Optimization of Chitosan+Activated Carbon Nanocomposite. DFT Study

David Hernández Benitez and Juan Horacio Pacheco Sánchez* Division of Postgraduate Studies and Research of the Technological Institute of Toluca, Mexico Received: October 01, 2018; Published: October 09, 2018 *Corresponding author: Juan Horacio Pacheco Sánchez, Division of Postgraduate Studies and Research of the Technological Institute of Toluca, Av. Tecnológico s/n, Agrícola Bellavista, 52149 México


Introduction
With the aim to figure out a molecular complex formed through the interaction between a system of 48 carbons arranged in planar way and a copolymer unit of chitosan, potential energy surfaces were built [1,2] using single point step by step calculations. The problem is studied considering that a molecular complex is obtained by changing smearing value according to the energy value convergence. Considering that electrons occupy orbitals with the lowest energies and with an integral occupation number in calculations of density functionals, a smearing change indicates a fractional occupation in virtual orbitals within this space of occupation. The smearing calculations correspond to the explicit inclusion of the fractional occupation numbers of the DFT calculations, requiring an additional term to achieve a functional energy from variation theory [35]. The contribution of this term to the density functional force exactly cancels the correction term as a function of the change in the occupation number. For occupation numbers satisfying a Fermi distribution, the variation total-energy functional is identical in form to the grand potential [3][4][5][6]. From the grand canonical distribution or Gibbs distribution, the normalized probability distribution of finding the system in a state with n particles and energy [7], the Z grand partition function of the system, and the number of particles remains according to the Fermi energy ℰ f =μ(T,V,n). When T = 0 the fermion gas is in the state of minimum energy in which the particles occupy the n states of of lower energy, since the exclusion principle of Pauli does not allow more than one particle in each state. Therefore, the Fermi function (ℰ) gives the probability that certain states of available electron energy are occupied at a given temperature.
Other options for the shape of the occupancy numbers result from the different associated functional with finite temperature to DFT but without physical meaning, such as the temperature or the entropy associated with this term [3]. These terms, although numerically small must be included in the practical calculations that allow numbers of fractional occupation [3,8]. To consider the scope of smearing, it is known that electrons occupy orbitals with the lowest energies, and occupancy numbers are integers; nonetheless, there is a need for a fractional occupation in virtual orbitals within this space of occupation. We apply this when the HOMO-LUMO gap

