An ab initio study of the p,π interaction: III. Interaction of an ether oxygen atom with a double bond

RHF/6-311G(d) calculations were performed for the H₂C=CHOCH₃ and H₂C=CClOCH₃ molecules with full geometry optimization and at varied angles of rotation of the methoxy group about the C-O bond, with all the other geometric parameters optimized. The first molecule has one energy minimum and one transition state, and the second molecule, two minima. Changes in the populations of the p _y orbitals of the olefinic carbon and oxygen atoms (orbitals whose symmetry axes are perpendicular to the molecular plane) and in the fractional charges on these carbon atoms, occurring upon rotation of the methoxy groups about the C-O bonds, cannot be attributed to changes in the extent of the p,π conjugation between the lone electron pairs of the oxygen atoms and π electrons of the C=C bonds.     

An ab initio study of the p,π interaction: IV. Interaction of an ether oxygen atom with a carbonyl group

RHF/6-311G(d) calculations were performed for the H₃COCOH molecule with full geometry optimization and at varied angles of rotation of the methoxy group about the C-O bond, with all the other geometric parameters optimized. The molecule can exist in two stable conformations with the dihedral angle O¹C¹O²C² of 0.00° and 179.99°. The influence of the rotation angle on the population of the p _y orbital of the carbonyl oxygen atom in compounds with different types of the adjacent bond is essentially similar. The results obtained are inconsistent with the concept of the p,π conjugation involving the p _y orbitals of the planar molecular fragment (orbitals whose symmetry axes are perpendicular to this fragment).     

Molecular structure of acetyldeyiethylphosphine,MeC(O)PMe2: II. CNDO/2 calculations

The sp, spd and spd' approximations of the CNDO/2 method have been applied to energy calculations for some models of the acetyldimethylphosphine molecule generated during treatment of the electron diffraction data. The results obtained for trial configurations with different angles of rotation of the acetyl group about the PC _ac bond predict two symmetric energy minima separated by a rather low barrier. This is in agreement with the electron diffraction data which are compatible with the suggestion of large amplitude torsional vibrations of the acetyl group. Energy calculations have also been performed for the final electron diffraction models. The calculations, however, fail to remove ambiguity from the question of a preferred model of the acetyldimethylphosphine molecule.     

The structures of dicyclopentadienylsilenes and related compounds

The most stable form, according to MNDO calculations, of the silene (C₅H₅)₂Si is the bis-monohapto isomer, in which the angle (CSiC) is 105.4°, and the conformation is such that the dihedral angles δ (HCSiC) are zero. The bis-pentahapto isomer is of comparable energy, and has minimum energy for a structure of D_5d symmetry: this isomer does not represent a genuine energy minimum. Entirely similar conclusions result from calculations on the isoelectronic (C₅H₅)₂P⁺, but for (C₅H₅)₂Al^?, although the lowest energy form is again (η⁵-C₅H₅)₂Al^? , the (η⁵-C₅H₅)₂Al^? isomer has only C_2v symmetry with angle (XAlX) 151.5°. In the silene derivatives (η¹-C₅H₅)SiCY₂, the unique SiC interaction is a genuine SiC double bond and the molecular skeleton C₂SiCY₂ is planar: however in the isomeric species (η⁵-C₅H₅)₂SiCY₂, which do not represent genuine energy minima, the unique SiC interaction is a long, highly polar bond in a twisted X₂SiCY₂ skeleton in which the X₂SiC and SiCY₂ planes are perpendicular.     

Ab initio molecular orbital calculations on H3AlOH2, (H2AlOH)2, and some related species

Ab initio molecular orbital calculations have been carried out on H₃AlOH₂, (H₂AlOH)₂, and some related species, and the charge distribution and bonding are discussed on the basis of population analyses. It is found that the equilibrium conformation around the O atom in H₃AlOH and (H₂AlOH)₂ is intermediate between trigonal and tetrahedral. The energy minima are, however, very shallow. In H₃AlOH₂ the angle between the Al-O bond and the H₂O plane is 27°, in (H₂AlOH)₂ the angle between the two O-H bonds and the Al₂O₂ ring plane is 25°. The energy of a planar conformation of H₃AlOH₂ is 0.19 kcal mol^-1, the energy of a planar conformation of (H₂AlOH)₂ 0.35 kcal mol^-1 above the equilibrium conformation. There is no indication for the formation of dative pπ-dπ bonds between O and Al in the two molecules. It is suggested that the conformation adopted by analogous alkyl derivatives, R₃AlOR'₂ and (R₂AlOR')_n is determined by intramolecular van der Waals repulsion.     

