Ab initio study of the structures and stabilities of the dimer of ethyl cation, (C(2)H(+)(5))(2) and related C(4)H(10)(2+) isomers.

Ab initio calculations at the MP4(SDTQ)/6-311G//MP2/6-31G level were performed to study the structures and stabilities of the dimer of ethyl cation, (C(2)H(+)(5))(2), and related C(4)H(10)(2+) isomers. Two doubly hydrogen bridged diborane type trans 1 and cis 2 isomers were located as minima. The trans isomer was found to be more favorable than cis isomer by only 0.6 kcal/mol. Several other minima for C(4)H(10)(2+) were also located. However, the global energy minimum corresponds to C-H (C(4) position) protonated 2-butyl cation 10. Structure 10 was computed to be substantially more stable than 1 by 31.7 kcal/mol. The structure 10 was found to be lower in energy than 2-butyl cation 13 by 34.4 kcal/mol.     

Thermochemistry of disputed soot formation intermediates C4H3 and C4H5

Accurate isomeric energy differences and standard enthalpies of formation for disputed intermediates in soot formation, C(4)H(3) and C(4)H(5), have been determined through systematic extrapolations of ab initio energies. Electron correlation has been included through second-order Z-averaged perturbation theory (ZAPT2), and spin-restricted, open-shell coupled-cluster methods through triple excitations [ROCCSD, ROCCSD(T), and ROCCSDT] utilizing the correlation-consistent hierarchy of basis sets, cc-pVXZ (X = D, T, Q, 5, and 6), followed by extrapolations to the complete basis set limit via the focal point method of Allen and co-workers. Reference geometries were fully optimized at the ROCCSD(T) level with a TZ(2d1f,2p1d) basis set. Our analysis finds that the resonance-stabilized i-C(4)H(3) and i-C(4)H(5) isomers lie 11.8 and 10.7 kcal mol(-1) below E-n-C(4)H(3) and E-n-C(4)H(5), respectively, several kcal mol(-1) (more, less) than reported in recent (diffusion Monte Carlo, B3LYP density-functional) studies. Moreover, in these systems Gaussian-3 (G3) theory suffers from large spin contamination in electronic wave functions, poor reference geometries, and anomalous vibrational frequencies, but fortuitous cancellation of these sizable errors leads to isomerization energies apparently accurate to 1 kcal mol(-1). Using focal-point extrapolations for isodesmic reactions, we determine the enthalpies of formation (delta(f)H(0) (composite function)) for i-C(4)H(3), Z-n-C(4)H(3), E-n-C(4)H(3), i-C(4)H(5), Z-n-C(4)H(5), and E-n-C(4)H(5) to be 119.0, 130.8, 130.8, 78.4, 89.7, and 89.1 kcal mol(-1), respectively. These definitive values remove any remaining uncertainty surrounding the thermochemistry of these isomers in combustion models, allowing for better assessment of whether even-carbon pathways contribute to soot formation.     

Identification and chemistry of C4H3 and C4H5 isomers in fuel-rich flames

Quantitative identification of isomers of hydrocarbon radicals in flames is critical to understanding soot formation. Isomers of C4H3 and C4H5 in flames fueled by allene, propyne, cyclopentene, or benzene are identified by comparison of the observed photoionization efficiencies with theoretical simulations based on calculated ionization energies and Franck-Condon factors. The experiments combine molecular-beam mass spectrometry (MBMS) with photoionization by tunable vacuum-ultraviolet synchrotron radiation. The theoretical simulations employ the rovibrational properties obtained with B3LYP/6-311++G(d,p) density functional theory and electronic energies obtained from QCISD(T) ab initio calculations extrapolated to the complete basis set limit. For C4H3, the comparisons reveal the presence of the resonantly stabilized CH2CCCH isomer (i-C4H3). For C4H5, contributions from the CH2CHCCH2 (i-C4H5) and some combination of the CH3CCCH2 and CH3CHCCH isomers are evident. Quantitative concentration estimates for these species are made for allene, cyclopentene, and benzene flames. Because of low Franck-Condon factors, sensitivity to n-isomers of both C4H3 and C4H5 is limited. Adiabatic ionization energies, as obtained from fits of the theoretical predictions to the experimental photoionization efficiency curves, are within the error bars of the QCISD(T) calculations. For i-C4H3 and i-C4H5, these fitted adiabatic ionization energies are (8.06 +/- 0.05) eV and (7.60 +/- 0.05) eV, respectively. The good agreement between the fitted and theoretical ionization thresholds suggests that the corresponding theoretically predicted radical heats of formation (119.1, 76.3, 78.7, and 79.1 kcal/mol at 0 K for i-C4H3, i-C4H5, CH3CCCH2, and CH3CHCCH, respectively) are also quite accurate.     

