Many computer simulation studies for liquids and liquid mixtures
composed of rigid molecules
have been carried out for the last three decades.
The structure and dynamics for classical liquids
have been studied by using computer simulation
(e.g., Allen and Tildesley, 1987).
Little attention has, however, been paid to the molecules
having the degrees of freedom of internal rotation around dihedral angle,
because these motions in flexible molecules
are not easy to treat and distinguish from other motions
such as the rotational motion and translational motion.
The physical properties of chain molecules are somewhat related
to their flexibility.
A complicated nature of the liquid structures
arising both from intermolecular and intramolecular
interactions prevented us from understanding the roles played by the
degrees of freedom of internal rotation.
It is well-known that the distribution of dihedral angle
depends significantly on the density and temperature.
The dynamical feature of the torsional motion
is also sensitive to such external conditions.
The dihedral angle distribution is
a measure of solvent effects typical to liquid states,
and the mechanism of torsional motion of the dihedral angle
in the liquid is expected to differ from that in dilute gas state.
However, this difference has not yet been accounted for.
The interactions between the solvent and the solute alter
the topography of potential energy hypersurface which is
different from that in vacuum.
This, in turn, affects
the conformational equilibrium of the solute.
Conformational changes in liquid state, which occur less frequently
than
the relaxation process of surrounding solvent molecules,
are closely related to this topography.
In the series of present studies,
molecular dynamics (MD) simulations for flexible molecules,
have been performed
to examine the liquid structure in connection with the coupling between
intra- and inter-molecular interactions and its effect
on the torsional motions.
Two flexible molecules are adopted:
butane (n-butane) as the simplest flexible molecule and
ethylene glycol (ethane-1,2-diol,~EG) as the simplest polyol.
Butane is one of n-alkanes which are high theoretical and industrial interest substances.
Polyols are well known characteristic of some interesting phenomena such as
the prevention of denaturating protein and the presence of
`non-freezable water' in aqueous solution at subzero temperatures (Franks, 1982).
The effects in terms of the torsional motions are examined
since these complicated static and dynamical properties arise from
the coupling mentioned above.
I. Conformational equilibria of n-butane molecules
It is believed that the distribution of the dihedral angle of
flexible molecule in the liquid state is fairly different
from that in the ideal gas state.
However, the origin of this difference is not clear.
The distribution of dihedral angle is a measure of the effect
of intermolecular interaction on the
internal degree of freedom.
Historically,
this distribution in the condensed phase has been discussed in terms of
the random distribution or the short range packing effect.
The former view proposed by Flory (1969) was based on
the consideration that the distribution is dominated by random packing,
and therefore, it should be the same as that in the ideal gas state.
On the other hand, statistical mechanical theory predicted
that the distribution shifted to the gauche form in favor of the
short range packing. In fact, various methods such as the packing fraction
theory, and superposition approximation
have been proposed to evaluate the distribution of the dihedral angle.
According to these approximate methods, an increase in the population of
the gauche conformation is estimated to be as large as 10%
(e.g., Jorgensen et al., 1981; Jorgensen, 1981).
In a more realistic treatment with the reference interaction-site model (RISM)
by Pratt and Chandler
(Chandler and Pratt, 1976; Pratt and Chandler, 1977;
Pratt, Hsu and Chandler, 1978), the increase is 7%.
The recent computer simulation studies
(Edberg et al., 1986, 1987; Wielopolski and Smith,
1986; Brown and Clarke, 1990)
support the latter view.
However, the results are likely to be
dependent on the models used, the simulation time,
the existence of the attractive forces, and other simulation conditions.
Therefore, n-butane as the simplest molecule is adopted,
in which only a single degree of freedom of internal rotation is included
and other stretching and bending vibrational motions are ignored.
Furthermore, the effect of the attractive forces on the dihedral angle
distribution for n-butane
has been examined by the molecular dynamics (MD) simulations.
II. The torsional dynamics of n-butane molecule
The chemical reaction rate and its mechanism in liquid state are
somewhat different from that in the ideal gas state.
However, the origin of this difference has not been accounted for.
It is believed that the interaction between the solvent and the solute
forces to alter the topography of potential energy hypersurface.
The dynamics of infrequent molecular events are closely related to
this topography.
In the case that the system has stronger interaction
between the solvent and the solute,
we must consider the whole effects of many solvent molecules
to interact concurrently with the solute molecules.
In the opposite case, the existence of the solvent molecules
also plays a significant role in the conformational equilibrium of
solute molecules.
The interactions between the solvent molecules and the solute molecules
are `co-operative' effects which affect indirectly the equilibrium and
the reaction path of internal rotation of the flexible molecule.
