bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Statistical Mechanical Models of Elastic Polyelectrolytes and Proteins
Authors: Hill Terrell L. 
Published: January 2005

Three statistical mechanical models are developed for use in connection with the problem of muscle action. In addition, the models should apply to certain other systems, for example, polyelectrolyte fibers or gels, fibrous proteins in general, and ion exchange resins.
The first model is a statistical mechanical version of the ``autone'' model of Varga, Szent-Gyorgyi, Gergely, and Laki, but we extend the theory to include the effect of an adsorbed substance (e.g., ATP) on the length of the elastic element.
The second model is a charged rubber-like cylindrical fiber. The charges on the molecular chains of the network may be permanent or may result from the adsorption of ions from solution (e.g., hydrogen ions, or ATP). The approximate free energy of the system is computed by combining the Flory-Rehner swelling theory, the Fowler-Langmuir adsorption model, and an electrostatic free energy based on a ``smeared'' uniform charge density inside the fiber (electrolyte is also present), as suggested by the work of Hermans and Overbeeck. If the radius of the cylinder is large compared to the radius of the Debye-Hückel ionic atmosphere, it is not necessary to linearize the Boltzmann factor in the Poisson-Boltzmann equation. From the free energy of the system one obtains the interconnected pressure-volume, length-tension and adsorption isotherm relations. Important special cases are isotropic swelling (zero tension) with the gel under pressure or not, and the elasticity of the fiber (with adsorption) under zero pressure. When the fiber is constrained to a constant radius, it is possible to get a phase change in the length-tension curve (see below).
The third model is an equilibrium statistical theory of the well-known α—β transformation in fibrous proteins (such as keratin and myosin). Adsorption of ions from solution and electrostatic effects can be included here as well as in the preceding model, but the discussion is concerned primarily with an analysis of the elasticity of a sheet of polypeptide chains with α- and β-units statistically scrambled, taking into account as a nearest-neighbor problem in statistical mechanics (using the quasi-chemical method) lateral β—β hydrogen bonds and vertical α—α hydrogen bonds. From the theory it would appear that critical phenomena, phase changes (for example, a considerable increase in length at constant tension, representing a phase change from primarily vertical α—α crystallization to primarily lateral β—β crystallization) and hysteresis are to be expected. These phenomena are observed experimentally, though modified in most cases by superimposed non equilibrium effects. It is pointed out that a fiber operating (on stretching and retraction) between the two ``ends'' of a phase change would be particularly suitable in the muscle problem, because of the sensitivity of the length of the fiber at constant tension to small changes in environment (e.g., pH).
Although a few illustrative examples are given, further applications are reserved for a later paper.
The Absolute Quantum Yields of the Fluorescence of Chlorophyll Solutions
Authors: Forster Leslie S. , Livingston Robert 
Published: January 2005

An integrating sphere has been adapted to the measurement of the quantum yield of the fluorescence of solutions of pigments. The intensities of the fluorescence and of the absorbed light were determined separately with a thermopile.
Chlorophylls a and b dissolved in various solvents have been studied with this apparatus over a range of concentrations, and the measured yields corrected for autoabsorption. The yield for chlorophyll a is 0.25 and is in general independent of solvent and excitation wavelength. The yield for chlorophyll b is 0.11 for ether solutions and 0.06 for methanol solutions. The absolute fluorescent yields of solutions of fluorescein, eosine, magdala red, and rubrene were also measured. These results are in reasonable agreement with the published values of the yields for the same compounds.
Dipoles on a Lattice : the Spherical Model
Authors: Lax Melvin 
Published: January 2005