Langsame Inversion am pyramidal gebundenen Stickstoff: Konfiguration und Konformation beim Strukturtyp der N,N-Dialkoxy-alkylamine aus der Sicht eines semiempirischen MO-Modells

Nitrogen inversion and rotation around the N-O single bond in N, N-dialkoxyalkylamine systems are discussed in terms of a semi-empirical MO method which is essentially based on the concepts discussed by Mulliken in connection with the “magic formula”. By taking a simplified structural model and adjusting one empirical parameter, a satisfying agreement with experimental results is obtained. The results allow a chemically transparent interpretation and confirm, to a more quantitative extent, the previously discussed concepts [1]. The (sp^x → p) promotion of the nitrogen lone pair strongly inhibits the inversion process and dominates the simultanous lowering of the σ-bond energies due to (i) the gain of s-character in the σ-involved nitrogen hybrid-AO's and (ii) the increased σ-bond overlaps. This dominance is considerably enhanced when electronegative ligands are attached to nitrogen. The total repulsion energy turns out to favour strongly the planar transition state and is essentially determined by the repulsions between the lone pair and the σ-bonds at nitrogen. Factorization into several repulsive contributions reveals that among these only one inhibits the inversion process, namely the repulsions between the nitrogen lone pair and the bonded and non-bonded electron pairs on the ligands. For the process of rotation around the N-O single bond a potential curve is obtained with two energy minima. The repulsion energy analysis shows that the shape of the potential curve is governed by the repulsions between the lone pairs on oxygen and nitrogen as well as the formally more or less “lone pair-like” σ_NC-bond. This situation is compared to the more general one in which essentially two lone pairs or formally more or less “lone pair-like” σ-bonds, on each of two adjacent centers, repel each other by conjugative destabilization; a situation which is realized for instance in molecules that show the anomeric effect.     

Site epimerization in ansa-zirconocene polymerization catalysts

Metallocene alkyl cations for polymerization of olefins possess two active sites involved in migratory insertion. Site epimerization, with an inversion at the metal atom, is considered to be one of the major causes for break-down of the alternating propagation model, resulting in stereoerrors whenever the two catalytic sites have substantially different enantioface selectivities. Density functional theory has been used to determine the intrinsic reaction coordinate that connects the optimized minima and transition states of inversion in the parent ansa-zirconocene [{H₂C(Cp)₂}Zr-Pr]⁺ (Pr = n-propyl). These calculations yield a three-step reaction path for site epimerization. Starting from the pyramidal β-agostic complex, an activated rotation around the Zr-Pr bond first produces an α-agostic conformation. Continued rotation leads to an equivalent second α-agostic intermediate and then finally to the inverted β-agostic complex. The second step is rate-determining and proceeds through a planar three-coordinate transition state. In the case of [{H₂C(Cp)₂}Zr-ⁱBu]⁺ (ⁱBu = iso-butyl), the situation is more complicated, because there are several interconvertible α-, β- and γ-agostic intermediates, but the rate-limiting step is again an inversion process connecting two different α-agostic conformers with the alkyl group on opposite enantiosides. For both ansa-zirconocene catalysts, the computed free-energy barriers for epimerization are around 11-12 kcal/mol and almost independent of temperature, while those for insertion increase with temperature due to the entropic cost of association. According to the computational results for the isolated catalysts, insertion remains favored over epimerization for the experimentally relevant temperature range in the n-propyl case, whereas both processes are competitive in the iso-butyl case. Inclusion of bulk solvent effects by a continuum solvation model does not affect the results much, while explicit consideration of a coordinating counterion causes larger changes. The present model calculations on the role of site epimerization should thus be most relevant for propene polymerization with non-coordinating counterions.     

A square‐planar hydrated cationic tetrakis(methimazole)gold(III) complex

The cationic pseudo‐square‐planar complex tetrakis(1‐methyl‐2,3‐dihydro‐1H‐imidazole‐2‐thione‐κS)gold(III) trichloride sesquihydrate, [Au(C₄H₆N₂S)₄]Cl₃·1.5H₂O, was isolated as dark‐red crystals from the reaction of chloroauric acid trihydrate (HAuCl₄·3H₂O) with four equivalents of methimazole in methanol. The Au^III atoms reside at the corners of the unit cell on an inversion center and are bound by the S atoms of four methimazole ligands in a planar arrangement, with S—Au—S bond angles of approximately 90°.     

