bluuebunny/crossref_metadata_2025_split huggingface dataset:
Reformulation of the Virial Series for Classical Fluids
Authors: Ree Francis H. , Hoover William G. 
Published: January 2005

The usual graphical representation of the virial coefficients is reformulated in terms of graphs containing not only Mayer f functions, but also f̃ functions [f̃≡f+1≡exp(−φ/kT)].
This reformulation has three main advantages:
(1) The number of integrals of topological graphs contributing to the virial coefficients is reduced; this simplifies numerical calculations.
(2) In Mayer's formulation none of the star integrals contributing to the virial coefficients (for hard potentials, at least) could be ignored; each made a nonnegligible contribution. In the new formulation (again, for hard potentials) many integrals make negligible (or even zero) contributions; the extensive cancellation of positive and negative terms found in Mayer's formulation is reduced.
(3) Several new ways of summing the virial series by successive approximation are suggested by the new formulation. One such way is worked out, in the first three approximations, for gases of hard parallel squares and cubes; the third approximation reproduces the first five virial coefficients exactly.
The reformulation is not restricted to the virial series alone. We also generalize our treatment to the radial distribution function. It can be applied to any series whose coefficients are integrals of graphs.
Spectral Emissivities and Integrated Intensities of the 1.87-, 1.38-, and 1.14-μ H2O Bands between 1000° and 2200°K
Authors: Ferriso C. C. , Ludwig C. B. 
Published: January 2005

Spectral emissivities of the overtone and combination bands of H2O in the 1- to 2-μ region have been measured between 1000° and 2200°K. The hot water vapor samples were produced in a small supersonic burner using H2 and O2. The measurements were made at the exit of the burner where the interactions of the hot gas jet with the ambient atmosphere are small. The variation of the spectral emissivities of H2O in the optically thin absorption region as a function of temperature are given for a total pressure of 1 atm and a constant amount of H2O in the optical path.
The integrated intensities of the bands have been determined from the emissivity spectra at the various temperatures. The values of the integrated intensities of the 1.87-, 1.38-, and 1.14-μ H2O bands at 273.2°K are 26.0, 21.2, and 1.92 (cm—2·atm—1), respectively. The integrated intensity variations with temperature of the bands have been used to determine the absolute intensity contributions from the numerous overtone and combination transitions which make up these bands.
Nuclear Magnetic Resonance Study of Cobalt—Chlorine Complexes in Methanol
Authors: Luz Z. 
Published: January 2005

An NMR study of complex formation of Co+ + ion with Cl— ion in methanol between —80° and +80°C is reported. This work is an extension of the study reported in the preceding paper (referred to as IV) to a much wider temperature range. It is shown that, below +15°C in solutions containing up to 1M chloride ion, the monochloro octahedral complex is the only cobalt—chlorine compound formed. The equilibrium constant for the formation of this complex as function of temperature and chloride ion concentration was determined. From the broadening of the NMR peaks rate of methanol exchange between the solvation shell of the monochloro complex and the bulk solvent were obtained. Evidence for the formation of ion pairs of the form [Co(MeOH)6]+ +Cl— is presented.
Above +15° the blue tetrahedral complexes became progressively more important. In this temperature range the NMR and optical spectra can be correlated, but the large number of complexes allow only a qualitative analysis of the NMR results.
X 1Σg+—A 3Σu+ Excitation Energy in N2
Authors: Huber Lee M. , Thorson Walter R. 
Published: January 2005

The valence-bond method is employed to calculate the energy separations of the potential surfaces for the X 1Σg+ and A 3Σu+ states of the nitrogen molecule for internuclear distances between the respective equilibrium positions (i.e., 1.094 to 1.29 Å). The radiative π—π* transition between these states gives rise to the well-known Vegard—Kaplan bands. The N2 molecule is treated as a 10-electron problem. Separation into σ and π groups of electrons is made and excitation assumed to affect only the latter. The self-energy of the σ core is not explicitly evaluated. The σ—π interactions are nearly insensitive to variations in the σ-core bonds, a result which justifies the variational calculation of the π energy plus σ—π interactions as a valid determination of the π-electron wavefunctions.
The resulting energy separation has an almost constant error, 1.1 to 1.3 eV lower than experiment; the energies themselves are more sensitive to the wavefunction than is the separation. The invariance of the error, both as obtained by several widely different calculations and as a function of internuclear separation, suggests strongly that it arises from correlation energy of two possible types, discussed below. Such an error may be ``typical'' of the error involved in a σ—π separation treatment for π—π* intersystem transitions. Within the error involved, the results justify the ``chemical'' description of these states of the nitrogen molecule.
Gas-Phase Photolysis of Methyl Iodide. Reactions of Hot Methyl Radicals with Added Organic Compounds
Authors: Doepker Richard D. , Ausloos P. 
Published: January 2005

