Investigations with the finite element method on the Cyber 205

We are trying to investigate systematically the application of the finite element method (FEM) for solving the Schrödinger equation. The present paper is devoted to the calculation of vibrational transition probabilities for the collinear reactive system A + BC (i.e. H+H₂ and their isotopes). The calculations are fully two-dimensional and the results are compared with earlier FEM calculations and conventional basis set expansion methods using the the R-matrix or S-matrix propagation.We made extensive analysis of FEM on the vector-computer Cyber 205 and developed a vector code for the efficient use in two dimensions, so that in the near future applications even in three dimensions will be possible.For the hydrogen exchange reactions we investigated the following isotope combinations: (a) H + H₂, b) H + DH, D + HD and H + MuH (symmetric reaction), (c) D + HH, H + DD and Mu + DD (asymmetric reaction). We calculated the transition probabilities for up to five open vibrational channels and found excellent agreement with known exact values.     

R-matrix theory for collinear chemical reactions

We apply R-matrix theory to the collinear II + II₂ exchange reaction. Within a natural collision coordinate frame we generalize the standard R-matrix formulae to apply to reactive systems which have two asymptotic matching surfaces. After writing the hamiltonian as H = H⁰ + V where H⁰ is a soluble reactive scaltering hamiltonian, we derive the Buttle correction which accounts for H⁰ exactly. The Buttle correction is necessary to speed convergence of the numerical results. Using a rather crude set of basis functions which are an orthonormal set of solutions of H⁰ we find that 150 even and odd type functions are necessary to achieve adequate agreement of transmission probabilities with close coupled results. Fewer functions are needed to account for the threshold behavior but the full number are needed to portray the resonance at 22.2 kcal/mole. Finally we generalize our formulae to apply to asymmetric exchange reactions.     

On the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics: Application to O + CS2 → SO + CS

We explore the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics. These coordinates provide the natural extension to polyatomic systems of the familiar atom—diatom model of “rolling a marble” on a skewed and scaled potential surface in that they reduce the kinetic energy of an arbitrary system to one equivalent to that of a single mass point moving in 3N - 3 dimensions. For any given number of atoms, usually several distinct types of mass scaled cluster coordinates can be introduced, all of which are interrelated by orthogonal transformations, and many of which are convenient for describing trajectory motion in one or more arrangement channels. We illustrate these points by an application to the collinear O + CS₂ → SO + CS reaction. For this system, the reagent to product coordinate transformation is conveniently described in terms of two Euler angles α and β, for which β is analogous to the atom—diatom skew angle, and α determines how the reagent vibrational normal modes relate to the product degrees of freedom. Examination of trajectory behavior indicates that the rather small value of π - α (21.7°) leads to a rather clean correlation between CS₂ asymmetric stretch motion and product CS vibrational motion, and between CS₂ symmetric stretch and a combination of SO stretch and product translation. This explains why symmetric stretch mode excitation enhances the O + CS₂ reaction rate more efficiently than asymmetric stretch mode excitation. We also find for O + CS₂ (and many other reactions for which the unbroken bond does not significantly change its length during the reaction) that the reagent and product segments of the minimum energy path are coplanar. This means that a natural partitioning of the reaction dynamics exists in which motions parallel to this plane tend to be active in promoting the reaction whereas motions perpendicular tend to be inactive. A study of trajectory motions and product state energy partitioning for O + CS₂ confirms this.     

Electronic transitions in collinear H+ + D2 (ν = 0) → HD+ (ν = 0,1) + D via classical trajectories in complex time and complex phase space

A semiclassical treatment of electronic transitions in the collinear rearrangement H⁺ + D₂ (ν = 0) → HD⁺ (ν = 0,1) + D is presented. The treatment represents an extension of Stueckelberg's method for a single nuclear degree of freedom to collisions involving several nuclear degrees of freedom. The classical limit of scattering amplitudes (S-matrix elements) is calculated for the transition between the two adiabatic potential energy surfaces corresponding to the two lowest singlet states of HD⁺₂. S-matrix elements are constructed from trajectories propagating in complex time and complex phase space, which make localized transitions between the two surfaces by crossing their complex line of intersection. The action along each trajectory acquires an imaginary part, which contributes exponential damping to the corresponding amplitude for electronic transition.     

