On the dimerization process of nitroso compounds

Summary Many organic C-nitroso compounds R-NO form stable dimers with a covalent NN bond. To gain insight into the dimerization reaction 2 R-NO (R-NO)₂ a theoretical study of the dimerization to atrans-form was performed using HNO as a model compound. Complete geometry optimizations were carried out at the HF, MP2 and QCISD levels using a 6–31G* basis. In the stationary points energies were calculated at the MP4(SDTQ) and QCISD(T) levels. For the equilibrium structure of the monomer and dimers stable RHF solutions were found, whereas for the TS UHF and UMPn calculations were applied. Extensive spin contamination was found in the UHF wavefunction, and projections up tos+4 were invoked. Relative energies were corrected for differences in ZPE. Calculations were made (a) for the least-motion path (C _2h symmetry) and (b) for a path with complete relaxation of all internal coordinates. Along the latter path a TS having virtuallyC _i symmetry was found. Along path (a) an activation energy of around 150 kcal/mol was predicted, in conformity with a symmetry forbidden reaction. On the relaxed path (b) the barrier to dimerization was estimated to be 10.7 kcal/mol at the MP4(SDTQ)//MP2 level, and 10.9 kcal/mol at the QCISD(T)//QCISD level. Unscaled ZPE corrections, calculated at the SCF level, changed these values to 12.7 and 12.9 kcal/mol, respectively. The reaction energy for the dimerization process is predicted to be – 17.2 kcal/mol at the MP4(SDTQ)//MP2 level corrected for ZPE. Calculations at the G1 level gave a corresponding value of – 16.4 kcal/mol. The equilibrium constant for the association to thetrans dimer is estimated to beK _p =259 atm, indicating that the dimer should be an observable species in the gas phase.     

Nontotally symmetric trifurcation of an SN2 reaction pathway

A new type of reaction pathway which involves a nontotally symmetric trifurcation was found and investigated for a typical S_N2‐type reaction, NC^‐ + CH₃X → NC? CH₃ + X^‐ (X = F, Cl). A nontotally symmetric valley‐ridge inflection (VRI) point was located along the C_3v reaction path. For X = F, the minimum energy path (MEP) starting from the transition state (TS) leads to a second‐order saddle point with C_3v symmetry, which connects three product minima of C_s symmetry. For X = Cl, four product minima have been observed, of which three belong to C_s symmetry and one to C_3v symmetry. The branching path from the VRI point to the lower symmetry minima was determined by a linear interpolation technique. The branching mechanism is discussed based on the reaction path curvature and net atomic charges, and the possibility of a nonotally symmetric n‐furcation is discussed. © 2015 Wiley Periodicals, Inc.     

Theoretical Investigation on the Topochemical Polymerization of Diacetylenes

Abstract

The solid-state polymerization of diacetylenes (MDA-PBT-PDA) is studied with a concerted reaction model and the calculation method of EHMO-ASED and EHCO-ASED, where MDA = crystalline molecular diacetylenes, PBT = polybutatrienes, and PDA = polydiacetylenes. As the reaction goes on, the symmetry of frontier orbitals inverts at state PBT, HOCO from C ₂-antisymmetry to C ₂-symmetry and LUCO from C ₂-symmetry to C ₂-antisymmetry, which means completion of the 1,4-addition. Two necessary conditions must be satisfied for the reaction to take place: 1) the geometric parameters must undergo a series of concerted changes to make the conformation suitable for the intermolecular 1,4-addition, which should overcome an energy barrier E_b ; 2) the symmetry match between the frontier crystal orbitals of the reactant and the product must be satisfied-electrons of the reactant should be excited from HOCO (C ₂-antisymmetry) into LUCO (C ₂-symmetry), which faces an energy gap E _g. At state MDA, there is E _g(MDA) ≈ 5.6 eV. If MDA and PDA are analyzed according to Woodward-Hoffmann's rules, this reaction would be considered photochemically allowed but thermochemically forbidden. It has been shown that the E _g gradually decreases along the reaction coordinate from state MDA to PBT. At state PBT there is E _g(PBT) ≤ 0.1 eV, and the electrons of the reactant can be easily excited there. Since E_b ≤ 1.0 eV is not very large and E_g (PBT) ≤ 0.1 eV is very small, the two necessary conditions mentioned above can be satisfied thermally. Therefore, thermal polymerization can take place smoothly. By this pathway the apparent activation energy of the reaction will be E_a ≤ 1.0 eV, which is consistent with the activation energies of the polymerizations of diacetylenes in the literature.     