The statistical treatment of a lattice of classical dipoles, electric or magnetic, has been intractable because of the ``strong'' condition that all dipoles have a fixed length. The spherical model consists in replacing the above strong condition by the weaker condition that the sum of the squares of the dipole vectors have the correct value, thus permitting some, but not much, fluctuation from the true situation.
The previous work of Berlin and Thomsen using the spherical model and nearest neighbor interactions is generalized to include a mixture of long and short range interactions. The evaluation of the partition sum in the presence of long-range forces requires care because some of the eigenvalues depend on specimen shape. A formula has been derived for the susceptibility, however, in which the shape dependence is explicitly shown to cancel. In fact, it is proven that in the spherical model a permanent dipole lattice is equivalent to an induced dipole lattice with a certain effective polarizability. Expansion of this polarizability in inverse powers of the temperature shows precise agreement to terms of order (1/T)3 with an exact evaluation of the corresponding expansion coefficients.
All qualitative results are in agreement with those of Berlin and Thomsen. One- and two-dimensional lattices show no transition. A simple cubic lattice (the case they treat) shows an antiferroelectric transition bounded by a critical field curve E=Ec[1—(T/Tc)]½.
The effective field and its application to an elementary quantum mechanical treatment of the ferromagnetic problem are described.
N-Representability Problem for Fermion Density Matrices. I. The Second-Order Density Matrix with N =3
Authors: Smith Darwin W. 
Published: January 2005

The N representability problem is the problem of how to recognize whether a given pth-order reduced density matrix is derivable from an antisymmetaic N-particle wavefunction ψ by integrating out all but coordinates from ψ*ψ.
The conditions under which a given second-order density matrix is N representable by a three-particle wavefunction are discussed.
Correlation Energy Calculation for the 1Σg+ Ground State of the Nitrogen Molecule
Authors: Grimaldi François 
Published: January 2005

Starting from a molecular Hartree—Fock wavefunction an extensive configuration-interaction calculation (201 configurations) has been carried out for the 1Σg+ ground state of N2. The matrix elements of the electrostatic Hamiltonian were calculated automatically. Both Brillouin—Wigner and Rayleigh—Schrödinger perturbation expansions, carried to a sufficient order, are shown to be good tools to find the lowest eigenvalue and eigenvector of very large matrices. Fifty percent of correlation energy is attained by this exact treatment.
Since the second-order Rayleigh—Schrödinger perturbation expansions are a good approximation to the exact results, it supplies, in addition to a good test for the selecting of configurations, a practical means of evaluating pair correlations. By using this approximation and 3043 configurations, 66% of the correlation energy was found.
Molecular g Value, Magnetic Properties, and the Ground-State Electronic Structure of Fluoroacetylene
Authors: Weiss V. W. , Todd H. D. , Lo Mei-Kuo , Gutowsky H. S. , Flygare W. H. 
Published: January 2005

The first-order molecular Zeeman effect observed in the J=0→J=1 rotational transition of FC≡CH gives the magnitude of the molecular g value perpendicular to the molecular axis to be 0.0071±0.0004. When combined with an estimate of the molar susceptibility, the molecular g value leads to an average value of r2 for electrons from the center of mass. The result is 〈ψ0|Σiri2|ψ0〉=37.9×10−16 cm2. An upper limit on the magnitudes of the proton and fluorine spin—rotation interaction constants of 6–8 kHz was established by high-resolution, microwave linewidth studies of the J=0→J=1 transition.
The ground electronic state of fluoroacetylene is described by a set of 11 hybrid molecular orbitals, employing various hybridization and ionic parameters. The average values of nine one-electron operators were calculated using the 16 atomic-orbital functions included in the minimal basis LCAO MO set. The Coulson—Barnett expansion technique was used in the calculation of the two- and three-center integrals. The calculations of the one-electron operators were made for considerable ranges in the adjustable parameters of the wavefunction.
A best-fit wavefunction was obtained by fitting six of the one-electron operators to the experimentally determined properties. It was then used to compute the average value of r2 and the H and F diamagnetic shielding. The latter are combined with available chemical-shift data to yield the H and F paramagnetic shielding and spin—rotation constants. The results for the spin—rotation constants are consistent with the upper limit established by the linewidths. Also, the theoretical value of r2 agrees very well with that determined experimentally. Several features of the electronic structure and ground-state wavefunction are discussed. For instance, we found negligible s character in the fluorine atomic orbitals participating in the F–C sigma bound but a significant fluorine contribution to the F–C pi bond.
Excited States of Nucleotides and Singlet Energy Transfer in Polynucleotides
Authors: Guéron M. , Eisinger J. , Shulman R. G. 
Published: January 2005

