# Showing papers in "Journal of Chemical Physics in 1968"

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TL;DR: In this article, the free-ion energy-level schemes of the Pr3+, Nd3+, Pm3+, Sm3+, Dy3, Dy3+, Ho3+, Er3+, and Tm3+ aquo ions have been determined from their absorption spectra in dilute acid solution at 25°.

Abstract: The free‐ion energy‐level schemes of the Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+ aquo ions have been determined from their absorption spectra in dilute acid solution at 25°. Energy‐level assignments were made by comparison with crystal spectra, and on the basis of correlations between calculated and observed band intensities. For most of the ions, it was possible to identify several transitions giving rise to bands at energies as high as 45 000–50 000 cm−1. Sufficient numbers of assignments were made to justify inclusion of the effects of configuration interaction in the calculation of the energy‐level parameters. Variation of the electrostatic, spin–orbit coupling, and configuration‐interaction parameters across the lanthanide series is examined.

2,408 citations

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TL;DR: In this article, the authors demonstrate that definite mass/charge states can be formed by electrospraying a dilute polymer solution into an evaporation chamber, negative macroions can be produced and a molecular beam formed by sampling the gaseous mixture of macroions, solvent and nitrogen molecules with a nozzle-skimmer system of the Kantrowitz-Gray type.

Abstract: By means of electrospraying a dilute polymer solution into an evaporation chamber, negative macroions can be produced and a molecular beam formed by sampling the gaseous mixture of macroions, solvent, and nitrogen molecules with a nozzle‐skimmer system of the Kantrowitz–Gray type. The macroion current can be detected by a Faraday cage after the light ions have been repelled from the beam by negative voltages on a repeller grid. Theoretical repeller voltages which best agree with the observed are those calculated by assuming a macroion velocity within 2% of the estimated supersonic beam velocity of 743 m sec−1. Polystyrene macroions of 51 000 weight‐average amu tend to form dimers and trimers in the beam while larger polystyrene macroions of 411 000 weight‐average amu appear mostly to be multiply charged single species. The results demonstrate that definite mass/charge states can be formed by the electrospray technique, that a considerable monochromatization of macroion velocities in the beam takes place, and that the macroions become highly concentrated relative to low‐molecular‐weight solvent and nitrogen ions during the transit time in the supersonic beam.

1,532 citations

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TL;DR: In this article, the CNDO method was modified by substitution of semi-empirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by introducing a new empirical parameter κ to differentiate resonance integrals between σ orbitals from those between π orbitals.

Abstract: The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser‐Parr‐Pople method, and by the introduction of a new empirical parameter κ to differentiate resonance integrals between σ orbitals from those between π orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyridazine, pyrimidine, and pyrazine. The results obtained were refined by a limited CI calculation and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both n→π* and π→π* singlet‐singlet transitions. The relative energies of the pi and lone‐pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the “lone pairs” in these compounds is discussed.

1,171 citations

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1,140 citations

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TL;DR: In this article, the authors made a Monte Carlo determination of the pressure and absolute entropy of the hard-sphere solid, and used these solid-phase thermodynamic properties, coupled with known fluid-phase data, to confirm the existence of a first-order melting transition for a classical many-body system of hard spheres and to discover the densities of the coexisting phases.

Abstract: In order to confirm the existence of a first‐order melting transition for a classical many‐body system of hard spheres and to discover the densities of the coexisting phases, we have made a Monte Carlo determination of the pressure and absolute entropy of the hard‐sphere solid. We use these solid‐phase thermodynamic properties, coupled with known fluid‐phase data, to show that the hard‐sphere solid, at a density of 0.74 relative to close packing, and the hard‐sphere fluid, at a density of 0.67 relative to close packing, satisfy the thermodynamic equilibrium conditions of equal pressure and chemical potential at constant temperature. To get the solid‐phase entropy, we integrated the Monte Carlo pressure–volume equation of state for a “single‐occupancy” system in which the center of each hard sphere was constrained to occupy its own private cell. Such a system is no different from the ordinary solid at high density, but at low density its entropy and pressure are both lower. The difference in entropy between an unconstrained system of particles and a constrained one, with one particle per cell, is the so‐called “communal entropy,” the determination of which has been a fundamental problem in the theory of liquids. Our Monte Carlo measurements show that communal entropy is nearly a linear function of density.