Chemical applications of topology and group theory

This paper characterizesforbidden polyhedra, which are polyhedra with fewer than 9 vertices which cannot be formed using only the 9s,p, andd atomic orbitals. In this connection polyhedra are of particular interest if their symmetry groups are direct product groups of the typeR × C′ _s in whichR is a group containing only proper rotations andC′ _s is eitherC _s orC _i in which the non-identity element is an inversion center or a reflection plane which is called theprimary plane of the groupR ×C′ _s . Using this terminology polyhedra of the following types are shown always to be forbidden polyhedra: (1) Polyhedra having 8 vertices, such direct product symmetry point groups, and either an inversion center or aprimary plane fixing either 0 or 6 vertices; (2) Polyhedra having a 6-fold or higherC _n rotation axis. However, these conditions are not necessary for a polyhedron to be forbidden since in addition to one 7-vertex polyhedron and ten 8-vertex polyhedra satisfying one or both of the above conditions there are two forbiddenC _3v 8-vertex polyhedra which satisfy neither of the above conditions. For part 15 of this series see reference 1.     

Approximate symmetry characteristics using fuzzy-subset theory study for chiral transitions of allene-1,3,-dihalides

Based on our study of the application of fuzzy-subset theory to the characterization of imperfect symmetry in some stable molecular systems and simple dynamic molecular systems, we analyze the internal rotation process of allene-1,3- dihalides. Allene-1,3-dihalides (CHX=C=CHY, where X and Y may be the same or different halogen atoms) are optically chiral nonplanar molecules. The two end-groups may internally rotate about the near straight linear C=C=C axis, and the molecule may change its chirality. The internal rotation process may pass through two different planar transition state (TS): cis-TS and trans-TS, which belong to C_2v and C_2h point groups (as X and Y to be same), respectively. The intrinsic reaction coordinate (IRC) corresponding to the two TS processes is denoted as cis-IRC and trans-IRC. However, for the whole IRC reaction process, only their subgroup C₂ well-defined symmetry remains. Other symmetry transformations in C_2v and C_2h point groups can only be examined in terms of imperfect symmetry, although there appear certain reaction reversal joint point group G(R_cC_2v) and G(R_tC_2h) well-defined symmetry in the dynamics through the IRC processes. If X and Y are different, the stable molecule has no conventional nontrivial point group symmetry. The internal rotation processes may pass through two different planar TS’s (cis-and trans-TS). The TS will still be a planar molecule belonging to C_S point group with the molecule plane as its symmetry plane. Other states in the IRC may belong to certain reaction reversal joint point groups, G(RM)_C and G(RM)_T. We have thus examined the approximate symmetry of MO’s related to C₂ point group. Moreover, we have also analyzed the membership functions, representation components, and their relationships shown in the MO fuzzy main representation correlation diagrams.     

A density matrix renormalization group study of low-lying excitations of polythiophene within a Pariser-Parr-Pople model

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to e_xplore the nature of the ground and low-lying e_xcited states of long polythiophene oligomers. We have e_xploitedC ₂ symmetry and spin parity of the system to obtain e_xcited states of experimental interest, and studied the lowest dipole allowed e_xcited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed e_xcited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge e_xcitation gap and the binding energy of the 1¹B _u ⁻ exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium e_xcited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

On the forbidden 2000 Å transition of trans-1,3-butadiene

The sharp, weak absorption bands that overlay the descending tail of the intense NV absorption system of trans-1,3-butadiene are shown to comprise a forbidden electronic transition that is made visible by vibrations of the a_u symmetry species of the C_2h symmetry group to which this molecule belongs.     

rac‐9‐Ethyl‐12a‐hydroxytetradecahydrotriphenylene‐1,5(2H,4bH)‐dione: stabilization of a new isomer of a functionalized perhydrotriphenylene through a tandem Michael addition–aldol reaction

