Electronic states and barriers to internal rotation in silaallenes

The electronic states and barriers to internal rotation in allene ( 1a ), 1-silaallene ( 2a ), and 2-silaallene ( 3a ) are investigated computationally using ab-initio molecular orbital methods. Planar geometries with two-, three-, and four-π-electron configurations have been considered as possible transition states ( 1b–3d ). Structures have been optimized at the Hartree–Fock level with a small split valence basis set (3-21G) and higher level calculations with basis sets of split valence (6-31G ) and split valence plus polarization function (6-31G *) quality include correlation energy estimates from Møller–Plesset second-and third-order perturbation theory. The electronic barrier to internal rotation in allene is estimated near 53 kcal/mol whereas the corresponding barriers in 1-silaallene and 2-silaallene are considerably smaller, ca. 35 and 20 kcal/mol, respectively. The transition states are predicted to possess bent geometries in all three molecules with open-shell singlet, three-π-electron configurations in 1 and 2 ( 1c, 2c ) but a closed-shell singlet, two-π-electron configuration in 3 (3d) .     

Quantum mechanical calculations on barriers to internal rotation

SCF LCAO MO calculations are reported for the borazane molecule BH₃NH₃, for different values of the dihedral angle (0°, 20°, 40°, 60°). The lower energy was found equal to -82.59651 a.u. for the staggered form. The theoretical barrier height, 0.00524 a.u.=3.29 kcal/mole, is very close to the one, 0.00577 a.u., computed by Clementi for the ethane molecule. A study of the electronic density maps seems to indicate that some care should be exercised in the use of the population analysis. According to the criterion of Bader andal., the bond density map seems characteristic of ionic binding.

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Zusammenfassung Die Ergebnisse von SCF LCAO MO Rechnungen für Borazan werden mitgeteilt, und zwar für verschiedene Verdrillungswinkel. Die tiefste Energie zeigt die Konformation mit den auf Lücke stehenden H-Atomen. Die Energieschwelle für die innere Rotation ist mit 3.29 Kcal/mol fast genau so groß wie die (von Clementi berechnete) für Äthan.Das Bindungsdichte-Diagramm deutet bei Anwendung des Baderschen Kriteriums auf eine ionische Bindung hin. Eine Untersuchung der Elektronendichte legt ferner die Vermutung nahe, daß die Resultate einer Populationsanalyse mit Vorsicht betrachtet werden müssen.

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Résumé La molécule de borazane a été etudiée par la méthode SCF LCAO MO pour différentes valeurs de l'angle dièdre (0°, 20°, 40°, 60°). L'énergie la plus basse, égale à -82.59651 u.a., a été obtenue pour la conformation decalée. La barrière de rotation théorique, égale à 0.00524 u.a. = 3.29 kcal/mole, est très proche de la valeur 0.00577 u.a. obtenue par Clementi pour la molécule d'éthane. L'étude simultanée de l'analyse de population et des contours de densité isoélectronique semble indiquer qu'une certaine prudence s'impose dans l'interprétation des populations. La liaison B-N apparait comme ionique si l'on on utilise les critères de Baderet al.

     

Quantum mechanical calculations on barriers to internal rotation

The barrier to internal rotation in hydrazine has been studied by the non empirical SCF-LCAO method, in the gaussian approximation. Calculations have been performed for values 0°, 60°, 120°, 180° and 94° (equilibrium conformation) of the dihedral angle, with all other bond angles and bond lengths fixed. The gaussian basis set used consisted of 9s + 3p for nitrogen and 3s for hydrogen. The calculated total molecular energy for the equilibrium conformation, –111.030 a.u., is 0.865 a.u. higher than the experimental value. The theoretical dihedral angle 94° is in good agreement with experimental indications of 90–95°. The computed rotation barriers are 11.5 kcal/mole for the cis position and 4.7 kcal/mole for the trans.

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Zusammenfassung Die Rotationsbarriere von Hydrazin wurde mit Gaußfunktionen nach einer nicht-empirischen SCF-LCAO-Methode studiert. Rechnungen wurden für die Werte 0°, 60°, 120°, 180°, 94° (Gleichgewichtslage) des Diederwinkels durchgeführt, wobei alle übrigen Bindungswinkel und -längen festgehalten wurden. Der Basissatz von Gaußfunktionen bestand aus 9s- und 3p Funktionen für Stickstoff und 3s-Funktionen für Wasserstoff. Die berechnete Gesamtenergie der Gleichgewichtskonformation, –111,030 at. E. liegt um 0,865 at. E. höher als der experimentelle Wert. Der theoretische Diederwinkel von 94° stimmt gut mit den experimentellen Daten von 90–95° überein. Die berechneten Rotationsbarrieren sind 11,5 kcal/mol für die cis- und 4,7 kcal/mol für die trans-Lage.

