Accurate torsional potentials in conjugated systems: ab initio and density functional calculations on 1,3-butadiene and monohalogenated butadienes

Theoretical Study of the Thermal Rate Coefficients of the H3+ + C2H4 Reaction: Dynamics Study on a Full-Dimensional Potential Energy Surface

Ion-molecular reactions play a significant role in molecular evolution within the interstellar medium. In this study, the entrance channel reaction, H3+ + C2H4 → H2 + C2H5+, was investigated using classical molecular dynamic (classical MD) and ring polymer molecular dynamic (RPMD) simulation techniques. We developed an analytical potential energy surface function with a permutationally invariant polynomial basis, specifically employing the monomial symmetrized approach. Our dynamic simulations reproduced the rate coefficient of 300 K for H3+ + C2H4 → H2 + C2H5+, aligning reasonably well with the values in the kinetic database commonly utilized in astrochemistry. The thermal rate coefficients obtained using both the classical MD and RPMD techniques exhibited an increase from 100 K to 300 K as the temperature rose. Additionally, we analyzed the excess energy distribution of the C2H5+ fragment with respect to temperature to investigate the indirect reaction pathway of C2H5+ → H2 + C2H3+. This result suggests that the indirect reaction pathway of C2H5+ → H2 + C2H3+ holds minor significance, although the distribution highly depends on the collisional temperature.

Reactivity and kinetics of 1,3-butadiene under ultraviolet irradiation at 254 nm

The reaction process of gaseous 1,3-butadiene following ultraviolet irradiation at the temperature range from 298 to 323 K under nitrogen atmosphere was monitored by UV–vis spectrophotometry. A gaseous mini-reactor was used as a reaction vessel and could be directly monitored in a UV–vis spectrophotometer. We investigated the reactivity and kinetics of 1,3-butadiene under non-UV and UV irradiation to evaluate its photochemical stability. A second-order kinetic model with 50.48 kJ·mol^–1 activation energy fitted the reaction data for non-UV irradiation, whereas a first-order kinetic model was appropriate in the case of UV irradiation with activation energies of 19.92–43.65 kJ mol^–1. This indicates that ultraviolet light could accelerate the photolysis reaction rate of 1,3-butadiene. In addition, the reaction products were determined using gas chromatography-mass spectrometry (GC–MS), and the reaction pathways were identified. The photolysis of 1,3-butadiene gave rise to various volatile products by cleavage and rearrangement of single C–C bonds. The differences between dimerization and dissociation of 1,3-butadiene under ultraviolet irradiation were elucidated by combining experimental and theoretical methods. The present findings provide fundamental insight into the photochemistry of 1,3-butadiene compounds.

Torsional Potentials of Glyoxal, Oxalyl Halides, and Their Thiocarbonyl Derivatives: Challenges for Popular Density Functional Approximations

The reliability of popular density functionals was studied for the description of torsional profiles of 36 molecules: glyoxal, oxalyl halides, and their thiocarbonyl derivatives. HF and 18 functionals of varying complexity, from local density to range-separated hybrid approximations and double-hybrid, have been considered and benchmarked against CCSD(T)-level rotational profiles. For molecules containing heavy halogens, most functionals fail to reproduce barrier heights accurately and a number of functionals introduce spurious minima. Dispersion corrections show no improvement. Calibrated torsion-corrected atom-centered potentials rectify the shortcomings of PBE and also improve on σ-hole based intermolecular binding in dimers and crystals.

Reaction pathways by quantum Monte Carlo: insight on the torsion barrier of 1,3-butadiene, and the conrotatory ring opening of cyclobutene

Quantum Monte Carlo (QMC) methods are used to investigate the intramolecular reaction pathways of 1,3-butadiene. The ground state geometries of the three conformers s-trans, s-cis, and gauche, as well as the cyclobutene structure are fully optimised at the variational Monte Carlo (VMC) level, obtaining an excellent agreement with the experimental results and other quantum chemistry high level calculations. Transition state geometries are also estimated at the VMC level for the s-trans to gauche torsion barrier of 1,3-butadiene and for the conrotatory ring opening of cyclobutene to the gauche-1,3-butadiene conformer. The energies of the conformers and the reaction barriers are calculated at both variational and diffusional Monte Carlo levels providing a precise picture of the potential energy surface of 1,3-butadiene and supporting one of the two model profiles recently obtained by Raman spectroscopy [Boopalachandran et al., J. Phys. Chem. A 115, 8920 (2011)]. Considering the good scaling of QMC techniques with the system's size, our results also demonstrate how variational Monte Carlo calculations can be applied in the future to properly investigate the reaction pathways of large and correlated molecular systems.

