238
GIAO Calculations of Chemical Shifts of NMR Spectra of
1H and
13C of the Hexahydroindoles Products
Abdelilah Benallou
a*, Habib El Alaoui El Abdallaoui
a. Hocine Garmes
b.
aTeam of chemoinformatics research and spectroscopy and quantum chemistry, Department of chemistry, physical and chemistry lab, Faculty of Science El Jadida.
blaboratory of bio-organic chemistry, Department of chemistry, Faculty of Science El Jadida.
University Chouaib Doukkali, B. P. 20, 24000 El Jadida, Morroco.
*Corresponding author. E-mail : abdo_benallou@yahoo.fr Received 01 Jan 2014, Revised 2 Fev 2015, Accepted 15 Fec 2015
Abstract
Isotropic 1H and 13C nuclear magnetic shielding constants of hexahydroindoles products of intramolecular Diels-Alder of the triene-amide reaction have been calculated by employing the gauge-including-atomic- orbital (GIAO), Continuous Set of Gauge Transformations (CSGT) and a slight variation on the CSGT (IGAIM) methods at the B3LYP/6-311(d,p) density functional level of theory. Geometry of each compound has been optimized employing 6-31G(d,p) basis sets. The comparison of the theoretical results to the experimental results of the Ha compound shows that the GIAO method is the most reliable. On the other hand we calculate the chemicals shifts of the carbon (13C) and hydrogen (1H) of the Hb and Hc compounds.
This calculation was performed using the B3LYP functional, using the GIAO method at the level of the following bases: 6-31G, 6-31 G(d), 6-31G(d,p), 6-311G, 6-311G(d). The theoretical trends are compared with experimental data taken from the literature. The least squares regression analyses of the results indicate R-square values greater than 0.90 in the range for total data set.
Keywords: 1H, 13C, NMR, DFT, Diels Alder, GIAO calculation.
1. Introduction
The hexahydroindoles are classified in the indole family, belong to the heterocyclic organic products containing nitrogen, they form the basis of many structures of substances resources [1], known by its variety and their profile activities [1,2]. NMR spectroscopy proved to be an exceptional tool to elucidate the structure and the molecular conformation. The DFT computing of shielding NMR at very precise levels of approximation and are widely available at literature [3-18]. There are many more methods to calculate chemical shifts to: CSGT (Continuous Set of Gauge Transformations), IGAIM (a slight variation on the CSGT method) and GIAO (gauge independent gold invariant gold including atomic orbital). The GIAO/DFT [19] approach is known to give satisfactory chemical shifts for different nuclei [19, 20, 21] with larger molecules. These calculations in quantum chemistry, however, often must be limited to isolated molecules (gas phase) and certain privileged structures (optimized), the experimental NMR spectra are commonly from means static affected by dynamic processes, such as the conformational equilibrium but
239 also by intra or intermolecular interactions. This paper applies the DFT method for analyzing experimental data of NMR 1H and 13C of the observed (hexahydroindoles) in IMDA cycloaddition of triene-amide reaction [22].
The aim of this work is to calculate the theoretical chemical shifts of the molecular structure of majority products exo_α of the hexahydroindole substitutes [23] in the IMDA of triene-amide reaction (scheme. 1) based on the proper attribution of resonances 1H and 13C by using the appropriate method of calcul and the basis set. The calculated of chemical shifts are then compared with experimental values. To manner this study, the Gaussian software gives the possibility of calculating the screen tensors by three different computational methodes [24], namely GIAO [25,26,27,28,29], CSGT [28,29,30], and IGAIM [31,32] . To this object, we have used through DFT combined with these methods that are restricted to finite and isolated systems (molecules or clusters), and used for the calculation of the electronic screen tensors isotropic σiso
and subsequently of the nuclear magnetic resonance (NMR) of 1H and 13C chemical shifts using equation (1) mentioned below.
