Approximations to complete basis set-extrapolated, highly correlated non-covalent interaction energies.

The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)∕aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)∕aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent absolute deviation of only 1.7%, relative to the (estimated) complete basis set CCSD(T) results. Use of this composite approach to an additional set of eight dimers gave binding energies to within 1% of previously published high-level data. It is also shown that binding within parallel and parallel-crossed conformations of naphthalene dimer is predicted by the composite approach to be 9% greater than that previously reported in the literature. The ability of some recently developed dispersion-corrected density-functional theory methods to predict the binding energies of the set of ten small dimers was also examined.

Ring-opening radical clock reactions: many density functionals have difficulty keeping time.

The ability of several density-functional theory methods to describe the kinetics and energetics of a series of ring-opening reactions of cyclopropyl and cyclobutyl-type radicals was explored. PBE, B971 and B3LYP perform quite well in their ability to replicate experiment, based upon the ring opening of cyclopropylcarbinyl, two α-trialkylsilyloxycyclopropylmethyl radicals, pentamethylcyclopropylcarbinyl, cyclobutylcarbinyl and 1-cyclobutylethylcarbinyl. The other functionals tested, which includes BLYP, CAM-B3LYP, BHandHLYP, B2PLYP and B2PLYP-D, as well as functionals designed for kinetics applications, namely MPW1K, BMK and M06-2X, all perform poorly. The latter of these functionals display some integration grid dependencies.

CO2 adsorption by nitrogen-doped carbon nanotubes predicted by density-functional theory with dispersion-correcting potentials.

The interaction of CO(2) to the interior and exterior walls of pristine and nitrogen-doped single-walled carbon nanotubes (SWNT) has been studied using density-functional theory with dispersion-correcting potentials (DCPs). Our calculations predict Gibbs energies of binding between SWNT and CO(2) of up to 9.1 kcal mol(-1), with strongest binding observed for a zigzag [10,0] nanotube, compared to armchair [6,6] (8.3 kcal mol(-1)) and chiral [8,4] (7.0 kcal mol(-1)). Doping of the [10,0] tube with nitrogen increases the Gibbs energies of binding of CO(2) by ca. 3 kcal mol(-1), but slightly reduced binding is found when [6,6] and [8,4] SWNT are doped in similar fashion. The Gibbs energy of binding of CO(2) to the exterior of the tubes is quite small compared to the binding that occurs inside the tubes. These findings suggest that the zigzag SWNT show greater promise as a means of CO(2) gas-capture.

Accurate dispersion interactions from standard density-functional theory methods with small basis sets.

B971, PBE and PBE1 density functionals with 6-31G(d) basis sets are shown to accurately describe the binding in dispersion bound dimers. This is achieved through the use of dispersion-correcting potentials (DCPs) in conjunction with counterpoise corrections. DCPs resemble and are applied like conventional effective core potentials that can be used with most computational chemistry programs without code modification. Rather, DCPs are implemented by simple appendage to the input files for these types of programs. Binding energies are predicted to within ca. 11% and monomer separations to within ca. 0.06 A of high-level wavefunction data using B971/6-31G(d)-DCP. Similar results are obtained for PBE and PBE1 with the 6-31G(d) basis sets and DCPs. Although results found using the 3-21G(d) are not as impressive, they never-the-less show promise as a means of initial study for a wide variety of dimers, including those dominated by dispersion, hydrogen-bonding and a mixture of interactions. Notable improvement is found in comparison to M06-2X/6-31G(d) data, e.g., mean absolute deviations for the S22-set of dimers of ca. 13.6 and 16.5% for B971/6-31G(d)-DCP and M06-2X, respectively. However, it should be pointed out that the latter data were obtained using a larger integration grid size since a smaller grid results in different binding energies and geometries for simple dispersion-bound dimers such as methane and ethene.

Binding in thiophene and benzothiophene dimers investigated by density functional theory with dispersion-correcting potentials.

