Geminal Product Research Articles

ChemInform Abstract: UNUSUAL REGIOSELECTIVE HYDROSILYLATION OF ETHYNYLMETHYLDICHLOROSILANE WITH DIMETHYLCHLOROSILANE CATALYZED BY TETRAKIS(TRIPHENYLPHOSPHINE)PLATINUM(0)

AbstractDie Hydrosilylierung des Alkins (I) mit dem Silan (II) führt in Gegenwart des Platin‐ Komplexes (III) mit hoher Regioselektivität zum geminalen Olefin (IV).

UNUSUAL REGIOSELECTIVE HYDROSILYLATION OF ETHYNYLMETHYLDICHLOROSILANE WITH DIMETHYLCHLOROSILANE CATALYZED BY TETRAKIS(TRIPHENYLPHOSPHINE)PLATINUM(0)

Abstract The hydrosilylation of ethynylmethyldichlorosilane with dimethylchlorosilane catalyzed by tetrakis(triphenylphosphine)platinum(0) was found to show quite an unusual regioselectivity to afford the geminal product, 1-(methyldichlorosilyl)-1-(dimethylchlorosilyl)ethene, almost exclusively.

Laryngeal adjustments in the production of consonant clusters and geminates in American English

The glottal opening gesture and its timing control in various sequences of voiceless obstruents were investigated by the combined techniques of electromyography, photo-electric glottography, and fiberoptic endoscopy. The results obtained at both electromyographic and movement levels revealed that the glottal opening gesture is characterized by a one-, two-, or more-than-two-peaked pattern in a regular fashion according to the phonetic nature of the voiceless segments: each voiceless obstruent or geminate accompanied by aspiration or frication noise tends to require a single separate peak of the opening gesture, while an unaspirated stop embedded in a voiceless environment can be produced within the opening gesture attributed to an adjacent aspirated stop or fricative. Such an independent opening gesture of the glottis for the production of voiceless aspirated stops or voiceless fricatives even in sequentially unvoiced contexts can be interpreted as assuring the aerodynamic requirements for turbulent noise production during the aspirated stop or fricative segment.

Coupled perturbation theory within the antisymmetrized product of separated geminals (APSG) framework

AbstractA coupled perturbation theory for the antisymmetrized product of separated geminals (APSG) approximation is derived. The variational principle for the APSG wave function in an external oscillating field is employed and a set of equations of the form analogous to the normal RPA is obtained. At this level the reduced resolvent in the form of a spectral expansion is written and it is used for the evaluation of the second‐order properties.

Antisymmetric product of geminals in the context of the method of moments

AbstractA scheme for obtaining approximate solutions of the electronic Schrödinger equation is formulated within the context of the method of moments. The flexibility of the method of moments is utilized in the construction of a model based on an antisymmetric product of geminals (APG). This APG model is compared with a model based on an antisymmetric product of strongly orthogonal geminals (APSG). As a test example the advocated APG model is applied to the ground state of ammonia. Our best APG function recovers 37% of the total molecular correlation energy to be compared with an estimated 31% for the best APSG function.

Photolysis of Dibenzoyl Peroxide under Direct and Singlet Sensitized Irradiations. Mechanism for the Formation of the Geminate Product

Abstract Attempts have been made to elucidate the mechanism for the efficient production of phenyl benzoate, the geminate product, from direct and singlet sensitized irradiations of dibenzoyl peroxide in solution. It is concluded that these irradiations produce a reactive state of the peroxide which can undergo two-bond cleavage of the O–O and C(α)–C(carbonyl) bonds to give a phenyl–benzoyloxy radical pair in a solvent cage, followed by the recombination of the component radicals to give the geminate product or by their diffusion out of the solvent cage to give diffusion products.

Molecular wavefunctions in geminal product approximation

A method is presented for the optimization of a molecular wavefunction in the form of an antisymmetrized product of strong-orthogonal geminals. Each geminal function is expressed in a natural orbital expansion, orbitals and expansion coefficients both being fully optimized. An illustrative application is given, confirming the efficiency of the method and the ability of this type of wavefunction to give an accurate description of bond-breaking processes. The connection with valence bond theory is discussed.

Zur Synthese von Norbornanonen mit geminaler Dimethylgruppe

The synthesis ofgem-dimethylnorbornanones is described. One synthetic pathway after aDiels-Alder reaction involves the transformation of the nitro group into the oxo group with subsequent methylation into the geminal dimethyl product. A shorter way by [4+2]-cycloaddition of cyclopentadiene with a suitable dimethylated dienophile (e.g. 2-methyl-1-nitropropene) failed, probably by steric hindrance of the dienophile. 7-Oxanorbornanones, with agem-dimethyl group could not be prepared. A second synthetic approach togem-dimethylnorbornanones is opened byLewis acid catalyzed rearrangement of cyclohexenylcarbaldehydes.

