Showing papers in "Molecular Physics in 1958"
TL;DR: The first six coefficients in the expansion of the susceptibility χ, and its inverse, χ −1, in ascending powers of the reciprocal temperature, have been determined for the Heisenberg model of a ferromagnetic, for any spin value, S, and any lattice as discussed by the authors.
Abstract: The first six coefficients in the expansion of the susceptibility χ, and its inverse, χ −1, in ascending powers of the reciprocal temperature, have been determined for the Heisenberg model of a ferromagnetic, for any spin value, S, and any lattice. The first five coefficients appropriate to the magnetic specific heat, C, have also been found. For the body-centred and face-centred cubic lattices, the χ and C coefficients are tabulated for half-integral S from 1/2 to 3. From these coefficients estimates have been made of the reduced Curie temperatures, θs c= k T c/J. It is found that for the simple, body-centred and face-centred cubic lattices the formula reproduces the estimated Curie temperatures fairly accurately. Here X=S(S+1) and z is the lattice coordination-number. It is found that, suitably scaled, the theoretical curves for inverse susceptibility against temperature above the Curie point are rather insensitive to the spin value and to the precise lattice structure. The ratio of their initial to the...
496 citations
TL;DR: In this paper, the usual lcao perturbation theory is generalized to take account of the imaginary magnetic shielding constants in aromatic molecules, and the molecular orbital theory is adapted to the calculation of magnetic shield constants in molecules.
Abstract: The molecular orbital theory is adapted to the calculation of magnetic shielding constants in aromatic molecules. The usual lcao perturbation theory is generalized to take account of the imaginary ...
289 citations
TL;DR: In this paper, a simplified method for calculations of proton shielding in molecules by using wave functions which are constructed from gauge invariant atomic orbitals is discussed, applied to the hydrogen molecule by means of a simple lcao mo description.
Abstract: A simplified method is discussed for calculations of proton shielding in molecules by using wave functions which are constructed from gauge invariant atomic orbitals. The method is applied to the hydrogen molecule by means of a simple lcao mo description. The computed total nuclear shielding constant is 3·2×10−5.
223 citations
TL;DR: In this paper, the London theory of diamagnetic susceptibility of conjugated hydrocarbons is extended in a manner which leads to detailed information about the distribution of interatomic currents induced by a general magnetic field.
Abstract: The London theory of the diamagnetic susceptibility of conjugated hydrocarbons is extended in a manner which leads to detailed information about the distribution of interatomic currents induced by a general magnetic field. The method is illustrated by a calculation of the currents flowing round the two closed rings of azulene in a uniform field. This suggests that the larger current flows in the five-membered ring.
223 citations
TL;DR: A theory of the broadening of multiplet components in magnetic resonance spectra of coupled nuclei due to electric quadrupole spin-lattice relaxation is presented in this article.
Abstract: A theory of the broadening of multiplet components in magnetic resonance spectra of coupled nuclei due to electric quadrupole spin-lattice relaxation is presented. It is shovm that the broadening of the components of the 1: 1: 1 triplet for nuclei of spin 1/2 coupled to a nucleus of spin 1, is 3/2 as great for the outer lines as for the central one, provided that the rate of quadrupole relaxation is not too large. This is in agreement with experimental observations on N14H3 A theory of the line shape of the partiy collapsed multiplet at higher rates of quadrupole relaxation is also given.
219 citations
TL;DR: The electron resonance hyperfine splitting of a H produced by protons of a methyl group attached to one of the aromatic carbon atoms of a π-electron radical is calculated by the valence bond theory, treating the exchange interaction between the odd electron and the methyl group as a perturbation.
Abstract: The electron resonance hyperfine splitting a H produced by protons of a methyl group attached to one of the aromatic carbon atoms of a π-electron radical is calculated by the valence bond theory, treating the exchange inter-action between the odd electron and the methyl group as a perturbation. The formula a H = Q ρ which relates a H for a ring proton with the spin density ρ on the aromatic carbon atom also holds for methyl protons. Q is predicted to be positive with a theoretical value of about 28 gauss in the ethyl radical. Experimental data for several radicals indicate that Q is about 25 gauss. It is suggested that the CH3 and CH2 protons appear to be equivalent in the spectrunl of the ethyl radical because Q has the same magnitude for both. The spectra of some Wurster's blue ions are interpreted on the assumption that hyperconjugation takes place between methyl groups and the nitrogen atoms.
