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  • 1985-1989
  • 1975-1979
  • 1970-1974  (445)
  • 1971  (445)
  • Chemical Engineering  (386)
  • Atomic, Molecular and Optical Physics  (59)
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  • 1985-1989
  • 1975-1979
  • 1970-1974  (445)
Year
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 1-11 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The finite Gaussian Expansion method for molecular integrals proposed by Taketa, O-ohata and Huzinaga has been extended to the integrals of molecular properties. The integral formulas of so-called moment, field and field gradient integrals have been derived. It has been numerically shown that in order to evaluate the field and the field gradient integrals based on Slater type orbitals, eight- or ten-term Gaussian expansions are sufficient but this method fails to attain sufficient effective numbers for the moment integrals.
    Additional Material: 3 Tab.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 239-263 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A one-dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass-springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second-order, and it is shown that the perturbation series converges in this range.An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut-off frequency of the linear crystal is determined to be very small, λ ≦ 104 sec -;1.The rate for the lattice relaxation process corresponds to a line-width λ = 6 cm -1 at 0K.An explanation for the thermal quenching of the low-temperature luminescence of SO2 is based upon induced cascade-phonon emission.
    Additional Material: 3 Ill.
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  • 3
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new interpretation of the ordinate in a Walsh diagram for a polyatomic molecule is suggested in terms of the Hellmann-Feynman theorem. This makes use of the fact that in a single-configurational MO wave function the total one-electron density is the sum of individual densities in the occupied orbitals. Walsh-type diagrams have been constructed for three different molecules, water, ammonia and hydrogen peroxide.In H2O and NH3 calculation of the force, and thus of the energy, in terms of the valence angle, is made on the assumption that the central (heavy) atom is kept fixed while each of the lighter atoms moves in a plane containing the principal symmetry axis and the relevant bond, in a totally symmetric fashion; for H2O2 the two oxygen atoms are kept fixed.The angular correlation diagrams obtained reproduce the general features of those obtained by plotting Hartree-Fock MO energies as functions of the valence angles. The conclusion emerges that the force formulation provides a satisfactory pictorial basis for understanding molecular geometry in terms of the balance between the electron-nucleus attractive forces resulting from the charge densities in the occupied MO'S, and the nuclear repulsive forces. However, in the absence of highly accurate charge distributions such an approach is unsuitable for the quantitative prediction of molecular quantities such as valence angles, force constants or energy barriers.
    Additional Material: 8 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 477-478 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 557-563 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this work, we report an all-electron SCF-LCGO-CO computation for the ground state wave-function of an infinite polyenic chain. This work demonstrates that ab initio calculations on the electronic structure of polymers become actually feasible. Our results are compared with previously obtained semi-empirical ones.
    Additional Material: 1 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 549-556 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Casimir-Polder retarded dispersion energy is calculated for non-symmetric molecules and the energy is expressed in terms of body fixed axes for the dipole transition moments on each molecule. In the special case of molecules with cylindrical symmetry the potential energy is given in terms of the transverse and longitudinal polarizabilities and in terms of the angles defining the orientation of the axes of the molecules with respect to the intermolecular direction. In the limit of no retardation (R ≪ λ) the result becomes that of London and in the opposite limit of full retardation at large R the potential energy tends to that of Craig and Power.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A kinetic model employing calculated atom and bond localization energies to approximate relative activation energies of reaction is used to analyse previously obtained experimental results for in vitro and in vivo chemical binding of polycyclic aromatic hydrocarbons to nucleic acids. It is found that in vitro linkage of hydrocarbons to DNA induced by a microsomal hydroxylating system is compatible with mechanisms involving either attack at the most reactive hydrocarbon center or attack at the most reactive hydrocarbon bond. Independent evidence leads us to favor the former mechanism. Further, the limited experimental data for in vivo linkage of hydrocarbons to DNA is found to be consistent with a model involving attack at the most reactive bond of the molecule: the “K region”. This model is supported by a close parallelism found between extent of hydrocarbons bound to DNA in vivo and the experimentally determined relative reactivities of their K regions.
    Additional Material: 4 Ill.
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  • 9
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Separated Electron Pair (SEP) model (Strongly Orthogonal Geminals) and methods for its systematic extension has been applied to the series: NH4+, NH3, NH2-, NH2- and N3-. On going from NH4+ to N3-, the SEP model, in its most general form, recovers 85-75% of the intrapair correlation energy and 60-55% of the interpair correlation energy obtainable with the given basis set. The best wave functions for each species recovered about 45-50% of the total empirical correlation energy which is expected to be very close to the basis set limit. It was apparent that the SEP model yields a set of one-electron functions that are very useful for further improvement of the wave function. This fact apparently remains true even when the SEP model itself gives very poor energies.
    Additional Material: 7 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 273-296 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The problem of intermolecular interaction is examined by using spatial wave functions and the theory of permutation groups. In the special case of interacting 2-electron systems it is proven that the Rayleigh-Schrödinger perturbation method, when starting from the ground state of the unperturbed system, could only give the physically inadmissible mathematical ground state of the complex (totally symmetric spatial eigenfunction). Then this property is considered in the case of arbitrary interacting systems and a general proof is proposed. From these results a general explanation of the inadequacy of the Rayleigh-Schrödinger expansion for the treatment of short range intermolecular interaction is proposed.
    Additional Material: 5 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 319-333 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Hartree-Fock wave functions for the He and Be isoelectronic sequences of ions are calculated using orbitals which are linear combinations of simple exponential functions. By a full optimization of the exponents and coefficients close approximations to the HartreeFock energies were obtained. To the same order of accuracy the resulting Hartree-Fock orbitals require fewer basis functions than used previously. A number of difficulties which arise in the numerical procedures as the size of the basis set is increased are analysed in detail. Similar results are obtained for the Li sequence using the Unrestricted HartreeFock method with and without projection.
    Additional Material: 7 Tab.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 497-503 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A MO-LCAO-SCF treatment is performed on water, ammonia and methane using a recently proposed approximate method.The procedure is found capable of predicting total and orbital energies in close agreement with the results of accurate computations using double ζ basis sets of Slater type orbitals.A comparison is made with the results of similar approximate ab initio procedures.
