Hydrogen-bonded networks in crystals of 1-(diamino­methyl­ene)­thio­uron-1-ium perchlorate, hydrogen sulfate, dihydrogen phosphate and dihydrogen arsenate

Crystals of the title compounds, namely 1-(diamino­methyl­ene)thio­uron-1-ium perchlorate, C₂H₇N₄S⁺·ClO₄⁻, 1-(di­amino­methyl­ene)thio­uron-1-ium hydrogen sulfate, C₂H₇N₄S⁺·HSO₄⁻, 1-(diamino­methyl­ene)thio­uron-1-ium dihydrogen phosphate, C₂H₇N₄S⁺·H₂PO₄⁻, and its isomorphic relative 1-(di­amino­methyl­ene)thio­uron-1-ium dihydrogen arsenate, C₂H₇N₄S⁺·H₂AsO₄⁻, are built up from a nonplanar 1-(di­amino­methyl­ene)thio­uron-1-ium cation and the respective anion linked together via N—H...O hydrogen bonds. Both arms of the cation are planar, but they are twisted with respect to one another around the central N atom. Ionic and extensive hydrogen-bonding inter­actions join oppositely charged units into layers in the perchlorate, double layers in the hydrogen sulfate, and a three-dimensional network in the dihydrogen phosphate and dihydrogen arsenate salts. This work demonstrates the usefulness of 1-(diamino­methyl­ene)­thio­urea in crystal engineering for the formation of supra­molecular networks with acids.

S1. Comment

1-(Diaminomethylene)thiourea and its imino tautomer, i.e. 2-imino-4-thiobiuret, are potentially interesting compounds that can be used in crystal engineering to build up extended frameworks, since they contain arrays of hydrogen-bonding sites (Janczak & Perpétuo, 2008). In addition, both tautomers have different potential coordination modes, since they can act as N,N or N,S ligands and can form several different types of complexes with metal ions. The coordination of metal ions by these tautomers is possible by both the neutral and the deprotonated (anionic) forms (Doxiadi et al., 2003). Beyond these known complexes, 2-imino-4-thiobiuret and 1-(diaminomethylene)thiourea can form salts with acids (Perpétuo & Janczak, 2008). We present here the crystal structures of 1-(diaminomethylene)thiouron-1-ium perchlorate, (Ia), and hydrogen sulfate, (Ib), as well as the isomorphic dihydrogen phosphate, (Ic), and dihydrogen arsenate, (Id); the conformations of the cations are compared with that of the neutral molecule as well as with those in the chloride, bromide and iodide salts.

The asymmetric units of the title compounds are illustrated in Figs. 1(a)–1(d). The two arms of the 1-(diaminomethylene)thiouron-1-ium cation containing the N1/C2/N3/N4 and N1/C1/N2/S1 fragments are planar but twisted from coplanarity at the central atom N1. The dihedral angle between the planes defined by the N1/C2/N3/N4 and N1/C1/N2/S1 arms is 1.4 (1)° in (Ia), 9.8 (1)° in (Ib), 4.4 (1)° in (Ic) and 2.1 (1)° in (Id). Therefore, the 1-(diaminomethylene)thiouron-1-ium cations in the crystals of (Ia) and (Id) are almost planar [the deviations of the non-H atoms from the mean plane are smaller than 0.021 (1) Å in (Ia) and 0.058 (1) Å in (Id); see Table 6]. A similar nonplanar, twisted conformation of the cation is observed in the crystals of other salts, as shown by their dihedral angles [22.9 (1)° for the chloride, 15.2 (1)° for the bromide and 4.2 (1)° for the iodide (Perpétuo & Janczak, 2008)]. Ab-initio molecular orbital (MO) calculations indicate that the most stable conformation of the 1-(diaminomethylene)thiouron-1-ium cation is twisted with a dihedral angle of 6.2° (Perpétuo & Janczak, 2008). In single crystals, the neutral 1-(diaminomethylene)thiourea molecule also has a twisted conformation, with a dihedral angle of 22.2 (1)°, while the MO-calculated dihedral angle is 6.6° (Janczak & Perpétuo, 2008).

