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  • 11
    Electronic Resource
    Electronic Resource
    Reply to "Comment on: ‘Translation–rotation invariance for N-particle systems: Internal coordinates and search for stationary points in reduced spaces' '' (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 3581-3581 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450193
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  • 12
    Electronic Resource
    Electronic Resource
    Translation-rotation invariance for N-particle systems: Internal coordinates and search for stationary points in reduced spaces (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 3500-3506 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Using the translational and rotational invariance of the energy, we show that for an N-body system there exists a subset of 3N−6 Cartesian coordinates such that the derivatives of the energy of a given order with respect to the members of this subset form an independent and complete set. That is, all other derivatives can be calculated knowing these independent derivatives. We further show that this subset of coordinates can be chosen to be a bonafide set of internal coordinates. Since these coordinates are a subset of the 3N Cartesian coordinates, they are orthonormal and uniform. Applications have been made of such internal coordinates in algorithms which search for stationary points on potential energy surfaces. It is shown that the surface walking algorithms are exactly separable for these coordinates. Thus the problem can be reexpressed in terms of (3N−6) Cartesian variables without the annoying zero eigenvalues of the Hessian (of the energy) matrix corresponding to the translational and rotational eigenvalues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449154
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  • 13
    Electronic Resource
    Electronic Resource
    Translational and rotational symmetries in integral derivatives (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 4566-4576 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Based upon the invariance under translations and rotations of quantum chemical one- and two-electron integrals, a method for obtaining a complete set of independent relations among integral derivatives is presented. Due to the unitary form of the operators corresponding to finite translations and rotations, this analysis is generally applicable to all orders of integral derivatives. It is shown that the number of dependent integral derivatives is equal to the number of such independent relations. These dependent integral derivatives can thus be straightforwardly determined in terms of the remaining derivatives which must be explicitly calculated. For example, out of a total of 21, 45, and 78 second-derivative integrals for the two- , three- , and four-center cases, respectively, only 1, 6, and 21 such integral derivatives need be explicitly calculated. The set of such independent and dependent integral derivatives can be chosen in a manner which imposes no restrictions on the allowable geometries of the nuclear positions. The special case of colinear nuclear centers is also separately analyzed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448713
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  • 14
    Electronic Resource
    Electronic Resource
    Physiologische Untersuchungen an Micrococcus denitrificans Beijerinck und auxotrophen Mutanten (1966)
    Springer
    Archives of microbiology 53 (1966), S. 107-131 
    Details
    ISSN: 1432-072X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Summary 1. The penicillin-method for isolation of auxotrophic mutants from Micrococcus denitrificans strain 11 has been standardized. A preincubation of 8 hrs was found necessary for using up the intracellular nitrogenous compounds. A single treatment with 1000 IU penicilin/ml lasting 6 hrs led to a 4-fold enrichment of the mutants. An effective enrichment could be attained through repetition of the penicillin treatment for at least three times. 2. The isolated mutants required methionine or leucine. The methionine-requiring mutants were blocked before either cysteine or cystathionine. 3. Growth experiments with the intermediate products of methionine-synthesis showed that the cystathionine pathway was present in strain 11. Indications were obtained that cysteine might be formed from methionine through an unknown pathway and not by reversal of the methionine-synthesis via cystathionine. 4. Cell-free extracts of the wild-type and mutants catalyzed the cleavage of cystathionine with the formation of homocysteine, pyruvic acid, and ammonia. The reaction is stimulated by pyridoxal-phosphate. The pH-optimum lies at 9,0; the K m -value with dl(+)-allocystathionine was found to be 4.8·10-3 m.