Theoretical study of the C6H3 potential energy surface and rate constants and product branching ratios of the C2H(2Sigma+) + C4H2(1Sigma(g)+) and C4H(2Sigma+) + C2H2(1Sigma(g)+) reactions

Ab initio CCSD(T)cc-pVTZ//B3LYP6-311G(**) and CCSD(T)/complete basis set (CBS) calculations of stationary points on the C(6)H(3) potential energy surface have been performed to investigate the reaction mechanism of C(2)H with diacetylene and C(4)H with acetylene. Totally, 25 different C(6)H(3) isomers and 40 transition states are located and all possible bimolecular decomposition products are also characterized. 1,2,3- and 1,2,4-tridehydrobenzene and H(2)CCCCCCH isomers are found to be the most stable thermodynamically residing 77.2, 75.1, and 75.7 kcal/mol lower in energy than C(2)H + C(4)H(2), respectively, at the CCSD(T)/CBS level of theory. The results show that the most favorable C(2)H + C(4)H(2) entrance channel is C(2)H addition to a terminal carbon of C(4)H(2) producing HCCCHCCCH, 70.2 kcal/mol below the reactants. This adduct loses a hydrogen atom from the nonterminal position to give the HCCCCCCH (triacetylene) product exothermic by 29.7 kcal/mol via an exit barrier of 5.3 kcal/mol. Based on Rice-Ramsperger-Kassel-Marcus calculations under single-collision conditions, triacetylene+H are concluded to be the only reaction products, with more than 98% of them formed directly from HCCCHCCCH. The C(2)H + C(4)H(2) reaction rate constants calculated by employing canonical variational transition state theory are found to be similar to those for the related C(2)H + C(2)H(2) reaction in the order of magnitude of 10(-10) cm(3) molecule(-1) s(-1) for T = 298-63 K, and to show a negative temperature dependence at low T. A general mechanism for the growth of polyyne chains involving C(2)H + H(C[triple bond]C)(n)H --> H(C[triple bond]C)(n+1)H + H reactions has been suggested based on a comparison of the reactions of ethynyl radical with acetylene and diacetylene. The C(4)H + C(2)H(2) reaction is also predicted to readily produce triacetylene + H via barrierless C(4)H addition to acetylene, followed by H elimination.     

Ring opening of 2,5-didehydrothiophene: structures and rearrangements of C4H2S isomers

Electronic structures and rearrangement pathways of several C4H2S isomers are computationally investigated by methods based on coupled cluster theory and density functional theory. Six singlet C4H2S isomers lie within ca. 30 kcal/mol above butatrienethione (6), the apparent global minimum. Ethynylthioketene (7) lies only 2 kcal/mol higher in energy than cumulene 6. Two open-chain isomers, butadiynylthiol (8) and diethynyl sulfide (9), reside ca. 9 and 24 kcal/mol above 6, respectively. Lying 30 kcal/mol above 6, two cyclic singlet isomers, ethynylthiirene (10) and cyclopropenylidenemethanthione (11), are nearly degenerate in energy. Thiophene-2,5-diyl (12) lies substantially higher in energy than 6 (ca. 45 kcal/mol) and is predicted to rearrange preferentially by C-S bond cleavage, leading to thioketene 7, rather than by C-C bond cleavage, leading to diethynyl sulfide (9; retro-Bergman cyclization). Accurate spectroscopic properties of these C4H2S isomers, as well as an understanding of their rearrangement pathways, should facilitate the detection and characterization of these isomers in the laboratory and the interstellar medium.     