The photolysis of CH3I and CD3I at 2537 and 3130 Å has been investigated in the presence of CD3CH3, C2D6, CH3CD2CH3, CD3CH2CD3, C4H10–C4D10 (1:1) mixtures, (CH3)3CD, (CH3)3CCD3, C6H6, C6H12, CH3OCH3, CH3COOCD3, CD3OH, C2D5OH, and CD3CH2OH. All mixtures were saturated with iodine in order to prevent the formation of methane by the reaction of thermal methyl radicals. It is shown that, under these conditions, the measured quantum yield of methane formation can be considered to be the probability that a ``hot'' methyl radical with 32 kcal will react with CH3I or the additive. The following observations were made: (1) Intramolecular and intermolecular isotope effects are of minor importance. (2) The probability of abstraction of an H or a D atom from a molecule by a ``hot'' methyl radical increases with the number of available H or D atoms, or with a decrease in the ΔH of the reaction. For instance, it is seen that the relative probabilities per atom for abstraction of a primary, secondary, or tertiary H atom in a hydrocarbon molecule are 1:3.6:10.0. A variation in wavelength, from 2537 Å to 3130 Å, lowers the methane quantum yield by a factor of 10 but does not greatly affect the relative probabilities of abstraction from different sites within a molecule. (3) The quantum yield of methane in the photolysis of CH3I or CH3I—hydrocarbon mixtures is nearly twice that observed for CD3I or the corresponding CD3I—hydrocarbon mixtures at the same wavelength.
It is concluded that systematic studies of this type may prove to be useful in determining a priori the probability of reaction with other related organic compounds.
Chemical Shifts, Ring Currents, and Magnetic Anisotropy in Aromatic Hydrocarbons
Authors: Dailey B. P. 
Published: January 2005

Both the chemical shifts of nuclear magnetic resonances and molecular diamagnetic susceptibilities have their origin in the electronic currents induced by an external magnetic field. For the aromatic hydrocarbons detailed chemical-shift measurements and extensive measurements of the magnetic anisotropies are available to aid in a study of the validity of various theories connecting magnetic properties with magnetic electron currents.
The available experimental data seem to present a definite paradox. The chemical shifts due to ring currents are theoretically directly proportional to the values of Δχ, the anisotropy in the diamagnetic susceptibility; yet the experimental values of Δχ are much larger than those calculated from theory, while the experimental chemical shifts are substantially smaller than the theoretical ones.
Hoarau has suggested that only a part, χL, of the total anisotropy Δχ arises from the π electrons involved in the ring current and that one should add Δχσ, a contribution from the electrons in the σ bonds, and Δχp, the contribution due to the localized p electrons. The SCF—MO calculations of χL for benzene give a value of approximately —30×10—6, which is only about half the experimentally observed value of —59.7×10—6. Rough calculations are presented which indicate that the contributions of the σ and localized p electrons are large enough to account for the observed values of Δχ and χz for the aromatic hydrocarbons.
An analysis of the chemical shifts of the aromatic hydrocarbons shows that they are in agreement with a Δχ value for benzene of approximately —31×10—6 in good agreement with the SCF—MO value of χL. Calculations of the chemical shifts due to localized magnetic anisotropies show that they are quite small and can frequently be neglected. In calculating ring current contributions to the chemical shift in NMR spectroscopy it is recommended that the SCF—MO value of χL, —30×10—6, be used in place of the classical value, —49.5×10—6.
Study of Molecular Orbital Degeneracy in C7H7
Authors: Silverstone H. J. , Wood D. E. , McConnell H. M. 
Published: January 2005