Density functionals with broad applicability in chemistry

Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy "across-the-board" for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06-2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate functional for transition metals and is the only local functional (no Hartree-Fock exchange) with better across-the-board average performance than B3LYP; this is very important because only local functionals are affordable for many demanding applications on very large systems; (d) M06-HF has good performance for valence, Rydberg, and charge transfer excited states with minimal sacrifice of ground-state accuracy. In this Account, we compared the performance of the M06-class functionals and one M05-class functional (M05-2X) to that of some popular functionals for diverse databases and their performance on several difficult cases. The tests include barrier heights, conformational energy, and the trend in bond dissociation energies of Grubbs' ruthenium catalysts for olefin metathesis. Based on these tests, we recommend (1) the M06-2X, BMK, and M05-2X functionals for main-group thermochemistry and kinetics, (2) M06-2X and M06 for systems where main-group thermochemistry, kinetics, and noncovalent interactions are all important, (3) M06-L and M06 for transition metal thermochemistry, (4) M06 for problems involving multireference rearrangements or reactions where both organic and transition-metal bonds are formed or broken, (5) M06-2X, M05-2X, M06-HF, M06, and M06-L for the study of noncovalent interactions, (6) M06-HF when the use of full Hartree-Fock exchange is important, for example, to avoid the error of self-interaction at long-range, (7) M06-L when a local functional is required, because a local functional has much lower cost for large systems.

Thermodynamic calculations for molecules with asymmetric internal rotors—application to 1,3-butadiene

We present quantum mechanical partition functions, free energies, entropies, and heat capacities of 1,3-butadiene derived from ab initio calculations. Our technique makes use of a reaction path-like Hamiltonian to couple all 23 vibrational modes to the large-amplitude torsion, which involves heavy asymmetric functional groups. Ab initio calculations were performed at the B3LYP, MP2, and CCSD(T) levels of theory and compared with experimental values as a reference case. By using the ab initio potentials and projected frequencies, simple perturbative expressions are presented for computing the couplings of all the vibrational modes to the large-amplitude torsion. The expressions are particularly suited for programming in the new STAR-P software platform which automatically parallelizes our codes with distributed memory via a familiar MATLAB interface. Using the efficient parallelization scheme of STAR-P, we obtain thermodynamic properties of 1,3-butadiene for temperatures ranging from 50 to 500 K. The free energies, entropies, and heat capacities obtained from our perturbative formulas are compared with conventional approximations and experimental values found in thermodynamic tables.

Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories

The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within approximately 0.2 eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense pi(-2) pi(*+1) satellite at approximately 13.1 eV in the ionization spectrum of the s-trans conformer.

Intrinsic Information Content of NMR Dipolar Couplings: A Conformational Investigation of 1,3-Butadiene in a Nematic Phase

