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Volume 45, Issue 5, 01 September 1966
45(1966); http://dx.doi.org/10.1063/1.1727769View Description Hide Description
The lower‐energy electronic states of a series of saturated sulfur compounds have been investigated theoretically and experimentally. The compounds investigated fell into two categories: the monosulfide series ABS in which the substituents A and B were varied, and the polysulfide series R2S n , where n=1, 2, 3, and 4 and where R was usually CH3. The data collected included ultraviolet vapor spectra, solution spectra,solvent shifts, and vibrational data. Computations followed an approach related to that of Wolfsberg and Helmholz. This theoretical method closely approximates the experimentally observed energies in the compounds containing a single sulfur atom but encounters difficulties when two or more sulfurs are present because of the large 3d S−3d S and 4s S−4s S interactions which are predicted. It is indicated that the lower‐energy excited electronic states of all the monosulfide compounds investigated are of a molecular nature in which the 4s S and 3d S atomic orbitals of sulfur play particularly dominant but by no means exclusive roles. The lower‐energy excited states of the molecules R2S n , n=2, 3, and 4, also contain significant 4s and 3d character; additionally, however, they are of S–S antibonding nature.
Calculation of the Lowest Energy Configurations of Nucleotide Base Pairs on the Basis of an Electrostatic Model45(1966); http://dx.doi.org/10.1063/1.1727770View Description Hide Description
In this report we have taken as a point of departure the idea that the principal force acting between two nucleotide bases is the Coulomb law force between the localized formal charges on each atom of one base and each atom of the other base. The charges were computed by semiempirical quantum‐mechanical methods for both σ and π electrons separately and added together. The energies of attraction between all possible pairs of the four common bases adenine, uracil, cytosine, and guanine in all possible coplanar orientations were computed automatically on a Honeywell 800 digital computer. Twenty‐seven deep potential‐energy minima were found. Although it was not possible to find gas‐phase geometries and energies with which to compare these computed stable states, the energies in solution and known geometries in crystals, cocrystals, and polymer fibers were, with a single possible exception, completely consistent with the predicted structures and relative energies. Examination of the computed structures showed that, with few exceptions, the N–H···O and N–H···N short contacts are essentially linear, so that although the forces which led to these geometries were purely electrostatic in nature, the complexes may for convenience be thought of as being ``hydrogenbonded complexes.'' In several of the computed structures, nonlinear N–H···O and N–H···N close contacts were observed and these can be conveniently thought of as ``bifurcated hydrogenbond complexes'' which have been observed in nature although not, as yet, in purine and pyrimidine complexes.
The need for employing formal charges to reproduce the electrostatic forces was demonstrated by showing that dipole—dipole forces do not lead to potential minima and/or stable structures. Tests with a variety of computed charge densities showed that variation in the charges does not affect the equilibrium geometries or their relative stabilities although it does affect the absolute energies.
The method described therefore appears to be a satisfactory method for obtaining trial geometries for x‐ray‐diffraction analyses of crystals and fibers, and for estimating relative stabilities for use in predicting which pairings can occur where choice is possible, i.e., in codon—anticodon complexes, in hairpin‐folded RNA complexes, as well as in cocrystals.
Matrix‐Isolation Study of the Photolysis of Cyanogen Azide. II. The Symmetric Stretching Fundamental of the Free Radical NCN45(1966); http://dx.doi.org/10.1063/1.1727771View Description Hide Description
The photolysis of Ar:N3CN samples at 14°K with the full light of a cadmium arc has been found to permit complete conversion of the cyanogen azide to the free radical NCN, plus molecular nitrogen. At the high concentration of NCN thus achieved, a weak absorption appears at 2672 cm−1. The photolytic behavior of this feature and its shifts upon isotopic substitution support its assignment as the combination band (ν1+ν3) of NCN, permitting deduction of a value of 1197 cm−1 for ν1 of this species. The thermodynamic properties of NCN have been revised in accord with this assignment. The carbon—nitrogen stretching force constant approaches a value characteristic of a doubly bonded species, and the stretching interaction constant is relatively large and positive. Cyanogen azide photolyzes in both its 2750‐ and its 2200‐Å absorption regions to produce NCN+N2. However, NCN itself photolyzes when subjected to radiation near 2500 Å, producing carbon atoms in the 3 P state, which, in turn, may react with N2 to form the free radical CNN.