Investigations with the finite element method. II. The collinear F + H2 reaction

We are investigating systematically the use of the finite element method (FEM) for solving the Schrödinger equation. The present work is devoted to the calculation of vibrational transition probabilities for the collinear reactive system F + H₂. The calculations are fully two-dimensional and the results are compared with the conventional basis set expansion methods using the R-matrix or S-matrix propagation. Extensive analysis of FEM on the vector computer Cyber 205 was made and a vector code for the efficient use in two dimensions was developed, so that in the near future applications even in three dimensions will be possible. The details of our FEM calculations are the following: The integration area was discretized into triangles where quadratic polynomials for the local wavefunction were defined. Convergent results can be reached with this simple ansatz with roughly 10000 grid points.     

Secondary reactions in controlled potential coulometry: Part V. Reversal coulometric study of the reduction of cis- and trans-thioindigo in the presence of carbon dioxide,cinnamonitrile and acrylonitrile

Controlled potential reversal coulometry was applied to the following systems: (I) C+neR; R+C → RC; RC+ne → products. (II) as in (I) except RC not electroactive. (III) C+neR; R+X → RX; RX+ne → products. Equations for these e.c.e. and e.c. mechanisms were obtained and solved numerically. Working curves are presented for the calculation of the rate constants of the homogeneous reactions. This treatment was applied to studies of the reduction of thioindigo (TI) alone and in the presence of several reactants. For TI alone the reaction mechanism involves reaction of the radical anion (TI^?_·) with parent molecule followed by a second electron transfer. In the presence of excess dissolved CO₂, acrylonitrile (AN), or cinnamonitrile (CN), reaction of TI^?_· with these followed by a second electron transfer was proposed. Rate constants for the TI?TI^?_· coupling reaction were 82 (cis-thioindigo), and 323 (trans-thioindigo) l mol^?1 s^?1; pseudo-first-order reactions of TI^?_· were 0.016 (trans-) and 0.047 (cis-) s^?1 with CO₂; 0.023 (trans-) and 0.033 (cis-) s^?1 with CN; 0.022 (trans-) and 0.032 (cis-) s^?1 with AN.     

MM3 force field prediction of the enantioselective preference in the asymmetric synthesis of a chiral 2-cyclohexen-1-ol using a chiral lithium amide reagent

Enantioselective preference in the asymmetric synthesis where cyclohexene oxide is transformed enantioselectively to chiral (S)- or (R)-2-cyclohexen-1-ol by the reaction with the appropriate chiral lithium amide reagent has been evaluated theoretically using the MM3 force field. The plausible possible structures for each precursor (reaction intermediate complex) leading to a (S)- or (R)-2-cyclohexen-1-ol have been optimized with the extended MM3 force field applicable to the lithium amide functional group, and the populations of their (S)- or (R)-reaction intermediate complexes at an ambient temperature (298 K) were calculated. The initial structure for evaluating the reaction intermediates of this asymmetric synthesis was constructed on the basis of the optimized ab initio transition state structure (MP2/6-31+G^∗) comprising lithium amide LiNH₂ and propene oxide. To the thus obtained transition state structure composed of LiNH₂ and propene oxide, the other remaining Cartesian coordinates for the actual reaction intermediates composed of the chiral lithium amides and cyclohexene oxide were added to make the reaction intermediate structure. The conformational search for the reaction intermediate has been carried out by using the Stochastic search Algorithm, and the optimized geometries and their conformational energies (steric energies) have been calculated by the MM3 force field. The populations calculated from the conformational energies of the reaction intermediate leading to the (S)- or (R)-2-cyclohexen-1-ol were shown to be linearly well correlated with the experimentally reported enantiomer excess (% ee) values. The critical factors to control the enantioselectivity were investigated on the basis of the optimized structures of the reaction intermediate complexes. The MM3 force field approach was shown to be applicable to the theoretical evaluation of the enantioselectivity and be useful for designing a new functional chiral lithium amide reagent for the asymmetric synthesis.     

