Arequipa Perú
II PLANTEAMIENTO TEORICO
2. MARCO CONCEPTUAL: 1 LACTATO:
MP2small
]
(5.2)where the final two terms give the coupled cluster correction. Our choice of small basis set was aDZ. However, for our stacked dimers, CCSD(T)/aDZ still proved intractable, due to disk space requirements. We therefore decided to use density fitting (Chapter 2, Section 2.8) to reduce the computational demands. In the case of coupled cluster, density fitting only affords significant computational savings when applied in conjunction with the local orbital approximation203 (Chapter 2, Section 2.9). We therefore used the df-LCCSD(T)/aDZ level of theory. For MP2, we used density fitting, but not the local approximation. Equation 5.2 therefore becomes:
𝐸df−LCCSD(T)aQZ ≈ 𝐸df−MP2aQZ + [𝐸df−LCCSD(T) aDZ − 𝐸df−MP2aDZ ] (5.3) All single-point calculations were carried out using Molpro 2010.1.204 At each explicitly calculated level of theory (df-MP2/aDZ, df-MP2/aQZ and df-LCCSD(T)/aDZ), the stacking energies of each dimer were evaluated using Equation 5.1. That is, at each level of theory, three quantities were calculated for each dimer – the energies of X/Y, X and Y – all using the dimer-centred basis set. The vertical counterpoise correction was accomplished in this case by using the “Dummy” keyword in Molpro to specify the ghost atoms. Finally, the CP-corrected stacking energies for df- LCCSD(T)/aQZ were estimated using Equation 5.3.
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Table
5.3
Mean
df-MP2/aug-cc-pVDZ,
df-MP2/aug-cc-pVQZ,
df-
LCCSD(T)/aug-cc-pVDZ and estimated df-LCCSD(T)/aug-cc-pVQZ interaction
energies (kcal/mol) for each type of experimental dimer
Type
E
mean(df-MP2)
E
mean(df-LCCSD(T))
aug-cc-pVDZ aug-cc-pVQZ aug-cc-pVDZ aug-cc-pVQZ
Type X/Y
BrU/A
−7.05
−7.54
−6.19
−6.68
T/A
−5.85
−6.45
−4.85
−5.44
BrU/C
−5.03
−5.42
−4.09
−4.48
T/C
−4.71
−5.27
−3.73
−4.30
BrU/G
−6.29
−6.78
−5.46
−5.96
T/G
−5.41
−5.78
−4.97
−5.34
BrU/T
−4.01
−4.84
−3.10
−3.93
T/T
−4.04
−4.68
−3.18
−3.81
Type Y/X
A/BrU
−8.19
−9.10
−7.02
−7.93
A/T
−7.74
−8.46
−7.38
−8.10
C/BrU
−8.15
−8.88
−7.15
−7.87
C/T
−6.10
−6.72
−5.41
−6.04
G/BrU
−6.67
−7.39
−5.54
−6.26
G/T
−5.92
−6.70
−4.77
−5.55
T/BrU
−5.49
−6.13
−4.74
−5.38
T/T
−4.04
−4.68
−3.18
−3.81
All X + Y
aBrU + A
−7.62
−8.32
−6.60
−7.31
T + A
−7.06
−7.74
−6.48
−7.15
BrU + C
−6.59
−7.15
−5.62
−6.18
T + C
−5.24
−5.83
−4.38
−4.97
BrU + G
−6.49
−7.11
−5.50
−6.12
T + G
−5.66
−6.24
−4.87
−5.44
BrU + T
−4.56
−5.32
−3.72
−4.48
T + T
−4.04
−4.68
−3.18
−3.81
X = T or BrU; Y = A, C, G or T.
aWith X/Y and Y/X grouped together.
With df-MP2/aDZ, the mean BrU stacking is stronger than the mean T stacking for all comparisons except 5’-X/T-3’, for which the energy difference is < 0.05 kcal/mol in favour of T. The largest difference in favour of BrU is 2.05 kcal/mol, for 5’-C/X-3’. The individual interaction energies ranged from −1.78 kcal/mol (3OH9-T/T) to −10.32 kcal/mol (1DCR-BrU/G). These were also the least and most strongly bound dimers, respectively, with MP2/6-31+G(d).