1,135 citations

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TL;DR: The thermodynamic theory of symmetry breaking instabilities in dissipative systems is presented in this article, where several kinetic schemes which lead to an unstable behavior are indicated, and the role of diffusion is studied in more detailed way.

Abstract: The thermodynamic theory of symmetry breaking instabilities in dissipative systems is presented. Several kinetic schemes which lead to an unstable behavior are indicated. The role of diffusion is studied in a more detailed way. Moreover we devote some attention to the problem of occurrence of time order in dissipative systems. It is concluded that there exists now a firm theoretical basis for the understanding of chemical dissipative structures. It may therefore be stated that a theoretical basis also exists for the understanding of structural and functional order in chemical open systems.

1,132 citations

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TL;DR: In this article, a simple empirical equation P = Kρ02φ, K = 15.58, φ = NM1 /NM1/NM2Q 1/Q1/2, detonation velocities by the equation D = Aφ1φ 1/Aφ 2/Bρ0, A

Abstract: Detonation pressures of C–H–N–O explosives at initial densities above 1.0 g/cc may be calculated by means of the simple empirical equation P = Kρ02φ, K = 15.58, φ = NM1 / 2Q1 / 2, detonation velocities by the equation D = Aφ1 / 2(1 + Bρ0), A = 1.01, B = 1.30. N is the number of moles of gaseous detonation products per gram of explosive, M is the average weight of these gases, Q is the chemical energy of the detonation reaction ( − ΔH0per gram), and ρ0 is the initial density. Values of N, M, and Q may be estimated from the H2O–CO2 arbitrary decomposition assumption, so that the calculations require no other imput information than the explosive's elemental composition, heat of formation, and loading density. Detonation pressures derived in this manner correspond quite closely to values predicted by a computer code known as RUBY, which employs the most recent parameters and covolume factors with the Kistiakowsky‐Wilson equation of state.

1,085 citations

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TL;DR: In this paper, it was shown that the Percus-Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite.

Abstract: It is shown that the Percus–Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite. The results show a first‐order phase transition which appears to be of the type observed numerically for the Lennard‐Jones 12–6 potential.

1,043 citations

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TL;DR: In this paper, the authors considered a theory for intramolecular radiationless transitions in an isolated molecule and derived the validity criteria for the occurrence of an unimolecular radii-less transition and for exponential decay.

Abstract: In this paper we consider a theory for intramolecular radiationless transitions in an isolated molecule. The Born–Oppenheimer zero‐order excited states are not pure in view of configuration interaction between nearly degenerate zero‐order states, leading to the broadening of the excited state, the line shape being Lorentzian. The optically excited state can be described in terms of a superposition of molecular eigenstates, and the resulting wavefunction exhibits an exponential nonradiative decay. The linewidth and the radiationless lifetime are expressed in terms of a single molecular parameter, that is the square of the interaction energy between the zero‐order state and the manifold of all vibronic states located within one energy unit around that state. The validity criteria for the occurrence of an unimolecular radiationless transition and for exponential decay in an isolated molecule are derived. Provided that the density of vibrational states is large enough (i.e., exceeds the reciprocal of the interaction matrix element) radiationless transitions are expected to take place. The gross effects of molecular structure on the relevant molecular parameters are discussed.

1,041 citations

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TL;DR: In this article, the experimentally determined band intensities in the solution absorption spectra of the trivalent lanthanides were correlated with a theoretical expression derived by Judd, and the spectra were measured in a single medium, dilute acid solution, and, in most cases, in the range ≈6000-50 000 cm−1.