    Additional Material: 2 Tab.
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 505-512 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The various multicenter exchange, hybrid and Coulomb electron repulsion integrals that occur in molecular quantum mechanics are shown to satisfy a Poisson equation in which an overlap integral plays the role of a source distribution function. Two-, three-and four-center exchange integrals arise from four-center source functions; two- and three-center hybrid integrals arise from three-center distributions; and one- and two-center Coulomb integrals have two-center sources.
    Additional Material: 1 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 539-548 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method for the use of natural orbital iterations in limited CI calculations is discussed. This method is then applied to the ground X2II state of the nitric oxide molecule at its experimental equilibrium internuclear separation to yield the total energy, dipole moment, spin densities at each nucleus, and approximate natural spin orbitals for this molecule.
    Additional Material: 3 Tab.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 13-34 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A function analogue of the formal operator theory of Goldberger and Watson for the decay of prepared states is developed with a modification that permits treatment of degenerate, interacting intermediate states. The theory is applied to the problem of absorption of radiation by an absorber in a very intense monochromatic beam. In particular, a simple two-level absorber in a resonant monochromatic beam of sufficient intensity to induce transitions from the ground state at a rate exceeding the spontaneous emission rate from the excited state, but still lying well below the optical frequency characterizing the transition, is investigated with the conclusion that the absorption cross-section falls off with the one-half power of the incident intensity. Conditions for the possible experimental verification of this result are presented.
    Additional Material: 1 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 111-113 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 119-130 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A relation between the cluster expansion theory of many electron wave functions and the correlated wave functions method is established. In this way, the theoretical basis of the method is elucidated and the approximations involved in its application become apparent. General forms of the correlated wave function, differing in certain important respects from that form usually assumed, are derived.
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  • 19
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron density and the Fermi hole of the ground states of the atoms He, Be, Ne, Mg, Ar, Ca, Zn, and Kr are studied in the restricted Hartree-Fock approximation. The use of single Slater-type orbitals for the free atoms is also discussed.
    Additional Material: 11 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 221-234 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The absorption and emission spectra of a diatomic “molecule” connected to an unstrained linear crystal are calculated for the circumstance where the diatomic undergoes a change of equilibrium internuclear separation in the electronic transition. The expansion (or contraction) of the diatomic results in a frequency dependent line-width in the customary Lorentzian expression, and is manifested in the absorption spectrum as an asymmetric tailing to the blue, and in the emission spectrum as an asymmetric tailing to the red. The interaction of the diatomic with the lattice also produces a blue-shift of the absorption spectrum and a red-shift of the emission spectrum. An important consequence of the asymmetry is the apparent loss of integrated intensity of the line. The striking similarity, both in the width and the over-all shape, of the emission line calculated here with those observed in the Vegard-Kaplan band of N2 dissolved in rare gas crystals is discussed.
    Additional Material: 2 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 297-309 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The optimum projection technique is the determination of the best function in the space spanned by a set off f(N, S) linearly independent antisymmetric space-spin eigenfunctions of S2 obtainable from a spatial function made of a product of N-independent orbitals. This is formulated in the spin-free framework. We consider several sets of predetermined orbitals for the lithium 2S state. Both the energy and spin-density are determined for each optimum projected function. The behavior of certain results is explained in terms of the “closeness” of the ls and ls′ split-shell core orbitals.
    Additional Material: 3 Tab.
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  • 22
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 335-357 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Wave functions of the 1S (ground state), 3P and 1P states for the beryllium isoelectronic sequence have been obtained in various approximations.The HF 2p orbitals for the 1P and 3P states are similar except for Be, where the 2p orbital is quite diffuse for the 1P state.The difference between the experimental E(1P) - E(3P) and the HF E(1P) - E(3P) is 0.62 eV for Be and 1.17 ∼ 1.40 eV for B+ ∼ F5+. The disagreements are attributed to the correlation effects between the 2s and 2p electrons. This is confirmed by ci calculations.It is shown that a limited basis SCF calculation reproduces the above feature of the HF results if we treat the orbital exponents as the variational parameters. The use of the Slater values for the orbital exponents is shown to be inadequate especially for the Be 1P state.The conclusions of this paper will be useful for discussing the V-T separations of H2 and C2H4.
    Additional Material: 4 Ill.
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  • 23
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 395-409 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The model of complete loge localization is employed here to develop a practical method for handling correlation effects in atomic and molecular many electron systems. Intraloge correlation is dealt with by an independent variational treatment of pair functions which are continuous and vanish outside a given loge. It is shown that in the context of the model it is possible to compute pair correlation energies for localized single and double bonds in molecules by evaluating only modified atomic integrals. We bypass in this manner the evaluation of multicenter integrals necessary in other formalisms. In addition, the corrections to the model are discussed and in particular it is shown that part of the interloge correlation effects are already described by the loge localized wave function.
    Additional Material: 1 Ill.
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  • 24
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 455-467 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The infinite summation of intermolecular ring diagrams is extended to any pair of interacting molecules with isotropic polarizabilities. The calculation no longer requires the use of a minimal basis set. The polarizabilities α,α′ may be factorized at all orders, and an expression is derived, which gives modified Van der Waals energies. For heavy atoms the series converges if αα′/R6 is smaller than 1, R being the interatomic distance. This inequality is easily satisfied for the Van der Waals distances, and in practice the correction due to the high orders of the perturbation expansion remains weak. The role of the EPV diagrams and the connection with a configuration interaction treatment are discussed.
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  • 25
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 583-598 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The singly-excited two-electron states 1s2s 3S and ls3s 3S have been investigated by means of the variational perturbation theory procedure. The wave functions have been constructed as linear combinations of Hylleraas terms with hyperbolic factors in t, and the results obtained by carrying the computations through to 10th perturbation order and with 36(37)- 57(58)- and 85(86)-term basic sets, respectively, are reported. These results compare favourably with the corresponding best values from previous conventional variational calculations.
    Additional Material: 3 Ill.
