Probing the structural, electronic and optical properties of pure and B, N, or Li substituted Cyclo-18 ring: density functional theory investigations

Employing the quantum computational approach by using the Density Functional Theory along with GGA exchange correlation functional, we have investigated the structural, electronic, and optical properties of Cyclo-18 ring containing 18 sp hybridized carbon atoms and substituted Cyclo-C17X (X = B, N, and Li) ring. The Cyclo-18 ring has two opposite π electron system that can be organized as a D9h polyynic and D18h cumulene form. Our computational simulations suggest that D9h polyynic structure is minimum energy structure. Alkali metal doping makes C18 metallic by lowering the band gap when compared to the pure C18 (5.02eV). The strength of the chemical bonding analyzed using average binding energies for the Li, B, and N substituted Cyclo-C18 ring which are −4.58 eV, −4.65 eV, and −2.83 eV respectively. The positive charges on B, N and Li and negative charges on the Cyclo-18 ring demonstrate the partial Coulomb interactions and also charge transfer from B, N, and Li to Cyclo-18 ring. It is also found that the dominant adsorption IR peak at 2049 cm−1, 1329 cm−1, and 1011 cm−1 for B, N, and Li substituted C18 ring. There is an enhancement in optical absorption in the visible region due to doping which makes the system suitable for photo-catalytic applications.