We report the use of a newly developed dispersion-corrected density functional approach to study noncovalent binding in a series of thiophene and benzothiophene dimers. These are of interest in both petrochemistry and molecular electronics. We find increasing influence of dispersion forces over dipole interactions as the number of benzene moieties increases from 0 (thiophene) to 3 (tribenzothiophene). Binding in dimers of thiophene was benchmarked vs previously published CCSD(T) data (J. Am. Chem. Soc. 2002, 124, 12200). We have determined the fully optimized geometries and energies of 15 dimers of thiophene, 26 dimers of benzothiophene, 10 of dibenzothiophene, and 11 of tribenzothiophene using B971/6-31+G(d,p) with dispersion-correcting potentials (DCPs). These represent a mixture of T-shaped, tilted-T-shaped, pi-stacked, and coplanar structures. For thiophene we find the lowest energy T-shaped and pi-stacked dimers to bind by 3.0 and 2.5 kcal/mol, respectively. However, for benzothiophene the lowest energy structure is pi-stacked with binding energy, BE = 5.8 kcal/mol, which compares to the most bound T-shaped dimer, BE = 4.1 kcal/mol. This difference between pi-stacked and T-shaped dimer binding increases further going to dibenzothiophene and tribenzothiophene (difference = ca. 6.0 and 6.7 kcal/mol, respectively). When calculations without dispersion corrections are performed on the dimer structures, many display significant changes in structural motif and reductions in binding energies of up to 80%. Therefore, the inclusion of dispersion corrections, for example, through the use of DCPs, is essential in describing the potential energy landscape of these complexes.

Thermal rearrangements of 2-ethynylbiphenyl: a DFT study of competing reaction mechanisms.

Mechanistic pathways for high-temperature rearrangements of 2-ethynylbiphenyl have been investigated by calculations at the B3LYP/6-31G(d) level of theory, with free energy estimates at 625 degrees C. Two different routes for high temperature thermal rearrangement can lead to phenanthrene, which was the major product observed by Brown and co-workers (J. Chem. Soc. Chem. Commun. 1974, 123). 1,2-Hydrogen shift (Hopf type B mechanism) affords a vinylidene which proceeds to the major product by sequential electrocyclic closure and a 1,2-shift, rather than the expected aryl C-H insertion. Alternatively, insertion of the vinylidene into a ring double bond would lead directly to the observed minor product, benzazulene. Along a competitive pathway, electrocyclic closure to an isophenanthrene is predicted to be nearly isoenergetic. This intermediate should have a planar allene structure, with substantial diradical character. Sequential hydrogen shifts lead to phenanthrene but with higher cumulative barriers than for the vinylidene route. Calculation of 625 degrees C free energies shows that the carbene mechanism is of lower energy, primarily because of the lower entropic cost. Predictions are made for the unusually facile hydrogen atom dissociation from isoaromatics at high temperature, a consequence of aryl radical formation. Isophenanthrene, isobenzene (1,2,4-cyclohexatriene) and several isonaphthalenes are also predicted to have unusually low C-H bond dissociation energies. Potential significance as a source of aryl radicals in high temperature and combustion chemistry is discussed.

Reaction of phenols with the 2,2-diphenyl-1-picrylhydrazyl radical. Kinetics and DFT calculations applied to determine ArO-H bond dissociation enthalpies and reaction mechanism.

The formal H-atom abstraction by the 2,2-diphenyl-1-picrylhydrazyl (dpph(*)) radical from 27 phenols and two unsaturated hydrocarbons has been investigated by a combination of kinetic measurements in apolar solvents and density functional theory (DFT). The computed minimum energy structure of dpph(*) shows that the access to its divalent N is strongly hindered by an ortho H atom on each of the phenyl rings and by the o-NO(2) groups of the picryl ring. Remarkably small Arrhenius pre-exponential factors for the phenols [range (1.3-19) x 10(5) M(-1) s(-1)] are attributed to steric effects. Indeed, the entropy barrier accounts for up to ca. 70% of the free-energy barrier to reaction. Nevertheless, rate differences for different phenols are largely due to differences in the activation energy, E(a,1) (range 2 to 10 kcal/mol). In phenols, electronic effects of the substituents and intramolecular H-bonds have a large influence on the activation energies and on the ArO-H BDEs. There is a linear Evans-Polanyi relationship between E(a,1) and the ArO-H BDEs: E(a,1)/kcal x mol(-1) = 0.918 BDE(ArO-H)/kcal x mol(-1) - 70.273. The proportionality constant, 0.918, is large and implies a "late" or "product-like" transition state (TS), a conclusion that is congruent with the small deuterium kinetic isotope effects (range 1.3-3.3). This Evans-Polanyi relationship, though questionable on theoretical grounds, has profitably been used to estimate several ArO-H BDEs. Experimental ArO-H BDEs are generally in good agreement with the DFT calculations. Significant deviations between experimental and DFT calculated ArO-H BDEs were found, however, when an intramolecular H-bond to the O(*) center was present in the phenoxyl radical, e.g., in ortho semiquinone radicals. In these cases, the coupled cluster with single and double excitations correlated wave function technique with complete basis set extrapolation gave excellent results. The TSs for the reactions of dpph(*) with phenol, 3- and 4-methoxyphenol, and 1,4-cyclohexadiene were also computed. Surprisingly, these TS structures for the phenols show that the reactions cannot be described as occurring exclusively by either a HAT or a PCET mechanism, while with 1,4-cyclohexadiene the PCET character in the reaction coordinate is much better defined and shows a strong pi-pi stacking interaction between the incipient cyclohexadienyl radical and a phenyl ring of the dpph(*) radical.

