# Key Points To Know

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• Computational Science
• Computational Chemistry
• Basic Quantum Chemistry
• Schrodinger's Equation
• Atomic Units
• The Born Oppenheimer Approximation
• The Hartree Fock Approximation

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• ## Computational Science

• Scientific Research can be classified into four main categories:
1. Observational Science
2. Experimental Science
3. Theoretical Science
4. Computational Science

• Computational Science uses everything that scientists already know about a problem and incorporates it into a mathematical problem which can be solved. The mathematical model which then develops gives scientists more information about the problem.

• Computational Science is beneficial for to main reasons:
1. It is a cheaper method of conducting experiments.
2. It provides scientists with extra information which helps them to better plan and hypothesize about experiments.

## Computational Chemistry

• Computational chemistry is a branch of chemistry that generates data, which complements experimental data on the structures, properties and reactions of substances. The calculations are based primarily on Schroedinger's equation.

• Computational chemistry is particularly useful for determining molecular properties which are inaccessible experimentally and for interpreting experimental data

• With computational chemistry, you can calculate:
1. electronic structure determinations
2. geometry optimizations
3. frequency calculations
4. transition structures
5. protein calculations, i.e. docking
6. electron and charge distributions
7. potential energy surfaces (PES)
8. rate constants for chemical reactions (kinetics)
9. thermodynamic calculations- heat of reactions, energy of activation

• There are three main types of calculations:
1. Ab Initio: (Latin for "from scratch") a group of methods in which molecular structures can be calculated using nothing but the Schroedinger equation, the values of the fundamental constants and the atomic numbers of the atoms present (Atkins, 1991).
2. Semi-empirical: techniques use approximations from empirical (experimental) data to provide the input into the mathematical models.
3. Molecular mechanics: uses classical physics to explain and interpret the behavior of atoms and molecules

## Basic Quantum Chemistry

• Bohr model states that electrons are particles which move around the nucleus in fixed orbitals.

• Electrons need a certain amount of energy to move between orbitals. The equation to find the amount of energy needed is: • Quantum model states that electrons are not particles, but have wavelike characteristics and so do not move in uniform orbitals.

• Various properties of the electrons can be calculated with the Schroëdinger's Equation:
H = E • Bohr's radius is an important constant in the Schroëdinger's Equation. In an atom, for the first orbit where n=1, the radius r is called the Bohr radius, and is symbolized as a0: ## Atomic Units

• Bohr radius: atomic unit of length • Hartree: the Coulomb repulsion between two electrons separated by one bohr • Table of constants and conversion factors.

## The Born Oppenheimer Approximation

• This approximation helps in finding the Schroëdinger's Equation for large systems. It is an equation describing the motion of one electron assuming the nucleus is not moving. (False assumption, but helps in simplifying equation.)

• Shown below is the equation for the "electronic" Hamiltonian (one that neglects the kinetic energy term for the nuclei). • Below is the Hamiltonian used in the Schroëdinger equation describing the motion of electrons in a field of fixed nuclei, shown in the first equation • This Hamiltonian is used for nuclear motion, describing the vibrational, rotational, and translational states of the nuclei.

## The Hartree Fock Approximation

The Hartree Fock Approximation is what is known as a Self-Consistent Field Method (SCF). The Method:
1. begin with a set of approximate orbitals for all the electrons in the system
2. one electron is selected, and the potential in which it moves is calculated by freezing the distribution of all the other electrons and treating their averaged distribution as the centrosymmetric source of potential
3. the Schrodinger equation is solved for this potential, which gives a new orbital for it
4. the procedure is repeated for all the other electrons in the system, using the electrons in the frozen orbitals as the source of the potential
5. at the end of one cycle, there are new orbitals from the original set
6. the process is repeated until there is little or no change in the orbitals
Things to keep in mind:
• defined as the wavefunction of an electron in an atom
• square of the AO gives the probability density
• any electron described by an orbital is said to occupy that orbital
• atomic orbitals have a well-defined significance only for hydrogenic atoms
• hydrogenic atoms are used in many of the computational approximations
• the orbital is a mathematical expression, describing the probability of finding an electron at some point near the nucleus

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