Jaan Laane

Periodic potential functions for pseudorotation and internal rotation

Abstract A computer program which uses matrix diagonalization techniques has been developed for determining the energy levels and wave-functions for periodic potential functions of the form V = 1 2 ∑Vn(1-cosnφ), where terms with n ranging from 1 to 6 can be used. The mass related internal rotation constant B is also allowed to vary as a function of the phase φ. The energy level patterns of eight different types of potential functions, which are typical for internal rotation and pseudorotation, have been determined. Several applications of such calculations for the interpretation of vibrational data are discussed.

Structures and conformations of non-rigid molecules

From the beginnings of modern chemistry, molecular structure has been a lively area of research and speculation. For more than half a century spectroscopy and other methods have been available to characterize the structures and shapes of molecules, particularly those that are rigid. However, most molecules are at least to some degree non-rigid and this non-rigidity plays an important role in such diverse areas as biological activity, energy transfer, and chemical reactivity. In addition, the large-amplitude vibrations present in non-rigid molecules give rise to unusual low-energy vibrational level patterns which have a dramatic effect on the thermodynamic properties of these systems. Only in recent years has a coherent picture of the energetics and dynamics of the conformational changes inherent in non-rigid (and semi-rigid) molecules begun to emerge. Advances have been made in a number of different experimental areas: vibrational (infrared and Raman) spectroscopy, rotational (microwave) spectroscopy, electron diffraction, and, most recently, laser techniques probing both the ground and excited electronic states. Theoretically, the proliferation of powerful computers coupled with scientific insight has allowed both empirical and ab initio methods to increase our understanding of the forces responsible for the structures and energies of non-rigid systems. The development of theory (group theoretical methods and potential energy surfaces) to understand the unique characteristics of the spectra of these floppy molecules has also been necessary to reach our present level of understanding. The thirty chapters in this volume contributed by the key speakers at the Workshop are divided over the various areas. Both vibrational and rotational spectroscopy have been effective at determining the potential energy surfaces for non-rigid molecules, often in a complementary manner. Recent laser fluorescence work has extended these types of studies to electronic excited states. Electronic diffraction methods provide radial distribution functions from which both molecular structures and compositions of conformational mixtures can be found. Ab initio calculations have progressed substantially over the past few years, and, when carried out at a sufficiently high level, can accurately reproduce (or predict ahead of time) experimental findings. Much of the controversy of the ARW related to the question of when an ab initio is reliable. Since the computer programs are readily available, many poor calculations have been carried out. However, excellent results can be obtained from computations when properly done. A similar situation exists for experimental analyses. The complexities of non-rigid molecules are many, but major strides have been taken to understand their structures and conformational processes.

Far‐Infrared Spectra of Ring Compounds. II. The Spectrum and Ring‐Puckering Potential Function of Cyclopentene

The infrared spectrum of cyclopentene has been recorded in the range 18–300 cm−1. Two series of thirteen and nine Q branches, respectively, were observed, both of which arise from the strongly anharmonic energy levels of the B1 ring‐puckering vibration. The longer, more intense series is assigned to molecules in the ground vibrational state of all the other vibrations, and the shorter, weaker series to molecules in the first excited state of the A2 ring‐twisting vibration. Each set of Q branches can be fitted to transitions between the energy levels of a double‐minimum potential function of the form V=a(x4—bx2), where x is the B1 ring‐puckering coordinate. The height of the barrier opposing planarity is calculated to be 232±5 cm−1, and the equilibrium angle between the two dihedral planes of the puckered ring to be 23.3°±1°.

Far‐Infrared Spectra of Ring Compounds. III. Spectrum, Structure, and Ring‐Puckering Potential of Silacyclobutane

The infrared spectra of gaseous silacyclobutane and silacyclobutane‐1, 1‐d2 have been recorded in the range 24‐300 cm−1. Both molecules show the complicated vibrational fine structure expected from a double‐minimum potential for the ring‐puckering vibration. The absorption maxima of silacyclobutane were fitted to a potential of the form V = a (x4 − bx2), where x is the ring‐puckering coordinate. The potential barrier is calculated as 440 ± 3 cm−1, and the dihedral angle of the puckered ring as 35.9 ± 2°. The spectrum of silacyclobutane‐1, 1‐d2 can be interpreted with the same potential function but the quantitative agreement with observed levels above the barrier is less accurate. The discrepancy is ascribed to interaction between the ring‐puckering mode and the SiD2 rocking vibration.

Eigenvalues of the Potential Function V=z4±Bz2 and the Effect of Sixth Power Terms

The one-dimensional Schrödinger equation in reduced form is solved for the potential function V = z4+Bz2 where B may be positive or negative. The first 17 eigenvalues are reported for 58 values of B in the range −50⩽B⩽100. The interval of B between the tabulated values is sufficiently small so that the eigenvalues for any B in this range can be found by interpolation. At the limits of the range of B the potential function approaches that of a harmonic oscillator with only small anharmonicity. The effect of a small Cz6 term on this potential is studied and it is concluded that a previously reported approximation formula is quite applicable but only for positive values of B. The success of the quartic—harmonic potential function for the analysis of the ring-puckering vibration is shown; it is also demonstrated that the same potential serves as a useful approximation for many other systems, especially those of the double minimum type.

