1. Quantum Calculations

2. Computational chemistry :
 a branch of chemistry that uses computers to assist
in solving chemical problems.
 uses the results of theoretical
chemistry, incorporated into efficient computer
programs, to calculate the structures and properties
of molecules and solids.
 it can (in some cases) predict hitherto unobserved
chemical phenomena.
 widely used in the design of new drugs and
materials.

3. Computational chemistry background
Basically two ways to calculate molecular structure:
1. Molecular Mechanics
( MM )
2. Quantum Mechanics
( QM )

5. Molecular Mechanics method:
 It views the molecule as a collection of atoms held
together by bonds and expresses the molecular
energy in terms of force constants for bond
bending and stretching and other parameters.

6.  Does not use a molecular Hamiltonian operator
or wave function.
 can be applied to proteins and other large
biological molecules.
potential energy of molecules is calculated based
on a given force field .
The potential energy of the molecular system:
E = E covalent + E non-covalent

7. Quantum mechanics
Based on the Schrödinger Equation:
HΨ = EΨ
Hamiltonian operator for a molecule:
H = KN + Ke + VNN + VNe + Vee
 Use the Born-Oppenheimer approximation

8.  second approximation:
ψel = ψ1 ψ2 ψ3 … ψ
ψi = ∑j=1 Cij χj

9. QUANTUM MECHANICAL APROACHES :
a) semi-empirical methods
(AM1, PM3, PPP, INDO, MINDO, ...)
b) non empirical methods :
 Ab Initio
 Density Functional Theory ( DFT )

10. Semi-empirical methods:
Use a simpler Hamiltonian than correct molecular
Hamiltonian
 Semi-empirical quantum chemistry methods are
based on the Hrtree-Fock formalism, but make
many approximations and obtain some
parameters from empirical data.
 model only the valence electrons
 limited to hundred of atoms
 can be used to study ground and excited
molecular states
 an example is the Huckel MO treatment of
conjugated hydrocarbons

11. non empirical methods :
 do not require empirical parameters .
 can be used for any molecular system .
 limited to tens of atoms .
 can be used to study ground and excited
molecular states .

12. Ab initio methods:
 use the correct Hamiltonian .
 Not use experimental data other than the values of the
fundamental physical constants.
 The simplest type of ab initio electronic structure calculation
is the Hartree Fock (HF) scheme, in which the correlated
electron–electron repulsion is not specifically taken into
account; only its average effect is included in the calculation.
 As the basis set size is increased, the energy and wave
function tend towards a limit called the Hartree–Fock limit.
 an example is a Hartree-Fock SCF calculation.

13. Density Functional Theory (DFT) :
 It’s a new method
 Not use wave function
 In DFT, the total energy is expressed in terms of the total
one electron density rather than the wave function.
 there is an approximate Hamiltonian and an approximate
expression for the total electron density.
 Some methods combine the density functional exchange
functional with the Hartree–Fock exchange term and are
known as hybrid functional methods.
 Most popular DFT method is B3LYP. (Becke 3‐Parameter
method for calculating that part of the molecular energy
due to overlapping orbitals, plus the Lee‐Yang‐Parr method
of accounting for correlation.)

14.  Program packages in molecular electronic
structure calculations :
1. Gaussian 2. Gamess
3. DeFT 4. DALTON
5. Mopac
Molecular structure and properties
visualization programs:
1. GaussView 2. Molekel
3. Raswin 4. Hyperchem
5. Molden

15. Gaussian:
Gaussian is arguably the most-used computational
quantum-chemistry program. It does electronic-structure
calculations and standard quantum chemical calculations.
Among the methods available are semi-empirical
methods (such as CNDO), Hartree-Fock (restricted and
unrestricted), MPn (Mollar-Plesset perturbation theory of
order n=2,3,4), CI (Configuration-Interaction), CC (Coupled-
Cluster), Multi-configurational SCF (such as CAS-SCF) and
various DFT (Density-Functional Theory) methods and …

16. Gaussian Capabilities:
It can be used to obtain electronic
properties, molecular geometries, vibrational
frequencies, orbitals, reaction profiles, IR and
Raman spectra, Polarizabilities, Thermochemical
analysis, Atomic charges, Dipole moment, Electron
affinities, Electrostatic potential and much more…

21. Energies for Particle in a Gaussian Potential Well