We have measured the absorption, fluorescence, and phosphorescence spectra of nucleotides at 77°K. The order of decreasing energies is A, U, T, G, C for the singlet, and U−, C, G, T−, A, T for the triplet. Besides the quantum yields of fluorescence and phosphorescence, we also determined the yield for intersystem crossing to the triplet, using the amplitude of the Δm=2 triplet ESR signal. We find internal conversion occurring from both the singlet and triplet states. From the excitation energies in the neutral and ionized molecules, the stability of the ionizable proton in the excited states can be compared to that in the ground state, and the results are applied to the question of proton transfer from T to A in DNA.
From a discussion of the various cases of intermolecular energy transfer for singlets, and considering the broadband spectra of the nucleotides, it is shown that Förster's ``very weak case'' is applicable. We emphasize that two subcases must be distinguished, depending on whether transfer occurs faster than, or slower than, vibrational relaxation. The justification of the approximations in our treatment is given in the Appendix.
Assuming dipole—dipole coupling, the rate of transfer is estimated in the nucleotides in the ``before relaxation'' subcase. In the ``after relaxation'' subcase the rate of transfer is calculated using the emission data obtained in this study. In a majority of the pairs of nucleotides, ``after relaxation transfer'' at the Watson—Crick distances is allowed. These considerations are discussed briefly in reference to transfer in polyadenylic acid and DNA.
Mössbauer Spectrum of Fe2+ in a Square-Planar Environment
Authors: Clark Michael G. , Bancroft G. Michael , Stone Anthony J. 
Published: January 2005

The Mössbauer spectrum of high-spin Fe2+, square planar coordinated by oxygens in BaFeSi4O10, has been studied in the temperature range 80°—650°K. The spectrum, a quadrupole doublet, was analyzed by computer fitting, and the results statistically tested using the concept of internal and external consistency. Quadrupole splitting and center shift data are reported for the whole range 80°—650°K, and the widths and relative intensities of the lines have been measured at 80° and 295°K. The quadrupole splitting has been successfully correlated with the magnetic susceptibility and electronic spectrum of Fe2+ in BaFeSi4O10. The lattice contribution is found to be slightly larger in magnitude than the valence contribution, and of opposite sign. By studying both randomized and oriented samples the sign of the quadrupole splitting has been determined experimentally, and the anisotropy of the recoil-free fraction measured. The temperature variation of the center shift has been analyzed in terms of the second-order Doppler shift, and information on the vibrational motion of the iron atom obtained. The theoretical basis of the method used for analyzing the second-order Doppler-shift data is briefly discussed.
A correlation between center shift values and coordination number for minerals containing high-spin ferrous iron is noted; and interesting observations concerning the linewidths, and the effects of heat treatment on the Mössbauer spectrum of gillespite, are reported.
Vibronic Coupling in the Exciton States of the Rigid-Lattice Model of Molecular Crystals
Authors: Philpott M. R. 
Published: January 2005

The vibrational structure of the Frenkel exciton states of a molecular crystal is investigated by a variational technique using a rigid-lattice-model Hamiltonian. The spirit of the weak coupling formalism is strictly adhered to by constructing crystal wavefunctions from products of isolated molecule wavefunctions so that the only parameters of the theory are Franck—Condon factors and vibrational frequency shifts. The basis set consists of all vibronic, i.e., single particle, states belonging to the same electronic state transforming according to a given wave vector, plus a set of two-particle states in which vibronic and ground vibrational excitation occupy different sites. Interactions between single-particle states are treated in detail, as are interactions between one- and two-particle states. However, part of the interaction between certain two-particle states is neglected and this makes the treatment progressively less accurate for higher vibrational states and stronger coupling. Electron exchange effects, coupling of excitons to photons, higher electronic states, and ion-pair states are not considered.
It is shown how each element of the conventional weak coupling energy matrix is supplemented by terms which account for the interaction between one- and two-particle states as well as interactions among the two-particle states. For a given wave vector each single-particle state is accompanied by a family of two-particle bands which rapidly increases in size for higher vibrational states. In the weak coupling limit the families are widely separated, while intermediate coupling corresponds to two-particle bandwidths comparable with the vibrational spacing. The onset of strong coupling corresponds to overlapping of adjacent families.
Further Investigations on the Microwave Spectrum of NSF: Evaluation of the Molecular Force Field, Centrifugal Distortion Constants, and the Dipole Moment
Authors: Cook Robert L. , Kirchhoff William H. 
Published: January 2005

