Torsional Coordinate Research Articles

Vibration-torsion interaction in the microwave spectrum of internally hydrogen-bonded methylmalonaldehyde

The microwave spectrum of methylmalonaldehyde has been measured and the molecule shown to be in an intramolecularly hydrogen-bonded (chelate ring) form in the gas phase. The spectrum shows the effects of two large amplitude internal motions: the torsion of the methyl group about its symmetry axis and the tunneling of the hydrogen-bond hydrogen through a potential barrier to an equivalent position (combined with an appropriate CH 3 rotation). The two motions are coupled through the torsion-inversion potential energy term of threefold symmetry in the torsional coordinate. A two vibration-plus-rotation model is developed and applied to explain the sizeable perturbations of the pure rotational transitions from a rigid rotor pattern in four ground-state sublevels. The observed torsion-inversion splittings in the nondegenerate level (2.8004 cm −1 for OCHC(CH 3)CHOH , 0.35920 cm −1 for OCHC(CH 3)CHOD and 0.92590 cm −1 for OCHC(CD 3)CHOH) are quite well determined and, as expected, depend strongly upon appropriate isotopic substitutions. The experimentally derived parameters are discussed in terms of an effective inversion-torsion potential surface. The data are not in disagreement with a range of barrier values determined from comparison of ab initio full geometry-optimized and constrained C 2 v geometry-optimized molecular orbital calculations. Because of the expected isotope dependence of the effective surface and the large number of parameters involved, it is not clear whether more accurate fitting to the data is justified.

Relationship between torsional angles and ring-puckering coordinates

A relationship between torsional angles and ring puckering coordinates, applicable to any puckered ring, is deduced assuming infinitesimal displacements from a planar reference conformation. For equilateral polygons there is only one maximum torsion angle θ m and one phase angle φ m for each value of m, whereas for non-equilateral polygons there is one maximum θ m j,j+1 and a correction, ϵ m j,j+1 , to be applied to the phase angle φ m for each torsion angle θ j,j+1 . The resulting expressions for equilateral pentagons and hexagons are equivalent to the empirical ones proposed previously.

An investigation of the low-frequency torsional modes of trans-stilbene using Raman spectroscopy

Evidence is presented which suggests that trans-stilbene is nonplanar in fluid phases. The nearly planar molecule of the solid distorts along the Au torsional coordination in the melt and in solution, and distorts further in the vapour until the angle between the phenyl and ethylene groups is about 30°. Approximate constants for the torsional coordinates have been found up to υ = 10 for the Au and υ = 4 for the Bg modes in the solid. The coordinates are quite anharmonic and strongly coupled.

On the treatment of torsional coordinates in vibrational analyses

On the treatment of torsional coordinates in vibrational analyses

The energy levels of the CH3 asymmetric bending vibrations of toluene

The energy levels of the CH3 asymmetric bending vibrations of toluene were calculated by the use of a finite element method for the two dimensional vibrational Schrödinger equation on the basis of a C2v symmetry of the molecule. The totally symmetric CH3 torsion was only considered and some boundary conditions were used for the CH3 asymmetric bending vibrations. The splittings of the energy levels were examined in relation to the interaction potential V2 or V6′ with the CH3 asymmetric bending and the CH3 torsional coordinates. The ir spectrum was observed in the region of those vibrations at room temperature and the Raman experiments at about −140 °C. The observed bands were assigned by comparing them with the calculated levels.

Vibrational Spectra of Dimethylaminosulfonyl Chloride and Its C-Deuterated Derivative

Abstract The infrared and Raman spectra of dimethylaminosulfonyl chloride and its C-deuterated derivative have been recorded in the liquid state. The fundamental frequencies have been assigned by referring to the band intensities, Raman depolarization ratios and isotopic frequency shifts. A normal coordinate analysis based on a planar Cs molecular model has been carried out by using a simple Urey-Bradley force field for stretching and bending coordinates and a valence force field for torsional coordinates. The calculated frequencies based on a refined set of force constants agree well with the observed ones.

