Probing the Structural, electronic and optical properties of pure and B, N, or Li substituted Cyclo-18 ring: Density Functional Theory Investigations

doi:10.21203/rs.3.rs-2106919/v1

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Probing the Structural, electronic and optical properties of pure and B, N, or Li substituted Cyclo-18 ring: Density Functional Theory Investigations

https://doi.org/10.21203/rs.3.rs-2106919/v1

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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 D_9h pollyene and D_18h cumulene form. Our computational simulations suggest that D_9h pollyene structure is minimum energy structure. The stability of the system has been discussed by analyzing HOMO-LUMO gap; quadrupole moments, and higher multipole moments. Pure C₁₈ system exhibits semiconductor in nature whereas doping can tune both electronic and optical properties. There is an enhancement in optical absorption in the visible region due to doping which makes the system suitable for photo-catalytic applications. Interestingly, there is a red shift in the UV-V spectra due to doping.

Cyclo-18 ring

Density Functional Theory

Optical Absorption

HOMO-LUMO gap

Natural population analysis

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. [1–9]

The behaviour of carbon clusters is interesting and because it changes from linear chains to a circular rings and then closed cages to nanotube as the size of cluster increases. It is also very interesting that as the size of clusters increases, the stability of rings also extending due to increase 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 sp² 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 [12–14] 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 C₆ C₈, C₁₈, C₁₄ in cumulene rings [18–20]. 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 C₆ ring isomer via experimental study is reported by Zajafman et al. [16]. Wakabayashi et al. [17] also investigated the stability factor of C_4n + 2 rings. Spectroscopic identification of C₆ and C₈ ring were also presented by Presiila J.D. et al. [18] and Wang S.L. et al. [19]. Diederich et al. [20] reported the synthesis of C₁₈ ring. Researchers also studied the Raman spectra and fluorescene spectra of C₁₄, C₁₆, C₁₈ rings and found that these rings were attributed to cumulenes ring. [21]. In 2005, Boguslavskiy A.E. et al [22] reported the vibrational spectra of cyclo-18 and 22 rings in gas phase and they obtained that there are several transition phase of cyclo-18 ring with D_9h point group symmetry for cumulenic (monocyclic) isomers while D_11h symmetry for C₂₂ ring. Very recently, Kaiser et al. [23] generated cyclo-18 ring using atom manipulation on bilayer NaCl on Cu(111) at 5K by eliminating CO from a cyclocarbon oxide molecule C₂₄O₆ and they predicted that polyyne D_9h form is the ground state. So up to now, great progress has been made in identifying C₁₈ ring by experimental study.

To understand the ground state properties of C18, several theoretical simulations have been reported using MP2 [24–25], HF [26–27], SCF [25], DFT [28–31], and Quantum Monte carlo [32] techniques. In this direction, researchers have produced reliable DFT results for linear and non-linear small carbon C_n molecules [12–14] with ring and chain structures. These theoretical investigations showed that all-carboatomic C₁₈ 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. [33] on B3LYP level using TZ (triple Zeta) basis sets observed that D_18h structure is the ground state structure. However Matrin et al. [34] reported a detail theoretical investigation at DFT level using cc-pVDZ basis sets and found D_9h pollynic form is ground state structure for C₁₈ ring. Torelli and Mitas [35] 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. [36] 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 C₁₈ ring of D_9h symmetry with alternating single and triple C-C bond. Similarly, Suresh and Ramaya [37] 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 eg. exohedral (outside the cage), endohedral (inside the cage) or by replacing one atom (substitution) [38–49]. 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 [38, 50, 51, 52 ]. Hou Xiufang et. al. [53] employed density functional theory to investigate electronic characteristics of pristine cyclo-C₁₈ and heteroatom-doped cyclo-C₁₇M (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 aim of the present study is to reproduce the experimentally determined pollynic structure of the cyclo C₁₈ ring and then to understand the effect of doping on its electronic and optical properties. This would be helpful in fabricating functionalized C₁₈ for various applications.