The measurements of the microwave spectrum of NSF have been extended to include transitions involving J as high as 40 and the centrifugal-distortion effects have been accounted for. By combining the analysis of the vibrational and rotational spectra, the molecular force field for NSF has been calculated and the following quadratic potential constants, in millidynes per angstrom, were obtained: f1=10.703, f2=2.872, Fα/d2=0.411, and f2α/d=0.014. Here 1 refers to the SN bond, 2 to the SF bond, α to the NSF bond angle, and d is the geometric mean of the SN and SF bond distances. It was found that the data were too insensitive to calculate f1α and f12 and these constants were assumed to be zero.
The dipole moment was calculated from the Stark effect of the 51,4→42,3 transition and was found to be 1.902±0.012D, where the uncertainty represents the spread in the value of the dipole moment obtained from different methods of treating the data.
Near-Infrared Band Progressions of Ring Molecules and Ring-Puckering Motion
Authors: Ueda Toyotoshi , Shimanouchi Takehiko 
Published: January 2005

A series of bands found in the 2900–2600-cm−1 region of infrared spectra of 2,5-dihydrofuran, trimethylene oxide, cyclopentene, 2,5-dihydrothiophene, 2,3-dihydrofuran and 2,3-dihydrothiophene are assigned to the ring-puckering difference spectra, of which the reference band is the CH2 symmetrical stretching vibration.
The assignments were confirmed for 2,5-dihydrofuran and trimethylene oxide, for which the pure ring-puckering bands had already been analyzed in detail. From the difference spectra the puckering potential of cyclopentene was determined as V(Z)=0.551×104Z2+0.533×106Z4+0.554×103exp(−100Z2) with the central barrier of 244.6 cm−1, and that of 2,5-dihydrothiophene was V(Z)=0.1396×105Z2+0.6637×106Z4, where V is in cm−1 and Z is in angstroms.
The spectrum showed that 2,3-dihydrofuran has the nonplanar structure with the potential barrier height of about 86.8 cm−1. For 2,3-dihydrothiophene tentative assignments were given and the puckering potential was calculated.
Reduced Density Matrices of Atoms and Molecules. II. On the N-Representability Problem
Authors: Weinhold Frank , Wilson E. Bright 
Published: January 2005

For the 2-matrix of the ``double occupancy configuration interaction'' (DOCI) wavefunction described in a previous paper, the N-representability problem is stated in terms of algebraic equations relating the density-matrix elements λi, Λij, λij to the wavefunction coefficients CK. An operator formalism is developed and used to derive a number of necessary N-representability conditions for both diagonal and off-diagonal elements of the DOCI 2-matrix. These conditions consist principally of certain linear inequalities for the diagonal elements and nonnegativity requirements for the eigenvalues of certain synthetic matrices built from both diagonal and off-diagonal 2-matrix elements. A hole-particle duality is noted and used to expedite the derivations. Four special cases for which all the N-representability conditions can be explicitly given are used to show that the conditions obtained are not yet sufficient for DOCI N representability.
It is then proved that the DOCI diagonal N-representability conditions apply with equal necessity to the diagonal elements of any N-representable 2-matrix. These new necessary conditions for the general N-representability problem are given a simple and satisfying probability interpretation in terms of the Pauli exclusion principle for fermion pair distributions. Off-diagonal conditions are generated by requiring that the diagonal conditions be maintained under all possible unitary transformations of the orbital basis set. This latter procedure is illustrated by an application to the DOCI 2-matrix which accounts for all off-diagonal conditions previously obtained.
Thermodynamic Properties of Octafluoropropane from 14°K to Its Normal Boiling Point. An Estimate of the Barrier to Internal Rotation from the Entropy and Heat Capacity of the Gas
Authors: Pace E. L. , Plaush A. C. 
Published: January 2005