Structural properties of 3-dimensional carbon clusters

Structural properties of 3d carbon clusters were calculated employing recently developed model potential energy functions for carbon. Primarily, spherical shell structures were included in the present investigation. Configurations corresponding to local energy minima were calculated for various shells of an icosahedron containing different number of C atoms. For C₆₀, the two low-lying isomers, the buckminsterfullerene and truncated dodecahedron, were found to be almost isoenergetic. It was also found that fully relaxed structures of C₉₀ and C₁₂₀ have energies very comparable to that of C₆₀. Furthermore, a systematic analysis carried out in this study for carbon clusters with varying dimensionalities, revealed an interesting relationship between the bond lengths and the distribution of bond angles. In all cases, shorter bond distances were found to be associated with larger bond angles.     

Conformations of triplet carbonyl compounds: Formaldehyde, acetaldehyde, propionaldehyde and acetone

A conformational study on the lowest triplet states of formaldehyde, acetaldehyde, propionaldehyde and acetone has been done using a minimal basis set, within the unrestricted Hartree—Fock framework.For the C₃H₆O species, the energy hypersurfaces (E θ₁, θ₂, θ₃) were generated, where energy is a function of the methyl rotations (θ₁, θ₂) and C---O out-of-plane bending for acetone, and a function of methyl rotation (θ₁), C₂H₅---C rotation (θ₂) and CHO out-of-plane deformation (θ₃) for propionaldehyde.The analysis of the hypersurface equations revealed the location and relative energies of the critical points (minima, first and second order saddle points as well as maxima): the barriers to inversion at the carbonyl group were 2.7 kcal mol⁻¹ for acetone and 4.2 kcal mol⁻¹ for propionaldehyde. Partial geometry optimization reduced these barriers to 2.5 and 2.4 kcal mol⁻¹ respectively.For comparison, both the pyramidal minimum and planar saddle point for the inversion of triplet formaldehyde and acetaldehyde were totally optimized; the resultant barriers were 2.0 kcal mol⁻¹ and 2.3 kcal mol⁻¹, respectively. The barrier to rotation about the bond to the α-carbon was 1.1 kcal mol⁻¹ for pyramidal acetone, 1.0 for acetaldehyde and ranged from 0.8 to 1.8 kcal mol⁻¹ for the various propionaldehyde conformers.     

Orthorhombic polymorphs of two trans‐4‐aminoazoxybenzenes

The two isomeric compounds 4‐amino‐ONN‐azoxy­benzene [or 1‐(4‐amino­phenyl)‐2‐phenyl­diazene 2‐oxide], i.e. the α isomer, and 4‐amino‐NNO‐azoxy­benzene [or 2‐(4‐amino­phenyl)‐1‐phenyl­diazene 2‐oxide], i.e. the β isomer, both C₁₂H₁₁N₃O, crystallized from a polar solvent in orthorhombic space groups, and their crystal and molecular structures have been determined using X‐ray diffraction. There are no significant differences in the bond lengths and valence angles in the two isomers, in comparison with their monoclinic polymorphs. However, the conformations of the mol­ecules are different due to rotation along the Ar—N bonds. In the α isomer, the benzene rings are twisted by 31.5 (2) and 14.4 (2)° towards the plane of the azoxy group; the torsion angles along the Ar—N bond in the β isomer are 24.3 (3) and 23.5 (3)°. Quantum‐mechanical calculations indicate that planar conformations are energetically favourable for both isomers. The N—H?O hydrogen bonds observed in both networks may be responsible for the deformation of these flexible mol­ecules.     

