This work attempts to improve the theoretical reproduction of thermodynamic properties, such as entropies and heat capacities of gas-phase n-alkanes, by using a more precise quantum-mechanical treatment of the internal rotations. Present ab initio methods all handle the internal modes in the harmonic oscillator approach. It has already been noted that this approach underestimates the microscopic partition functions (Van Speybroeck et al., J. Phys. Chem. A 2000, 104, 10939). In this work, an uncoupled scheme for internal rotations is applied to a large number of n-alkanes within the DFT formalism at the B3LYP/6-311g** level. The method being examined in this paper drastically improves the agreement between theoretical and experimental thermodynamic properties. Moreover, the method has been shown to be efficient and to be easily implemented in each ab initio software package.

No abstract

Large-amplitude motions, particularly internal rotations, are known to affect substantially thermodynamic functions and rate constants of reactions in which flexible molecules are involved. Up to now all methods for computing the partition functions of these motions rely on the Pitzer approximation of more than 50 years ago, in which the large-amplitude motion is treated in complete independence of the other (vibrational) degrees of freedom. In this paper an extended hindered-rotor model (EHR) is developed in which the vibrational modes, treated harmonically, are correctly separated from the large-amplitude motion and in which relaxation effects (the changes in the kinetic-energy matrix and potential curvature) are taken into account as one moves along the large-amplitude path. The model also relies on a specific coordinate system in which the Coriolis terms vanish at all times in the Hamiltonian. In this way an increased level of consistency between the various internal modes is achieved, as compared with the more usual hindered-rotor (HR) description. The method is illustrated by calculating the entropies and heat capacities on 1,3-butadiene and 1-butene (with, respectively, one and two internal rotors) and the rate constant for the addition reaction of a vinyl radical to ethene. We also discuss various variants of the one-dimensional hindered-rotor scheme existing in the literature and its relation with the EHR model. It is argued why in most cases the HR approach is already quite successful.

The chain-length dependence of the propagation rate coefficient for the free-radical polymerization of ethylene was investigated on an ab initio basis. Polyethylene was chosen as a test system because of its structural simplicity. Ab initio density functional theory at the B3LYP/6-31g(d) level was applied to study the kinetics of a set of addition reactions of a systematically growing radical alkyl chain to ethylene. These reactions are propagation steps in the free-radical polymerization of ethylene. Special attention was paid to low normal modes corresponding to internal rotations (IR), since the latter are important for an accurate description of the partition functions. The effect of coupling of the IR modes is also discussed. A comparison is made with the propagation rate constant derived from experiment. The results indicate that the propagation rate coefficient has largely converged by the hexyl radical stage, though a weaker chain-length dependence of k(p) for longer chains was detected.

Silicalite-1 zeolite exhibits a characteristic pentasil framework vibration around 540−550 cm−1. In the initial stages of zeolite synthesis, however, this band is observed at much higher wavenumbers: literature shows this vibration to depend on particle size and to shift over 100 cm−1 with increasing condensation. In this work, the pentasil vibration frequency was derived from theoretical molecular dynamics simulations to obtain the correct IR band assignments for important nanoparticles. The IR spectroscopic fingerprint of oligomeric five-ring containing precursors proposed in the literature was computed and compared with experimental data. Our theoretical results show that, while isolated five-membered rings show characteristic vibrational bands around 650 cm−1, the combination of five-membered rings in the full MFI-type structure readily generates the bathochromic shift to the typical pentasil vibration around 550 cm−1. As opposed to what was previously believed, the IR band does not shift gradually as nanoparticle size increases, but it is highly dependent on the specific way structural units are added. The most important feature is the appearance of an additional band when double five-membered rings are included, which allows for a clear distinction between the key stages of early zeolite nucleation. Furthermore, the combination of the simulated spectra with the experimental observation of this spectral feature in nanoparticles extracted from silicalite-1 clear solutions supports their structured nature. The theoretical insights on the dependency of pentasil vibrations with the degree of condensation offer valuable support toward future investigations on the genesis of a zeolite crystal.