The heat capacity of octafluoropropane has been measured from 14°K to its normal boiling point of 236.42°K for a sample of greater than 99.99 mole % purity. The following heats of transition and transition temperatures were found: Crystal I—Crystal II, 849.8 cal/mole, 99.37°K; Crystal I—liquid, 114.1 cal/mole, 125.46°K; and liquid—vapor (1 atm), 4723 cal/mole, 236.42°K. The vapor pressure up to 1 atm pressure is represented by the equation log10Pmm=20.85981−(1584.677/T)−4.750509 log10T,and the density of the liquid between 197° and 234°K by the equation d(g/ml)=2.471−0.003628T.
The value of the entropy of the ideal gas at 1 atm pressure at the normal boiling point calculated from the calorimetric data is 88.75 cal/ (mole·°K).
An average potential barrier of 3300 cal/mole restricting the rotation of the trifluoromethyl groups is estimated from the entropy computed from molecular data. A reasonable but not an entirely satisfactory interpretation of the heat capacity of the gas is also obtained with a barrier of the above order of magnitude.
Surface Tension and Energy of Liquid Xenon
Authors: Smith B. L. , Gardner P. R. , Parker E. H. C. 
Published: January 2005

The surface tension of liquid xenon was measured in the temperature range 189°—286°K by a capillary-rise method. The results may be represented by γ=γ0[1 − (T/289.74) ]p, with γ0=54.6±0.1 dyn cm−1 and p=1.287±0.017.
The experimental method is discussed and the results compared with existing theory and experimental data.
Intersystem Crossing in Gaseous Molecules
Authors: Robinson G. Wilse 
Published: January 2005

The theory of electronic relaxation in the solid phase is discussed in terms of gaseous molecules. Two limits are examined—the ``small-molecule limit'' (α limit), where electronic relaxation cannot occur in the free molecule, and the ``big-molecule limit'' (ω limit), where electronic relaxation at a rate virtually identical with that in the solid can take place in the absence of any external perturbation. An ``intermediate case'' (μ case) is described where no relaxation can occur in the completely free molecule, but where only extremely minute perturbations are required to induce such a process. Intersystem crossing B2u1→B1u3 in benzene is close to the borderline between the ω limit and the μ case. Although the concepts are somewhat inexact quantitatively because of the difficulty in estimating matrix elements and the vibrational density-of-state function, the theory does indicate that the zero-point level of the 1B2u state could behave like a μ case, while the excited vibrational levels of this electronic state, those mainly reached in past experiments, may lie in the ω limit. Available experimental data support the idea that the higher vibrational levels of the 1B2u state of benzene very likely lie in the ω limit, but cannot shed light on the behavior of the zero-point level.
Theoretical expressions for the rate of intersystem crossing, the fluorescence lifetime, and the fluorescence yield as functions of pressure are worked out. Theory shows that in both the α limit and in the μ case the absolute fluorescence yield approaches unity in the limit of zero pressure. For the ω limit, the absolute fluorescence yield can very well be less than unity even for a molecule in free space. Some new experiments are suggested by the theoretical conclusions.
Correlation of Ionization Probabilities with Geometric Charge Cross Sections
Authors: King A. Bruce 
Published: January 2005

The previous study of the ionization probabilities has been extended to include additional high molecular weight unsubstituted polynuclear aromatic hydrocarbons. The charge distributions for these ions were calculated using Hückel molecular orbitals. These charge distributions were used to calculate a geometric charge cross section by an impact parameter approach assuming a simple classical collision model. The geometric charge cross sections were found to correlate with the molecular ionization probabilities for the unsubstituted compounds, suggesting that the relative ionization probabilities for these compounds result from purely geometric considerations.
The polymethylbenzene series was studied to determine whether the marked effect of substituent groups is purely geometric or whether additional group effects exist. It was found that a 3.3-fold greater group efficiency of methyl groups relative to the ring carbon atoms was necessary to correlate with these data. A number of nitrogen heterocyclics were also studied. The single-ring heterocyclic series showed a significant reduction of the ionization probability with nitrogen substitution. These results did not agree with the HMO calculations suggesting that ionization of the π-electron system does not play a dominant role in the threshold ionization probability for these compounds. By contrast, the quinolines and phenazine gave agreement with the geometric charge cross section due to their lower π-ionization energies.