Comment on the determination of the intermolecular potential energy function of neon from spectroscopic,equilibrium and transport data

A quantum-mechanical treatment of the dynamics of relaxation of a twolevel mode coupled to a thermal bath is presented. The Zwanzig-Mori projection-operator formalism is employed to derive exact equations of motion for the correlation function and the excess population , where and are the coordinate and number operators associated with the two-level mode. In the van Hove weak-coupling limit it is shown that |G _ν|² and Δn decay exponentially with time constants τ and τ′, respectively. Explicit expressions for τ and τ′ are determined and the relationship between them clearly established. The application of the model to the specific problem of the effects of vibrational relaxation on isotropic Raman spectral lineshapes in dense media is emphasized.     

Thermodynamic parameters for gaseous sulphate ion

Electrostatic energies and Madelung parameters for M ₂SO₄ (M = Li, Na, K, Rb and Cs) and for MSO₄ (M = Ca) are reported. An assessment of the charge distribution within the sulphate ion (q ₀ = -0·80) is made and values:

and

are assigned to the enthalpies of formation and solvation of the gaseous sulphate ion. The total lattice potential energies are found to be

A value of -1267 kJ mol^-1 is assigned for the oxide ion affinity of sulphur trioxide.     

Spectral intensities of the trivalent lanthanides

The variation of the Judd-Ofelt parameters across the isostructural series of ions, [LnW₁₀O₃₅]^7- is considered. The parameters are shown to vary in the manner predicted by the Judd-Ofelt theory involving only a static intensity—gaining mechanism. parameters are shown to vary randomly. The results are contrasted with those previously published for Ln³⁺ doped in Y₂O₃. The variation of for the lanthanide aquo ions is briefly discussed.     

On the effective Zeeman Hamiltonian for a linear molecule in an orbitally degenerate state

Values of the dissociation energies and the interaction constants in the long-range potential

for the B ³Π_Ou+ states of Br₂ and Cl₂ have been obtained from least-squares fits to the attractive part of the Rydberg-Klein-Rees potentials. The term in r ^-6 is not negligible even at large internuclear distances corresponding to the last few vibrational levels. The validity of the long-range inverse-power expansion in the internuclear distance r has been investigated. The expansion is valid outside the electron-overlap region given by

in agreement with the result found in the analysis of I₂.     

The molecular g values,magnetic susceptibility anisotropies,and the molecular quadrupole moments in ethylene sulphide

The first and second-order Zeeman effect has been observed in the rotational transitions in ethylene sulphide to yield the molecular g values and magnetic susceptibility anisotropies. These data are

and

The a axis bisects the CSC angle and the b axis is also in the molecular plane. Only the relative signs of the molecular g values can be obtained experimentally. However, by comparing the molecular quadrupole moments calculated with both sets of g values, we can assign the signs as shown above.

The molecular quadrupole moments are

and

all in units of 10^-26 e.s.u. cm². These molecular quadrupole moments are compared to other similar molecules. The values of the diagonal elements in the paramagnetic susceptibility tensor are

and

all in units of 10^-6 erg/g ² mole. The anisotropies in the second moment of the electronic charge distributions are

and

all in units of 10^-16 cm².     

Isometric groups of non-rigid molecules: homomorphisms and reformulation of a theorem on semi-direct product factorization

The structure of isometric groups of semi-rigid molecules is considered from the point of view of homomorphisms relating various representations defining isometric groups. From the kernels of the group homomorphisms the existence of a number of invariant subgroups (, , etc.) is demonstrated.

One of these homomorphisms is shown to relate the problem of the decomposition of isometric groups into semi-direct products to the analogous problem of molecular covering groups. Based on this relation a theorem reported earlier is reformulated by stating explicitly general conditions under which proper semi-factorization is possible or impossible respectively. The latter situation exists only for certain normal cyclic subgroups of cyclic and dihedral groups, whose order is a product of powers of primes.     

The gas-phase electron paramagnetic resonance spectrum of vibrationally excited SO radicals

Gas-phase E.P.R. spectra from the first six vibrational levels in X ³Σ^- SO have been detected and analysed using a Hund's case (b) formalism. The spectra can be fitted using the following molecular constants:

The first and second derivatives of with respect to the normalized internuclear distance ξ were calculated from these constants. A simple analytic formalism is described which enables the variation of with internuclear distance to be separated into contributions from the matrix elements and from the change in energy spacing between interacting states. Both effects are important in the derivatives of , but it is suggested that in SO most of the variation of with rotational and vibrational state is due to the increase in the second-order part of the parameter as the separation between the ground and the dominant perturbing state decreases. This explanation implies that the expression proposed recently by Veseth and Lofthus for the rotational variation of is not accurate, and enables the conflict between the results of their analysis and ab initio calculations to be resolved.     

