## Journal of Chemical Sciences | Lupine Publishers

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Abstract

## Introduction

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 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 C48 carbinoid, C24 carbyne-ring, and C9 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 HC2nH [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 C4N and C4N+2 families of rings [14-16]. 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 -NH2 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 (σg, πg) and antibonding (σu, πu) orbitals of hydrogen, carbon, nitrogen and oxygen diatomic molecules, whose H2, C2, N2, and O2 groundstate electronic configurations are and with 2, 8, 10 and 12 valence electrons, respectively. Actually, the reactivity sites in a molecule correspond to the highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO). HOMO as base (donor), and LUMO as acid (acceptor) are particularly important MOs to predict reactivity in many types of reaction [28,29]. Activated carbon and chitosan have been independently applied as sorption materials to increase environmental quality standards. Then, we expect AC-Ch nanocomposite to have a powerful handleable adsorption property of pollutants that can be applied not only in wastewater treatment, but also in medicine against intoxication, in batteries to increase storage capacity, in electrodes of fuel cells, and in more possible applications, according to the pore size distribution to be generated on this new material.

## Methodology

Single point potential energy curves were constructed [1,2] by using smearing. The following conditions to find AC+Ch (Activated Carbon+Chitosan) interaction energy are: functional GGA-PW91 [31,33-36], unrestricted spin, dnd bases, and orbital occupation with various smearing values. Considering that we obtained a solution for the energy value convergence, the interaction by changing the smearing value was studied. Since electrons occupy orbitals with lower energies and integral occupation numbers in calculations of density functional, a smearing change indicates fractional occupation and virtual orbital within this occupation space [19]. When generating a fractional occupation, virtual orbitals are in this occupation space generated, if the HOMO-LUMO gap is small, and there is certain density near the Fermi level [1], then it is implemented the fractional occupation term kT. This pattern of fractional occupation depends on temperature. Covalent connectivity calculations [37] according to DMol3 on no-bonding to s- and f-shell scheme, bond type, and converting representation to Kekulé, for bond length tolerances from 0.6 to 1.15 Ǻ were accomplished in this molecular complex mostly composed of carbon. Area calculations have been carried out by inserting triangles in each amorphous carbon ring and using the

Heron formula: where P=(a+b+c)/2 is the perimeter of a triangle of a, b, c sides; while the pore size diameter (PSD) is calculated as an approximation to the circle area. Periodic systems can be constructed using amorphous builder of BIOVIA Materials Studio, these are useful to calculate Radial Distribution Functions and the area under the curve on a significant interval.

## Results

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**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] as: 𝛿𝐸 = 𝑇𝑘; where k is Boltzmann
constant. Considering a model in which the electrons are free and
given that clouds of electrons are being a Fermi gas considered.
The pressure is: 2/3 δE/δV [38]. From the latter two previous equations,
temperature and pressure change is observed in Table 1 given the
𝛿𝐸 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 Å2, each eight-carbon ring
along with this has an area 8.74 Å2, each eight-carbon ring along
with the sixteen-carbon ring has an area 8.55 Å2, and the sixteencarbon
ring has an area 27.32 Å2. 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 2:**C48 Carbon and Chitosan molecular systems. a) Input-Output of a C48 carbon system geometry optimization. Carbon atoms in gray color. b) Chitosan molecule (C14H24N2O9) without optimization. Hydrogen atoms in white color, Nitrogen in blue color and oxygen in red color.

**Figure 3:**INPUT for interaction among activated carbon (AC) and one copolymer unit of Chitosan (Ch). a) Chitosan without geometry optimization. b) Potential energy curve with well depth of 30Kcal/mol for smearing: 0.05Ha. c) Potential energy curve with well depth of -1089 kcal/mol for smearing of 0.03 Ha.

**Figure 4:**OUTPUT for interaction among activated carbon (AC)and one copolymer unit of Chitosan (Ch) after DFT geometry optimization using smearing at 0.02Ha.

**Figure 5:**Connectivity applied after geometry optimization of CA+ Ch interaction (smearing at 0.02 Ha)

**Figure 6:**We applied highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) to the previous AC+Ch molecular complex. a) HOMO. b) LUMO. c) HOMO-LUMO. Blue and yellow isosurfaces of the HOMO and LUMO denote positive and negative wave function phases, respectively.

**Figure 7:**After covalent connectivity and another geometry optimization at smearing 0.02 Ha we mostly obtain highest occupied molecular orbitals a) HOMO; and we scarcely obtain lowest unoccupied molecular orbitals b) LUMO. The most molecular orbitals c) HOMOLUMO correspond to bonds of carbon atoms.

**Table 1:**Change of temperature and pressure due to smearing variation 𝛿𝐸[𝐻𝑎] at temperature T [K] and pressure P [atm], for a volumen of 638 Å3.

**Figure 8:**OUTPUT of the AC+Ch interaction after geometry optimization using smearing at 0.00175 Ha, corresponding to 552.6 K and 78.68 atm according to Table 1.

**Figure 9:**After another geometry optimization at smearing 0.00175 Ha: a) we mostly obtain highest occupied molecular orbitals HOMO, b) we scarcely obtain lowest unoccupied molecular orbitals LUMO, c) the greatest part of molecular orbitals HOMOLUMO correspond to bonds of carbon atoms.

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** Chitosan Optimized Without Smearing**

First of all, the C24 carbyne-type ring alternating single and
triple bonds is obtained by applying connectivity [37] and bond
type to a C24 carbon ring which is the output of the input shown
in Figure 10a corresponding to the geometry optimization of two
hypothetical C12-carbon chains (Figure 10b). Then, Figure 10c
exhibits an alternating single and triple bonds C24-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 C24
and Ch systems as shown in Figure 10f in the Input of a C24-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 is a good
example of the possibility of modifying the pore size distribution
of chitosan when it is embedded into activated carbon. Here we
consider INPUT and OUTPUT for applying geometry optimization
on activated carbon and chitosan C14H24N2O9 system after each part
has been previously optimized, and we also applied bond criteria
for connectivity, bond type and kekulé representation. The C24-ring is
carbyne type, and the chitosan copolymer molecule has been
optimized in three dimensions in this case. The position of C24-
ring surrounding a chitosan copolymer molecule has been only
proposed.**Figure 10:**Here we consider INPUT and OUTPUT of the corresponding geometry optimization, and also applying bond criteria for connectivity, bond type and Kekulé representation. a) Input among two hypothetical C12-carbon chains. b) Output showing a disconnected C24-ring. c) The previous C24-ring linked using bond criteria. d) Input of a chitosan copolymer molecule. e) Output exhibiting the optimization of the previous molecule. f) Input of a C24-ring surrounding a chitosan copolymer molecule, g) Output of the previous CA-Chitosan, h) Bonding criteria applied to the previous output

**Figure 11:**Here we consider INPUT and OUTPUT of the geometry optimization among a cumulene C9-ring and a Chitosan C14H24N2O9 molecule, and also applying bond criteria for connectivity, bond type and Kekulé representation. a) Input among a hypothetical C4- and C5- chains. b) Output showing a C9-ring. c) Input among the C9-ring and chitosan molecule. d) Output exhibiting the complex C9-ring into chitosan. e) Bonding criteria applied to the previous output.

## Discussion

The strongly dependence on smearing means very closely spaced energy levels (high degeneracy) near Fermi level. When there is a degenerate electron state, any symmetrical position of the 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:C6H13O5N) in different configurations, whereas we consider a chitosan copolymer molecule: C14H24N2O9 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

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