William Michael Davis
Research Interests
RESEARCH PROPOSAL
Theoretical Developments in Density Functional Theory:
Basis Set and Functional Developments.
In quantum chemistry, the theoretical study of the electronic structure
and properties of molecules and solids can be made simpler if the atomic
core electrons are considered invariant for a given element from molecule
to molecule. The complexity of the computations of electronic properties
increases rapidly with the number of electrons treated. The computational
effort scales as N3 to N5, where N is the number of electrons explicitly
treated, depending on the implementation of the SCF scheme. Thus,
dramatic savings can be realized if the core electrons can be removed from
consideration by some rigorous approach and only the valence electrons
explicitly considered. Valence electron only methods are required,
which, in order to be truly effective, must be competitive with the all-electron
treatments in terms of the accuracy of predicted molecular properties.
Ab initio effective core potentials are derived from atomic all-electron
calculations. These potentials are then used in valence-only molecular
calculations where the atomic cores can be treated as chemically inactive.
The methodology, programs and techniques used to re-optimize a set of Hartree-Fock
based effective core potentials for use in density functional calculations
have been implemented previously.
I propose to extend the methodology implemented previously to other
atoms of the periodic table and thus develop efficient and accurate effective
core potentials and valence basis sets to be used in density functional
calculations. These new developments will allow studies of larger
molecules to be carried out inexpensively.
The use of DFT methods in computational chemistry has expanded greatly
over the past 7 years. Despite this expansion, there are many questions
that need to be answered about the use of the various exchange-correlation
potentials in the literature: how does the choice of basis set and
functional effect the molecular properties?; is there a "best" functional
for all calculations or does the choice of functional depend on the molecular
systems to be studied?; can the Becke parameters be adjusted to give
more accurate molecular properties?; is there a new form of exchange-correlation
functional that will be more accurate than those previously?
I propose to investigate these questions through a systematic study
of the structures, vibrational frequencies and energetics for species of
real chemical interest with a specific interest in molecules of environmental
importance. Several collaborations with experimentalists are possible
for these intensive projects. Selected exchange-correlation functionals
will be tested and several new equations will be developed and tested.
The effective core potentials and basis sets developed will be tested as
well for an interesting comparison of both functional and basis set effects
within the given resources.
Theoretical Studies of Combustion and Atmospheric Reactions
The combination of free radicals with molecular oxygen to from peroxyl
radicals features significantly in the description of gaseous oxidation
reactions, both in atmospheric processes and in combustion. There
has, however been no systematic theoretical study on these peroxyl radical
reactions. It has been shown recently that benzylperoxyl radicals
can have a marked effect on the spontaneous ignition of diesel fuel, and
some preliminary calculations have been reported. The series
of peroxyl radicals containing up to eight carbons will be studied.
These theoretical studies will be performed using ab initio quantum
chemical techniques, with inclusion of electron correlation. Such techniques
accurately reproduce experimental data such as reaction energetics for
a wide range of compounds, and can supply further information which is
not amenable to experimental observation. Even where experimental information
is available, computations can provide complementary information.
Group Interaction Modelling of Polymer Properties
Polymers are established as an extremely important class of materials and
are found in almost every facet of modern life from the most advanced adhesive
to the humble computer keyboard. The single most important characteristic
of polymers is their diversity in composition which gives rise to different
molecular states such as liquidlike, rubberlike, amorphous glass, oriented,
crystalline, liquid crystal or almost any combination of the above.
Until recently, there has been no systematic way to efficiently model
the characteristics of polymers without resorting to a plethora of experimental
parameterization. An ideal model for polymers would allow the interrelations
between physical properties to be expressed in a straightforward analytical
equation, with polymer structural parameters as dependent variables.
This approach is used in the Group Interaction Modelling (GIM) method
where the properties of polymers are modelled as a function of six parameters.
These six model parameters are based upon molar additive functions, where
the parameters for each group can be summed to give the total value for
the mer unit in question. The model parameters M (molecular weight),
Vw (van der Waals volume), Ecoh (cohesive energy) and N (degrees of freedom)
are all group additive and can be easily calculated from previous experimental
values. The parameter L (length) can be calculated using any standard
molecular modelling package. The remaining parameter ?1 is calculated
using the selection rules of GIM. In this way we can use this simple
model theory to calculate many thermal and dynamic mechanical properties
of interest.
Research will be carried out on the relationship between dynamic mechanical
properties of polymers and their chemical structure. Detailed study
will include blends and multiphase polymers and polymers under large static
load as well as other thermal and electric properties of interest.
Polymers for Sound Damping
All real bodies are naturally damped, albeit most bodies damp only modestly.
Polymers, especially near their glass transition temperatures, damp much
more. Commercially, polymers may be applied to the surface of the
vibrating substrate to increase damping. Both single-layer (extensional)
and two-layer (constrained) systems are in use.
The complex modulus E* can be expressed as E* = E’ + iE”, where E’
is the storage modulus and E” is the loss modulus. E’ is essentially
a measure of the energy stored elastically and E” is the equivalent energy
lost as heat during the interaction of the polymer with the sound waves.
Thus, the polymer actually heats up during the interaction. The equation
expressing the heat gained is
where ?0 represents the maximum deformation of the polymer. A
further quantity of interest is the loss tangent
where the ratio of the two modulii represents an extremely useful damping
quantity. The two quantities E” and tan ? are usually the prime parameters
of interest for damping. If these quantities are small at a given
temperature and frequency, damping will be small, and vice-versa.
A large number of polyurethanes are currently under investigation both
experimentally and theoretically. The mechanical properties are measured
experimentally using differential scanning calorimetry (DSC), differential
thermal analysis (DTA), dynamic mechanical analysis (DMA), dielectric analysis
(DEA), and thermagravimetric alalysis (TGA) and the experimental results
are used to compare to our calculated results for the properties of interest.
These experimental values are also used to help refine our parameter set.
The main goal of this research is to eventually be able to design an
exact polymer for use under specific damping conditions, given only the
type of polymer needed and the general operating conditions under which
the polymer is to be used. There is a strong interest in this
type of polymer modelling in industry as it saves an inordinate amount
of time and money over more conventional “trial and error” methods.
The modelling methods used for sound damping materials can be extended
to the study of other properties including conductivity, aging and creep.
In this way it is possible to design polymers with exact physical properties
given the values of the six GIM properties.