Abstract: We have correlated the experimentally determined band intensities in the solution absorption spectra of the trivalent lanthanides with a theoretical expression derived by Judd. The spectra were measured in a single medium, dilute acid solution, and, in most cases, in the range ≈6000–50 000 cm−1. In general, the correlation between calculated and observed intensities was very good, even at higher energies. The variation of the intensity parameters over the series is discussed as is the somewhat unexpected degree of correlation obtained in the ultraviolet region.

962 citations

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TL;DR: The pulsed gradient, spin-echo technique has been used to study self-diffusion of protons in several colloidal systems in order to examine the usefulness of that technique in determining the extent to which the free movement of molecules in these systems is restricted by the colloidal structures present as discussed by the authors.

Abstract: The pulsed‐gradient, spin‐echo technique has been used to study self‐diffusion of protons in several colloidal systems in order to examine the usefulness of that technique in determining the extent to which the free movement of molecules in these systems is restricted by the colloidal structures present. The pulsed‐gradient experiment is preferred to the steady‐gradient experiment because it affords better definition and control over the time during which diffusion is observed. Diffusion times between 1 sec and 10−3 sec have been used. One artificial system of thin liquid layers, three different kinds of plant cells, and one emulsion have been studied. Clear indications of restricted diffusion are found in all the systems. When fitted to theoretical expressions derived for such behavior, the data yielded a description of each system, as seen by the diffusing molecules, adequately in agreement with the known structure and properties. Critiera for recognizing and analyzing restricted diffusion are discussed. Necessary conditions for the successful study of restricted diffusion are also discussed.

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TL;DR: In this paper, an analytic expression is given for the distribution maintained by the vibration-vibration mechanism of a simple harmonic oscillator, which reduces to the usual Boltzmann-like distribution defined by a single vibrational temperature.

Abstract: The terms in the master equation for vibrational relaxation of anharmonic oscillators are ordered according to the rates of the relaxation processes (vibrational exchange, vibrational‐energy transfer to translation). The population distributions in the master equation are expanded about their values when the vibration‐vibration mechanism is the only one present. An analytic expression is given for the distribution maintained by the vibration‐vibration mechanism. In the limiting case of the simple harmonic oscillator, this distribution reduces to the usual Boltzmann‐like distribution defined by a single vibrational temperature. The general solution also applies to a mixture of simple‐harmonic‐oscillator gases of different fundamental frequencies. For such a mixture, each gas relaxes in a Boltzmann‐like distribution, but the different gases have different (but related) vibrational temperatures at any given time. The relaxation of the first moment of the distribution function also has been investigated. Anharmonicity causes a marked departure from the Landau‐Teller model of vibrational relaxation under conditions of high vibrational energy, coupled with low translational temperature. For such conditions, the populations of the lower vibrational states can be considerably lower than those predicted by the Landau‐Teller model. Furthermore, the over‐all energy relaxation rate can be accelerated.

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TL;DR: In this article, the free-ion energy level of Eu3+ (aquo) to ∼40 000 cm−1 has been determined from the absorption spectrum in dilute acid solution at 25°.

Abstract: The free‐ion energy level scheme of Eu3+ (aquo) to ∼40 000 cm−1 has been determined from the absorption spectrum of Eu3+ in dilute acid solution at 25°. Energy‐level assignments were made on the basis of correlations between calculated and observed intensities. A least‐squares fit of 26 J levels, including the effects of configuration interaction, gave an rms deviation of 40 cm−1. The parameter values were E1 = 5573.0, E2 = 26.708, E3 = 557.39, ζ4f = 1326.0, α = 25.336, β = − 580.25, and γ = 1155.7.

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TL;DR: An inductive method for a systematic selection of energy functions of interatomic interactions in large families of molecules is suggested and is applied to the family of cycloalkane and n−alkane molecules as mentioned in this paper.