N
R3 Z
R1 R2
O R4
T°(C) Toluène /
N
R1 R2 R3
Z
COR4 H
G:Triene-Am ide substitute H: Hexahydroindole
Ga: R1=H, R2=CH3, R3=H, R4=CH3, Z=CN;
Gb: R1=H, R2=H, R3=H, R4=CH3, Z=CO2CH3;
Gc: R1=CH3, R2=H, R3=H, R4=CH3, Z=CO2CH2CH3.
H
[4 2
Scheme 1. Preparation of the derivatives of the hexahydroindole from the intramolecular Diels–Alder of triene-amide reaction.
2. Materials and methods
The geometry optimizations were performed at the B3LYP/6-31G(d,p) levels with GAUSSIAN G09 program package [33]. The 1H and 13C chemical shifts were calculated with the B3LYP [34,35] and basis sets [36,37] 6-311G(d,p), 6-31G(d,p), 6-31G(d), 6-31G, 6-311G, 6-311G(d) at optimized geometries by GIAO/CSGT/IGAIM methods. (CH4)4Si was used as a reference in calculating the 1H and 13C chemical shifts. Linear correlation analyses were performed using the program (SIGMAPLOT/MYSTAT) and visualization of the output files are performed using the Gauss-View 5.0.8 software. The quality of each correlation was found with the R value, which called the correlation coefficient of Pearson [38].
The isotropic chemical shift calculation δiso, are obtained by the relationship (1):
( )
iso iso ref
Where σref is the tensor of corresponding electronic form a reference tetra-methyl silane (TMS) substance.
3. Results and Discussions
a) Choice of reliable method for the calculation of 1H and 13C theoretical chemical shifts.
The values of chemical shift δ, calculated and experimental, are reported in table 1 (α, β), the values obtained are compared with the experimental data, the study is carried out arbitrarily to Ha product (figure
240 1) at basis set 6-311G (d,p) according to the DFT method, the found results are reported in table 1 (α, β) and linear correlations are determined using figure 1.
Figure 1. Default Numbering of Gauss-View software of the Ha product.
Table. 1α. 1H Chemical shift isotropic δiso (DFT) obtained by the GIAO, CSGT, IGAIM methods at the level of the basis set 6-311G (d,p) and experimental (in ppm) of the Ha product.
Nuclei δexp
δGIAO δCSGT δIGAIM
DFT 6-311G**
DFT 6-311G**
DFT 6-311G**
H17 2.35 2.20 2.62 2.63
H18 2.35 2.24 2.71 2.71
H19 6.07 5.80 6.32 6.31
H20 5.68 5.63 6.50 6.50
H21 4.73 4.34 4.77 4.77
H22 2.25 1.98 2.76 2.77
H23 2.91 2.65 3.17 3.18
H24 2.04 1.77 2.20 2.20
H25 2.04 1.87 2.40 2.40
H26 2.04 2.02 2.52 2.52
H27 3.70 3.59 4.14 4.14
H28 3.17 3.00 3.58 3.58
H29 2.15 1.75 2.86 2.87
H30 1.60 1.52 2.36 2.37
H31 1.29 1.02 1.92 1.93
H32 0.97 1.12 1.99 1.99
H33 0.97 0.92 1.87 1.87
H34 0.97 0.71 1.71 1.71
The data in table 1(α, β) we arrive to trace the curves of the experimental chemical shifts according to the theoretical chemical shifts, we got a straight line with the equation: δexp = aδcalc + b (figure2), according to the DFT calculation method.
The parameters of the equations of correlations shown in figure 2 (a, b and R2) are directories in table 2.
The results of the regression analysis of different methods given in table 2 corresponding to the GIAO, CSGT and IGAIM. Shows that it is a linearity between experimental and theoretical values such as δexp = aδcalc + b. Otherwise, the correlation coefficient of R2 = {0.993, 0.979, 0,978} / 1H and {0.997, 0.996,
241 0.995} / 13C respectively of (GIAO, CSGT and IGAIM) methods. Which indicates that there is a very good connection between the curves and data. We observe an evolution at the level of the GIAO method, which was higher by report other methods. There as well as the correlation is even better for the GIAO method, then this method is the most reliable to calculate the theoretical chemical shifts.
