organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890

N,N′-Di­cyclo­hexyl-N′′,N′′-di­methyl­phospho­ric tri­amide

aDepartment of Chemistry, Islamic Azad University–Zanjan Branch, PO Box 49195-467, Zanjan, Iran, bDepartment of Chemistry, Ferdowsi University of Mashhad, Mashhad 91779, Iran, and cDepartment of Chemistry, Tarbiat Modares University, Tehran, Iran
*Correspondence e-mail: fahimeh_sabbaghi@yahoo.com

(Received 14 January 2011; accepted 21 January 2011; online 26 January 2011)

In the title compound, C14H30N3OP, both cyclo­hexyl groups adopt chair conformations with the NH unit in an equatorial position. The P atom adopts a slightly distorted tetra­hedral environment. In the (CH3)2NP(O) unit, the O—P—N—C torsion angles, showing the orientations of the methyl groups with respect to the phosphoryl group, are −166.6 (3) and 34.6 (4)°. The O atom of the P=O group acts as a double hydrogen-bond acceptor and is involved in two different inter­molecular N—H⋯OP hydrogen bonds, building R22(8) rings that are further linked into chains running parallel to the b axis.

Related literature

For the structure of a phospho­ramidate with a [(CH3)2N]P(O) unit, see: Ghadimi et al. (2009[Ghadimi, S., Pourayoubi, M. & Ebrahimi Valmoozi, A. A. (2009). Z. Naturforsch. Teil B, 64, 565-569.]). For bond distances in related structures, see: Sabbaghi et al. (2010[Sabbaghi, F., Pourayoubi, M., Toghraee, M. & Divjakovic, V. (2010). Acta Cryst. E66, o344.]). For hydrogen-bond motifs, see: Etter et al. (1990[Etter, M. C., MacDonald, J. C. & Bernstein, J. (1990). Acta Cryst. B46, 256-262.]); Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]). For double hydrogen-bond acceptors, see: Steiner (2002[Steiner, T. (2002). Angew. Chem. Int. Ed. 41, 48-76.]).

[Scheme 1]

Experimental

Crystal data
  • C14H30N3OP

  • Mr = 287.38

  • Monoclinic, P 21 /n

  • a = 11.742 (4) Å

  • b = 7.712 (3) Å

  • c = 18.366 (6) Å

  • β = 102.120 (7)°

  • V = 1626.0 (10) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.17 mm−1

  • T = 120 K

  • 0.23 × 0.19 × 0.13 mm

Data collection
  • Bruker SMART 1000 CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1998[Sheldrick, G. M. (1998). SADABS. University of Göttingen, Germany.]) Tmin = 0.932, Tmax = 0.974

  • 11336 measured reflections

  • 3507 independent reflections

  • 1873 reflections with I > 2σ(I)

  • Rint = 0.103

Refinement
  • R[F2 > 2σ(F2)] = 0.072

  • wR(F2) = 0.199

  • S = 1.04

  • 3507 reflections

  • 174 parameters

  • H-atom parameters constrained

  • Δρmax = 0.51 e Å−3

  • Δρmin = −0.47 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N2—H2⋯O1i 0.90 2.16 3.017 (4) 160
N3—H3⋯O1ii 0.90 2.03 2.911 (4) 165
Symmetry codes: (i) [-x+{\script{1\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]; (ii) [-x+{\script{1\over 2}}, y+{\script{1\over 2}}, -z+{\script{1\over 2}}].

Data collection: SMART (Bruker, 1998[Bruker (1998). SAINT-Plus and SMART, Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT-Plus (Bruker, 1998[Bruker (1998). SAINT-Plus and SMART, Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT-Plus; program(s) used to solve structure: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL and Mercury (Macrae et al., 2008[Macrae, C. F., Bruno, I. J., Chisholm, J. A., Edgington, P. R., McCabe, P., Pidcock, E., Rodriguez-Monge, L., Taylor, R., van de Streek, J. & Wood, P. A. (2008). J. Appl. Cryst. 41, 466-470.]); software used to prepare material for publication: SHELXTL.

Supporting information


Comment top

The structure determination was performed as a part of a project on the synthesis of new phosphorus compounds having a [(CH3)2N]P(O) moiety (Ghadimi et al., 2009).