Controllable stereoinversion in DNA-catalyzed olefin cyclopropanation via cofactor modification

The assembly of DNA with metal-complex cofactors can form promising biocatalysts for asymmetric reactions, although catalytic performance is typically limited by low enantioselectivities and stereo-control remains a challenge. Here, we engineer G-quadruplex-based DNA biocatalysts for an asymmetric cyclopropanation reaction, achieving enantiomeric excess (ee_trans) values of up to +91% with controllable stereoinversion, where the enantioselectivity switches to −72% ee_trans through modification of the Fe-porphyrin cofactor. Complementary circular dichroism, nuclear magnetic resonance, and fluorescence titration experiments show that the porphyrin ligand of the cofactor participates in the regulation of the catalytic enantioselectivity via a synergetic effect with DNA residues at the active site. These findings underline the important role of cofactor modification in DNA catalysis and thus pave the way for the rational engineering of DNA-based biocatalysts.

Cofactor modification in a DNA-catalyzed olefin cyclopropanation reaction enables controllable stereoinversion and achieves enantioselectivities of up to +91% and −72% ee_trans.     

Theoretical analysis of catalytic current-potential curves: Part II. First-order regeneraration reactions coupled with dimeric product of the electrode reaction

Equations of the polarographic current-potential curves are derived for electrode reactions of the type 2A+ze^?k_s,α→B coupled by an irreversible chemical regeneration reaction B+C^k→2A+D. Analytical solutions based on a general treatment were derived, including reversible, irreversible and quasi-reversible electrode processes. The kinetic domain over which an irreversible following chemical reaction affects the half-wave potentials is defined.     

Finding minimum energy reaction paths on ab initio potential energy surfaces using the fast marching method

The fast marching method (FMM) for determining minimum-cost paths has been extended to compute the minimum-energy reaction coordinates in chemical reactions. This was accomplished by building an interface between FMM and the Gaussian program. We demonstrate the new method using an S _N 2 reaction, the isomerization of HSCN to HNCS, and a gas-phase rearrangement reaction of relevance in mass spectrometry.     

Asymmetric Henry reactions catalyzed by metal complexes of chiral oxazoline based ligands

Chiral oxazolines have been synthesized from norephedrine and pyrrole nitrile or benzoyl chloride and applied to the catalytic asymmetric Henry reactions of p-nitro aldehydes with nitromethane to provide β-hydroxy nitroalkanols in high conversion (up to 92%). The reaction was then optimized in terms of the metal, solvent, temperature, and amount of chiral ligand. The corresponding catalyst with Cu(OTf)₂ and isopropanol as the solvent gave the best enantioselectivities (up to 84% ee) of the corresponding β-nitroalkanol for p-nitrobenzaldehyde.     

Highly diastereo- and enantioselective reactions of enecarbamates with an aldehyde

Catalytic asymmetric addition reactions of enecarbamates with ethyl glyoxylate have been developed using CuClO₄·4CH₃CN and a diimine ligand as the catalyst. Highly diastereo- and enantioselective addition reactions of α-mono-substituted enecarbamates have been also achieved. These reactions afforded the corresponding adducts with high selectivity; that is, syn adducts from Z-enecarbamates and anti adducts from E-enecarbamates. The proposed reaction mechanism is an aza-ene type pathway, where the proton of an enecarbamate's N-H group plays an important role, not only for accelerating the reaction but also for providing a transition state suitable for the highly selective chiral induction.     