192 citations
TL;DR: In this article, the Renner effect was used to interpret the observations of Dressler and Ramsay on the vibronic absorption spectrum of the NH2 radical, which confirmed the view of these authors that the absorption band is associated with transitions between the components of an electronic II state which are widely separated by electronic-vibrational interaction.
Abstract: The observations of Dressler and Ramsay on the vibronic absorption spectrum of the NH2 radical are interpreted quantitatively in terms of the Renner effect. The use of a perturbation method leads to frequency predictions which are in good accord with experiment and confirm the view of these authors that the absorption band is associated with transitions between the components of an electronic II state which are widely separated by electronic-vibrational interaction.
188 citations
TL;DR: The intensity distribution of a composite spectral line with exchange narrowing is calculated by integrating a matrix expression derived by Anderson as discussed by the authors, where the intensity distribution is derived by integrating the matrix expression with Anderson's matrix expression.
Abstract: The intensity distribution of a composite spectral line with exchange narrowing is calculated by integrating a matrix expression derived by Anderson
153 citations
TL;DR: In this article, a quantum-mechanical treatment of the vibrational problem of the latter type has been carried out and is presented in the Appendix and good agreement has been found between the theoretically predicted energy levels and the experimental data.
Abstract: The infra-red spectra of KH2PO4, NH4H2PO4, NaH2PO4, KH2AsO4, NH2H2AsO4, Ag2H3IO6 and (NH4)2H3IO6 and of their deuterated analogues have been recorded at room temperature and some of them also at low temperature in the ferroelectric phase. The interpretation of the particularly interesting spectral region between 3000 and 1500 cm−1, containing several OH bands, has been made in terms of the tunnelling of the protons between two minima of potential energy. These were taken to be of equal depth in the non-ferroelectric phase and unsymmetrical in the ferroelectric form. A quantum-mechanical treatment of the vibrational problem of the latter type has been carried out and is presented in the Appendix. Good agreement has been found between the theoretically predicted energy levels and the experimental data.
136 citations
TL;DR: In this paper, the nuclear magnetic screening constant of a hydrogen atom in a uniform electric field is calculated, neglecting any effect of electron spin, and the screening is found to be reduced by the electric field for all directions of the applied magnetic field, the reduction being greatest if the two fields are perpendicular.
Abstract: The nuclear magnetic screening constant of a hydrogen atom in a uniform electric field is calculated, neglecting any effect of electron spin. The screening is found to be reduced by the electric field for all directions of the applied magnetic field, the reduction being greatest if the two fields are perpendicular.
114 citations
TL;DR: In this paper, the decay times of the three-singlet transition in benzene and acetone were derived from the degree to which excited singlet states are mixed with the triplet state.
Abstract: Calculations have been performed on the probabilities of triplet-singlet transitions in benzene and acetone in connection with the decay times of the phosphorescence. The transition probability was determined from the extent to which excited singlet states are mixed with the triplet state. The assumption that in benzene the phosphorescent state has 3 B2u properties—so that the 1 B1u singlet state is mixed with it-—yields the best agreement with the experimental data. In the case of acetone the phosphorescence was considered as a triplet-singlet transition in which only the electrons of the CO group are involved. In both cases the agreement with experiment is as satisfactory as in other calculations on transition probabilities, the figures for the decay times being 190 and 7 seconds for benzene and 7·8 and 0·6 milliseconds for acetone. The ratio of the calculated decay times is in good agreement with the experimental result (2·4×104 and 1·2×1O4).
TL;DR: In this paper, a statistical mechanical description based on the Lennard-Jones and Devonshire model has been applied to the gas hydrates, which enables one to calculate dissociation pressures, compositions and heats of dissociation of several such gas hyddrates and the agreement between the calctilated values and the experimental data at present available supports the theory.