The antisymmetrized product of weak nonorthogonal geminals

AbstractMost commonly the nonorthogonality of geminals is weakly expressed so that the exchange and overlap integrals ζ(η), φ(η) are negligible for large exchange parameters η. The conditions which allow the terms with large η to be discarded are considered. The integrals ζ(η), φ(η) are derived for η = 2, 3, 4.

The external magnetic field effect on the singlet sensitized photolysis of dibenzoyl peroxide

The external magnetic field effect upon the singlet sensitized photolysis of dibenzoyl peroxide in toluene was measured at 20°C in the presence of a field of 0–4.3 T. The yield of phenyl benzoata, the geminate product, decreases by 8% and the yields of free radical products increase by 2% in the presence of a magnetic field of 4.3 T. The decrease in the phenyl benzoate yield due to an external magnetic field is proportional to the square root of the applied strength. The observed magnetic field effect is quatitatively interpreted by the radical-pair theory of CIDNP developed by Kaptein.

A group theoretical approach to geminal product matrix elements

Expressions enabling systematic compilation of Hamiltonian and overlap matrix elements for an antisymmetrized multiterm geminal product trial function are derived, using double coset (DC) decompositions and subgroup adapted irreducible representations of the symmetric group, SN. The trial function may describe an even electron atomic or molecular system in any total spin eigenstate, and the geminals may be nonorthogonal, have arbitrary permutational symmetry, and be explicit functions of interelectronic distance. A DC decomposition is used to factor out permutations not exchanging particle labels between geminals (elements of the interior pair group, Sn2, n≡N/2). This reduces the sum over N! permutations to a sum over DC generators. If the irreducible representation λ (S) of SN is adapted to Sn2 each geminal is projected into its singlet or triplet component. The DC generators are chosen such that each has the form QP, where Q permutes odd particle labels only and P is a permutation of geminals (element of the exterior pair group, S?). With the aid of matrices called DC symbols an algorithm for these generators is derived, and used to find explicit sets for N=2, 4, 6, and 8. The N-electron Hamiltonian and overlap integrals arising with a particular DC generator QP are factored into products of smaller integrals, called cluster integrals, according to the cycle structure of Q. The cluster integrals are of only three main types—overlap, one-cluster energy, and two-cluster energy (analogs of orbital overlap, 1-electron, and 2-electron integrals) —and are further classified by order (number of geminals), geminal permutational symmetry, and in some cases pattern of connection. Matrix element compilation is systematic in that all N-electron integrals are products of a relatively small number of different types of cluster integral, and that N-electron integrals with similar factored forms are collected together in the summation. From counting the different cluster integrals required, it is concluded that a geminal product calculation not using orbital expansion is feasible only for systems with eight or less electrons. In some cases semiempirical calculations with correlated geminals might be considered, for the more complex cluster integrals (those of high order) are quite small for a system approximating a collection of localized electron pairs. The matrix element expressions are specialized for three cases—all geminals being singlets, strongly orthogonal geminals, and identical geminals. Comparison is made with a recently developed diagrammatical method.

THE EFFECT OF EXTERNAL MAGNETIC FIELD ON PHOTOCHEMICAL FREE RADICAL REACTIONS. THE SINGLET AND TRIPLET SENSITIZED PHOTOLYSIS OF DIBENZOYL PEROXIDE

Abstract Application of external magnetic field (0–14 kG) on the singlet and triplet sensitized photolysis of dibenzoyl peroxide scarcely affects the yield of phenyl benzoate resulting from cage recombination between benzoxyl and phenyl radicals, suggesting that only a slight fraction of the geminate product arises from radical pairs which can suffer the effect of magnetic field.

An instrumental study of consonant gemination

An experiment is described aimed at investigating differences between single and geminate consonants in word-interior intervocalic position and at word boundaries. In addition the difference between short and long geminates, differences between the manifestations of geminates at word boundary in two languages and differences in production of geminates by native and non-native speakers of the two languages were examined. The two languages chosen were Estonian and American English, the consonants were bilabial plosives, and the principal technique employed was electromyography. Evidence was found of rearticulation in the production of Estonian intervocalic long and overlong consonants as well as junctural C + C sequences. There was no evidence for rearticulation in English junctural C + C sequences. Both speakers carried their articulation patterns over from the native to the non-native language.

Diagrammatical Method for Geminals. I. Theory

A diagrammatical method, based on the second quantization formalism, time-independent Wick's theorem and Feynman-like diagrams, is developed for the calculation of arbitrary matrix elements of n-particle spin-independent operators between the states represented by antisymmetrized products of geminals of an arbitrary kind (i.e., strongly or weakly orthogonal, interacting, nonorthogonal or identical geminals). The method greatly facilitates any algebraic manipulation with geminal type functions, particularly when strong orthogonality is not assumed, and enables one to write down directly the algebraic expressions for the matrix elements of an arbitrary spin-independent operator between the single antisymmetrized products of arbitrary geminals, solely on the basis of simple graphs, which are easily constructed.

Diagrammatical Method for Geminals. II. Applications

The diagrammatical method for the calculation of the matrix elements of an arbitrary spin-independent operator in the basis of single antisymmetrized geminal products, developed in Part I, is applied to derive the overlap and energy mean value expressions for various types of geminal wavefunctions, namely for strongly and weakly orthogonal, nonorthogonal and identical geminals. The applications to other problems and the use of molecular symmetry in this formalism are also briefly discussed.

Geminal Localization in the Separated-Pair π-Electronic Model of Benzene

A problem of the geminal ``localization'' in the separated-pair π-electronic model of benzene is studied for a wide range of a coupling constant using the Pariser—Parr—Pople-type Hamiltonian. The general form of the ``localized geminals'' leading to the separated-pair wavefunction of the C3h symmetry is found as a function of two free parameters. These geminals are used in the separated-pair model calculation, showing that the previously used localization corresponding to the equivalent orbitals (i.e., the localized Hartree—Fock orbitals) is not the best one from the separated-pair model viewpoint, except for vanishingly small coupling constants. The optimization is also carried out after the projection of the single antisymmetrized product of geminals function onto the totally symmetric subspace of the D6h point group. Finally, the general implications of the ``symmetry dilemma'' are briefly discussed for both independent-particle and separated-pair models.

Geminal Product Wavefunctions: A General Formalism

We consider the construction of a wavefunction composed of Nβ singlet coupled geminals and Nα − Nβ α spin orbitals where Nα + Nβ is the total number of electrons. An orthonormal basis {χ} is introduced and each geminal and orbital is expanded in this basis. The wavefunction is expressed as a linear combination of determinants over the {χ} basis and the energy expression is obtained. It is suggested that the geminal and orbital expansion coefficients be obtained using a numerical minimization technique. As an example we construct an APG function for LiH and BH (using only σ orbitals) and compare the energies obtained with this model to the corresponding MO–SCF, APSG, and CI results over the same (σ) basis. We find that the APG function recovers 99.9% and 98.0% of the energy difference between the CI and MO–SCF, while our APSG function recovers 96.6% and 80% for these two molecules. Since most pair function models of electronic structure may be viewed as special cases of the parent APG model, this approach includes these models and in addition allows one to construct wavefunctions within a unified formalism in which different pairs in a given molecule may be treated at different levels of accuracy.

Electron Correlation and Separated Pair Approximation in Diatomic Molecules. II. Lithium Hydride and Boron Hydride

By use of the variational principle, nearly optimal antisymmetrized products of separated geminals have been determined for lithium hydride, boron hydride, and their separated atoms. The geminals are determined in terms of their natural orbitals, which are represented as expansions of Slater-type atomic orbitals. By comparison of the fully optimized wavefunctions of the hydrides at their equilibrium distances with the corresponding wavefunctions for the separated atoms, it is shown that the inner shells are essentially invariant upon molecule formation and that the detailed correlation structure of the inner geminal can be neglected for the determination of difference properties. From a partitioning of the geminal expansions into a principal part and a correlation part, a corresponding partitioning is obtained for the total wavefunction and the energy. With the help of this partitioning the detailed correlation interactions are analyzed and the sources of intrapair correlations are exhibited. Comparisons are made with previous calculations in terms of this analysis. A method is developed for obtaining potential curves from many-parameter wavefunctions in which the wavefunction is reoptimized at a few selected values of the internuclear separation. Moreover, at these few points, the correlating natural orbitals of the inner shells can be omitted during the course of the minimization. From the fact that the parameters are smooth and slowly varying functions of the internuclear distance, an interpolation scheme is proposed for determining the entire potential curve. From these potential curves the spectroscopic constants are calculated on the basis of the Dunham analysis.

Electron Correlation and Separated Pair Approximation in Diatomic Molecules. I. Theory

The theory of antisymmetrized products of separated geminals for many-electron systems is developed for arbitrary spin states. The geminals are expanded in terms of their natural spin orbitals, and methods are developed for their optimal determination. New variational equations are derived and cast in the form of one pseudoeigenvalue equation for all natural spin orbitals. An alternative scheme is given for finding optimal symmetry-adapted natural orbitals in terms of an orthonormalized basis set by direct energy minimization. A strategy for optimization is discussed which was found useful in calculations of the ground states of the molecules LiH, BH, NH, and their separated atoms.

Bilinear Orbital Expansion of Geminal-Product Correlated Wavefunctions

Bilinear orbital expansions of geminals are proposed for use in forming a total electronic wavefunction from a single antisymmetrized product of geminals. This gives rise to a more general analytical form for the wavefunction than that represented by the previously discussed interacting, separated, or identical geminal models. Variational determinations of the geminals are enhanced by this more general scheme although additional algebraic complexities arise as well. Explicit expressions are given for the geminal expansions, density matrices, energy, and variational equations in the case of two singlet pairs of electrons.