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  • 26
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 637-646 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper a fully coupled variation-perturbation theory has been introduced for handling open-shell atomic systems in the presence of static perturbations. The static dipolar and quadrupolar polarizabilities and shielding factors for Li, Be+, B2+, B, C+, Na and Al have been calculated and compared with available results. Important sources of discrepancies in previous calculations of shielding factors have been noticed and critically examined. The dipolar shielding factors calculated in this paper show satisfactory agreement with the theoretical N/Z ratio. In the absence of any theoretical test for the quadrupolar shielding factor, the accuracy of the calculations of γ∞, should be judged in the light of the accuracy of the corresponding β∞ values.
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  • 27
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 435-453 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The classical intermolecular Rayleigh-Schrödinger perturbation expansion is used with a finite basis of simple products of single determinants. For two hydrogen molecules with a minimal basis set, one shows that the ring and ladder diagrams dominate the perturbation series. The contributions of the purely intermolecular convex and concave ring diagrams are summed at all orders. The mixed ladder-ring diagrams are also included. The series converges if the norm of the first order perturbed wave function is smaller than ½. The summation multiplies the Van der Waals-London forces by an explicit factor.
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  • 28
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 475-475 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 29
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    International Journal of Quantum Chemistry 5 (1971), S. 479-495 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The molecular orbital configuration for the ground-state of O2 generates the valence formula . “Increased-valence” formulae for triatomic and polyatomic molecules have been developed recently. In them, more electrons participate in bonding than is possible for the familiar valence-bond formulae. Using oxyhaemoglobin as an example of an oxygen carrier, various increased-valence formulae are generated for the FeO2 groups. In the low-energy formulae, the iron is bonded to the above valence formula for O2. Therefore, in contrast to the bonding schemes of Pauling and Coryell, Griffith and Weiss, little reorganization of O2 need occur on formation of HbO2. This conclusion is independent of the mode of co-ordination of iron to the O2.
    Additional Material: 1 Ill.
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  • 30
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    International Journal of Quantum Chemistry 5 (1971), S. 525-537 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Upper and lower bound expressions are derived to the second-order energy relating to an unperturbed degenerate excited state in those cases where both the first-order energy and the off diagonal matrix elements in the secular equation vanish, making use of the partitioning technique, operator inequalities and inner projection approach. These expressions, which involve an arbitrary basis, are then developed to yield reasonably good bounds to van der Waals dispersion energies for systems of the type H (first excited state)  -  other atom b (ground state). The particular choice of basis used in the development yields the latter bounds easy to evaluate by expressing them in terms of the ground state sum rule values, S(k) of atom b. This same choice is also utilized in Lindner and Löwdin's expressions [1] to obtain bounds to systems of the type H (ground state)  -  other atom b (ground state) that are comparable to those found by other more elaborate semi-empirical methods.
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  • 31
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    International Journal of Quantum Chemistry 5 (1971), S. 565-574 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: General expressions for the time-dependent probability amplitudes of the quantum states of two arbitrary, interacting atoms are calculated when one atom is initially in an excited p state and the other atom is in an s ground state. The lifetimes of the excited states and the line shape of the emitted radiation are obtained as functions of both the atomic separation and the energy difference between the excited states of the two atoms. The emission line shape is shown to be doubly peaked and to agree with the line shape of the radiation scattered by a system of two interacting atoms. The expressions for the lifetimes of the excited states are found to be identical to those obtained for the radiation scattering situation.
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  • 32
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    International Journal of Quantum Chemistry 5 (1971), S. 599-603 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By means of second quantization formalism and angular momenta coupling techniques, we show the reason why the irrational part of the coefficients of the Slater integrals Rk(ab, cd) in the expression \documentclass{article}\pagestyle{empty}\begin{document}$ (\Psi |\sum\limits_{i 〈 j} {e^2 /r_{ij} |\Psi } ') $\end{document} is common to all values of k, a, b, c, d, and depends only on (Ψ∣ and ∣Ψ′).
    Additional Material: 1 Ill.
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  • 33
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    International Journal of Quantum Chemistry 5 (1971), S. 657-668 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.
    Additional Material: 3 Ill.
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  • 34
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    International Journal of Quantum Chemistry 5 (1971), S. 683-697 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy-localization method is examined for continuous degeneracy using a grouptheoretic approach. Conditions for the degenerate orbitals are obtained and an enumeration of symmetry groups where continuous degeneracy may occur is given. It is found that the orbitals may be equivalent under operations not contained in the total symmetry group. An alternative explanation for the free rotation of the lone pairs in F2 is offered.
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  • 35
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    International Journal of Quantum Chemistry 5 (1971), S. 115-115 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 36
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    International Journal of Quantum Chemistry 5 (1971), S. 101-110 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Variable Electronegativity Pariser-Parr-Pople method has been successfully applied to calculate the potential energy curve for the formation of a 1: 1 complex between quinone and hydroquinone. A consistent evaluation of core and electronic repulsion integrals is important to obtain a meaningful curve. A computationally simple procedure has been suggested for separating interactions due to electron exchange between the components from other intermolecular interactions. In agreement with experimental deductions the preferred configuration for the quinone-hydroquinone complex is found to be one in which the molecules are in parallel planes with their C - O bonds parallel. The equilibrium separation between the molecular planes is found to be 2.3 Å and the stabilization energy in this position is 1.2 eV. In this equilibrium position forces due to electron exchange constitute the major contributing factor to the stability of the complex.
    Additional Material: 4 Ill.
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  • 37
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The [N, M] Padé approximants to functions formally associated to power series expanssions are expressed in terms of expectation values of inverse matrices. These formulae, which can be derived by the inner-projection technique, lead to a simple analysis of the properties of serveral approximation methods and their inter-relationships, in particular Gaussian integration, continued factorization and Padé approximations, which are of current interest in the calculation of physical properties. A relation with Fredholm integral equations and expansions of the resolvent is also discussed.The use of operator inequalities in a systematic fashion is particularly convenient when both the function being approximated and the coefficients of the power series have physically meaningful expressions as moments of operators.