Synthetic studies of microtubule stabilizing agent peloruside A: an asymmetric synthesis of C10C24 segment

An asymmetric synthesis of the C₁₀C₂₄ fragment of the potent antitumor macrolide, peloruside A is described. All three stereogenic centers have been enantioselectively constructed utilizing Evans alkylation, Brown asymmetric allylboration, and a substrate controlled epoxide formation. Other key reactions involved Grubbs's ring-closing olefin metathesis and Ando's Z-selective olefination reaction.     

Quantum-mechanical rearrangement processes: Off-shell vibrorotational sudden approximation to the dynamics

A vibrorotational sudden approximation for atom—diatom reactive scattering is developed, based on a T-matrix formulation of the process. The theory characteristically involves off-shell T-matrices that have been recently applied with remarkable success to the simpler atom—diatom subreactive regime. From the computational point of view, the scattering calculations must be performed in two successive steps. In the first, the scattering wavefunction, in the vibrorotational sudden approximation, must be evaluated and, for this purpose, standard computer packages of the inelastic regime can be immediately applied. This wavefunction must be used, next, to evaluate the off-shell T-matrix of the theory, by numerical quadrature. For this purpose, an efficient computational scheme is developed, that combines kinematical constraints and partial wave analysis requirements. The simplicity of the formalism and the off-shell constraint on the T-matrix suggest that the theory could be usefully applied for a rationalization of a large body of data in chemical reactions.     

Palladium asymmetric reduction of β-carboline imines mediated by chiral auxiliaries assisted by microwave irradiation

An alternative synthetic approach for the introduction of chirality in β-carboline moiety through in situ reduction of N-acyliminium ion intermediates generated from imine 2 and chloroformate of 8-phenylmenthyl as chiral auxiliary was achieved. The method applied microwave-assisted irradiation and used PdCl₂/Et₃SiH protocol as a mild reducing agent, which decreased reaction times to minutes when compared to the conventional thermal reactions. The diastereoselectivity (4-12:1) of the reduction produced R-amines, which were assigned after chiral auxiliary removal and spectroscopic data compared to products obtained from Noyori asymmetric hydrogenation catalyst.     

On the Calculation of the Anharmonic Effect of Unimolecular Reactions of HOCO

HOCO is the intermediate of the reaction H + CO₂ → HO + CO. In this study, all the geometries in the collision reaction H + CO₂ were optimized at MP2/6‐311++G** level with Gaussian 03 program and a potential energy surface which shows that three unimolecular reactions were in the process of HOCO → HO + CO. For the three reactions, YL method proposed by L. Yao and S. H. Lin is applied to calculate the anharmonic and harmonic total number of states, the density of states and rate constants. The anharmonic values for rate constants calculated in this study are much lower than harmonic values, which indicate that anharmonic effects are significant and can not be neglected. After convert the experimental lifetime of HOCO into rate constants, the values are close to the calculations in our research, which shows that YL method used in our study is suitable for studying the rate constants of unimolecular reaction.     

Asymmetric synthesis of pharmaceutically relevant 1-aryl-2-heteroaryl- and 1,2-diheteroarylcyclopropane-1-carboxylates

This study describes general methods for the enantioselective syntheses of pharmaceutically relevant 1-aryl-2-heteroaryl- and 1,2-diheteroarylcyclopropane-1-carboxylates through dirhodium tetracarboxylate-catalysed asymmetric cyclopropanation of vinyl heterocycles with aryl- or heteroaryldiazoacetates. The reactions are highly diastereoselective and high asymmetric induction could be achieved using either (R)-pantolactone as a chiral auxiliary or chiral dirhodium tetracarboxylate catalysts. For meta- or para-substituted aryl- or heteroaryldiazoacetates the optimum catalyst was Rh₂(R-p-Ph-TPCP)₄. In the case of ortho-substituted aryl- or heteroaryldiazoacetates, the optimum catalyst was Rh₂(R-TPPTTL)₄. For a highly enantioselective reaction with the ortho-substituted substrates, 2-chloropyridine was required as an additive in the presence of either 4 Å molecular sieves or 1,1,1,3,3,3-hexafluoroisopropanol (HFIP). Under the optimized conditions, the cyclopropanation could be conducted in the presence of a variety of heterocycles, such as pyridines, pyrazines, quinolines, indoles, oxadiazoles, thiophenes and pyrazoles.