The C4H7+ cation. A theoretical investigation

The potential energy surface of the C4H7+ cation has been investigated with ab initio quantum chemical theory. Extended basis set calculations, including electronic correlation, show that cyclobutyl and cyclopropylcarbinyl cation are equally stable isomers. The saddle point connecting these isomers lies 0.6 kcal/mol above the minima. The global C4H7+ minimum corresponds to the 1-methylallyl cation, which is 9.0 kcal/mol more stable than the cyclobutyl and the cyclopropylcarbinyl cation and 9.5 kcal/mol below the 2-methylallyl cation. These results are in excellent agreement with experimental data.     

Theoretical study on structures and stability of C4P isomers

The structures, energetics, spectroscopies, and stabilities of doublet C(4)P isomeric species are explored at the DFT/B3LYP, QCISD, and CCSD(T) (singlet-point) levels. A total of 12 minimum isomers and 27 interconversion transition states are located. At the CCSD(T)/6-311G(2df)//QCISD/6-311G(d)+ZPVE level, the lowest-lying isomer is a floppy CCCCP 1 (0.0 kcal/mol) mainly featuring a cumulenic structure |C=C=C=C=P*|, which differs much from the analogous C4N radical (|*C-C[triple bond]C-C[triple bond]N|). The quasi-linearity and the low bending mode of 1 are in contrast to the previous prediction. The second energetically followed isomer PC-cCCC 3 (14.9 kcal/mol) possesses a CCC ring-bonded to CP. The two low-lying isomers are separated by a high-energy ring-closure/open transition state (26.5 kcal/mol) and thus are very promising candidates for future laboratory and astrophysical detection. Furthermore, four high-energy isomers, that is, two bent isomers CCPCC 2 (68.4 kcal/mol) and CCPCC 2' (68.5 kcal/mol) and two cagelike species 10 (56.0 kcal/mol) and 11 (67.9 kcal/mol), are also stabilized by considerable barriers. The present work is the first detailed potential energy survey of CnP clusters and can provide useful information for the investigation of larger CnP radicals and for understanding the isomerism of P-doped C vaporization processes.     

Hydricities of BzNADH, CH5Mo(PMe3)(CO)2H, and C5Me5Mo(PMe3)(CO)2H in acetonitrile

The thermodynamic hydride donor abilities of 1-benzyl-1,4-dihydronicotinamide (BzNADH, 59 +/- 2 kcal/mol), C(5)H(5)Mo(PMe(3))(CO)(2)H (55 +/- 3 kcal/mol), and C(5)Me(5)Mo(PMe(3))(CO)(2)H (58 +/- 2 kcal/mol) have been measured in acetonitrile by calorimetric and/or equilibrium methods. The hydride donor abilities of BzNADH and C(5)H(5)Mo(PMe(3))(CO)(2)H differ by 13 and 24 kcal/mol, respectively, from those reported previously for these compounds in acetonitrile. These results require significant revisions of the hydricities reported for related NADH analogues and metal hydrides. These compounds are moderate hydride donors as compared to previously determined compounds.     

Theoretical study on structures and stabilities of [H,Ge,C,N

Theoretical investigations are performed for the first time on the simplest hydrogenated germanium cyanide [H,Ge,C,N], whose analogs [H,C(2),N] and [H,Si,C,N] have been detected in space and laboratory, respectively. The detailed potential energy surfaces in both singlet and triplet states are constructed at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-31G(d)+ZPVE level, including 18 minimum isomers and 26 interconversion transition states. The former three low-lying and kinetically stabilized isomers are HGeCN (1)1 (0.0 kcal/mol), HGeNC (1)2 (5.1 kcal/mol), and cyclic cCHNGe(1)7 (11.1 kcal/mol). In addition, five isomers HCNGe (1)3 (33.8), HNCGe (1)5 (29.8), cNHCGe (1)8 (37.9), HGeCN (3)1 (30.1), and HNCGe (3)5 (26.5) each have considerable barriers, despite their high energies. Future laboratory characterization and astrophysical detection of the eight [H,Ge,C,N] isomers, especially the former three low-lying species (1)1, (1)2, and (1)7, are highly recommended. The accurate spectroscopic data at the QCISD/6-311G(d,p) level are provided. For some species, the CBS-QB3 calculations are also performed. Wherever possible, comparisons with the analogous [H,C(2),N] and [H,Si,C,N] are made on the structural, energetic, and bonding properties.     

