Theoretical investigation of the zirconium carbide nano-sheet: A study of NMR, NBO, EPR and Polar

Introduction

The three known allotropes of carbon are amorphous carbon, graphite, and diamond. New allotropes of carbon that are being synthesized around the world include fullerenes, carbon nano tubes (CNTs) and graphene due to their fantastic physical and chemical properties^1-20. Graphene is a single-atom-thick planar sheet of carbon atoms hexagonally arranged in a honeycomb crystal lattice, and has gained lots of attention due to its structure and electrical properties^21-25. Graphene is unanimously considered a very promising material to be used in various fields, such as energy production and storage, gas detection, and electronics. In the view of structure, it has one or a few layers thickness of sp²-hybridized carbon atoms arranged in a honeycomb pattern, which makes it to possess electrical, optical, electrochemical and mechanical properties. Therefore, several methods for the synthesis of graphene and its derivatives have been developed ^26-30. This study was carried out to explore zirconium carbide nano-sheet (ZrC nano-sheet). ZrC nano-sheet is similar to that of graphene, except that Zr is one among the alternative carbons. Zirconium carbide, due to its unique physical and chemical properties, such as high melting point (~3540°C), high hardness (~25 Gpa), wear resistance, high thermal conductivity, excellent mechanical properties and good chemical stability at high temperature, is used in industries, especially for high temperature applications^31-41. It is used in different applications such as cutting tools, covering of the tip of the drill, grinding wheels and abrasives for mechanical as well as structural components in chemical and electronic industries. Also, it has potential applications as coating material for nuclear fuel ^42-44.

In this study, the molecular mechanic and ab-initio methods were applied to calculate the natural bond orbital (NBO), Nuclear magnetic resonance (NMR), Electron paramagnetic resonance (EPR) and polar of ZrC nano-sheet, using the Gaussian 09 program package.

Materials and Methods

Ab initio methods were carried out for the zirconium carbide nano-sheet using the Gaussian 09 program for the first time (Figure 1.). B3LYP was selected for calculating the natural bond orbital (NBO), Nuclear magnetic resonance (NMR), Electron paramagnetic resonance (EPR) and polar.

Results and Discussion

The E_HOMO and E_LUMO calculated using the B3LYP method were -0.18646 and -0.16892 (a.u.) , respectively. The Band Gap (Fermi energy), Dipole moment, Quadrupole moment, Traceless Quadrupole moment and Octapole moment were calculated using the B3LYP method shown in Table 1.

Table 1: Polar determinant and band gap  (Fermi energy) obtained for ZrC nano-sheet.

Dipole moment (Debye)	35.215
Quadrupole moment (Debye-Ang)	-64119124.96
Traceless Quadrupole moment (Debye-Ang)	-98480.8764
Octapole moment (Debye-Ang)	-79586.9398
Hexadecapole moment (Debye-Ang)	6.53E+11
Distance matrix (angstrom)	-1.46E+54
Band Gap Energy (a.u.)	-0.01754

 

Tables 2, 3 and 4 show the calculated parameters of electron paramagnetic resonance (EPR) for ZrC nano-sheet. Atomic bonds, charge of atoms and voltages were determined using the B3LYP method. The ∆V, ∆Vʹ and ∆V Mulliken for all bonds were calculated.

The formula used given as follow:

 

Where (V₁,V₂, ∆V₁₂ and ∆Vʹ₁₂), (V₅,V₆, ∆V₅₆ and ∆Vʹ₅₆) and (V₉,V₁₀,∆V₉₁₀ and ∆Vʹ₉₁₀) were calculated from the obtained data of EPR that include; (Electrostatic properties “Atomic unit” (X,Y,Z)), (Electric Field Gradient(XY,XZ,YZ)) and (Electric Field Gradient “tensor representation” Eigen values), respectively. Also, (V₁₁,V₁₂, ∆V₁₁₁₂ and ∆Vʹ₁₁₁₂), (V₃,V₄,∆V₃₄ and ∆Vʹ₃₄) and

Table 2: EPR calculated parameters for the ZrC nano-sheet.   Click here to View table

 

(V₇,V₈,∆V₇₈ and ∆Vʹ₇₈) were calculated from the obtained data of EPR that include; (Electric Field Gradient “tensor representation” (3XX-RR, 3YY-RR, 3ZZ-RR)), (Electric Field Gradient (XX,YY,ZZ)) and (Electric Field Gradient Eigen values), respectively.

By comparison of the obtained voltages (voltage difference) ;  ∆V, ∆Vʹ and ∆V_Mulliken in Tables 2 and 3 were in similar range, but in Table 4, ∆V and ∆Vʹ were in a different range of ∆V_Mulliken.

Table 3: EPR calculated parameters for the ZrC nano-sheet.

