In this earlier post, I noted some aspects of the calculated structures of both Z- and B-DNA duplexes. These calculations involved optimising the positions of around 250-254 atoms, for d(CGCG)2 and d(ATAT)2, an undertaking which has taken about two months of computer time! The geometries are finally optimised to the point where 2nd derivatives can be calculated, and which reveal up to 756 all-positive force constants and 6 translations and rotations which are close to zero! This now lets one compute the thermodynamic relative energies using ωB97XD/6-31G(d) (for 2nd derivatives) and 6-31G(d,p) (for dispersion terms). All geometries are optimized using a continuum solvent field (water), and are calculated, without a counterion, as hexa-anions.
| Relative thermodynamic energies (kcal mol-1) of DNA duplexes. | |||||||
|---|---|---|---|---|---|---|---|
| system | Total energy (duplex) | Dispersion term | ΔΔH298 | Δ(-T.ΔS298) | ΔΔG298 duplex | ΔG298 single chain | ΔΔG298 (Duplex) |
| Z-CGCG | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -60.3 |
| B-CGCG | 6.2 | -4.2 | 8.0 | 3.9 | 11.9 | +3.1 | -54.7 |
| Z-ATAT | 0.0 | 0.0 | 0.0 | 0. | 0.0 | 0.0 | -44.9 |
| B-ATAT | -7.6 | -12.8 | -7.0 | 2.7 | -4.3 | -1.8 | -45.7 |
Note how the CGCG duplex is more stable as a Z-helix, whilst the ATAT duplex prefers the B-helix. I will discuss the precise reasons for this elsewhere.
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