Quantum-mechanical simulation
of the electronic structure in solids
Instructions: Autumn 2008
Aim: to introduce modern computational chemistry software and its applications.
By the end of the 'experiment', you should have experience of setting up
a calculation or series of calculations to help solve a chemical problem.
Questions related to this computational experiment can be directed
to
Prof. Nicholas Harrison
and Dr Giuseppe Mallia.
Introduction
The properties of solids depend on the electronic structure,
which is related to the nature of the interaction between atoms.
In this laboratory
you will use a quantum-mechanical program to calculate and compare the
electronic structure of ionic, covalent, molecular and
metallic crystals. The differences among the materials will be analysed in terms of
- charge density (both in 3D and 2D by using an isosurfaces and isolines, respectively),
- band structure and
- density of states.
The Software: RedHat Linux, DLVisualize and CRYSTAL
Linux provides an excellent environment for numerical
simulations so the first step is to reboot your computer into RedHat
Linux.
The environment is not hugely dissimilar to that provided by Microsoft Windows.
You will find a web browser (Mozilla) on the tool bar and under the Start Menu you
will find some office tools (Writer, Math etc.) which are similar to those in
Microsoft Office (Word, Excel etc.) and you may find them useful in plotting your
data and writing your report.
DLVisualize is a general purpose graphical user interface for
modelling. It will give you relatively easy access to a number of
quantum mechanical and empirical simulation codes. In this case
the interface to the code CRYSTAL.
The CRYSTAL program computes the ground state energy,
electronic wave function and properties of periodic systems
within Hartree Fock, density functional or various hybrid approximations,
will be used.
There are web sites devoted to both DLV and CRYSTAL where you can find
some additional information.
Further information about
DLV
Further information about
CRYSTAL
Before starting the exercises it is recommended to have a look
the CRYSTAL input and output structure.
A quick tour of CRYSTAL input and output
Exercises:
Ionic crystals
Compare the results for MgO, LiF and NaCl as obtained in the following exercises.
- MgO
MgO geometry input
MgO_geometry output
Run a MgO wavefunction calculation
Run a MgO properties calculation: 3D Charge Density
Run a MgO properties calculation: Charge Density Slide
Run a MgO properties calculation: Band Structure
Run a MgO properties calculation: Density of States
Run a MgO properties calculation: Band Structure + Density of States
Optimise the MgO structure
Calculate the coefficient of compressibility and the bulk modulus for MgO
- LiF
Create an input for LiF by setting the cell parameter equal to 4.02
Angstrom, the experimental value [4],
and by using the basis set for
Li and F
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
- NaCl
Create an input for NaCl by setting the cell parameter equal to 5.64
Angstrom, the experimental value [4],
and by using the basis set for
Na and Cl
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
- NaF - optional
Create an input for NaF by setting the cell parameter equal to 4.64
Angstrom, the experimental value [4],
and by using the basis set for
Na and F
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
- LiCl - optional
Create an input for LiCl by setting the cell parameter equal to 5.14
Angstrom, the experimental value [4],
and by using the basis set for
Li and Cl
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
Covalent crystals
Compare the results for diamond, silicon and germanium as obtained in the following exercises.
- C (C.inp)
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
- Si (Si.inp)
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
- Ge (Ge.inp)
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Optimise the structure
Calculate the bulk modulus
Molecular crystal
- Urea - CO(NH2)2
  (Urea.inp)
Urea geometry input
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Metallic crystal
- Be
(Be.inp)
Run a wavefunction calculation
Run a properties calculation: 3D Charge Density
Run a properties calculation: Charge Density Slide
Run a properties calculation: Band Structure
Run a properties calculation: Density of States
Run a properties calculation: Band Structure + Density of States
Additional material
-
"How Chemistry and Physics Meet in the Solid State"
By Roald Hoffmann, Angew Chem Inr. Ed Engl 26 (1987) 846-878
- "Electronic Structure of Materials" by Adrian P. Sutton,
Oxford Science Publications
- "Bonding and structure of molecules and solids" by David Pettifor,
Oxford Science Publications
- "Basic Solid State Chemistry" by Anthony R. West,
John Wiley and Sons
-
Notes