Abstract: A statistical mechanical description based on the Lennard-Jones and Devonshire model has been applied to the gas hydrates. The theory enables one to calculate dissociation pressures, compositions and heats of dissociation of several such gas hydrates. The agreement between the calctilated values and the experimental data at present available supports the theory.
TL;DR: In this article, the absorption spectra between 2200 A and 10 000 A have been measured of the conjugate acids of a number of aromatic hydrocarbons dissolved in oxygen-free, anhydrous HF and HF-BF3 mixtures, using a specially constructed cell.
Abstract: The absorption spectra between 2200 A and 10 000 A have been measured of the conjugate acids of a number of aromatic hydrocarbons dissolved in oxygen-free, anhydrous HF and HF-BF3 mixtures, using a specially constructed cell. All spectra show very intense and characteristic absorption bands in the visible or near-ultra-violet region. In order to interpret these spectra, self-consistent field molecular orbital calculations have been made for the ground and excited states. The calculations, based on a π-electron model, were performed on an electronic digital computer. It could be shown in a number of cases that the aromatic hydrocarbon (in the absence of oxygen) is present in the acid solution as one type of protonated species. In these cases good agreement is found between the experimental and calculated spectra. Conversely, the theoretical predictions allowed of the interpretation of other cases where the aromatic hydrocarbon, when dissolved in the acid, forms a mixture of different ions, corresponding to...
TL;DR: In this article, the authors derived a formula for the integrated intensity of pressure-induced rotational transitions in pure gases and gas mixtures at moderate pressures, and applied it to the pressure induced rotational spectrum of hydrogen, described in a previous article.
Abstract: A formula is derived for the integrated intensity of pressure-induced rotational transitions in pure gases and gas mixtures at moderate pressures. This formula is applied to the pressure induced rotational spectrum of hydrogen, described in a previous article. A good agreement between the observed and the calculated intensities can be obtained if it is assumed that the induction of the transition moments is mainly caused by the quadrupole field of the hydrogen molecule. In an analogous way, the intensity of the induced simultaneous vibrational-rotational transition in mixtures of carbon monoxide and hydrogen is calculated.
TL;DR: In this paper, the effect of molecular interactions on magnetic shielding constants in gases and liquids is considered using simple statistical mechanics and treating the molecules as points, and the magnitude of these effects is estimated and their relative importance in different molecules is discussed.
Abstract: The effect of molecular interactions on magnetic shielding constants in gases and liquids is considered using simple statistical mechanics and treating the molecules as points. For gases at ordinary pressures the effects are small. For liquids and solutions two effects may be important. (i) Magnetic moments induced in neighbouring molecules give rise to a magnetic field at the nucleus of the molecule considered. (ii) The electron distribution in the molecule may be distorted by the electric field due to neighbouring molecules and a change in the intramolecular shielding constant will then take place. The magnitude of these effects is estimated and their relative importance in different molecules is discussed.
TL;DR: Carbon-13 hyperfine splittings equal to 41±3 gauss have been observed in the paramagnetic resonance of a mixture of C12H3 and C13H3 radicals produced by x-irradiation of CH3I at 77°k as discussed by the authors.
Abstract: Carbon-13 hyperfine splittings equal to 41±3 gauss have been observed in the paramagnetic resonance of a mixture of C12H3 and C13H3 radicals produced by x-irradiation of CH3I at 77°k. The observed splitting provides strong evidence that CH3 is a planar molecule.
TL;DR: In this article, the N.M.R. spectra of aromatic carbonium ions obtained by dissolving highly basic aromatic hydrocarbons in CF3COOH+H2O were measured.
Abstract: N.M.R. spectra of aromatic carbonium ions obtained by dissolving highly basic aromatic hydrocarbons in CF3COOH+H2O.BF3 or HF+BF3 were measured. The resonance of the protons in the CH2 group in the carbonium ion was detected. It was concluded that this configuration, formed by the addition of the proton to the most reactive carbon atom in the hydrocarbon, has an ‘aliphatic’ character. In most instances the N.M.R. spectra of the carbonium ions are blurred by exchange reactions. The character of these reactions is discussed.