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  • 38
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    International Journal of Quantum Chemistry 5 (1971) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 39
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    International Journal of Quantum Chemistry 5 (1971), S. 387-394 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Schrödinger equation for helium is written as a generalized eigenvalue equation which is solved for the ground state using perturbation theory. Two zero order equations are used and defined implicitly by specifying their eigenvalues and eigenfunctions. In both cases the eigenfunctions are taken to be the complete discrete set of products of eigenfunctions of the generalized eigenvalue equation for the hydrogen atom. To complete the definition the zero order eigenvalues are needed and two different intuitive choices are made. In the better of our two calculations an energy of -2.9014 a.u. is obtained for helium using the perturbation theory to second order.
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  • 40
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    International Journal of Quantum Chemistry 5 (1971), S. 469-473 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The relativistic long-range intermolecular interaction energy term of Mavroyannis and Stephen is estimated for some amino acids by using optical rotatory dispersion data and for hexahelicene by using theoretical values of excitation energies and rotational strengths. The result shows that the interaction energy may be significant for the interaction between some essentially dissymmetric chromophores such as hexahelicene, but that it is unimportant for other cases.
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  • 41
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    International Journal of Quantum Chemistry 5 (1971), S. 478-478 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 42
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    International Journal of Quantum Chemistry 5 (1971), S. 647-655 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A variation perturbation method in the Hartree-Fock scheme has been described to calculate excited 3P state wave functions of atoms. The starting wave functions are obtained from a study of the singularities in the dynamic polarizability calculation [1]. The 23P, 33P and 43P states of He, Li+, Be2+, B3+ and C4+ are studied. The results obtained are in satisfactory agreement with experimental values and with other accurate theoretical estimates.
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  • 43
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    International Journal of Quantum Chemistry 5 (1971), S. 699-702 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The super-secular-equation has been introduced by Löwdin to discuss the Schrödinger equation in terms of a linearly dependent basis. The method is shown to be particularly simple when the basis is a symmetry adapted one. By expanding the secular equation a formula giving a good estimate of the eigenvalue is obtained.
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  • 44
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    International Journal of Quantum Chemistry 5 (1971), S. 513-524 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The results of the calculations of π-π* transition energies of some free hydrazyl radicals, their ionic forms and initial hydrazines by the SCF-MO-LCAO method with restricted configuration interaction are presented. The comparison of the data obtained with the electronic spectra experimentally found, revealed that the absorption of radical solutions in the visible area was due to the electronic structure of radical molecules, the contribution of ionic forms to the absorption being negligible.
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  • 45
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    International Journal of Quantum Chemistry 5 (1971), S. 85-99 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The interaction energies in the ground (X1Σg+) and the first excited (b3Σu+)states of the hydrogen molecule were calculated using the modified Jansen and Byers Brown perturbation method. Calculations were performed for nine values of the internuclear distance R in the range 5 a.u. ≦ R ≦ 9 a.u. The present results were compared with the interaction energies calculated by four other perturbation methods as the expectation values of the H - E0 operator with the function accurate up to the first order. The results show that the method can give satisfactory values of the interaction energies.
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  • 46
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The probability interpretation of density matrics is reviewed and certain quantities suggested for study by means of diagrams. The case of a “spin-symmetric ensemble” is further discussed.
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  • 47
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    International Journal of Quantum Chemistry 5 (1971), S. 215-220 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A recent formula of Braun and Rebane for variational bounds to overlap is shown to be closely related to the methods of Rayner and of Weinhold for the same problem, and is extended to give upper and lower bounds to overlap in both ground and excited states.
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  • 48
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    International Journal of Quantum Chemistry 5 (1971), S. 67-84 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The LCAO form of the Hartree-Fock method is discussed in its application to crystals. General formulae are given for obtaining Fourier coefficient of electronic density (in direct space) as well as of the band structure (in momentum space). Finally, it is shown that in its LCAO form, Slater-Hartree-Fock equations are very simple and that this method is of interest for numerical applications. Special integrals occurring in this formalism are evaluated for a Gaussian basis in the last part of this paper.
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  • 49
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    International Journal of Quantum Chemistry 5 (1971) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 50
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    International Journal of Quantum Chemistry 5 (1971), S. 157-175 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A study of X-ray and fast electron scattering by light atoms and ions has been carried out in the first Born approximation. Coherent and incoherent scattering factors calculated with configuration interaction wave functions are compared with those obtained with Hartree-Fock wave functions. These configuration interaction wave functions involve only L-shell correlation. It is shown that the changes in the coherent scattering factors due to configuration interaction are not negligible and that the electron correlation effects on the incoherent scattering factors are important. Tables of coherent and incoherent scattering factors for light atomic systems are given.
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  • 51
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    International Journal of Quantum Chemistry 5 (1971), S. 235-238 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Tab.
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  • 52
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    International Journal of Quantum Chemistry 5 (1971), S. 265-272 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Triplet energy levels and triplet-triplet transition in benzene have been calculated semi-empirically by considering CI up to and including doubly excited configurations and using various values of the core resonance and electron repulsion integrals. The usual method of calibrating β (core resonance integral) from one of the observed transitions in the semi-empirical methods is critically examined with respect to the triplet levels of this molecule. Semi-empirical parameters are found to have a pronounced effect on the energy of the triplets and the triplet-triplet transitions; but the intensities of such transitions are quite insensitive to the choice of such parameters.Numerical results show several 3B1u → 3E2g transitions of various intensities. Out of these, the transitions which correspond energetically to the observed triplet-triplet bands are found to have low intensity. Some strong triplet-triplet bands are predicted in the far ultra violet region.
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  • 53
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    International Journal of Quantum Chemistry 5 (1971), S. 311-317 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Hellmann-Feynman theorem has been used to prove some energy relations. In this paper it is shown that in a scaled co-ordinate system both the charge density and the potential field of neutral atoms may be scaled so that the corresponding scaled quantities are independent of the atomic number. In the proof the momentum theorem of real functions is used.