The paramagnetic resonance of the cycloheptatrienyl radical (C7H7) has been observed in single crystals of thiourea and naphthalene and in polycrystalline thiourea, naphthalene, cycloheptatriene, and argon at temperatures ranging from 4.2° to 300°K. The spectra are of two types: (a) high-temperature spectra—eight equally spaced lines with splittings in the range 3.5–4.1 G; (b) low-temperature spectra—highly anisotropic spectra which are markedly different for each crystalline environment. The transitions from (a) to (b) occur within 5°K, and the transition temperatures are 40°, 20°, and around 13°K in thiourea, naphthalene, and cycloheptatriene, respectively.
The high-temperature spectra are readily accounted for in terms of seven equivalent protons and a uniform electron spin distribution about the ring. The high-temperature spectra thus provide evidence that there is no significant static (Jahn—Teller) distortion of C7H7. The uniform spin distribution around the molecular ring is brought about by the combined effects of rapid molecular reorientation about the seven-fold axis, plus the crystalline electric-field splitting of the orbital degeneracy. That is, in a sense, the crystal field splitting ``locks'' the spin distribution to the lattice, and molecular reorientation moves the nuclei relative to a fixed spin distribution. The low-temperature spectra correspond to the electronic ground state of (nonreorienting) C7H7, as determined by the crystalline electric field. The observed low-temperature spectra of C7H7 in naphthalene are compared with spectra calculated using the Hückel, valence-bond, approximate unrestricted Hartree—Fock LCAO—MO, and Pariser—Parr approximations to the molecular electronic structure of C7H7. The observed spectra appear to be in semiquantitative agreement with calculations based on the Hartree—Fock and Pariser—Parr approximations. However, detailed comparisons between these theoretical calculations and experiment are uncertain since both vibronic interactions as well as torsional molecular oscillations have an effect on the low-temperature spin distribution.
Strong Collision Model for Energy Transfer in Systems of Oscillators
Authors: Hoare Michael 
Published: January 2005

Transition probabilities are formulated for single quantized oscillators which interact with a similar heat bath such that vibrational energy is conserved and randomly distributed between collision partners. Explicit solutions have been obtained for the corresponding relaxation and mean-passage-time problem, and results for the latter are compared with both ``equilibrium'' behavior and the predictions of the Landau—Teller scheme. Deviations from the equilibrium hypothesis tend toward a well-defined limit as the level spacing decreases to zero but are effectively negligible except where dissociation occurs within about 10 collisions.
It is shown that the notion of random energy distribution leads to a ``principal relaxation time'' of two collision intervals, which seems likely to be a lower bound for realizable energy-transfer models.
Study of Two-Center Integrals Useful in Calculations on Molecular Structure. V. General Methods for Diatomic Integrals Applicable to Digital Computers
Authors: Wahl Arnold C. , Cade Paul E. , Roothaan C. C. J. 
Published: January 2005

The calculation of the electronic structure of atomic and molecular systems involves the determination of a number of integrals over the electronic coordinates. These calculations are feasible only by the use of high-speed, large-memory digital computers.
This discussion is based on a culmination of experience obtained in this laboratory with regard to methods useful in the evaluation of two-center integrals by means of digital computers. The ground work for this paper, in terms of the analysis employed, is given in a series of papers by Roothaan, Ruedenberg, and Jaunzemis, but significant changes have evolved which offer considerable improvements and more economical calculations. The analysis presented here is especially the result of efforts to take full advantage of the capabilities of present digital computers. The methods advocated here are thought to be near optimal to a completely reliable and automatic computation of the electronic integrals in question with the desired accuracy. A not insignificant aspect of the methods given here is that an approach was sought which is unfailingly reliable and accurate regardless of the AO's involved in the integrals and at the same time as economical as possible.
Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment
Authors: Marcus R. A. 
Published: January 2005

