Molecular modeling (Leach)

  1. An Introdiction to Computational Quantum Mechanics

3.ab initio Methods, Density Functional Theory and Solid-state Quantum Mechanics

4.Empirical Force Field Models: Molecular Mechanics

  1. Energy Minimisation and Related Methods for Exploring the Energy Surface
  1. Computer Simulation Methods
  1. Molecular Dynamics Simulation Methods
  1. Monte Carlo Simulation Methods
  1. Conformational analysis
  1. 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

One-elctron Atoms

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

spherical symmetry, therefore we can put it in polar coordinates

H and He

atomic units

Bohr (Bohr distance)

1 unit of mass

Hartree (energy)

1 unit of charge

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...

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Polyelectronic Atoms and Molecules

Molecular Orbital Calculations

The Hartree-Fock Equations

Mol properties using ab initio QM

Approximate Mol Orb Theory

Huckel Theory

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

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

Pauli principle no two electrons can have the same set of quantum number

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.