Methyl rotational potentials of trimethyl metal compounds studied by inelastic and quasielastic neutron scattering

doi:10.1016/S0301-0104(03)00207-6

Chemical Physics

Volume 292, Issues 2–3, 1 August 2003, Pages 161-169

https://doi.org/10.1016/S0301-0104(03)00207-6 Get rights and content

Abstract

Neutron scattering data on classical and quantum rotation of methyl groups in the organometallic molecular crystal In(CH₃)₃ are presented. The tunneling spectra are analyzed using the mean field single particle model of rotational tunneling. The presence of six inequivalent rotors of equal occurrence probabilities in In(CH₃)₃ is reflected in the number and intensities of the transitions. In a similar way classical spectra are interpreted as superposition of quasielastic Lorentzians. A consistent combination of tunneling and quasielastic spectroscopies is based on equal relative intensities of the respective spectral components and allows a determination of the coefficients of a Fourier expansion of the rotational potentials up to second order with only a few percent of uncertainty. The results are compared to published data on the homologues Al and Ga compounds on the basis of the molecular and crystal structures. Intra- and intermolecular interactions are found to be of similar importance.

Introduction

One of the most fundamental and most simple dynamical processes is the rotation of a methyl group into a new equilibrium orientation. The potential which describes this dynamics is determined by the intermolecular interactions with the neighboring atoms which may be parameterized as universal force fields (UFF), pair interaction potentials or in ab initio program codes.

Neutron scattering has developed two techniques to explore molecular rotation in solids. On the one hand quasielastic spectroscopy reveals the classical motion of an individual atom [1]. If this atom is bound to a molecule or a molecular side group it monitors its rotational dynamics. The spectra are analyzed with the concept of the elastic incoherent structure factor. The output from this method are the jump geometry including jump distances, the related jump times, phase transitions as a discontinuity in the evolution of the dynamics with increasing temperature, etc. On the other hand molecules show a quantum behavior at low temperatures. The quantum excitations of a rotor are observed by rotational tunneling [2], [3] and vibrational spectroscopies.

Both theories represent in their standard forms single particle descriptions. The rotor is characterized by its momentum of inertia and the environment is represented by a potential. It is this potential which links the results of the two techniques to each other. The topology of the potential/environment determines the jump geometry; the barrier height determines the classical jump rate at a given temperature. The shape and height of the same potential determine also the eigenstates and eigenvalues of a rotor which – vice versa – allow to determine the potential parameters.

An important property of the single particle model is its transferability. The symmetry of the rotational potential is only determined by the rotor and is the same in any material. In cases of coupling a second degree of freedom has to be considered. The mathematical description has to be formulated newly for each new type of coupling. This is done for very few cases only like direct rotor–rotor coupling or the so-called rotation–translation coupling [4]. Even here a new symmetry already requires the development of a new mathematical theory. Thus, in spite of weak points the single particle model remains the standard description of tunneling methyl groups.

The following discussion is restricted to the one-dimensional rotation of a methyl group present in the In(CH₃)₃ compound. In(CH₃)₃ like many other materials contains inequivalent rotors. Their number is determined by the crystal structure and eventually disorder. By combining quasielastic and tunneling spectroscopies rotational potentials of all inequivalent rotors can be obtained with high accuracy and confidence. A comparison to results from the homologues Ga and Al compounds will allow an evaluation of the relative importance of intra- and intermolecular interactions.

Section snippets

Rotational tunneling

The methyl rotational potential in the single particle model [2], [3] shows the threefold symmetry of the molecule and is expressed in form of a Fourier expansion $V(ϕ)=∑_{n=1}^{N} V_{3n} 2 (1− cos (3nϕ−ϕ_{3n})).$ Arbitrarily one can chose ϕ₃=0. The potential determines the excitations of the hindered rotor through the eigenvalues of the single particle Schrödinger equation [2] $−B ∂^{2} ∂ ϕ^{2} +V(ϕ) Ψ_{i} =E_{i} Ψ_{i} .$ The more eigenvalues are measured the better the shape of the potential – including phase factors – can be determined. ϕ₆

Trimethylindium In(CH₃)₃

In(CH₃)₃ is very similar to the recently studied Ga(CH₃)₃ [8]. Both materials are used for doping semiconductors by thermal decomposition of the molecules. Since the isolated molecules form flat equilateral triangles with In at the center and methyl groups at the corners there is no tendency to form dimers as the first member of group IIIa trimethyl compounds, Al(CH₃)₃. A room temperature X-ray crystal structure determination shows a tetragonal space group P4₂/n(Z=8) with three inequivalent

Trimethylaluminum Al(CH₃)₃

Trimethylaluminum is of special interest. At first this is due to its technical importance as starting material for doping semiconductors and as catalyst. Secondly trimethylaluminum is the prototype of an electron deficiency compound involving methyl groups. The monomer resembles a tetrahedron with one corner cut away. The free electron density at this corner leads already in the gas phase to the formation of dimers of the shape of two tetrahedra connected by a common edge. The coordination

Structure–potential relation

Due to the lack of precise knowledge of the atomic positions in the low temperature phases of Ga(CH₃)₃ and In(CH₃)₃ the discussion will be based on properties of the molecules and general parameters of the known high temperature structures [9], [11], [15]. The relevant information is presented in Table 4.

We first discuss the pair Ga and In. Table 4 shows an average increase of the In–C bond length by about 0.17 Å compared to the Ga–C bond length. This leads to a reduction of the intramolecular

General conclusions

Quasielastic spectra and tunneling splittings of rotational groundstates of methyl groups in group IIIa trimethyl compounds are consistently interpreted by the single particle model of rotation. This shows that even for molecules which interact with each other via their shell of methyl groups the potential energy due to interaction with the static lattice dominates effects of coupling. The similarities of rotational potentials in the three homologue compounds with different bondlengths and

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Methyl rotational potentials of trimethyl metal compounds studied by inelastic and quasielastic neutron scattering

Abstract

Introduction

Section snippets

Rotational tunneling

Trimethylindium In(CH3)3

Trimethylaluminum Al(CH3)3

Structure–potential relation

General conclusions

Phys. B

Quasielastic Neutron Scattering

Chem. Rev.

J. Phys.: Condens. Mat.

J. Phys. C

J. Chem. Phys.

Trimethylindium In(CH₃)₃

Trimethylaluminum Al(CH₃)₃