Abstract: An inductive method for a systematic selection of energy functions of interatomic interactions in large families of molecules is suggested and is applied to the family of cycloalkane and n‐alkane molecules. Equilibrium conformations, vibrational frequencies, and excess enthalpies, including strain energies and vibrational enthalpies, are all derived from the same set of energy functions. The energy‐function parameters are optimized by a least‐squares algorithm to give the best possible agreement with a large amount and variety of observed data. Analytical derivatives of the various calculated quantities with respect to the energy parameters help to facilitate the computational procedures. The resulting agreement with experiment is used as a measure of success of the energy functions with optimized parameters, referred to as “consistent force field” (CFF). Different CFF's are compared and selected according to their relative success. Energy functions commonly used in conformational analysis are examined in...

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TL;DR: In this article, the Hartree-Fock wave function was used as an approximate wave function for the direct calculation of force constants and dipole-moment derivatives from SCF-MO wavefunctions.

Abstract: General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂φi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.

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TL;DR: In this paper, the electric dipole moment of OCS has been determined by measuring pure Stark transitions with molecular-beam electric resonance methods and the value obtained is 0.71521 ± 0.00020 D.

Abstract: The electric dipole moment of OCS has been determined by measuring pure Stark transitions with molecular‐beam electric resonance methods. The value obtained is 0.71521 ± 0.00020 D, which is in disagreement with a previous measurement of 0.7124 ± 0.0002 D.

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TL;DR: The Ferroelectric Ba0.27Sr0.75Nb2O5.78 as discussed by the authors is a tungsten bronze-type structure crystallizing in the tetragonal system, with lattice constants a = 12.43024

Abstract: Ferroelectric Ba0.27Sr0.75Nb2O5.78, with Tc = 348° ± 15°K, is a tungsten bronze‐type structure crystallizing in the tetragonal system, with lattice constants a = 12.43024 ± 0.00002 and c = 3.91341 ± 0.00001 A at 298°K, space group P4bm, and five formulas in the unit cell. The integrated intensities of 6781 structure factors were measured with PEXRAD, 875 symmetry‐independent structure factors being significantly above background. The metal‐atom positions were determined from the three‐dimensional Patterson function and the oxygen atoms from subsequent Fourier series. The final agreement factor between measured and calculated structure factors is 0.0508. The structure consists of close‐packed slightly puckered layers of oxygen atoms separated by nearly c / 2. The Nb atoms are slightly displaced from one layer, the Ba and Sr atoms from the other and in the same sense. The oxygen atoms in the Ba and Sr layer are disordered. Neither of the two independent sites occupied by the Ba and Sr atoms is fully filled....

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TL;DR: In this article, Kivelson's formula for a −1 transition was tested over a wide range of quantum numbers, and convergence difficulties in the least square fit of Kirtman's formula were revealed.

Abstract: In a study of internal rotation in methanol, the millimeter wave spectra of CH3OH, CD3OH, and CH3OD have been investigated between 90 and 200 Gc/sec. In the analysis of the spectra, torsion–vibration–rotation interactions were treated as adjustable parameters in semiempirical formulas. Kivelson's formula for a‐type ΔK = 0 transitions was tested over a wide range of quantum numbers. It reproduced the CH3OH and CD3OH spectra quite well, but the approximations used in the calculations appear to start breaking down for the larger asymmetry of CH3OD. For assignment of b‐type ΔK = ± 1 transitions, a method was developed based on the wide spectral range of the millimeter wave spectrometer. Sufficient b‐type data were obtained for CH3OH to permit a test of Kirtman's formula for origins of Q branches. Convergence difficulties in the Q‐branch least‐squares fit prompted a re‐examination of the theory, which revealed an interesting linear relation coupling six of the parameters. This relation shows that for any molec...

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TL;DR: In this paper, the potential energy curve for the electronic ground state of the hydrogen molecule has been calculated for double precision using a 100-term expansion of the electronic wavefunction, and the vibrational equation has been solved for all isotopes and for the rotational quantum number.

