Normal Mode analysis for Adenine
1. Deduce the numbering from the connectivity in Z-matrix in the Gaussian output file.
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Z-MATRIX (ANGSTROMS AND DEGREES)
CD Cent Atom N1 Length/X N2 Alpha/Y N3 Beta/Z J
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1 1 N
2 2 C 1 1.367811( 1)
3 3 N 2 1.367181( 2) 1 128.129( 15)
4 4 C 3 1.362226( 3) 2 111.574( 16) 1 -0.003( 28) 0
5 5 C 4 1.417589( 4) 3 126.439( 17) 2 -0.004( 29) 0
6 6 C 5 1.420802( 5) 4 116.666( 18) 3 0.006( 30) 0
7 7 N 6 1.366063( 6) 5 122.855( 19) 4 179.984( 31) 0
8 8 N 5 1.413517( 7) 4 111.099( 20) 3 -179.997( 32) 0
9 9 C 8 1.341311( 8) 5 104.226( 21) 4 0.001( 33) 0
10 10 N 9 1.405394( 9) 8 112.719( 22) 5 -0.005( 34) 0
11 11 H 2 1.090541( 10) 1 115.731( 23) 6 -179.993( 35) 0
12 12 H 7 1.014940( 11) 6 118.767( 24) 5 -179.974( 36) 0
13 13 H 7 1.014435( 12) 6 120.575( 25) 5 0.020( 37) 0
14 14 H 9 1.084684( 13) 8 125.187( 26) 5 180.001( 38) 0
15 15 H 10 1.016021( 14) 9 127.643( 27) 8 180.000( 39) 0
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The connectivity is shown below:
2. Determine the number of normal vibrational modes:
For a total of 15 nuclei there are 3x15 - 6 = 39 normal modes of vibration:
There are 2x15 - 3 = 27 in-plane modes.
There are 15 - 3 = 12 out-of-plane modes.
The symmetry coordinates for in-plane vibrations are:
1. N1 - C2 stretch R12
2. C2 - N3 stretch R23
3. N3 - C4 stretch R34
4. C4 - C5 stretch R45
5. C5 - C6 stretch R56
6. C6 - N1 stretch R61
7. C5 - N8 stretch R58
8. N8 - C9 stretch R89
9. C9 - N10 stretch R9,10
10. N10 - C4 stretch R10,4
11. C2 - H11 stretch R2,11
12. C9 - H14 stretch R9,14
13. N10 - H15 stretch R10,15
14. C6 - N7 stretch R6,7
15. N7 - H12 stretch R6,12
16. N7 - H13 stretch R6,13
17. Six-membered ring trigonal deformation
(1/
Ö6)(A612 - A123 + A234 - A345 + A456 - A561)18. Six-membered ring anti-symmetric deformation
(1/
Ö12)(2A612 - A123 - A234 +2A345 - A456 - A561)19. Six-membered ring anti-symmetric deformation
(1/2)(A123 - A234 + A456 - A561)
20. Five-membered ring deformation
A89,10 + a(A458 + A10,4,5) + b(A589 + A4,10,9)
21. Five-membered ring deformation
(a - b)(A458 - A10,4,5) + (1 - a)(A589 - A4,10,9)
a = cos 144, b = cos 72
22. C2 - H11 bend (1/
Ö2)(A1,2,11 - A 3,2,11)23. N10 - H15 bend (1/
Ö2)(A4,10,15 - A9,10,15)24. C9 - H14 bend (1/
Ö2)(A8,9,14 - A10,9,14)25. C6 - N7 bend (1/
Ö2)(A167 - A567)26. H13- N7 - H12 scissor-bend A13,7,12
27. H13- N7 - H12 rocking bend (1/
Ö2)(A6,7,13 - A6,7,12)