# Showing papers in "Journal of Chemical Physics in 1967"

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TL;DR: In this paper, the authors study the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations, and employ a method developed by Coleman and Noll to find the general restrictions which the Clausius-Duhem inequality places on response functions.

Abstract: This is a study of the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations. After employing a method developed by Coleman and Noll to find the general restrictions which the Clausius—Duhem inequality places on response functions, we analyze various types of dynamical stability that can be exhibited by solutions of the internal evolution equations. We also discuss integral dissipation inequalities, conditions under which temperatures can be associated with internal states, and the forms taken by response functions when the material is a fluid.

1,582 citations

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TL;DR: In this article, the perturbation theory for the 6:12 potential is applied to more realistic potentials with soft repulsion, and the configuration integral is expanded in a double-power series in the inverse-steepness and depth parameters.

Abstract: The perturbation theory previously shown to give good results for the equation of state of a square‐well fluid at liquid densities and temperatures is applied to more realistic potentials with soft repulsion, in particular the 6:12 potential. For an arbitrary potential function a modified potential is defined involving three parameters, namely a hard‐sphere diameter, an inverse‐steepness parameter for the repulsive region, and a depth parameter for the attractive region. When the latter parameters are zero, the modified potential becomes the hard‐sphere potential; when they are one, it becomes the original potential. The configuration integral is expanded in a double‐power series in the inverse‐steepness and depth parameters, the hard‐sphere diameter being chosen so that the first‐order term in the inverse‐steepness parameter is zero. The first‐order term in the depth parameter is evaluated essentially exactly and the second‐order term approximately: other second‐order terms and all higher‐order terms are neglected. The resulting equation of state is in good agreement with molecular dynamics, Monte Carlo results, and experimental data for argon at all temperatures and densities relevant for fluids.

1,469 citations

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TL;DR: The Intermediate Neglect of Differential Overlap (INDO) method proposed in this article is an improvement over the CNDO method, in that atomic term-level splittings and unpaired spin distributions are better accommodated.

Abstract: A new approximate self‐consistent‐field method for the determination of molecular orbitals for all valence electrons of a molecule is proposed. This method features neglect of differential overlap in all electron‐interaction integrals except those involving one center only. The parameters involved in the calculation are generally obtained semi‐empirically. The new method is known as the Intermediate Neglect of Differential Overlap (INDO) method, and may be regarded as an improvement over the CNDO method proposed in Part I, in that atomic term‐level splittings and unpaired spin distributions are better accommodated. Calculations on geometries of AB2 and AB3 molecules are reported to substantiate the proposed method, and calculated unpaired spin distributions for methyl and ethyl radicals are discussed.

1,380 citations

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TL;DR: In this article, minimal basis set atomic functions for ground state atoms from Rb(Z=37) to Rn(Z =86) are presented, in order to obtain systematic data for the screening constants and atomic radii following the work initiated by Slater.

Abstract: Minimal basis‐set atomic functions for the ground‐state atoms from Rb(Z=37) to Rn(Z=86) are presented. These functions are analyzed in order to obtain systematic data for the screening constants and atomic radii following the work initiated by Slater.

1,215 citations

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TL;DR: In this article, the rotational Hamiltonian of an asymmetric-top molecule in a given vibrational state, obtained by the usual vibrational perturbation treatment, is transformed by means of a unitary transformation to a reduced Hamiltonian which is suitable for fitting to observed energies.

Abstract: The rotational Hamiltonian of an asymmetric‐top molecule in a given vibrational state, obtained by the usual vibrational perturbation treatment, contains more parameters than can be determined from the observed energy levels. This Hamiltonian is therefore transformed by means of a unitary transformation to a reduced Hamiltonian which is suitable for fitting to observed energies. The unitary transformation can be chosen so that the reduced Hamiltonian has the following properties: (i) It is totally symmetric in the point group D2, regardless of the symmetry of the molecule; (ii) It contains only (n+1) independent terms of total degree n in the components of the total angular momentum, for each even value of n; (iii) Its matrix elements in a symmetric‐top basis satisfy the selection rule ΔK=0, ±2. This paper is concerned mainly with the possibility of carrying out this reduction in general. However, the reduced Hamiltonian described above contains one less quartic coefficient than has been used previously, and this particular case is discussed in more detail.