Abstract: The potential‐energy curve for the electronic ground state of the hydrogen molecule has been calculated for 1 ≤ R ≤ 3.2 a.u. in double precision and using a 100‐term expansion for the electronic wavefunction. Accuracy of the previously computed diagonal corrections for nuclear motion has been tested. The vibrational equation has been solved for all isotopes of the hydrogen molecule and for the rotational quantum number J ≤ 10. The calculated adiabatic dissociation energy of H2, corrected for relativistic and radiative effects, is by 3.8 cm−1 larger than the experimental value, hence the theoretical total energy is by the same amount lower than the experimental value. The calculated vibrational quanta for H2 are by 0.5–0.9 cm−1 larger than the experimental ones.

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TL;DR: In this article, the separability of the X-H stretching vibrations from the hydrogen bond vibrations is analyzed in the spirit of the adiabatic approximation for the linear triatomic X −H··· system, and the quantitative reconstitution of the experimental spectra and predictions for the effect of isotopic substitution of H by D are confirmed.

Abstract: For the linear triatomic X–H··· system, the separability of the X–H stretching vibrations from the hydrogen bond vibrations is analyzed in the spirit of the adiabatic approximation. The adiabatic wavefunctions for X–H stretching vibrations are shown to be suitable functions for the evaluation of the principal factors determining the infrared spectral properties of the actual species of carboxylic acid dimers and imidazole crystal. Theoretical infrared spectra in the X–H stretching region of these systems are then obtained and compared with the experimental ones. The quantitative reconstitution of the experimental spectra and, in particular, the predictions for the effect of isotopic substitution of H by D are confirmed. The principal features of the unusual spectral properties of the X–H stretching vibrations in hydrogenbonded systems seem therefore to result from a somewhat peculiar coupling mechanism suggested in the theory.

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TL;DR: In this article, the equations of state for periodic systems of hard disks and hard spheres in the solid phase have been accurately determined and used to evaluate the coefficients in the expansion of the pressure in powers of the relative free volume.

Abstract: The equations of state for periodic systems of hard disks and hard spheres in the solid phase have been accurately determined and used to evaluate the coefficients in the expansion of the pressure in powers of the relative free volume, α = (V − V0) / V0, where V0 is the close‐packed volume. For disks pV / NkT = 2 / α + 1.90 + 0.67α + O(α2) and for spheres pV / NkT = 3 / α + 2.56 + 0.56α + O(α2). These coefficients are compared to cell models, and those models which include correlations between neighboring particles work best. An equivalent expansion of other thermodynamic properties requires the entropy constant to be evaluated in the close‐packed limit. This constant is obtained here by integrating the equation of state over the entire density region. The Lennard‐Jones–Devonshire cell‐theory estimates of the entropy constant are nearly correct; that is, the cell‐theory estimate is too small by 0.06Nk for disks and too large by 0.24Nk for spheres. The pressure difference and hence the entropy difference b...

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TL;DR: In this article, a skeleton model was proposed for the solubility of urea to water, where water was represented as a two-species mixture of dense and bulky constituents and the dissolved hydrocarbon is represented as dissolving separately in these constituents.

Abstract: The finding of Wetlaufer et al., that addition of urea to water increases the (mole fraction) solubility of hydrocarbon gases (except methane) while making them dissolve with a smaller evolution of heat, is interpreted as a primarily statistical phenomenon. For this purpose, it is treated in terms of a skeleton model in which not only is water represented as a two‐species mixture of dense and bulky constituents but the dissolved hydrocarbon is represented as dissolving separately in these constituents, as if it were distributed between two phases, i.e., between a quasiclathrate solution in the bulky constituent and a quasilattice or “regular” solution in the dense one. Added urea is pictured as being able to enter only one of the solutions, the quasilattice one in the dense water, with the result that it acts as a structure breaker. A statistical‐thermodynamic analysis of this model leads to equations for the chemical potentials and the partial molal enthalpies and entropies of the hydrocarbon and the ure...

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TL;DR: An electrostatic lens system which compensates for chromatic aberration has been tested in an electron spectrometer and the results indicate that this lens is suitable for comparisons of peak intensities in electron impact spectra.