Introduction
Consistent search for materials with desired properties is an active and interesting area of research in materials science where doping and substitutions of elements provide a new way to tune the properties.Carbon is a special element in nature which can form large number of compounds and allotropes with different properties.Carbon allotropes and their derivatives can find applications in nanoelectronics, sensors, solar cells, energy storage and optical devices [1][2][3][4][5][6][7][8][9].
The behaviour of carbon clusters is interesting because it changes from linear chains to a circular ring and then closed cages to nanotube.It is also very interesting that as the size of clusters increases, the stability of rings also extend due to decrease in angle strain [10].The carbon allotropes built from rings of two coordinate atoms known as Cyclo (n) carbon rings [11].If the hybridization between sp and sp 2 forms strong bending of carbon allotropes, such allotropes called cyclic polynes and cumulenes.In this direction, researchers produce reliable set of Density Functional Theory (DFT) results for linear and non-linear small carbon C n molecules [12][13][14] with ring and chain structures.Chains containing up to 27 atoms were captured in argon matrices from carbon vapor [15].Several experimental studies have shown that the formation of C 6 C 8 , C 18 , and C 14 in cumulene rings [16][17][18].Several transition phases of moncyclic cumulenic isomers have also been observed.It has also been shown that the ground state form of the Cyclo-18 ring is the pollynic form.Identification of a nonlinear C 6 ring isomer via experimental study is reported by Zajafman et al [19].Wakabayashi et al [20] also investigated the stability factor of C 4n+2 rings.Further the work reported by Xia Wang et al [16] revealed that Cyclo [16] carbon Precursor, C 18 Br 6 is aromatic in nature and predicted that C 18 Br 6 is a globally aromatic species with lower aromaticity than cyclo [16] carbon.Similarly, molecular assembly with a figure-of-eight nanohoop as a strategy for the collection and stabilization of Cyclo-18 carbon has been investigated recently Liu Zeyu et al [17].The electronic spectra and (hyper) polarizability of C 18 -(CO) n (n = 2, 4, and 6) are studied using theoretical calculations [18] to reveal the effect of introducing carbonyl (-CO) groups on the molecular optical properties.The bonding character, electron delocalization, and aromaticity of C 18 -(CO) n (n = 6, 4, and 2) were studied by advanced theoretical means.The difference of electron delocalization between two sets of π-conjugated systems and significant influence of the number of -CO groups on them were focused on, and the essential reason for the distinct difference in molecular aromaticity was elucidated by Wang Xia et al [21].The optical properties of the Li@C18 complex can be effectively regulated by switching the location of doped Li atom between inside and outside the carbon ring.With the help of various wavefunction analysis methods, the nature of the discrepancies in the properties of Li@C 18 complex with different configurations was deeply revealed [22].Very recently, Kaiser et al [11] generated Cyclo-18 ring using atom manipulation on bilayer NaCl on Cu (111) at 5 K by eliminating CO from a cyclocarbon oxide molecule C 24 O 6 and they predicted that polyyne D 9h form is the ground state.So up to now, great progress has been made in identifying Cyclo-18 ring by experimental study.
To understand the ground state properties of Cyclo-18, several theoretical simulations have been reported using MP2 [23][24][25][26][27], HF [28,29], SCF [25], DFT [30][31][32][33], and Quantum Monte carlo [34] techniques.In this direction, researchers have produced reliable DFT results for linear and non-linear small carbon C n molecules [12][13][14] with ring and chain structures.These theoretical investigations showed that all-carboatomic C 18 molecule exhibit in-plane and out of plane π electron system due to the special 'sp' hybrid form.Some theoretical methods Hartree-Fock (HF), Self Consistent Field (SCF), Quantum Monte Carlo (QMC) supported the polyyne structure with alternate single and triple bond as the ground state configuration whereas the DFT method with functional B3LYP, B3PW91 predicted all double bond (C=C) cumulene structure as stable.A DFT prediction done by Hutter et al [35] on B3LYP level using TZ (triple Zeta) basis sets observed that D 18h structure is the ground state structure.However Matrin et al [36] reported a detail theoretical investigation at DFT level using c.c.-pVDZ basis sets and found D 9h pollynic form is ground state structure for C 18 ring.Torelli and Mitas [37] explained the failure of DFT results and it is due to the overestimation of electronic correlation effect.Recently, computational study done by the Barishinkov et al [38] on Cyclo-18 ring with an increase percentage of HF method relative to B3LYP functional proposed to get ground state structure.BMK (42% HF), M06-2X (54% HFE), BH and HLYP (50% HFE) all of them provide pollyne type minimum energy structure of Cyclo-18 ring of D 9h symmetry with alternating single and triple C-C bond.Similarly, Suresh and Ramaya [39] observed a cumulenic ground state structure using Meta GGA functional.However, even though experimentally there is evidence that pollynic form of Cyclo-18 ring with D 9h symmetry is the stable ground state structure, most of the theoretical DFT simulations have not been able to show unambiguously if the stable ground state is D 9h pollynic or D 18h cumulenic.
It is well known that doping can tune the electronic and optical properties of different carbon allotropes such as amorphous carbon, carbon nanotube, quatum dots, fullerene etc.The tuning of these properties depends not only on the dopant but also on the site at which it is doped e.g.exohedral (outside the cage), endohedral (inside the cage) or by replacing one atom (substitution) [40][41][42][43][44][45][46][47][48][49][50][51].Recently, some important methods such as functionalization/ doping and size-dependent have been used to enhance or control the material properties [52][53][54][55].Among them, doping process has been subject of intensive research to make suitable material properties for use of it in wide range of applications nitrogen doping in graphene modifies its property suitable for biosensor applications whereas nitrogen and sulphur co doped CN nanotubes were found to be effective for desulphurization of liquid phases [40,[56][57][58].Hou Xiufang et al [24] employed density functional theory to investigate electronic characteristics of pristine Cyclo-C 18 and heteroatom-doped Cyclo-C 17 M (M = Li, Na, Be, Mg, B, Al, Ga, and In) and found that electronic properties could be adjusted according to the different doping atoms.
The goal of this work is to understand how doping affects the electrical and optical properties of the Cyclo-18 ring by first reproducing its experimentally confirmed pollynic structure as ground state structure.This study's primary goal is to adjust the light molecule's optical characteristics such that it can be utilized as a photo-catalyst for CO 2 reduction or water splitting.The doped system can also be employed as transition metal free spintronic devices once it becomes magnetic.This might be useful for creating a functionalized Cyclo-18 for a range of uses.