The local 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 Gaussian 16 simulation package based on density functional theory (DFT) [54]. Cyclo-18 ring [D_9h pollyene and D_18h cumulene], and doped-C₁₈ ring were fully optimized at B3LYP/LANL2DZ, and M062X/6–31 + + g(d) level of theory. We found that the results calculated using M062X/6–31 + + g(d) level of theory sounds good and match with other reported data so for all further calculation, we used only M062X/6–31 + + g(d) functional and basis sets [34–35]. Initial, C₁₇N, C₁₇B and C₁₇Li geometries were obtained by replacing one C atom in C₁₈ ring with and 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 strcutre when the maximum force, the root-mean-square (RMS) force, the maximum displacement of atoms, and the RMS displacement of atoms have magnitudes less than 0.00045 Ry, 0.0003 Ry, 0.0018 a.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 relative energy ordering. 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 [55]. To find the orbital-orbital interactions the total Density of States (DOS) and the partial density of states (PDOS) was calculated using VASP [56–59].

At the first stage of computation, the accuracy of basis set for B, N, Li and C, H atoms were validated with works from literature [60–61]. To check the reliability of our method, we have calculated C-C and C-B, C-N, and C-Li distances for D_9h pollyene C-18 ring. We have compared our data with the existing theoretical and experimental data [23].The calculated bond lengths for C-C and C-B, C-N, and C-Li are 3.17– 3.46 Å and 2.78–3.35 Å, in the range of the experimental value of 3.10–3.45 Å and 2.72–3.21 Å for C₁₈ ring and cyclo-C₁₇M (M = Li, Na, Be, Mg, B, Al, Ga, and In) respectively [23].

3.1 Structure analysis and stability of pure C₁₈ ring–

The overall idea of the present study is to find whether the ground state geometry is D_18h cumulenic or D_9h polyynic and also to see the impact of doping of B, N, and Li in C₁₈ ring. By using DFT quantum simulation along with B3LYP functionals support the D_18h symmetric minimum energy structure while the simulations using M062X/6-311 + + G(d) hybrid meta-GGA type functional result in a D_9h polyynic ground state structure as reported in recent investigations [62–64]. The optimized minimum energy structures have shown in Fig. 1.

The results derived using the M062X/6-311 + + G(d) level of theory agree well with Parasuk et al. [62] who did ab-initio calculations and confirmed that the D_9h polyynic structure is the minimum energy structure. The present simulation work accurately predict the ground state structures of the cyclo-18 ring and the structures obtained using M062X calculations are in well agreement with some previous theoretical and experimental reports [23, 34, 36]. So the reported work on Cyclo-C₁₈ ring predict that the DFT theory with 6-311 + + G(d) type basis sets at M062X 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.

Table 1

Dipole moments (in Debye) and quadrupole (in Debye-Angs) moments for cumulenic (D_18h) and polyynic (D_9h)
Polyynic (D_9h)
Sr. No.	Moment	X	Y	Z	Total
1	Dipole	0.0009	0.0006	-0.0009	0.0014
2	Quadrupole	XX= -99.03	YY = -99.83	ZZ = -98.77
		XY = 0.62	XZ = 0.06	YZ = -0.02
Cumulenic (D_18h)
Sr. No.	Moment	X	Y	Z	Total
1	Dipole	0.0001	0.0016	0.000	0.0017
2	Quadrupole	-97.15	-99.07	-97.85
		XY = 0.78	XZ = 0.34	YZ = -0.12

Quadrupole moment is the second order term in the expansion of the total electron distribution, and provides insight into its overall shape [63]. Denis J. [65] explored the stability on different molecules by using similar parameters. It was explained [65] 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 − 98.77 Debye-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.

3.2 Structure analysis and stability of C₁₈ ring substituted with B, N, and Li –

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 C₁₈ ring. Here again first the minimum energy structures are obtained upon full relaxation under the DFT framework. The optimized structure shown in Fig. 2, indicate that compared to C-C bond length of 1.27Å, the bond length of B-C, N-C, and Li-C becomes 1.43Å, 1.31Å, 2.03Å respectively. This elongation in bond length is just due to substitution of B, N, and Li in the C18 ring that modifies the spherical shape of the polyynic C₁₈ structure.