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Résumé La barrière de rotation interne de l'hydrazine a été étudiée par la méthode LCAO-SCF dans l'approximation des orbitales gaussiennes. Les calculs ont été effectués pour des valeurs de l'angle dièdre de 0°, 60°, 120°, 180° et 94° (valeur correspondant à l'équilibre), tout en gardant constants les autres angles et les longueurs des liaisons. On obtient pour la position d'équilibre une énergie moléculaire totale de –111.030 u.a., l'écart avec l'énergie expérimentale étant de 0.865 u.a. La valeur obtenue pour l'angle dièdre, 94°, est en bon accord avec les indications expérimentales de 90–95°. Les barrières de rotation théoriques sont de 11.5 kcal/mole pour la position cis et de 4.7 kcal/mole pour la position trans.

     

Far-infrared spectra and barriers to internal rotation of ethyl nitrate

The far-infrared spectra of gaseous and solid ethyl nitrate, CH₃CH₂ONO₂, have been recorded from 500 to 50 cm⁻¹. The fundamental asymmetric torsion of the trans conformer which has a heavy atom plane has been observed at 112.50 cm⁻¹ with two excited states failing to lower frequencies, and the corresponding fundamental torsion of the gauche conformer was observed at 109.62 cm⁻¹ with two excited states also falling to lower frequencies. The results of a variable temperature Raman study indicate that the trans conformer is more stable than the gauche conformer by 328 ± 96 cm⁻¹ (938 ± 275 cal mol⁻¹). An asymmetric potential function governing the internal rotation about the CH₂O bond is reported which gives a trans to gauche barrier of 894 ± 15 cm⁻¹ (2.56 ± 0.04 kcal mol⁻¹) and a gauche to gauche barrier of 3063 ± 68 cm⁻¹ (8.76 ± 0.20 kcal mol⁻¹) with the trans conformer more stable by 220 ± 148 cm⁻¹ (0.63 ± 0.42 kcal mol⁻¹). Transitions arising from the symmetric CH₃ and NO₂ torsions are observed for both conformers, from which the threefold and twofold periodic barriers to internal rotation have been calculated. For the trans conformer the values are 1002 cm⁻¹ (2.87 kcal mol⁻¹) and 2355 ± 145 cm⁻¹ (6.73 ± 0.42 kcal mol⁻¹) and for the gauche conformer they are 981 cm⁻¹ (2.81 kcal mol⁻¹) and 2736 ± 632 cm⁻¹ (7.82 ± 1.81 kcal mol⁻¹) for the CH₃ and NO₂ rotors, respectively. These results are compared to the corresponding quantities for some similar molecules.     

Theoretical study of the barriers to internal rotation in nitrous acid

Nitrous acid, HONO, has been studied for three geometries by the ab initio LCAO SCF MO method with a basis of accurate gaussian atomic orbitals. The trans geometry is correctly predicted to be most stable, lying about 2 kcal/mole lower than the cis form, and 9 kcal/mole lower than the 90° form (experimental estimates being 0.4 and 11.6 kcal/mole, respectively). Population analysis, dipole moment components, and properties related to nuclear-nuclear and nuclear-electron potentials all show a partial breaking of the hydroxyl oxygen-nitrogen bond at 90° compared to cis and trans, as well as the effects of electronic rearrangement for nuclear screening in the high nuclear repulsion cis form. The cis to 90° barrier is dominated by the attractive components of the total energy, while the trans to 90° one is dominated by repulsive components, in agreement with our analysis and an earlier prediction by Allen.     

Phospha-Michael additions to activated internal alkenes: steric and electronic effects

The addition of P(O)-H bonds to internal alkenes has been accomplished under solvent-free conditions without the addition of a catalyst or radical initiator. Using a prototypical secondary phosphine oxide, a range of substrates including cinnamates, crotonates, coumarins, sulfones, and chalcones were successfully functionalized. Highly activated acceptors such as isopropylidenemalononitrile and ethyl 2-cyano-3-methyl-2-butenoate underwent the phospha-Michael reaction upon simple trituration of the reagents at room temperature, whereas less activated substrates such as ethyl cinnamate and methyl crotonate required heating (>150 °C) in a microwave reactor to achieve significant consumption of the starting alkenes. For the latter alkenes, a competing reaction involving disproportionation of the ditolylphosphine oxide into ditolylphosphinic acid and ditolylphosphine was observed at the high temperatures needed to promote the addition reaction.     

The internal rotation potential functions of the methacryloyl chloride molecule in the ground and excited electronic states

The systems of torsional vibration levels of the trans and cis methacryloyl chloride isomers in the ground (S ₀) and excited (S ₁) electronic states obtained by analyzing the vibrational structure of the gas-phase UV spectrum were used to reproduce the internal rotation potential functions of the molecule in both electronic states. The kinematic F factor in the S ₀ and S ₁ electronic states was calculated taking into account the relaxation of geometric parameters depending on the internal rotation angle. The internal rotation potential function parameters in the S ₀ state are substantially different from the parameters obtained using the torsional levels of the IR Fourier transform spectrum; at the same time, they are substantiated by quantum-mechanical calculations.     

Impact of molecular conformation on barriers to internal methyl rotation: the rotational spectrum of m-methylbenzaldehyde

The ground state spectrum of m-methylbenzaldehyde (m-MBA) was measured with a chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer. The methyl rotor on m-MBA introduces an internal rotation barrier, which leads to splitting of the torsional energy level degeneracy into A and E states. Ab initio calculations predict a low torsional barrier for both the O-cis and O-trans conformers, resulting in a large doublet splitting up to several gigahertz in the frequency spectrum. The rotational constants, distortion terms, and V(3) values for both species have been determined from the ground state rotational spectrum using the BELGI-C(s) fitting program. There are significant differences in the torsional potential for the O-cis and O-trans m-MBA conformers. Molecular orbitals and resonance structures for each conformer are analyzed to understand the difference in torsional barrier height as well as the irregular shape of the O-trans torsional potential.     

Steric and electronic contributions to barriers of internal rotation in 1,8-dibenzoylnaphthalenes

Restricted rotation about the naphthalenylcarbonyl bonds in the title compounds resulted in mixtures of cis and trans rotamers, the equilibrium and the rotational barriers depending on the substituents. For 2,7-dimethyl-1,8-di-(p-toluoyl)-naphthalene (1) ΔH° = 3.66 ± 0.14 kJ mol^?1, ΔS° = 1.67 ± 0.63 J mol^?1 K^?1, ΔH^≠_ct = 55.5 ± 1.3 kJ mol^?1, ΔH^≠_ct = 51.9 ± 1.3 kJ mol^?1, ΔS^≠_ct = ?41.3±4.1 J mol^?1 K^?1 and ΔS^≠_ct = ?42.9±4.1 J mol^?1 K^?1. The rotation about the phenylcarbonyl bond requires ΔH^≠ = ?56.9±4.4 kJ mol^?1 and ΔS^≠ = ?20.5±15.3 J mol^?1 K^?1 for the cis rotamer, and ΔH^≠ = 43.5Δ0.4 kJ mol^?1 and ΔS^≠ =± ?22.4Δ1.3 J mol^?1 K^?1 for the trans rotamer. The role of electronic factors is likely to be virtually the same for both these rotamers but steric interaction between the two phenyl rings occurs in the cis rotamer only. Hence, the difference of the activation enthalpies obtained for the cis and trans rotamers, ΔΔH^?1 = 13.4 kJ mol^?1, provides a basis for the estimation of the role of steric factors in this rotation. For the tetracarboxylic acid 2 and its tetramethyl ester 3 the equilibrium is even more shifted towards the trans form because of enhanced steric and electrostatic interactions between the substituents in the cis form. The barriers for the rotation around the phenylcarbonyl bond and the cis-trans isomerization are lowered; an explanation for this result is presented.     

Effects of substitution on nitrogen on barriers to rotation of amides. 2—Evaluation of the importance of resonance effects

Analogs of N-acetyl- and N-benzoyl-azacyclohex-2-enes having an oxygen atom, a methylene-d₂ group or a carbonyl group in place of the C-4 methylene group have been synthesized. The amide rotational barriers in these compounds have been measured by the total line-shape analysis of variable-temperature ¹H NMR spectra. The free energies of activation for both the N-acetyl and N-benzoyl series decrease in the sequence O?CD₂ > C?O. The barriers for the first two compounds in each series are similar to those of the corresponding saturated analogs, a result which confirms recent reports that the long accepted barrier-decreasing effect of an α-olefinic substituent on nitrogen is counteracted. Evidence is presented that resonance stabilization of the rotational transition state in the unsaturated compounds still obtains. It is suggested that the introduction of an α-olefinic substituent on nitrogen has a negligible effect on the amide rotational barriers in the cases of the oxygen and methylene-d₂ analogs, since any increase in the stabilization of the transition state by resonance is offset by the accompanying decrease in the sp³ character of the nitrogen atom. In cases in which a substituent on the olefinic group can interact directly with the lone pair on nitrogen, for example in the carbonyl analogs, then the resonance stabilization of the transition state is dominant.     

