Ethane-like Molecules Research Articles

A novel predictive model for formation enthalpies of Si and Ge hydrides with propane‐ and butane‐like structures

Butane- and propane-like silicon-germanium hydrides and chlorinated derivatives represent a new class of precursors for the fabrication of novel metastable materials at low-temperature regimes compatible with selective growth and commensurate with the emerging demand for the reduced thermal budgets of complementary metal oxide semiconductor integration. However, predictive simulation studies of the growth process and reaction mechanisms of these new compounds, needed to accelerate their deployment and fine-tune the unprecedented low-temperature and low-pressure synthesis protocols, require experimental thermodynamic data, which are currently unavailable. Furthermore, traditional quantum chemistry approaches lack the accuracy needed to treat large molecules containing third-row elements such as Ge. Accordingly, here we develop a method to accurately predict the formation enthalpy of these compounds using atom-wise corrections for Si, Ge, Cl, and H. For a test set of 15 well-known hydrides of Si and Ge and their chlorides, such as Si(3)H(8), Ge(2)H(6), SiGeH(6), SiHCl(3), and GeCl(4), our approach reduces the deviations between the experimental and predicted formation enthalpies obtained from complete basis set (CBS-QB3), G2, and B3LPY thermochemistry to levels of 1-3 kcal/mol, or a factor of ∼5 over the corresponding uncorrected values. We show that our approach yields results comparable or better than those obtained using homodesmic reactions while circumventing the need for thermochemical data of the associated reaction species. Optimized atom-wise corrections are then used to generate accurate enthalpies of formation for 39 pure Si-Ge hydrides and a selected group of 20 chlorinated analogs, of which some have recently been synthesized for the first time. Our corrected enthalpies perfectly reproduce the experimental stability trends of heavy butane-like compounds containing Ge. This is in contrast to the direct application of the CBS-QB3 method, which yields erratic predictions. Our approach also provides quantitative bond-additivity rules for the chlorination of these heavier species. Finally, we discuss structure and bonding trends across the entire sequence of butane-, propane-, and ethane-like molecules with a special focus on the isomeric variations.

Vibrational symmetry classification and torsional tunneling splitting patterns in G6(EM), G12, and G36(EM) molecules

It is shown that the torsional splitting patterns in methanol-like molecules, with the excitation of small amplitude vibrational modes in the methyl group, are determined by mechanisms that can be formulated in an almost identical fashion to that for ethane-like molecules. This is achieved by treating ethane-like molecules by the internal axis method (IAM) and methanol-like molecules by the principal axis method (PAM) or rho-axis method (RAM). Using the extended molecular groups G6(EM) or C6v(M) for methanol and G36(EM) for ethane, vibrations perpendicular to the internal rotation axis are conveniently described by modes of higher degeneracy (E for methanol and Gs for ethane) in the absence of coupling of top and frame. Head–tail coupling operators, except the cos-type barrier terms, lower the degeneracy, causing vibrational splittings. Coupled vibrational pairs with torsional splitting patterns that we call ‘regular’ (pure A1, A2 pairs for methanol and pure E1d, E2d pairs for ethane) or ‘inverted’ (pure B1, B2 pairs for methanol and pure E1s, E2s pairs for ethane) can be formed as limit cases. Actual splitting patterns occur between the above limits, and are basically determined by torsional Coriolis coupling, which can tune more or less to resonance pairs of uncoupled basis levels linked by specific head-tail coupling operators. The inversion of torsional splitting patterns, observed in perpendicular vibrational modes of the methyl group of methanol, can be predicted by these theoretical considerations. Similar considerations apply to molecules of G12 symmetry.

Rotation–torsion analysis of the Si2H6 infrared fundamental ν9, perturbed by excited torsional levels of the vibrational ground state

The lowest infrared active perpendicular fundamental ν9 of disilane has been analysed on a Fourier transform spectrum between 320 and 430 cm−1, at the spectral resolution of 0.0012 cm−1. The rotation–torsion structure of this band is affected by x,y Coriolis interactions with excited torsional levels of the vibrational ground state, correlating with components of 3ν4 and 4ν4 in the high barrier limit. The interaction of ν9 and 4ν4, forbidden in the D3d symmetry limit, is allowed between components of E torsional symmetry under the G36(EM) extended molecular group, because of the large amplitude of the internal rotation motion. We could determine the values of the main vibration–rotation–torsion parameters of ν9, interaction parameters, and the vibrational wavenumbers of the four torsional components of 3ν4 and of the E3d component of 4ν4. The intrinsic torsional splitting of ν9 is found to be smaller than in the ground vibrational state by 0.0066 cm−1, in good agreement with our theoretical predictions. The possibility of observing the effects of D3d-forbidden interactions in the spectra of ethane-like molecules is also discussed.