Theoretical prediction of the heats of formation of C2H5O* radicals derived from ethanol and of the kinetics of beta-C-C scission in the ethoxy radical

Thermochemical parameters of three C(2)H(5)O* radicals derived from ethanol were reevaluated using coupled-cluster theory CCSD(T) calculations, with the aug-cc-pVnZ (n = D, T, Q) basis sets, that allow the CC energies to be extrapolated at the CBS limit. Theoretical results obtained for methanol and two CH(3)O* radicals were found to agree within +/-0.5 kcal/mol with the experiment values. A set of consistent values was determined for ethanol and its radicals: (a) heats of formation (298 K) DeltaHf(C(2)H(5)OH) = -56.4 +/- 0.8 kcal/mol (exptl: -56.21 +/- 0.12 kcal/mol), DeltaHf(CH(3)C*HOH) = -13.1 +/- 0.8 kcal/mol, DeltaHf(C*H(2)CH(2)OH) = -6.2 +/- 0.8 kcal/mol, and DeltaHf(CH(3)CH(2)O*) = -2.7 +/- 0.8 kcal/mol; (b) bond dissociation energies (BDEs) of ethanol (0 K) BDE(CH(3)CHOH-H) = 93.9 +/- 0.8 kcal/mol, BDE(CH(2)CH(2)OH-H) = 100.6 +/- 0.8 kcal/mol, and BDE(CH(3)CH(2)O-H) = 104.5 +/- 0.8 kcal/mol. The present results support the experimental ionization energies and electron affinities of the radicals, and appearance energy of (CH(3)CHOH+) cation. Beta-C-C bond scission in the ethoxy radical, CH(3)CH2O*, leading to the formation of C*H3 and CH(2)=O, is characterized by a C-C bond energy of 9.6 kcal/mol at 0 K, a zero-point-corrected energy barrier of E0++ = 17.2 kcal/mol, an activation energy of Ea = 18.0 kcal/mol and a high-pressure thermal rate coefficient of k(infinity)(298 K) = 3.9 s(-1), including a tunneling correction. The latter value is in excellent agreement with the value of 5.2 s(-1) from the most recent experimental kinetic data. Using RRKM theory, we obtain a general rate expression of k(T,p) = 1.26 x 10(9)p(0.793) exp(-15.5/RT) s(-1) in the temperature range (T) from 198 to 1998 K and pressure range (p) from 0.1 to 8360.1 Torr with N2 as the collision partners, where k(298 K, 760 Torr) = 2.7 s(-1), without tunneling and k = 3.2 s(-1) with the tunneling correction. Evidence is provided that heavy atom tunneling can play a role in the rate constant for beta-C-C bond scission in alkoxy radicals.     

Protonated tert-pentyl dication (C5H122+, isopentane dication)

Structures of the tert-pentyl cation (C(5)H(11)(+)) and its protonated dication (C(5)H(12)(2+), isopentane dication) were studied using ab initio methods at the MP2/cc-pVTZ level. Both C-C and C-H hyperconjugatively stabilized structures 1 and 2 , respectively, were found to be minima on the potential energy surface (PES) of the tert-pentyl cation. Structure 1 was computed to be about as stable as structure 2 (slightly more stable by 0.5 kcal mol(-1)). Inter-conversion between 1 and 2 through transition state 3 has a kinetic barrier of only 1.5 kcal mol(-1). The C-H protonated form (H(3)C)(2)C(+)CH(2)CH(4)(+)4 was found to be the global minimum for the protonated tert-pentyl dication. Charges and (13)C NMR chemical shifts of the dication 4 were calculated and compared to those of monocation 1 to study the effect of the additional charge in the dication.     