Table. 1β. 13H Chemical shift isotropic δiso (DFT) obtained by the GIAO, CSGT, IGAIM methods at the level of the basis 6-311G (d, p) and experimental (in ppm) of the Ha product.
Nuclei δexp
δGIAO δCSGT δIGAIM
DFT 6-311G**
DFT 6-311G**
DFT 6-311G**
C1 24.13 27.30 28.65 28.63
C2 124.53 129.73 131.01 134.00
C3 126.68 135.87 135.49 135.48
C4 53.71 58.60 59.62 59.62
C5 42.83 50.07 51.05 51.05
C6 25.12 26.98 29.51 29.50
C8 169.35 169.43 166.23 166.23
C10 22.59 22.56 23.34 23.31
C11 51.64 54.26 55.24 55.23
C12 40.93 42.57 45.62 45.62
C13 24.71 29.69 32.93 32.92
C14 11.79 13.32 16.71 16.69
C15 121.54 124.67 123.08 123.08
C1 24.13 27.30 28.65 28.63
C2 124.53 129.73 131.01 134.00
C3 126.68 135.87 135.49 135.48
C4 53.71 58.60 59.62 59.62
C5 42.83 50.07 51.05 51.05
Figure 2. Graphical representation of results found the experimental and theoretical chemical shifts in ppm with GIAO, CSGT and IGAIM methods calculated with the basis set 6-311G (d, p).
242 Table. 2. The parameters of the equation a, b and R2 of the GIAO, IGAIM, CSGT methods at the level of the basis set 6-311 (d,p).
Method Nuclei Equation /Correlation GIAO CSGT IGAIM
DFT
1H
a 0.9957 0.9759 0.9779
b 0.216 -0.3039 -0.3133
R2 0.993 0.979 0.978
13C
a 0.988 1.0175 1.0109
b -2.6864 -5.7445 -5.5087
R2 0.997 0.996 0.995
b) Study of the accuracy of the basis sets of calculation to the GIAO method.
Once the GIAO method thus validated, we apply it to Hb and Hc products (figure 3) thus we measured the carbon (13C) and hydrogen (1H) chemical shifts. We also use the GIAO method (gauge independent atomic orbitals) implemented in the Gaussian 09 program, were using basis sets: 6-31G, 6-31G (d), 6-31G (d, p) 6- 311G, 6-311G (d), the results of the values the 13C and 1H chemical shifts in the Hb and Hc products, are grouped in tables 3 and 5.
Product Hb Product Hc
Figure 3. Default numbering of Gauss-View software of Hb and Hc products.
i) Product Hb.
The graphic representation of the results so the parameters of the equations of correlations are presented in figure 4 and table 4 (a, b and R2).
The mathematical analysis is performed to determine the parameters of the equation δexp = aδcalc + b thus the linear correlation R2, the results are given in table 4.
Following the figure 4 we look a linearity between experimental and theoretical values and table 4 shows that the DFT method with the basis set, that admitting the largest value of the linear regression are given at the basis set 6-31G(d,p), for nuclear magnetic resonance 1H with a correlation of 0.940 and slope analysis of 0.9316ppm, and the basis set 6-31 G (d) with a slope of 0.9667ppm and correlation of 0.997 for nuclear magnetic resonance 13C. According with these results we note that the correlation to the DFT calculation is very good for 1H and 13C, therefore this method is reliable giving comparable results to the experimental results.
243 Table. 3. 1H and 13C Chemical shifts experimental δexp and theoretical δcalc of the DFT method (in ppm) calculated with basis sets 6-31G(d,p), 6-31G(d), 6-31G, 6-311G and 6-311G(d) of the Hb product.