Vibrational Spectra of Hydantoin and Its C- and N,N′-Deuterated Compounds

Abstract Infrared and Raman spectra of hydantoin and its C- and N,N′-deuterated derivatives in the solid state have been recorded. The fundamental frequencies were assigned by referring to isotopic frequency shifts and vibrational spectra of related compounds. Normal coordinate analysis was carried out by using a planar Cs molecular model. A simple Urey-Bradley force field was used for the stretching and the bending coordinates and a valence force field for the out-of-plane deformation and the torsional coordinates. The force constants were refined by the least squares method to reproduce the observed frequencies.

Torsional internal coordinates in normal coordinate calculations

Expressions for the s vectors of atoms whose motions constitute a torsional internal coordinate are derived by different methods and the relationships between the various forms appearing in the literature are demonstrated. The expressions for the simple case of a four-atom chain are extended to the general case, as exemplified by the alkanes. Certain errors and ambiguities in the treatment of torsional coordinates are noted. Torsional force constants for ethane, propane, isobutane, and neopentane are presented, being obtained by use of the prescribed methods in normal coordinate calculations.

Vibrational Spectra of Ethyleneurea and Its C,C′- and N,N′-Deuterated Derivatives

Abstract Infrared and Raman spectra of ethyleneurea and its C,C′- and N,N′-deuterated compounds have been measured. The fundamental frequencies have been assigned by referring to isotopic frequency shifts and Raman depolarization ratios. A normal coordinate analysis has been carried out for the infrared active vibrations of a planar C2V molecular model. A Urey-Bradley potential function supplemented by valence type constants for the outof-plane deformation and the torsional coordinates has been used. The calculated frequencies based on a refined set of force constants agree well with the observed.

Application of Newton-Raphson optimization techniques in molecular mechanics calculations

Applications of the Newton-Raphson optimization technique to molecular mechanics calculations are discussed. The theory for applying this method is developed in terms of the spectroscopic Wilson S vectors for stretching, bending and torsional internal coordinates. An exact method for calculating the geometries of transition states for interconversion processes is shown to follow directly from the use of Newton-Raphson optimization. Also, a precise method is developed for calculating the detailed minimum energy pathway for interconversions. A computer program EMIN is described, and applications of this program to geometry optimization, normal coordinate analysis, thermodynamic calculations and synthesis of electron diffraction radial distribution curves are illustrated using the molecule cyclohexane.

Molecular vibrations of complexes with trigonal ligands. Part V. Symmetry coordinates for tetrahedral complexes

Ligands of C 3V symmetry are assumed to be a part of a T d complex. Suitable combinations of C 3v ( a 2 + e) symmetry coordinates, which fit into the T d model, are studied. The results constitute a useful supplement to the C 3V ( a 1 + e) type coordinates studied previously. Torsional coordinates in the Ni(PF 3) 4 type model are treated in particular.

Vibrational spectra and torsional barriers for multitop molecules: Trimethylarsine, trimethylarsine oxide and trimethylarsine sulfide

Raman spectra are presented for liquid (CH 3) 3As and sublimed films of (CH 3) 3As, (CH 3) 3AsO and (CH 3) 3AsS. Far i.r. spectra are also shown for (CH 3) 3As and (CD 3) 3As and vibrational assignments are offered for all compounds. From spectra of the low temperature films, and by means of isotopic substitution, the A 2 and E torsional frequencies have been identified for most compounds. Potential barrier parameters are calculated for several common models and it is found that an analysis which includes mixing between the E torsion and skeletal bending coordinates is desirable if accurate barriers (better than ∼10%) are sought. Methyl top—top interaction terms are even more sensitive to the potential model used. Barrier values of 820, 1130 and 920 cm −1 are obtained for (CH 3) 3As, (CH 3) 3AsO and (CH 3) 3AsS respectively while the corresponding top—top coupling terms are −91 and −206 cm −1 for (CH 3) 3As and (CH 3) 3AsO. These values are summarized with results for other C 3ν, multi-top molecules and all are discussed in terms of non-bonded interactions between methyl hydrogens and the other atoms in the molecules.