Anion photoelectron spectroscopy of C(5)H(-)

Anion photoelectron spectroscopy is performed on the C(5)H(-) species. Analogous to C(3)H(-) and C(3)D(-), photodetachment transitions are observed from multiple, energetically close-lying isomers of the anion. A linear and a cyclic structure are found to have electron binding energies of 2.421+/-0.019 eV and 2.857+/-0.028 eV, respectively. A cyclic excited state is also found to be 1.136 eV above the linear (2)Pi C(5)H ground state. Based on our assignments of the observed transitions and previous calculations on the energetics of neutral C(5)H isomers, the cyclic (1)A(1) anion state is found to lie 0.163 eV below the (3)A linear anion.     

Enediyne isomers of tetraethynylethene

Three isomers of tetraethynylethene (1, C10H4) have been prepared by palladium-catalyzed Negishi coupling of a trimethylsilylbutadiynyl zinc reagent with a bromoalkene, followed by mild deprotection with potassium carbonate in methanol. The unsubstituted enynes, 3-ethynyloct-3-ene-1,5,7-triyne (2), trans-dec-5-ene-1,3,7,9-tetrayne (3), and cis-dec-5-ene-1,3,7,9-tetrayne (4), exhibit modest stability at -20 degrees C but decompose rapidly at room temperature. Electronic absorption spectra of 2, 3, and 4 reveal a characteristic vibronic progression at 260-320 nm. Spectral features at shorter wavelength discriminate among the isomers, and permit the assignment of 2 and 3 as apparent dimerization products of triplet carbene H-CC-C-CC-H in matrices at low temperature. Computed relative energies of these C10H4 isomers (MP2/6-31G) are 1 (14.0 kcal/mol), 2 (6.8 kcal/mol), 3 (0.0 kcal/mol), and 4 (1.0 kcal/mol).     

Establishment of the C(2)H(5)+O(2) reaction mechanism: a combustion archetype

The celebrated C(2)H(5)+O(2) reaction is an archetype for hydrocarbon combustion, and the critical step in the process is the concerted elimination of HO(2) from the ethylperoxy intermediate (C(2)H(5)O(2)). Master equation kinetic models fitted to measured reaction rates place the concerted elimination barrier 3.0 kcal mol(-1) below the C(2)H(5)+O(2) reactants, whereas the best previous electronic structure computations yield a barrier more than 2.0 kcal mol(-1) higher. We resolve this discrepancy here by means of the most rigorous computations to date, using focal point methods to converge on the ab initio limit. Explicit computations were executed with basis sets as large as cc-pV5Z and correlation treatments as extensive as coupled cluster through full triples with a perturbative inclusion of quadruple excitations [CCSDT(Q)]. The final predicted barrier is -3.0 kcal mol(-1), bringing the concerted elimination mechanism into precise agreement with experiment. This work demonstrates that higher correlation treatments such as CCSDT(Q) are not only feasible on systems of chemical interest but are necessary to supply accuracy beyond 0.5 kcal mol(-1), which is not obtained with the "gold standard" CCSD(T) method. Finally, we compute the enthalpy of formation of C(2)H(5)O(2) to be Delta(f)H degrees (298 K)=-5.3+/-0.5 kcal mol(-1) and Delta(f)H degrees (0 K)=-1.5+/-0.5 kcal mol(-1).     

