1. -0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x (y=0)
E/eV CI TS
2B1
2A2
MIN
1D slice of the PES through the conical intersection (to the right) will be used throughout this presentation to show the value of energy fixed for each iso-energy surface.

2. Hyperspherical Coordinates
3D PES of Cyclic-N3 in the
Hyperspherical Coordinates
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x (y=0)
E/eV CI TS
E=0.02 eV
MIN
Sits at the bottom of the wells...
(there are three)

3. Hyperspherical Coordinates
3D PES of Cyclic-N3 in the
Hyperspherical Coordinates
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x (y=0)
E/eV CI
E=0.034 eV TS
MIN
Reaches transition states...
(there are three)

4. Hyperspherical Coordinates
3D PES of Cyclic-N3 in the
Hyperspherical Coordinates
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x (y=0)
E/eV CI
E=0.16 eV TS
MIN
Ground vibrational state energy
(Quantum ZPE)
allows pseudo-rotation!

5. Hyperspherical Coordinates
3D PES of Cyclic-N3 in the
Hyperspherical Coordinates
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x (y=0)
E/eV CI
E = 0.52 eV TS
MIN
Approaches conical intersection...

6. Explanation of the Hyper-spherical
Coordinates:
tan(q/2) r f x y

7. Examples of vibrational wavefunctions for Cyclic-N3
Assignment: (symmetric stretch, bend, anti-symmetric stretch)
(0,0,0)
(0,0,2)
(0,1,0)
(0,1,2)