atomic bond	V9 (a.u.)	V10 (a.u.)	∆V910 (V)	∆Vʹ910 (V)	V11 (a.u.)	V12 (a.u.)	∆V1112 (V)	∆Vʹ1112 (V)
C1-H26	0.5015	1.3454	10.8302	22.8781	0.4169	0.8813	5.9601	12.5899
C1-H27	0.5015	0.2203	10.0598	7.6233	0.4169	0.5749	2.1556	4.2834
C1-Zr15	0.5015	0.5447	0.2692	1.1712	0.4169	0.5436	0.7891	3.4348
Zr15-C4	0.5447	1.2056	4.1198	17.9170	0.5436	1.2049	4.1212	17.9278
Zr15-C3	0.5447	0.6960	0.9417	4.1017	0.5436	0.6959	0.9489	4.1289
C3-H31	0.6960	1.2653	7.3051	15.4337	0.6959	0.4621	2.9995	6.3383
C3-Zr14	0.6960	0.5961	0.6220	2.7083	0.6959	0.5960	0.6220	2.7083
Zr14-C8	0.5961	1.2506	7.4232	17.7435	0.5960	1.2506	4.0795	17.7462
C8-Zr20	1.2506	0.6258	3.8937	16.9383	1.2506	0.6258	3.8938	16.9383
Zr20-C4	0.6258	1.2056	3.6129	15.7184	0.6258	1.2049	3.6086	15.6994
C4-Zr16	1.2056	0.5077	4.3502	18.9201	1.2049	0.5042	4.3675	18.9960
Zr16-C5	0.5077	2.0533	9.6336	41.9012	0.5042	1.1409	3.9686	17.2609
Zr16-C10	0.5077	1.5770	6.6657	28.9887	0.5042	1.2071	4.3804	19.0556
C10-Zr21	1.5770	0.2103	7.5384	37.0512	1.2071	0.3656	5.2444	22.8131
Zr21-H36	0.3676	0.6902	2.5776	8.7457	0.3656	0.2707	0.7574	2.5727
Zr21-C9	0.3676	1.1280	4.7390	20.6144	0.3656	1.1278	4.7505	20.6632
C9-Zr20	1.1280	0.3198	3.1330	21.9103	1.1278	0.6258	3.1291	13.6092
C9-Zr24	1.1280	0.4314	4.3416	18.8848	1.1278	0.4312	4.3416	18.8848
Zr24-H39	0.4314	0.6808	1.9929	6.7612	0.4312	0.2219	1.6718	5.6741
Zr24-C13	0.4314	1.1359	4.3905	19.0990	0.4312	1.1359	4.3920	19.1044
C13-Zr19	1.1359	0.6269	3.1723	13.7990	1.1359	0.6269	3.1723	13.7990
C13-Zr23	1.2776	0.4209	4.4568	23.2251	1.1359	0.4206	5.7254	19.3918
Zr23-H38	0.4209	0.6796	2.0664	7.0134	0.4206	0.2250	1.5624	5.3027
Zr23-C12	0.4209	1.0254	3.7620	16.3880	0.4206	1.0252	3.7684	16.3907
C12-Zr22	1.0254	0.5658	2.8641	12.4598	1.0252	0.5658	2.1960	12.4543
C12-Zr25	1.0254	0.2866	4.6051	20.0289	1.0252	0.2173	5.0356	21.9022
Zr25-H41	0.2866	0.6656	3.0283	10.2747	0.2173	0.6647	3.5740	12.1290
Zr25-H43	0.2866	0.6438	2.8540	9.6837	0.2173	0.2867	0.2433	1.8814
Zr22-C11	0.5658	1.2776	4.4366	19.2969	0.5658	0.9183	2.1960	9.5563
Zr22-C7	0.5658	1.2273	4.1227	17.9333	0.5658	1.2267	4.1198	17.9170
Zr18-C7	0.5796	1.2273	4.0363	17.5591	0.5794	1.2267	4.0348	17.5483
Zr18-C6	0.5796	0.6358	0.3499	1.5236	0.5794	0.6273	0.2980	1.2986
C6-H33	0.6358	1.2751	8.2036	17.3314	0.6273	0.5017	1.6113	3.4050
C6-Zr17	0.6358	0.4387	1.2283	5.3434	0.6273	0.4163	1.3147	5.7202
Zr17-C11	0.4387	1.2776	5.2286	22.7426	0.4163	0.9183	3.1291	13.6092
C7-Zr19	1.2273	0.6269	3.7425	16.2768	1.2267	0.6269	3.7382	16.2606
Zr19-C8	0.6269	1.2506	3.8880	16.9085	0.6269	1.2506	3.8880	16.9085
Zr14-C8	0.5961	1.2506	7.4232	17.7435	0.5960	1.2506	4.0795	17.7462
Zr14-C2	0.5961	0.7081	0.6969	3.0363	0.5960	0.7078	0.6955	3.0309
C2-H30	0.7081	1.2580	7.0574	14.9078	0.7078	0.4551	3.2428	6.8507
Zr18-C2	0.5796	0.7081	0.8006	3.4836	0.5794	0.7078	0.7992	3.4809

 

Figure 1: Structure of ZrC nano-sheet.   Click here to View figure

 

Table 4    Click here to View table

 

The NMR calculated parameters include isotropic shielding tensor (σ_iso), anisotropic shielding tensor (σ_aniso), asymmetry (η), span (Ω) and skew (K)^45-51.

In this study, the NMR calculated parameters of ZrC nano-sheets obtained using the B3LYP method are shown in Tables 5 to 8.  The equations used are as follows ⁵¹:

 

Where η, Ω, K, ξ were calculated for Zr, H and C, in ZrC nano-sheets. Radii (R) is the distance of He or Ne from ZrC nano-sheets.

Some of the asymmetry in the range
0 ≤  η  ≤1   is not listed in Tables
5-8 and the amount in the table is empty.

Figures 2 and 3 show the diagram of η, σ_aniso, σ_iso, HF(Hartree-Fock) and K of  ZrC nano-sheets with different distance (R) of He and Ne.

Data obtained for natural bond orbital (NBO) are shown in Tables 9 to 15.

E2, Ei- Ej and F (i,j) represent the energy hyper conjugative interaction (stabilization energy), Energy difference between donor and accepter NBO orbital, and the Fock matrix element between i and j orbitals, respectively.

The highest and lowest stabilization energy in ZrC nano-sheet were 181.25 and 0.93 kcal/mol for [LP*(2) Zr18, BD*(1) C7-Zr18] and [BD (1) C4-Zr15, RY*(8) Zr20], respectively.

Table 10 shows the bonding and anti-bonding orbitals and hybridization of atomic orbitals in ZrC nano-sheet.

The orbital occupancy is the number of electrons, or “natural population” of the orbital, and the orbital energy is in atomic units: 1 a.u. = 627.5 kcal/mol.

The number of core (CR), 2-center bond (BD) and lone pair (LP) NBOs are in the natural Lewis structure; these labels give the type (BD for 2-center bond, CR for
1-center core pair, LP for 1-center valence lone pair, RY* for 1-center Rydberg, and BD* for 2-center anti-bond) the un-starred and starred labels corresponding to the Lewis and non-Lewis NBOs, respectively.

Tables 11-15 allow quick identification of the principal delocalizing acceptor orbitals associated with each donor NBO, and their topological relationship with NBO, that is, whether they are attached to the same atom (geminal, “g”), or to an adjacent bonded atom (vicinal, “v”), or to a more remote (“r”) site. For example, from Tables 11-15, the highest-occupancy, highest-energy and primarily delocalized were 1.99986 electrons, -10.0997 a.u. and 137(v) for CR (1) C5, respectively. ,However, the lowest-occupancy, was 0.00002 electrons for RY*(9) Zr15

Figure 2: Diagrams of η, σaniso, σiso, HF and K of   ZrC nano-sheets with different distance (R) of He.  Click here to View figure

 

Figure 3: Diagrams of η, σaniso, σiso, HF and K of ZrC nano-sheets with different distance (R) of Ne. Click here to View figure

 

Table 5: NMR calculated parameters (ppm) for ZrC nano-sheets.