TL;DR: Open shell calculations are made for all the three-electron atomic systems of the second period of the periodic table as discussed by the authors, and the results are compared with corresponding two-and experimental energies.
Abstract: Open shell calculations are made for all the three-electron atomic systems of the second period of the periodic table These results are compared with corresponding two-electron and experimental energies It is noted that the improvement of open shell over closed shell calculations becomes less with increasing atomic number In parallel trend the disparity of both from the experimental results increases with Z An electron affinity of zero is found for the helium atom
TL;DR: In this article, an attempt is made to account in a qualitative way for the observed spin-spin couplings by ascribing them largely to hyperconjugation between methyl group orbitals and π-electron orbitals.
Abstract: Indirect spin-spin couplings between methyl groups attached to unsaturated organic molecules and protons directly bonded to unsaturated carbon atoms have been observed in several molecules. An attempt is made to account in a qualitative way for the observed spin-spin couplings by ascribing them largely to hyperconjugation between methyl group orbitals and π-electron orbitals. The connection of these observations with electron spin resonance spectra is mentioned.
TL;DR: In this paper, a new statistical procedure is described for obtaining the thermodynamic properties of a molecular system directly as functions of the pressure, which differs in principle from that suggested in this paper.
Abstract: A new statistical procedure is described for obtaining the thermodynamic properties of a molecular system directly as functions of the pressure. This procedure differs in principle from that sugges...
TL;DR: In this article, the classification of high-resolution nuclear magnetic resonance spectra of substituted ethanes and similar molecules is discussed, and the use of nuclear resonance data to deduce information about the rate of internal rotation is discussed in detail.
Abstract: This paper deals with the classification of high-resolution nuclear magnetic resonance spectra of substituted ethanes and similar molecules. In particular, the forms of the spectra for individual rotational isomers of long lifetime are compared with those appropriate to rapid internal conversion. The use of nuclear resonance data to deduce information about the rate of internal rotation is discussed in detail.
TL;DR: In this article, a simplified kinetic theory for spherical molecules interacting according to a square well potential is described, which correspond closely to those of Longuet-Higgins' and Pople's theory of dense fluids of rigid spheres.
Abstract: A simplified kinetic theory is described for spherical molecules interacting according to a square well potential. The statistical premises of this theory correspond closely to those of Longuet-Higgins' and Pople's theory of dense fluids of rigid spheres. The thermal conductivity λ, shear viscosity η and bulk viscosity κ are predicted to be in the ratio where k is Boltzmann's constant and m the mass of a molecule. To calculate any of these coefficients absolutely requires independent information about the equilibrium pair distribution. This may be obtained from the self-diffusion constant D, whose value is also given by the theory. For argon the measured value of D leads to a theoretical value for η which is in good agreement with experiment; for this liquid however the observed ratio κ:η is very much smaller than predicted.
TL;DR: Some results obtained during the last years from x-ray investigations of solid addition compounds thought to be formed by electron transfer between molecules containing closed shell atoms are discussed in this article, where it is hoped that the results which apply directly to solids only might contribute to the understanding of the bonds formed also in the complexes which have been proved to be present also in liquid mixtures.
Abstract: Some results obtained during the last years from x-ray investigations of solid addition compounds thought to be formed by electron transfer between molecules containing closed shell atoms are discussed. It is hoped that the results which apply directly to solids only might contribute to the understanding of the bonds formed also in the complexes which have been proved to be present also in liquid mixtures.
TL;DR: In this paper, a theory of the coupling of nuclear spins in a molecule by the induction of electronic orbital currents is presented, and an approximate expression for the contribution of this effect to the total coupling constant is derived in terms of the anisotropy of the magnetic screening of the nuclei involved.
Abstract: A theory is presented of the coupling of nuclear spins in a molecule by the induction of electronic orbital currents. An approximate expression for the contribution of this effect to the total coupling constant is derived in terms of the anisotropy of the magnetic screening of the nuclei involved. The theory is applied to some coupling constants involving fluorine nuclei, for which the electron orbital contribution is found to be an appreciable but not dominant part. It can have either sign, but is usually positive.