Rapidly calculated DFT relaxed iso-potential ϕ/ψ maps: β-cellobiose

New cellobiose ϕ_H/ψ_H maps are generated using a mixed basis set DFTr method, found to achieve a high level of confidence while reducing computer resources dramatically. Relaxed iso-potential maps are created for different conformational states of cellobiose, showing how glycosidic bond dihedral angles vary as different sets of hydroxymethyl rotamers and hydroxyl directions are examined. These maps are generated, fixing the dihedral ϕ_H and ψ_H values at ten degree intervals and energy optimizing the remaining geometry using the B3LYP/6-31+G* functional for all atoms except carbon atoms, where the functional B3LYP was used with the mixed basis set, 4-31G. Mapping results are compared between in vacuo structures using the mixed basis set, in vacuo using the full basis set, and those in which the implicit solvent method, COSMO, is included with the mixed basis set. Results show significant changes in position of energy minima with variation in hydroxyl rotamers and with application of solvent. Unique to this study is the mapping of the hydration energy at each ϕ_H/ψ_H point on the map using the energy derived at each point by applying COSMO. Using hydration gradients as a guide one observes directional solvent driven changes in the minimum energy positions. Interesting internal coordinate variances are described.     

Aluminum and gallium clusters — a comparative study using simulated annealing

Density functional calculations with simulated annealing have been performed for clusters of aluminum and gallium with up to 10 atoms. There are many local minima in the energy surfaces and numerous stable isomers. As cluster size increases, there is a transition from planar to non-planar structures atn=5. All structures show regular patterns of bond and dihedral angles similar those found in the bulk materials. The bonds in gallium clusters are consistentlyshorter than those in clusters of the lighter element aluminum.     

Bispidine Platform as a Tool for Studying Amide Configuration Stability

In this work, the solution conformations of seventeen 3,7-diacyl bispidines were studied by means of NMR spectroscopy including VT NMR experiments. The acyl groups included alkyl, alkenyl, aryl, hetaryl, and ferrocene moieties. The presence of syn/anti-isomers and their ratios were estimated, and some reasons explaining experimental facts were formulated. In particular, all aliphatic and heterocyclic units in the acylic R(CO) fragments led to an increased content of the syn-form in DMSO-d₆ solutions. In contrast, only the anti-form was detected in DMSO-d₆ and CDCl₃ in the case when R = Ph, ferrocenyl, (R)-myrtenyl. In the case of a chiral compound derived from the natural terpene myrtene, a new dynamic process was found in addition to the expected inversion around the amide N-C(O) bond. Here, rotation around the CO-C=C bond in the acylic R fragment was detected, and its energy was estimated. For this compound, ΔG for amide N-C(O) inversion was found to be equal to 15.0 ± 0.2 kcal/mol, and for the rotation around the N(CO)–C^2′ bond, it was equal to 15.6 ± 0.3 kcal/mol. NMR analysis of the chiral bispidine-based bis-amide was conducted for the first time. Two X-ray structures are reported. For the first time, the unique syn-form was found in the crystal of an acyclic bispidine-based bis-amide. Quantum chemical calculations revealed the unexpected mechanism for amide bond inversion. It was found that the reaction does not proceed as direct N-C(O) bond inversion in the double-chair (CC) conformation but rather requires the conformational transformation into the chair–boat (CB) form first. The amide bond inversion in the latter requires less energy than in the CC form.     

Study of internal rotation of radical center in <Emphasis Type="Italic">n</Emphasis>-alkyl radicals

A quantum-mechanical study of internal rotation around C-C^· bond in n-alkyl radicals from C₂H₅ to C₇H₁₅ was carried out using B3LYP/6-311++G(3df, 3pd) approach. The values of barriers and local minima were found. Analysis of the distribution of electron density was carried out. By application of the methods of mathematical statistics different types of representation of the potential functions of internal rotation were analyzed and the optimal approximation was revealed. Contributions to the thermodynamic properties of the considered radicals were calculated. The generalized function of internal rotation was suggested for the radicals of the type C _n H_2n+1, n > 4.     

Phenomenology and scaling of electron scattering cross sections from “almost spherical” molecules over a wide energy range

Total cross sections for electron scattering on “quasi spherical” (CH₄, SiH₄, GeH₄) molecules have been analyzed phenomenologically over a wide energy range. Regions, at low and high energies can be usefully represented by simple analytical formulae. Regularities associated with characteristic points such as the Ramsauer minima have been exposed. Comparison with other simple hydrides (NH₃, H₂O, H₂S) allows the demonstration of a possible correlation between the maximum value of the total cross section and the bond length. Some points of contact with first-principles theory are noted and in particular the energy at which the maximum cross section occurs, is related to the occurrence of a partial wave resonance. In the absence of complete data for GeH₄, prediction of characteristic points in the low energy cross section proves possible via the phenomenological analysis. Similarly, in the high energy regime, predictions of the cross section for SnH₄ is made from data on the lighter molecules of the series, using non-relativistic Thomas-Fermi self consistent field scaling.     