Element	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11
σiso	141.96	43.16	56.39	-179.19	29136.49	-6.20	-442.05	-1046.76	-1425.72	-21223.15	-403.53
σaniso	65.40	180.07	160.56	1707.28	124456.00	188.85	779.98	1385.54	5094.02	78717.80	601.11
Ω	105.56	207.48	204.91	1909.02	132544.60	233.63	890.17	2247.63	6016.72	79720.61	846.94
K	-0.52	0.00	0.13	0.57	0.75	0.23	0.50	-0.53	0.39	0.94	-0.16
η		0.46	0.87	0.41		0.79		0.55		0.27
ξ	43.60	120.04	107.03	1138.18	82971.09	125.90	519.99	923.69	3396.01	52478.53	400.74
R	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
σiso	153.45	3.88	24.62	-14.04	40918.97	-5.50	-509.65	-430.98	-1043.45	29525.46	-709.89
σaniso	102.46	142.55	85.92	210.45	164676.10	143.82	464.45	499.71	5622.66	104482.51	1241.93
Ω	178.92	191.69	159.17	2120.08	171737.20	191.02	540.21	726.27	7577.59	106169.90	1565.31
K	-0.71	-0.03	0.02	0.98	0.84	0.01	0.44	-0.25	-0.03	0.94	0.17
η				0.26	0.00			0.34	0.74	0.31	0.07
ξ	68.31	95.03	57.28	1406.30	109784.10	95.88	309.63	333.14	3748.44	69655.01	827.95
R	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10
σiso	154.57	6.62	25.92	5.64	42357.01	0.36	-490.29	-417.69	-1164.12	30616.87	-703.76
σaniso	101.78	143.07	83.64	2164.73	169836.30	137.31	464.25	633.11	5771.51	107709.13	1185.63
Ω	183.01	187.17	159.02	2181.16	176587.80	186.86	536.26	804.41	7900.71	109413.57	1503.48
K	-0.78	0.06	-0.90	0.97	0.85	-0.06	0.46	0.15	-0.08	0.94	0.15
η		0.95		0.21				0.34	0.73	0.31	0.04
ξ	67.86	95.38	55.76	1443.15	113224.20	91.54	309.50	422.07	3847.67	71806.09	790.42
R	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50
σiso	158.23	20.11	37.46	37.43	45630.36	-7.09	-517.82	-466.09	-903.80	32698.15	-687.47
σaniso	104.51	138.38	99.08	2218.61	181147.00	111.53	234.93	539.41	5431.11	114385.07	1442.14
Ω	188.01	179.31	179.48	2244.48	187815.40	156.62	416.65	788.02	7176.18	116222.32	1675.77
K	-0.78	0.09	-0.79	0.95	0.86	-0.15	-0.74	-0.26	0.03	0.31	0.44
η		0.89		0.20		0.82	0.28	0.80	0.77	0.32	1.00
ξ	69.68	92.25	66.05	1479.07	120764.70	74.36	156.62	359.61	3620.74	76256.71	961.42
R	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70
σiso	159.08	8.84	25.70	141.39	55597.53	-21.07	-704.10	-359.77	-1938.58	40217.86	-563.20
σaniso	132.00	117.29	135.06	2693.51	216551.90	60.15	831.45	1173.07	7488.47	137412.19	2091.16
Ω	242.05	138.06	191.27	2762.75	221357.60	100.79	1097.97	1260.22	10938.03	139459.76	2300.61
K	-0.82	0.40	-0.18	0.87	0.91	0.61	0.03	0.72	-0.26	0.00	0.64
η	0.20	0.68	0.87	0.04		0.84	0.83	0.28	0.67	0.31	0.78
ξ	88.00	78.19	90.04	1795.68	144368.00	40.10	0.83	782.05	4992.31	91608.13	1394.11
R	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30
σiso	183.40	133.88	151.11	-28.19	33177.84	128.20	-382.42	-673.18	127.77	24859.92	-1650.17
σaniso	74.46	503.06	529.69	1201.57	140085.90	543.48	1826.70	1421.05	2922.23	88258.42	4137.09
Ω	108.27	537.19	585.71	1461.90	147807.00	572.39	2010.45	1919.16	3450.95	89278.21	5489.37
K	-0.08	0.00	0.62	0.29	0.75	0.12	0.63	0.04	0.39	0.95	0.00
η	0.73	0.21	0.42	0.30		0.20	0.18	0.62	0.89	0.27	0.90
ξ	49.64	335.38	353.13	801.05	0.59	362.32	1217.80	947.37	1948.15	58838.95	2758.06
R	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90

 

Table 6: NMR calculated parameters (ppm) for ZrC nano-sheets.    Click here to View table

 

Table 7: NMR calculated parameters (ppm) for ZrC nano-sheets.

Element	Zr23	Zr24	Zr25	H26	H27	H28	H29	H30	H31	H32	H33
σiso	-256.11	-381.93	-395.75	160.25	69.74	69.73	30.79	30.80	34.80	34.80	27.55
σaniso	301.41	112.91	121.69	450.61	106.18	106.20	21.92	21.91	15.46	15.39	39.26
Ω	387.79	441.70	182.54	519.96	126.02	126.04	23.55	23.51	22.54	22.43	60.95
K	0.11	-0.10	-0.33	0.47	-0.42	0.37	0.72	0.73	-0.26	-0.26	-0.42
η	0.79		0.38				0.46	0.46	0.32	0.32
ξ	200.94	75.28	81.12	300.40	70.79	70.80	14.61	14.61	10.31	10.26	26.18
R	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
σiso	-305.22	-371.76	-309.43	200.21	80.21	80.61	27.69	28.83	29.46	29.79	23.43
σaniso	54.93	138.01	60.33	621.78	156.13	156.80	26.61	26.16	31.08	31.82	34.77
Ω	69.67	254.47	98.78	711.72	180.91	181.82	43.03	41.18	46.40	47.53	48.10
K	0.15	-0.83	-0.56	0.16	0.45	0.45	-0.53	-0.46	-0.32	-0.32	-0.11
η	1.00		0.32				0.36	0.32	0.23	0.24	0.51
ξ	36.62	92.00	40.22	414.52	104.09	104.53	17.74	17.44	20.72	21.22	23.18
R	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10
σiso	-301.52	-374.73	-310.52	205.03	81.85	82.29	27.37	28.24	29.51	30.30	23.88
σaniso	60.85	146.38	59.77	643.38	163.02	163.63	28.94	26.60	32.26	33.28	34.60
Ω	68.48	265.86	96.70	735.61	188.21	189.19	46.32	43.36	48.20	49.88	47.58
K	0.18	-0.80	-0.53	0.50	0.46	0.46	-0.50	-0.55	-0.32	-0.33	-0.09
η	0.38		0.33				0.24	0.15	0.30	0.31	0.48
ξ	40.56	97.59	39.84	428.92	108.68	109.09	19.29	17.73	21.51	22.19	23.06
R	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50
σiso	-325.20	-363.81	-305.35	-219.59	85.73	86.16	27.01	28.38	32.11	32.10	22.08
σaniso	51.56	141.61	52.14	686.10	172.25	173.63	31.23	22.70	30.48	27.32	38.55
Ω	95.38	268.93	102.14	779.00	197.31	198.71	34.32	27.20	42.12	39.48	50.79
K	-0.84	-0.89	-0.96	0.52	0.49	0.50	0.64	0.34	-0.10	-0.23	0.04
η	0.20	94.41	0.04				0.66	0.67	0.49	0.36	0.59
ξ	34.38	94.41	34.76	457.40	114.83	115.76	20.82	15.13	20.32	18.22	25.70
R	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70
σiso	-308.86	-369.81	-300.88	250.24	95.45	96.15	24.41	24.06	31.18	30.53	14.44
σaniso	73.12	200.70	151.98	838.44	219.40	220.75	31.60	30.91	52.99	51.35	49.86
Ω	92.25	358.46	241.55	951.07	249.60	250.98	51.37	51.16	78.52	77.00	64.74
K	0.01	-0.76	-0.48	0.53	0.52	0.52	0.54	-0.58	-0.30	-0.33	0.08
η	0.75		0.23				0.34	0.25	0.60	0.56
ξ	48.74	133.80	101.32	558.96	146.27	147.17	21.07	20.61	35.32	34.23	33.24
R	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30
σiso	-381.54	-292.79	-379.97	196.89	87.49	86.74	47.01	44.10	65.02	65.73	67.37
σaniso	177.07	358.92	550.47	485.77	127.46	124.12	56.47	56.44	167.62	169.38	129.52
Ω	246.00	510.61	891.29	534.86	140.63	136.44	73.04	76.00	204.97	207.17	153.76
K	-0.12	-0.19	-0.53	0.63	0.63	0.64	0.09	-0.03	0.27	0.27	0.37
η	0.38		0.84						0.01	0.07
ξ	118.04	239.28	336.98	323.85	84.97	82.75	37.65	37.63	111.75	112.92	86.35
R	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90