TL;DR: In this paper, the absorption intensities of the two infra-red active vibrations in methane have been obtained from a perturbation calculation on the equilibrium wave functions derived in the preceding paper.
Abstract: The absorption intensities of the two infra-red active vibrations in methane have been obtained from a perturbation calculation on the equilibrium wave functions derived in the preceding paper. The perturbation field is the change in the potential field due to the nuclei which results from moving the nuclei in the vibrational coordinate concerned, and a simplified form of second order perturbation theory, developed by Pople and Schofield, is used for the calculation. The main approximation involved is the neglect of f and higher harmonics in the spherical harmonic expansion of the nuclear field. The resulting dipole moment derivatives are approximately three times larger than the experimental values, but they show qualitative features and sign relationships which are significant. The experimental intensity measurements are interpreted and discussed in relation to these results.
TL;DR: In this article, a comparison is made between MO calculations of electron spin densities in alternant hydrocarbon mono-negative and mono-positive ions and in odd alternant radicals.
Abstract: A comparison is made between MO calculations of electron spin densities in alternant hydrocarbon mono-negative and mono-positive ions and in odd alternant hydrocarbon radicals. For the positive and negative ions the Huckel MO treatment leads to satisfactory results, whereas for radicals configuration interaction must be taken into account. In a preliminary communication McConnell and Chesnut (see ref [14]) also noticed the necessity of π-π interaction in the MO calculations of electron spin densities of hydrocarbon free radicals. In this way negative spin densities are found for those carbon atoms in the radical at which in the non-bonding MO the electron densities are zero. This difference between alternant ions and radicals is due to the fact that in the singly charged ions the odd electron (‘positive hole’) may approximately be considered to move in the electrostatic field of the neutral carbon atoms of the hydrocarbon molecule, whereas in odd alternant hydrocarbon radicals the odd electron forms an in...
TL;DR: In this paper, simplified calculations have been performed on the electric dipole moments of pyridine, pyrimidine and pyridazine, quinoline, isoquinoline and phthalazine on the assumptions that an important contribution to the total moment results from the hybridization of the lone pair electrons of the nitrogen atoms and that the π electron moment may be calculated with a simple lcao calculation.
Abstract: Some simplified calculations have been performed on the electric dipole moments of pyridine, pyrimidine, pyridazine, quinoline, isoquinoline and phthalazine on the assumptions that an important contribution to the total moment results from the hybridization of the lone pair electrons of the nitrogen atoms and that the π electron moment may be calculated with a simple lcao calculation, taking the Coulomb integral of the nitrogen αNN=αCC+0·4βCC. The deviations between theoretical and experimental results are less than 6 per cent.
TL;DR: In this article, the Hartree-Fock S.C.F. wave functions were calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms.
Abstract: If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed.
TL;DR: In this article, the paramagnetic contributions to the susceptibilities of compounds of B-subgroup ions and the chemical shifts observed in their nuclear magnetic resonance spectra were shown to depend on interconfigurational mixing brought about by environments of less than cubic symmetry.
Abstract: The paramagnetic contributions to the susceptibilities of compounds of B-subgroup ions and the chemical shifts observed in their nuclear magnetic resonance spectra are shown to depend on interconfigurational mixing brought about by environments of less than cubic symmetry. Order of magnitude calculations are made for Pb2+ compounds and agree reasonably well with experiment.
TL;DR: In this article, the average life-time τ of the fluorescent electronic state, as calculated from the measurements, amounts to about 2×10−6 sec for benzene and 5 ×10−7 sec for naphthalene.
Abstract: Measurements on the concentration dependence of the fluorescence intensity of dilute solutions of various acenes in n-hexane at 25°c show that the concentration quenching for benzene as a solute can be explained by simple collisional quenching. In solutions of naphthalene and anthracene the concentration quenching proceeds via an unstable excited complex resulting from the interaction of an excited and a non-excited molecule. The remarkable shape of the concentration curve of naphthalene is attributed to a contribution of the excited naphthalene complex to the total fluorescence intensity. The average life-time τ of the fluorescent electronic state, as calculated from the measurements, amounts to about 2×10−6 sec for benzene and 5×10−7 sec for naphthalene.