Quantum Calculations

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.

Computational chemistry background

Basically two ways to calculate molecular

structure:

1. Molecular Mechanics

( MM )

2. Quantum Mechanics

( QM )

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.

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

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

second approximation:

ψel = ψ1 ψ2 ψ3 … ψ

ψi = ∑j=1 Cij χj

QUANTUM MECHANICAL APROACHES :

a) semi-empirical methods (AM1, PM3, PPP, INDO, MINDO, ...)

b) non empirical methods : Ab Initio Density Functional Theory ( DFT )

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

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 .

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.

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.)

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

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 …

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…

Energies for Particle in a Gaussian Potential Well