In this paper we give the
results of computing the effect of non-additivity of long range forces on the
fourth virial coefficient of a Lennard-Jones 12-6 gas. We have considered only
dipolar effects but have included all terms up to the fourth order of perturbation
theory. We have also calculated the effect of the fourth-order triple-dipole
term on the third virial coefficient. For the fourth virial coefficient we find
that the dispersion non-additivity, while being positive at low reduced
temperatures, goes through a negative minimum at a reduced temperature of about
1.25 before becoming small and positive at high temperatures. This is in
contradistinction to the behaviour of the third virial co-efficient where the
dispersion non-additivity is always positive.
The concentration profile
in a multilayer model of a system containing two immiscible fluid phases is
given by the solution of a non-linear, second-order difference equation. The
surface excess thermodynamic functions of the system can be evaluated only if
this solution is known. Assuming that the solution is symmetric, attempts to
obtain an exact solution using a method described by Ono were unsuccessful, but
a numerical method is described which enables approximate solutions of any
desired accuracy to be obtained. The possible existence of asymmetric solutions
has been examined. Symmetric solutions have also been obtained by methods that
do not require any explicit assumption of symmetry.
Vibrational wave functions
and Franck-Condon factors are calculated for the n → π* transition
in α,β-unsaturated ketones by approximating
vibrations of the chromophore by those of a diatomic moiety (CO). Comparison of
the results with recent c.d. and u.v. absorption measurements indicates that
the principal effect of hydrogen bonding on the n → π* system of
these ketones arises from a differential lengthening of the CO bond in the
excited electronic state as compared with the ground electronic state. It is these
bond length changes which cause (through the Franck-Condon factors) the
redistribution of intensity between vibrational sub-bands which is such a
striking feature of recent highly resolved c.d. spectra.
In this paper we give the
results of computing the third virial coefficient and the cohesive energy of
the crystal for argon taking into account the higher-order multipole terms in
the long-range three- body interaction as recently calculated by Bell. The Barker-Pompe potential has been used as the two-body potential
function. We find that the third virial coefficient values for argon computed
with this more complete non-additive energy function agree very much better
with the experimental values than when only the triple-dipole term is used.
This is particularly true at lower temperatures. The results also show that
better agreement would be obtained if some form of repulsive non- addivity were included in the computation. For the cohesive
energy of the crystal we find that the dipole-dipole-quadrupole energy is
one-third as large as the triple-dipole energy and so cannot be neglected in
these lattice computations. Furthermore, we find that these higher- order
three-body forces do not stabilize the face-centred-cubic lattice for argon,
the hexagonal-close-packed lattice having a slightly lower energy.
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