Thermochemistry of key soot formation intermediates: C3H3 isomers

Accurate standard enthalpies of formation for allene, propyne, and four C3H3 isomers involved in soot formation mechanisms have been determined through systematic focal point extrapolations of ab initio energies. Auxiliary corrections have been applied for anharmonic zero-point vibrational energy, core electron correlation, the diagonal Born-Oppenheimer correction (DBOC), and scalar relativistic effects. Electron correlation has been accounted for via second-order Z-averaged perturbation theory (ZAPT2) and primarily through coupled-cluster theory, including single, double, and triple excitations, as well as a perturbative treatment of connected quadruple excitations [ROCCSD, ROCCSD(T), ROCCSDT, and UCCSDT(Q)]. The correlation-consistent hierarchy of basis sets, cc-pVXZ (X = D, T, Q, 5, 6), was employed. The CCSDT(Q) corrections do not exceed 0.12 kcal mol(-)1 for the relative energies of the systems considered here, indicating a high degree of electron correlation convergence in the present results. Our recommended values for the enthalpies of formation are as follows: Delta(f)H(o)(0)(propargyl) = 84.76, Delta(f)H(o)(0) (1-propynyl) = 126.60, Delta(f)H(o)(0) (cycloprop-1-enyl) = 126.28, Delta(f)H(o)(0)(cycloprop-2-enyl) = 117.36, Delta(f)H(o)(0)(allene) = 47.41, and Delta(f)H(o)(0)(propyne) = 46.33 kcal mol(-1), with estimated errors no larger than 0.3 kcal mol(-1). The corresponding C3H3 isomerization energies are about 1 kcal mol(-1) larger than previous coupled-cluster results and several kcal mol(-1) below those previously obtained using density functional theory.     

Thermochemical stabilities and structures of the cluster ions OCS+, S2+, H+(OCS), and C2H5+ with OCS molecules in the gas phase

The gas-phase clustering reactions of OCS+, S2+, H+(OCS), and C2H5+ ions with carbonyl sulfide (OCS) molecules were studied using a pulsed electron-beam high-pressure mass spectrometer and applying density functional theory (DFT) calculations. In the cluster ions OCS+(OCS)(n) and H+(OCS)(OCS)(n), a moderately strong, here referred to as "semi-covalent", bond was formed with n = 1. However, the nature of bonding changed from semi-covalent to electrostatic with n = 1 --> 2. The bond energy of S2(+)(OCS) was determined experimentally to be 12.9 +/- 1 kcal/mol, which is significantly smaller than that of the isovalent S2(+)(CS2) complex (30.9 +/- 1.5 kcal/mol). DFT based calculations predicted the presence of several isomeric structures for H+(OCS)(OCS)(n) complexes. The bond energies in the C2H5+(OCS)(n) clusters showed an irregular decrease for n = 1 --> 2 and 7 --> 8. The nonclassical bridge structure for the free C2H5+ isomerized to form a semi-covalent bond with one OCS ligand, [H3CCH2...SCO]+, i.e., reverted to classical structure. However, the nonclassical bridge structure of C2H5+ was preserved in the cluster ions C2H5+(OCS)(n) below 140 K attributable to the lack of thermal energy for the isomerization. DFT calculations revealed that stability orders of the geometric isomers of H+(OCS)(OCS)(n) and C2H5+(OCS)(n) changed with increasing n values.     

Exploring the dynamics of reaction C(3P) + C2H4 with crossed beam/photoionization experiments and quantum chemical calculations

We investigated the title reaction at collision energy 3.5 kcal mol(-1) in a crossed molecular beam apparatus using undulator radiation as an ionization source. Time-of-flight (TOF) spectra of product C(3)H(3) were measured in laboratory angles from 20° to 100° using two photoionization energies 9.5 and 11.6 eV. These two sets of experimental data exhibit almost the same TOF distributions and laboratory angular distributions. From the best simulation, seven angle-specific kinetic-energy distributions and a nearly isotropic angular distribution are derived for product channel C(3)H(3) + H that has an average kinetic-energy release of 15.5 kcal mol(-1), corresponding to an average internal energy of 33.3 kcal mol(-1) in C(3)H(3). Furthermore, TOF spectra of product C(3)H(3) were measured at laboratory angle 52° with ionizing photon energies from 7 to 12 eV. The appearance of TOF spectra remains almost the same, indicating that a species exclusively contributes to product C(3)H(3); the species is identified as H(2)CCCH (propargyl) based on the ionization energy of 8.6 ± 0.2 eV and the maximal kinetic-energy release of 49 kcal mol(-1). Theoretical calculations indicate that the rapid inversion mechanism and rotation in intermediate H(2)CCCH(2) can result in a forward-backward symmetric angular distribution for product C(3)H(3) + H. The present work avoids the interference of reactions of C((1)D) and C(2) radicals with C(2)H(4) and rules out the probability of production of other isomers like c-C(3)H(3) and H(3)CCC proposed in the previous work at least at the investigated collision energy.     