1,131 citations

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TL;DR: In this paper, the equation of state for a fluid of molecules interacting according to the square-well potential is evaluated by treating the attractive potential as a perturbation on the hard-sphere potential.

Abstract: The equation of state for a fluid of molecules interacting according to the square‐well potential is evaluated by treating the attractive potential as a perturbation on the hard‐sphere potential. This leads to an expansion in inverse powers of the temperature. The first‐order term is evaluated exactly (except for the approximation of using the Percus—Yevick expression for the hard‐sphere radial distribution function). Two slightly different approximations for the second‐order term are given and shown to lead to similar results. With first‐and second‐order terms included, the calculated equation of state is in excellent agreement with quasiexperimental Monte Carlo and molecular‐dynamics results at all temperatures including the lowest temperatures for which such calculations have been made, far below the critical temperature and at liquid densities. The reasons for this good agreement, particularly at high densities, are discussed in terms of a novel formulation of the perturbation theory, and the implications of the results for fluids with more realistic potential functions are considered.

983 citations

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TL;DR: In this article, a vibrational and attendant conformational analysis of the liquid n-paraffins and molten polyethylene is presented, and a valence force field is derived which is applicable to both planar and nonplanar chains.

Abstract: A vibrational and attendant conformational analysis of the liquid n‐paraffins and molten polyethylene is presented. For the purposes of the analysis a valence force field was derived which is applicable to both planar and nonplanar chains. The force field was evaluated from observed frequencies of trans (T) and gauche (G) n‐C4H10; TT and GT n‐C5H12; TTT, GTT, and TGT n‐C6H14; and (T)∞ polyethylene, all of whose infrared spectra were assigned in detail. Infrared spectra of the liquid‐n‐paraffins n‐C4H10 through n‐C17H36 were measured at room temperature and n‐C4H10 through n‐C12H26 also at a temperature just above their melting point. Frequencies and normal coordinates were calculated for the extended forms and for forms having one gauche bond of n‐C4H10 through n‐C8H18. These quantities were also calculated for the conformations of n‐C5H12 through n‐C7H16 having two gauche bonds and for the nonplanar but regular conformations (TG)∞ and (G)∞ of polyethylene. Some bands attributable to forms of n‐C5H12 and ...

717 citations

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TL;DR: In this article, a new crystalline form of carbon, hexagonal diamond, has been synthesized in the laboratory under conditions of static pressure exceeding about 130 kbar and temperature greater than about 1000°C.

Abstract: A new crystalline form of carbon—hexagonal diamond—has been synthesized in the laboratory under conditions of static pressure exceeding about 130 kbar and temperature greater than about 1000°C. It is necessary to start with well‐crystallized graphite in which the c axes of the crystallites are parallel to each other and to the direction of compression. There is electrical evidence that the transformation starts at room temperature but hexagonal diamond is not retrieved unless a setting temperature exceeding about 1000°C is applied. The electrical and crystal characteristics have been studied. The crystal structure is hexagonal with a=2.52 A and c=4.12 A. The theoretical density is 3.51+g/cm3, same as cubic diamond. It has also been prepared recently in another laboratory from crystalline graphite by a method involving intense shock compression and strong thermal quenching. More recently it has been discovered to be present to the extent of over 30% in the Canyon Diablo meteorite diamonds.

579 citations

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Philips

^{1}TL;DR: In this paper, the fluorescence of a number of new Ce3+activated phosphors is described and discussed, and conditions for visible Ce3−activated phosphor emission are indicated, viz., large crystal-field splittings (Y3Al5O12−Ce) or a large Stokes shift (SrY2O4•Ce).

Abstract: The fluorescence of a number of new Ce3+‐activated phosphors is described and discussed. Only host lattices with a sublattice consisting of trivalent lanthanide ions are used to avoid charge compensation of the Ce3+ ion. Usually the Ce3+ emission is in the near‐ultraviolet region. Y3Al5O12–Ce and SrY2O4–Ce, however, show emission in the visible region with a maximum in the green. Conditions for visible Ce3+ emission are indicated, viz., large crystal‐field splittings (Y3Al5O12–Ce) or a large Stokes shift (SrY2O4–Ce). In a number of cases we were able to observe all crystal‐field components of the excited 5d level of Ce3+. The cubic crystal‐field splitting of the 5d level varies strongly with host lattice from 7000 to 14 000 cm−1. The position of the center of the 5d levels in oxides is about 30% lower than in the free ion. For some phosphors we observed more than one emission band at room temperature. This is due to fluorescence from higher excited levels. Efficient energy transfer from Ce3+ to Cr3+ was observed in Y3Al5O12.