Torsional Line Splittings in the (ν 4+ν 8)−ν 4 Hot Transitions of C 2H 6 between 1400 and 1510 cm −1

A detailed investigation of the high-resolution infrared spectrum of ethane revealed the occurrence of features belonging to the hot perpendicular system (ν 4+ν 8)−ν 4 between 1400 and 1510 cm −1. Transition lines of the subbranches with K″Δ K from −7 to 4, exhibiting torsional splittings of several tenths of a cm −1, were observed and measured in this region. The observed line splittings are strongly influenced by the interaction between the ν 4+ν 8 and 2ν 4+ν 12 states and change with the values of K″Δ K, depending on the zero-order energy separation of the interacting levels. We found by numerical extrapolation that splittings still occur far from resonance, showing that the intrinsic torsional splittings of the combining states ν 4+ν 8 and ν 4 are quite different. We determined the intrinsic torsional splitting of ν 4+ν 8 to be less than 0.083 cm −1, compared with 0.236 cm −1 estimated for the ν 4 state. This result is in agreement with the expected effects of torsional Coriolis and head–tail coupling and is consistent with previous observations on vibrationally degenerate states of ethane-like molecules.

Physical behavior, symmetry classification and quantum numbers of vibrational–torsional states in ethane-like molecules

The symmetry species of vibrational and vibrational–torsional states of ethane-like molecules are labeled and classified by the values of quantum numbers related to the vibrational contribution to the z-axis rotational and torsional angular momenta. It is emphasized that the symmetry behavior of degenerate vibrational states of this class of molecules depends on the joint action of end-to-end and torsional Coriolis coupling by a complex mechanism, with group theoretical implications. A new vibration–torsion quantum number is defined, to account for the arbitrariness of the symmetry classification of the degenerate vibrational modes. The classification of the vibrational states of a G s+ G s combination is studied in detail. The limit case where the value of the Coriolis coefficient is equal to one in both partners of the combination is examined, accounting for the effects of end-to-end and torsional Coriolis interactions, and the results are shown to be in agreement with the predictions from group theory. The occurrence of vibrational ℓ and ℓ i splittings in a G s+ G s combination, analogous to the vibrational ℓ-doubling in E+ E combinations, is also discussed. It is pointed out that the complex mechanisms of end-to-end and torsional Coriolis coupling, which can affect the torsional splittings significantly, might contain relevant general features also applicable to other classes of molecules with internal rotation.

Head and Tail Deformations, Torsional Coriolis Coupling, and E1d-E2d Vibrational Mixing in Ethane-Like Molecules

The mechanism of torsional Coriolis interaction of E1d and E2d vibrational modes in ethane-like molecules is investigated, and it is shown that this coupling can drastically affect the torsional splitting in the degenerate vibrational states. A basic point of our treatment is that the sets of coordinates of head and tail which combine with the + sign to generate E1d normal coordinates are in general different from those which combine with the − sign to generate E2d normal coordinates. It is shown that the ζγ torsional Coriolis coefficients calculated by the usual methods of normal mode analysis are related to the vibrational angular momenta within head and tail referred to the internal rotor axis systems. With knowledge of the L and L−1 matrices it is possible to transform these coefficients for reference to the molecule-fixed frame. It is peculiar that torsional Coriolis matrix elements occur between E1d and E2d vibrational components with the same x or y orientation in the molecule-fixed frame. The matrix elements of the torsional Coriolis operator and other operators responsible for the end-to-end coupling are determined, and a method for calculating vibration–torsion energies, and then torsional splittings, in degenerate vibrational states is outlined. Detailed calculations require a global model, involving all the degenerate vibrational basis states in a complex mechanism of interactions, but it is shown that useful information can be obtained by means of simplified models. Our semiempirical rule that degenerate vibrational states with a large negative value of the diagonal vibration–rotation Coriolis coefficient are likely to deviate much from the behavior of E1d or E2d vibrational states, with a sensible decrease of the torsional splittings, is confirmed.

Influence of molecular top deformations on the internal rotation barrier

The influence of molecular top deformations on the potential barrier is investigated. For some ethane-like molecules, it is shown that the deformation makes a pronounced contribution to the height of the torsion barrier.