Calculation of kinetic energy terms for the vibrational Hamiltonian: Application to large-amplitude vibrations using one-, two-, and three-dimensional models

Abstract One-, two-, and three-dimensional models involving large-amplitude vibrations have been used to calculate kinetic energy terms. Principle G matrix elements as well as cross terms in the kinetic energy were determined. Calculations were done on models involving the ring-puckering and PH inversion vibrations for 3-phospholene and the ring-puckering, ring deformation, and SiH 2 in-phase rocking vibrations for 1,3-disilacyclobutane. Kinetic energy expansions for g 44 and g 45 type terms were determined. Calculations show a coordinate dependence of the principle G matrix elements as well as of the g 45 terms. The vectorial models used in these calculations make it possible to treat vibrations in a one-, two-, or three-dimensional model separate from the other vibrations without carrying out a coordinate transformation, which would be necessary for the Wilson GF high- or low-frequency separation.

Vector representation of large-amplitude vibrations for the determination of kinetic energy functions

Abstract In order to calculate the reduced mass for a particular vibrational motion it is necessary to determine the coordinates of each of the atoms as a function of the vibrational coordinate. This work describes how the use of vectors simplifies the representation of the molecular structure. The ring puckering, ring angle deformation, and M H 2 rocking motions of a four-membered ring, and the ring puckering, ring twisting, and M - X inversion motions of a five-membered ring are examined in detail.

Far‐Infrared Spectra and the Ring‐Puckering Potential Function of Silacyclopent‐3‐ene and Silacyclopent‐3‐ene‐1,1‐d2

A series of a far‐infrared absorption bands have been observed between 35 and 100 cm−1 in the spectra of silacyclopent‐3‐ene, CH2CH=CHCH2SiH2, and silacyclopent‐3‐ene‐1,1‐d2. These absorptions result from the transitions between the various energy levels of the ring‐puckering vibration. The frequencies of the bands can be calculated quite accurately using a pure quartic potential, V = 14.34Z4 for the hydride and V = 13.20Z4 for the deuteride where Z is the ring‐puckering coordinate in reduced form. A slightly better fit for each spectrum is obtained by adding a small positive quadratic term to the potential function. The ring‐puckering potential for this molecule shows that the structure of the five‐membered ring is a planar one and that it has no barrier to inversion like that in cyclopentene. This lack of a potential barrier is attributed to a smaller barrier to internal rotation in the –CH2–SiH2– bond as compared to –CH2–CH2–. Also there is evidence from the isotope shift of the frequencies (which is r...

Far‐Infrared Spectrum and the Barrier to Pseudorotation of Silacyclopentane

The far‐infrared spectrum arising from the transitions between the pseudorotational levels in silacyclopentane has been observed. Thirteen absorption maxima were found for the υ = 0 (radial ground) state and eight for the υ = 1 state. For each series a potential of the form V = (V2 / 2) (1 + cos2φ) predicts frequencies which agree very closely with the observed values. The values of V2, which represent the barriers to pseudorotation, were found to be 1362 ± 25 cm−1 for the radial ground state and 1301 ± 50 cm−1 for the first excited state. The pseudorotation constants for the two radial states were found to be B0 = 1.966 and B1 = 2.033 cm−1. The observed pseudorotation barrier of 3.89 kcal/mole represents the energy required to go from the more stable C2 half‐chair conformation to the Cs envelope form and is higher than expected from previously derived formulas.

Raman Spectroscopy Analysis of Botryococcene Hydrocarbons from the Green Microalga Botryococcus braunii

Botryococcus braunii, B race is a unique green microalga that produces large amounts of liquid hydrocarbons known as botryococcenes that can be used as a fuel for internal combustion engines. The simplest botryococcene (C30) is metabolized by methylation to give intermediates of C31, C32, C33, and C34, with C34 being the predominant botryococcene in some strains. In the present work we have used Raman spectroscopy to characterize the structure of botryococcenes in an attempt to identify and localize botryococcenes within B. braunii cells. The spectral region from 1600–1700 cm−1 showed ν(C=C) stretching bands specific for botryococcenes. Distinct botryococcene Raman bands at 1640 and 1647 cm−1 were assigned to the stretching of the C=C bond in the botryococcene branch and the exomethylene C=C bonds produced by the methylations, respectively. A Raman band at 1670 cm−1 was assigned to the backbone C=C bond stretching. Density function theory calculations were used to determine the Raman spectra of all botryococcenes to compare computed theoretical values with those observed. The analysis showed that the ν(C=C) stretching bands at 1647 and 1670 cm−1 are actually composed of several closely spaced bands arising from the six individual C=C bonds in the molecule. We also used confocal Raman microspectroscopy to map the presence and location of methylated botryococcenes within a colony of B. braunii cells based on the methylation-specific 1647 cm−1 botryococcene Raman shift.