The conformational equilibrium of flexible molecule
is considered to be one of chemical reaction in a condensed phase
(Chandler, 1978).
The intramolecular rearrangement is regarded as
energy transformation process.
The trans-gauche isomerization of n-butane is a simple model for
first-order chemical reaction
since the torsional potential for n-butane is one-dimensional.
Many investigations have been carried out in order to
evaluate the rate constants from molecular dynamics
of n-butane using statistical mechanical approaches
(Rosenberg et al., 1980)
and transition state theory (TST)
(Edberg et al., 1986,1987; Brown and Clarke, 1990).
In this work, to clarify the torsional motion of the flexible molecule,
n-butane molecule is adopted as
the simplest flexible molecule among n-alkanes.
Only a single degree of freedom for torsional motion is included
and other stretching and bending vibrational motions are ignored.
The molecular dynamics (MD) simulations of the n-butane molecule
in non-polar molecules Xe
are carried out,
which is spherical but has a fairly high melting point.
To analyze the torsional motion of n-butane, the kinetic energy
of n-butane is divided into three terms, which are arising from
the translational, rotational and torsional motions.
By analyzing the time development of these kinetic and potential energies
of n-butane, we investigate how the reaction path of internal
rotation of n-butane molecule changes
under the influence of the solvent molecules.
III. Aqueous Solution of Ethylene Glycol
Protein in polyol solvents is not easily denatured,
while most proteins are not stable against heating, cooling or pH changes
and easily undergo rearrangements to other stable states.
The proteins in polyol solvents or aqueous polyol solutions, however,
seem to retain a highly ordered structure than those in pure water.
Non-freezing glassy water is a very interesting example
in which pure water does not become glassy upon cooling.
A recent proton NMR study (Forsyth and MacFarlane, 1990) has shown that
diol molecules can interact strongly
with water by means of hydrogen bonds.
However, it is not possible to say whether or not the
diol solutes reduce the ability of water to form hydrogen-bonded networks
and thus prevent the water molecules from nucleating to form ice.
Many investigations have been carried out
in order to clarify the origins of these phenomena,
but their mechanisms are still unclear.
These characteristic properties undoubtedly arise from
the coupling of intermolecular interactions with intramolecular interactions
in the polyol molecules
as well as from hydrogen bonding between the polyol hydroxy groups
and water molecules.
The torsional motions of flexible molecules are dependent
on the nature of the solvent species in a condensed phase
as well as on the torsional potential.
The dynamics of the torsional motions are highly cooperative in the liquid state.
The conformational equilibrium is somewhat
different from that in a vacuum.
Therefore, investigations of the role of solvent molecules
on the equilibrium properties and dynamics of torsional motions
are very important.
Ethylene glycol
is the simplest of polyols and a biologically important substance.
Because each EG molecule has two OH groups,
three-dimensional (3D) networks can be formed
with water, with other EG molecules, and with itself by hydrogen bonding
in aqueous EG solutions.
Some of the physical properties of EG are different from
those of other monohydric
alcohols (Podo et al., 1974) which can form only linear hydrogen bonds.
The internal equilibrium configuration of the EG molecule
has been measured by electron diffraction (Bastiansen, 1949)
and IR spectroscopic methods (Krueger and Mettee, 1965;
Buckley and Gigu\`ere, 1967),
and has been calculated
using energy minimization of rotational isomers
(Podo et al., 1974; van Alsenoy et al., 1984).
Recently, conformational analyses have been performed
using
MC perturbation simulations (Nagy et al., 1991)
and the Potential Mean Force (PMF) was also calculated (Hooft et al., 1992).
In the present molecular dynamics (MD) simulation,
we aim to clarify the torsional motion of EG
in aqueous solutions of finite EG composition
in connection with inter- and intra-molecular hydrogen bonds.
To this end, we make a comparison of this system
with an EG+Xenon mixture.
In order to investigate how the intramolecular interaction affects
intermolecular hydrogen bonds, some rigid-EG models are also examined.
Scope of the Present Study
MD simulations on n-butane and aqueous solutions of EG have been
carried out in the present study.
In the next chapter, the scheme of constraint-MD method is given
with some improvements.
In chapter II, the conformational equilibria of n-butane molecules
are discussed.
Chapter III deals with the torsional dynamics of n-butane molecule
to analyze the motion of n-butane.
Chapter IV is devoted to MD calculations for aqueous solution of
EG.
The torsional motions of EG in aqueous solutions
of finite EG composition are presented and clarified
in connection with inter- and intra-molecular hydrogen bonds.
General conclusion of this work is given in the final chapter.