Vibration-Torsion Dynamics of Ethane-like Molecules in Degenerate Vibrational States

We examine the mechanisms of interaction between the deformations of the two identical halves of ethane-like molecules in degenerate vibrational states, in order to determine the most convenient symmetries of the degenerate vibrational wavefunctions, in the molecular symmetry group G 36( EM). In moderate barrier molecules this is related to the problem of the vibration-torsion symmetry labeling of the tunneling split components, in the order of increasing energies, in given rotational states. Numerical calculations have been performed as a guide to explore several different situations. It has been proved that the torsional splittings in degenerate vibrational states of molecules with a moderate barrier depend dramatically on the value of the γ-Coriolis coefficient and, unlike the splittings in nondegenerate vibrational states, are not determined only by the effective torsional potential function. Theory and numerical predictions support the experimental result that all normal modes of ethane behave as E 1 d , E 2 d pairs.

A classical insight of the γ-Coriolis coupling in ethane-like molecules

The mechanisms of interaction between the deformations of the two moieties of ethane-like molecules in degenerate vibrational modes are investigated by simple methods of classical mechanics. Special attention is given to γ-Coriolis interaction in degenerate vibrational states, which generates first order vibration-torsion coupling. It is shown that the level splitting due to tunneling through the torsional barrier in degenerate vibrational states is strongly affected by the value of the Coriolis ξ coefficient. Simple classical considerations can explain the recent experimental result that all degenerate normal modes of ethane form E1d, E2d paired representations of the G36(EM) molecular symmetry group.

A GF-Matrix Approach to the End-to-End Coupling in Ethane-like Molecules

We examine the effect of end-to-end coupling on the degenerate vibrational deformations of ethane-like molecules by considering the form of the dependence of the elements of the G and F matrices on the internal rotation angle γ. This can be done by simple geometrical considerations, in a basis of internal vibrational coordinates. After transformation to symmetry coordinates belonging to different species of the G36(EM) extended molecular group, the product G(0)F(0) of the γ-independent parts of the G and F matrices is diagonalized. The resulting zero-order normal modes and their conjugate momenta are used in building up the vibration-torsion Hamiltonian, including the γ-dependent terms. We find that (i) in the case of a low barrier hindering the internal rotation the most convenient sets of degenerate normal coordinates are either Gs (in the case of a weak effect of the end-to-end coupling on the relative deformations) or E1d, E2d; (ii) degenerate vibrational coordinates whose top and frame components have at the least one common atom lead to E1d, E2d normal modes regardless of the barrier height; (iii) "unpaired" degenerate vibrational coordinates, such as the skeletal bending of dimethylzinc, always contribute an E1d normal mode; and (iv) in the case of high or moderate barriers, Gs normal modes are unlikely to occur, and the most probable normal mode symmetries are E1d, E2d.

Bonded hard-sphere theory and computer simulations of polyatomic hard-sphere models of alkanes and their derivatives

The equation of state of the first two members of a homologous series of model alkane-like molecules which incorporate the identities of the backbone and substituent atoms as hard-sphere sites is examined. These polyatomic molecules are formed from tangentially bonded hard spheres with diameters σ1 and σ2, where spheres of type 1 make up the backbone of the chain, and spheres of type 2 represent the substituent atoms. The spheres are bonded together in a tetrahedral geometry so that all of the bond angles are ω = 109°; for the second and higher homologues dihedral angles χ about the 1–1 bonds also have to be specified. In order to test the predictions of a recent bonded hard-sphere (BHS) theory, isothermal-isobaric Monte Carlo (MC-NPT) simulations are undertaken for methane- and ethane-like molecules with different diameter ratios σ2/σ1 over a range of densities in the fluid state. In the case of the ethane-like molecules trans (χ = 30°) and freely rotating geometries are examined. The simulation data are...

MS-SCF-X α calculation of the rotational barriers in ethane-like molecules

MS-X α calculations are performed for the rotational barriers of C 2H 6, Si 2H 6, Ge 2H 6, C 2F 6, in the rigid rotor approximation with different sets of sphere radii. While the results show a large dependence on the radii employed, good results can be obtained with a particular choice based on previously proposed criteria.

Theory of torsion-vibration-rotation interaction in ethane and analysis of the band ν11 + ν4

The theory of torsion vibration-rotation interaction as applied to high barrier to internal rotation ethanelike molecules is discussed. It is shown that the effects of internal rotation can be described by one parameter X which introduces an oscillatory behavior in subband origins. Also, the effects of xy Coriolis interaction between A and E vibrational states on the energy levels and effective band constants of the E state are discussed. The band ν 11 + ν 4 of ethane has been measured with high resolution and analyzed. The barrier to internal rotation in ν 11 has been found to be 3330 ± 23 cal/mole.