Nuclei δexp
δcal δcal δcal δcal δcal
DFT 6-31G**
DFT 6-31G*
DFT 6-31G
DFT 6-311G
DFT 6-311G*
H13 2.42 3.06 2.04 2.04 2.16 2.61
H14 2.42 2.14 1.05 1.13 1.26 1.75
H15 5.67 6.01 5.13 5.05 5.03 5.46
H16 5.99 5.98 4.98 5.03 4.90 5.34
H17 4.55 4.14 2.80 2.92 2.89 3.62
H18 2.32 3.12 2.00 2.31 2.38 2.74
H19 2.88 2.64 1.48 1.71 1.79 2.27
H20 2.04 1.80 1.24 0.77 0.88 1.41
H21 2.04 1.98 1.04 1.05 1.09 1.51
H22 2.04 2.04 1.13 1.12 1.16 1.58
H23 3.51 3.57 2.58 2.58 2.61 3.09
H24 3.51 3.53 2.48 2.57 2.64 3.08
H25 2.08 2.06 0.95 1.23 1.14 1.56
H26 2.08 1.75 0.78 0.68 0.79 1.35
H31 3.76 3.94 3.05 3.01 3.08 3.44
H32 3.76 3.61 2.83 2.73 2.76 3.19
H33 3.76 3.87 3.02 2.94 3.02 3.38
C1 24.99 15.18 1.60 11.42 18.45 24.14
C2 125.11 113.79 108.22 111.05 128.11 132.90
C3 125.62 114.49 108.58 112.12 128.34 132.86
C4 53.66 46.79 29.71 44.05 51.42 57.57
C5 39.45 31.47 14.45 28.59 36.74 42.37
C6 36.92 32.85 18.16 31.01 38.32 43.18
C8 174.65 148.46 152.50 147.14 164.27 169.44
C10 22.72 13.01 4.96 10.70 17.36 22.52
C11 45.93 36.65 22.95 33.23 40.87 47.06
C12 28.01 19.45 6.53 16.79 24.51 29.50
C27 169.36 157.16 156.00 159.55 178.33 180.22
C30 51.80 42.14 31.93 38.29 46.62 52.71
244 Figure 4. Graphical representation of results found of the experimental and theoretical (DFT) chemical shifts in ppm with basis sets 6-31G (d, p), 6-31G (d), 6-31G, 6-311G and 6-311G (d).
Table. 4. The parameters of the equation a, b and R2 obtained with different bases.
Methods Basis set Nuclei a b R2
DFT/GIAO
6-31G(d,p)
1H
0.9316 0.1982 0.940
6-31G(d) 0.923 1.1307 0.920
6-31G 0.9209 1.1197 0.915
6-311G 0.9454 1.0243 0.908
6-311G(d) 0.9673 0.5294 0.933
6-31G(d,p)
13C
1.0674 6.2335 0.995
6-31G(d) 0.9667 22.036 0.997
6-31G 1.0444 10.105 0.994
6-311G 0.9604 4.9533 0.993
6-311G(d) 0.9738 0.9781 0.995
ii) Product Hc.
The graphic representation of the results thus the parameters of the equations of correlations are presented in figure 5 and table 6 (a, b and R2).
The mathematical analysis is performed to determine the parameters of the equation δexp = aδcalc + b consequently the linear correlation R2, the results are given in table 6.
Next the figure 5 we look a linearity between experimental and theoretical values and table 6 shows that the bases, that allowing the largest value of the linear regression are given to basis set 6-31G(d) for 1H with a correlation of 0.910 and a analytical sloping of 0.8929ppm, and the basis sets 6-31G (d), 6-31G(d,p) and 6- 311G(d) with a slope respectively of 1.0866ppm, 1.0973ppm and 0.9945ppm and equal correlation of 0.992 for 13C. According these results we remark that the correlation to the DFT calculation is high to the 1H and
13C chemical shift, we detect also that the correlation to decreased at the calculation of nuclear magnetic resonance NMR of 1H chemical shift, contrary to the calculated 13C chemical shift have great correlation close to 1, make these methods with the most advantageous studied basis sets for 13C of this compound giving approximately similar results to the experimental results.
245 Table. 5. 1H and 13C Chemical shifts δcal of the calculated (DFT method) and δexp experimental in ppm with basis sets 6-31G (d, p), 6-31G (d), 6-31G, 6-311G and 6-311G (d) of the Hc product.
