Making a parallel to nanocone systems, we believe that passivation effects may be neglect in a first approximation and that the main characteristics of the electronic properties are preserved within this simple model. The LDOS is calculated in terms of the discrete amplitude probability,

, (15) where (16) as it is shown in the subsection ‘Discrete position approach.’ The local electric charge (LEC) related to the π electrons is calculated by assuming that the other five electrons and the six protons of the carbon atom act as a net charge +e. Assuming zero temperature and the independent electron approximation, only the states 1≤j≤n F will be occupied, where (17) Taking into account that the states below n F contribute with −2e and the fact that the n F state contribution depends on the parity of the number of atoms in the system,

the LEC is written as (18) DAPT purchase with γ=0 and 1, for N C even and odd, respectively. Optical absorption coefficients α ε (ω) are calculated by considering perpendicular ( ), and parallel ( ) polarizations, in relation to the cone axis, (19) with ε i,j corresponding to the energies of occupied and unoccupied PRIMA-1MET states, respectively. The oscillator strength may be written in terms of the spatial operators ( , , and ) [20], i.e., (20) where is calculated to first order in s, using (30) of the subsection ‘Discrete position approach,’ (21) Discrete Thalidomide position approach A discrete position scheme in terms of the states was used to represent functions of the position given in terms of the atomic base, since they satisfy the same properties of the position states, i.e., orthogonality (22) and completeness (23) in a N C -dimensional subspace. The identity operator may also be constructed using

the s≠0 base as (24) with the S −1≈Δ (0)−s Δ (1)+O(s 2) matrix being different from the N C ×N C identity matrix Δ (0). We take |π 0〉 as the discrete position state and assume that the matrix elements of position-dependent functions are known in the s=0 representation, (25) Differently from the f R matrices, f Angiogenesis inhibitor matrices in the s≠0 representation (26) are not diagonal. However, by performing the similarity transformation (27) we may obtain the unknown f matrix in terms of the known f R matrix, provided the transformation rule between the π 0 and π bases is known. By assuming , the s≠0 representation may be found. The coefficients and are obtained by using the identity (23) into Equation (5), (28) and, to first order in s, ( and ) we have (29) By replacing (29) in (27), one obtains (30) as the matrix elements of a position-dependent function in the π-base. Results and discussion Electronic density of states In what follows, we present numerical results for systems composed of up to 5,000 atoms.