45(1966); http://dx.doi.org/10.1063/1.1727772View Description Hide Description
The infrared spectra of isotopic cis‐ and trans‐nitrous acid molecules including the 15N and D species have been obtained in the vapor and solid phases. All fundamentals of the normal cis and trans isomers have been identified, and previous assignments of two modes have been revised. From the isotopic frequencies of the torsion fundamental and the temperature dependence of two pairs of fundamentals, the potential‐energy minimum of the cis isomer was deduced to be 0.39±1.0 kcal/mole above that of the trans isomer. The torsion barrier above the trans‐isomer minimum was calculated to be 11.57±0.2 kcal/mole. Valence force constants for the cis and trans nitrous acids have been derived also. These constants reproduced the experimental 18O frequencies reasonably well.
45(1966); http://dx.doi.org/10.1063/1.1727773View Description Hide Description
The infrared spectra of two crystalline modifications, I and II of CH2I2, have been measured at various temperatures ranging from 3° to −196°C between 4000 and 400 cm−1. The transition between the two crystal forms I→II has been demonstrated to be monotropic.
The absence of the A 2 fundamental in Form I allows a C 2v site symmetry to be established, while for Form II the activity of the A 2 fundamental and the observed factor‐group splitting for A 1, B 1, and B 2 fundamentals is consistent only with trivial site symmetry.
Among the multiplicity of factor groups consistent with the observed crystal spectra, a choice is possible using packing considerations. Orthorhombic, (D 2h 5) or (D 2h 13), and monoclinic (C 2h 5) structure are proposed for Forms I and II, respectively, which are consistent with the ir crystal spectra and densities of the two crystalline solids.
45(1966); http://dx.doi.org/10.1063/1.1727774View Description Hide Description
Paramagnetic relaxation within the ground manifold of chromium in rutile is studied experimentally and theoretically. Relaxation proceeds solely by direct transitions between two Kramers doublets and, at low temperatures, approaches the behavior identified with the usual Orbach mechanism. The three characteristic decay times in this four‐level system are expressed in terms of two temperature‐independent parameters, which are evaluated from measurements of the longest two time constants. The decay times are independent of Zeeman field and chromium concentration and show the expected temperature variation. Strong‐field crystalline‐field theory is applied to the microwave spectrum and the relaxation process; theory explains the spectrum satisfactorily but is only marginally successful in explaining the behavior of the relaxation times.
45(1966); http://dx.doi.org/10.1063/1.1727775View Description Hide Description
Thermal conductivities of nitrous and nitric oxides, carbon tetrafluoride, silicon tetrafluoride, sulfur hexafluoride, and boron trifluoride have been determined at moderately high temperatures, ranging from about 60° to about 400°C in different cases. The experimental results (including the collision numbers for rotational relaxation) are compared with the results of several different approximate theories of heat conduction in polyatomic gases, and with values obtained for several modifications of the rough‐sphere model. Generally, the Mason—Monchick theory is found to give good agreement with experiment if the average rotational collision number in the temperature range is treated as an adjustable parameter. For N2O and SF6, the modified Eucken expression based on the diffusion mechanism theory of heat conduction was successful in accounting for the experimental results over the entire temperature range.
45(1966); http://dx.doi.org/10.1063/1.1727776View Description Hide Description
45(1966); http://dx.doi.org/10.1063/1.1727777View Description Hide Description
The thermodynamics of the lambda transition in liquid sulfur is examined in terms of the Pippard relations. Using West's specific‐heat results and critically evaluated thermal‐expansion data, the initial slope of the λ line in p—T space, (∂p/∂T)λ, is estimated as ∼−42 bar deg−1. It is suggested that the ultrasonic measurements for liquid sulfur are inadequate, especially near the lambda transition, and that there is, hence, insufficient knowledge of the compressibilities. The present estimate for (∂p/∂T)λ compares favorably with that predicted from a theory of equilibrium polymerization and the two approaches are suggested to be complementary.
45(1966); http://dx.doi.org/10.1063/1.1727778View Description Hide Description
Absorption and emission optical spectra are reported for Cm3+ in LaCl3 between 3000 and 8000 Å. These data are explained in terms of the Racah, spin—orbit, and configuration‐interaction parameters: E 0=4939.29 E 1=4621.47, E 2=17.70, E 3=399.42, ζ=2841.66, α=57.08, β=−4761.60 cm−1, respectively. Crystal‐field splitting of the ground state is observed.
