Normal Mode analysis for Uracil
Deduce the numbering from the connectivity in Z-matrix in the Gaussian output file.
Following Rush et al. (J. Phys. Chem., 1995, 99, 14647-14658) the symmetry coordinates 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. N1 - H9 stretch R19
8. C2 - O7 stretch R27
9. N3 - H10 stretch R3,10
10. C4 - O8 stretch R48
11. C5 - H11 stretch R5,11
12. C6 - H12 stretch R6,12
13. Ring deformation no. 1
(1/
Ö6)(A612 - A123 + A234 - A345 + A456 - A561)14. Ring deformation no. 2
(1/
Ö12)(2A612 - A123 - A234 +2A345 - A456 - A561)15. Ring deformation no. 3
(1/2)(A123 - A234 + A456 - A561)
16. N1 - H9 bend (1/
Ö2)(A916 - A 912)17. C2 - O7 bend (1/
Ö2)(A721 - A723)18. N3 - H10 bend (1/
Ö2)(A10,3,2 - A10,3,4)19. C4 - O8 bend (1/
Ö2)(A843 - A845)20. C5 - H11 bend (1/
Ö2)(A11,5,4 - A11,5,6)21. C6 - H12 bend (1/
Ö2)(A12,6,5 - A12,6,1)22. ring deformation no. 4 (oop)
(1/
Ö6)(t6123 - t 1234 + t 2345 - t3465 + t4561 - t5612)23. ring deformation no. 5 (oop)
(1/2)(
t6123 - t1234+ t3465 - t4561)24. ring deformation no. 5 (oop)
(1/
Ö12)( - t6123 - t1234+ 2t2345 - t3465 - t4561+ 2t5612)25. N1 - H9 wag
g912626. C2 - O7 wag
g723127. N3 - H10 wag
g10,3,4,228. C4 - O8 wag
g845329. C5 - H11 wag
g11,5,6,430. C6 - H12 wag
g 12,6,5,1
Input into bmat_setup is different from examples for umat_setup since we must form symmetry coordinates in order to create a number of internal coordinates that is equal to 3N-6 and still maintains a basis the includes all motions of the molecule with equal weight.
Bond stretching
Stretches can be treated in the same way as for umat, e.g. as below
1 ! Internal coordinate type for bond stretch
N1-C2 ! coordinate label
1 ! first atom
2 ! second atom
1 ! symmetry factor
Valence angle bends
These are entered as symmetry coordinates. This means that the symmetry factor is no longer 1.
For example, for ring deformation
(1/
Ö6)(A612 - A123 + A234 - A345 + A456 - A561)the symmetry factor is 1/
Ö6 or 0.408286The input will have the form
2 ! Internal coordinate type number for angle bend
C6-N1-C2 ! Enter coordinate label:
1 ! apex atom
2 ! last atom in bend
0.408286 ! Enter symmetry factor:
Because the symmetry factor is not equal to 1 the program will prompt you
1 ! Create symmetry coordinate 1 ? [1=Yes, 0=No]
Repeat this procedure for the other coordinates to make the above symmetry coordinate for angle bending. The labels of the other bends are
N1-C2-N3
C2-N3-C4
N3-C4-C5
C4-C5-C6
C5-C6-N1
After the last symmetry coordinate type 0 to terminate this linear combination
0 ! Create symmetry coordinate 1 ? [1=Yes, 0=No]
There are a large number of commands to type in here. One way to make life easier is to use redirection. Type the input commands in a file and save it as bmat_setup.inp then run bmat using the < operator that reads the file line by line and feeds the input to bmat command line.
