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ISSN: 2056-9890

Bis(2-tri­fluoro­methyl-1H-benzimidazol-3-ium) naphthalene-1,5-di­sulfonate

aOrdered Matter Science Research Center, Southeast University, Nanjing 211189, People's Republic of China
*Correspondence e-mail: jgsdxlml@163.com

(Received 29 December 2011; accepted 1 January 2012; online 11 January 2012)

The asymmetric unit of the title compound, C8H6F3N2+·0.5C10H6O6S22−, consists of one 2-trifluoro­methyl-1H-benz­imidazol-3-ium cation and a half naphthalene-1,5-disulfate anion, which are linked by an N—H⋯O hydrogen bond. The anion sits across a centre of symmetry. The atoms of the benzimidazole ring are nearly coplanar (r.m.s. deviation of the fitted atoms = 0.0085 Å) and the triflouromethyl group lies out of this plane. In the crystal, the cations are linked to adjacent anions by N—H⋯O hydrogen bonds, forming a ladder structure parallel to the a axis in which the anions form the rungs. Adjacent ladders are linked by weak C—H⋯O inter­actions, forming sheets parallel to the ac plane.

Related literature

The title compound was studied as part of a search for ferroelectric complexes. For background to ferroelectric complexes, see: Fu et al. (2011[Fu, D. W., Zhang, W., Cai, H. L., Zhang, Y., Ge, J. Z., Xiong, R. G. & Huang, S. P. (2011). J. Am. Chem. Soc. 133, 12780-12786.]); Zhang et al. (2010[Zhang, W., Chen, L. Z., Gou, M., Li, Y. H., Fu, D. W. & Xiong, R. G. (2010). Cryst. Growth Des. 10, 1025-1027.]). For related structures, see: Liu (2011a[Liu, M.-L. (2011a). Acta Cryst. E67, o2821.],b[Liu, M.-L. (2011b). Acta Cryst. E67, o3473.]). For graph-set analysis, see: Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]).

[Scheme 1]

Experimental

Crystal data
  • 2C8H6F3N2+·C10H6O6S22−

  • Mr = 660.56

  • Triclinic, [P \overline 1]

  • a = 9.3910 (19) Å

  • b = 9.4943 (19) Å

  • c = 9.976 (2) Å

  • α = 109.32 (3)°

  • β = 96.86 (3)°

  • γ = 119.59 (3)°

  • V = 685.2 (5) Å3

  • Z = 1

  • Mo Kα radiation

  • μ = 0.29 mm−1

  • T = 293 K

  • 0.36 × 0.32 × 0.28 mm

Data collection
  • Rigaku Mercury2 diffractometer

  • Absorption correction: multi-scan (CrystalClear; Rigaku, 2005[Rigaku (2005). CrystalClear. Rigaku Corporation, Tokyo, Japan.]) Tmin = 0.903, Tmax = 0.921

  • 7215 measured reflections

  • 3136 independent reflections

  • 2361 reflections with I > 2σ(I)

  • Rint = 0.042

Refinement
  • R[F2 > 2σ(F2)] = 0.053

  • wR(F2) = 0.132

  • S = 1.10

  • 3136 reflections

  • 227 parameters

  • 36 restraints

  • H-atom parameters constrained

  • Δρmax = 0.23 e Å−3

  • Δρmin = −0.42 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N3—H3⋯O1 0.86 1.81 2.661 (3) 172
N1—H1⋯O2i 0.86 1.84 2.650 (3) 155
C12—H12⋯O3ii 0.93 2.55 3.440 (3) 159
Symmetry codes: (i) x-1, y, z; (ii) -x+2, -y+1, -z+1.

Data collection: CrystalClear (Rigaku, 2005[Rigaku (2005). CrystalClear. Rigaku Corporation, Tokyo, Japan.]); cell refinement: CrystalClear; data reduction: CrystalClear; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: PLATON (Spek, 2009)[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]; software used to prepare material for publication: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]).

Supporting information


Comment top

Recently much attention has been devoted to crystals containing organic ions and inorganic ions due to the possibility of tuning their special structural features and their potential ferroelectrics properties (Fu et al., 2011; Zhang et al., 2010.). In our laboratory, the title compound has been synthesized and its crystal structure is herein reported.