In its usual classical form, activated-complex theory assumes a particular expression for the kinetic energy of the reacting system, one being associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic-energy expression. A rate equation of the customary form is obtained: krate=(kT/h)exp[−(F‡−Fr)/kT], where F‡ is the free energy of a system constrained to exist on a hypersurface in n-dimensional space and Fr is the free energy of the reactants. The usual derivation is then reinterpreted, in terms of geodesic normal coordinates, to be somewhat more general than it appears.
Normally, rotation—vibration interaction is neglected, as in the above derivation, although not in treatments of some special reactions in the literature for which the centrifugal potential is important. A derivation is given which includes the influence of this centrifugal potential but which omits Coriolis effects.
Role of Electrostatic Energy Barriers in the Expansion of Lamellar Crystals
Authors: Hurst C. A. , Jordine E. St. A. 
Published: January 2005

The method of Fourier transforms has been used in the investigation of the electrical forces between the platelets of the montmorillonite crystal. The potential-energy curve, as a function of the distance 2D between the platelets, is shown to have two turning points. The one with the smaller value of D is a minimum and is therefore a point of stable equilibrium, while the one with the larger value of D is a maximum and is a point of unstable equilibrium. For small separations of the platelets the potential energy is positive and increases with decreasing separation, while at large separations the potential energy is negative and decreases linearly with increasing separation. The foregoing is shown to be in complete accord with accumulated experimental findings over the years. Physically, the basis of the shape of the energy curve is that at small separations the repulsive ion—solvent and ion-image forces prevail whereas at intermediate distances the attractive surface-ion terms become important; finally the surface—surface terms dominate at larger distances.
It is also shown that by suitable expansions the Fourier transform method can be used to generate the required sets of electrostatic images developed in an earlier work by the optical analog.
Appearance Potentials of the Fragment Ions from CF3I
Authors: Dorman F. H. 
Published: January 2005

The ionization-efficiency curves for the parent and fragment ions from CF3I have been examined using Morrison's second differential method. Accurate appearance potentials can be obtained only for some ions, i.e., CF3I+=10.5±0.1 eV, CF3+=11.5±0.1 eV, and I+=13.4±0.1 eV, but not for the ions CF2I+, CF2+, and CF+ by this or any other method.
The kinetic energy of the fragment ions near their threshold has been determined using a retardation method.
Integral Hellmann—Feynman Theorem
Authors: Kim Ho Jing , Parr Robert G. 
Published: January 2005

In the Born—Oppenheimer approximation, it is shown that for any molecular isoelectronic process the total energy change, excluding nuclear kinetic energy, is given by the formula ΔW=ΔVnn+ ∫ ρ(1)H′(1)dτ(1).Here ΔVnn is the nuclear—nuclear repulsion-energy change, and H′ is the change in the one-electron nuclear—electron attraction operator. The function ρ(1) is the normalized transition density for the change, the integral over Electrons 2 through N of the product of the initial and final electronic wavefunctions, multiplied by N and divided by the overlap integral between the initial and final wavefunctions. For infinitesimal changes, it is demonstrated that this theorem reduces to the conventional Hellmann—Feynman theorem.
A corresponding differential equation and its equivalent variational principle are derived. Use of approximate wavefunctions in the several formulas is discussed, and various possible applications of the theorem are indicated. The theorem is shown to provide a rigorous basis for a pseudoclassical theory of molecular vibrations, and shown to indicate why electron-correlation effects ordinarily do not control molecular deformation.
Nuclear Relaxation in Coupled Spin Systems
Authors: Noggle Joseph H. 
Published: January 2005

The density-matrix theory of relaxation for coupled spin systems in the liquid state is reviewed and equations are derived for the calculation of nuclear Overhauser effects and free decay. The theory is applied to the results of saturation-recovery experiments on 2,3-dibromothiophene (CS2 solution). The equations derived and the experimental method are in principle applicable for coupled spin systems with any number of spins. The saturation-recovery experiment proved capable of separating the contributions of internal and external dipole interactions to the relaxation of the protons in 2,3-dibromothiophene. The rotational correlation time for internal dipole—dipole relaxation was measured to be τc=(2.2±0.2)×10−12 sec.
The theory of correlations among the interactions of two (or more) spins with external spins is discussed. The external interactions of the two protons on 2,3-dibromothiophene were found to be 75% correlated.
Molecular Orbital Theory for Octahedral and Tetrahedral Metal Complexes
Authors: Basch Harold , Viste Arlen , Gray Harry B. 
Published: January 2005