The title compound, C₂₀H₃₀O₃, is a new functionalized perhydrotriphenylene derivative formed via a tandem Michael addition–aldol reaction. The structural study reveals that the system of fused rings approximates a C₂ point symmetry, with trans–cis–cis ring junctions, while highly symmetric all‐trans perhydrotriphenylene, previously characterized, approximates a D₃ symmetry. The perhydrotriphenylene nucleus of the title compound corresponds to the third stable stereoisomer isolated for this polycyclic system. Considering that the C_s isomer was obtained recently through a similar tandem reaction, a general strategy is proposed which may help to obtain other stable stereoisomers of perhydrotriphenylene.     

Semiempirical MO calculations on symmetry governed reactions

Two symmetry governed reactions, the electrocyclic transformation of planar cyclopropyl cation to allyl cation and the dimerization of ethylene to cyclobutane, are examined using a modified INDO method. Results for the cyclopropyl-allyl cation reaction agree well with previously publishedab initio results, and are much improved over previously published CNDO results. The symmetry-allowed disrotatory path is predicted to be significantly favored over the forbidden conrotatory transition. For the ethylene-cyclobutane system two surprising results are predicted within the constraints imposed upon the reaction path: first, that the entire reaction should occur within a small range in the separation of the two ethylene molecules as they approach one another, and second, that the symmetry-forbidden [2 _s +2 _s addition should be slightly favored over the symmetry-allowed [2 _s +2 _a addition. Since the Woodward-Hoffmann rules deal exclusively with changes in electronic energy, it is suggested that they should be applied with some caution to reactions in which changes in nuclear repulsion are quite large during the reaction process.     

Femtochemistry of trans‐Azomethane: A Combined Experimental and Theoretical Study

The dissociation dynamics of trans‐azomethane upon excitation to the S₁(n,π*) state with a total energy of 93 kcal mol^?1 is investigated using femtosecond‐resolved mass spectrometry in a molecular beam. The transient signal shows an opposite pump–probe excitation feature for the UV (307 nm) and the visible (615 nm) pulses at the perpendicular polarization in comparison with the signal obtained at the parallel polarization: The one‐photon symmetry‐forbidden process excited by the UV pulse is dominant at the perpendicular polarization, whereas the two‐photon symmetry‐allowed process initiated by the visible pulse prevails at the parallel polarization. At the perpendicular polarization, we found that the two C? N bonds of the molecule break in a stepwise manner, that is, the first C? N bond breaks in ≈70 fs followed by the second one in ≈100 fs, with the intermediate characterized. At the parallel polarization, the first C? N bond cleavage was found to occur in 100 fs with the intensity of the symmetry‐allowed transition being one order of magnitude greater than the intensity of the symmetry‐forbidden transition at the perpendicular polarization. Theoretical calculations using time‐dependent density functional theory (TDDFT) and the complete active space self‐consistent field (CASSCF) method have been carried out to characterize the potential energy surface for the ground state, the low‐lying excited states, and the cationic ground state at various levels of theory. Combining the experimental and theoretical results, we identified the elementary steps in the mechanism: The initial driving force of the ultrafast bond‐breaking process of trans‐azomethane (at the perpendicular polarization) is due to the CNNC torsional motion initiated by the vibronic coupling through an intensity‐borrowing mechanism for the symmetry‐forbidden n–π* transition. Following this torsional motion and the associated molecular symmetry breaking, an S₀/S₁ conical intersection (CI) can be reached at a torsional angle of 93.1° (predicted at the CASSCF(8,7)/cc‐pVDZ level of theory). Funneling through the S₀/S₁ CI could activate the asymmetric C? N stretching motion, which is the key motion for the consecutive C? N bond breakages on the femtosecond time scale.     

Comparison between the symmetry-correlation examination and the perturbation method

A comparison between the construction of symmetry-correlation diagrams and the perturbation method for studying chemical reactions is carried out. The perturbation method consists of decomposing the system Hamiltonian H into a sum, H = H₀ + H′. Various symmetry correlation schemes appearing in the literature may be explained by the nonuniqueness of the decomposition scheme. All symmetry selection rules may be viewed as the varieties. By examining the symmetry-correlation diagrams, processes under investigation may be called “forbidden” or “allowed,” depending on the topological feature. Of particular importance is the topology associated with the “avoided crossing.” By making the comparison, we can establish the correspondence of the two methods and conclude that the perturbation order furnishes the origin of the “forbiddenness” of a process.     