In the crystal structure of the title compound the two cyclohexyl groups are in a chair conformation with the NH units in equatorial positions (Fig. 1). The P atom is in a slightly distorted tetrahedral environment with bond angles in the range of 100.87 (17)° [N3—P1— N1] to 118.64 (16)° [O1—P1—N3]. In the (CH3)2NP(O) moiety, the dihedral angles O—P—N—C are -166.6 (3)° and 34.6 (4)°. The P—N bond lengths are comparable to those in similar compounds like for example in P(O)[NHC(O)C6H4(4-NO2)][NHC6H11]2 (Sabbaghi et al., 2010).

The molecules are linked by two intermolecular N—H···OP hydrogen bonds into chains in the direction of the b axis in which the O atom of the PO group acts as a double H-acceptors (Steiner, 2002) (Fig. 2). From this arrangement R22(8) rings are formed (Etter et al., 1990; Bernstein et al., 1995).

Related literature top

For the structure of a phosphoramidate having a [(CH3)2N]P(O) unit, see: Ghadimi et al. (2009). For bond distances in related structures, see: Sabbaghi et al. (2010). For hydrogen-bond motifs, see: Etter et al. (1990); Bernstein et al. (1995). For double hydrogen-bond acceptors, see: Steiner (2002).

Experimental top

Synthesis of ((CH3)2N)P(O)Cl2 [(CH3)2NH2]Cl (15.00 g, 0.184 mol) and P(O)Cl3 (84.62 g, 0.552 mol) were refluxed for 8 h and afterwards the excess of P(O)Cl3 was removed in vacuum.

Synthesis of title compound To a solution of ((CH3)2N)P(O)Cl2 (0.60 g, 3.7 mmol) in chloroform (15 mL), a solution of cyclohexylamine (1.47 g, 14.8 mmol) in chloroform (10 mL) was added at 273 K. After 4 h stirring, the solvent was removed and product was washed with deionized water and recrystallized from chloroform/methanol (4:1 v/v) at room temperature.

Refinement top

The hydrogen atoms of NH groups were located by difference Fourier synthesis and normalized at standard value 0.90 Å, whereas the C-H H atoms were positioned with idealized geometry. All H atoms were refined isotropic with Uiso(H) = 1.2Ueq(C, N) (1.5 for methyl H atoms) using a riding model.