Computational methodology
The structural relaxation and energy evaluation are performed using the exchange-correlation functional within the hybrid and hybrid meta-GGA type functional as implemented in the Gaussian16 simulation package based on density functional theory (DFT) [59].Cyclo-18 ring [D 9h polyynic and D 18h cumulene, and doped-C 18 ring were fully optimized at M06-2X/6-311++G(d) level of theory and then further optimized in conjunction with a def2-TZVP basis set.We found that the results calculated using M06-2X/6-311++G(d) level of theory sounds good and match with other reported data.We used only M06-2X/6-311++G(d) functional and basis sets [36,37] for all further calculation.Initial, Cyclo-(C-17N, C-17B and C-17Li) geometries were obtained by replacing one C atom in Cyclo-18 ring with N, B, or Li atom.We also investigated the Low and higher spin electronic states to get the multiplicity of the ground state.However, low-spin multiplicity is more favorable.Here, we consider the geometries as minimum energy structure when the maximum force, the root-meansquare (RMS) force, the maximum displacement of atoms, and the RMS displacement of atoms have magnitudes less than 0.00045 Ry, 0.0003 Ry, 0.0018a.u,and 0.0012 a.u., respectively.Furthermore, we did not include zero point energy because ring size is small and almost the same, it will not affect the order of relative energy.Vibrational frequency calculations were performed at the same level of theory to verify the nature of the stationary points.To get insight into charge transfer mechanism, HOMO-LUMO (Highest Occupied Molecular Orbital and Lowest Unoccupied Molecular Orbital], and contour map, we have analyzed natural population analysis [60].To find the interactions among different orbital's, we analyzed the total Density of States (DOS) and the partial density of states (PDOS).Further to check thermodynamical stability, Ab Initio Molecular Dynamics simulation has been performed by placing the system microcannonical ensemble (NVE) by increasing the temperature from 0 to 300 K.
At the first stage of computation, the accuracy of basis set for B, N, Li and C, H atoms were validated with literature [61,62].To check the reliability of our method, we have calculated C-C, C≡C, C-B, C-N, and C-Li bond length for D 9h polyynic C-18 ring.We have compared our data with the existing reported values [23][24][25]

Results and analysis
3.1.Structure analysis and stability of pure C 18 ring Employing Density functional theory with 6-311 ++ G(d) type basis sets at M06-2X hybrid functional, we have obtained pollynic form of Cyclo-18 ring with D 9h symmetry as the stable ground state structure as per the experimental and theoretical data [23,63,64] whereas most of the theoretical DFT simulations have not been able to show unambiguously if the stable ground state is D 9h pollynic or D 18h cumulenic.The optimized minimum energy structures have shown in figure 1.
The results derived using the M06-2X/6-311++G(d) level of theory confirmed that the D 9h polyynic structure is the minimum energy structure and agree well with some previous theoretical and experimental reports [23,36,38,62].So the reported work on Cyclo-C 18 ring predict that the DFT theory with 6-311++G(d) type basis sets at M06-2X hybrid functional level will be very useful and can be used to obtain qualitative results for C 4n+2 carbon ring where n = 4. Simulation software Gaussian also predicts quadrupole moments and higher multipole moments (through hexadecapole) to explore the idea about structural stability.The calculated dipole and quadrupole moments of D 18h cumulenic and D 9h polyynic forms are shown in table 1.
Quadrupole moment is the second order term in the expansion of the total electron distribution, and provides insight into its overall shape [65].Denis [66] explored the stability on different molecules by using similar parameters.It was explained [66] that equal values of quadrupole parameters point towards the stability of the system.Similarly, here the values of XX, YY, and ZZ (quadrupole) components are nearly equal which indicate a spherical distribution as shown in table 1.On the other hand XY, XZ, and YZ indicate trans-axial distortion means stretching or compressing mode.In the present calculations, the values of XX, YY, and ZZ components of polynic are −99.03,−99.83, and −98.77Debye-Angs respectively, very close to each other and similarly, the XY, XZ, and YZ components are 0.62, 0.06, and −0.02 Debye-Angs respectively, less than the Cumulenic structure which indicates the stability of polyynic structure rather than Cumulenic.Further to explain the stability of Cyclo-C 17 X (X = B, N, and Li) ring it can be clearly seen from the table 2, that substitution of boron atom in Cyclo-18 ring results in nearly equal values of within 1%)of XX, YY, and ZZ components of the quadrupole moment, resulting in a structure with nearly spherical geometry.However, on substitutions of N and Li, The values of XX, YY, ZZ, are within 2% and 14%, thus explain the distortion in the circular ring structure as shown in figure 2. The values of XY, XZ, and YZ components of the quadrupole moment which give a measure of the trans-axial distortion indicate that the stretching mode for N and Li substitutions will be distorted only in the XY directions as shown in figure 2.