Dissociation of diimide

Parts of the potential energy surface of N₂H₂ have been studied using CASSCF- and contracted CI-methods. Of particular interest was the concerted dissociation of cis- and trans-diimide into N₂ and H₂, since the trans-dissociation is symmetry allowed and the cis-dissociation forbidden. Three different saddle points were located, of which only one, of C ₂- symmetry, is a true transition state. Elaborate numerical gradient methods using exact Hessians and update procedures had to be used to find these saddle points on the unexpectedly complex N₂H₂-surface. The barrier height with respect to trans-diimide is 61 kcal/mol after vibration correction. Since this energy is higher than the barrier for interconversion, cis- and trans-diimide have the same transition state. It is further found that diimide preferably dissociates stepwise, by losing one hydrogen at a time, rather than in a concerted way. This conclusion is drawn basically because the geometry of the transition state for the concerted dissociation has a very long H-H distance of 5.6 a.u. The N-H bond energy in trans-diimide is 56 kcal/mol after vibration correction.     

Orbital Correspondence Analysis in Maximum Symmetry

A method is described in which the ‘allowed’ course of a reaction is determined by means of an analysis – within the symmetry point group common to reactants and products – of their molecular orbitals and of the distortions that occur along the reaction path connecting them. The procedure, and its relation to and advantages over conventional correlation methods, is illustrated with a few very well known reactions: Cyclization of hexatriene, the ‘photochemical Diels-Alder reaction’ and the stepwise and concerted [2+2]-cycloadditions.     

Orbital Theory of Heterolytic Fragmentation and Remote Effects on Nitrogen Inversion Equilibria

From a molecular orbital study of model systems we derive the electronic requirements for the Grob fragmentation. The necessary condition for an allowed fragmentation in an X-C₁-C₂-C₃-N system, or the amino cation ⁺C₁-C₂-C₃-N is the level ordering A below S . This in turn is set by maximal through-bond coupling of the empty cation orbital and the nitrogen lone pair. The conformational dependence of through-bond coupling is exactly that derived by Grob, namely parallel orientation of the cation orbital (or the C-X bond), the C₂-C₃-σ-bond, and the N-lone-pair. When the C₁-C₂-C₃ and C₂-C₃-N angles are small, the through-space interaction dominates, reversing the level ordering to S below A , and consequently makes the fragmentation forbidden even though the conformational requirements for it are met. Ring closure becomes allowed. Some examples exploiting this result are presented, as well as procedures for enhancing through-bond coupling and thus fragmentation. The through-bond-effect has also kinetic consequences, allowing the definition of a new type of remote neighbouring group participation operative through bonds and not by direct overlap. The position of equilibria in nitrogen inversion processes should also be influenced by remote substituents which are π-acceptors or donors.     

Gas-phase structures of 1-adamantylphosphines,PH<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(1-Ad)<Subscript>3−<Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–3)

The gas-phase structure of 1-adamantylphosphine has been determined by electron diffraction, supplemented with data from ab initio and DFT calculations. The adamantyl fragment was modeled with local C _3v symmetry and the phosphino group was found to be in a position almost bisecting a mirror plane of the adamantyl group, giving the molecule overall approximate C _s symmetry. There is a small displacement of the C–P bond from the local threefold axis of the adamantyl group. Geometry optimizations were also performed for bis-(1-adamantyl)phosphine (C ₁ point-group symmetry) and tris-(1-adamantyl)phosphine (C ₃ symmetry), demonstrating extremely crowded environments around the phosphorus atoms leading to adamantyl groups that were much less symmetric. The adamantyl groups were also found to twist by a significant amount to minimize the strain.     