The conformational equilibrium of 1,3-butadiene in a condensed fluid phase is investigated by liquid-crystal NMR spectroscopy. The full set of D(HH) and D(CH) dipolar couplings is determined from the analysis of the (1)H spectra of the three 1,3-butadiene most-abundant isotopomers (i.e. the all (12)C and the two single-labeled (13)C isotopomers) for a total of 21 independent dipolar couplings. A very good starting set of spectral parameters for the analysis of the (1)H spectrum is determined in a semiautomated way by the analysis of the (N-1) (specifically, N=6, the number of 1/2 spin nuclei in the spin system) quantum refocused (5QR), and not (5Q), spectra. As an alternative approach, a Monte Carlo (MC) numerical simulation, capable of predicting the solute ordering, is tested to simulate the 5QR spectrum. The set of D(ij) couplings is very good, proving that the MC method can represent a novel, valid alternative to the existing spectral simplification procedures. The experimentally determined dipolar-coupling data set is fully compatible with the 1,3-butadiene conformational distribution reported in the literature for isolated molecules, indicating the presence of about 99 % of s-trans conformer. With regards to the remaining 1 %, in spite of the direct and very strong dependence of the observables on the molecular structure, it was not possible to discriminate between the planar s-cis and s-gauche forms, both of which produce a very good fit of the dipolar couplings. Vibrational corrections, up to the anharmonic term, were applied; the calculated geometrical parameters are in good- although not exact-agreement with those reported in the literature from experimental and theoretical investigations. This result can be considered as supporting the methodology used for obtaining the structure and conformational distribution of a flexible molecule in a liquid phase.

Assessment of Density Functionals for π Systems: Energy Differences between Cumulenes and Poly-ynes; Proton Affinities, Bond Length Alternation, and Torsional Potentials of Conjugated Polyenes; and Proton Affinities of Conjugated Shiff Bases

Woodcock et al. [J. Phys. Chem. A 2002, 106, 11923] pointed out that no density functional was able to obtain the correct sign of the relative energies of the allene and propyne isomers of C3H4 and that density functional theory (DFT) predicts that poly-ynes are insufficiently stabilized over cumulenes for higher homologues. In the present work, we show that the recent M05 density functional predicts the correct ordering of allene and propyne and gives a mean unsigned error (MUE) of only 1.8 kcal/mol for the relative energies of the two isomers of C3H4, C5H4, and C7H4. Two other recent functionals, M05-2X and PWB6K, also give reasonably low MUEs, 2.7 and 3.0 kcal/mol, respectively, as compared to 6.2 kcal/mol for the popular B3LYP functional. Another challenging problem for density functionals has been a tendency to overpolarize conjugated pi systems. We test this here by considering proton affinities of conjugated polyenes and conjugated Schiff bases. Again M05-2X performs quite well, with MUEs of 2.1 and 3.9 kcal/ mol, respectively, as compared to 5.8 and 5.9 kcal/mol for B3LYP. Averaged over the three problems, M05-2X has a MUE of 3.0 kcal/mol, the BMK functional of Boese et al. has an MUE of 3.2 kcal/mol, and M05 has an MUE of 5.1 kcal/mol. Twenty-two other tested functionals have MUEs of 5.2-8.1 kcal/mol averaged over the three test problems. Both M05 and M05-2X do quite well, compared to other density functionals, for torsion potentials in butadiene and styrene, and M05 does very well for bond length alternation in conjugated polyenes. Since the M05 functional has broad accuracy for main group and transition metal chemistry and M05-2X has broad accuracy for main group chemistry, we conclude that significant progress is being made in improving the performance of DFT across a wide range of problem types.

Solvent Dependent Conformational Relaxation of cis-1,3,5-Hexatriene

Ultrafast transient absorption spectroscopy was used to study the conformational relaxation dynamics of 1,3,5-cis-hexatriene (Z-HT) produced in the photochemical ring-opening reaction of 1,3-cyclohexadiene (CHD) in methanol and n-propanol solvents. The results are compared with earlier investigations performed using cyclohexane and hexadecane solvents [Anderson, N. A.; Pullen, S. H.; Walker II, L. A.; Shiang, J. J.; Sension, R. J.; J. Phys. Chem. A 1998, 102, 10588-10598.]. The conformational relaxation between hot cZc-HT, cZt-HT, and tZt-HT, where the labels c and t designate cis and trans configurations about the single bonds, is much faster in alcohol solvents than in alkane solvents. The hot Z-HT produced in the photochemical ring-opening reaction evolves from the conformationally strained cZc-HT form to the more stable cZt-HT form on a time scale of 2 ps in alcohols compared with 6 ps in alkanes. The overall decay of the internal vibrational temperature of the hot Z-HT is faster in alcohols (5-6 ps) than alkanes (12-20 ps) and is weakly dependent on the specific alcohol or alkane solvent. A small population of cZt-HT (5-10%) is trapped as the solute equilibrates with the surrounding solvent following UV excitation of CHD or direct UV excitation of Z-HT. The influence of solvent on conformational relaxation of Z-HT was investigated further by probing the temperature dependence of the decay of this thermally equilibrated cZt-HT population. The apparent barrier for the cZt --> tZt conformational isomerization is lower in alcohols (17.4 kJ/mol) than in alkanes (23.5 kJ/mol). However the equilibrium Arrhenius prefactor (A(h)) is an order of magnitude smaller for alcohols (ca. 4 x 10(12)) than alkanes (ca. 6 x 10(13)) resulting in an absolute rate of decay that is faster in the alkane than in the alcohol solvents. These results are discussed in the context of transition state theory and Kramers' theory for condensed phase reaction dynamics.