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  • 54
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The equations of the coupled-pair many-electron theory (CPMET) for the closed shell systems are rederived both in the spin-orbital and orbital forms without the use of second quantization, Wick's theorem or the technique of Feynman-like diagrams. Only the Slater rules are used for the calculation of necessary matrix elements. A comparison with earlier papers shows clearly the usefulness and conceptual simplicity of the mathematical methods of quantum field theory both in the derivation of the CPMET, in spin-orbital form, and in the process of excluding spin variables.
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  • 55
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    International Journal of Quantum Chemistry 5 (1971), S. 669-682 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electronic state calculations for the ions H4+ (with symmetries D4 and C2v) and H+5 (with symmetries D5 and D2d) are made using the valence-bond method. All the configurations obtained from the given set of 1s-functions of Slater type are taken into account. Space functions are used throughout the computation (“spin-free quantum chemistry”). Preliminary quasidiagonalization of the secular equation is implemented by the construction of the multiplet eigenfunctions 2S+1Γ(α) from the initial variational functions. The results of the calculations are as follows: the ion H+4 is unstable, the ion H+5 is stable with equilibrium nuclear conformation of symmetry D2d and with the energy of dissociation into H+3 and H2 near 4 eV.
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  • 56
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    International Journal of Quantum Chemistry 5 (1971) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 57
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    International Journal of Quantum Chemistry 5 (1971), S. 381-386 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An orthonormal set of irreducible fifth-rank tensors having the required permutation symmetry is constructed. Various problems not encountered in the analogous problem for tensors of ranks two, three, four and six are discussed.
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  • 58
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    International Journal of Quantum Chemistry 5 (1971) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 59
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    International Journal of Quantum Chemistry 5 (1971), S. 35-65 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantum theory of light absorption by a pair of neighboring absorbers is developed in the point dipole approximation for the circumstance where excited states decay only by radiative damping. Comparison with classical local field theories, in which the monomers are represented by constant, frequency-dependent complex polarizabilities, shows that these local field theories are valid for non-harmonic absorbers only in the weak interaction limit, and only when there exist no states with both monomers simultaneously excited (e.g. one excited vibrationally, the other electronically) that are nearly degenerate with the single excitation states and also connected to them by appreciable transition moments. Failure of the local field theories is, thus, shown to be a consequence of the non-harmonic nature of real absorbers.Using a general relation between the level-shift function and complex polarizability, a recipe is formulated for calculating the complex polarizability and spectrum of a dimer.
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  • 60
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    AIChE Journal 17 (1971), S. 3-4 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Enthalpies of the coexisting equilibrium vapor and liquid mixtures of the ethane-n-butane-n-pentane system are computed at several pressures. Saturated liquid enthalpies are obtained by using a new multicomponent Clapeyron equation with the B-W-R equation of state and the experimental temperature-composition data for the ternary mixture. Saturated vapor enthalpies are calculated by applying the B-W-R equation to the vapor mixture. Ideal gas state enthalpies are used in both vapor and liquid enthalpy calculations.
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  • 61
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    AIChE Journal 17 (1971), S. 30-37 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: For certain classes of chemical reactions, it is possible to increase the yield of the desired products by choosing appropriate variable-volume operating policies. An analysis of the steady state and semibatch operation of a stirred tank reactor demonstrates operating policies for both the isothermal and adiabatic case to maximize the steady state yield and to produce an improved semibatch yield. Computations carried out by using an analogue computer with a digital logic expansion system demonstrate further relationships between yield increase and operating policy.
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  • 62
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    AIChE Journal 17 (1971), S. 51-56 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Models for the laminar sublayer of turbulent pipe flow are reviewed. The observations of the sublayer by Popovich and Hummel and the experimental fluctuation frequencies obtained by Shaw and Hanratty are used with the models to evaluate experimental heat and mass transfer data. The eddy diffusivity model and a parallel conductance model appear to be consistent with the experimental data.
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  • 63
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    AIChE Journal 17 (1971), S. 81-85 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effect of viscosity and diffusivity variations on concentration polarization during the ultrafiltration of protein solutions in two-dimensional stagnation flows is investigated by numerical integration of the equations of continuity and motion. It is found that these effects are surprisingly small and insensitive to the forms of concentration dependence postulated. The high Schmidt numbers and low permeation rates characteristic of these systems result in considerable simplification of the analysis and permit use of a modified Chilton-Colburn relation for predicting the onset of sludge formation at the membrane-solution interface. The predicted dependence on Schmidt number agrees with published experimental data for other boundary-layer flows and suggests the possibility of improved prediction of equipment performance.
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  • 64
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    AIChE Journal 17 (1971), S. 246-248 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Tab.
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  • 65
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    AIChE Journal 17 (1971), S. 255-256 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Ill.
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  • 66
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 67
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    AIChE Journal 17 (1971), S. 272-280 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The kinetics of simultaneous, noncatalytic solid-gas reaction systems has been analyzed in terms of the selectivity and effectiveness factor, based on the unreacted core shrinking model. The reaction systems discussed include the first-order independent, parallel, and consecutive reactions with the simultaneous influences of heat and mass transfer. The effects of various chemical and transport properties on the stability, selectivity, and effectiveness factor of the system are discussed. The pseudosteady state approximation is employed to reduce the mathematical difficulties.
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  • 68
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    AIChE Journal 17 (1971), S. 291-294 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An analysis is made of the Van der Waals forces of two different species when separated by a third continuous component. Results show that under certain circumstances, attractions as well as repulsions can exist between the two different species. The theory is applied to a fibrous bed coalescer to determine what type of material would best serve as a coalescence medium.
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  • 69
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    AIChE Journal 17 (1971), S. 335-342 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The periodic process utilizes a rapid pressure swing cycle in an adsorbent bed to effect the separation of gas mixtures. During the first portion of a cycle the compressed gas mixture flows into the adsorbent-filled column. Next, while the feed gas is restrained, an exhaust orifice is opened at the feed end of the column providing depressurization. The product stream is enriched in the component exhibiting the lowest coefficient of adsorption.A mathematical model based upon the assumption of instantaneous equilibrium between the gas phase and the adsorbed gas was formulated and solved to simulate the periodic, adsorption process. The measured nitrogen content of the product gas stream was found to correlate with the ratio of the product gas rate to the feed gas rate.At 24°C. the calculated pressure response, feed gas flow rate, and product gas composition correspond favorably with related experimental measurements for all values of the feed gas pressure, cycling frequency, and product gas flow rate within the ranges investigated.