45(1966); http://dx.doi.org/10.1063/1.1727779View Description Hide Description
When polyethylene has been irradiated with high‐energy radiations ultraviolet absorption bands having peaks at 229, 236, 245, 258, 264, 275, 285, 288, 307, 323, 340, 359, and 396 mμ can be observed. The bands are most clearly distinct at liquid‐nitrogen temperature, but some can only be observed after the decay of free radicals on admission of oxygen at room temperature. The assignment of these bands to conjugated polyene and polyenyl free‐radical groups is given and discussed.
Radiation Chemistry of Polyethylene. VIII. Kinetics of Growth and Decay of Polyene and Polyenyl Free Radical Groups45(1966); http://dx.doi.org/10.1063/1.1727780View Description Hide Description
Free radicals produced as intermediates during the radiolysis of polyethylene have been most frequently studied by ESR techniques. We have now used ultraviolet absorption spectroscopy because the uv absorption bands of the allyl, dienyl, and trienyl conjugated free radicals are well separated on the wavelength scale and do not overlap as do the ESR signals from these intermediates. Stable polyenes are also produced by the radiolysis and these groups can also be studied quantitatively by ultraviolet spectroscopy. In contrast to the diene groups whose concentration grows linearly with the dose, the allyl and dienyl free radicals as well as conjugated trienes grow with increasing rates as the irradiation proceeds. In fact, a statistical calculation of the triene growth reaction rate constant in terms of the diene concentration and a probability factor based on the vinylene growth rate has been quite successful. From this result and others it is concluded that trienes and allyl, dienyl, and trienyl free radicals are not primary products of the irradiation. The effect of ultraviolet light on the allyl and dienyl free radicals has also been studied. In agreement with others we find that uv light decreases the allyl free radical concentration; however, the dienyl and trienyl concentrations increase. On standing after the uv irradiation the allyl groups recover practically their initial abundance—but the dienyl and trienyl free radical concentrations continue to grow. Various mechanisms are discussed.
45(1966); http://dx.doi.org/10.1063/1.1727781View Description Hide Description
A three‐electron wavefunction containing exponential correlation factors for each pair of electrons is proposed for the ground state of three‐electron atoms. A scheme for reducing the electronic energy matrix elements to a form suitable for numerical computation is described.
45(1966); http://dx.doi.org/10.1063/1.1727782View Description Hide Description
Buff and Wilson's modification of Slater's ``new approach'' to unimolecular rate theory is used to calculate a pressure‐dependent transmission coefficient for the isomerization of a restricted rotor. The calculation takes account of the possibility that a newly produced product ``molecule'' may back react before it is collisionally stabilized.
45(1966); http://dx.doi.org/10.1063/1.1727783View Description Hide Description
The rate constant for a unimolecular reaction is obtained in alternative ways from the Liouville equation supplemented by the strong collision assumption. The final expression for the rate constant explicitly includes the details of the interactions between the collision process and intramolecular processes. The ``new‐approach'' formula, obtained by Slater on intuitive grounds, is recovered when the collisional relaxation time is evaluated from the kinetic theory collision constant.
With this assumption, the rate constant is expressed in terms of the eigenvalue problem generated by the Liouville operator of the isolated molecule in its interesting states. This expression provides a basis for a perturbative evaluation of the rate constant.
Statistical arguments are used to develop consistency theorems for checking experimental data. Reversible isomerizationreactions are discussed, and a transmission coefficient which monotonically increases with pressure is deduced.
45(1966); http://dx.doi.org/10.1063/1.1727784View Description Hide Description
Characteristic flow properties for each of the three nominal mesophase types have been empirically established. Results are given for the nematic, smectic, and cholesteric types of mesophase. Discussion is centered on mesophases or liquid crystals exhibited by pure compounds within defined temperature intervals between the regular solid and the isotropic liquid. For nematic mesophases, the prominent flow orientation, consequent low viscosity, and the unusual flow behavior near the nematic—isotropic transition are discussed. The remarkably high and shear‐dependent viscosities of cholesteric mesophases are contrasted to the simple flow properties of these cholesterol derivatives at temperatures for their respective isotropic liquids. Descriptions of flow properties for smectic mesophases are based essentially upon data on a single compound, ethyl‐p‐azoxybenzoate. Viscosity data on this compound from several sources are intercompared for the first time. Some of the new empirical conclusions given here are at variance with those reported previously in several reviews.