Conformational analysis,barriers to internal rotation and vibrational assignment for dimethylethylamine

The IR (50–3500 cm^?1) and Raman (20–3500 cm^?1) spectra have been recorded for gaseous and solid dimethylethylamine. Additionally, the Raman spectrum of the liquid has been recorded and qualitative depolarization values have been obtained. Due to the fact that three distinct Raman lines disappear on going from the fluid phases to the solid state, it is concluded that the molecule exists as a mixture of the gauche and trans conformers in the fluid phases with the gauche conformer being more stable and the only one present in the spectra of the unannealed solid. From the temperature study of the Raman spectrum of the liquid a rough estimate of 3.9 kcal mol^?1 has been obtained for ΔH. Relying mainly on group frequencies and relative intensities of the IR and Raman lines, a complete vibrational assignment is proposed for the gauche conformer. The potential functions for the three methyl rotors have been obtained, and the barriers to internal rotation for the two CH₃ rotors attached to the nitrogen atom have been calculated to be 3.51 and 3.43 kcal mol^?1, whereas the barrier for the CH₃ rotor of the ethyl group has been calculated to be 3.71 kcal mol^?1. The asymmetric torsional mode for the gauche conformer has been observed in both the IR and Raman spectra of the gas at 105 cm^?1 with at least one hot band at a lower frequency. Since the corresponding mode has not been observed for the trans conformer, it is not possible to obtain the potential function for the asymmetric rotation although estimates on the magnitudes of some of the terms have been made. Significant changes occur in the low-frequency IR and Raman spectra of the solid with repeated annealing; several possible reasons for these changes are discussed and one possible explanation is that a conformational change is taking place in the solid where the trans form is stabilized by crystal packing forces. These results are compared to the corresponding quantities for some similar amines.     

Barriers to the internal rotation and observables of the ground state for hydrogen peroxyde

SCF energy and one electron properties of the H₂O₂ molecule have been calculated by using a basis of 52 STO's. The minimum total energy reached is –150.83188 a.u. By carrying out the calculation for three different geometrical configurations a reasonable agreement with experimental values of the barriers to the internal rotation is obtained.

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Zusammenfassung Die SCF-Energie und die Einelektroneneigenschaften des H₂O₂-Moleküls werden mit einer Basis von 52 Slaterorbitalen berechnet. Als minimale Gesamtenergie werden der Wert von –150,83188 a.E. erreicht. Die Ergebnisse für 3 verschiedene Geometrien liefern eine befriedigende Übereinstimmung mit dem experimentellen Wert der Barriere für die innere Rotation.

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Résumé L'énergie SCF et les propriétés monoélectroniques de la molécule H₂O₂ ont été calculées en utilisant une base de 52 orbitales de Slater. L'énergie minimum totale atteinte est –150.83188 u.a. Un accord raisonnable avec les valeurs expérimentales des barrières de rotation est obtenu en effectuant les calculs pour trois configurations géométriques différentes.

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Note. When this paper was completed, we have received the work of Dunning and Winter. Their main results are quoted in Table 4. The agreement of the result for the trans barrier is very good. As in the case of Ref. [4] and [8] the geometry optimization contributes heavily (75% of the total value) to the result for the trans barrier.     

Theoretical study of the barriers to internal rotation in dimethyl ether,methoxysilane and disiloxane

The barriers to internal rotation have been computed by ab initio methods for CH₃OCH₃, CH₃OSiH₃ and SiH₃OSiH₃. It is shown that minimal basis set results agree fairly well with experimental results for CH₃OCH₃ and to a lesser extent for SiH₃OSiH₃. To predict a correct ordering of the CH₃ and SiH₃ rotation barriers in CH₃OSiH₃, a split valence basis set has to be used. Attention is also paid to the influence of geometry optimization on the barriers to internal rotation.     