564 citations

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TL;DR: In this article, Hartree-Fock wavefunctions are presented for the NaH(X1Σ+), MgH (X2Σ+) and AlH(AlH+), SiH(H2Πr), PH(X3Σ−), SH(X 2Πi), and HCl(X 1 Σ+) molecules.

Abstract: Hartree—Fock wavefunctions are presented for the NaH(X1Σ+), MgH(X2Σ+), AlH(X1Σ+), SiH(X2Πr), PH(X3Σ−), SH(X2Πi), and HCl(X1Σ+) molecules. These are the analytic self‐consistent‐field wavefunctions obtained from the solutions of the Hartree—Fock—Roothaan equations. Large basis sets of Slater‐type functions centered on both nuclei were used and extensive optimization of the orbital exponents has been carried out. The total energies obtained for Re(exptl) are −162.3928, −200.1566, −242.4634, −289.4361, −341.2932, −398.1015, and −460.1103 hartrees, respectively, for the hydrides listed. The first ionization potentials, which are obtained from the Hartree—Fock energy differences between the AH and AH+ systems, are 6.14, 6.76, 7.36, 7.36, 9.65, 9.31, and 11.84 eV, respectively. In addition, potential curves, spectroscopic constants, and certain other energetic quantities are presented. Crude estimates of the correlation energy of the second‐row hydrides are made and such quantities are compared within the serie...

551 citations

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TL;DR: In this paper, the least square derivation of non-bonded potential parameters from crystalline aromatic hydrocarbons was extended to include non-aromatic molecules, and the potentials obtained from the combined observational equations gave better fits to the nonaromatics than to the aromatics.

Abstract: The previously described least‐squares derivation of nonbonded potential parameters from crystalline aromatic hydrocarbons was extended to include nonaromatic hydrocarbons. Further evidence was obtained that no specially large energy effects are present in the aromatic crystal structures with their π‐electron systems. A better separation of the nonbonded energy into C···C, C···H, and H···H components was obtained when the observational equations for the aromatic and nonaromatic structures were combined. The potentials obtained from the combined observational equations gave better fits to the nonaromatics than to the aromatics. Evidence is presented favoring an H–C–H angle of less than 106° in crystalline n‐pentane and n‐hexane. The parallel packing of molecular chains in the n‐hexane crystal and the nonparallel packing in the n‐pentane crystal were reproduced by a steepest descent minimization of the lattice energy using the observed lattice constants.

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TL;DR: In this paper, the Hartree-Fock determinant minimization of the energy expectation value was derived using the language familiar in quantum chemistry and the stability conditions for closed-shell electronic systems were specified.

Abstract: The stability conditions which ensure that the Hartree—Fock determinant minimizes the energy expectation value are rederived using the language familiar in quantum chemistry. These stability conditions are then specified for the case of closed‐shell electronic systems which allow additional simplification of the conditions as well as a certain classification of the instabilities.Examples of the instabilities of different types are presented and the case of the so‐called singlet instabilities—most interesting from the physical point of view—is studied in detail for the pi‐electron model of cyclic polyenes.

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TL;DR: In this paper, the authors investigate the possibility of an instability in purely dissipative systems involving chemical reactions and transport processes such as diffusion, but no hydrodynamic motion, and demonstrate that for well defined values of the constraints such as the chemical affinities of the over-all reactions and the constants involved, such systems can indeed become unstable.

Abstract: The theory of hydrodynamic instability has always been an important part of fluid dynamics [see, e.g., Chandrasekhar, in Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford, England, 1961) and Non‐Equilibrium Thermodynamics, Variation Techniques, and Stability, R. J. Donnelly, R. Herman, and I. Prigogine, Eds. (University of Chicago Press, Chicago, Ill., 1966)]. Such instabilities involve both convective processes (such as mechanical flow) and dissipative processes (such as viscous dissipation). We investigate the possibility of an instability in purely dissipative systems involving chemical reactions and transport processes such as diffusion, but no hydrodynamic motion. We demonstrate that for well‐defined values of the constraints such as the chemical affinities of the over‐all reactions and the constants involved, such systems can indeed become unstable. Such an instability is investigated following an example of autocatalytic reactions first proposed by Turing. The major feature of this ...