Abstract: An electrostatic lens system which compensates for chromatic aberration has been tested in an electron spectrometer. The results indicate that this lens is suitable for comparisons of peak intensities in electron‐impact spectra. Relative intensities in vibrational progressions that belong to a single electronic transition have been studied in N2, CO, and NH3 and found to be nearly independent of the scattering angle. Electron‐impact spectra have been reported for helium, nitrogen, oxygen, argon, nitric oxide, nitrous oxide, ammonia, water vapor, carbon dioxide, ethylene, acetylene, and benzene at electron kinetic energies between 33 and 100 eV. Spectral regions of special interest are encountered in CO2 and C6H6. At excitation energies of 7–10 eV in CO2 a change in intensity distribution, attributed to transition from an electric‐quadrupole to an electric‐dipole spectrum, is observed as the kinetic energy is raised. In the case of C6H6 a change in the spectrum with angle is encountered which strongly sugg...

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TL;DR: In this article, the authors interpreted solvent-solute interactions in aqueous solutions of nonelectrolytes using both lattice and distribution function theories of the dissolved state.

Abstract: Solute‐solute interactions in aqueous solutions of nonelectrolytes are interpreted using both lattice and distribution function theories of the dissolved state. Experimental activity data of high precision can be obtained from the literature for aqueous solutions of many nonelectrolytes. If the logarithm of the solvent activity coefficient (γ1) is expressed as a power series in the mole fraction of the solute (x2), lnγ1 = Bx22 + Cx23 + ···, then the coefficients B and C can be determined analytically from the experimental measurements. Values of B were obtained for 52 aqueous mixtures; values of C were obtained for 39 of these mixtures. The solutes considered include aliphatic alcohols, amines, amides, ketones, fatty acids, amino acids, and sugars. In some cases, experimental data were available from which the temperature dependence of the quantities B and C could also be determined. The effect of solute size on the coefficients B and C was investigated using the lattice theories of Flory, Huggins, and Gu...

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TL;DR: In this article, a general method for quantum-mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure is proposed, which consists of the calculation of self-consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations.

Abstract: A general method is proposed for quantum‐mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure. This consists of the calculation of self‐consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations. The general theory of such methods is presented together with a preliminary discussion of numerical error.

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TL;DR: In this paper, the modified CNDO method was used to calculate the electronic spectra of cyclopentadiene, the Cyclopentadienide ion, pyrrole, furan, pyrazole, imidazole, 2-pyrrolecarboxaldehyde, and furfural.

Abstract: The modified CNDO method previously reported has been used to calculate the electronic spectra of cyclopentadiene, the cyclopentadienide ion, pyrrole, furan, pyrazole, imidazole, 2‐pyrrolecarboxaldehyde, and furfural. In general, the results obtained agree quite well with experimental data. Because the CNDO method treats explicitly all σ and π valence electrons of a molecule, the results of the calculations are used to discuss some of the σ–π interactions which previously could not be treated. The calculations are successful in reflecting changes in the electronic spectra of compounds as a result of extending conjugation or addition of a substituent.

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TL;DR: In this article, the self-consistent perturbation theory developed in earlier papers is extended to the open-shell case and density matrices for both shells are calculated iteratively until first-order selfconsistency is achieved.

Abstract: The self‐consistent perturbation theory developed in earlier papers is extended to the open‐shell case. Density matrices for both shells are calculated iteratively until first‐order self‐consistency is achieved. A numerical application indicates the importance of considering both shells separately when discussing the effects of polarization on the charge density and the spin density.

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TL;DR: In this article, the absorption coefficients of ozone have been measured in the ultraviolet and visible regions using essentially 100% pure ozone, and the results confirm those of Inn and Tanaka in ultraviolet, and those of Vigroux in the visible region.

Abstract: The absorption coefficients of ozone have been measured in the ultraviolet and visible regions using essentially 100% pure ozone. The results confirm those of Inn and Tanaka in the ultraviolet, and those of Vigroux in the visible region.

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TL;DR: Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory using matrix elements was studied in this paper, where transformation theory was used to solve the problem of matrix elements calculation.

Abstract: Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory