Excess enthalpies of binary mixtures of 1-hexene with some branched alkanes at the temperature 298.15 K

Measurements of excess molar enthalpies at the temperature 298.15 K in a flow microcalorimeter are reported for the five binary mixtures formed by mixing 1-hexene with the branched alkanes: 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, 2,3-dimethylbutane, and 2,2,4-trimethylpentane. Smooth Redlich–Kister representations of the results are described. It was found that the Liebermann–Fried model also provided good representations of the results.     

Excess Enthalpies of Binary Mixtures of 1-Hexene with Some Ethers at 25°C

Measurements of excess molar enthalpies at 25°C in a flow microcalorimeter, are reported for the four binary mixtures formed by mixing 1-hexene with either 2- methyltetrahydrofuran, or methyl tert-butyl ether, or diisopropyl ether, or di-n-butyl ether. Smooth Redlich–Kister representations of the results are presented. It was found that the Liebermann–Fried model also provided good representations of the results.     

On the interrelation between orbits and double cosets

Orbits and double cosets are intimately related: double cosets can always be looked upon as being orbits and often orbits can be identified with double cosets, in reverse. This note presents two such situations where orbits can be traced back to double cosets: the restriction of transitive permutation representations to subgroups and the cartesian product of two transitive permutation representations. These results readily apply to standard topics in chemical combinatorics dealing with isomers and isomerizations but equally like to less familiar combinatorial schemes such as Redfield's.     

A paradox of grid-based representation techniques: accurate eigenvalues from inaccurate matrix elements

Several approximately variational grid-based representation techniques devised to solve the time-independent nuclear-motion Schrödinger equation share a similar behavior: while the computed eigenpairs, the only results which are of genuine interest, are accurate, many of the underlying Hamiltonian matrix elements are inaccurate, deviating substantially from their values in a variational basis representation. Examples are presented for the discrete variable representation and the Lagrange-mesh approaches, demonstrating that highly accurate eigenvalues and eigenfunctions can be obtained even if some or even all of the Hamiltonian matrix elements in these grid-based representations are inaccurate. It is shown how the apparent contradiction of obtaining accurate eigenpairs with far less accurate individual matrix elements can be resolved by considering the unitary transformation between the representations. Furthermore, the relations connecting orthonormal bases and the corresponding Lagrange bases are generalized to relations connecting nonorthogonal, regularized bases and the corresponding nonorthogonal, regularized Lagrange bases.     

Direct subduction of Q-conjugacy representations to give characteristic monomials for combinatorial enumeration

Characteristic monomials for a finite group are obtained by direct subductions of Q-conjugate representations. They are shown to give a generating function that is capable of solving enumeration problems. Received: 1 May 1998 / Accepted: 16 July 1998 / Published online: 18 September 1998     

A labeling scheme for young tableaux spanning representations of permutation group S(N)

A structure‐dependent labeling scheme for the Standard Young Tableaux spanning the representations of the permutation group is outlined in the present work. This scheme is used to generate the representations of a select class of permutations such as dense cycles and general transpositions of the group using minimal storage requirements. Two distinct approaches are outlined for generating the tableaux in the present labeling scheme. Detailed application has been made to two‐column Young diagram representations that are extremely useful in electron correlation studies in molecules. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 185–190, 2000     

Permutational–symmetry-adapted powers of representations of the point groups deduced from the unitary group

The construction of symmetrized powers of representations of the point groups can be deduced by decomposing the appropriate representation of the unitary group into the representations of the group of the sphere, and then mapping these representations onto the point group. The method is generally simpler than the traditional method based on the character tables of the symmetric group. As an example, the symmetry-adapted powers (N) of the representations of the icosahedral group are presented for 2≤N≤5.     

Symmetrization of eigenfunctions of angular momentum in point groups

The eigenfunctions |jm〉 of angular momentum can combine linearly to make basis functions of irreducible representations of point groups. We surmount the projection operator and find a new method to calculate the combination coefficients. It is proven that these coefficients are components of eigenvectors of some hermitian matrices, and that for all pure rotation point groups, the coefficients can be made real numbers by properly choosing the azimuth angles of symmetry elements of point groups in the coordinate system. We apply the coupling theory of angular momentum to obtain the general formulas of the basis functions of point groups. By use of our formulas, we have calculated the basis functions with half‐integers j from 1/2 to 13/2 of double‐valued irreducible representations for the icosahedral group. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 286–302, 2001     

About using the approximate fields to calculate the electrostatic potential distribution of membrane channels

By the example of gramicidine channel, a comparative analysis of different approximate representations (heavy atoms, polar protons, near-by atoms) of AMBER force field has been carried out to calculate the electrostatic potential distribution of ionic channels in biological membranes. The results obtained are compared with the potential computed in a full-atom representation. The use of approximate representations is shown to lead to estimated errors of the potential.     

Clebsch–Gordan coefficients for the group chains O ⊃ T ⊃ D2 and Td ⊃ T ⊃D2 by the method of projective representations

The spinor representations for the groups forming the chains O ? T ? D ₂ and T _d ? T ? D ₂ are constructed as projective representations. The Clebsch–Gordan coefficients are then calculated using a standard method. Projective factor systems, irreducible representations, canonical bases, and tables of Clebsch–Gordan coefficients are given. The subduction from O to D ₃ is discussed.     

DB-Curve: a novel 2D method of DNA sequence visualization and representation

The large number of bases in a DNA sequence and the cryptic nature of the 4-alphabet representation make graphical visualization of DNA sequences useful for biologists. However, existing 3D graphical representations are complicated, whereas existing 2D graphical representations suffer from high degeneracy, and many features in a DNA sequence cannot be visualized clearly. This Letter introduces a novel 2D method of DNA representation: the DB-Curve (Dual-Base Curve), which overcomes some of the limitations in existing 2D graphical representations. Many properties of DNA sequences can be observed and visualized easily using a combination of DB-Curves. The new representation can avoid degeneracy completely compared to existing 2D graphical representations of DNA sequences. Unlike 3D graphical representations, no 2D projection is required for the DB-Curve, and this allows for easier analysis of DNA sequences. The DB-Curve provides a useful graphical tool for the visualization and study of DNA sequences.     

Excess Enthalpies of (2,2,4-Trimethylpentane or Cyclohexane) + Methyl tert-Butyl Ether + tert-Amyl Methyl Ether at 25°C

Microcalormetric measurements of excess molar enthalpies at 25°C are reported for two ternary mixtures 2,2,4-trimethylpentane + methyltert-butyl ether +tert-amyl methyl ether and cyclohexane + methyltert-butyl ether +tert-amyl methyl ether. Smooth representations of the results are presented and used to construct constant-enthalpy contours on Roozeboom diagrams. Comparisons of the experimental results with estimates based on the Flory theory of mixtures are also described.     

Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method

A decomposition of Legendre polynomials into propagating angular waves is derived with the aid of an amplitude-phase method. This decomposition is compared with the ’Nussenzveig/Fuller’ so called near/far-side decomposition of Legendre polynomials. The latter decomposition requires the Legendre function of the second kind. This is not the case with the amplitude-phase decomposition. Both representations have the same asymptotic expressions for large values of \((l+1/2)\sin \theta \), where l and \(\theta \) are the polynomial degree and the angle respectively. Furthermore, both components of both representations satisfy the Legendre differential equation. However, we show the two representations are not identical.     

Many‐particle Dirac identities for arbitrary elementary spins

The eigenvalues of arbitrary conjugacy class‐sums of the symmetric group, within subspaces that contain irreducible representations with at most k rows, are considered. Explicit expressions for these eigenvalues in terms of the eigenvalues of single‐cycle class‐sums with cycle lengths up to k are obtained. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 407–411, 2000     

Bit-string methods for selective compound acquisition

Selective compound acquisition programs need to ensure that the compounds that are chosen do not contain undesirable functionality. This is easy to achieve if a supplier is prepared to provide unambiguous structure representations for the compounds that they have available: this paper discusses selection techniques that can be used when a supplier is prepared to make available only fragment bit-string representations for the compounds in their catalog. Experiments with three databases and three types of bit-string show that a simple k-nearest-neighbor searching method provides a surprisingly effective, although far from perfect, way of selecting compounds when only bit-string representations are available. A second approach, based on the use of a fragment weighting scheme analogous to those used in substructural analysis studies, proved to be noticeably less effective in operation.     

Symmetry of localized orbitals in molecules with spin-orbit interaction

We construct representations of crystallographic point groups induced by double-valued irreducible representations of their local subgroups. Using the tetrahedral molecule Bi₄ as an example, we illustrate application of the results obtained to the symmetry analysis of localized molecular orbitals obtained from relativistic calculations.Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 24, No. 1, pp. 91–95, January–February, 1988.     

Quantum mechanical study of the correlation of attack and recoil angles for the Cl + H2 reaction using the stereodirected and discrete variable representations on two potential energy surfaces

The zero total angular momentum (J = 0) S matrix elements, calculated using a time-dependent wave packet method for the Cl (2P) + H2 reaction on two different potential energy surfaces, have been matrix transformed to the stereodirected and Gauss-Legendre discrete variable representations. Although the results in the two representations are (as expected) quantitatively different with respect to the angular selectivity and specificity of the reactive process, the qualitative similarity has allowed us to draw for the first time conclusions with respect to some characteristics of the potential energy surface.     

Using n-mode potentials for reactive scattering: Application to the 6D H2 + Pt(1 1 1) problem

The accuracy of n-mode representations of potential energy surfaces (PESs) is investigated, for a reaction involving six degrees of freedom. Probabilities computed with the time-dependent wave packet (TDWP) method for reaction of (v = 0,1; j = 0) H₂ on Pt(1 1 1) employing a 5-mode (4-mode) PES show quantitative (semi-quantitative) agreement with results for the full PES. The ratio of the v = 1 and v = 0 reaction probabilities obtained with the 5-mode PES is in quantitative agreement with full PES results for most of the energy range considered. The results suggest that n-mode representations can be employed successfully to study reactions of polyatomic molecules with surfaces.     

Representation of pure fluid coexistence curves by series expansion

We give a systematic recipe for constructing the coexistence curve associated with a pure fluid described by an analytical equation of state. The novelty of our result lies not in its theoretical basis, which is well known, but in the high degree of accuracy that it will routinely yield over a broad range of density and temperature for a relatively modest expenditure of computing effort. Our results are quite general: they may be applied to any analytical equation of state. The effectiveness of our method is illustrated by applying our general solution to four widely known model equations of state: van der Waals, Dieterici, Soave-Redlich-Kwong, and Carnahan-Starling with van der Waals tail term. These models show a considerable diversity of coexistence curve shapes, and our method yields accurate representations for each model. An investigation is also initiated of the representation of experimental coexistence curves that exhibit pronounced “non-classical” behavior over an appreciable range of densities.