Table 8: NMR calculated parameters (ppm) for ZrC nano-sheets.

Element	H34	H35	H36	H37	H38	H39	H40	H41	H42	H43	He44	Ne44
σiso	27.56	101.04	101.04	29.42	29.42	34.23	34.23	24.53	20.15	20.15	0.00	27.56
σaniso	39.24	239.51	239.49	15.62	15.50	46.00	45.95	15.52	23.89	23.89	0.00	39.24
Ω	60.91	252.79	252.76	20.39	20.25	59.35	59.30	25.35	41.44	41.40	0.00	60.91
K	-0.42	0.79	0.79	0.06	0.06	0.10	0.10	-0.55	-0.69	-0.69	0.00	-0.42
η				0.18	0.18	0.12	0.12		0.71	0.71	0.00
ξ	26.16	159.68	159.66	10.41	10.34	30.66	30.63	10.35	15.93	15.93	0.00	26.16
R	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
σiso	24.41	123.98	124.04	29.07	30.33	39.62	38.93	24.78	24.04	24.34	5.91	24.41
σaniso	33.85	326.61	326.52	27.71	29.83	55.02	49.69	12.21	18.81	18.11	33.94	33.85
Ω	48.95	343.18	342.98	36.21	37.93	64.91	60.84	20.68	32.39	31.76	39.77	48.95
K	-0.23	0.81	0.81	0.06	0.05	0.13	0.27	-0.64	-0.68	-0.72	0.14	-0.23
η	0.52			0.24	0.34	0.17	0.22				0.47	0.52
ξ	22.56	217.74	217.68	18.47	19.89	36.68	33.12	8.14	12.54	12.07	22.63	22.56
R	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10	2.10
σiso	24.94	126.72	127.08	29.43	30.90	40.15	39.53	24.83	24.14	24.41	6.90	24.94
σaniso	33.79	337.13	337.76	27.59	30.70	56.78	50.19	12.26	18.88	18.16	32.35	33.79
Ω	48.78	354.50	354.93	36.20	38.80	66.44	61.73	20.68	32.61	31.95	40.67	48.78
K	-0.23	0.80	0.81	0.05	0.16	0.42	0.25	-0.63	-0.68	-0.72	0.18	-0.23
η	0.50			0.24	0.40	0.14	0.22		12.59		0.12	0.50
ξ	22.53	224.75	225.18	18.39	20.46	37.85	33.46	8.18	12.59	12.10	21.57	22.53
R	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50
σiso	23.60	133.99	133.38	30.11	28.86	41.43	41.03	25.70	24.59	24.41	11.20	0.00
σaniso	39.67	356.58	355.88	31.39	27.30	60.49	56.46	10.63	17.95	17.99	29.87	0.00
Ω	51.71	373.39	372.76	39.77	36.36	69.42	66.52	19.40	31.78	30.89	39.47	0.00
K	0.07	0.82	0.82	0.16	0.00	0.49	0.40	-0.81	-0.74	-0.67	0.03	0.00
η	0.65			0.25	0.13	0.33	0.35					0.00
ξ	26.45	237.72	237.25	20.93	18.20	40.33	37.64	7.09	11.97	11.99	19.91	0.00
R	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	3.70	0.00
σiso	16.56	155.53	154.42	32.85	31.31	47.11	46.97	28.29	23.46	24.05	0.00	643.11
σaniso	49.55	438.77	435.51	34.86	43.34	60.04	60.18	12.88	22.52	21.46	0.00	898.70
Ω	64.06	461.39	458.31	48.94	57.49	68.19	69.42	21.62	37.13	36.05	0.00	1107.73
K	0.09	0.80	0.27	0.15	0.02	0.52	0.47	-0.62	-0.57	-0.62	0.00	0.25
η	0.95			0.15	0.03	0.30	0.31				0.00	0.02
ξ	33.03	292.51	290.34	23.24	28.90	40.03	40.12	8.59	15.01	14.30	0.00	599.13
R	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	2.30	0.00	2.30
σiso	65.62	109.09	110.97	19.39	24.88	30.23	34.19	16.09	33.33	33.30	0.00	-388.79
σaniso	133.60	255.72	260.18	37.72	37.65	53.68	49.51	48.64	40.06	43.65	0.00	270.40
Ω	159.30	268.32	272.67	51.23	48.48	69.85	69.78	81.22	52.08	56.50	0.00	514.57
K	0.35	0.81	0.27	0.06	0.11	0.07	0.06	-0.60	0.08	0.17	0.00	-0.90
η				0.35	0.67	0.66	0.95	0.30	0.31	0.45	0.00	0.05
ξ	89.07	170.48	173.45	25.15	25.10	35.79	33.01	32.42	26.71	29.10	0.00	180.26
R	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	3.90	0.00	3.90

 

Table 9: Donor NBO, acceptor NBO, E2, Ei- Ej and F(i,j) for ZrC nano-sheet.