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TL;DR: In this paper, the integrated Raman intensities of the spectral contour arising from the intermolecular librational motions of pure water have been obtained in the temperature range of ∼10°-95°C.

Abstract: Integrated Raman intensities of the spectral contour arising from the intermolecular librational motions of pure water have been obtained in the temperature range of ∼10°—95°C. In addition, integrated intensities of nearly symmetric librational components centered near ∼475 and ∼710 cm−1 were obtained from manual contour analysis according to two components. However, contour analysis was also accomplished by means of a special‐purpose analog computer, and three Gaussian librational components having average frequencies of 439, 538, and 717 cm−1 were thus revealed. The total contour intensity, the manually determined component intensities, and the Gaussian component intensities were found to have the same temperature dependence, and that dependence was found to be in excellent quantitative agreement with the previously reported temperature dependence of the hydrogen‐bond‐stretching intensity [J. Chem. Phys. 44, 1546 (1966)]. Integrated Raman intensities of pure water were also obtained in the temperature range of 10°—90°C for the intramolecular valence and deformation contours in the spectral region of ∼2800–3900 cm−1, and near 1645 cm−1, respectively. The integrated intensity of the deformation contour was found to be nearly independent of temperature, but the total integrated intensity of the intramolecular valence contour was found to decrease with increasing temperature. However, heights of the high‐frequency portion of the intramolecular valence contour were observed to increase, whereas heights of the low‐frequency portion were observed to decrease at nearly the same rate, with increasing temperature. An isosbestic point was also found at approximately 3460 cm−1. Further, computeranalysis revealed the existence of four Gaussian components having opposite temperature dependences in pairs—two intense valence components at ∼3247 and ∼3435 cm−1 were found to decrease in intensity with increasing temperature, and two weak components at ∼3535 and ∼3622 cm−1 were found to increase in intensity. Computeranalysis of infrared absorbance spectra also revealed four Gaussian components at approximately 3240, 3435, 3540, and 3620 cm−1. The quantitative agreements involving temperature dependences of the intermolecular hydrogen‐bond‐stretching and librational intensities, as well as the intramolecular valence data, would appear to preclude models of water structure involving consecutive hydrogen‐bond breakage. Continuum models of water structure are also precluded by the inter‐ and intramolecular intensity dependences, and particularly by the isosbestic point in the intramolecular valence region, but a model involving an equilibrium between two forms of water is consistent with all of the data. The two forms refer to water molecules which have or have not surmounted a barrier arising from a partially covalent hydrogen‐bond potential of C 2v symmetry, and they may be described as nonhydrogen‐bonded monomeric water, and as lattice water, respectively. Polarized argon‐ion‐laser—Raman spectra were also obtained in the intermolecular frequency region of the water spectrum, and the depolarization ratios of the intermolecular Raman bands were found to be in complete agreement with predictions from intermolecular C 2v symmetry. Studies of the intramolecular valence region were also made with polarized mercury excitation, and the spectra were analyzed by the analog method. Short‐lived CS intramolecular perturbations were indicated by the observed depolarization ratios of the four Gaussian valence components. Accordingly, CS intramolecular valence perturbations occur in the lattice water, as well as in the nonhydrogen‐bonded water, but the perturbations are of little importance on the intermolecular time scale.

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TL;DR: In this paper, the CNDO method is extended to molecules containing the elements sodium through chlorine and used to examine the importance of the 3D orbitals of these elements to molecular properties.

Abstract: The CNDO method is extended to molecules containing the elements sodium through chlorine and used to examine the importance of the 3d orbitals of these elements to molecular properties. An examination of the radial dependence of the 3d orbitals is carried out by performing parallel calculations with three different basis sets on a selection of molecules. A basis set in which the 3d orbitals are somewhat contracted is found to best predict molecular geometries, dipole moments, and bending force constants. The molecular dipole moments are found to present the most persuasive evidence for 3d participation, while most molecular geometries are relatively insensitive to inclusion of atomic orbitals of d symmetry.

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TL;DR: A generalized treatment of gas transport in porous media is presented as developed on the basis of the ''dusty gas'' model, a model in which a porous medium is described as consisting of uniformly distributed, giant molecules (dust) held stationary in space as mentioned in this paper.