Raman spectra and torsional barriers for multitop molecules: trimethylphosphine, trimethylphosphine oxide, trimethylphosphine sulfide and trimethylphosphine selenide

Raman spectra are presented for liquid (CH 3) 3P, single crystal (CH 3) 3PS and sublimed films of (CH 3) 3P, (CH 3) 3PO, (CH 3) 3PS and (CH 3) 3PSe. Vibrational assignments are offered for all compounds and, by means of low temperature spectroscopy and isotopic substitution, both the A 2 and E torsional frequencies are identified. Tests of several common models used to deduce potential barrier parameters are made, and it is found that inclusion of some mixing between the torsional and skeletal bending coordinates can change the barrier values by as much as 10%. Methyl—methyl interaction terms are even more sensitive to the potential model used. Barrier values of 1100, 1460, 1280 and 1160 cm −1 are obtained for (CH 3) 3P, (CH 3) 3PO, (CH 3) 3PS and (CH 3) 3PSe respectively while the corresponding top—top coupling terms are −92, −213, −67 and −57 cm −1. The magnitudes and signs of these potential parameters are discussed in terms of nonbonded interactions between methyl hydrogens and the other atoms in the molecules.

Static and dynamical potential surface distortions in aromatic aldehyde 3A″ (nπ*) states

Two quanta of the aldehyde H-wag vibrational mode are observed with relatively constant activity in the vibrational structure of 3A″ (nπ*) → 1A′ phosphorescence spectra of benzaldehyde, deuterated benzaldehydes, pyridine aldehydes, p-methylbenzaldehyde, p-fluorobenzaldehyde, and p-chlorobenzaldehyde at 4.2°K in a methylcyclohexane polycrystalline environment. The fundamental is either missing or very weak. Contrasted to the aldehyde H-wag mode, higher quanta of the CHO torsional mode are observed in the phosphorescence of the same molecules with variable intensity and progression length. These results are interpreted in terms of a static (i.e., valence) distortion of the 3nπ potential surface along the aldehyde H-wagging coordinate, and pseudo-Jahn-Teller distortion along the CHO torsional coordinate. The valence distortion is analogous to a distortion found for the 3nπ* state in propynal and its origin probably lies in excess electron density at the carbonyl carbon in the excited state. The dynamical Jahn-Teller distortion is ascribed to vibronic interaction between 3A″ (nπ) and the nearest 3A′(nπ*) states.

S vectors for torsional coordinates in polyatomic molecules

S vectors for torsional coordinates in polyatomic molecules

The microwave spectrum of 1-fluorobicyclo[2.2.2] octane: An interal motion with large amplitude

Eleven rotational transitions of the 1-fluorobicyclo[2.2.2]octane were observed. The spectrum consists of very rich satellites, which are assigned to the excited states of the skeletal torsion. There are two strong lines of nearly equal intensity, and the progression, which is regular in the high-frequency side of the main lines, becomes suddenly irregular near the ground-state line. These features of the spectrum are indicative of double-minimum potential for the torsion, and in fact the vibration-rotation constants α v are well accounted for by assuming the potential function of the form, V(φ) = −V 2φ 2 + V 4φ 4 + V 6φ 6 , where φ denotes the torsional coordinate. It is, however, found that additional information is necessary to specify the torsional coordinate uniquely, and the final results are obtained only after the torsional energy levels (or level separations) are measured quantitatively, by the measurement of relative intensities in the present case. The three potential constants obtained, V 2 = 1477 cm −1 (4.2 2 kcal/mole), V 4 = 6243 cm −1 (17. 8 kcal/mole), and V 6 = 22 337 cm −1 (64 kcal/mole), are therefore not very accurate, but the potential barrier V 0 between the two minima and the equilibrium angle φ 0 are determined to be 191 ± 52 cal/mole and 16.4 ± 2.6°, respectively. The spectra of the 13C species suggest that the bicyclo[2.2.2]octane ring is deformed on substitution of a fluorine atom at the C 1 position: the C 1C 2 bond length becomes shorter and the FC 1C 2 angle narrower. The spectrum of the 1-chlorobicyclo[2.2.2]octane was reinvestigated, and was analyzed also in terms of the double-minimum potential for the skeletal torsion. The values of V 0 and φ 0 obtained are 134 ± 67 cal/mole and 16.2 ± 4°, respectively. A model, in which the double-minimum potential results from balance of intramolecular forces due to internal rotation and to the strain of the valence angles, is critically examined, and it is found that the potential constants obtained by the present analysis are compatible with this model.