Self-consistent charge and configuration (SCCC) molecular orbital calculations are reported for 32 selected octahedral and tetrahedral first-row transition-metal complexes containing halide and chalcogenide ligands. It is found that for the range of metal oxidation states II through IV, Fσ, chosen to fit the experimental Δ, is a function of only the metal atomic number for constant Fπ. In the range of formal metal oxidation numbers V through VII, Fσ is also a function of oxidation number.
Calculated and observed trends in covalency, Δ values, and first L→M charge-transfer energies are compared. The conclusion is drawn that the molecular orbital method, in its present formulation, gives a reasonable account of the ground states and low excited states in simple metal complexes.
Calculation of Chemical Reaction Probabilities from Elastic Scattering Data
Authors: Rosenfeld J. L. J. , Ross J. 
Published: January 2005

We discuss the validity of the expression PR(E,b)=1−[σobs(E,χ)/σ0(E,χ)]previously used in reactive systems of the kind A+BC→AB+C to evaluate the probability of reaction PR for given relative kinetic energy E and impact parameter b. The nonreactive differential scattering cross section σobs(E, χ) is derived from measurements as a function of the relative scattering angle χ and the elastic scattering cross section σ0(E, χ) is obtained from an exp−6 potential made to fit the observed scattering in angular regions apparently unaffected by reaction, as the rainbow region in some examples.
By using an optical model and assuming the validity of a semiclassical description, we show that this expression holds whenever | dPR/db |≪2k(π−χ)[1−PR(E,b)];  E=12μk2ℏ2.
The simple expression for the probability of reaction is also shown to be approximately valid in a first-order distorted wave approximation and random phase approximation for σ0(E, χ).
Vapor Pressures of the Deuterated Ethanes
Authors: Van Hook W. Alexander 
Published: January 2005

The vapor pressures of all 10 deutero—protio-ethane isomers C2HiD6—i (0≤i≤6) have been measured over the temperature range 115° to 200°K [∼1 mm C2H6 to 1600 mm C2H6] by direct manometry. The isotope effects are inverse and go through maxima between 125° and 140°K. At the maxima they are on the order of 1.2% per D atom. Deviations from the law of the mean are small, but for the three sets of equivalent isomers 1,1- and 1,2-C2H4D2; 1,1,1- and 1,1,2-C2H3D3; and 1,1,1,2- and 1,1,2,2-C2H2D4 significant differences in vapor pressure are observed. The more unsymmetrically substituted compound has the higher vapor pressure in all cases.
The data are interpreted in the light of the statistical theory of isotope effects in condensed systems. A model calculation is made within the framework of this theory in its harmonic-cell approximation using reasonable force fields. It is necessary to invoke temperature-dependent force constants for the low-energy (u=hv/kT&lt;2π) modes in order to rationalize the temperature dependency below 140°K. The agreement between the model calculation and experiment is excellent.
The calculations reveal that the torsional motion, which must be blue shifted on condensation, is the single most important contributor to the isotope effects between equivalent isomers.
The results constitute the second independent confirmation of the statistical theory of isotope effects in condensed systems as applied to molecules exhibiting higher-order quantum effects.
Vacuum-Ultraviolet Photochemistry. IV. Primary Processes in the Photolysis of Water at 1470 Å
Authors: Stief L. J. 
Published: January 2005

Water has been photolyzed at 1470 Å in the absence and presence of ethylene which acts as a scavenger for hydrogen atoms. Mixtures of D2O and C2H4 were used to distinguish between hydrogen from the photolysis of water and from the photolysis of ethylene.
In the presence of 5% and 20% C2H4, the rate of D2 production from the photolysis of D2O is 6% of that in the absence of C2H4. It is concluded that in the photolysis of D2O at 1470 Å, there are two primary processes occurring: D2O+hv1470Å→D+OD,D2O+hv1470Å→D2+O.Direct production of molecular hydrogen and atomic oxygen accounts for 6% of the primary processes.