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- Dr. Peter Taylor (San Diego Supercomputer Center) Mail |

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#### Molecules (Atoms and Connectivities) are Defined by their Molecular Structure.

Structure can be specified in various ways:

**I. Cartesian Coordinates: x, y, z**- Cartesian Coordinate System
- a) set of 3N values
- b) external frame of reference
- c) nonredundant set of coordinates
- d) used often in computer manipulation
- e) difficult to converse with

- Cartesian Coordinate System
**II. Internal Coordinates:**- Example of Internal Coordinate Discription
- a) bond lengths, bond angles, bond torsions, etc.
- b) internal frame of reference
- c) can be a redundant set of coordinates
- d) used often to discuss molecular structure, as it can serve as a 'pictorial' model
- e) can serve as 'empirical parameters' for chemical structure

### Energy as a Function of Structure:

#### E =

*f*(structure)- Example: Potential Energy Surface (PES)

#### dE/dt = d[

*f*(structure)]/dt- Example: Reactivity

### E =

*f*(structure) Models:### A. 'Cartesianal' Coordinate Approach

- Schrodinger Equation
- Can be a very accurate model
- Can be extremely costly in terms of time and effort
- No 'back-of-the-envelope' shortcuts for estimation.

- Schrodinger Equation
### B. 'Internal' Coordinate Approach:

## E = E(bond) + E(angle) + E(torsional) + ...

- Assume a mechanical model for molecules, (i.e., balls & springs)
- Knowledge of ALL terms of this equation can provide knowledge of individual components (fairly impossible!!)
- Energy is 'parameterized' as a function of internal coordinates of the molecular system.
- "Empirical" Approach - fit to experimental quantities.