Electronic spectra and electron structure of fullerene complex (η2-C60)Fe(CO)4

The electronic spectrum of the C₆₀Fe(CO)₄ complex was studied in a toluene solution. The more intense absorption of C₆₀Fe(CO)₄ in the visible region, relative to the free C₆₀, can be attributed to the effect of lower symmetry of the C₆₀ fullerene cage in C₆₀Fe(CO)₄ and, thus, relaxation of selection rules for forbidden internal electronic transitions of C₆₀. No bands of the charge transfer from 3d(Fe) to C₆₀ orbitals were observed in the visible region of the complex spectrum. Assignment of the bands was confirmed by semiempirical calculations of the electronic spectrum.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1453–1458, June, 1996     

Electronic rearrangements during chemical reactions. II. Planar dissociation of ethylene

The direct dissociation of ethylene into two methylenes is studied along the least motion reaction path by means of an ab initio multiconfiguration self-consistent-field (MCSCF ) calculation. All eight configurations arising from those valence orbitals that form the CC bonds, seven of them singlet coupled and one triplet coupled, are taken into account. The HCH bond angle is optimized along the entire reaction path. Separate MCSCF optimizations are carried through for the lowest two states of ¹A_g symmetry. The (¹A_gσ²π²) ethylene ground state dissociates into two (³B₁σπ) ground-state methylenes. The (¹A_gσ²π*²) excited state of ethylene dissociates into two (¹A₁σ²) excited methylenes. It is established that both these dissociations proceed without any barrier in the energy curve. In the ground state, where orbital symmetry is conserved, the π-bond breaks before the σ-bond, and the calculated heat of reaction agrees within 6 kcal/mol with the experimental value. In the excited state, where orbital symmetry is not conserved, the nonbonded repulsion between methylene σ₂ lone pairs is found to blend into the antibonding character of the excited ethylene, yielding an energy curve that is everywhere repulsive. However, the variation of the HCH angle during the dissociation process is not simple, initially it expands and subsequently it contracts. Quantitative analytical approaches are developed which furnish conceptual interpretations of the orbital changes and configurational changes along the reaction path.     

A Conformational Study on Silacyclohexane. Comparison of ab initio (HF,MP2), DFT,and Molecular Mechanics Calculations. Conformational Energy Surface of Silacyclohexane

The structures and relative energies for the basic conformations of silacyclohexane 1 have been calculated using HF, RI‐MP2, RI‐DFT and MM3 methods. All methods predict the chair form to be the dominant conformation and all of them predict structures which are in good agreement with experimental data. The conformational energy surface of 1 has been calculated using MM3. It is found that there are two symmetric lowest energy pathways for the chair‐to‐chair inversion. Each of them consists of two sofa‐like transition states, two twist forms with C₁ symmetry (twist‐C₁), two boat forms with Si in a gunnel position (C₁ symmetry), and one twist form with C₂ symmetry (twist‐C₂). All methods calculate the relative energy to increase in the order chair < twist‐C₂ < twist‐C₁ < boat. At the MP2 level of theory and using TZVP and TZVPP (Si atoms) basis sets the relative energies are calculated to be 3.76, 4.80, and 5.47 kcal mol^–1 for the twist‐C₂, twist‐C₁, and boat conformations, respectively. The energy barrier from the chair to the twisted conformations of 1 is found to be 6.6 and 5.7 kcal mol^–1 from MM3 and RI‐DFT calculations, respectively. The boat form with Si at the prow (C_s symmetry) does not correspond to a local minimum nor a saddle point on the MM3 energy surface, whereas a RI‐DFT optimization under C_s symmetry constraint resulted in a local minimum. In both cases its energy is above that of the chair‐to‐twist‐C₁ transition state, however, and it is clearly not a part of the chair‐to‐chair inversion.     

Dimethyl‐ and diethyl­dithio­cyanato­tin(IV)

The structures of dimethyl­dithio­cyanato­tin(IV), [Sn(CH₃)₂(NCS)₂], and diethyl­dithio­cyanato­tin(IV), [Sn(C₂H₅)₂(NCS)₂], have been determined. The dimethyl derivative has 2mm crystallographic symmetry and the diethyl derivative has twofold crystallographic symmetry. The experimental differences in the distances and angles around the Sn atom between the two structures agree reasonably well with the differences expected from the reaction path mapped previously [Britton & Dunitz (1981). J. Am. Chem. Soc. 103 , 2971–2979].