Table 2

Dipole moments (in Debye) and quadrupole moments (in Debye-Angs) of B, N, and Li substitute polyynic (D_9h)
B substituted Polyynic (D_9h)
Sr. No.		X	Y	Z	Total
1	Dipole	0.50	0.27	0.10	0.5869
2	Quadrupole	XX= -100.07	YY = -98.94	ZZ = -97.88
		XY = 2.7	XZ = -1.34	YZ = -0.47
N substituted Polyynic (D_9h)
Sr. No.		X	Y	Z	Total
1	Dipole	-0.5534	0.7536	-0.0000	0.9350
2	Quadrupole	XX= -103.10	YY = -100.80	ZZ = -99.24
		XY = 0.66	XZ = 0.00	YZ = 0.00
Li substituted Polyynic (D_9h)
Sr. No.		X	Y	Z	Total
1	Dipole	-1.02	0.20	-0.0000	1.04
2	Quadrupole	XX = -83.99	YY = -102.82	ZZ = -99.10
		XY = -3.6	XZ = 0.00	YZ = 0.00

Further to explain the stability of cyclo C₁₇X (X = B, N, and Li) ring it can be clearly seen from the Table 2, that substitution of boron atom in C₁₈ 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 distrortion in the circular ring structure as shown in Fig. 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 Fig. 2.

3.3 Charge transfer mechanism, molecular orbitals, and contour map of charge distributions -

After calculation of the ground state electronic structure we analyzed atomic charges distribution using the natural bond orbital (NBO) analysis (Population = NPA) [55] 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 C₁₈ ring and making covalent bonds. Our calculated HOMO-LUMO plots also support the same as illustrated in Fig. 3(a-d). The charge population of present system is similar to the system studied by the Yingqian chen et al. [66], 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 C₁₈ 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 1.27Å, and 1.28Å respectively, while the bond length of B-C, N-C, and Li-C changes to 1.31Å, 1.43Å, and 2.03Å respectively due to the charge transfer which point towards the distortion of C₁₈ 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 Fig. 3. It can be seen that all the occupied MO’s have an equal pair of spin, giving net spin zero. 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 C₁₈ system, the HOMO is an orbital formed from Py orbital’s from the carbon atoms while LUMO is formed from s orbitals of carbon atoms. The HOMO-LUMO gap is around 5.3 eV showing chemical stability of the pure C₁₈ cyclo ring similar to the value predicted by P. Fabio [67].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 Fig. 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 C₁₈ ring as shown in Fig. 3b. Moreover, to verify the orbital charge density on the C₁₈ and B, N, and Li doped C₁₈ system, the contours map is plotted which allows one to display volumetric results in a selected plane as presented in the Fig. 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 [68]. 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 C₁₈ 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 C₁₈ 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 [69].

Table 3

Natural population analysis to illustrate charge transfer in C₁₈ and B, N, Li doped C₁₈
Atom	No	Natural atomic charge difference in terms of e
		Pure C18	B@C17	N@C17	Li@C17
C	1	-0.58	-0.56	0.30	-0.57
C	2	0.89	0.60	0.24	0.85
C	3	-0.28	0.61	-0.25	0.27
C	4	-0.01	0.59	-0.01	0.01
C	5	-0.00	0.06	-0.00	0.02
C	6	-0.29	-0.04	-0.15	-0.17
C	7	-0.00	0.02	0.17	0.30
C	8	-0.01	0.07	0.28	0.37
C	9	-0.27	-0.09	-0.17	-0.02
C	10	0.88	0.64	0.57	0.04
C	11	-0.24	0.14	-0.03	-0.02
C	12	-0.60	-0.44	-0.35	-0.21
C	13	-0.27	-1.67	0.32	-0.12
C	14	-1.91	-1.48	-1.73	-0.51
C	15	0.42	0.8	0.42	0.52
C	16	-0.50	0.83	0.32	-1.01
C	17	-0.00	0.28	1.55	0.25
C/B/N/Li	18	0.039	B = 1.62	N = 0.78	Li = 0.40

3.4 Density of States Analysis

In this section, we investigated the interaction mechanism and presented the electronic properties of B, N, and Li substitution in C₁₈ ring through the total and partial density of states as illustrated in Fig. 4a. As VASP [56–59] code employs periodic boundary conditions, in order to avoid the interaction between adjacent periodic images, a vacuum of 15 Å was inserted in all directions and C₁₈ was placed in the middle of the simulation box. We can observe that there are delocalized electronic states of C₁₈ and doped C₁₈ ring in the total density of states as shown Fig. 4a. The pure C₁₈ 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 C₁₈ 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 Fig. 4(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 Fig. 4b, 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 the system. On the other hand, substitution of N in isolated C₁₈ 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 Fig. 4(b) while conduction band region is empty near Fermi level. For N-substituted C₁₈ there is a gap at Fermi level indicating semiconductor character for N-C₁₈ system, matching nicely with the work done on the DyMg system [70]. Metallic nature can be seen for Li substitution as there are finite electronic states at the Fermi level.

