Estructura del mercado interno de productos petrolíferos

All the calculations in this present work are performed with the Gaussian 09 program37. An overview of the equation used for evaluating the different components of the diagonalized hyperfine interaction tensor with in the density functional theory (DFT) framework, and their performance, have been presented by Malkin et al.38 and by Barone.39

The initial geometry parameters for geometry optimization are adopted directly from crystal structures determined by X-ray diffraction techniques.31, 32, 36, 40, 41 Two-layer ONIOM method is applied for geometry optimizations. The radicals of interest, i.e., the deprotonated cation or the protonated anion, are set as model system and are fully relaxed. Atoms, including the deprotonated proton from the cation radical, in the surrounding environment as parts of the real cluster system are fixed in their Cartesian coordinates. Frequency calculations are conducted to ensure the structures of the model systems were local minima on potential energy surfaces. Here, one probably will question the legitimacy of partitioning the deprotonated site and protonated site into two ONIOM layers and freezing the deprotonated hydrogen in the cation radical system. The reason for doing this is because we cannot simulate effective proton shuttling paths42 within our simulation due to limited system sizes. An effective shuttling requires three components, a proton donator (the cation radical), a path to transfer proton (the chain reaction path), and a final proton acceptor (the anion radical). In our simulation jobs, we put either a single cation or anion radical in each job. The direct proton acceptor near a cation radical or the direct proton donor near an anion radical will be rendered as unstable cation or anion due to the lack of effective shuttling mechanisms; and the expected protonation procedure is prone to be reversed. The above mentioned constraints are added in order to reproduce experimental conditions.

Subsequently, single point calculations are carried out on models of different levels of completeness that are extracted from the optimization jobs, from single radicals in gas phase, to partially including the H-bonding environment, to finally including the complete H-bonding environment. These single point calculations are conducted with M05/6-2X, B3LYP (or B3PW91) functionals. Upon all the optimization calculations, direct inversion in the iterative subspace (GDIIS)43 has been implemented when relatively flat regions of the potential energy surface are encountered. The detailed calculation procedures are as follows:

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Single cytosine and guanine radicals are small compared with 5’-dCMP and 5’-GMP radicals. Thus, more complete environmental effects for the model radical are included for geometry optimizations of the N1 deprotonated cytosine cation and the native guanine cation. For the N1 deprotonated cytosine cation with in cytosine monohydrate single crystal, the nearest 7 cytosine base molecules and all the nearby water molecules around the radical, are included in its geometry optimization job at ONIOM(uB3LYP/aug-cc-pvtz:uB3LYP/3-21+g*) level of theory. The native guanine cation radical is optimized within two different scales of system within the Guanine Hydrochloride Monohydrate single crystal environment. Here we refer these two optimizations as Gm-Opt-1 and Gm-Opt-2. The Gm-Opt-1 optimization includes the N7- deprotonated guanine cation radical, its eight nearest chloride ions, and the O-6 protonated guanine cation; this system is optimized on ONIOM(B3LYP/6-31+g(d):hf/6-31+g(d)) level of theory. The Gm-Opt-2 optimization includes another 5 nearest guanine bases based on the Gm- Opt-1 system, and it is optimized on ONIOM(B3LYP/6-31+g(d):B3LYP/3-21g) level of theory.

Similarly, two optimizations with different system scale are carried out for the N3 deprotonated 5’-dCMP cation radical within the 5’-dGMP Monohydrate single crystal environment. Here we refer these two optimizations as 5’-dCMP-Opt-1 and 5’-dCMP-Opt-2. The 5’-dCMP-Opt-1 optimization includes the N3-deprotonated radical, the corresponding OIII protonated cation, and waters and another three 5’dCMP molecules that covers all H-bonding environmental effects of the model radical. The 5’-dCMP-Opt-2 optimization further includes another eight 5’dCMP molecules to give a more complete electrostatic environment. Both the 5’- dCMP-Opt-1 and the 5’-dCMP-Opt-2 systems are optimized on ONIOM(uB3LYP/6-

31+g(d):uB3LYP/3-21g) level of theory.

For the calculations on the N7-H, O6-H protonated 5’-GMP anion radical within the 5’- GMP single crystal structure, whose uniqueness resides on its large Hydrogen bonding networks within the crystalline structure, both 3-layer and 2-layer ONIOM optimizations are carried out at systems with various sizes. The aim of these optimizations is to find an effective yet less

computationally demanding way to treat systems with such a large scale of Hydrogen bonding interactions. These optimizations are on ONIOM(uB3LYP/6-31g(d):uB3LYP/3-21g) or ONIOM(uB3LYP/6-31g(d):uB3LYP/3-21g:PM6) levels of theory, where the PM6 semi- empirical method is developed to improve its performance on H-bonds.44 London dispersion

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energy plays a key role in determining the biomolecular as well as crystal system. While, in the present case, London dispersion may not be as significant among the Van der Waals forces as the interactions involving molecular dipoles or ionic charges, it should be important for such a long range interaction to decide H-bonding structures, especially when all surrounding molecules, which forms Hydrogen bonds with the model radical, are frozen. However, calculations by Cerny and coworkers45 have shown that current hybrid DFT methods fail to describe the dispersion energy. As a result, they fail to describe base stacking or the interaction of amino acids in the crystal geometry. M052x do not model the asymptotic dipolar nature of dispersive interactions explicitly. As a result, although M05/62x functionals demonstrate significant improvements over traditional density functionals in describing the medium-range part of non- covalent interactions,46 their incapability to describe non-covalent interactions at lone range (>6 ) limit its use in describing dispersive interactions, which is inherently long range electron correlation effect. 47 So, in our future work in examining environmental effects on accurate HFCC calculations, we might choose the long range corrected functionals for the real system or the inter-median system, and M06-2X for the model system. However, it is interesting to notice that, as demonstrated by Polo et al.48, the traditional DFT’s exchange self-interaction error did mimic long range (non-dynamic) pair correlation effects.

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