Abstract
First, the minimum energy (geometry optimization DFT-DMol 3 ) is obtained among C 48 optimized ring carbon-system, and one non-optimized chitosan copolymer unit. Second, C 24 and C 9 optimized rings, each one interacting with an optimized chitosan copolymer unit (Ch) . With the aim to investigate structural properties, the first case is optimized by applying smearing; and the second without smearing. Two parallel hypothetical carbon chains of 12 carbon atoms, symmetrically arranged are optimized in C 24 carbyne ring; and one hypothetical 5 carbon-chain parallel to another 4 carbon-chain end optimized in a cumulene C 9 -ring. These carbon-ring structures here defined as activated carbons (AC) , correspond to big pore size diameter obtained without chemical agent acting on them. Single point calculations are to build potential energy surfaces with GGA-PW91 functional to deal with exchange correlation energies for unrestricted spin, all-electron with dnd basis set. Only in the first case, orbital occupation is optimized with diverse smearing values. To determine structure stability, the minimum energy criterion is applied on AC+Ch nanocomposite. To generate fractional occupation, virtual orbitals are formed in this occupation space, whether homo-lumo gap is small and there is certain density near Fermi level. This fractional occupation pattern depends on the temperature. It must be noticed that when AC and Ch are solids, there is no adsorption; however, by applying smearing it was possible to find potential energy surfaces with a high equilibrium energy indicating glass phase transition in Chitosan due to the chemisorption given at the minimum of energy. AC+Ch molecular complex nanocomposite is expected to be applied not only in medicine but also in high technology.
is small and there is especially a significant density near of Fermi level [9], thus in order to obtain the fractional occupation a kT term is implemented. This fractional occupation pattern depends on the temperature. The systems C 48 carbinoid, C 24 carbyne-ring, and C 9 cumulene-ring (almost-planar) are arrangements obtained through DFT geometry optimization of two hypothetical parallel zigzag linear carbon chains. We consider these systems as carbon physically activated, due to the pore size diameter, and since no activating chemical agent has been applied. Carbyne is known as linear carbons alternating single and triple bonds (-C≡C-) n or with double bonds (=C=C=) n (cumulene) [10]. Polyyne is known as a allotrope carbon having H(-C≡C-) nH chemical structure repeating chain, with alternating single and triple bonds [11] and hydrogen at every extremity, corresponding to hydrogenated linear carbon chain as any member of the polyyne family HC 2n H [12] with sp hybridization atoms. It is known that polyyne, carbyne and carbinoid have been actually synthesized as documented by Cataldo [13]. Bond length alternation (BLA) of carbyne pattern is retained in the rings having an even number of atoms [10]. Additional care must be taken with carbyne rings since the Jahn-Teller distortion (the counterpart of Peierls instability in non-linear molecules) is different in the C 4N and C 4N+2 families of rings [14][15][16]. There is a great variety of applications of activated carbon as an adsorbent material, and it has been used in areas related to the energy, and the environment, generating materials with a high-energy storage capacity [17].
Chitin is, after cellulose, the most abundant biopolymer in nature. When the degree of deacetylation of chitin reaches about 50% (depending on the origin of the polymer), it becomes soluble in aqueous acidic media and is called chitosan [18]. Chitosan is applied to remediation of heavy metals in drinking water and other contaminants by adsorption. The affinity of chitosan with heavy metals makes the bisorption process stable and advantageous, being only by the alginates present in brown algae matched [19]. The glass transition temperature of chitosan is 203°C (476.15 K) according to Sakurai et al. [20], 225°C (498.15 K) according to Kadokawa [21], and 280°C (553.15 K) according to Cardona-Trujillo [22].
One can differentiate specific reactions involving the -NH 2 group at nonspecific reactions of -OH groups. This is important to difference between chitosan and cellulose, where three -OH groups of nearly equal reactivity are available [23,24]. In industrial applications, several solids having pores close to molecular dimensions (micropores < 20 Å) are used as selective adsorbents because of the physicochemical specificity they display towards certain molecules in contrast to the mesoporous substrates (20-500 Å) and macropores (> 500 Å). Adsorbents with these selective properties include activated carbon among others [25]. Chitosan-based highly activated carbons have also application for hydrogen storage [26].
In principle, electronic structure of diatomic molecules has been built through the overlapping knowledge of the interacting atomic orbitals [27]. In this case, the orbitals correspond to bonding (σ g , π g ) and antibonding (σu, πu) orbitals of hydrogen, carbon, nitrogen and oxygen diatomic molecules, whose H 2 , C 2 , N 2 , and O 2 groundstate electronic configurations are

Methodology
The interaction between an activated carbon molecule (AC) and a unit of the chitosan copolymer (Ch) is studied by means of DFT-

