1. Molecular Specification Anan Wu 2014-10-10

2. Typical Gaussian Input Molecular specification This input section mainly specifies the nuclear positions. There are several ways In which the nuclear configuration can be specified: as a Z-matrix, as Cartesian Coordinates, or as a mixture of the two.

3. Gaussian Input file in Cartesian coordinates and in Z-matrix CartesianZ-matrix Z-matrix: is a way to represent a system build of atoms. A Z-matrix is also known as internal coordinate representation. It provides a description of each molecule in terms of bond length, bond angle and dihedral angel, the so-called internal coordinates. 9 variables 3 variables (2 effective)

4. What’s the difference between Cartesian coordinates and Z-matrix Why one needs to specify the nuclear configuration in Z-matrix? How to?

5. Degrees of freedom  A degree of freedom of a physical system refer to a real parameter that is necessary to characterize the state of a physical system In 3-D space, one can describe the n-particles system with 3N Cartesian coordinates. However, are all these Cartesian coordinates chemically relevant?

6. Degrees of freedom Let’s say the C atom has coordinate (x1,y1,z1) and the O atom has coordinate (x2,y2,z2) with z2 unknown. Application of the formula for distance between two atoms results in one equation with one unknown, in which we can solve for z2. R describes the internal motion between two atoms. Hence, it’s called internal coordinate.

7. Degrees of freedom 3N = 6 = 3 + 2 + 1 Translation Rotation Vibration

8. Degrees of freedom

9. MonatomicLinear MoleculesNon-Linear Molecules Translation (x, y and z) 333 Rotation (x, y and z) 023 Vibration03N-53N-6 Total33N chemically relevant We generally use the bond length, bond angle and dihedral angle to describe the internal motions (vibrations) of the molecule. This representation is called Z-matrix representation. A skillful choice of internal coordinates can make the interpretation of results straightforward.

10. Why one needs to specify the nuclear configuration in Z-matrix?

11. Why Z-matrix? In certain cases, Cartesian coordinates are inappropriate to describe internal motions.

12. How to construct Z-matrix? Bond length: 2-1 2-1+1 N-1 Bond angle: 3-1 3-1+1 N-2 Dihedral angle: 4-1 4-1+1 N-3 3N - 6

13. Examples: N2ON2O CH 3 OH

14. Dummy atom N2ON2O N2ON2O

16. Tasks ： Group 1 ： How to describe the puckering motion of cyclic molecules? Group 2 ： How to determine the symmetry of a molecule given the atomic coordinates?