Origin of the E.S.R. hyperfine anisotropy and the cos2 θ rule of the β-fluorine couplings

The origin of the hyperfine couplings of β-fluorine nuclei in free radicals has been studied using the hyperfine tensors determined for and in single crystals. The direction of the maximum principal element of the β-fluorine coupling tensor in was found to be very close to the direction of the maximum overlap of the fluorine 2p π orbital with the half-filled carbon 2p π orbital. This means that the spin density in the fluorine 2p π orbital is mainly due to the direct overlap with the carbon 2p π orbital and the contributions from the hyperconjugation and the spin polarization mechanisms are less important. The cos²θ rule, B ₀ + B cos²θ, for the β-fluorine coupling tensor was also derived from the conformational dependence of the overlap integral. Using the ratio of B/B ₀ calculated from the overlap integral together with the observed hyperfine tensor for , the absolute values of B ₂ and B were determined and results were applied to the β-fluorine coupling tensor of the rotating CF₃ group in . The calculated tensor is in very good agreement with the one observed.     

On the determination of the intermolecular potential between a tetrahedral molecule and an atom or a linear or a tetrahedral molecule—application to CH4 molecule

A brief summary of the general theory of the long-range potential energy between two molecules, previously developed by Buckingham, is first presented. Then the first detailed expressions of this potential energy are given for the three following molecular pairs : tetrahedral molecule-atom, tetrahedral molecule-linear molecule and tetrahedral molecule-tetrahedral molecule. These expressions are applied to the calculation of the spectral moments of the far infra-red pressure induced absorption band, the second virial coefficient and the intermolecular mean square torque. This allows a discussion of the magnitude of the various terms contributing to this potential energy and leads to a determination, for CH₄, of the octupole and hexadecapole moments, and of the hyperpolarizability:

     

Ab initio potential surfaces for the à and states of HCN+

Ab initio configuration interaction calculations for the à ²Σ⁺ and states of HCN⁺ are presented. Minima occur at r _CH = 2·03 a ₀, r _CN = 2·25 a ₀ (à ²Σ⁺) and r _CH = 2·75 a₀, r _CN = 2·26 a ₀ (). The potential surface for the state has a local maximum as the hydrogen atom is pulled away from CN. The barrier height is calculated to be 0·27 eV.     

Padé approximant for lennard-jones 6–12 fluid

A solution for the time-dependent Schrödinger equation is given for an N-level system interacting with a sinusoidal field of arbitrary amplitude , frequency v and phase δ, in the presence of an applied static field of arbitrary strength . The solution is obtained by a modification of a previous exact method of solution for and retains the essential analytic features of the exact wavefunction for the problem. The Floquet form of the solution yields (a) the location and the widths of allowed transitions and the location of forbidden transitions, by use of characteristic exponent plots, but without evaluating the spectrum, and (b) convenient expressions for the steady-state induced transition probabilities, including the effects of a uniform relaxation mechanism, that only require the solution of the wave equation over the initial period of the hamiltonian. The approach is equally applicable to Stark (or Zeeman) frequency sweep or tuning problems. The ability to incorporate the effects of static fields in the solution is important since a variety of problems (e.g. anti-crossing spectroscopy) involve the application of such fields to a level configuration interacting with a sinusoidal field. As a detailed specific example, the multi-photon steady-state induced transition probabilities and characteristic exponents are studied, as a function of frequency v, for the unperturbed and the perturbed two-level system under saturating conditions. It is also demonstrated, for the coupling strengths of interest in multi-photon calculations, that the method of solution discussed here is a viable unified alternative to dressed-atom techniques.     

Electron spin resonance spectrum of trapped in a single crystal matrix

The radical , labelled with ¹³C in the position shown, has been prepared by X-irradiation of single crystals of . The ¹³C hyperfine coupling tensor of this radical confirms previous conclusions from a study of the corresponding unlabelled species that the electron is essentially localized on the carbon atom. At room temperature the methylene group undergoes rapid reorientation about the P-C bond while comparison of the ¹³C tensors at 300 K and 77 K suggests that the barrier to rotation has a strong two-fold component but contains intermediate minima.     