Etude de la structure de carbanions en α du soufre

Carbanions α to sulfoxides and sulfones C₆H₅S(O)nCH₂M (n  1, 2; M  Li or K) have been studied by infrared and Raman spectroscopy. A strong increase of the force constant of the SCH₂M bond, and a similar decrease of that of the SO bond(s) are observed. This implies that the negative charge is delocalized over the carbon and oxygen atoms. ¹H NMR shows that carbanions α to sulfoxides are configurationally stable at low temperature. The interconversion energy depends on the polarizing ability of the counter-ion (Li⁺: ΔG

13.6 kcal mol^-1; K⁺: ΔG

10.7 kcal mol^-1). The coupling constant of the methylenic hydrogens (J_AB 2 Hz) confirms the nearly planar configuration of the anionic carbon in the α metallated sulfoxides.     

A density functional study of the structure and potential energy surface of dibenzenechromium and its alkylated derivatives

Density functional calculations were performed with the nonempirically constructed PBE functional and TZ2p basis set to study the potential energy surfaces of several dibenzenechromium derivatives containing methy1 and tert-buty1 groups in aromatic ligands. The method was shown to correctly describe the structure and intramolecular dynamics of bis-arenechromium complexes. It allows barriers to rotation about the metal-ligand bond to be calculated and detailed information to be obtained about the shape of the potential curves that correspond to this rotation. The potential energy surfaces of polymethylated dibenzenechromium derivatives contained several minima close in energy; these minima largely corresponded to eclipsed conformers. The potential curves for rotation about the metal-ligand bond in dibenzenechromium and its methylated derivatives reveal the presence of staggered conformers as transition states. Irrespective of the number of methyl groups present in both ligands, we observed no substantial changes in barrier heights, which were about 1 kcal/mol. Conversely, the introduction of bulky tert-butyl groups destabilized eclipsed conformations. Ensuing steric strain caused substantial out-of-ring-plane displacements of the C_ipso-t-Bu bonds away from the chromium atom, distorted aromatic ring planarity, and substantially increased barriers to rotation, to 8–10 kcal/mol.     

Theoretical design of planar molecules with a nona- and decacoordinate central atom

The maximum coordination number of the central atom in planar molecules generated by now in mole-cular beams was 8. We made use of the chemical bond model developed for planar boron clusters to check the possibility of existence of planar molecules with the coordination numbers 9 and 10. The objects of or study were the AlB₉ and AlB ₁₀ ⁺ clusters which have local minima corresponding to highly symmetrical D _9h and D _10h structures, respectively. According to our calculations, the highly symmetrical structure of AlB₉ is a global minimum or a low-lying isomer, and, therefore, it holds promise as a new ligand for coordination chemistry. The energy of the highly symmetrical structure of AlB ₁₀ ⁺ with the coordination number 10 is too high, and this structure is hardly synthetically feasible. Thus, 9 is presently the maximum coordination number of an atom in a planar molecule.     

Structural relaxations and energy effects of intramolecular motions inN,N-dimethylnitramine: A theoretical study

The equilibrium geometry of theN,N-dimethylnitramine molecule and changes in the energy and structural parameters due to the internal rotation of the nitro group and the inversion of the N atom in the amino fragment were calculated by the restricted Hartree-Fock (RHF) method and at the second-order Møller-Plesset (MP2) level of perturbation theory with inclusion of electron correlation using the 6–31 G^* and 6–31 G^** basis sets. The one-dimensional potential functions of these motions calculated at the RHF/6–31 G^* level were approximated by a truncated Fourier and power series, respectively. The frequencies of torsional and inversion transitions were determined by solving direct vibrational problems for a non-rigid model,i.e., taking into account the molecular geometry relaxation. The equilibrium conformation of the molecular skeleton ofN,N-dimethylnitramine is nonplanar. Transition states of the internal rotation of the nitro group and inversion of the amine N atom are characterized by pronounced concerted changes in its bond angles and the length of the N?N bond. In the MP2/6–31 G^* approximation, the height of the barrier to internal rotation calculated taking into account the difference in the zero-point vibrational energies is equal to 9.7 kcal mol^?1. Inversion in the amino fragment is accompanied by a relatively small energy change at the barrier height of ?1.0 kcal mol^?1 calculated in the same approximation.