Binding energy
Further to study about the relative stability of the substituted C-17X (X = B, N, and Li) ring, we analysed thermodynamical parameter binding energy (BE) using the following equation , and N, here n 17 1

Charge transfer mechanism
We have also analyzed the atomic charges distribution using the natural bond orbital (NBO) analysis (Population = NPA) [60] and these atomic charges can be used to identify the electron transfer and spin distribution.The simulated values of NBO charges are listed in table 3. It can be seen that B, N, and Li atoms are losing charge and it has transferred to C 18 ring and making covalent bonds.Our calculated HOMO-LUMO plots also support the same as illustrated in figures 3(a)-(d).The charge population of present system is similar to the system studied by the Yingqian chen et al [70], where it was found that the distributions of charge are most likely a result of the covalent bonding in the system.It is also noted that the distortion in the C 18 clusters is mainly due to the charge distributions or transfer between C atom and the N or Li atom.As we can see, for example the bond length of C-C and C≡C are 1.27 Å, and 1.28 Å respectively, while the bond length of B-C, N-C, and Li-C changes to 1.31 Å, 1.43 Å, and 2.03 Å respectively due to the charge transfer which point towards the distortion of C 18 ring.The positive charges on B, N and Li and negative charges on the Cyclo-18 ring demonstrate the partial Coulomb interactions and also charge transfer from B, N, and Li to Cyclo-18 ring.It is also important to mention that the atomic charge redistribution in the doped system affects the energy of the system by changing the electronic states and make them useful for electronic and optical applications.The Charge transfer mechanism can also be seen by the HOMO-LUMO frontier molecular orbital which are formed  by the orbital-orbital interaction of two bonding atoms.The alignments of these orbital are shown in figure 3. It can be seen that all the occupied MO's have an equal pair of spin, giving net spin zero.

HOMO-LUMO gap
As we discussed in charge transfer, the carbon ring is negatively charged predicted by natural population analysis due to the substitutions of B, N, and Li.Interestingly the LUMO molecular orbitals are localize on these cyclo-18  carbon atoms and this is due to the excessive accumulation of the negative charge on the C atoms transferred from the dopants.In Cyclo-18 system, the HOMO and LUMO of C 18 is a π molecular orbital and thus fully contributed by 2p atomic orbitals.
The HOMO and LUMO energy level of pure C 18 ring is −7.26 eV and −2.32 eV respectively, i.e. the energy gap is around 4.94 eV similar to the value predicted by Fabio [71] which implying that the high kinetic energy stability and low chemical reactivity.The bandgap of pristine C 18 ring has disappeared when substituted with B, N, and Li atom, which affords an efficient charge transfer from HOMO to LUMO [55].The doping of boron formed primarily Px, and Py orbital from the carbon and boron atoms as we can see HOMO, and LUMO image in figures 3(a)-(d).In the HOMO, the orbital's have similar signs and so they combine to form a bonding π molecular orbital's, while in the LUMO, they have up and down direction, indicating that they combine to form an antibonding π * molecular orbital's.The same behavior can be seen for Li doped C 18 ring as shown in figure 3(b).

Contour map display (charge density)
Moreover, to verify the orbital charge density on the C 18 and B, N, and Li doped C 18 system, the contours map is plotted which allows one to display volumetric results in a selected plane as presented in the figures 3(a)-(d).A representation of electrostatic potential through total charge density 'ρ(r)' in the plane of (0,0,1,0) has been shown.These contour lines give the information about the character of each type of bonding between the atoms [72].The maxima occur at the nuclear sites and ρ(r) decays in a nearly spherical manner away from the nuclei.Comparing the electronic density contour lines, we found that the atoms share electrons leading with large covalent interactions.This analysis also predicts that C 18 ring is charge gaining when doped with B, N and Li, which correlates well with the electro negativity difference between the species.The charge redistribution between C 18 ring and dopant (B, Li, and N) illustrates that the electronic characteristics can be adjusted by changing the dopant atom and this knowledge can be exploited in the development of electronic devices [73].The charge transfer analysis of our present work is in good agreement with reported work [24].The charge transfer is from C atom to the doped atom, is in the same line as per the reference paper.The energy gap between HOMO and LUMO of doped C 17 M (M = B, N, and Li) is smaller than that of pristine Cyclo-18 which is similar (a)