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SAINT-Plus (Bruker, 1998); data reduction: SAINT-Plus (Bruker, 1998); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008) and Mercury (Macrae et al., 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. Molecular structure of title compound with labeling and displacement ellipsoids drawn at the 50% probability level.
[Figure 2] Fig. 2. Part of the crystal structure of the title compound with hydrogen bonding shown as dotted lines (the C—H hydrogen atoms are omitted for clarity).
N,N'-Dicyclohexyl-N'',N''-dimethylphosphoric triamide top
Crystal data top
C14H30N3OPF(000) = 632
Mr = 287.38Dx = 1.174 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 1063 reflections
a = 11.742 (4) Åθ = 2.3–26.9°
b = 7.712 (3) ŵ = 0.17 mm1
c = 18.366 (6) ÅT = 120 K
β = 102.120 (7)°Prizm, colorless
V = 1626.0 (10) Å30.23 × 0.19 × 0.13 mm
Z = 4
Data collection top
Bruker SMART 1000 CCD area-detector
diffractometer
3507 independent reflections
Radiation source: normal-focus sealed tube1873 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.103
ϕ and ω scansθmax = 27.0°, θmin = 1.9°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1998)
h = 1514
Tmin = 0.932, Tmax = 0.974k = 99
11336 measured reflectionsl = 2322
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)] = 0.072Hydrogen site location: mixed
wR(F2) = 0.199H-atom parameters constrained
S = 1.04 w = 1/[σ2(Fo2) + (0.062P)2 + 2.1669P]
where P = (Fo2 + 2Fc2)/3
3507 reflections(Δ/σ)max < 0.001
174 parametersΔρmax = 0.51 e Å3
0 restraintsΔρmin = 0.47 e Å3
Crystal data top
C14H30N3OPV = 1626.0 (10) Å3
Mr = 287.38Z = 4
Monoclinic, P21/nMo Kα radiation
a = 11.742 (4) ŵ = 0.17 mm1
b = 7.712 (3) ÅT = 120 K
c = 18.366 (6) Å0.23 × 0.19 × 0.13 mm
β = 102.120 (7)°
Data collection top
Bruker SMART 1000 CCD area-detector
diffractometer
3507 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1998)
1873 reflections with I > 2σ(I)
Tmin = 0.932, Tmax = 0.974Rint = 0.103
11336 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0720 restraints
wR(F2) = 0.199H-atom parameters constrained
S = 1.04Δρmax = 0.51 e Å3
3507 reflectionsΔρmin = 0.47 e Å3
174 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s 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 > σ(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*/Ueq
P10.15685 (9)0.10911 (13)0.22176 (6)0.0231 (3)
O10.2842 (2)0.0799 (3)0.23095 (15)0.0261 (6)
N10.1077 (3)0.2079 (4)0.14150 (19)0.0287 (8)
N20.0944 (3)0.0770 (4)0.23092 (18)0.0250 (8)
H20.14650.16330.24350.030*
N30.1111 (3)0.2411 (4)0.27929 (18)0.0242 (8)
H30.13590.35180.28190.029*
C10.1595 (4)0.1671 (6)0.0782 (2)0.0385 (11)
H1A0.16620.27330.05010.058*
H1B0.11010.08340.04580.058*
H1C0.23710.11700.09600.058*
C20.0065 (4)0.2895 (6)0.1205 (3)0.0371 (11)
H2A0.00100.40070.09610.056*
H2B0.03810.30900.16520.056*
H2C0.05910.21350.08610.056*
C30.0309 (3)0.1127 (5)0.2152 (2)0.0229 (8)
H3A0.07250.00330.22300.027*
C40.0756 (3)0.1728 (5)0.1348 (2)0.0281 (9)
H4A0.06160.08070.10020.034*
H4B0.03200.27740.12520.034*
C50.2050 (4)0.2142 (6)0.1202 (2)0.0302 (10)
H5A0.23120.25510.06820.036*
H5B0.24920.10790.12640.036*
C60.2297 (4)0.3535 (5)0.1737 (2)0.0299 (10)
H6A0.31450.37660.16420.036*