Isotope effect and temperature effect in the 2H N MR spectra of partly deuterated hydrates - theoretical treatment

Recent experimental work has shown that isotope substitution and variation of temperature produce a shift in the quadrupole coupling constant of opposite sign to that which could be predicted on the basis of a previous theory (Bayer theory). The problem is solved by investigating, one by one, all the possible sources of vibrational effects: both the internal field and the interaction with the neighbouring molecules are studied as functions of intramolecular and intermolecular vibrations. It is shown that the expereimental effect can be explained by considering the change in conjugation of the atomic orbitals involved in the hydrogen bond with torsional coordinates.

Spectroscopy of CF3COZ compounds—III

Abstract In an extension of the work of Dodd et al. [J. Chem. Soc. 2783 (1957)], the infrared spectrum of CF3CHO (gas and solid) has been investigated in the region 4000-33 cm−1. The infrared spectrum of CF3CDO was also obtained, and a complete vibrational assignment is suggested which diners in some respects from that of the earlier workers. Of particular interest is the torsional frequency (~55 cm−1 for gas-phase CF3CHO), which implies a barrier to internal rotation of 190–240 cm−1, significantly lower than the barrier obtained in a recent microwave study. The discrepancy may be due to mixing of the torsion and other internal coordinates of the molecule. Barriers for three CF3COZ compounds (Z = H, F, Cl) are compared with those found in the corresponding CH3COZ compounds. The infrared spectrum of the solid shows that no hydrogen bonding takes place and that at least two crystalline forms are present. These facts are consistent with a structure similar to that suggested by schneideb and BERNSTEIN [Trans. Faraday Soc. 52, 13 (1956)] for formaldehyde and acetaldehyde.

Mean Amplitudes of Vibration in Molecules with Internal Rotation. IV. Theory with Application to Disulfur Dichloride

A normal-coordinate analysis has been performed for disulfur dichloride, and used to calculate the mean amplitudes of vibration. A generalized definition of framework mean amplitudes is proposed, and is applicable to cases where the torsional mode (for internal rotation) is kinematically coupled with other normal modes of vibration. According to this definition the total mean-square amplitude is composed of a sum of the framework mean-square amplitude and the torsional mean-square amplitude; the latter quantity contains all contributions where the torsional coordinate is involved. Numerical results of framework and torsional mean amplitudes are reported for S2Cl2 at various temperatures as functions of the angle of rotation θ. The approximate formula for framework mean-square amplitudes, 〈Δρ2〉frm = (α + β cosθ + γ cos2θ) / ρ2, has been subjected to detailed studies. The α, β, and γ coefficients were evaluated in terms of certain mean-square amplitude quantities, and the following statement was deduced from the properties of their classical limits at high temperatures: α(θ, T), β(θ, T), and γ(θ, T) approach θ-independent values when T → ∞. Furthermore, it is explained why the above formula with constant coefficients may give a very good approximation even at low temperatures when the conditions of classical limits are not fulfilled. This feature was actually found for S2Cl2 even at absolute zero.

Erratum: Torsional Coordinates in Vibrational Anharmonicity; Application to Ethylene

Formulas for the first through third derivatives of torsional coordinates with respect to difference Cartesian coordinates are given. These formulas may also be used for out‐of‐plane bending coordinates. A sample calculation of an anharmonic potential function involving these coordinates has been made for ethylene and ethylene‐d4. The procedure of anharmonicity calculation for polyatomic molecules is formulated by the use of matrix direct product notation and is discussed.