Abstract: A generalized treatment of gas transport in porous media is presented as developed on the basis of the ``dusty‐gas'' model, a model in which a porous medium is described as consisting of uniformly distributed, giant molecules (dust) held stationary in space. The problem is broken down into a series of special cases which involve the various combinations of gradients in composition, pressure, and temperature.Equations are given for the description of several well‐known phenomena. These include isobaric, isothermal diffusion; diffusion under the influence of a pressure gradient; Poiseuille's flow equation, including the Knudsen minimum; the Kramers—Kistemaker effect; thermal transpiration; and the effect of pressure on the thermal‐diffusion factor. The results are likewise applicable to capillaries by a suitable substitution for geometric parameters.

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TL;DR: In this paper, the Raman effect of corundum (sapphire) was measured with an Ar+ laser source and the seven expected Raman active phonons were found and their symmetry characters determined.

Abstract: The Raman effect of corundum (sapphire) was measured with an Ar+ laser source. The seven expected Raman active phonons were found and their symmetry characters determined. Assignment of the internal and external vibrations of the crystals was made and the effect of birefringence in the Raman selection rules is discussed.

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TL;DR: In this article, a variation perturbation method has been employed to calculate the static dipole polarizabilities of the hydrogen molecule, represented by an expansion in elliptic coordinates including the interelectronic distance.

Abstract: A variation perturbation method has been employed to calculate the static dipole polarizabilities of the hydrogen molecule. The wavefunction was represented by an expansion in elliptic coordinates including the interelectronic distance. A 54‐term expansion was used for the zero‐order wavefunction and 34 terms for the first‐order corrections. The polarizabilities computed for several values of the internuclear distance (0.4≤R≤4.0) were averaged for various vibrational and rotational states of H2, HD, and D2. The results are in a satisfactory agreement with the experimental values.

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TL;DR: In this article, an interpretation of the chemical binding found in first-row homonuclear diatomic molecules is presented based upon the one-electron density distribution and the forces which it exerts on the nuclei.

Abstract: This paper presents an interpretation of the chemical binding found in the first‐row homonuclear diatomic molecules. The interpretation is based upon the one‐electron density distribution and the forces which it exerts on the nuclei. The general topographical features of the density distributions are discussed in relation to ``molecular size'' and the manner in which the total charge is partitioned between different spatial regions. The binding in these molecules is discussed in terms of the density difference distributions which picture the redistribution of charge which results from the formation of the molecule. It is proposed that the density difference distribution, or Δρ map, may be taken as the pictorial representation of the ``bond density.'' The forces exerted on the nuclei in the molecule are related to the changes in the charge distribution pictured in the ``bond density'' and a quantitative discussion of the manner in which electrostatic equilibrium is attained to give a stable molecule is giv...

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TL;DR: In this paper, the Franck-Condon factor (F) was investigated for a system consisting of a polyatomic molecule in a medium where vibrational relaxation is rapid and the transition rate was governed by a vibronic matrix element and a vibrational overlap factor.

Abstract: Radiationless transitions between two electronic states are studied for a system consisting of a polyatomic molecule in a medium where vibrational relaxation is rapid. The transition rate is then governed by a vibronic matrix element and a vibrational overlap factor. Only the latter, known as the Franck—Condon factor and denoted by F, is investigated in detail. For harmonic oscillators F derives from shifts in equilibrium distance (displacements) and shifts in frequency (distortions). It is shown that for radiationless transitions involving large energy gaps (E), F is dominated by distortions, whereas for optical transitions it is dominated by displacements of the oscillators. These distortions lead to an approximately exponential decrease of F with increasing E. An isotope rule for F is derived which is valid for both displaced and distorted oscillators provided E is not too small. Since all formulas are of the form F (E), where E is the principal variable, comparison with experiment is only possible for...

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TL;DR: In this paper, the theory of Part I is applied to nonradiative transitions from the lowest triplet state to the ground state of aromatic hydrocarbons, and a previously communicated empirical relation between triplet energy, triplet lifetime, and the relative number of hydrogen atoms per molecule is substantiated.