(C8H6F3N2)+.0.5(C10H6O6S2)2- has an asymmetric unit that consists of one 2-trifluoromethyl-1H-benzimidazol cation and a half 1,5-naphthalene disulphate anion linked by a N—H···O hydrogen bond (Fig 1). The atoms of the benzimidazole ring (including H atoms) are nearly coplanar (r.m.s. deviation of the fitted atoms = 0.0085 Å) and the triflouromethyl group which is disordered lies out of this plane. In the crystal structure, the 2-trifluoromethyl-1H-benzimidazole cations are linked the adjacent 1,5-naphthalene disulphate anions by the N1—H1A···O2 and N2—H2a···O1(-1+x,y,z) to form R44(26) rings Bernstein et al. (1995). These rings are linked to form a ladder structure which runs parallel to the a axis. Adjacent ladders are linked by a weak C12—H12···O3(2-x,1-y,1-z) interaction to form sheets which lie parallel to the ac plane. The supramolecular structure is further reinforced by a π···π interaction involving the phenyl ring of the benzimidazole cations at (x,y,z) and (1-x,1-y,y,1-z). The centroid to centroid distance is 3.758 (2)Å, the ring perpendicular distance is 3.5120 (14)Å and the offset is 1.336Å.

Related literature top

The title compound was studied as part of a search for ferroelectric complexes. For background to ferroelectric complexes, see: Fu et al. (2011); Zhang et al. (2010). For related structures, see: Liu (2011a,b). For graph-set analysis, see: Bernstein et al. (1995).

Experimental top

0.144 g (1 mmol) of 2-trifluoromethyl-1H-benzimidazol was firstly dissolved in 30 ml of ethanol, to which 0.288 g (1 mmol) of 1,5-naphthalene disulfonic acid was added to give a solution at the ambient temperature. Single crystals suitable for X-ray structure analysis were obtained by the slow evaporation of the above solution after 3 days in air.

The dielectric constant of the compound as a function of temperature indicates that the permittivity is basically temperature-independent (ε = C/(T–T0)), suggesting that this compound is not ferroelectric or there may be no distinct phase transition occurring within the measured temperature (below the melting point).

Refinement top

H atoms were placed in calculated positions (N—H = 0.89 Å; C—H = 0.93Å for Csp2 atoms and C—H = 0.96Å and 0.97Å for Csp3 atoms), assigned fixed Uiso values [Uiso = 1.2Ueq(Csp2) and 1.5Ueq(Csp3,N)] and allowed to ride. The trifluoromethyl group is disordered over two sites. The site occupancies were refined and restraints were applied to the thermal parameters.