where bmat_setup.inp for uracil is
URACIL
u_631g.cor ! COORDINATE FILE
12 ! NUMBER OF ATOMS
62 !NUMBER OF INTERNAL COORDINATES
1 !STRETCH 1
N1-C2
1
2
1
1 !STRETCH 2
C2-N3
2
3
1
1 !STRETCH 3
N3-C4
3
4
1
1 !STRETCH 4
C4-C5
4
5
1
1 !STRETCH 5
C5-C6
5
6
1
1 !STRETCH 6
C6-N1
6
1
1
1 !STRETCH 7
N1-H9
1
9
1
1 !STRETCH 8
C2-O7
2
7
1
1 !STRETCH 9
N3-H10
3
10
1
1 !STRETCH 10
C4-O8
4
8
1
1 !STRETCH 11
C5-H11
5
11
1
1 !STRETCH 12
C6-H12
6
12
1
2 !SYMMETRY COORDINATE 13 FOR RING BENDING
C6-N1-C2
6
1
2
0.408248
1
2
N1-C2-N3
1
2
3
-0.408248
1
2
C2-N3-C4
2
3
4
0.408248
1
2
N3-C4-C5
3
4
5
-0.408248
1
2
C4-C5-C6
4
5
6
0.408248
1
2
C5-C6-N1
5
6
1
-0.408248
0
2 !SYMMETRY COORDINATE 14 FOR RING BENDING
C6-N1-C2
6
1
2
0.57735
1
2
N1-C2-N3
1
2
3
-0.288675
1
2
C2-N3-C4
2
3
4
-0.288675
1
2
N3-C4-C5
3
4
5
0.57735
1
2
C4-C5-C6
4
5
6
-0.288675
1
2
C5-C6-N1
5
6
1
-0.288675
0
2 !SYMMETRY COORDINATE 15 FOR RING BENDING
N1-C2-N3
1
2
3
0.5
1
2
C2-N3-C4
2
3
4
-0.5
1
2
C4-C5-C6
4
5
6
0.5
1
2
C5-C6-N1
5
6
1
-0.5
0
2 !SYMMETRY COORDINATE 16 FOR IN-PLANE H BENDING
C6-N1-H9
6
1
9
0.7070
1
2
C2-N1-H9
2
1
9
-0.7070
0
2 !SYMMETRY COORDINATE 17 FOR INPLANE O BENDING
N1-C2-O7
1
2
7
0.7070
1
2
N3-C2-O7
3
2
7
-0.7070
0
2 !SYMMETRY COORDINATE 18 FOR IN-PLANE H BENDING
C2-N3-H10
2
3
10
0.7070
1
2
C4-N3-H10
4
3
10
-0.7070
0
2 !SYMMETRY COORDINATE 19 FOR INPLANE O BENDING
N3-C4-O8
3
4
8
0.7070
1
2
C5-C4-O8
5
4
8
-0.7070
0
2 !SYMMETRY COORDINATE 20 FOR IN-PLANE H BENDING
C4-C5-H11
4
5
11
0.7070
1
2
C6-C5-H11
6
5
11
-0.7070
0
2 !SYMMETRY COORDINATE 21 FOR IN-PLANE H BENDING
C5-C6-H12
5
6
12
0.7070
1
2
N1-C6-H12
1
6
12
-0.7070
0
4 !SYMMETRY COORDINATE 22 FOR TORSION
C6-N1-C2-N3
2
1
2
2
6
9
3
7
0.408248
1
N1-C2-N3-C4
2
2
3
2
1
7
4
10
-0.408248
1
4
C2-N3-C4-C5
2
3
4
2
2
10
5
8
0.408248
1
4
N3-C4-C5-C6
2
4
5
2
3
8
6
11
-0.408248
1
4
C4-C5-C6-C1
2
5
6
2
4
11
1
12
0.408248
0
4
C5-C6-N1-C2
2
6
1
2
5
12
2
9
-0.408248
0
4
C6-N1-C2-N3
2
1
2
2
6
9
3
7
-0.288675
1
N1-C2-N3-C4
2
2
3
2
1
7
4
10
-0.288675
1
4
C2-N3-C4-C5
2
3
4
2
2
10
5
8
0.57735
1
4
N3-C4-C5-C6
2
4
5
2
3
8
6
11
-0.288675
1
4
C4-C5-C6-C1
2
5
6
2
4
11
1
12
-0.288675
0
4
C5-C6-N1-C2
2
6
1
2
5
12
2
9
0.57735
0
4
C6-N1-C2-N3
2
1
2
2
6
9
3
7
0.5
1
N1-C2-N3-C4
2
2
3
2
1
7
4
10
-0.5
1
4
N3-C4-C5-C6
2
4
5
2
3
8
6
11
0.5
1
4
C4-C5-C6-C1
2
5
6
2
4
11
1
12
-0.5
0
3 !OUT-OF-PLANE WAG
H9-N1-C2-C6
9
1
2
6
1
3 !OUT-OF-PLANE WAG
O7-C2-N3-N1
7
2
3
1
1
3 !OUT-OF-PLANE WAG
H10-N3-C4-C2
10
3
4
2
1
3 !OUT-OF-PLANE WAG
O8-C4-C5-N3
8
4
5
3
1
3 !OUT-OF-PLANE WAG
H11-C5-C6-C4
11
5
6
2
1
3 !OUT-OF-PLANE WAG
H12-C6-N1-C5
12
6
1
5
1
u_631g.bin