H6B0.18990.46240.16510.036*
C70.1876 (3)0.2957 (5)0.2534 (2)0.0279 (9)
H7A0.20120.38970.28730.033*
H7B0.23290.19310.26310.033*
C80.0574 (4)0.2497 (5)0.2699 (2)0.0272 (9)
H8A0.01130.35550.26610.033*
H8B0.03420.20490.32140.033*
C90.1053 (3)0.1887 (5)0.3554 (2)0.0229 (9)
H9A0.05960.07840.35170.027*
C100.0390 (4)0.3243 (5)0.3902 (2)0.0295 (10)
H10A0.03860.34320.35760.035*
H10B0.08190.43560.39470.035*
C110.0243 (4)0.2654 (6)0.4670 (3)0.0362 (11)
H11A0.02340.15860.46210.043*
H11B0.01680.35630.48950.043*
C120.1444 (4)0.2298 (6)0.5181 (2)0.0385 (11)
H12A0.18940.33910.52680.046*
H12B0.13340.18630.56690.046*
C130.2116 (4)0.0969 (6)0.4830 (2)0.0362 (10)
H13A0.17070.01600.47970.043*
H13B0.29000.08140.51500.043*
C140.2238 (3)0.1534 (6)0.4049 (2)0.0298 (10)
H14A0.27200.25960.40860.036*
H14B0.26370.06110.38220.036*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
P10.0193 (5)0.0217 (5)0.0295 (6)0.0005 (4)0.0079 (4)0.0001 (4)
O10.0198 (14)0.0238 (15)0.0363 (16)0.0024 (11)0.0096 (12)0.0017 (12)
N10.028 (2)0.0280 (19)0.031 (2)0.0039 (15)0.0084 (15)0.0020 (15)
N20.0175 (17)0.0233 (18)0.0352 (19)0.0007 (13)0.0077 (14)0.0006 (14)
N30.0225 (18)0.0228 (18)0.0289 (19)0.0022 (13)0.0087 (14)0.0016 (14)
C10.055 (3)0.030 (2)0.034 (3)0.004 (2)0.019 (2)0.0054 (19)
C20.033 (3)0.034 (2)0.043 (3)0.006 (2)0.003 (2)0.007 (2)
C30.0155 (19)0.0207 (19)0.033 (2)0.0009 (16)0.0064 (16)0.0002 (17)
C40.029 (2)0.027 (2)0.031 (2)0.0042 (18)0.0119 (18)0.0033 (18)
C50.026 (2)0.036 (2)0.029 (2)0.0036 (18)0.0054 (18)0.0019 (18)
C60.021 (2)0.029 (2)0.041 (3)0.0014 (17)0.0086 (18)0.0020 (19)
C70.024 (2)0.025 (2)0.038 (2)0.0022 (17)0.0133 (18)0.0024 (18)
C80.026 (2)0.025 (2)0.031 (2)0.0017 (17)0.0058 (17)0.0008 (17)
C90.019 (2)0.023 (2)0.029 (2)0.0053 (16)0.0085 (16)0.0014 (17)
C100.028 (2)0.026 (2)0.039 (2)0.0008 (18)0.0164 (19)0.0023 (18)
C110.038 (3)0.036 (3)0.041 (3)0.000 (2)0.020 (2)0.001 (2)
C120.046 (3)0.045 (3)0.024 (2)0.007 (2)0.006 (2)0.002 (2)
C130.031 (2)0.041 (3)0.036 (2)0.005 (2)0.0048 (19)0.006 (2)
C140.024 (2)0.031 (2)0.035 (2)0.0026 (17)0.0082 (18)0.0004 (18)
Geometric parameters (Å, º) top
P1—O11.486 (3)C6—C71.511 (6)
P1—N21.636 (3)C6—H6A0.9900
P1—N31.637 (3)C6—H6B0.9900
P1—N11.652 (4)C7—C81.536 (6)
N1—C21.457 (5)C7—H7A0.9900
N1—C11.456 (5)C7—H7B0.9900
N2—C31.465 (5)C8—H8A0.9900
N2—H20.9000C8—H8B0.9900
N3—C91.471 (5)C9—C141.518 (5)
N3—H30.9000C9—C101.522 (5)
C1—H1A0.9800C9—H9A1.0000
C1—H1B0.9800C10—C111.526 (6)
C1—H1C0.9800C10—H10A0.9900
C2—H2A0.9800C10—H10B0.9900
C2—H2B0.9800C11—C121.545 (6)
C2—H2C0.9800C11—H11A0.9900
C3—C41.532 (5)C11—H11B0.9900
C3—C81.534 (5)C12—C131.518 (6)
C3—H3A1.0000C12—H12A0.9900
C4—C51.521 (6)C12—H12B0.9900
C4—H4A0.9900C13—C141.535 (6)
C4—H4B0.9900C13—H13A0.9900
C5—C61.524 (6)C13—H13B0.9900
C5—H5A0.9900C14—H14A0.9900
C5—H5B0.9900C14—H14B0.9900
O1—P1—N2108.49 (16)H6A—C6—H6B108.1
O1—P1—N3118.64 (16)C6—C7—C8111.7 (3)
N2—P1—N3105.33 (17)C6—C7—H7A109.3
O1—P1—N1109.04 (17)C8—C7—H7A109.3
N2—P1—N1114.59 (17)C6—C7—H7B109.3
N3—P1—N1100.87 (17)C8—C7—H7B109.3
C2—N1—C1113.4 (3)H7A—C7—H7B108.0
C2—N1—P1124.4 (3)C7—C8—C3111.1 (3)
C1—N1—P1119.1 (3)C7—C8—H8A109.4
C3—N2—P1126.7 (3)C3—C8—H8A109.4
C3—N2—H2120.8C7—C8—H8B109.4
P1—N2—H2112.3C3—C8—H8B109.4
C9—N3—P1122.0 (3)H8A—C8—H8B108.0
