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Molecular modeling (Leach) (An Introdiction to Computational Quantum…
Molecular modeling (Leach)
An Introdiction to Computational Quantum Mechanics
One-elctron Atoms
spherical symmetry, therefore we can put it in
polar coordinates
in, particular
theta - angle to z axis
phi - angel from the x axis in the xy plane
r
r and teta depend on radial function (R(r))
and spheric harmonic, or angular function (Y(teta, phi))
the wavefunctions can be referred to as
orbitals
that are charactarised by three quantum numbers:
l: azimuthal q. number:0,1,..(n-1)
m: magnetic q number: -l, -(-l-1), ...0...(l-1),l
n: principal quantum number: 1, 2, 3...
H and He
atomic units
Bohr (Bohr distance)
1 unit of mass
Hartree (energy)
1 unit of charge
boundary condition
you have to put certain conditoins(requirements) to solve the Shrodinger equation
wavefunction is said to be normalized when equal 1
orthogonal = 0
Kronecker delta
Polyelectronic Atoms and Molecules
all solutions for many-body problem are approximate
spin is quantized and can have projection on the z axis either +h-bar or -h-bar (up and down)
therefore we have spin orbital
Aufbau principle
, each orbital can contain two electrons with paired spin.
Hund's rule
- electrons occupy degenerate states with a maximum number of unpaired electrons. In some situation it is more preferable to place electron on the higher energy orbital than pair it.
electrons are
indistinguishable
. If we exchange any pair of electrons, the distribution of electron density stays the same
Pauli principle
no two electrons can have the same set of quantum number
Hartree product
does not take to the account that the electron motion corralates with each other and the spin nature of electron
Therefore, we are using Slater determinant
Molecular Orbital Calculations
on the example of H2
molecular orbit can have the tiplet state with two unpaired electrons (orthohedrogen)
exchange interaction
is needed to stabilize the triplet stae of H2. It has the effect of making electrons of the same spin to avoid each other. As a result, each electron can be considered to have a hole - exchange hole or Fermi hole.
The Hartree-Fock Equations
Mol properties using ab initio QM
Approximate Mol Orb Theory
Huckel Theory
3.
ab initio
Methods, Density Functional Theory and Solid-state Quantum Mechanics
4.Empirical Force Field Models: Molecular Mechanics
Energy Minimisation and Related Methods for Exploring the Energy Surface
Computer Simulation Methods
Molecular Dynamics Simulation Methods
Monte Carlo Simulation Methods
Conformational analysis
Protein Structure Prediciton, Sequence Analysis and Protein Folding
Four Challenges in Molecular Modelling: Free Energies, Solvation, Reactions and Solid-state Defects
The Use of Molecular Modeling and Chemoinformatics to Discover and Design New Molecules