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  • 70
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    AIChE Journal 17 (1971), S. 365-371 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The optimal control problem for multiple beds is formulated and a distributed maximum principle derived. Gradient methods are then used to synthesize the optimal control policies for some examples in three-bed isothermal and adiabatic reactors. Finally, examples are worked to illustrate the computational algorithm in adiabatic beds when optimal catalyst loading is to be determined, and when it is desired to distribute the feed in an optimal fashion between the beds. Reasonably good convergence was obtained in all the examples, so that the method appears quite feasible for determining optimal control policies in multiple reactors subject to catalyst decay.
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  • 71
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    AIChE Journal 17 (1971), S. 383-390 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The nature of flow choking has been studied as steam-water mixtures are passed through a tube with ever increasing pressure gradient. Choked flow for two-phase, one-component mixtures has been characterized with a separated flow model as resulting from maximization of the ratio of gas to liquid velocities, or slip ratio. Slip ratios at choking were measured and found to increase from 1.2 to 5.0 at 30 lb./sq.in. exit plane pressure with decrease in quality from 0.95 to 0.02. Separated models predict either 9.3 or 28.4 with no quality dependence. The difference is attributed to liquid entrainment. Flow regimes were observed to vary from purely entrained to annular entrained to slug entrained as quality decreased. Normal shock waves were observed in the free jet at qualities above 0.25. Choking flow rates were predicted with an average error of less than 2% with a stagnation energy balance model using an empirically developed slip ratio relation corrected for entrainment.
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  • 72
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    AIChE Journal 17 (1971), S. 257-257 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 73
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    AIChE Journal 17 (1971), S. 259-265 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Relationships have been developed for the calculation of second virial coefficients of polar fluids from the critical constants, acentric factor w, and fourth parameter x of the substance. Coefficients for the expansion of the reduced second virial coefficient in w and x are presented for 0.64 ≤TR ≤ 0.94. Comparisons with available experimental data indicate that good results are obtained by the method of this study for most polar fluids. The second virial coefficient for water is found to exhibit anomalous behavior. Procedures have also been established for extending the relationships for pure fluids to the second virial coefficient of mixtures containing nonpolar or polar components.
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  • 74
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    AIChE Journal 17 (1971), S. 281-285 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The modification of the Blake-Kozeny equation for porous media flow using the power law has been shown to hold for molten polymers as well as for the previous cases for polymer solutions. The present work extended the correlation of friction factor with Reynolds number an additional three decades.It was also shown, however, that the modified Blake-Kozeny equation broke down when bed shear rates were in the range of excessive curvature on the polymer flow curves (shear stress-shear rate). In such cases it is suggested that the Newtonian Blake-Kozeny equation, together with apparent viscosity data, could be used to correlate such porous media flow of non-Newtonians.Appearance of viscoelastic effects at the critical Deborah number value of 0.05 predicted earlier were not found to hold. The data of the present investigation show that such a critical value must be at least 0.19 or even higher. This result helps to resolve partially the anomalous results obtained by previous investigators.
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  • 75
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    AIChE Journal 17 (1971), S. 322-325 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Velocity profiles were calculated for transient fluid flow in the hydrodynamic entrance regions of a long narrow slit and of a long tube. The solutions were obtained by use of a linearized momentum equation. An estimate was also made of the manner in which the resistance to flow of the entrance region develops with time.
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  • 76
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    AIChE Journal 17 (1971), S. 349-352 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Torque measurements were made in experiments carried out using a cylindrical Couette apparatus with the inner cylinder rotating and the outer one stationary. The fluid systems employed consisted of distilled water, 50% distilled-water glycerine solutions, and these with several concentrations of suspended polystyrene spheres (through 40 on 70 mesh). The parameters employed by Bjorklund and Kays were found to correlate the data successfully when suspension viscosities were used for the two-phase systems.
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  • 77
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    AIChE Journal 17 (1971), S. 419-424 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A three-stage procexsss of reduction of acid chromate (HCrO4-), with NaHSO3 followed by precipitation of Cr(III) with NaOH followed by flotation with an anionic surfactant, provides 97% removal of chromium from aqueous suspensions containing 48.3 mg./liter Cr (0.929 mM). The required dosage of surfactant (sodium laurylsulfate) is 0.093 mole SLS/mole Cr, compared to a dosage of 1.1 mole cationic surfactant/mole Cr, used to ion float soluble acid chromate. The precipitate flotation process is pH dependent: below pH 6.3, soluble chromium species become appreciable and the flotation results agree with calculated soluble chromium concentrations; above pH 9.7, the charge of the precipitate is reversed, as indicated by surface potential measurements. The optimum pH range for flotation is 7.0 to 8.8. The effect of initial surfactant concentration on the flotation efficiency is established. Small quantities of calcium enhance the flotation of Cr, while higher concentrations, 0.5 mM and greater, decrease flotation efficiency. For suspensions with a doubled chromium concentration (96.6 mg./liter), the optimum pH range for flotation is lowered and narrowed to 6.3 to 6.5, indicating modifications in particle surface characteristics validated by measurements of surface potential and surfactant adsorption. Eighty-seven percent flotation is achieved at a 0.093 mole/mole ratio.
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  • 78
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    AIChE Journal 17 (1971), S. 2-2 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 79
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    AIChE Journal 17 (1971), S. 25-30 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A numerical study was performed to investigate improvement in mass transfer rates obtainable by introduction of secondary convection into a proposed membrane blood oxygenator. The three-dimensional Navier-Stokes equations were solved numerically for the velocity field in channel and the results used in the numerical solution for the local Po2 in the oxygenator. The convective diffusion equation solved is nonlinear, in addition to being three-dimensional, because of the presence of red cell oxygen sinks.The convection introduced was generated by moving one wall of the blood flow channel laterally to the main flow. Decreases in blood side film resistance up to 5 × 104 were predicted. In the presence of moderate to strong convection, the limiting factor on oxygenation rate is imposed by the membrane situated between blood and gas phases. It appears that a considerable decrease in required blood priming volume would be possible if the method discussed here were implemented.
