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Es werden Schwingkreismodelle angegeben, deren Säkulargleichungen mit denen formal identisch sind, die sich bei der Anwendung der Methode der Moleküleigenfunktionen auf das Problem der π -Elektronenzustände in Molekülen ungesättigter und aromatischer Kohlenwasserstoffe ergeben. Damit ergibt sich die Möglichkeit, die quantenmechanischen Säkularprobleme durch Messung der Eigenfrequenzen der Modelle zu bestimmen.
The ribonucleic acid of reovirus was extracted with 2 M sodium perchlorate solution and spread by the protein monolayer technique. Areas of the monolayer were transferred to support films, rotary shadowed, and observed in the electron microscope. Filaments of RNA obtained by extraction prior to spreading were similar in appearance and in distribution of contour lengths (0.2 to 1.2 μ) to those obtained by phenol extraction of the virus. Most of the filaments resulting from extraction of the virus suspension during spreading on a sodium perchlorate solution, however, were longer than 1 μ. The lengths of the longest filaments exceeded the 5 μ length predicted from chemical data for one single piece of complementary-stranded RNA in the reovirus particle.
The short filaments, 1.2 μ and less in length, fell into a tri-modal pattern of length distribution with peaks at 0.35 μ, 0.60 μ and 1.10 μ. These shorter lengths probably resulted from breakage of the intact RNA during the extraction procedures. The consistently observed pattern of length distribution suggests that they represent relatively stable subunits of the molecule.
Sodium perchlorate extracted reovirus RNA was thermally denatured in formaldehyde prior to spreading by the protein monolayer technique. Length distributions and relative numbers of filaments in the peaks of the tri-modal distribution pattern were similar to those found for unheated material when extracted prior to spreading. This similarity indicates that heating subsequent to extraction produced no further filament breakage. The thin, kinky appearance of the heated filaments, and the appearance of congruent pairs, indicated that heating had separated the strands of the complementary-stranded RNA subunits.
LANGEVIN equations of the type dn× (t)/dtn+...+c × (t)=K (t) constitute the starting point of a phenomenological fluctuation theory of irreversible processes. These equations are not constructed from transport equations (as in the older theory), but via a generalized MASTER equation from phase space mechanics. The MARKOFF processes of first and higher order defined by the various LANGEVIN equations are studied by the prediction theory of stationary stochastic processes. Instead of the variation principle of the ONSAGEB–MACHLUP theory one has the minimization of the prediction error. The mean relaxation path and the entropy of the considered processes are calculated. It is shown that the entropy consists of one part which is given by the relaxation path and another which is determined by the prediction error.
Thermal denaturation of RNA free coat proteins of tobacco mosaic virus (TMV) was studied for wildtype TMV (vulgare) and the temperature-sensitive mutant, Ni 118. The ability to form soluble aggregates as well as the optical properties (ORD, UV-difference spectra), and the sedimentation behavior were used as criteria for the native state.
At pH 7.5, I= 0.02 denaturation is reversible for both proteins. The ORD data indicate that the denatured proteins contain residual secondary structure. The “melting temperatures”, as defined by ORD measurements (cp = 0.02 mM), are 39.5 ± 1°C for vulgare and 27 ± 1°C for Ni 118 at pH 7.5, I= 0.02. By means of the aggregation test (cp = 0.05 mM) somewhat lower melting temperatures were found under the same solvent conditions. The difference between the primary structures of vulgare and Ni 118 proteins being a proline → leucine (pos. 20) replacement, the results suggest the cyclic structure of proline (20) to have a specific stabilizing function in the three dimensional protein structure. This conclusion is supported by preliminary experiments on a temperature-sensitive mutant with a threonine residue in pos. 20.
On the basis of the results obtained in a previous paper it is shown that in the thermodynamic limit the analogues of the Massieu-Plandc functions are linked with each other by means of the Legendre transformation. The existence of the limiting function φk(∞) implies the existence of the limiting function φl(∞) (l<k) under the same assumptions. Passage to the limit and derivation with respect to all independent variables commute. A statistical derivation of the thermodynamic stability condition in its most general form is given which leads naturally to a statistical interpretation of the concept of thermodynamic stability.
Within the framework of the eigenchannel reaction theory above the two-particle thresholdcluster channels are introduced. The eigenchannels of the S-matrix are used, i. e. continuum stateswhich diagonalize both the S-matrix and the nuclear Hamiltonian and represent for each reactionenergy a discrete set of coupled channel wave functions with a common (eigen-) phase. Especiallythe emission of a deuteron is discussed. It is shown that the cluster channels supplement the energy-correlated channels describing the energy partition £1 + e2 = E —Ef and that asymptotic channelorthogonality holds. The characteristic feature of the cluster channels as compared to the energy-correlated channels is that their final state interaction is not limited to a finite matching volumecomparable to nuclear sizes.
It is shown that, for all conceivable ensembles of statistical thermodynamics, at the thermodynamic limit, the frequency function of the fluctuations of macroscopic extensive parameters equals a Gaussian. The proof is based on a generalisation of Khinchin's method using the concept of "smoothed frequency functions."
The relations of the theory of real gases which have first been derived by Mayer and his co-workers can be obtained in a simple way by the functional method. In this case the assumption of the pairwise additivity of the intermolecular potential can be dropped. Apart from some new relations for distributions functions the expansion of the direct correlation functions is obtained as a power series in density with coefficients consisting of integrals over Husimi functions.
Expectation values of kinetic and potential energy are calculated for some lower antibonding orbital states of simple diatomic molecules using H2+ and HeH2+ as test cases. Common LCAO-MO theory and a scaling procedure are applied which allow an analysis of atomic orbital interactions in terms of RUEDENBERG'S1 promotion and interference effect at various internuclear distances. Contributions to the total energy at different regions of interatomic separations are discussed in detail. A characteristic increase of the kinetic energy is observed for antibonding linear combinations at distances where chemical bonding occurs.