Thermodynamic properties of the C5, C6, and C8 n-alkanes from ab initio electronic structure theory

The heats of formation for the n-alkanes C(n)H(n+2) for n = 5, 6, and 8 have been calculated using ab initio molecular orbital theory. Coupled-cluster calculations with perturbative triples (CCSD(T)) were employed for the total valence electronic energies. Correlation-consistent basis sets were used, up through the augmented quadruple zeta, to extrapolate to the complete basis set limit. Geometries were optimized at the B3LYP/TZVP and MP2/aug-cc-pVTZ levels. The MP2 geometries were used in the CCSD(T) calculations. Frequencies were determined at the density functional level (B3LYP/TZVP), and scaled zero point energies were calculated from the B3LYP frequencies. Core/valence, scalar relativistic, and spin-orbit corrections were included in an additive fashion to predict the atomization energies. The core/valence corrections are not small, (approximately 1.1 kcal/mol per carbon unit) and cannot be neglected for chemical accuracy. The calculated deltaH(298)f values are -35.0, -40.2, and -50.2 kcal/mol for C5H12, C6H14, and C8H18, respectively, in excellent agreement with the respective experimental values of -35.11 +/- 0.19, -39.89 +/- 0.19, and -49.90 +/- 0.31 kcal/mol. Isodesmic reaction energies are presented for some simple reactions involving C8H18 and are shown not to be strongly method dependent.     

C7H12(2+): a prototype hexacoordinate carbonium ion

C(7)H(12)(2+) (1), the prototype hexacoordinate carbonium dication was found to be a viable minimum at the MP2/6-31G** and MP2/cc-pVTZ levels. Structure 1 is a propeller shaped molecule resembling a complex involving a C(2+) with three ethylene molecules resulting in the formation of three two-electron, three-center (2e-3c) bonds. Isomeric structure 2 was found to be 21.8 kcal/mol more stable than structure 1. However, conversion of 1 into 2 through transition structure 3 has a barrier of 5.7 kcal/mol. Related structures 4, 5, and 8 were also located as minima for C(7)H(12)(2+). The isoelectronic boron analogue BC(6)H(12)(+) (10) was also computed to be a minimum at the same level of calculations.     

On the viability of small endohedral hydrocarbon cage complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, AND X@C16H16

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H(+), H, He, Ne, Ar, Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,+,2+)) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C(4)H(4), T(d)()) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C(8)H(8), O(h)()) and bicyclo[2.2.2]octane (C(8)H(14), D(3)(h)()) minima are limited to encapsulating species smaller than Ne and Na(+). Despite its intermediate size, adamantane (C(10)H(16), T(d)()) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li(0,+), Be(0,+,2+), Na(0,+), and Mg(2+). In contrast, the truncated tetrahedrane (C(12)H(12), T(d)()) encapsulates fewer species, while the D(4)(d)() symmetric C(16)H(16) hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg(+) species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C-C bonding and C-H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E(endo)) to the sum of their isolated components (E(inc) = E(endo) - E(cage) - E(x)) and to their exohedral isomer energies (E(isom) = E(endo) - E(exo)). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E(isom) is always exothermic), Be(2+)@C(10)H(16) (T(d)(); -235.5 kcal/mol), Li(+)@C(12)H(12) (T(d)(); 50.2 kcal/mol), Be(2+)@C(12)H(12) (T(d)(); -181.2 kcal/mol), Mg(2+)@C(12)H(12) (T(d)(); -45.0 kcal/mol), Li(+)@C(16)H(16) (D(4)(d)(); 13.3 kcal/mol), Be(+)@C(16)H(16) (C(4)(v)(); 31.8 kcal/mol), Be(2+)@C(16)H(16) (D(4)(d)(); -239.2 kcal/mol), and Mg(2+)@C(16)H(16) (D(4)(d)(); -37.7 kcal/mol) are relatively stable as compared to experimentally known He@C(20)H(20) (I(h)()), which has an E(inc) = 37.9 kcal/mol and E(isom) = -35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.