Assessing a new nonempirical density functional: Difficulties in treating π-conjugation effects

The reliability of the Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation functional for the description of conjugation effects in model pi-conjugated systems has been thoroughly assessed through the calculation of torsion energy profiles. The functional reproduces qualitatively the shape of torsional potentials but, interestingly, the mixing of TPSS and exact exchange governs the quantitative results: thus, well-defined hybrid extensions of the functional are consistently employed to improve the results. The hybrid approaches led to more accurate descriptions of conjugation effects but, however, the finest performance along the whole range of dihedral angles was obtained by a customized mixing of pure or hybrid TPSS functionals and wave function methods in a multicoefficient fashion. Despite the successful construction of this nonempirical functional, higher rungs of the ladder of methods in which TPSS is based are hoped to reduce the errors with respect to reference data for pi-conjugated systems.

Coexistence of 1,3-butadiene conformers in ionization energies and Dyson orbitals

The minimum-energy structures on the torsional potential-energy surface of 1,3-butadiene have been studied quantum mechanically using a range of models including ab initio Hartree-Fock and second-order Møller-Plesset theories, outer valence Green's function, and density-functional theory with a hybrid functional and statistical average orbital potential model in order to understand the binding-energy (ionization energy) spectra and orbital cross sections observed by experiments. The unique full geometry optimization process locates the s-trans-1,3-butadiene as the global minimum structure and the s-gauche-1,3-butadiene as the local minimum structure. The latter possesses the dihedral angle of the central carbon bond of 32.81 degrees in agreement with the range of 30 degrees-41 degrees obtained by other theoretical models. Ionization energies in the outer valence space of the conformer pair have been obtained using Hartree-Fock, outer valence Green's function, and density-functional (statistical average orbital potentials) models, respectively. The Hartree-Fock results indicate that electron correlation (and orbital relaxation) effects become more significant towards the inner shell. The spectroscopic pole strengths calculated in the Green's function model are in the range of 0.85-0.91, suggesting that the independent particle picture is a good approximation in the present study. The binding energies from the density-functional (statisticaly averaged orbital potential) model are in good agreement with photoelectron spectroscopy, and the simulated Dyson orbitals in momentum space approximated by the density-functional orbitals using plane-wave impulse approximation agree well with those from experimental electron momentum spectroscopy. The coexistence of the conformer pair under the experimental conditions is supported by the approximated experimental binding-energy spectra due to the split conformer orbital energies, as well as the orbital momentum distributions of the mixed conformer pair observed in the orbital cross sections of electron momentum spectroscopy.

Assessment of Recently Developed Multicoefficient Strategies for the Treatment of π-Conjugated Molecules

Newly developed hybrid functionals (MPW1k and BB1k) have been systematically applied for the description of conjugation effects in organic molecules. These functionals are also used as part of the recently developed general-purpose multicoefficient methods MC3MPW and MC3BB. The performance of the various approaches is compared not only for relative energies but also through the calculation of torsion energy profiles for critical comparison with available reference data; thus, a numerical criterion depending on local behavior could be correspondingly defined. The results show that MC3-based methods are very accurate when faced to other approaches having comparable computational cost; thus, paving the way toward new applications and achievements in the field of conjugated materials.