By comparison with Table 5.2, it can be seen that the df-MP2/aDZ interaction energies are already larger than the MP2/6-31+G(d) energies, presumably due to the greater size of this basis set (even
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though they are both double-ζ). We attempted MP2/aDZ calculations (without density fitting) for comparison, but they proved impracticable, due to disk space requirements.
With df-MP2/aQZ, the mean BrU stacking is stronger than the mean T stacking for all comparisons. The largest mean difference in favour of BrU is 2.16 kcal/mol, for 5’-C/X-3’. The mean interaction energies are larger than with the aDZ basis set. The individual interaction energies ranged from −2.36 kcal/mol (2L5K-G/T) to −11.13 kcal/mol (1DCR-BrU/G).
With df-LCCSD(T)/aDZ, the mean BrU stacking is stronger than the mean T stacking for all comparisons except 5’-A/X-3’, where the difference in favour of T is 0.36 kcal/mol, and 5’-X/T-3’, for which the mean difference is < 0.1 kcal/mol. The largest mean difference in favour of BrU is 1.74 kcal/mol, for 5’-C/X-3’. The individual interaction energies ranged from +0.33 kcal/mol (2W7N- BrU/T) to −9.79 kcal/mol (2L5K-A/T).
With df-LCCSD(T)/aQZ – the highest level of theory – the mean BrU stacking is stronger than the mean T stacking for all comparisons except 5’-A/X-3’, where the difference in favour of T is 0.17 kcal/mol. The largest mean difference in favour of BrU is 1.83 kcal/mol, for 5’-C/X-3’. The individual interaction energies ranged from −0.93 kcal/mol (2W7N-BrU/T) to −10.73 kcal/mol (2L5K-A/T).
With all four methods, when X/Y and Y/X are grouped together, the only partner base (Y) for which the mean stacking energy of BrU exceeds that of T by more than 1 kcal/mol is cytosine.
It must be noted that there is an inconsistency between the two Hamiltonians employed: df- LCCSD(T) uses localised orbitals, while df-MP2 does not. This may call into question the accuracy of our coupled cluster correction, the addition of which to the df-MP2/aQZ energies yields the df- LCCSD(T)/aQZ energies. It was not possible to avoid this mismatch by using df-CCSD(T) or df- LMP2. The former yields negligible computational savings compared to full coupled cluster (as noted above),203 and therefore requires more computer memory than we had at our disposal. The latter, which should in principle be computationally cheaper than df-MP2, also proved impracticable on our hardware, for reasons apparently related to memory.
In a review of theoretical studies of stacking, Šponer et al.120 noted that the coupled cluster correction, ΔCC, is usually large and positive (repulsive). In our own calculations, ΔCC is on average positive for each type of dimer (compare the second and fourth columns in Table 5.3), but it is negative for eight specific dimers – in one case by over 1 kcal/mol (the A/T dimer from 2L5K, for which ΔCC = −1.4 kcal/mol). However, Sponer et al.192 had earlier calculated CCSD(T) corrections in the range of −0.1 to +2.5 kcal/mol for DNA base pair steps, i.e. ΔCC can occasionally be weakly attractive.
To estimate the density fitting error in our results, we calculated the Hartree–Fock total energies of two dimers (1D9R-BrU/G and 1A35-A/T) with and without density fitting. The differences were small (~0.2 kcal/mol) in the aDZ basis and negligible (<0.05 kcal/mol) in the aTZ and aQZ bases.
5.2.3. RI-mPW2PLYP-D
The double hybrid functional RI-mPW2PLYP-D consists of the mPW2PLYP114 functional(modified Perdew–Wang exchange with 55% contribution from Hartree–Fock, and Lee–Yang–Parr correlation
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with 25% contribution from RI-PT2), supplemented with the 2006 version of Grimme's D2 empirical dispersion correction.117
The RI-mPW2PLYP-D calculations were carried out using Orca 2.8.205 The keyword “vdw” was used to invoke Grimme’s D2-type dispersion correction. The counterpoise correction was applied by specifying ghost atoms in the geometry inputs, and the interaction energy was defined as above. The interaction energies are shown in Table 5.4.