The dirhodium tetracarboxylate-catalysed asymmetric cyclopropanation has been applied to the enantioselective syntheses of pharmaceutically relevant 1-aryl-2-heteroaryl- and 1,2-diheteroarylcyclopropane-1-carboxylates.     

Comparison of close-coupling and approximate methods for F(2P12) + H2 non-reactive collisions: Translational wavefunction analysis

Electronic-rotational energy transfer in F(²P_{$\text{1}\text{2}$}) + H₂ (j = 0) non-reactive collisions is studied by analyzing the translational wavefunctions (TW) and transition probabilities of four model problems: full close-coupling (CC), diabatic (DDW) and adiabatic (ADW) distorted-wave Born theories, and an asymptotic sine-wave model. Comparisons among the approximate models are discussed and their accuracy is examined. DIM theory provides the diabatic electronic matrix elements, and the close-coupled equations are solved by the R-matrix method. The resulting S-matrix elements times their appropriate asymptotic wavefunctions when propagated in along the reaction coordinate generate the TW. For the CC results, relations between the TW and the adiabatic electrotational energy correlation diagrams are emphasized, while for the other models the effects of classical turning points, diabatic energy level structure, unitarization techniques, and other dynamical factors on the state-to-state transition probabilities are examined.     

Synthesis and properties of isocyanate and isothiocyanate d1- and d2-complexes of vanadocene

The reactions of vanadocene and its halides Cp₂VCl and Cp₂VCl₂ with R₃MNCX (M  Sn, Si, X  O, S) and R₂M(NCX)₂ in various molar ratios have been studied. The reactions proceed either by an exchange of groups, with no change in the oxidation state of vanadium, or by an oxidative addition of pseudohalide ligand: V^II → V^III; V^III → V^IV. Oxidative addition results in the formation of (R₃M)₂ or gaseous hydrogen (in the reaction with HCl) in the reaction products.We have prepared the first ever monomeric and readily oxidisable d²-complexes of V^III of Cp₂VNCX-type and asymmetric d¹-complexes of Cp₂V(Cl)NCX type, which, although rather stable in air, undergo disproportionation into symmetric d¹-complexes on heating. In transmetallation reactions the ligand activity is found to increase in the order C1 < NCO < NCS. The complexes were characterised by GLC analysis, IR and ESR spectroscopy. A general scheme for the disproportionation reaction of asymmetric complexes of vanadocene is supported by differential thermal analysis data.     

Investigations of enantioreversal in both direct and directed enantioselective aldol reactions catalyzed by CuCl2[(−)-sparteine] and NiCl2[(−)-sparteine] complexes

The use of structurally well-defined chiral [CuCl₂(sparteine)] 1 and [NiCl₂(sparteine)] 2 complexes as catalysts under fluoride anion-promoted double catalytic activation (DCA) conditions cause enantioreversal in the asymmetric Mukaiyama aldol reaction of 1-phenyl-1-trimethylsiloxyethylene with various aromatic aldehydes. A similar enantioreversal also occurs in the direct aldol reaction between methyl vinyl ketone and various aromatic aldehydes under Et₃N promoted DCA conditions. We have quantitatively analyzed using group theoretical analysis via symmetry deformation coordinates, the molecular structures of 1 and 2 from the X-ray structural data; the results from the study show that the innate stereochemical differences that are present in their molecular structures, form the basis for the enantioreversal phenomenon in the asymmetric C–C bond-forming aldol reactions.