Interactions in large, polyaromatic hydrocarbon dimers: application of density functional theory with dispersion corrections.

The interactions within two models for graphene, coronene and hexabenzocoronene (HBC), and (H 3C(CH 2) 5) 6-HBC, a synthesizable model for asphaltenes, were studied using density functional theory (DFT) with dispersion corrections. The corrections were implemented using carbon atom-centered effective core-type potentials that were designed to correct the erroneous long-range behavior of several DFT methods. The potentials can be used with any computational chemistry program package that can handle standard effective core potential input, without the need for software modification. Testing on a set of common noncovalently bonded dimers shows that the potentials improve calculated binding energies by factors of 2-3 over those obtained without the potentials. Binding energies are predicted to within ca. 15%, and monomer separations to within ca. 0.1 A, of high-level wave function data. The application of the present approach predicts binding energies and structures of the coronene dimer that are in excellent agreement with the results of other DFT methods in which dispersion is taken into account. Dimers of HBC show extensive binding in pi-stacking arrangements, with the largest binding energy, 44.8 kcal/mol, obtained for a parallel-displaced structure. This structure is inline with the published crystal structure. Conformations in which the monomers are perpendicular to one another are much more weakly bound and have binding energies less than 10 kcal/mol. For dimers of (H 3C(CH 2) 5) 6-HBC, which contain 336 atoms, we find that a slipped-parallel structure with C s symmetry has a binding energy of 52.4 kcal/mol, 8.9 kcal/mol lower than that of a bowl-like, C 6 v -symmetric structure.

Thermochemical and kinetic study of the carbocation ring contraction of cyclohexylium to methylcyclopentylium.

The isomerization of cyclohexylium to methylcyclopentylium is a model for a key step required in sterol and triterpene biosynthesis and is important in catalytic processes associated with ring-opening reactions in upgrading petroleum fractions. Using high-level, correlated wave function techniques based on QCISD, the mechanism for this isomerization was found to be very different from that first proposed more than 35 years ago. On the basis of our mechanism, a first-order rate constant expression was derived and used with complete basis set-extrapolated QCISD(T) energies to obtain Ea = 6.9 kcal/mol and A = 1011.18 s-1, in excellent agreement with values of 7.4 +/- 1 kcal/mol and A = 1012 +/- 1.3 s-1 measured in the gas phase. The B3LYP and MP2 methods, two commonly used computational approaches, were found to predict incorrect mechanisms and, in some cases, poor kinetic parameters. The PBE method, however, produced a reaction profile and kinetic parameters in reasonable agreement with those obtained with the complete basis set-extrapolated QCISD(T) method.

Strain estimates for small-ring cyclic allenes and butatrienes.

Isodesmic and homodesmic equations at the B3LYP/6-311+G(d,p)+ZPVE level of theory have been used to estimate strain for the homologous series of cyclic allenes and cyclic butatrienes. A simple fragment deformation approach also has been applied and appears to work better for the larger rings. For the cyclic allene series, estimates for allene functional group strain (kcal/mol) include: 1,2-cyclobutadiene, 65; 1,2-cyclopentadiene, 51; 1,2-cyclohexadiene, 32; 1,2-cycloheptadiene, 14; 1,2-cyclooctadiene, 5; 1,2-cyclononadiene, 2; 1,2,4-cyclohexatriene, 34; and bicyclo[3.2.1]octa-2,3-diene, 39. For cyclic butatrienes, functional group strain estimates include: 1,2,3-cyclobutatriene, >100; 1,2,3-cyclopentatriene, 80; 1,2,3-cyclohexatriene, 50; 1,2,3-cycloheptatriene, 26; 1,2,3-cyclooctatriene, 17; and 1,2,3-cyclononatriene, 4. Barriers to interconversion of enantiomers in cyclic allenes are reduced with increasing strain. Newly predicted values include: 1,2-cyclopentadiene <1 kcal/mol and bicyclo[3.2.1]octa-2,3-diene, 7.4 kcal/mol. Estimated levels of strain parallel the known reactivity of these substances.

Molecular structures of arachno-decaborane derivatives 6,9-X2B8H10 (X = CH2, NH, Se) including a gas-phase electron-diffraction study of 6,9-C2B8H14.