Table 4

Natural electron configuration for pure C₁₈ ring and doped (B, N, and Li) C₁₈ ring
Atom	Different Orbital’s
C	2S = 0.88	2P = 3.08
B	2S = 0.3	2P = 1.4
N	2S = 1.19	2P = 4.09
Li	2S = 0.30	2P = 0.54

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 [55]. 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.

3.5 Optical Properties:

To investigate the optical response of C₁₈ and C₁₇X(X = B, N, and Li) we employed time dependent density functional theory. We found that the position of the adsorption peak in the UV-Vis spectra is related to its size and the electronic transition S₀ S₁ at 230 nm are of the HOMO-LUMO type for the pure C₁₈ ring, matching well with the recent experimental work done by Kaiser et al. [23] as shown in ESI Fig. 1 (electronic supplementary information). It could find an application in drug delivery system [71]. 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, 430 nm respectively as shown in ESI Fig. 1(electronic supplementary information). Due to this shifting, the absorption spectrum shows a red-shift as shown in ESI (electronic supplementary information). These electronic transition have character of HOMO-LUMO + 1, and HOMO-LUMO type with significant oscillator strength indicating significant probability of occurrence. Shifting of wavelength after substituting the B, N, and Li is in the visible range which also shows the suitability of these doped C₁₈ systems for photo-catalytic applications.

Density functional theory with 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 C₁₈ system. Our calculations show that the C₁₈ structure is stable even when doped with B, N, or Li atom. The dependence of the structural stability was analyzed through HOMO-LUMO gap, quadrupole moments and higher multipole moments (through hexadecapole). It is also found that the distortion in the C₁₈ clusters is mainly due to the charge distributions between C atom and the dopant 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. The present studies show that doping C₁₈ with different atoms like B, N, or Li can tune the Uv-Vis absorption spectra, by red shifting it, thus opening up the possibility of using doped C₁₈ for optoelectronic applications.

Funding

This work was supported by SERB files no. PDF/2021/003221 and Ravi Trivedi has received research support from Science and Engineering Research Board, New Delhi.

Competing Interests:

Conflict of interest: The authors declare that they do not have any conflict of interest

Author Contributions

R. Trivedi: Conceptualization, Data Curation, Data analysis, Writing-original draft.

Prafulla K Jha – Editing Draft Manuscript, Partly Analysis, Software

Nandini Garg – Editing Draft Manuscript, Data Analysis

Brahmananda Chakraborty: Supervision, Data Analysis, Editing Draft Manuscript

Data availability statement

The data that support this study are available upon reasonable request.

Acknowledgements

RKT thanks to SERB for providing funding. Authors acknowledge the super-computing facility of BARC and M.S. University of Baroda

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Probing the Structural, electronic and optical properties of pure and B, N, or Li substituted Cyclo-18 ring: Density Functional Theory Investigations

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Computational Methodology

3. Results And Analysis

3.1 Structure analysis and stability of pure C₁₈ ring–

3.2 Structure analysis and stability of C₁₈ ring substituted with B, N, and Li –

3.3 Charge transfer mechanism, molecular orbitals, and contour map of charge distributions -

3.4 Density of States Analysis

3.5 Optical Properties:

4. Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Probing the Structural, electronic and optical properties of pure and B, N, or Li substituted Cyclo-18 ring: Density Functional Theory Investigations

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Computational Methodology

3. Results And Analysis

3.1 Structure analysis and stability of pure C18 ring–

3.2 Structure analysis and stability of C18 ring substituted with B, N, and Li –

3.3 Charge transfer mechanism, molecular orbitals, and contour map of charge distributions -

3.4 Density of States Analysis

3.5 Optical Properties:

4. Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

3.1 Structure analysis and stability of pure C₁₈ ring–

3.2 Structure analysis and stability of C₁₈ ring substituted with B, N, and Li –