C9—N3—H3106.8N3—C9—C14113.4 (3)
P1—N3—H3118.5N3—C9—C10109.9 (3)
N1—C1—H1A109.5C14—C9—C10111.0 (3)
N1—C1—H1B109.5N3—C9—H9A107.4
H1A—C1—H1B109.5C14—C9—H9A107.4
N1—C1—H1C109.5C10—C9—H9A107.4
H1A—C1—H1C109.5C9—C10—C11110.5 (3)
H1B—C1—H1C109.5C9—C10—H10A109.6
N1—C2—H2A109.5C11—C10—H10A109.6
N1—C2—H2B109.5C9—C10—H10B109.6
H2A—C2—H2B109.5C11—C10—H10B109.6
N1—C2—H2C109.5H10A—C10—H10B108.1
H2A—C2—H2C109.5C10—C11—C12110.5 (3)
H2B—C2—H2C109.5C10—C11—H11A109.6
N2—C3—C4111.9 (3)C12—C11—H11A109.6
N2—C3—C8109.5 (3)C10—C11—H11B109.6
C4—C3—C8110.3 (3)C12—C11—H11B109.6
N2—C3—H3A108.3H11A—C11—H11B108.1
C4—C3—H3A108.3C13—C12—C11110.5 (4)
C8—C3—H3A108.3C13—C12—H12A109.5
C5—C4—C3111.2 (3)C11—C12—H12A109.5
C5—C4—H4A109.4C13—C12—H12B109.5
C3—C4—H4A109.4C11—C12—H12B109.5
C5—C4—H4B109.4H12A—C12—H12B108.1
C3—C4—H4B109.4C12—C13—C14111.4 (4)
H4A—C4—H4B108.0C12—C13—H13A109.3
C4—C5—C6110.6 (3)C14—C13—H13A109.3
C4—C5—H5A109.5C12—C13—H13B109.3
C6—C5—H5A109.5C14—C13—H13B109.3
C4—C5—H5B109.5H13A—C13—H13B108.0
C6—C5—H5B109.5C9—C14—C13110.9 (3)
H5A—C5—H5B108.1C9—C14—H14A109.5
C7—C6—C5110.4 (3)C13—C14—H14A109.5
C7—C6—H6A109.6C9—C14—H14B109.5
C5—C6—H6A109.6C13—C14—H14B109.5
C7—C6—H6B109.6H14A—C14—H14B108.1
C5—C6—H6B109.6
O1—P1—N1—C2166.6 (3)C3—C4—C5—C658.0 (4)
N2—P1—N1—C271.6 (4)C4—C5—C6—C757.8 (4)
N3—P1—N1—C240.9 (4)C5—C6—C7—C856.5 (4)
O1—P1—N1—C134.6 (4)C6—C7—C8—C355.2 (4)
N2—P1—N1—C187.2 (3)N2—C3—C8—C7177.9 (3)
N3—P1—N1—C1160.2 (3)C4—C3—C8—C754.3 (4)
O1—P1—N2—C3170.3 (3)P1—N3—C9—C1465.7 (4)
N3—P1—N2—C361.7 (3)P1—N3—C9—C10169.4 (3)
N1—P1—N2—C348.2 (4)N3—C9—C10—C11175.8 (3)
O1—P1—N3—C977.8 (3)C14—C9—C10—C1157.9 (4)
N2—P1—N3—C943.8 (3)C9—C10—C11—C1257.5 (5)
N1—P1—N3—C9163.3 (3)C10—C11—C12—C1356.5 (5)
P1—N2—C3—C491.1 (4)C11—C12—C13—C1455.4 (5)
P1—N2—C3—C8146.3 (3)N3—C9—C14—C13179.2 (3)
N2—C3—C4—C5178.3 (3)C10—C9—C14—C1356.6 (4)
C8—C3—C4—C556.1 (4)C12—C13—C14—C955.7 (5)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N2—H2···O1i0.902.163.017 (4)160
N3—H3···O1ii0.902.032.911 (4)165
Symmetry codes: (i) x+1/2, y1/2, z+1/2; (ii) x+1/2, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formulaC14H30N3OP
Mr287.38
Crystal system, space groupMonoclinic, P21/n
Temperature (K)120
a, b, c (Å)11.742 (4), 7.712 (3), 18.366 (6)
β (°) 102.120 (7)
V3)1626.0 (10)
Z4
Radiation typeMo Kα
µ (mm1)0.17
Crystal size (mm)0.23 × 0.19 × 0.13
Data collection
DiffractometerBruker SMART 1000 CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1998)
Tmin, Tmax0.932, 0.974
No. of measured, independent and
observed [I > 2σ(I)] reflections
11336, 3507, 1873
Rint0.103
(sin θ/λ)max1)0.639
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.072, 0.199, 1.04
No. of reflections3507
No. of parameters174
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.51, 0.47

Computer programs: SMART (Bruker, 1998), SAINT-Plus (Bruker, 1998), SHELXTL (Sheldrick, 2008) and Mercury (Macrae et al., 2008).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N2—H2···O1i0.902.163.017 (4)160
N3—H3···O1ii0.902.032.911 (4)165
Symmetry codes: (i) x+1/2, y1/2, z+1/2; (ii) x+1/2, y+1/2, z+1/2.
 

Acknowledgements

Support of this investigation by Islamic Azad University–Zanjan Branch is gratefully acknowledged.

References

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