Chitosan Optimized by Applying Smearing
The default smearing value of 0.005Ha corresponds to T=1578.87 K and P=224.806 atm. We now exhibit electron smearing behavior using the known Fermi-Dirac statistic [38]. Facing two hydrogen atoms and using geometry optimization calculations, we built energy as a function of smearing value. Figure 1 shows the total energy variation when the system is optimized with respect to smearing value [39] (Figure 1). The fractional occupational pattern depends on the temperature, and this is derived from the energy change of Fermi distribution [6] [38]. From the latter two previous equations, temperature and pressure change is observed in Table 1 given the smearing energy. The planar molecular hypothetical system of 48 carbons is built by applying geometry optimization at two linear chains of 24 carbons as shown in Figure 2a, and the chitosan copolymer molecular system is built without applying geometry optimization, as observed in Figure 2b. Approaching enough these two molecular systems we studied a new molecular complex at different smearing values. The molecular model of carbon is symmetrically arranged in planar geometry, and it is physically activated through geometry optimization. We called activated carbon (AC) to the resulting planar carbon system. The length of this planar system is comparable to that one of chitosan (Ch).
Each six-carbon ring has an area 4.34 Å 2 , each eight-carbon ring along with this has an area 8.74 Å 2 , each eight-carbon ring along with the sixteen-carbon ring has an area 8.55 Å 2 , and the sixteencarbon ring has an area 27.32 Å 2 . Considering each one of this area as circle areas the pore size diameter distribution is from 2.35 Å to 5.9 Å, which correspond to micropore size distribution of this carbon system. When considering the whole area of this system for calculating the pore size diameter 9.48 Å [40,41]. Chitosan is very well known to be macropore size [42] (Figure 2).   (Figure 4). Covalent connectivity [37] to the resulting system in Figure 4a was applied under the conditions previously mentioned in methodology, and the molecular complex observed in Figure 5 is obtained. In this complex the reactants and rings have double bonds in one side of the ring, and single and triple bonds in the other side; and C 6 ring has four double bonds and two single bonds. This whole carbon system has been activated by chitosan, and double bonds, and single and triple bonds are the representative characteristics of carbine-type molecules ( Figure 5).    After applying covalent connectivity [37] to the resulting system in Figure 6, we again applied geometry optimization for smearing 0.02Ha, and we obtain different molecular orbitals in the results, as shown in Figure 7. This molecular complex as seen in Figure 7 has HOMO-482 with E=-0.  Figure 7 has the same products previously mentioned. It must be noticed that the lowest unoccupied molecular orbitals (LUMO-acceptor) only draw orbitals in the CH 3 product, the rest of the molecular orbitals correspond to the highest occupied molecular orbitals (HOMO-donor) complex. Then, this is a very stable molecular system only allowing reactivity through the methyl radical CH 3 (Figure 7) The potential energy curve in Figure 3b is very near to physisorption;  [20][21][22].

Chitosan Optimized Without Smearing
First of all, the C 24 carbyne-type ring alternating single and triple bonds is obtained by applying connectivity [37] and bond type to a C 24 carbon ring which is the output of the input shown in Figure 10a corresponding to the geometry optimization of two hypothetical C 12 -carbon chains (Figure 10b). Then, Figure 10c exhibits an alternating single and triple bonds C 24 -ring. Second, applying clean of BIOVIA Materials Studio on chitosan copolymer molecule designed in Figure 2b, we obtain the input of a chitosan copolymer molecule as in Figure10d, and the Output exhibiting geometry optimization of the previous molecule is shown in Figure   10e. As we can observe, in this case chitosan remained complete.
We made this, after suspecting that the initial bonds lengths and angles were not right in our design of chitosan, because broken chitosan is not a satisfactory result. Then, mixing the optimized C 24 and Ch systems as shown in Figure 10f in the Input of a C 24 -ring surrounding a chitosan copolymer molecule, and after applying geometry optimization we obtain the Output of the previous CA-Ch nanocomposite see Figure 10g. Finally, we applied bonding scheme criteria as in Figure 10h.The nanocomposite in Figure 10h

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one previously optimized by applying geometry optimization to the whole system, and also considering the bond criteria for connectivity, bond type and Kekulé representation as shown in Figure 11e. The cumulene C 9 -ring and chitosan copolymer molecule have been optimized in three dimensions, and we clearly observe the cumulene passing from face to face to almost T-shape orientation taking three hydrogen atoms from chitosan. The input position of cumulene C 9 ring face to face with chitosan in that precise location has been proposed, and the result has been excellent.

Figure 11:
Here we consider INPUT and OUTPUT of the geometry optimization among a cumulene C 9 -ring and a Chitosan C 14 H 24 N 2 O 9 molecule, and also applying bond criteria for connectivity, bond type and Kekulé representation. a) Input among a hypothetical C 4 -and C 5 -chains. b) Output showing a C 9 -ring. c) Input among the C 9 -ring and chitosan molecule. d) Output exhibiting the complex C 9 -ring into chitosan. e) Bonding criteria applied to the previous output.