Donor NBO (i)	Acceptor NBO (j)	E(2)  kcal/mol	E(i)-E(j)  a.u.	F (i , j)  a.u.
BD(1)  C1-Zr15	LP*(2)  Zr15	1.02	0.54	0.02
BD(1)  C1-Zr15	LP*(2)  Zr16	1.29	0.59	0.03
BD(1)  C1-Zr15	RY*(5)  Zr15	2.08	1.80	0.06
BD(1)  C4-Zr15	RY*(8)  Zr20	0.93	1.55	0.03
BD(1)  C4-Zr16	LP*(3)  Zr15	8.10	0.58	0.06
BD(1)  C4-Zr16	RY*(2)  Zr15	1.61	0.77	0.03
BD(1)  C4-Zr16	BD*(1) C4-Zr15	1.96	0.51	0.03
BD(1)  C7-Zr22	LP*(4) Zr15	8.09	0.48	0.06
BD(1)  C7-Zr22	LP*(1) Zr19	42.10	0.58	0.15
BD(1)  C7-Zr22	RY*(6) Zr20	4.81	3.70	0.13
BD(1)  C8-Zr14	LP*(4) Zr20	17.58	0.60	0.09
BD(1)  C8-Zr14	RY*(5) Zr14	4.79	2.04	0.09
BD(1)  C8-Zr14	BD*(1) C2-Zr14	4.31	0.64	0.05
BD(3)  C11-Zr17	LP*(1) Zr22	20.44	0.28	0.07
BD(3)  C11-Zr17	RY*(1) C6	15.78	2.21	0.18
BD(3)  C11-Zr17	BD*(2) C7-Zr18	5.40	0.21	0.03
CR(1) Zr14	LP*(4) Zr14	2.96	2.00	0.07
CR(1) Zr14	RY*(2) C3	1.31	4.47	0.07
CR(3) Zr14	BD*(1) C8-Zr14	8.12	1.41	0.10
CR(3) Zr24	BD*(1) C9-Zr24	2.06	1.42	0.05
CR(1) Zr25	LP* Zr23	1.28	2.13	0.05
CR(1) Zr25	RY*(1) C12	1.38	4.31	0.07
CR(3) Zr25	BD*(1) Zr25-H41	7.11	1.48	0.09
LP(1) C4	LP*(3)  Zr16	65.91	0.06	0.07
LP(1) C4	RY*(3) C4	2.59	0.65	0.05
LP(1) C4	BD*(2) C9-Zr20	3.51	0.12	0.02
LP(1) C10	RY*(6) Zr21	1.56	2.23	0.06
LP(2) C10	LP*(1) Zr21	17.10	0.22	0.07
LP(2) C10	BD*(1) C10-Zr16	8.62	0.23	0.05
LP*(3) C10	LP*(3) Zr16	9.49	0.03	0.02
LP*(3) C10	RY*(3) Zr16	4.56	0.12	0.04
LP(1) C11	LP*(1) Zr22	73.50	0.62	0.20
LP*(2) Zr16	LP*(5) Zr16	36.02	0.08	0.13
LP*(2) Zr16	RY*(1) C4	9.82	2.44	0.40
LP*(2) Zr16	BD*(1) C9-Zr21	2.65	0.02	0.02
LP*(2) Zr18	BD*(1) C7-Zr18	181.25	0.02	0.19
LP*(1) Zr19	LP*(6) Zr21	1.45	0.03	0.01
BD*(1) C4-Zr16	LP*(2) Zr15	3.91	0.03	0.02
BD*(1) C4-Zr16	RY*(5) Zr16	6.47	0.86	0.19
BD*(1) C4-Zr16	BD*(1) C4-Zr16	26.24	0.06	0.09
BD*(1) C4-Zr20	LP*(3) Zr20	25.68	0.04	0.08
BD*(1) C4-Zr20	RY*(2) C9	2.46	2.04	0.26
BD*(1) C4-Zr20	BD*(1) C9-Zr21	3.06	0.04	0.04
BD*(1) C7-Zr22	LP*(6) Zr22	32.44	0.07	0.14
BD*(1) C7-Zr22	RY*92) C11	2.49	1.06	0.16
BD*(1) C7-Zr22	BD*(1) C6-Zr18	8.49	0.02	0.04
BD*(2) C8-Zr14	LP*(1) Zr20	19.48	0.06	0.06
BD*(2) C8-Zr14	RY*(8) Zr14	1.77	1.25	0.14
BD*(2) C8-Zr14	BD*(1) C2-Zr14	6.81	0.23	0.10
BD*(1) C10-Zr16	LP*(5) Zr16	18.85	0.17	0.14
BD*(1) C10-Zr16	RY*(1) C4	6.46	2.54	0.32
BD*(1) C10-Zr16	BD*(1) C4-Zr20	9.96	0.07	0.06

 

Table 10: NBO data obtained for ZrC nano-sheet.  Click here to View table

 

Table 11. NBO data obtained for ZrC nano-sheet.