Abstract: The theory of Part I is applied to nonradiative transitions from the lowest triplet state to the ground state of aromatic hydrocarbons. A previously communicated empirical relation between triplet energy, triplet lifetime, and the relative number of hydrogen atoms per molecule is substantiated and its physical implications are discussed. It is transformed into a relation between the Franck‐Condon factor of the transitions and the triplet energy. In this form it can be compared with the theoretical expressions derived in Part I. No satisfactory theoretical representation of the empirical formula could be obtained on the basis of a harmonic‐oscillator description of the normal modes of the molecules. However, introduction of anharmonicity leads to excellent agreement between theory and experiment. A one‐parameter formula is derived which accounts with good accuracy for the dependence of the triplet lifetime on the triplet energy and the number of carbon and hydrogen atoms in the molecule. This formula shows that the Franck‐Condon factors relevant to the radiationless triplet‐ground‐state transition are governed by CH or CD stretching modes, which behave in this respect as completely degenerate for a given molecule. The single adjustable parameter is related to the anharmonicities of these modes in the ground and triplet state. The analysis confirms that the purely radiative triplet lifetime of most if not all aromatic hydrocarbons is close to 30 sec and that the Franck‐Condon factor is the only parameter in the expression for the nonradiative triplet decay constant which varies considerably between different aromatic hydrocarbons. Finally the temperature dependence of the Franck‐Condon factors is considered. A theoretical treatment indicates a very small temperature dependence below 400°K. This result seems to be borne out by an analysis of recent experiments, leading to the conclusion that the observed temperature effects are associated with bimolecular processes. A notable exception is benzene, where the triplet lifetime is temperature‐dependent down to very low temperatures, possibly due to a Jahn‐Teller distortion.

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TL;DR: In this paper, the complete Waller-Hartree theory with all exchange terms has been used and incoherent scattering factors for all spherically symmetric free atoms have been computed from numerical SCF Hartree-Fock wavefunctions.

Abstract: Incoherent scattering factors for all spherically symmetric free atoms have been computed from numerical SCF Hartree—Fock wavefunctions. The complete Waller—Hartree theory with all exchange terms has been used.

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TL;DR: The paper contains an extensive statistical‐analytic treatment of the error characteristics of the new method, one that enables advance quantitative estimation of upper limits of error in the integration of various types of functions.

Abstract: A new method, of very general applicability and very easily programmed for an electronic computer, is proposed for the numerical integration of functions of many independent variables. This new method renders obsolete, in most applications, the commonly used Monte Carlo procedure and the more recent, original method of Haselgrove. In the new scheme the sample points are distributed systematically rather than at random and the ensemble of points forms a unique, closed, symmetrical pattern, which effectively fills the space of the multidimensional integration. The paper contains an extensive statistical‐analytic treatment of the error characteristics of the new method, one that enables advance quantitative estimation of upper limits of error in the integration of various types of functions. For continuous functions with bounded first derivatives, the error is shown ultimately to disappear at least as rapidly as the inverse square of the number of sample points; moreover, for runs of practical length the error limits with the new scheme are smaller—by a factor ranging from 2 to perhaps 104 or more—than those of any previous general procedure. The method employs certain rational constants which govern the arrangement of sample points. Tables of such constants, suitably optimized, which will permit the integration of functions with up to 12 independent variables, are provided along with a discussion of a method by which such constants may be obtained.

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TL;DR: In this paper, the rate of near-resonant exchange of vibrational energy between CO2 and N2 (ΔE=18 cm−1) has been measured.

Abstract: Laser‐excited vibrational fluorescence measurements have been made on the asymmetric‐stretching vibrational level (00°1) of CO2. Vibration→vibration energy‐transfer rates from this level due to collisions with CO2 and with a number of other collision partners are presented. The rate of near‐resonant exchange of vibrational energy between CO2 and N2 (ΔE=18 cm−1) has been measured. The kinetics of the CO2 laser system are analyzed in terms of a three‐level scheme. Observed laser performance is compared with that calculated by use of collisional and radiative coupling rates observed in nonionized gases and of electron activation and deactivation rates estimated from CO2 discharge systems. In accordance with the scheme presented, the relative effectiveness of small amounts of added H2, D2, and He on laser output parallels their effectiveness in deactivating the lower laser level. The criteria for selecting molecules with vibrational‐energy‐level patterns likely to produce laser systems are outlined. Attempts ...

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TL;DR: In this article, the mean square radii of outer electrons of free gaseous atoms were used to calculate the ionization cross sections for single ionization by electron impact on free gas atoms.