Computing details top

Data collection: CrystalClear (Rigaku, 2005); cell refinement: CrystalClear (Rigaku, 2005); data reduction: CrystalClear (Rigaku, 2005); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2009); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title compound, showing the atomic numbering scheme with 30% probability displacement ellipsoids. Atoms with labels suffixed with an a are in a centrosymmetrically related part of the anion.
[Figure 2] Fig. 2. View of the ladder structure which runs parallel to the a axis. For the sake of clarity only the major component of the disordered trifluoromethyl group is shown and H atoms not involved in the hydrogen bonding motif are omitted. Atoms labelled with a * (asterisk) are in the asymmetric unit at (-1+x,y,z) those labelled with a # (hash) are at (1+x,y,z).
2-Trifluoromethyl-1H-benzimidazol-3-ium naphthalene-1,5-disulfonate top
Crystal data top
2C8H6F3N2+·C10H6O6S22V = 685.2 (5) Å3
Mr = 660.56Z = 1
Triclinic, P1F(000) = 336
Hall symbol: -P 1Dx = 1.601 Mg m3
a = 9.3910 (19) ÅMo Kα radiation, λ = 0.71073 Å
b = 9.4943 (19) Åθ = 3.4–26°
c = 9.976 (2) ŵ = 0.29 mm1
α = 109.32 (3)°T = 293 K
β = 96.86 (3)°Block, colourless
γ = 119.59 (3)°0.36 × 0.32 × 0.28 mm
Data collection top
Rigaku Mercury2
diffractometer
3136 independent reflections
Radiation source: fine-focus sealed tube2361 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.042
CCD_Profile_fitting scansθmax = 27.5°, θmin = 3.2°
Absorption correction: multi-scan
(CrystalClear; Rigaku, 2005)
h = 1212
Tmin = 0.903, Tmax = 0.921k = 1212
7215 measured reflectionsl = 1212
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.053Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.132H-atom parameters constrained
S = 1.10 w = 1/[σ2(Fo2) + (0.0517P)2 + 0.2409P]
where P = (Fo2 + 2Fc2)/3
3136 reflections(Δ/σ)max = 0.011
227 parametersΔρmax = 0.23 e Å3
36 restraintsΔρmin = 0.42 e Å3
Crystal data top
2C8H6F3N2+·C10H6O6S22γ = 119.59 (3)°
Mr = 660.56V = 685.2 (5) Å3
Triclinic, P1Z = 1
a = 9.3910 (19) ÅMo Kα radiation
b = 9.4943 (19) ŵ = 0.29 mm1
c = 9.976 (2) ÅT = 293 K
α = 109.32 (3)°0.36 × 0.32 × 0.28 mm
β = 96.86 (3)°
Data collection top
Rigaku Mercury2
diffractometer
3136 independent reflections
Absorption correction: multi-scan
(CrystalClear; Rigaku, 2005)
2361 reflections with I > 2σ(I)
Tmin = 0.903, Tmax = 0.921Rint = 0.042
7215 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.05336 restraints
wR(F2) = 0.132H-atom parameters constrained
S = 1.10Δρmax = 0.23 e Å3
3136 reflectionsΔρmin = 0.42 e Å3
227 parameters
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2sigma(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
S11.05784 (8)0.72945 (9)0.37188 (7)0.03242 (19)
O10.9734 (2)0.8147 (3)0.3414 (2)0.0398 (4)
O21.2456 (2)0.8519 (2)0.4164 (2)0.0440 (5)
O31.0035 (3)0.6558 (3)0.4750 (2)0.0532 (5)
C110.9978 (3)0.5476 (3)0.1973 (3)0.0300 (5)
C120.9359 (3)0.3826 (3)0.1952 (3)0.0362 (6)
H120.92360.36790.28170.043*
C130.8913 (4)0.2364 (3)0.0616 (3)0.0413 (6)
H130.84680.12340.05940.050*
C140.9117 (3)0.2556 (3)0.0659 (3)0.0365 (6)
H140.88160.15590.15310.044*
C1101.0219 (3)0.5750 (3)0.0670 (3)0.0286 (5)
N10.4697 (3)0.7605 (3)0.4315 (2)0.0360 (5)
H10.37960.76070.40330.043*
N30.7062 (3)0.7706 (3)0.4334 (2)0.0339 (5)
H30.79240.77810.40660.041*
C20.5853 (3)0.7790 (3)0.3630 (3)0.0352 (6)
C40.4442 (4)0.7162 (4)0.6660 (4)0.0518 (7)
H40.34170.70940.66410.062*
C50.5303 (5)0.7028 (5)0.7769 (4)0.0608 (9)
H50.48510.68720.85280.073*
C60.6826 (5)0.7115 (5)0.7797 (4)0.0581 (8)
H60.73690.70270.85790.070*
C70.7555 (4)0.7326 (4)0.6704 (3)0.0468 (7)
H70.85670.73660.67180.056*
C80.6707 (3)0.7477 (3)0.5582 (3)0.0335 (5)
C90.5194 (3)0.7408 (3)0.5562 (3)0.0353 (6)
C210.5768 (4)0.8018 (5)0.2213 (4)0.0523 (7)
F10.5176 (12)0.9023 (10)0.2234 (8)0.0857 (19)0.653 (12)
F20.4588 (17)0.6460 (7)0.1027 (5)0.119 (3)0.653 (12)
F30.7210 (9)0.8792 (17)0.2048 (11)0.113 (3)0.653 (12)
F1A0.450 (2)0.797 (4)0.1674 (19)0.114 (5)0.347 (12)
F2A0.590 (3)0.6822 (19)0.1208 (11)0.086 (3)0.347 (12)
F3A0.720 (2)0.9515 (16)0.2418 (15)0.118 (6)0.347 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.0354 (3)0.0412 (4)0.0305 (3)0.0274 (3)0.0148 (3)0.0162 (3)
O10.0412 (10)0.0540 (11)0.0460 (10)0.0373 (9)0.0240 (8)0.0255 (9)