Bond orbital	Occupancy	Energy (a.u.)	Principal Delocalizations (geminal,vicinal,remote)
BD(1) C1-Zr15	1.98373	-0.38248	198(v),202(v),379(g),367(g),254(g),376(g),135(r),380(v)
BD(1) C1-H26	1.97552	-0.50224	129(v),376(v),198(r),130(v),
BD(1) C1-H27	1.96990	-0.51236	131(v),129(v),133(v),128(v),250(v),132(v)
BD(1) C1-H28	1.96990	-0.51236	131(v),129(v),133(v),128(v),250(v),132(v)
BD(1) C2-Zr14	1.87635	-0.39438	391(g),388(v),372(g),194(g),390(g),152(r),371(g),217(v)
BD(1) C2-Zr18	1.87918	-0.39632	388(g),391(v),153(r),371(g),194(g),387(g),281(g),372(g)
BD(1) C2-H29	1.94058	-0.52581	125(v),147(v),371(g),372(g),149(v),123(v),145(v),127(v)
BD(1) C2-H30	1.94058	-0.52581	125(v),147(v),371(g),372(g),149(v),123(v),145(v),127(v)
BD(1) C3-Zr14	1.88956	-0.40019	129(v),391(g),159(r),367(v),390(g),250(v),198(g),379(v)
BD(1) C3-Zr15	1.92367	-0.40181	391(v),375(g),198(g),379(g),254(g),202(v),158(r),124(v)
BD(1) C3-H31	1.94199	-0.52777	125(v),131(v),129(v),126(v),375(g),123(v),130(v),128(v)
BD(1) C3-H32	1.94199	-0.52777	125(v),131(v),129(v),126(v),375(g),123(v),130(v),128(v)
BD(1) C4-Zr15	1.84134	-0.37546	158(v),135(v),202(g),367(g),376(g),379(g),254(g),397(v)
BD(1) C4-Zr16	1.80468	-0.37983	130(v),156(v),158(v),201(g),376(v),380(g),251(v),266(g)
BD(1) C4-Zr20	1.83764	-0.40757	130(v),135(v),129(v),367(v),202(g),251(v),393(g),300(g)
BD(1) C5-Zr16	1.97472	-0.37614	137(g),397(g),226(v),380(g),201(v),263(g),225(v),130(r)
BD(1) C6-Zr17	1.91668	-0.38631	146(v),384(g),388(v),209(g),229(v),171(r),170(r),276(g)
BD(1) C6-Zr18	1.90495	-0.40200	388(g),170(r),140(v),398(v),143(v),387(g),389(v),209(g)
BD(1) C6-H33	1.94949	-0.53273	141(v),147(v),148(v),143(v),384(g),398(v),145(v),149(v)
BD(1) C6-H34	1.94949	-0.53272	141(v),147(v),148(v),143(v),384(g),398(v),145(v),149(v)
BD(1) C7-Zr18	1.84433	-0.37698	153(r),150(r),170(v),213(g),281(g),283(g),387(g),372(g)
BD(2) C7-Zr18	1.57708	-0.23816	150(r),153(r),372(g),389(g),155(r),401(v),291(r),214(g)
BD(1) C7-Zr22	1.78537	-0.4575	150(r),153(r),152(r),148(v),146(v),318(g),401(g),214(g)
BD(1) C8-Zr14	1.83807	-0.38263	159(r),156(r),152(v),217(g),245(g),390(g),371(g),375(g)
BD(2) C8-Zr14	1.58330	-0.23222	156(r),392(g),371(g),159(r),300(r),375(g),405(v),218(g)
BD(1) C8-Zr19	1.77726	-0.46424	156(r),158(r),159(r),124(v),126(v),405(g),291(g),218(g)
BD(1) C9-Zr20	1.80968	-0.35059	164(v),180(v),222(g),300(g),381(g),393(g),167(v),202(v)
BD(2) C9-Zr20	1.62616	-0.16274	163(v),179(v),113(v),118(r),394(g),182(v),166(v),409(v)
BD(1) C9-Zr21	1.80205	-0.34607	159(v),181(v),221(g),156(v),309(g),310(g),225(r),311(g)
BD(1) C9-Zr24	1.78070	-0.35801	158(v),165(v),159(v),335(g),221(g),162(v),153(r),333(g)
BD(1) C10-Zr16	1.74407	-0.21505	162(r),120(g),309(r),382(g),395(r),310(r),264(g),221(r)
BD(1) C11-Zr17	1.82339	-0.26782	168(r),170(r),389(r),318(r),384(v),210(v),281(r),315(r)
BD(2) C11-Zr17	1.73945	-0.20625	169(r),172(r),402(r),399(g),147(r)
BD(3) C11-Zr17	1.64828	-0.17603	383(g),168(r),209(v),229(g),170(r),276(g),144(g),273(g)
BD(1) C12-Zr22	1.81307	-0.35038	175(v),186(v),185(v),234(g),318(g),152(r),389(g),401(g)
BD(2) C12-Zr22	1.67215	-0.16192	184(v),174(v),117(v),177(v), 402(g),417(v),416(v),411(v)
BD(1) C12-Zr23	1.78745	-0.35910	170(v),186(v),168(v),171(v),185(v),327(g),152(r),233(g)
BD(1) C12-Zr25	1.77135	-0.34288	170(v),176(v),233(g),347(g),345(g),403(g),404(g),407(v)
BD(1) C13-Zr19	1.79781	-0.34458	180(v),175(v),291(g),239(g), 158(r),176(v),181(v),392(g)
BD(2) C13-Zr19	1.66267	-0.15947	179(v),174(v),118(v),117(r),177(v),406(g),182(v),413(v)
BD(1) C13-Zr23	1.77337	-0.34846	152(v),181(v),328(g),237(g),327(g),153(v),325(g),407(g)
BD(1) C13-Zr24	1.78062	-0.3465	153(v),176(v),150(v),237(g),335(g),333(g),338(g),158(r)
BD(1) Zr21-H35	1.97856	-0.27784	181(r),395(g),309(g),221(v),226(r),410(g),311(g),409(g)
BD(1) Zr21-H36	1.97856	-0.27784	181(r),395(g),309(g),221(v),226(r),410(g),311(g),409(g)
BD(1) Zr23-H37	1.97325	-0.26400	407(g),403(g),327(g),412(g), 328(g),181(r),411(g),325(g)
BD(1) Zr23-H38	1.97325	-0.26399	407(g),403(g),327(g),411(g),328(g),181(r),412(g),325(g)
BD(1) Zr24-H39	1.97263	-0.26403	335(g),408(g),396(g),414(g),333(g),176(r),413(g),338(g)
BD(1) Zr24-H40	1.97263	-0.26403	335(g),408(g),396(g),413(g),333(g),176(r),414(g),338(g)
BD(1) Zr25-H41	1.98279	-0.28534	176(r),233(v),403(v),347(g),345(g),415(g),404(g),186(g)
BD(1) Zr25-H42	1.98706	-0.28989	170(r),233(v),401(v),347(g),345(g),416(g),404(g),186(g)
BD(1) Zr25-H43	1.98708	-0.28988	170(r),233(v),401(v),347(g),345(g),417(g),404(g),186(g)

Table 12: NBO data obtained for ZrC nano-sheet.

Anti-bond orbital	occupancy	Energy (a.u.)	Principal Delocalizations (geminal,vicinal,remote)
BD*(1) C1-Zr15	0.08550	0.18061
BD*(1) C1-H26	0.00541	0.43210
BD*(1) C1-H27	0.00266	0.41015
BD*(1) C1-H28	0.00266	0.41015
BD*(1) C2-Zr14	0.05123	0.26086
BD*(1) C2-Zr18	0.05282	0.24344
BD*(1) C2-H29	0.00645	0.38445
BD*(1) C2-H30	0.00645	0.38445
BD*(1) C3-Zr14	0.04920	0.20248
BD*(1) C3-Zr15	0.09122	0.16266
BD*(1) C3-H31	0.00552	0.38286
BD*(1) C3-H32	0.00552	0.38286
BD*(1) C4-Zr15	0.06137	0.14929
BD*(1) C4-Zr16	0.25867	0.12714	397(g),135(g),382(g),138(g),367(v),263(g),264(g),167(r)
BD*(1) C4-Zr20	0.11472	0.17910	161(g),393(g),367(v),156(g),376(v),158(g),130(v),135(v)
BD*(1) C5-Zr16	0.07495	0.18628
BD*(1) C6-Zr17	0.05019	0.10942
BD*(1) C6-Zr18	0.04822	0.16615
BD*(1) C6-H33	0.00811	0.38476
BD*(1) C6-H34	0.00811	0.38476
BD*(1) C7-Zr18	0.07858	0.13874
BD*(2) C7-Zr18	0.18505	0.03638	391(r),398(r),148(g),372(g),142(r),387(g),389(g),194(v)
BD*(1) C7-Zr22	0.17446	0.14381	178(r),168(g),171(g),173(g),401(g),146(v),387(g),170(g)
BD*(1) C8-Zr14	0.07353	0.16132
BD*(2) C8-Zr14	0.18042	0.03385	388(r),156(r),371(g),248(g),148(r),126(g),132(r),398(r)
BD*(1) C8-Zr19	0.16937	0.16125	390(g),155(g),150(g),183(r),405(g),152(g),124(v),171(r)
BD*(1) C9-Zr20	0.10944	0.18614	161(g),381(g),158(g),159(g),156(g),152(r),382(r),392(r)
BD*(2) C9-Zr20	0.05482	-0.01496
BD*(1) C9-Zr21	0.05594	0.22193
BD*(1) C9-Zr24	0.05313	0.25934
BD*(1) C10-Zr16	0.24848	0.10963	162(r),380(g),382(g),138(g),137(g),263(g),165(r),381(v)
BD*(1) C11-Zr17	0.10723	0.03839	142(g),388(r),140(g),383(g),168(r),148(r),171(r),274(g)
BD*(2) C11-Zr17	0.01233	-0.06254
BD*(3) C11-Zr17	0.07111	-0.04834
BD*(1) C12-Zr22	0.11810	0.18386	173(g),170(g),168(g),389(g),171(g),186(v),318(g),393(r)
BD*(2) C12-Zr22	0.07090	-0.01535
BD*(1) C12-Zr23	0.05293	0.25962
BD*(1) C12-Zr25	0.02426	0.20015
BD*(1) C13-Zr19	0.10442	0.18157	155(g),152(g),161(r),150(g),392(g),153(g),291(g),403(v)
BD*(2) C13-Zr19	0.05090	-0.01106
BD*(1) C13-Zr23	0.05252	0.2651
BD*(1) C13-Zr24	0.05217	0.26843
BD*(1) Zr21-H35	0.03795	0.29819
BD*(1) Zr21-H36	0.03795	0.29819
BD*(1) Zr23-H37	0.03744	0.31509
BD*(1) Zr23-H38	0.03744	0.31509
BD*(1) Zr24-H39	0.03774	0.31342
BD*(1) Zr24-H40	0.03774	0.31342
BD*(1) Zr25-H41	0.02631	0.29533
BD*(1) Zr25-H42	0.02580	0.28437
BD*(1) Zr25-H43	0.02580	0.28434