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  • 80
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    AIChE Journal 17 (1971), S. 57-65 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effects of aliphatic alcohols on mass transfer and drag coefficients of a carbon dioxide bubble were investigated in very dilute aqueous solutions. A high speed photography technique provided an almost continuous record of the bubble volume, shape, and oscillation, as related to the height of the bubble in the liquid and the time elapsed from the moment of its release. The results showed that the concentration, molecular size, and structure of the investigated alcohols have a pronounced effect on mass transfer as well as drag coefficients of the rising bubble. The significance of these effects with respect to idealized models of a highly circulating bubble and a solid sphere was considered, and a functional relationship was found to exist. This relationship may be applied to systems more complex than a single bubble.
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    AIChE Journal 17 (1971), S. 75-81 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A steady state experimental technique for measuring fluxes of the components and diffusivities in binary liquid systems has been developed. Steady state diffusion is established through a sintered glass diaphragm of ultrafine porosity with a known concentration difference across the diaphragm. The concentrations are maintained by a flow of solution on one side of the diaphragm and an infinite sink on the other side. The fluxes and diffusivities are calculated from the measured flows and compositions. A syringe pump capable of delivering extremely small flow rates with good reproducibility is used to pump the solution past the sintered glass diaphragm. The diffusion cell design permits an accurate control of pressure drop across the diaphragm so that fluxes can be measured both with and without pressure gradients. The diffusion cell was calibrated by using the hydrochloric acid-water system.Three binary systems, ethanol-benzene, aniline-benzene, and aniline-carbon tetrachloride were chosen for diffusion studies. Diffusivity-composition data for these systems at 25°C. were used to test the existing correlations for the concentration dependence of binary diffusivity. Of these, the empirical correlation of Vignes (11) represents the data satisfactorily. In addition, experimental molar diffusion flux ratio data for the above systems at 25°C. with no pressure gradients are reported and found to be essentially equal to the ratio of molar volumes of the components.
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  • 82
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    AIChE Journal 17 (1971), S. 101-103 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Analyses of stretching of a viscoelastic liquid have been interpreted as showing that there is a maximum stretch rate to which the material can be subjected, and several physical phenomena have been explained on this basis. It is shown here theoretically and experimentally that the concept of a limiting stretch rate does not have general validity.
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    AIChE Journal 17 (1971), S. 115-121 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The stability of a capillary liquid bridge of given volume between two small, solid, equal, separated spheres is investigated by formulating and treating a minimum energy problem in the calculus of variations and by experiment. A conjecture is made that in the case of two solutions one and only one is minimizing, and that the case of one solution represents the limiting stable bridge. This theory agrees accurately with our stability experiments. Furthermore, it is possible to predict the cohesive force. For the case of spheres in contact, the theory presented here is in agreement with some experimental work and also with the theory of Fisher and calculations of cohesive force based on Melrose and Wallick's solution to the bridge problem. For the case of separated spheres, the agreement with the only available experimental data is excellent except for close separations.
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  • 84
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    AIChE Journal 17 (1971), S. 122-130 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Bubble size and distribution of bubble sizes were studied in an air fluidized bed, 11.5 in. in diam. and 3 ft. high, by taking motion pictures of the bubbles breaking the top surface of the bed and by determining the size of the bubbles from the film. The distribution of bubble volumes at a given bed height was expressed as a gamma distribution with parameters obtained from the observations. A statistical mechanical method proposed by Hulburt and Katz for studies in agglomeration of particles was used in the mathematical formulation of the problem. A proposed mechanism of bubble growth by coalescence in gas fluidized beds resulted in a one parameter model. Comparisons of the distributions predicted by the model to the experimentally obtained profiles yielded the parameter of the model.
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    AIChE Journal 17 (1971), S. 148-153 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new approach to separation calculations has been developed which has many practical advantages. The equations of conservation of mass and energy and of equilibrium are grouped by stage and then linearized. The resulting set of equations has a block-tridiagonal structure which permits solution by a simple technique. Thus a new way to apply the Newton-Raphson technique to separation calculations is devised. The method has been tried on a number of problems chosen to exhibit characteristics which cause other solution technique to fail. Most problems are solved with ten iterations or less.
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  • 86
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    AIChE Journal 17 (1971), S. 171-176 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Direct thermal parametric pumping separations of a NaCl-H2O-ion retardation resin system have been investigated. Experimental breakthrough curves and batch parapump runs were used to determine the lumped-parameter mass transfer coefficient λ and its dependence on velocity and temperature. Computer simulation of additional batch runs verified both the model and the STOP-GO algorithm used to solve it. Computer estimates of open-system behavior are presented.
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  • 87
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    AIChE Journal 17 (1971), S. 191-198 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A correlation based on conformal solution theory has been developed for the excess properties of the nitrogen-oxygen-argon systems. A better method for calculating the conformal parameters makes possible the simulataneous correlation of the three excess properties FE, HE, and VE. Each binary is characterized by a k12, c12 set which represents corrections to the geometric and arithmetic mean combination rules. These binary constants predict the ternary data. Also, the correlation based on data at one atm. (77° and 84°K.) predicts the FE data accurately up to the critical points (110° to 120°K.).
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  • 88
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    AIChE Journal 17 (1971), S. 215-219 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The problem treating an irreversible, first-order chemical reaction in an isothermal, tubular reactor operating under steady, non-Newtonian, laminar flow is studied. Numerical results for the eigenvalues, eigenfunctions, expansion coefficients and bulk concentration are reported for Ostwald-de Waele and Prandtl-Eyring fluids. Results show that chemical conversion in a tubular reactor may be significantly influenced by the non-Newtonian characteristics of a fluid.
