HCO with NO occurring by both singlet and triplet electronic state potential-energy surfaces (PESs) have been studied at the modified Gaussian-2 level of theory based on the geometric parameters optimized by the Becke-3 Lee-Yang-Parr/6-311G(d,p) method. There are two major reaction channels on both singlet and triplet PESs studied: one is direct H abstraction producing CO+HNO and the other is association forming a stable HC(O)NO (nitrosoformaldehyde) molecule. The dominant reaction is predicted to be the direct H abstraction occurring primarily by the lowest-energy path via a loose hydrogen-bonding singlet molecular complex, ON...HCO, with a 2.9-kcal/mol binding energy and a small decomposition barrier (1.9 kcal/mol). The commonly assumed HC(O)NO intermediate, predicted to lie below the reactants by 27.7 kcal/mol, has a high HNO-elimination barrier (34.5 kcal/mol). Bimolecular rate constants for the formation of the singlet products and their branching ratios have been calculated in the temperature range of 200-3000 K. The rate constant for the disproportionation process producing HNO+CO, found to be affected strongly by multiple reflections above the well of the complex at low temperature, is predicted to be k(HNO)=3.08 x 10(-12) T(0.10) exp(242T) for 200-500 K, and 1.72 x 10(-16) T(1.47) exp(888T) for 500-3000 K in units of cm(3) molecule(-1) s(-1). The high- and low-pressure rate constants for the association process forming HC(O)NO can be represented by k(infinity)=4.42 x 10(-11) T(0.25) exp(-28T) cm(3) molecule(-1) s(-1) (200-3000 K) and k(0)=7.30x10(-16) T(-5.75) exp(-719T) (200-1000 K) and 1.82 x 10(2) T(-11.92) exp(1846T) (1000-3000 K) cm(6) molecule(-2) s(-1) for N(2)-buffer gas. The absolute values of total rate constant, predicted to be weakly dependent negatively on temperature but positively on pressure, are in close agreement with most experimental data within their reported errors.     

Insights into dynamics of the S2 state of thiophosgene from ab initio calculations

The S2 potential energy surface for Cl2CS dissociation has been characterized with a combined complete active space self-consistent field and multireference configuration interaction method. The S3/S2 minimum-energy intersection has been determined with the state-averaged complete active space self-consistent field method. The S2 direct dissociation was found to have a barrier of 6.0 kcal/mol, leading to formation of Cl(X2P)+ClCS(A2A") in the excited electronic state. Dynamics of the S2 state of Cl2CS can be summarized as follows: (1) The S2-S0 fluorescence occurs with high quantum yield at low excess energies; (2) Both the S(2) dissociation and the S2-->S3 internal conversion cause the loss of the S2-S0 fluorescence upon photoexcitation at 235-253 nm; (3) The S2-->S3 internal conversion (IC) followed by the direct IC to the ground electronic state results in the fragments produced in the ground state, while the S2 dissociation leads to formation of the fragments in excited electronic states.     

Dicyclobuta[de,ij]naphthalene and dicyclopenta[cd,gh]pentalene: a theoretical study

The structures, energetics, and aromatic character of dicyclobuta[de,ij]naphthalene, 1, dicyclopenta[cd,gh]pentalene, 2, dihydrodicyclobuta[de,ij]naphthalene, 3, and dihydrocyclopenta[cd,gh]pentalene, 4, have been examined at the B3LYP/6-311++G//B3LYP/6-31G level of theory. All molecules are bowl-shaped, and the pentalene isomers, 2 and 4, are most stable. A comparison with other C(12)H(6) and C(12)H(8) isomers indicates that 2 is approximately 25 kcal/mol less stable than 1,5,9-tridehydro[12]annulene and 4 is approximately 100 kcal/mol higher in energy than acenaphthylene, both of which are synthetically accessible. The transition state structure for bowl-to-bowl inversion of 1 is planar (D(2)(h)()) and lies 30.9 kcal/mol higher in energy than the ground state; the transition state for inversion of 2 is C(2)(h)() and lies 46.6 kcal/mol higher in energy. Symmetry considerations, bond length alternations, and NICS values (a magnetic criterion) all indicate that the ground states of 1, 3, and 4 are very aromatic; however, HOMA values (a measure of bond delocalization) indicate that 3S and 4S are aromatic but that 1S is less so. NICS values for the ground state of 2 strongly indicate aromaticity; however, bond localization, symmetry, and HOMA values argue otherwise.     