Microwave spectra and barriers to internal rotation of z- and e-1-propenyl isocyanide

A synthetic procedure yielding a mixture of Z- and E-1-propenyl isocyanide (CH(3)CH═CHNC) is described. The microwave spectrum of this mixture has been recorded in the 12-100 GHz spectral range, and the spectra of the Z and E isomers have been assigned for the first time. Most transitions of the Z form were split into two components of equal intensity due to tunneling of the methyl group, which allowed the barrier to internal rotation of this group to be determined as 4.0124(12) kJ/mol by fitting 568 transitions with a maximum value of J = 46 using the computer program Xiam. This fit had a root-mean-square deviation as large as 4.325. The same transitions were therefore fitted anew using the more sophisticated program Erham. This fit has a rms deviation marginally better (4.136) than the Xiam fit. No split MW lines were found for E-1-propenyl isocyanide. The absence of splittings is ascribed to a barrier to internal rotation of the methyl group that is significantly higher than the barrier of the Z isomer. It is concluded that the barrier must be larger than 6 kJ/mol for the E form. The experimental work was augmented by quantum chemical calculations at CCSD/cc-pVTZ, B3LYP/cc-pVTZ, and MP2/cc-pVTZ levels of theory. The CCSD method predicts rotational constants of the Z and E forms well. The B3LYP barriers to internal rotation of a series of substituted propenes were calculated and found to be in good agreement with experiments. Calculations of the quartic centrifugal distortion constants of the two 1-propenyl isocyanides by the B3LYP and MP2 methods were less successful.     

Investigation of the barriers to retarded internal rotation in N-acyl-1-methyl-1,2,3,4-tetrahydroisoquinolines

The effect of a number of alkyl substituents attached to the carbon atom of the acyl group on the activation parameters of retarded internal rotation about the C-N bond in N-acyl-1-methyl-1,2,3,4-tetrahydroisoquinolines was studied. Correlation of the free energies of activation G ₂₉₈ with the steric factors (Es) and the ^* substituent constants was examined.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 502–505, April, 1984.     

Infrared and raman spectra,vibrational assignment and barriers to internal rotation for methyldisilylamine

The Raman spectra of gaseous and liquid (SiH₃)₂NCH₃ and (SiH₃)₂NCD₃ have been recorded to within 10 cm^?1 of the exciting line. The IR spectra of (SiH₃)₂NCH₃ and (SiH₃)₂NCD₃ have been recorded from 80 cm^?1 to 3800 cm^?1 in the gaseous state, and from 80 cm^?1 to 450 cm^?1 in the solid state. A vibrational assignment has been made, and from the low-frequency vibrational data, an upper limit of 3.3 kcal mol^?1 was calculated for the barrier to internal rotation of the silyi groups, whereas a barrier of ~450 cal was calculated for internal rotation of the methyl group. It is concluded that there exists a significantly strong d_π—p_π interaction in methyldisilylamine.     

Semiempirical calculations of internal barriers to rotation and ring puckering: II. Amindo/3 study

The MINDO/3 technique is examined for its applicability to rotational barriers and ring puckering of strained-ring compounds. Comparisons are made with MINDO/2' and INDO on the compounds ethane, acetone, isobutylene, 3-oxetanone, cyclobutane, cyclobutanone, methylenecyclobutane, and 1,1-difluorocyclobutane. The MINDO/3 method improperly predicts all ring compounds to energetically favor the planar conformation as does its predecessor. Some improvement in bond lengths and bond angles is observed by MINDO/3 but the rotational barriers are still underestimated.     

Sequence distribution effects on glass transition temperatures of copolymers: an extended Gibbs-DiMarzio equation in view of bond rotation flexibility

In view of bond rotation flexibility and the additivity of stiff energy, a new equation containing mole fractions of sequences and glass transition temperatures (Tg's) of periodic copolymers was proposed. Meanwhile, the effect of stereochemical sequences was also taken into account. Even for the case of all substitutions on primary (C1), second (C2), and third (C3) carbon atoms adjoining to the given bond (triad sequences effect) to be considered, no intractable parameters exist in the new equation if the periodic copolymers of poly[AB], poly[AAB], and poly[BBA] could be acquired. This may facilitate its convenient application in comparison with the Ham equation (Ham, G. E. J. Macromol. Sci. Chem. 1975, A9, 461), which also concerned triad contributions. The new equation was applied to methyl methacrylate-styrene, ethylene-methyl methacrylate, and ethylene-vinyl acetate copolymers, and excellent fittings were obtained. The parameters obtained may predict Tg values of periodic copolymers that have not been acquired as well as provide useful information on the bond rotation flexibility.     

Using redundant internal coordinates to optimize equilibrium geometries and transition states

A redundant internal coordinate system for optimizing molecular geometries is constructed from all bonds, all valence angles between bonded atoms, and all dihedral angles between bonded atoms. Redundancies are removed by using the generalized inverse of the G matrix; constraints can be added by using an appropriate projector. For minimizations, redundant internal coordinates provide substantial improvements in optimization efficiency over Cartesian and nonredundant internal coordinates, especially for flexible and polycyclic systems. Transition structure searches are also improved when redundant coordinates are used and when the initial steps are guided by the quadratic synchronous transit approach. © 1996 by John Wiley & Sons, Inc.