    Notes: Zusammenfassung 1. Die Penicillinmethode zur Isolierung auxotropher Mutanten wurde für Micrococcus denitrificans Stamm 11 standardisiert. Eine Präinkubation von 8 Std war erforderlich, um intracelluläre Stickstoffverbindungen aufbrauchen zu lassen. Eine einmalige 6 stündige Behandlung mit 1000 IE Penicillin/ml führte zu einer vierfachen Anreicherung der Mutanten. Eine wirksame Anreicherung auxotropher Mutanten wurde durch dreimalige Wiederholung der Penicillinbehandlung erzielt. 2. Die isolierten Mutanten benötigten Methionin bzw. Leucin. Die methioninbedürftigen Mutanten waren vor Cystein oder Cystathionin blockiert. 3. Wachstumsversuche mit den Intermediärprodukten der Methioninsynthese deuteten darauf hin, daß Stamm 11 über den Cystathioninweg verfügt. Es ergaben sich Hinweise dafür, daß Cystein auf einem noch unbekannten Weg aus Methionin und nicht durch Umkehr des Methioninsyntheseweges über Cystathionin gebildet wird. 4. Zellfreie Extrakte des Wildtyps und der Mutanten katalysieren die Spaltung des Cystathionins unter Bildung von Homocystein, Brenztraubensäure und Ammoniak. Die Reaktion wird durch Pyridoxalphosphat stimuliert. Das pH-Optimum liegt bei 9,0; der K m -Wert mit dl(+)-Allocystathionin als Substrat beträgt 4,8·10-3 m.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00413036
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  • 15
    Electronic Resource
    Electronic Resource
    The coupled-cluster method with a multiconfiguration reference state (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 19 (1981), S. 207-216 
    Details
    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 coupled-cluster approach to obtaining the bond-state wave functions of many-electron systems is extended, with a set of physically reasonable approximations, to admit a multiconfiguration reference state. This extension permits electronic structure calculations to be performed on correlated closed- or open-shell systems with potentially uniform precision for all molecular geometries. Explicit coupled cluster working equations are derived using a multiconfiguration reference state for the case in which the so-called cluster operator is approximated by its one- and two-particle components. The evaluation of the requisite matrix elements is facilitated by use of the unitary group generators which have recently received wide attention and use in the quantum chemistry community.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560190203
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  • 16
    Electronic Resource
    Electronic Resource
    Polarization Green's function with multiconfiguration self-consistent-field reference states (1979)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 16 (1979), S. 1209-1237 
    Details
    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
    Description / Table of Contents: Le formalisme des fonctions de Green de polarisation dans la notation utilisant les superopérateurs de Goscinski et Lukman a été réétabli avec un état de référence MC-SCF pour obtenir le métrique des superopérateurs. Les avantages potentiels de cet état de référence plus général ainsi que certains points faibles inhérents associés aux états de référence utilisés traditionnellement dans les théories de perturbation Hartree-Fock ou Rayleigh-Schrödinger sont discutés brièvement. L'hermiticité des superopérateurs est analysée dans le cadre des états de référence MC-SCF. Utilisant une notion d'ordre propre à cet état de référence on présente des formules explicites et des procédés de calcul pour la réalisation de cette théorie des fonctions de Green, qui sont spécialisés pour inclure des termes consistants jusqu'au second ordre.
    Abstract: Der Formalismus für Green'sche Funktionen von Polarisierungstyp in der Superoperatorbezeichnung von Goscinski und Lukman wird mittels eines MC-SCF-Referenzzustands hergeleitet. Die möglichen Vorteile mit diesem allgemeineren Referenzzustand und gewisse mit den in den traditionellen Hartree-Fock- oder Rayleigh-Schrödinger-Störungstheorien verwendeten Referenzzuständen verbundene eigene Schwächen werden kurz diskutiert. Die Hermitizität der Superoperatoren wird im Rahmen des MC-SCF-Referenzzustands analysiert. Mittels eines für diesen Referenzzustand geeigneten Ordnungsbegriffs werden explizite Formeln und Rechnungsverfahren für die Implementierung dieser Theorie von Green'schen Funktionen vorgelegt und spezialisiert um Glieder bis zur zweiten Ordnung einzuschliessen.
