Table 4. Pyridine Natural Internal Coordinates for CMA Applications.
| Description | Unnormalized natural internal coordinatea |
|---|---|
| ring breathing | S1(a1) = r(5,3) + r(3,1) + r(1,2) + r(2,4) + r(4,6) + r(6,5) |
| ring stretching def. | S2(b2) = r(5,3) – r(3,1) + r(1,2) – r(2,4) + r(4,6) – r(6,5) |
| ring stretching def. | S3(a1) = 2r(5,3) – r(3,1) – r(1,2) + 2r(2,4) – r(4,6) – r(6,5) |
| ring stretching def. | S4(b2) = 2r(5,3) + r(3,1) – r(1,2) – 2r(2,4) – r(4,6) + r(6,5) |
| ring stretching def. | S5(a1) = r(3,1) + r(1,2) – r(4,6) – r(6,5) |
| ring stretching def. | S6(b2) = r(3,1) – r(1,2) + r(4,6) – r(6,5) |
| sym. CH stretch | S7(a1) = r(5,11) + r(4,10) |
| antisym. CH stretch | S8(b2) = r(5,11) – r(4,10) |
| sym. CH stretch | S9(a1) = r(3,9) + r(2,8) |
| antisym. CH stretch | S10(b2) = r(3,9) – r(2,8) |
| CH stretch | S11(a1) = r(1,7) |
| ring stellation | S12(a1) = θ(4,6,5) – θ(6,5,3) + θ(5,3,1) – θ(3,1,2) + θ(1,2,4) – θ(2,4,6) |
| ring rectangulation | S13(a1) = 2θ(4,6,5) – θ(6,5,3) – θ(5,3,1) + 2θ(3,1,2) – θ(1,2,4) – θ(2,4,6) |
| ring shearing | S14(b2) = θ(6,5,3) – θ(5,3,1) + θ(1,2,4) – θ(2,4,6) |
| sym. i.p. CH rock | S15(a1) = θ(11,5,6) – θ(11,5,3) + θ(10,4,6) – θ(10,4,2) |
| antisym. i.p. CH rock | S16(b2) = θ(11,5,6) – θ(11,5,3) – θ(10,4,6) + θ(10,4,2) |
| sym. i.p. CH rock | S17(a1) = θ(9,3,5) – θ(9,3,1) + θ(8,2,4) – θ(8,2,1) |
| antisym. i.p. CH rock | S18(b2) = θ(9,3,5) – θ(9,3,1) – θ(8,2,4) + θ(8,2,1) |
| i.p. CH rock | S19(b2) = θ(7,1,2) – θ(7,1,3) |
| chair ring pucker | S20(b1) = τ(6,5,3,1) + τ(3,1,2,4) – τ(5,3,1,2) – τ(1,2,4,6) + τ(2,4,6,5) – τ(4,6,5,3) |
| boat ring pucker | S21(b1) = τ(3,1,2,4) – τ(5,3,1,2) – τ(2,4,6,5) + τ(4,6,5,3) |
| ring twist | S22(a2) = 2τ(6,5,3,1) – τ(5,3,1,2) – τ(3,1,2,4) + 2τ(1,2,4,6) – τ(2,4,6,5) – τ(4,6,5,3) |
| sym. o.o.p. CH wag | S23(b1) = γ(11,5,3,6) + γ(10,4,6,2) |
| antisym. o.o.p. CH wag | S24(a2) = γ(11,5,3,6) – γ(10,4,6,2) |
| sym. o.o.p. CH wag | S25(b1) = γ(9,3,1,5) + γ(8,2,4,1) |
| antisym. o.o.p. CH wag | S26(a2) = γ(9,3,1,5) – γ(8,2,4,1) |
| o.o.p. CH wag | S27(b1) = γ(7,1,2,3) |
a
r(i,j) = i–j bond distance; θ(i,j,k) = i–j–k bond angle; τ(i,j,k,l) = dihedral angle between i–j–k and j–k–l plane; γ(i,j,k,l) = signed angle of i–j bond out of the k–j–l plane.