Report on TS-vdW Method, and Code Development, and. Results

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1 Michael Pawley July, 21, 2010 Report on TS-vdW Method, and Code Development, and Results Introduction: Non-covalent Interactions have long been difficult to account for using Density Functional Theory(DFT), this is problematic since in Biological Systems, and many Nanomaterials, Non-covalent Interactions play a significant and important role. An example is the case of aromatic side chains of proteins are where van der Waal forces play significant factor in shape and folding. 1 The development and implementation of a simple method to take this into account could have a significant impact on the understanding, from first principles, of important biological and material processes and mechanisms. As a model system, the benzene dimer (D 6h ), was used. Method: The method used to take into account the van der Waal interactions 2, pioneered by Tkatchenko and Scheffler, takes the E = E DFT +E vdw where is calculated from first principles except for one semi-empirical parameter. The E vdw term takes the form:

2 Where f damp is simply a Fermi-type damping function, C 6ab is the coefficient for the pair of atom a and b in ev*a 6, which is calculated from first principles, and R ab is the distance between the two nuclei, a and b, in Angstroms. The purpose of the dampening function is to dampen out terms past a cut off radius, hence to take into account only the long-range effects, and remove any singularity issues at short distances. Above is a plot of the dampening function as a function the distance between the nuclei over the semi-empirical factor S r times the R o (cutoff distance) parameter. Where R ab is the distance between the two nuclei, s r is a parameter semi-empirically determined (0.94 for PBE), and R o a,b are calculated from first principles.

3 The C 6 parameter is calculated from first principles using the London Formula, using the homonuclear values of C 6, the static polarizability, and the ratio of the Volume effective to Volume free (V eff /V free ), free referring to the value for the free atom. The V eff /V free term was calculated using the equation: Where r is the distance from nucleus A, w(r ) is the Hirshfeld atomic partition, n(r ) is the total electron charge density of the system, n free (r ) is the free atom charge density. The effective homonuclear C6 parameter is given by the equation: Where C free 6aa is the homonuclear parameter. This value is then used in the London Equation: Where C 6ab is the effective C 6 between a given pair of atoms, k a,b is the static polarizability of the free atom a,b.

4 Results: Benzene dimer binding energy: This graph shows three curves, in green is the pure DFT energy as a function of distance, in orange is the vdw energy of the dimer as a function of distance, and in blue is the sum, the total energy surface of the dimer. The energy surface of the shows a minimum at ~3.9 Angstroms, and a Binding Energy of ~113.7 mev, this compares well with the values reported in the literature, CCSD(T) 8. The curve also show the correct behavior, at long ranges the curve approaches an asymptote, Non-covalent interaction proves to have a non-trivial effect on the energy at distances much larger than covalent radii.

5 Adenine on Graphene: In the graph above, we see the binding of adenine on graphene at an energy of around 790 mev and a distance ~3.33Ǻ. There are no know literature values to compare these values. This graph was obtained using the method outlined above.

6 Adenine with Approximations: The Infinity Approximation implies that the two systems, graphene and adenine are an independent of one another when calculating the C 6 parameters (as if they were an infinite distance apart), while the minimum case use the C 6 parameters at the minimum energy configuration (Exact is the Exact Solution calculating the C 6 parameters at each configuration using the method outlined above). This graph clearly shows a nontrivial difference between the Infinity Approximation and the Exact in terms of the Energy, which is important since the approximation makes a non-trivial difference in the Binding Energy.

7 Conclusions/Future Work: This method give binding energies and distances for large system, which need to evaluated against the other methods in the literature, the method needs to be run on the other nucleobases-graphene systems. The trend/order of binding energies for the nucleobases on graphene can be evaluated against the results obtained with other methods like DFT-D. References: 1) Grimme et al Org. Biomol. Chem., 2007, 5, ) Scheffler et al PRL 102, (2009) 3) Reuter et al PhysRevB 80, (2009) 4) Lundqvist et al PRL 76, 1, (1995) 5) Cooper PhysRevB 80, R (2010) 6) Hobza et al J. Chem. Theory Comput., 2008, 4 (11), pp ) N. Marom, A. Tkatchenko, M. Scheffler, and L. Kronik, J. Chem. Theory Comput. 6, (2010) 8) C. David Sherrill et al J. Am. Chem. Soc., 2002, 124 (36), pp