O20.0311 (10)0.0428 (11)0.0480 (11)0.0247 (9)0.0066 (8)0.0066 (9)
O30.0827 (15)0.0612 (13)0.0382 (11)0.0485 (12)0.0333 (11)0.0294 (10)
C110.0283 (12)0.0354 (13)0.0308 (12)0.0195 (11)0.0136 (10)0.0162 (10)
C120.0424 (14)0.0436 (15)0.0357 (13)0.0274 (13)0.0205 (11)0.0245 (12)
C130.0527 (17)0.0303 (13)0.0433 (15)0.0215 (13)0.0205 (13)0.0214 (12)
C140.0407 (14)0.0325 (13)0.0369 (14)0.0204 (12)0.0153 (11)0.0164 (11)
C1100.0250 (11)0.0332 (13)0.0311 (12)0.0174 (10)0.0121 (9)0.0162 (10)
N10.0281 (10)0.0427 (12)0.0436 (12)0.0242 (10)0.0138 (9)0.0189 (10)
N30.0331 (11)0.0426 (12)0.0399 (11)0.0274 (10)0.0193 (9)0.0212 (10)
C20.0352 (13)0.0353 (14)0.0383 (14)0.0233 (12)0.0143 (11)0.0143 (11)
C40.0491 (17)0.0541 (18)0.0566 (18)0.0284 (15)0.0328 (15)0.0261 (15)
C50.076 (2)0.064 (2)0.0495 (18)0.0369 (19)0.0368 (17)0.0315 (17)
C60.075 (2)0.067 (2)0.0467 (17)0.0448 (19)0.0222 (16)0.0333 (16)
C70.0507 (17)0.0555 (18)0.0481 (16)0.0368 (15)0.0179 (14)0.0270 (14)
C80.0351 (13)0.0331 (13)0.0366 (13)0.0214 (11)0.0159 (11)0.0154 (11)
C90.0336 (13)0.0346 (13)0.0404 (14)0.0205 (11)0.0171 (11)0.0164 (11)
C210.059 (2)0.069 (2)0.0493 (18)0.0446 (18)0.0237 (16)0.0337 (17)
F10.130 (6)0.112 (4)0.072 (4)0.096 (4)0.034 (3)0.056 (3)
F20.187 (8)0.079 (3)0.037 (2)0.052 (4)0.009 (3)0.0200 (19)
F30.086 (4)0.235 (9)0.130 (6)0.112 (5)0.079 (4)0.151 (6)
F1A0.083 (7)0.238 (15)0.095 (9)0.116 (9)0.044 (6)0.108 (10)
F2A0.161 (10)0.099 (7)0.036 (4)0.096 (7)0.043 (5)0.031 (4)
F3A0.160 (11)0.066 (5)0.068 (5)0.016 (5)0.056 (6)0.041 (4)
Geometric parameters (Å, º) top
S1—O31.435 (2)N3—H30.8600
S1—O21.451 (2)C2—C211.498 (4)
S1—O11.4547 (18)C4—C51.369 (5)
S1—C111.774 (3)C4—C91.395 (4)
C11—C121.367 (3)C4—H40.9300
C11—C1101.430 (3)C5—C61.388 (5)
C12—C131.395 (4)C5—H50.9300
C12—H120.9300C6—C71.373 (4)
C13—C141.366 (3)C6—H60.9300
C13—H130.9300C7—C81.384 (4)
C14—C110i1.414 (3)C7—H70.9300
C14—H140.9300C8—C91.386 (3)
C110—C14i1.414 (3)C21—F1A1.223 (11)
C110—C110i1.419 (5)C21—F31.246 (7)
N1—C21.321 (3)C21—F2A1.311 (8)
N1—C91.380 (3)C21—F21.314 (6)
N1—H10.8600C21—F3A1.314 (12)
N3—C21.312 (3)C21—F11.317 (6)
N3—C81.384 (3)
O3—S1—O2113.71 (13)N1—C2—C21124.3 (2)
O3—S1—O1112.87 (11)C5—C4—C9116.0 (3)
O2—S1—O1110.44 (11)C5—C4—H4122.0
O3—S1—C11107.83 (12)C9—C4—H4122.0
O2—S1—C11104.13 (11)C4—C5—C6122.2 (3)
O1—S1—C11107.24 (11)C4—C5—H5118.9
C12—C11—C110121.5 (2)C6—C5—H5118.9
C12—C11—S1117.00 (18)C7—C6—C5121.9 (3)
C110—C11—S1121.37 (17)C7—C6—H6119.0
C11—C12—C13119.2 (2)C5—C6—H6119.0
C11—C12—H12120.4C6—C7—C8116.5 (3)
C13—C12—H12120.4C6—C7—H7121.7
C14—C13—C12121.4 (2)C8—C7—H7121.7
C14—C13—H13119.3N3—C8—C7132.2 (2)
C12—C13—H13119.3N3—C8—C9106.2 (2)
C13—C14—C110i120.9 (2)C7—C8—C9121.5 (2)
C13—C14—H14119.6N1—C9—C8106.8 (2)
C110i—C14—H14119.6N1—C9—C4131.4 (3)
C14i—C110—C110i118.7 (3)C8—C9—C4121.7 (3)
C14i—C110—C11123.1 (2)F1A—C21—F2A110.9 (8)
C110i—C110—C11118.3 (3)F3—C21—F2112.5 (5)
C2—N1—C9107.7 (2)F1A—C21—F3A109.7 (11)
C2—N1—H1126.2F2A—C21—F3A99.4 (8)
C9—N1—H1126.2F3—C21—F1106.2 (5)
C2—N3—C8108.1 (2)F2—C21—F1103.2 (5)
C2—N3—H3126.0F3—C21—C2113.7 (4)
C8—N3—H3126.0F2—C21—C2110.7 (3)
N3—C2—N1111.2 (2)F1—C21—C2109.8 (4)
N3—C2—C21124.5 (2)
O3—S1—C11—C128.3 (2)C6—C7—C8—N3179.7 (3)
O2—S1—C11—C12112.8 (2)C6—C7—C8—C90.4 (4)
O1—S1—C11—C12130.1 (2)C2—N1—C9—C80.2 (3)
O3—S1—C11—C110174.97 (18)C2—N1—C9—C4179.7 (3)
O2—S1—C11—C11063.9 (2)N3—C8—C9—N10.3 (3)
O1—S1—C11—C11053.2 (2)C7—C8—C9—N1179.8 (2)
C110—C11—C12—C131.5 (4)N3—C8—C9—C4179.2 (2)
S1—C11—C12—C13178.29 (19)C7—C8—C9—C40.7 (4)
C11—C12—C13—C141.4 (4)C5—C4—C9—N1179.5 (3)
C12—C13—C14—C110i0.4 (4)C5—C4—C9—C81.1 (4)
C12—C11—C110—C14i179.0 (2)N3—C2—C21—F1A176.3 (14)
S1—C11—C110—C14i2.3 (3)N1—C2—C21—F1A2.1 (15)
C12—C11—C110—C110i0.6 (4)N3—C2—C21—F325.8 (8)
S1—C11—C110—C110i177.3 (2)N1—C2—C21—F3155.8 (7)
C8—N3—C2—N10.9 (3)N3—C2—C21—F2A50.4 (10)
C8—N3—C2—C21179.5 (2)N1—C2—C21—F2A128.0 (10)
C9—N1—C2—N30.7 (3)N3—C2—C21—F2101.9 (8)
C9—N1—C2—C21179.3 (2)N1—C2—C21—F276.5 (8)
C9—C4—C5—C60.5 (5)N3—C2—C21—F3A58.3 (10)
C4—C5—C6—C70.6 (5)N1—C2—C21—F3A123.3 (10)
C5—C6—C7—C81.0 (5)N3—C2—C21—F1144.7 (5)
C2—N3—C8—C7179.3 (3)N1—C2—C21—F136.9 (6)
C2—N3—C8—C90.7 (3)
Symmetry code: (i) x+2, y+1, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N3—H3···O10.861.812.661 (3)172
N1—H1···O2ii0.861.842.650 (3)155
C12—H12···O3iii0.932.553.440 (3)159
Symmetry codes: (ii) x1, y, z; (iii) x+2, y+1, z+1.