Table 13: NBO data obtained for ZrC nano-sheet.

Bond orbital	Hybrids	occupancy	Energy (a.u.)	Principal Delocalizations (geminal,vicinal,remote)
LP(1) C4	p1	1.08443	-0.13154	128(v),136(v),157(v),118(r),160(v),394(v),203(g),133(v)
LP(1) C5	sp0.26	1.93287	-0.49829	137(v),138(v),259(v),380(v), 382(g)
LP*(2) C5	p1	0.41763	-0.10948	134(v),261(v),136(v),208(g)
LP(1) C7	p1	1.07813	-0.13127	145(v),151(r),169(v),172(v),118(r),154(r),406(r),402(v)
LP(1) C8	p1	1.07686	-0.13332	123(v),157(r),151(v),113(r),117(r),154(v),160(r),394(r)
LP*(3) C10	p1	0.61329	-0.09993	134(v),163(r),136(v),261(v),166(r),227(g)
LP(1) C11	sp0.01	1.68229	-0.52044	168(r),171(r),398(g),140(v),173(r),318(r),142(v),170(r)
LP*(1) Zr14	p1d18.41	0.52930	-0.13087	118(v),127(g),131(r),128(r),147(r),145(r),219(v)
LP*(2) Zr14	sp3.55d1.43	0.08110	0.14065
LP*(3) Zr14	d1	0.06630	-0.12332
LP*(4) Zr14	sp1.11d1.51	0.05044	-0.02547
LP*(5) Zr14	p1d0.05	0.01962	-0.03089
LP*(1) Zr15	p1d20.57	0.52125	-0.12969	113(v),125(r),133(g),123(r),203(v),134(r)
LP*(3) Zr15	sp12.13d3.21	0.06205	0.20316
LP*(5) Zr15	sp0.24d1.15	0.02507	-0.05004
LP*(6) Zr15	p1d0.06	0.01702	-0.02474
LP(1) Zr16	d1	0.87838	-0.10625	115(v),121(v),157(r),208(v), 131(r),227(v),128(r)
LP*(2) Zr16	sp37.59d5.94	0.23225	0.20627	130(r),158(r),380(g),382(g),138(g),161(r),259(g),381(v)
LP*(3) Zr16	p1d17.86	0.20667	-0.07291	113(v),121(v),115(v)
LP*(5) Zr16	sp0.24d2.41	0.01268	0.28256
LP*(6) Zr16	sp0.5d47.53	0.00663	0.35322
LP*(2) Zr17	p1d20.52	0.03212	-0.11491
LP*(3) Zr17	sp1.34d3.36	0.01403	0.02117
LP*(4) Zr17	sp39.14d16.39	0.00749	0.12593
LP*(5) Zr17	sp7.19d26.54	0.00170	0.48873
LP*(1) Zr18	p1d18.07	0.51905	-0.12784	117(v),125(r),149(g),141(r), 123(r),215(v)
LP*(4) Zr18	sp3.38d1.87	0.05246	0.02255
LP*(5) Zr18	p1d0.06	0.01987	-0.02952
LP*(1) Zr19	sp0.02d3.32	0.42505	0.12366	392(g),146(r),155(g),405(g), 124(r),291(g),390(v),387(r)
LP*(5) Zr19	sp1d0.05	0.07903	0.01102
LP*(6) Zr19	sp0.01d1.70	0.01688	0.19351
LP*(1) Zr20	sp0.04d3.67	0.43730	0.09827	161(g),381(g),393(g),162(r), 124(r),300(g),379(v),391(r)
LP*(2) Zr20	d1	0.28767	-0.08721	113(v),118(r),151(r),
LP*(5) Zr20	p1d0.05	0.07839	0.00895
LP*(6) Zr20	sp0.01d1.92	0.01508	0.18303
LP*(1) Zr21	sp0.15d3.02	0.44749	0.09343	397(r),164(g),156(r),395(g),309(g),137(r),159(r),409(g)
LP*(3) Zr21	sp23.76d46.78	0.18557	0.05714	162(g),167(g),395(g),156(r),311(g),120(r),137(r),309(g)
LP*(5) Zr21	p1d0.10	0.04554	0.09303
LP*(1) Zr22	sp0.01d3.16	0.44506	0.10073	389(g),173(g),401(g),146(r), 140(r),383(r),318(g),387(v)
LP*(5) Zr22	p1d0.05	0.04554	0.09303
LP*(6) Zr22	sp0.01d2.04	0.01593	0.21149
LP*(1) Zr23	d1	0.21798	-0.02355	402(v),406(v),179(r)
LP*(4) Zr23	p1d0.1	0.06840	0.09729
LP*(5) Zr23	sp44.05d41.84	0.01931	0.14701
LP*(3) Zr24	p1d0.17	0.07833	0.20896
LP*(4) Zr24	p1d0.09	0.06521	0.09907
LP*(5) Zr24	sp43.43d41.74	0.01823	0.15747
LP*(1) Zr25	p1d5	0.14120	-0.00869	402(v),188(g),417(g),416(g)
LP*(5) Zr25	p1d0.45	0.00186	0.08665

 

Table 14: NBO data obtained for ZrC nano-sheet.