Nuclei δexp
δcal δcal δcal δcal δcal
DFT 6-31G**
DFT 6-31G*
DFT 6-31G
DFT 6-311G
DFT 6-311G*
H13 2.63 2.63 2.21 1.70 1.77 2.23
H14 2.73 3.38 2.93 2.60 2.66 2.95
H15 3.51 4.32 3.82 3.23 3.21 3.76
H16 2.04 1.81 1.31 0.78 0.90 1.43
H17 2.04 2.11 1.56 1.18 1.20 1.60
H18 2.04 2.09 1.57 1.19 1.21 1.61
H19 6.01 6.01 5.39 5.02 4.90 5.35
H20 5.71 6.02 5.43 5.06 5.05 5.48
H21 4.53 4.22 3.74 3.04 3.00 3.67
H22 2.51 3.03 2.50 2.00 2.12 2.58
H23 2.51 2.08 1.59 1.06 1.21 1.70
H24 1.94 2.26 1.80 1.40 1.37 1.76
H29 4.15 4.27 3.78 3.31 3.35 3.75
H30 4.15 4.23 3.74 3.27 3.31 3.71
H31 1.94 1.48 1.07 0.52 0.57 1.07
H33 1.70 0.80 0.39 -0.03 -0.06 0.37
H34 1.70 2.45 1.89 1.51 1.53 1.93
H35 1.70 0.37 0.30 -0.20 -0.12 0.38
H37 1.20 1.50 1.05 0.61 0.64 1.11
H38 1.20 1.50 1.05 0.62 0.65 1.12
H39 1.20 1.19 0.71 0.16 0.26 0.80
C1 37.00 32.62 33.36 30.79 38.28 43.04
C2 23.90 29.78 30.72 27.05 34.73 40.13
C3 29.80 26.11 27.39 23.94 31.69 36.42
C4 45.95 45.49 46.40 42.33 50.19 56.43
C6 174.00 149.40 149.57 148.04 165.41 170.56
C8 22.74 13.87 15.60 11.67 18.45 23.55
C9 125.40 114.13 114.73 111.62 127.66 132.27
C10 125.19 114.16 114.81 111.51 128.55 133.30
C11 53.71 47.39 48.18 44.56 52.28 58.31
C12 24.76 14.95 16.33 11.12 18.11 23.86
C25 169.00 157.09 157.08 159.54 177.71 179.54
C28 C32
60.81 14.21
52.43 10.22
53.68 12.02
48.67 7.15
58.24 13.28
64.26 18.77
C36 11.91 5.10 6.91 1.87 8.42 14.03
246 Figure 5. Graphical representation of results found of the experimental and theoretical (DFT) chemical shifts in ppm with basis sets 6-31G (d, p), 6-31G (d), 6-31G, 6-311G and 6-311G (d).
Table. 6. The parameters of the equation a, b and R2 obtained with different bases.
Method Basis set Nuclei a b R2
DFT/GIAO
6-31G(d,p)
1H
0.8502 0.3828 0.894
6-31G(d) 0.8929 0.6872 0.910
6-31G 0.8817 1.1243 0.898
6-311G 0.8984 1.0641 0.895
6-311G(d) 0.9087 0.6283 0.907
6-31G(d,p)
13C
1.0866 2.5179 0.992
6-31G(d) 1.0973 0.7938 0.992
6-31G 1.0652 6.2612 0.991
6-311G 0.9824 0.8272 0.991
6-311G(d) 0.9945 -5.0445 0.992
4. Conclusion
The studies carried out in the context of the DFT from nuclear magnetic properties of carbon (13C) and hydrogen (1H) in organic products of the Intramolecular Diels Alder (IMDA) reaction of Ha, Hb and Hc compounds, we note that:
- The theoretical calculation of chemical shift of Ha product by DFT to the basis set 6-311G(d,p) shows that the values is closest to the experimental result are those calculated by the GIAO method.
- The calculations of carbon (13C) and hydrogen (1H) chemical shifts for Hb and Hc products has been completed using the B3LYP, functional by means of the basis sets 6-31G(d,p), 6-31G(d), 6-31G, 6-311G and 6-311G(d). These studies show that the theoretical values obtained by these bases are in good agreement with the experimental values.
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