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    AIChE Journal 17 (1971), S. 252-254 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
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  • 90
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    AIChE Journal 17 (1971) 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 91
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    AIChE Journal 17 (1971), S. 258-510 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 92
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    AIChE Journal 17 (1971), S. 285-288 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The following nucleation rate and growth rate relationships for the aqueous, continuous, cooling crystallization of potassium dichromate were determined from experimental crystal size distributions: J = 3.9 × 1010 (C - Ceq)0.9; r = 3.0 × 103 (C - Ceq)1.7. Since nucleation rate is of lower kinetic order than growth rate, higher levels of supersaturation will yield crystal distributions with a larger mean size. Therefore for this system, batch or plug-flow reactors are preferred to continuous-stirred tanks.
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    AIChE Journal 17 (1971), S. 308-312 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An experimental facility for vapor-liquid equilibrium measurements at high pressures (100 to 15,000 lb./sq. in. abs.) and ordinary temperatures (100° to 300°F.) on multicomponent mixtures is described. The vapor-liquid phase behavior of a six-component hydrocarbon mixture, which simulated a natural gas and a condensate, was studied with this apparatus. Measurements were made at 150° and 250°F. and pressures ranging from 100 lb./sq. in. abs. to the single-phase pressures for these systems and temperatures.
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    AIChE Journal 17 (1971), S. 326-335 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method has been developed for applying classical minimization techniques to forms of algebraic performance indices for use in optimal adaptive control systems. Essentially, the derivative of a general objective function is constrained to be equal to the integrand of a desired integral performance index. This generates a set of linear algebraic equations, the solution of which results in an algebraic objective function which is explicit in the system parameters. Derivatives of this function can be taken with respect to the controllable parameters, set equal to zero, and solved for the settings which minimize the performance index over time. Alternatively, the function itself may be searched for its minimum on the controllable parameters.The method has been applied to a stirred tank chemical reactor with an exothermic first-order reaction in which heat removal was accomplished by cooling coils. The cooling water flow rate was controlled by a proportional-plus-integral controller and by a three-mode controller. The adaptive control system adjusted the controller settings periodically. The plant, which was third-order, was controlled to a second-order dynamic reference model. The responses to both initial offsets (start-up problem) and disturbances in system parameters were investigated. In all cases, the adaptive control system performance was markedly superior to that for the unadapted, ordinary feedback control system.
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    AIChE Journal 17 (1971), S. 353-356 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Available generalized correlations of fugacity coefficients of nonpolar liquids are reexamined in their lower temperature ranges, and these correlations are extended to a reduced temperature of 0.35. Generalized functions are constructed from literature data on vapor pressures and liquid densities. Two sets of functions are presented with w and zc, respectively, as third parameter. The results fulfill a need for basic information in the engineering of cryogenic systems.The same vapor pressure data are correlated in a generalized form down to Tr = 0.35 to give a one-parameter family of reduced vapor pressures curves. The correlation is compared with data on simple fluids, normal fluids, polar substances, and quantum fluids.
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    AIChE Journal 17 (1971), S. 379-383 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An analysis is made of diffusion and chemical reaction in an isothermal multicomponent fluid. Transient gas-phase reaction in a one-dimensional nonflow system and steady state gas-phase or surface reaction in a tubular reactor are considered. The equations are linearized around some state away from equilibrium. Multicomponent and binary diffusivity expressions are used and a series of reactions of varying complexity is considered. The possibility of oscillations increases as the complexity of the reactions is increased. These oscillations occur with time in the nonflow system and with space-time in the tubular reactor, and it appears that any reacting mixture which oscillates in one of these two systems will also oscillate in the other.
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    AIChE Journal 17 (1971), S. 402-409 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Pressure drag coefficients of spheres in a cubic packing of equal spheres have been determined at Reynolds numbers of 27,000, 10,000, 5,000 and 2,500, where NRe is based on superficial air velocity and a sphere diameter of 7 cm. Two cubic arrangements were used: in the regular arrangement, the mean flow was parallel to one of the principal axes, while in the skewed arrangement, the mean flow made equal angles with the three principal axes of the packing.The pressure drag coefficient of the central sphere has been measured for each of the 12 banks in the regular arrangement, and the effect of bed length has been determined for lengths varying between 1 and 12 banks. The pressure drag coefficient for the central sphere and the overall pressure drop in the skewed arrangement were found to be lower than for the regular arrangement at the same Reynolds number. From the distribution of local pressure measurements, the separation and reattachment points on the central sphere in each bank were determined, indicating that the boundary-layer behavior on a sphere in a packing is similar to that over a single sphere, when allowing for the effects of turbulence and of pressure gradient.
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    AIChE Journal 17 (1971), S. 425-427 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Sufficiency conditions for equality constrained extrema are formulated in terms of a transformed set of coordinates by means of a generalized inverse of the constraint Jacobian matrix. This procedure produces a computationally simple and efficient method for testing sufficiency of a previously established stationary point. Computation of Lagrange multipliers is also facilitated by the method.
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    AIChE Journal 17 (1971), S. 446-454 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The kinetic patterns of sorption, desorption, and sorbate exchange have been studied for several C2-C5 hydrocarbons in synthetic zeolites of the mordenite, T and Y structures. The rate observations can best be represented by a model of sorption on interstitial sites in the solid, rather than by a model based on the analogy with macroporous sorbents. Two cases of interstitial diffusion have to be distinguished for this purpose. The number of vacant sites changes in time during the process of sorption, whereas it can remain constant if one sorbate is exchanged against another one. Rate measurements for both types of processes are reported and their interrelation is discussed.
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    AIChE Journal 17 (1971), S. 470-475 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new method is presented for the determination of adsorption equilibria for pure components and mixtures both at high and low pressures. Isotherms for carbon dioxide, methane, ethane, propane, i-butane, n-butane, i-pentane, and n-pentane on activated carbon (Columbia grade NXC 8/10) and on silica gel (Mobil Sorbead H) at 75°, 125°, 200°, and 300°F. are given for pressures ranging from below atmospheric to 1,000 lb./sq. in. Also, adsorption equilibria data are presented for several multicomponent mixtures of the light hydrocarbon gases.The data collected were correlated with good accuracy by use of the two-layer kinetic model developed previously by Gonzalez.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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