45(1966); http://dx.doi.org/10.1063/1.1727785View Description Hide Description
Phase transitions in one dimension are discussed from the point of view of order—disorder transitions in linear polymers using the formalism of sequence generating functions due to Lifson. If the statistical weight vj of an ordered sequence of j units has the form (lnvj )/j=a—bj −α, then a phase transition occurs when 0<α<1. As demonstrated by Fisher, this will occur, for example, if certain many‐body interactions of short range are introduced. This behavior is obtained if we consider long‐range pair potentials of the form 1/r 1+α, for 0<α<1, occurring between all the units of an ordered sequence. An exponential potential, e −γx , gives a phase transition in the limit γ→0 if interactions are restricted to the units in an ordered sequence. The occurence of a phase transition arises from the convergence of the sequence generating function and its first derivative at the value of the unit partition function equal to the statistical weight of the ordered unit. This gives rise to a bend in the curve of the unit partition function as a function of temperature and, hence, a discontinuity in the population of ordered states. End effects in an ordered sequence in one dimension (the analog of surface effects in higher dimensions) are equivalent to the case of α=1; hence, as in polypeptides, one‐dimensional systems with end effects show no true discontinuities.
45(1966); http://dx.doi.org/10.1063/1.1727786View Description Hide Description
The double‐stranded helix found in nucleic acids suggests a model where order is represented by specific, one‐to‐one bonding between two infinite chains and where disorder arises from the formation of large loops. The statistical weight per unit in an unordered sequence (i.e., a loop) is given by (1/i) lnui =a—(1/i) (b+clni). This quantity becomes large, as i is increased, slower than 1/i because of the c lni term. From the previous paper, this suggests that a first‐order phase transition may take place. It is found that this happens if c>2, in which case both U(x) (the sequence generating function for loops) and ∂U(x)/∂x converge at the point where x 1 (the unit partition function) equals u 2 (the statistical weight per unit of an infinite loop, i.e., a free chain). If 2>c>1, then U(x) converges at x 1=u 2 but ∂U(x)/∂x does not. For a loop in three dimensions, c would be about (½ for each dimension); hence, there is no discontinuity in θ, the fraction of ordered states, for a real system. However, θ does behave nonanalytically at x 1=u 2, giving a continuous or higher‐order transition. Specifically, θ does go exactly to zero in the transition region. This is a qualitative difference from infinite polypeptides where the sigmoidal transition curve goes asymptotically to 1 and 0 at the extremes of temperature. Explicit calculations are given for various values of c to illustrate the behavior of the model.
45(1966); http://dx.doi.org/10.1063/1.1727787View Description Hide Description
The effects of excluded volume on the existence and nature of a phase transition in an infinitely long double‐stranded helical polymer are discussed in relation to the recent treatment of Poland and Scheraga, which showed that, if the entropy of a closed polymer loop of 2l links (corresponding to a diassociated length of lpolymer units) varies asthen a genuine phase transition should occur if c>1 but that θ, the fraction of ordered units, would be continuous at the transition unless c>2. The standard Markoffian models of a polymer chain neglect the excluded volume and yield c=½d for a general d‐dimensional system. Numerical data on self‐avoiding lattice chains and rings are reviewed and it is concluded that c≃1.46 and 1.75 are better estimates for d=2 and 3, respectively.
The transition should thus remain continuous but it becomes sharper since it is shown that θ varies as (Tt—T)(2−c)/(c−1) when the transition temperature Tt is approached from below (and 1<c<2).
45(1966); http://dx.doi.org/10.1063/1.1727788View Description Hide Description
Electron spin resonance(ESR),paramagnetic susceptibility, and polarographic measurements have been made of copper (II) citrate chelates over a wide range of pH. The signal observed at pH 4 is typical of that found for copper (II) in a distorted octahedral environment. With increasing pH the signal becomes less intense and is replaced by a much broader spin resonance observable at relatively high concentrations of copper (II) and in frozen solutions. At pH's of about 11, a third signal is observed. The broad signal has been interpreted in terms of dipole—dipole coupling of copper (II) ions arising from dimer formation. Measurements show that the paramagnetic susceptibility is independent of pH. Solution of the spin Hamiltonian including the dipole—dipole interaction has made possible calculation of the line shape for the dimer signal. The calculations have led to a value of 3.1 Å as the distance between the copper (II) dipoles and to the conclusion that each copper (II) ion is in a | 3z 2—r 2〉 ground state rather than | x 2—y 2〉. The ESR data provides very strong evidence for the formation of a dimer in solution and allows reinterpretation of the data found in the literature. The signal observed beyond pH 11, with its partly resolved hyperfine structure at room temperature, is attributed to a monomer formed as a result of replacement of the hydrogen from the hydroxy group of the citrate anion by copper (II).