Bond orbital	Hybrids	occupancy	Energy (a.u.)	Principal Delocalizations (geminal,vicinal,remote)
RY*(3) C1	sp1	0.00024	0.33256
RY*(4) C1	sp0.11	0.00007	0.92498
RY*(3) C2	p1	0.00041	0.43388
RY*(4) C2	sp0.01	0.00004	1.18757
RY*(3) C3	p1	0.00042	0.43448
RY*(4) C3	sp0.01	0.00004	1.20722
RY*(2) C5	sp7.01	0.00017	0.77147
RY*(3) C5	sp0.15	0.00006	0.92957
RY*(3) C7	p1	0.00090	0.52589
RY*(4) C7	s	0.00009	1.33142
RY*(1) C8	sp1	0.00260	2.61231
RY*(3) C9	p1	0.00165	0.56797
RY*(4) C9	s	0.00009	1.15787
RY*(3) C10	p1	0.00038	0.48718
RY*(4) C10	sp1	0.00007	1.13012
RY*(2) C11	sp50.44	0.00150	1.20168
RY*(3) C12	p1	0.00157	0.55631
RY*(4) C12	sp0.01	0.00013	1.12406
RY*(1) C13	p1	0.00221	2.22964
RY*(2) C13	p1	0.00168	0.57304
RY*(1) Zr14	sp1.27d56.72	0.00782	0.36402
RY*(5) Zr14	sp0.02d0.03	0.00063	1.66041
RY*(6) Zr14	p1d8.72	0.00051	0.18271
RY*(7) Zr14	sp63.63d2.23	0.00018	0.96663
RY*(8) Zr14	sp72.29d1.12	0.00013	1.28692
RY*(9) Zr14	p1d0.11	0.00006	0.14785
RY*(4) Zr15	p1d17.68	0.00063	0.20871
RY*(5) Zr15	sp0.1d0.02	0.00035	1.42188
RY*(6) Zr15	sp11.66d0.34	0.00017	0.43745
RY*(7) Zr15	p1d21.51	0.00014	0.20366
RY*(8) Zr15	sp43.68d2.83	0.00011	0.75233
RY*(9) Zr15	p1d0.1	0.00002	0.13125
RY*(9) Zr15	sp0.42d7.48	0.00026	1.70012
RY*(7) Zr20	sp16.74d0.07	0.00013	1.16867
RY*(8) Zr20	p4.86d0.01	0.00004	0.16653
RY*(9) Zr20	p1d0.04	0.00037	0.26992
RY*(4) Zr21	p1d43.68	0.00022	0.26198
RY*(5) Zr21	sp1d6.91	0.00015	1.72160
RY*(6) Zr21	sp0.02d0.01	0.00054	0.31591
RY*(2) Zr25	sp3.49d44.51	0.00024	0.34902
RY*(3) Zr25	sp0.47d7.32	0.00013	0.29668
RY*(4) Zr25	p1d15.74	0.00010	0.20213
RY*(5) Zr25	p1d8.24	0.00007	1.37764
RY*(6) Zr25	sp0.26d0.13	0.00003	0.47172
RY*(7) Zr25	sp15.90d1.55	0.00002	0.85348
RY*(8) Zr25	sp10.31d0.11	0.00084	0.95528
RY*(1) H26	s	0.00084	0.91930
RY*(1) H27	s	0.00140	1.33327
RY*(1) H39	s	0.00140	1.33327

 

Table 15: NBO data obtained for ZrC nano-sheet.

Bond orbital	Hybrids	occupancy	Energy (a.u.)	Principal Delocalizations (geminal,vicinal,remote)
CR ( 1)  C1	S	1.99928	-10.0579	129(v),250(v),349(v),252(v),350(v),351(v)
CR ( 1) C 2	S	1.99919	-10.0587	277(v),241(v),243(v),352(v),353(v),146(v)
CR ( 1) C 3	S	1.99919	-10.0596	129(v),252(v),243(v),250(v),242(v),130(v)
CR ( 1) C 4	S	1.99940	-10.0365	130(v),158(v),135(v),296(v),260(v),251(v)
CR ( 1) C 5	S	1.99986	-10.0997	137(v)
CR ( 1) C 6	S	1.99921	-10.0683	279(v),143(v),356(v),357(v),148(v)
CR ( 1) C 7	S	1.99939	-10.0352	150(r),153(r),148(v),152(r),170(v),171(v)
CR ( 1) C 8	S	1.99937	-10.0357	156(r),159(r),158(r),152(v),124(v),126(v),391(g)
CR ( 1) C 9	S	1.99945	-10.0062	159(v),295(v),181(v),165(v),158(v),167(v),332(v)
CR ( 1) C 10	S	1.99959	-10.0748	162(r),397(g),137(v),165(r),139(v),164(r)
CR ( 1) C 11	S	1.99958	-10.0937	168(r),171(r),140(v),398(g),315(r)
CR ( 2) Zr 15	P1	1.99113	-1.25942	376(g),367(g),375(v)
CR ( 4) Zr 15	P1	1.99637	-1.30639	113(v),133(g)
CR ( 3) Zr 17	P1	1.98472	-1.24792	398(g),400(g),383(g),168(r),171(r)
CR ( 1) Zr 18	S	1.97949	-2.02139	387(g),384(g),389(v),153(r),372(g),371(v),213(v)
CR ( 2) Zr 18	P1	1.99008	-1.25726	372(g),384(g),371(v)
CR ( 3) Zr 18	P1	1.98335	-1.24663	387(g),389(v),153(r),384(g),150(r)
CR ( 4) Zr 18	P1	1.99607	-1.30455	117(v),149(g)
CR ( 1) Zr 19	S	1.97309	-1.95986	405(g),239(v),214(r),387(r),392(g),218(v)
CR ( 2) Zr 19	P1	1.98709	-1.20913	392(g),390(v),387(r),388(r),158(r)
CR ( 3) Zr 19	P1	1.98499	-1.19880	405(g),408(v),407(v)
CR ( 4) Zr 19	P1	1.99638	-1.25218	154(g),118(v),117(r)
CR ( 1) Zr 21	S	1.99048	-1.91981	397(r),396(v),393(v),162(g),120(r),159(r),221(v)
CR ( 2) Zr 21	P1	1.98533	-1.17436	395(g),397(r),120(r),393(v),396(v),181(r)
CR ( 3) Zr 21	P1	1.98352	-1.17583	409(g),410(g),395(g),120(r),397(r)
CR ( 4) Zr 21	P1	1.98354	-1.18374	409(g),410(g),121(r),166(g)
CR ( 1) Zr 24	S	1.98720	-1.90073	393(v),405(v),407(v),395(v),396(g),159(r),165(r),413(g)
CR ( 2) Zr 24	P1	1.98232	-1.16198	396(g),408(g),393(v),405(v),407(v),395(v)
CR ( 3) Zr 24	P1	1.98283	-1.16487	413(g),414(g),408(g),396(g),407(v)
CR ( 4) Zr 24	P1	1.98546	-1.17348	413(g),414(g),182(g)

 

Conclusion

In this study, from the theoretical analysis of the zirconium carbide nano-sheets, the following were obtained: Polar determinant (Dipole moment, Quadrupole moment, Traceless Quadrupole moment and Octapole moment), EPR data (voltage and voltage difference), NMR parameters (isotropic shielding tensor, anisotropic shielding tensor, asymmetry, span and skew) and NBO data (bonding and anti-bonding orbitals, hybridization of atomic orbitals, energy and Principal Delocalizations).

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