The molecular structures of the three heterodecaboranes arachno-6,9-C2B8H14, arachno-6,9-N2B8H12, and arachno-6,9-Se2B8H10 have been determined by ab initio MO theory. In addition, the structure of arachno-6,9-C2B8H14 was experimentally determined using gas-phase electron diffraction (GED). The accuracy of all four of these structures has been confirmed by the good agreement of the (11)B chemical shifts calculated at the GIAO-MP2 level with the experimental values. A comparison of the GIAO-HF and GIAO-MP2 methods shows that for these heteroborane clusters, electron correlation effects on the computed delta((11)B) values are quite substantial and that it is necessary to go beyond the HF level in the NMR computation.

The structures of higher boron halides B8X12(X = F, Cl, Br and I) by gas-phase electron diffraction and ab initio calculations.

The structure of B8F12 has been shown by gas electron diffraction and computational methods (up to MP2/6-31+G*) to have the same highly asymmetric form observed in crystalline phases. The structure can be regarded as derived from a central B2 group, bridged by two BF2 groups to give a central B4 core that is folded, not planar, and with a very short bond [164.3 pm calculated, 164.2(19) pm experimental] along the fold line. There are also four terminal BF2 groups. One of the other four bonds in the core is consistently 20-30 pm longer than the others. This asymmetry has been attributed to many intra-molecular B...F interactions, particularly those between core boron atoms and fluorines of the terminal BF2 groups. Calculations for the chloro analogue lead to a structure similar to that for B8F12, but with the long core bond extended so that one of the bridging BCl2 groups may now be regarded as terminal. With bromine as the halogen the structure changes again, with one bromine atom taking up a bridging position. With iodine, this process continues further, and there are three bridging iodine atoms. However, in this case this is not the lowest energy structure, and instead a loosely associated dimer of B4I6 is preferred. In all these cases, and particularly with the heavier halogens, there are huge differences between the results obtained with different computational methods.

Gas-phase electron diffraction studies on two 11-vertex Dicarbaboranes, closo-2,3-C2B9H11 and nido-2,9-C2B9H13.

The molecular structures of two carbaboranes, closo-2,3-C(2)B(9)H(11) and nido-2,9-C(2)B(9)H(13), were determined experimentally for the first time using gas-phase electron diffraction (GED). For closo-2,3-C(2)B(9)H(11), a model with C(2)(v)() symmetry was refined to give C-B bond distances ranging 158.3-167.0 pm and B-B distances ranging 177.4-200.0 pm. The structure of nido-2,9-C(2)B(9)H(13) was refined using a model with C(s)() symmetry to give C-B bond lengths ranging 160.3-171.9 pm and B-B lengths ranging 173.0-196.1 pm. Ab initio computations (up to MP2/6-311+G) were also carried out on these and the related nido-7,8-C(2)B(9)H(13), which was not sufficiently stable to allow determination of its molecular structure by GED.

Crystal and molecular structure of methyl 4-O-methyl-beta-D-glucopyranosyl-(1-->4)-beta-D-glucopyranoside.

The cellulose model compound methyl 4-O-methyl-beta-D-glucopyranosyl-(1-->4)-beta-D-glucopyranoside (6) was synthesised in high overall yield from methyl beta-D-cellobioside. The compound was crystallised from methanol to give colourless prisms, and the crystal structure was determined. The monoclinic space group is P2(1) with Z=2 and unit cell parameters a=6.6060 (13), b=14.074 (3), c=9.3180 (19) A, beta=108.95(3) degrees. The structure was solved by direct methods and refined to R=0.0286 for 2528 reflections. Both glucopyranoses occur in the 4C(1) chair conformation with endocyclic bond angles in the range of standard values. The relative orientation of both units described by the interglycosidic torsional angles [phi (O-5' [bond] C-1' [bond] O-4 [bond] C-4) -89.1 degrees, Phi (C-1' [bond] O-4 [bond] C-4 [bond] C-5) -152.0 degrees] is responsible for the very flat shape of the molecule and is similar to those found in other cellodextrins. Different rotamers at the exocyclic hydroxymethyl group for both units are present. The hydroxymethyl group of the terminal glucose moiety displays a gauche-trans orientation, whereas the side chain of the reducing unit occurs in a gauche-gauche conformation. The solid state (13)C NMR spectrum of compound 6 exhibits all 14 carbon resonances. By using different cross polarisation times, the resonances of the two methyl groups and C-6 carbons can easily be distinguished. Distinct differences of the C-1 and C-4 chemical shifts in the solid and liquid states are found.