    Notes: The polarization Green's-function formalism in the superoperator notation of Goscinski and Lukman is re-derived using a multiconfiguration self-consistent-field (MC-SCF) reference state to establish the superoperator metric. The potential advantages of employing this more general reference state in Green's-function theories and certain inherent weaknesses associated with the traditional Hartree-Fock or Rayleigh-Schrödinger perturbation theory reference state choices are briefly discussed. The Hermiticity of the superoperators is analyzed within the framework of the MC-SCF reference state. Using a concept of order appropriate for this reference state choice, explicit formulas and computational procedures for the implementation of this Green's-function theory are presented and specialized to include terms consistent through second order.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560160604
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  • 17
    Electronic Resource
    Electronic Resource
    Discrete spatial symmetries in energy derivatives (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 31 (1987), S. 3-16 
    Details
    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: Based upon the invariance of N-particle systems under discrete operations of reflection, inversion, and rotation by 2π/n, a method for obtaining complete sets of relations among energy derivatives of all orders has been presented. The method is based on the criterion that, for a discrete symmetry operation such as reflection across a plane; the change in energy due to simultaneous arbitrary displacements of each particle is equal to another set of “conjugate” displacements of all particles. Applications of the above relations for particular molecular systems possessing a combination of symmetry operations is also presented. Here, via the row echelon analysis, the number of independent derivatives are found, and simple symmetry relations that allow determination of the remaining derivatives are presented. For example, for a homonuclear diatomic molecule with D2h symmetry only 1 of the 6 first derivatives and 1 of the 21 second derivatives need to be independently calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560310103
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  • 18
    Electronic Resource
    Electronic Resource
    Discrete spatial symmetries: Redundant coordinates and search for stationary points in reduced spaces (1988)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 33 (1988), S. 27-40 
    Details
    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: Given the invariance of an N-body system under discrete operations of reflection, inversion, a rotation by 2π/n, and the corresponding relations among the derivatives of energy, we have constructed through an invertible transformation a set of active and redundant coordinates. Movement along the active coordinates preserves all symmetry relations. We show that algorithms for locating stationary points or for calculating reaction paths are exactly separable in these active and redundant coordinates. We further show that this formalism is equally applicable when equations of constraints among coordinates are specified for the movement of particles. This includes geometrical constraints on bond lengths, angles, substituent group internal rotations, etc. This formalism enhances the efficiency since (laborious) cartesian derivatives need to be calculated only for the active variables and that the problem is reduced in term of m(≤3N) variables. We apply this procedure to obtain the equilibrium geometry of H2O molecule within the subspace of C2v symmetry configurations ab initio derivatives.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560330104
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  • 19
    Electronic Resource
    Electronic Resource
    Path integral approach to chemical dynamics: A test case of H + O2 ↔ OH + O reaction (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 311-323 
    Details
    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: Determining mechanisms of chemical reactions involves finding dynamical paths between desired (given) reactant and product states. We have developed a method that is based on recasting the principle of stationary action into a general and computationally tractable form that yields all dynamical paths connecting the initial and final configurations of the system. Thus the method has advantages over the traditional initial-value trajectory calculations for solving such boundary value problems. We give some examples of reaction paths for H(2S) + O2(3Σg-) ↔ OH(2II) + O(3P) on the ground state potential energy surfaces HO2(2A″).
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560400831
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  • 20
    Electronic Resource
    Electronic Resource
    Construction of orthogonal subspaces (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 39 (1991), S. 747-754 
    Details
    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 orthogonalization procedure is presented that allows construction of at least (n-m) vectors orthogonal to {Xj}, j equals; 1, m, by linear combinations solely among {ηi}, i equals; 1, n, n〉m, and 〈Xj/ηi〉≠0. An important application of the procedure is in effective core potential methods for which valence orbitals can be constructed that are orthogonal to the core orbitals and yet involve no component of the core. Thus, a separate calculation for only the valence electrons can be performed without any explicit reference to the core electrons (orbitals).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560390510
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