Abstract: Relative ionization cross sections for single ionization by electron impact on free gaseous atoms have been calculated by utilizing a summation of the mean‐square orbital radii of outer electrons. A previous calculation of the cross sections by Otvos and Stevenson was in only fair agreement with experimental data due to the use of incorrect mean‐square radii, and to the method of summation of electron‐shell contributions to the total cross sections. Hartree—Fock calculations of orbital wavefunctions have been carried out for all of the elements. Mean‐square radii of atomic orbitals from the Hartree—Fock calculations were corrected approximately for relativistic effects. The ionization cross sections obtained from the summations were normalized at argon and compared with experimental values. The computed maximum cross sections are a considerable improvement over past theoretical values.

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TL;DR: In this paper, a limit on the thermodynamic potential difference between ground and excited states of any photochemical system is established by evaluating the potential difference at which the rate of photon absorption and emission are equal.

Abstract: A limit on the thermodynamic potential difference between the ground and excited states of any photochemical system is established by evaluating the potential difference at which the rate of photon absorption and emission are equal; the relationship between absorption and emission is given by a Planck‐law relation, provided that there is thermal equilibrium between the sublevels of each electronic band. The actual potential developed may be evaluated if the quantum yield of luminescence is known. The maximum amount of power storage obtainable is evaluated by lowering the potential difference until the product of the potential difference and the fraction of the quanta retained is maximized. The history and applications of the Planck‐law relation between absorption and emission spectra are discussed briefly, and applications of the potential difference calculation are mentioned.

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TL;DR: Fluorescence polarization, nuclear magnetic resonance, and electron spin resonance experiments on appropriately labeled proteins give information about various angular correlation functions or correlation times for the reorientation of the label relating the rotation rate of the rigid protein and the rates of the internal rotations between the label and the protein.

Abstract: Fluorescence polarization, nuclear magnetic resonance, and electron spin resonance experiments on appropriately labeled proteins give information about various angular correlation functions or correlation times for the reorientation of the label. Expressions are derived relating these correlation functions and times to the rotation rate of the rigid protein and the rates of the internal rotations between the label and the protein. The effective correlation time for the label is simply a series of factors times the correlation time for the rigid protein. Each internal rotation which is much faster than the protein rotation contributes a single factor ½(3 cos2θ−1)2, where θ is the angle from the internal rotation axis of interest to the next internal rotation axis, or, for the last internal rotation, to the label axis of interest. The effect of internal rotations which are much slower than the protein rotation rate is the same as the effect of averaging over molecules with a permanent geometry corresponding...

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TL;DR: In this paper, a unified theory of the interaction between a polarizable charge distribution and an external electric field is presented and extended in a unified way, and relations between tensor components in systems of axial and spherical symmetry are given.

Abstract: Buckingham's theory of the interaction between a polarizable charge distribution and an external electric field is presented and extended in a unified way. Transformations of components of the molecular polarizability tensors under change of the coordinate origin are derived. Relationships between tensor components in systems of axial and spherical symmetry are given.

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TL;DR: In this paper, a general method for carrying out population analysis of wavefunctions calculated with arbitrary basis sets is presented, and the difficulties in defining orbital populations are discussed, and results are presented for the sequence BF, CO, and N2 which indicate that back transfer of charge in the π bond cancels the normal transfer of the charge in σ bond.

Abstract: A general method for carrying out population analysis of wavefunctions calculated with arbitrary basis sets is presented. The difficulties in defining orbital populations is discussed. Results are presented for the sequence BF, CO, and N2 which indicate that back‐transfer of charge in the π bond cancels the normal transfer of the charge in the σ bond. Contrary to popular belief, the more electronegative element has the larger degree of hybridization in each case. The amount of promotion of 2s electrons is greater on the less‐electronegative element, as expected.

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TL;DR: In this article, the Kimball-Neumark spherical Gaussian orbital model is extended to apply to the singlet ground states of the general molecule with localized orbitals and the results are discussed in detail.

Abstract: The Kimball—Neumark spherical Gaussian orbital model is extended to apply to the singlet ground states of the general molecule with localized orbitals Formulas are presented for energy, electron density, dipole moment, and the forces on nuclei and the computational procedure is described The model is applied to LiH and the results are discussed in detail