Molecular motions in plastic succinonitrile: correlation times from incoherent neutron scattering

In the plastic phase (233 K < T < 331 K), the succinonitrile molecule N≡C-(CH₂)₂-C≡N undergoes motions of isomerization between two gauche and a trans conformations and, when in its transform, rotational motions of reorientation from a diagonal of the b.c.c. unit cell to another. After an evaluation of the multiple scattering correction using both a Monte Carlo simulation technique and a semianalytical calculation, the experimental quasi-elastic neutron spectra measured at 302 K were corrected and a comparison is made to a model taking into account the two coupled molecular motions.

The correlation times found by fitting this model to the corrected data are: for the rotational motion, and for the reaction of isomerization gauche?trans.     

Nuclear spin relaxation in molecular fluids near the critical point

The Watson version of the molecular vibration-rotation hamiltonian is expanded in terms of the scalar invariants of the inverse of the moment of inertia tensor using the generalized Lucas polynomials. The resultant expansion consists of the matrices Î, , ² with coefficients depending on the normal coordinates. This is in contrast to the usual expansion as a power series in the matrix .     

A radio-tracer study of self-diffusion in the smectic phases iso-butyl 4-(4′-phenylbenzylideneamino) cinnamate [IBPBAC]

Average translational self-diffusion coefficients, , have been determined in the smectic E, B and A phases of unaligned samples of iso-butyl 4-(4′-phenylbenzylideneamino) cinnamate. A radiotracer technique was employed which was based on the serial sectioning method used in the study of diffusion in solids. In the smectic E phase is about 1 × 10^-14 m² s^-1. The self-diffusion in the smectic B phase fits reasonably well to an Arrhenius law with an activation enthalpy of 82 kJ mol^-1. The transition from the smectic B to A phase results in a dramatic rise in . In the smectic A phase the results fit an activation enthalpy for self-diffusion of about 168 kJ mol^-1. Similarities between the diffusion in the smectic E and B phases and in plastic solids are observed.     

Convergence of valence bond and molecular orbital theories

A comparison of the rate of convergence of valence bond (VB), symmetrically orthogonalized-orbital valence bond (), and configuration-interaction molecular orbital (SCF) calculations has been made for model π-electron systems in the minimum basis set approximation; the allyl radical, trans-butadiene, and the methylene cyclobutadienyl radical were studied. For excited states, as well as for the ground state, it is found that VB provides the best convergence in most cases and yields the worst results, with SCF typically falling in between. Properties examined include energy eigenvalues, charge and spin densities, transition energies, and transition dipole moments. Charge-density convergence is in opposite directions for the VB and SCF methods, with VB (and ) overemphasizing the charge on the atoms and SCF overemphasizing the charge in the bonding regions.     

Statistical mechanics of solid and liquid mixtures of ortho- and para-hydrogen

It is known from experimental measurements that the configurational free energy of solid and liquid mixtures of p-H₂ and o-H₂ is approximately of the form

where is the mole fraction of o-H₂. Assuming that this dependence of F _conf on is due solely to orientational forces a quantum-mechanical calculation of F _conf is developed which is valid for moderately low temperatures. A simplified statistical model is used consisting of a rigid lattice. The theoretical free energy obtained is however much smaller than the experimental one probably on account of the crudeness of the model. Various refinements are discussed.     

A re-interpretation of the E.P.R. spectrum of the 1,2,3,6,7,8-hexahydropyrene anion radical

The γ radiolysis of carbon tetrachloride at 77 K results in the formation of free radicals which are stable at 185 K and have been identified as ?Cl₃. These radicals trapped in crystallites of CCl₄ or at ‘boundaries’ give very different E.S.R. spectra. Their a _13C coupling constants are practically identical (117 G et 114 G). The structure of ?Cl₃ radicals has been determined: it is nonplanar and the angle has a value of 116°. The action of O₂ on the ?Cl₃ radicals leads to the CCl_{3 2} peroxide radicals whose a _13C coupling at 200 K is 6·15 G.

Après irradiation γ à 77 K du tétrachlorure de carbone, le seul radical stable à 185 K est le radical ?Cl₃. Le radical ?Cl₃, suivant qu'il est piégé au sein des cristallites de CCl₄ ou aux joints de grains, donne un spectre R.P.E. très différent.

Pour les deux types de radicaux, les constantes de couplage a _13C sont voisines (117 G et 114 G). On peut ainsi en déduire que le radical CCl₃ est non plan avec une valeur de 116° pour l'angle . Par action de l'oxygène sur le radical ?Cl₃, on a observé à 200 K le radical CCl_{3 2} dont la constante de couplage a _13C est 6,15 G.