Molecular orbital theory of E2 reactions and nuclear magnetic resonance spin-spin coupling in ethane-like molecules

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTMolecular orbital theory of E2 reactions and nuclear magnetic resonance spin-spin coupling in ethane-like moleculesJohn P. LoweCite this: J. Am. Chem. Soc. 1972, 94, 11, 3718–3727Publication Date (Print):May 1, 1972Publication History Published online1 May 2002Published inissue 1 May 1972https://doi.org/10.1021/ja00766a008RIGHTS & PERMISSIONSArticle Views97Altmetric-Citations13LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts Get e-Alerts

Commutation relations for the angular momentum operators in ethane-like molecules

Commutation relations for the angular momentum operators in ethane-like molecules

High-resolution infrared spectra of ethanelike molecules and the barrier to internal rotation: The ν9, ν13 band of dimethylacetylene

The infrared spectrum of dimethylacetylene was measured with high resolution in the region of the perpendicular band of the CH stretching vibration and the Q branches were partially resolved in the bunches of Q branches. The upper limit to the torsional barrier was estimated to be 4 cm −1.

Rotational isomerism. Part VIII. A calculation of the rotational barriers and rotamer energies of some halogenated compounds

A method is suggested for calculating internal rotation barriers and rotamer energy differences in halogenated ethane-like molecules. The total interaction energy in a Particular orientation is given by the summation of all steric and electrostatic interactions between non-bonded atoms plus a torsional term which is directly related to the intrinsic barrier to rotation in ethane. The electrostatic term includes all hydrogen–halogen attractive interactions besides the halogen–halogen repulsions. The derivation of parameters to describe the various interactions together with the selection of a consistent set of molecular geometries is discussed. The model reproduces barrier heights and rotamer energy differences of a large number of molecules satisfactorily. The consequences and limitations of the model are critically assessed.

Effects of Methyl and Hydroxyl Substitution on Barriers to Internal Rotation about Single Bonds

The electrostatic model for threefold barriers to internal rotation developed in earlier papers is updated. The barrier in methyl arsine is predicted to be 1.57 kcal/mole. It is also shown that the barrier recently measured for nitrosomethane is in fair agreement with the model result. The effect upon the barrier of methyl substitution in ethanelike molecules is shown to correlate well with the electronegativity of the central atom where substitution occurs. The very different barrier increases caused by methyl substitution in propene and methyl ketene are reproduced and shown to be simply related to structure. An explanation is proposed for the experimentally observed lowering of the barrier in going from acetaldehyde to acetone. The very low barrier in acetic acid is shown to be consistent with delocalization of hydroxyl pi electrons. A low barrier for ethanol is not supported by the model.

High resolution infrared spectra of ethane-like molecules and the barrier to internal rotation: Structure of the perpendicular bands of dimethylacetylene

The fine structure of the perpendicular bands of an ethane-like molecule with nearly free internal rotation is discussed from the point of view of determining the barrier to internal rotation. The existing theory is extended to take into account the variation of the rotational constants with vibrational state, the ( P x p x + P y p y )-Coriolis coupling between the fundamental levels of the degenerate generate and nondegenerate CH stretching vibrations, and the Fermi resonance between the fundamental levels of the CH bending vibration. The structure of several “hot” bands associated with the low frequency skeletal bending vibrations is also discussed.

Semiempirical Treatment of Hindered Rotation. II. Molecules Possessing Double Bonds

A method using electrostatic models, presented earlier for ethanelike molecules, is extended to include systems containing double bonds. Models are developed for the prototype molecules acetaldehyde, propylene, and methyl ketene. The principal barrier-producing features in these molecules, exclusive of the hydrogen adjacent to the methyl group, are taken to be, respectively, nonbonding, sp2 hybridized electron pairs on oxygen, the cis C–H bonding electrons, and the pi electrons in the C=O bond. These models are shown to predict reasonably well the barriers in vinyl silane and N-methylmethylenimine, and to be consistent with observed barriers for methyl isocyanate and methyl allene. They also are shown to be capable of rationalizing observed trends in barrier values upon halosubstitution for methine or carbonyl hydrogen in propylene and acetaldehyde when inductive and resonance effects are considered. Implications of the models for molecules with double bonds more removed from the methyl group, such as propionaldehyde, are considered, and conditions for steric repulsion are shown to be present in cases where the models fail. The connection between the models and the detailed shapes of the barriers is discussed, and some values of V6 as computed from the models, are given. Rough predictions are made of barriers for molecules derived from prototypes by halo substitution or by substitution of a methyl group by a silyl group. Problems involved in extending the method to molecules with onefold rotors are considered, and illustrative calculations are made for nitrous acid and formic acid.