2-Pyridinethiol/2-pyridinethione tautomeric equilibrium. A comparative experimental and computational study

The gas phase and solvent dependent preference of the tautomerization between 2-pyridinethiol (2SH) and 2-pyridinethione (2S) has been assessed using variable temperature Fourier transform infrared (FTIR) experiments, as well as ab initio and density functional theory computations. No spectroscopic evidence (nu(S)(-)(H) stretch) for 2SH was observed in toluene, C(6)D(6), heptane, or methylene chloride solutions. Although, C(s)() 2SH is 2.61 kcal/mol more stable than C(s)() 2S (CCSD(T)/cc-pVTZ//B3LYP/6-311+G(3df,2p)+ZPE), cyclohexane solvent-field relative energies (IPCM-MP2/6-311+G(3df,2p)) favor 2S by 1.96 kcal/mol. This is in accord with the FTIR observations and in quantitative agreement with the -2.6 kcal/mol solution (toluene or C(6)D(6)) calorimetric enthalpy for the 2S/2SH tautomerization favoring the thione. As the intramolecular transition state for the 2S, 2SH tautomerization (2TS) lies 25 (CBS-Q) to 30 kcal/mol (CCSD/cc-pVTZ) higher in energy than either tautomer, tautomerization probably occurs in the hydrogen bonded dimer. The B3LYP/6-311+G(3df,2p) optimized C(2) 2SH dimer is 10.23 kcal/mol + ZPE higher in energy than the C(2)(h)() 2S dimer and is only 2.95 kcal/mol + ZPE lower in energy than the C(2) 2TS dimer transition state. Dimerization equilibrium measurements (FTIR, C(6)D(6)) over the temperature range 22-63 degrees C agree: K(eq)(298) = 165 +/- 40 M(-)(1), DeltaH = -7.0 +/- 0.7 kcal/mol, and DeltaS = -13.4 +/- 3.0 cal/(mol deg). The difference between experimental and B3LYP/6-311+G(3df,2p) [-34.62 cal/(mol deg)] entropy changes is due to solvent effects. The B3LYP/6-311+G(3df,2p) nucleus independent chemical shifts (NICS) are -8.8 and -3.5 ppm 1 A above the 2SH and 2S ring centers, respectively, and the thiol is aromatic. Although the thione is not aromatic, it is stabilized by the thioamide resonance. In solvent, the large 2S dipole, 2-3 times greater than 2SH, favors the thione tautomer and, in conclusion, 2S is thermodynamically more stable than 2SH in solution.     

Heats of formation of xenon fluorides and the fluxionality of XeF(6) from high level electronic structure calculations

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted for XeF(+), XeF(-), XeF(2), XeF(4), XeF(5)(-), and XeF(6) from coupled cluster theory (CCSD(T)) calculations with new correlation-consistent basis sets for Xe. To achieve near chemical accuracy (+/-1 kcal/mol), up to four corrections were added to the complete basis set binding energies based on frozen core coupled cluster theory energies: a correction for core-valence effects, a correction for scalar relativistic effects, a correction for first-order atomic spin-orbit effects, and in some cases, a second-order spin-orbit correction. Vibrational zero-point energies were computed at the coupled cluster level of theory. The structure of XeF(6) is difficult to obtain with the C(3)(v)() and O(h)() structures having essentially the same energy. The O(h)() structure is only 0.19 kcal/mol below the C(3)(v)() one at the CCSD(T)/CBS level using an approximate geometry for the C(3)(v)() structure. With an optimized C(3)(v)() geometry, the C(3)(v)() structure would probably become slightly lower in energy than the O(h)() one. The calculated heats of formation for the neutral XeF(n)() fluorides are less negative than the experimental values from the equilibrium measurements by 2.0, 7.7, and 12.2 kcal/mol for n = 2, 4, and 6, respectively. For the experimental values, derived from the photoionization measurements, this discrepancy becomes even larger, suggesting a need for a redetermination of the experimental values. Evidence is presented for the fluxionality of XeF(6) caused by the presence of a sterically active, free valence electron pair on Xe.     