Discussion
We consider each carbon ring as physically activated through geometry optimization, due to pore size diameter remains in the average size compared against experimental measurements [41].
The C 48 optimized ring carbon-system and one non-optimized chitosan copolymer unit has been studied considering the result after geometry optimization, as a molecular complex obtained when smearing value changes for converging energy values.
Different elongation among single and triple carbon bonds in the carbyne-type are due to Jahn-Teller effect [14]. Then, C 24 carbynering when we optimize two carbon chains at 3.074 Å of separation distance, is due to the Jahn-Teller effect. The Jahn-Teller effect is also present in C48 carbinoid -ring for their C8-and C4-carbinoid -rings. Carbon rings C4N (N<~8) exhibit a substantial first-order Jahn-Teller distortion that leads to long/short (single/triple) bond alternation decreasing with increasing N [14]. Whether we want to draw HOMO-LUMO orbitals, it is necessary to ask for orbitals in the geometry optimization as input data. At this work, for smearing energy 0.02 Ha we found different HOMO LUMO orbital numbers among the initial system in Figure 5 without asking for orbitals in the geometry optimization calculation, and its output asking for orbitals in a new energy calculation shown in Figure 6. Again after practicing connectivity, bond type, and Kekulé representation at smearing energy 0.02 Ha, we asked for orbitals, and we found in nuclei (except when they are collinear) is unstable. As a result of this instability, the nuclei move in such a way that the symmetry of their configuration is destroyed, the degeneracy of the term is being completely removed [44,45]. High degeneracy indicates a high symmetry of the molecule, then the system tends to be distorted, in such way that when moving, the occupied levels are down and the unoccupied ones are up [46]. When levels are very densely spaced, convergence is hard to reach, since very small changes will occupy completely different states, and we get oscillations. These can be damped by smearing out the occupancy over more states, so that we turn off the binary occupancy of the states. We get down smearing width to glass transition temperature by decreasing the smearing parameter in steps to gradually stabilize our molecular complex system at the right temperature.
We initially observe distortion of chitosan system, and then its possible breaking in some products. This is partially in agreement with the results presented by Chigo et al. [46] in a study of the interaction among graphene-chitosan for a relaxed system doped with boron, in which they consider the interaction of pristine graphene with the monomer of chitosan (G + MCh:C 6 H 13 O 5 N) in different configurations, whereas we consider a chitosan copolymer molecule: C 14 H 24 N 2 O 9 in only one orientation. While Chigo et al. [46] found a perpendicular chitosan, molecule linked to a carbon nanotube system, we obtained a cumulene carbon ring almost perpendicularly linked to a chitosan copolymer molecule.

Conclusion
We found one mechanism to figure out an optimized big molecular complex system by using DFT geometry optimization. This mechanism is based on smearing calculations, and on decrements of smearing energy in the molecular complex system until reaching the glass transition temperature of one of the components, which in this case correspond to the chitosan copolymer molecule. In order to get a molecular complex system AC + Ch, it is needed a high temperature among them at least to the phase transition temperature of either AC or Ch, because when they are solids there is only a heterogeneous mixture at room temperature. The use of smearing allows to reach high temperatures because according to Table 1 temperature increases as the smearing energy increases.
We observed that the use of smearing to optimize a molecule as complex as the chitosan causes this to be fractionated, nevertheless when putting it in a plate of coal we obtained the glass transition temperature of the chitosan reported experimentally. The potential well depth providing chemisorption indicates existence of phase transition in one of our two molecular systems. This phase change is attributed to chitosan, due to carbon is more stable, and because we reach glass transition temperature of chitosan when dealing with the whole molecular complex system. In addition, when applying covalent connectivity, the activated carbon is the most stable molecular system keeping its molecular structure. According to HOMO and LUMO in Figures 6 -9, the sites with the greatest reactivity correspond to double and triple bonds. Besides, Figure   9 exhibits one amine functional group linked to the carbon system now C 51 carbon molecular complex formed with a particular pore size distribution. Considering that after geometry optimization physisorption provides bonding in two parts of the chitosan molecule, this is an indication of a more environmental linking than that caused by cross-linking solutions, because cross-linking solutions might be toxic in medicine applications. The first chitosan molecule used, and optimized using smearing resulted to be unstable, because finished brok en in several products. The second chitosan molecule used, and optimized without smearing, or with a very small smearing value resulted to be very stable, on which we were able to add activated carbon and to obtain good results.
We have been able to optimize chitosan and add activated carbon, and we have observed the change in pore size distribution, even though we are missing its calculation, to assign the type of material obtained (micropore, mesopore, or macropore). We are working on it.