Analysis of density of states
In this section, we investigated the interaction mechanism and presented the electronic properties of B, N, and Li substitution in C 18 ring through the total and partial density of states as illustrated in figure 4(a).We employed PAW pseudopotential for C, B, N, and Li atom with PBE-GGA as the exchange correlation functional [74] implemented in VASP [75][76][77] code.In order to avoid the interaction between adjacent periodic images, a vacuum of 15 Å was inserted in all directions and C 18 was placed in the middle of the simulation box.The Brillouin zones were sampled using a K point's mesh with Monkhorst-Pack scheme [78] grid of 1 × 1 × 1 for optimization and for accurate Density of States (DOS) calculations respectively.We can observe that there are delocalized electronic states of C 18 and doped C 18 ring in the total density of states as shown figure 4(a).The pure C 18 ring exhibits a semiconductor nature.It can also be observed that substitution of B and Li change the system into metallic while N substitution makes band gap opening which may be due to the redistribution of charge modifying the electronic characteristics of the system.
When we substitute the B, N, and Li atom in C 18 ring, the density of states of Li 's' orbital, B '2p' orbital and N '2p' at or below Fermi level decreases compare to isolated Li, B and N atom as displayed in figure 4  the system.On the other hand, substitution of N in isolated C 18 ring shows that the charge states in DOS are mainly composed by N 2p orbital in the valence band region near the Fermi level as illustrated in the figure 4(b) while conduction band region is empty near Fermi level.For N-substituted C 18 there is a gap at Fermi level indicating semiconductor character for C− 17 N system, matching nicely with the work done on the DyMg system [79].Metallic nature can be seen for Li substitution as there are finite electronic states at the Fermi level.
To further investigate the redistribution of charge and their effect on DOS, we are providing natural electron configuration data analysis (Electron configuration of only outer orbtials to see interaction) as obtained by NPA [60].Natural electron configuration shows distributions of electrons in atomic or molecular orbitals.As given in table 4, the occupancies of atomic orbitals are non integer in molecular environment.Here mostly 2p orbital is contributing in the interaction process which also verified by the PDOS.
Further to confirm the structural stability of pure C 18 ring and C 17 X(X = B, N, and Li), Ab Intio Molecular Dynamics simulation have been performed by increasing the temperature from 0 to 300 K with a step size of 1fs for a time period of 2 ps.It can be identified from the figures 5 (a)-(d) that there is 5%-7% fluctuation in the bond length, which is showing the thermal stability of the proposed system.Further we studied the position of the adsorption peak in the UV-vis spectra, which is related to its size and the electronic transition S 0 -S 1 at 230 nm, are of the HOMO-LUMO type for the pure C 18 ring, matching well with the recent experimental work done by Kaiser et al [11].It could find an application in drug delivery system [82] and solar cells application [83].When we substitute the B, N, and Li, the electronic states becomes more delocalized and it shifts to higher wavelengths at 360 nm, 410 nm, and 1250 nm respectively as shown in  oscillator strength indicating significant probability of occurrence.Shifting of wavelength after substituting the B, N, is in the visible range which also shows the suitability of these doped C 18 systems for photo-catalytic applications.

Conclusions
The present work aims to find out the structural, electronic, and optical properties of C 18 and C 17 X(X = B, N, and Li) system using Density functional theory.We found that the 6-311++G(d) type basis sets at M062X hybrid functional approach have shown to be sufficiently accurate in predicting the ground state structure of C 18 system.Ab Initio Molecular Dynamics calculation shows that C 18 and C 17 X(X = B, N, and Li) rings are stable.The stability of C 18 system is analyzed through HOMO-LUMO gap, quadrupole moments and higher multipole moments (through hexadecapole).It is also found that the distortion in the C 18 clusters is mainly due to the charge distributions between C atom and the substituted B, N, or Li atom.Natural population analysis and density of states supports each other and gives the information about the redistribution of charge and orbital-orbital interactions.Dominant adsorption IR peak at 2049 cm −1 , 1329 cm −1 , and 1011 cm −1 for B, N, and Li substituted C 18 ring indicating that there is an enhancement in optical absorption in the visible region by red shifting it due to doping which makes the system suitable for photo-catalytic and other optoelectronic applications.

Figure 1 .
Figure 1.Illustration of minimum energy structure of Cyclo-18 ring structure.