Dissociation dynamics of thiolactic acid at 193 nm: detection of the nascent OH product by laser-induced fluorescence

Electronically excited thiolactic acid (2-mercaptopropionic acid), H(3)C-CH(SH)-COOH, undergoes the C-OH bond cleavage on excitation to the S(2) state at 193 nm, generating the primary product OH (v,J), which is detected by laser-induced fluorescence technique in a collisionless condition of flow system. The partitioning of the available energy between vibrational, rotational, and translational degrees of freedom of nascent photofragments is obtained from relative intensities of ro-vibronic lines in laser-induced fluorescence spectrum of OH, and their Doppler profiles. The rotational population of OH (v(")=0) is characterized by rotational temperature of 408+/-25 K. OH is produced in a vibrationally cold state, i.e., mostly in v(")=0. The average translational energy of OH (v(")=0,J(")) is found to be 21.5+/-2.0 kcal/mol, which implies 25.6 kcal/mol of energy in relative translation of photoproducts corresponding to the f(t) value of approximately 0.6. The observed high translational energy is due to the presence of a barrier in the exit channel, implying that the C-OH bond scission takes place on an electronically excited potential energy surface. The observed partitioning of the available energy between various degrees of the photofragments is theoretically modeled, and the hybrid model, with 26.0 kcal/mol of barrier in the exit channel, is found to explain the measured data quite well. The experimental results are also supported with ab initio molecular orbital calculations for both the ground and the excited electronic states. Time-dependent density functional theory is used to understand the nature of various electronic transitions connecting the lower excited states. Potential energy curves as a function of the C-OH bond length of thiolactic acid suggest distinct exit barriers in the S(1), T(1), and T(2) states. But, we could locate the transition state structure for OH formation in the S(1) state alone. Thus, although thiolactic acid is excited to the S(2) state at 193 nm, it undergoes internal conversion to S(1) where it dissociates to yield OH. In addition to the OH channel from excited electronic states, we studied theoretically all probable dissociation channels occurring on the ground electronic state of thiolactic acid.     

Exploring two-state reaction pathways in the photodimerization of cyclohexadiene.

The ground- (S0) and lowest triplet-state (T1) pathways associated with dimerization of cyclohexadiene to give [2+2] and [4+2] cycloadducts have been theoretically studied at the UBLYP and UB3LYP levels of theory with the 6-31G* basis set. The DFT energies were validated by CCSD(T) single-point energy calculations. These cycloaddition reactions follow stepwise mechanisms with formation of bis-allylic biradical (BB) intermediates. In the S0 ground state, the interaction between two cyclohexadiene molecules with formation of BB intermediate IN(S0) has a large activation enthalpy of 32.0 kcal mol(-1). On the other hand, C-C bond-formation in the lowest triplet state (T1) leading to BB intermediate IN(T1) has a low activation enthalpy of 5.0 kcal mol(-1), but the subsequent ring closure involves a very large activation enthalpy of 43.4 kcal mol(-1). Triplet-to-singlet intersystem crossing from IN(T1) to IN(S0) favors cyclization to give the corresponding [2+2] and [4+2] cycloadducts.     

Chemo- and periselectivity in the addition of [OsO2(CH2)2] to ethylene: a theoretical study