Experimental details

Crystal data
Chemical formula2C8H6F3N2+·C10H6O6S22
Mr660.56
Crystal system, space groupTriclinic, P1
Temperature (K)293
a, b, c (Å)9.3910 (19), 9.4943 (19), 9.976 (2)
α, β, γ (°)109.32 (3), 96.86 (3), 119.59 (3)
V3)685.2 (5)
Z1
Radiation typeMo Kα
µ (mm1)0.29
Crystal size (mm)0.36 × 0.32 × 0.28
Data collection
DiffractometerRigaku Mercury2
diffractometer
Absorption correctionMulti-scan
(CrystalClear; Rigaku, 2005)
Tmin, Tmax0.903, 0.921
No. of measured, independent and
observed [I > 2σ(I)] reflections
7215, 3136, 2361
Rint0.042
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.053, 0.132, 1.10
No. of reflections3136
No. of parameters227
No. of restraints36
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.23, 0.42

Computer programs: CrystalClear (Rigaku, 2005), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), PLATON (Spek, 2009), SHELXTL (Sheldrick, 2008).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N3—H3···O10.861.812.661 (3)172
N1—H1···O2i0.861.842.650 (3)155
C12—H12···O3ii0.932.553.440 (3)159
Symmetry codes: (i) x1, y, z; (ii) x+2, y+1, z+1.
 

Acknowledgements

The author thanks an anonymous advisor from the Ordered Matter Science Research Centre, Southeast University, for great help in the revision of this paper.

References

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