3. 2 .
Structure and stability analysis 3.2.1.Diploe moment, and quadrupole moment Based on the quantum computational simulation, our next aim is to analyze the impact of B, N, and Li substitution on the electronic structures and other properties of Cyclo-18 ring.The optimized structure shown in figure 2, indicate that compared to C-C bond length of 1.27 Å, the bond length of B-C, N-C, and Li-C increases up to 1.43 Å, 1.31 Å, 2.03 Å respectively.This elongation in bond length is just due to substitution of B, N, and Li in the C 18 ring that modifies the spherical shape of the polyynic Cyclo-18 structure.

18 -
are the minimum energy of Cyclo-C 17 X, Cyclo-18 ring, and substituted atom i.e.Li, B, N. The magnitude of this energy of the clusters gives the information about the strength of the chemical bonding[67][68][69].The average binding energies for the Li, B, and N substituted Cyclo-C18 ring are −4.58eV, −4.65 eV, and −2.83 eV respectively which showing strong binding and stability of the substituted Cyclo-C18 ring.

Figure 3 .
Figure 3. HOMO-LUMO orbitals with charge density contour map for (a) Pure C 18 (b) Li doped C 18 (c) B doped C 18 (d) N doped C 18 .[The red color present charge lost region whereas green color present charge gain region].

Figure 4 .
Figure 4. (a) Total density of states of pure C 18 polyynic structure and B, N, and Li doped C 18 system figure 4(b) Partial Density of States (PDOS) comparison between 2p orbital's of isolated B, N, and Li atoms with doped C 17 X(X = B, N, and Li) [Vertical line is indicating Fermi level].
(b).This indicates a charge transfer from B, N and Li atom to the isolated C18 ring.Here we can notice that in case of B substitution as given in figure 4(b), (B) 2p orbital is mainly contributing near the Fermi level and the charge states are mainly accumulated in the valance band.Further the states at Fermi level show the metallic character of(b)

Table 4 .Figure 5 .
Figure 5. Variation of (a) C-C, (b) B-C, (c) N-C, and (d) Li-C bond length of Pristine C 18 ring and B, N, and Li doped C 18 ring with time step at 300 K simulated through molecular dynamics.

3. 7 .
Optical propertiesTo investigate the optical response of C 18 and C 17 X(X = B, N, and Li) we employed time dependent density functional theory implemented in Gaussian simulation[50] by using M06-2X/6-31++g(d) level of theory.The evaluation of vibration properties through the analysis of the IR/Raman spectra and UV-vis absorption of the pristine C 18 and C 17 X(X = B, N, and Li) has been shown in figures 6(a)-(d), which explore the realistic nature of the system.The electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra as explained by Joshi et al[80,81].TD-DFT gives the right path to study this interaction during optical properties calculation.We used TD-DFT in our present study to get excitation states for UV-absorption.It is well known that vibration of substituted atom [i.e.B, N, and Li in the present report] always contributes to the IR spectra while C 18 ring is mainly responsible for Raman spectra.The IR/Raman spectra were measured over a broad frequency range from 0 to 2500 cm −1 .The C-C stretching vibration show the prominent peak at 748 cm −1 in IR while 1780 cm −1 in Raman spectra respectively for pristine C 18 ring.If we replace one C atom by B, N, and Li atom in C18 ring, the vibrational peak corresponding to substitutions showed significantly changes.It can be identified that the dominant adsorption IR peak at 2049 cm −1 , 1329 cm −1 , and 1011 cm −1 for B, N, and Li substituted C 18 ring.The shifting of IR peak towards higher value is indicating bond strength and rigidity of doped cage showing red shift[45] while move of Raman modes towards lower frequencies in the same system showing blue shift.
figures 5(b)-(d).Due to this shifting, the absorption spectrum shows a red-shift as shown in figures 6(b)-(d).These electronic transition have character of HOMO-LUMO+1, and HOMO-LUMO type with significant

Figure 6 .
Figure 6.(a) position of the adsorption peak in the UV-vis spectra match with the experimental result and corresponding IR/Raman peaks (b-d) showing red shift after the substitutions of B, N, and Li atoms and their corresponding IR/Raman peaks.

Table 3 .
Natural population analysis to illustrate charge transfer in C 18 and B, N, Li doped C 18 .