Quantum chemical calculations by using density functional theory at the B3LYP level have been carried out to elucidate the reaction course for the addition of ethylene to [OsO2(CH2)2] (1). The calculations predict that the kinetically most favorable reaction proceeds with an activation barrier of 8.1 kcal mol(-1) via [3+2] addition across the O=Os=CH2 moiety. This reaction is -42.4 kcal mol(-1) exothermic. Alternatively, the [3+2] addition to the H2C=Os=CH2 fragment of 1 leads to the most stable addition product 4 (-72.7 kcal mol(-1)), yet this process has a higher activation barrier (13.0 kcal mol(-1)). The [3+2] addition to the O=Os=O fragment yielding 2 is kinetically (27.5 kcal mol(-1)) and thermodynamically (-7.0 kcal mol(-1)) the least favorable [3+2] reaction. The formal [2+2] addition to the Os=O and Os=CH2 double bonds proceeds by initial rearrangement of 1 to the metallaoxirane 1 a. The rearrangement 1-->1 a and the following [2+2] additions have significantly higher activation barriers (>30 kcal mol(-1)) than the [3+2] reactions. Another isomer of 1 is the dioxoosmacyclopropane 1 b, which is 56.2 kcal mol(-1) lower in energy than 1. The activation barrier for the 1-->1 b isomerization is 15.7 kcal mol(-1). The calculations predict that there are no energetically favorable addition reactions of ethylene with 1 b. The isomeric form 1 c containing a peroxo group is too high in energy to be relevant for the reaction course. The accuracy of the B3LYP results is corroborated by high level post-HF CCSD(T) calculations for a subset of species.     

Standard absolute entropy, S degrees 298 values from volume or density. 1. Inorganic materials

Standard absolute entropies of many inorganic materials are unknown; this precludes a full understanding of their thermodynamic stabilities. It is shown here that formula unit volume, V(m)(), can be employed for the general estimation of standard entropy, S degrees 298 values for inorganic materials of varying stoichiometry (including minerals), through a simple linear correlation between entropy and molar volume. V(m)() can be obtained from a number of possible sources, or alternatively density, rho, may be used as the source of data. The approach can also be extended to estimate entropies for hypothesized materials. The regression lines pass close to the origin, with the following formulas: For inorganic ionic salts, S degrees 298 /J K(-)(1) mol(-)(1) = 1360 (V(m)()/nm(3) formula unit(-)(1)) + 15 or = 2.258 [M/(rho/g cm(-)(3))] + 15. For ionic hydrates, S degrees 298 /J K(-)(1) mol(-)(1) = 1579 (V(m)()/nm(3) formula unit(-)(1)) + 6 or = 2.621 [M/(rho/g cm(-)(3))] + 6. For minerals, S degrees 298 /J K(-)(1) mol(-)(1) = 1262 (V(m)()/nm(3) formula unit(-)(1)) + 13 or = 2.095 [M/(rho/g cm(-)(3))] + 13. Coupled with our published procedures, which relate volume to other thermodynamic properties via lattice energy, the correlation reported here complements our development of a predictive approach to thermodynamics and ultimately permits the estimation of Gibbs energy data. Our procedures are simple, robust, and reliable and can be used by specialists and nonspecialists alike.     

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.     

Besides N(2), What Is the Most Stable Molecule Composed Only of Nitrogen Atoms?

Polynitrogen molecules have been studied systematically at high levels of ab initio and density functional theory (DFT). Besides N(2), the thermodynamically most stable N(n)() molecules, located with the help of a newly developed energy increment system, are all based on pentazole units. The geometric, energetic, and magnetic criteria establish pentazole (2) and its anion (3) to be as aromatic as their isoelectronic analogues, e.g., furan, pyrrole, and the cyclopentadienyl anion. The bond lengths in 2 and 3 are equalized; both have large aromatic stabilization energies (ASE) and also substantial magnetic susceptibility exaltations (Lambda). The C(s)() symmetric azidopentazole (14), a candidate for experimental investigation, is the lowest energy N(8) isomer but is still 196.7 kcal/mol higher in energy than four N(2) molecules. Octaazapentalene (12) with 10 pi electrons also is aromatic. The D(2)(d)() symmetric bispentazole (21) is the lowest energy N(10) minimum but is 260 kcal/mol higher in energy than five N(2) molecules. For strain-free molecules, the average deviation is +/-2.6 kcal/mol between the DFT energies and those based on the increment scheme. The increment scheme also provides estimates of the strain energies of polynitrogen compounds, e.g., tetraazatetrahedrane (8, 48.2 kcal/mol), octaazacubane (11, 192.6 kcal/mol), and N(20) (27, 294.6 kcal/mol), and is useful in searching for new high-energy-high-density materials.