SECTION A

1.         Polyimides  are  polymers   which  typically  have   very  high   melting  temperatures

compared to most other polymers (> 200 °C). A general overview can be found in Wikipedia   for   background   information   (https://en.wikipedia.org/wiki/Polyimide). These materials typically form semi-crystalline structures – you should refer to this article         for         an         overview         of         structure          of         polymers: https://en.wikipedia.org/wiki/Crystallization_of_polymers.

No  further  reading  or  knowledge  of  polymers  is  required  here  beyond  A-level chemistry.

Consider the series of related polyimides (A to D) which differ only in the structure of the link between the imide groups. Experimentally the value of n is of the order of 2000.

Outline a computational study based on molecular mechanics forcefield methods to investigate which of the materials (A to D) is most likely to form the higher melting point material and which forms the most crystalline (regularly ordered arrangement of polymer chains) material.

Your study should consider:

.    How to construct models of the polymer.

.    How to determine the preferred conformational structures of each polymer.

.    How might you treat different crystalline regions.

.    How you might simulate the melting of a model of each polymer structure you consider and how you would determine the relative melting temperature of these

models from your simulations.

.    Whether  the  study  of a  single  repeat  unit  (i.e.  the  molecule  where  n  =  1 terminated with hydrogen) would provide sufficient information to deduce the order of melting temperatures.

.    The interactions that the forcefield must be able to describe accurately for your study (although explicit selection of a forcefield is not required).

No calculations are expected. You may use the chemical drawings which are included in the appendix and here.

Note that you should consider for the purpose of this question that to simulate a “realistic (experimental)” single polymer chain (molecule) or assembly of chains is not feasible. The longest single chain that can be simulated is n = 10 and an assembly of at most 20 such chains can be constructed and studied. The ends of a single polymer chain can be considered a hydrogen atom.

Note also that polymers do not form perfect crystals. Rather they have regions where there is regular packing of polymer chains. Moreover, a chain may form a regular repeating arrangement with itself (see scheme A) as well as between different chains.

Scheme A:

https://commons.wikimedia.org/w/index.php?curid=10491297

[30 marks]

SECTION B

2.         (a)      Briefly describe the Hartree Product and  Slater Determinant approaches to writing the wavefunction of a multielectron system. Which approach is usually used and why?       [6 marks]

(b)          Compare and contrast the main principles/assumptions of Hartree-Fock theory and Density Functional Theory (DFT). By comparing the Hartree-Fockeigenvalue equation and the Kohn-Sham orbital eigenvalue equation, or otherwise, consider the extent to which these methods account for

.    Electron kinetic energy

.    Electron correlation

.    The Coulomb interaction

.    The exchange interaction

.    Electron-nuclear attraction

Note: for this part of the question you are not expected to comment on excited state calculation.        [14 marks]

(c)          Hydrogen Fluoride (HF) is believed to polymerize in the gas phase. Assuming a computational framework of either Restricted Hartree-Fock theory or Density Functional Theory, suggest what calculations using which basis sets should be used to compute the binding energy of a HF dimer as shown below:

H         F - - - --H         F

[5 marks]

(d)            The lowest excited singlet (!! ) state of polyenes, such as beta carotene shown below, are believed to have substantial contributions from double excitations, i.e. the lowest excited state is formed by exciting both electrons in the HOMO to the LUMO. Suggest one electronic structure method which could be used to compute the !!  excitation energy in beta carotene. Briefly describe the method, explaining its suitability for this system. Suggest any advantages this method has and any challenges the calculation may encounter.                         [5 marks]