In the present crystal structures, the respective C—N and C—S bond lengths are very similar (Table 5). The C—N bonds involving the central N1 atom are significantly longer than the C—N bonds linking the amine groups. The values of the C1—S1 bond lengths in these salts are shorter than that in the neutral molecule of 1-(diaminomethylene)thiourea [1.7364 (9) Å; Janczak & Perpétuo, 2008] and are comparable to those found in the crystals of 1-(diaminomethylene)thiouron-1-ium chloride, bromide and iodide (Perpétuo & Janczak, 2008) as well as in thiourea derivatives (average C—S distance of 1.663 Å; Allen et al. 1997). The C1—S1 bond lengths in (Ia)–(Id) are slightly longer than the pure double C═S bond as observed in thioformaldehyde, CH₂S [1.6109 (8) Å; Johnson et al., 1971], but shorter than the distance of 1.74 Å which represents 50% double-bond character (Abrahams, 1956; Allen et al. 1987). Thus the bond order of C1—S1 in (Ia)–(Id) is somewhat less than 2, because of the partial delocalization of the π electrons of the double C1—S1 and C2—N1 bonds over the single C—N bonds linking the NH₂ groups. This results in a shortening of the single C—NH₂ bonds and the elongation of the double double C1═S1 and C2═N1 bonds. Thus the bond order of the C—N bonds linking the amine groups is greater than that of the C—N bonds involving the central N1 atom. Ab-initio MO calculations show that interaction of atom S1 with the amine group (N4) leads to the rotation of both arms of the 1-(diaminomethylene)thiouron-1-ium cation around the C—N1 bond by 6.2°, as well as the distortion of the C—N—C, N—C—N and N—C—S angles from 120°, as expected for sp²-hydridization. The protonation of the central N1 atom decreases the steric effect of the lone-pair of electrons at atom N1 and makes the C1—N1—C2 angle greater by ~6° in comparison with the neutral molecule (Janczak & Perpétuo, 2008), which is consistent with the valence-shell electron-pair repulsion model (Gillespie, 1992). The anionic species of (Ia)–(Id) each exhibit a slightly distorted tetrahedral geometry, with bond lengths and angles typical of those found in several crystals of this kind (Allen, 2002).

In all of the title crystal structures, besides the interionic interactions, the oppositely charged units interact through hydrogen-bonding systems. Atom S1 contains two lone-pair electrons and so acts as a hydrogen-bond acceptor. The non-bonded S···H contact requires that the distance between the S and H atoms is shorter than the sum of the van der Waals radii of these atoms [r_S = 1.80 Å (Bondi, 1964) and r_H = 1.10 Å (Rowland & Taylor, 1996]. Besides S···H contacts, N—H···O contacts between the oppositely charged units with distances shorter than the sum of the van der Waals radii of O and H atoms are observed in these structures [r_O = 1.52 Å and r_H = 1.10 Å; Bondi, 1964; Pauling, 1960]. In (Ia) (Table 1), 1-(diaminomethylene)thiouron-1-ium cations related by inversion interact via a pair of N—H···S hydrogen bonds, forming a dimeric structure (Fig. 2a). These dimers are linked via N—H···O hydrogen bonds with ClO₄^- anions, forming layers that are arranged almost parallel to the (102) crystallographic plane and are separated by a distance of ~3.58 Å.

In (Ib), the 1-(diaminomethylene)thiouron-1-ium cations are discrete and they are surrounded by the HSO₄^- counter-ions (Fig. 2b). HSO₄^- anions related by inversion interact by a pair of O2—H2···O1ⁱ hydrogen bonds [O3—H3 in Table 2; also note that there are some small discrepancies between the O,N—H distances in Tables 1 and 2 and those given in the CIF _geom_bond loops], forming centrosymmetric dimers. The discrete 1-(diaminomethylene)thiouron-1-ium cations interact via N—H···O hydrogen bonds with the (HSO₄^-)₂ dimers, forming double layers that are parallel to the (001) crystallographic plane (Table 2). The sheets in the double layers are interconnected by N—H···O hydrogen bonds, while between the double layers no hydrogen bonds are observed (Fig. 2b). The sheets in the double layer are separated by a distance of ~3.22 Å and the double layers by ~2.92 Å.

In the isomorphic structures of (Ic) and (Id) (Tables 3 and 4), and as found in (Ia), the 1-(diaminomethylene)thiouron-1-ium cations interact via N—H···S hydrogen bonds, forming centrosymmetric dimers. The anions, i.e. H₂PO₄^- or H₂AsO₄^-, are involved in two pairs of almost linear O—H···O hydrogen bonds to form pseudo-one-dimensional chains that run almost parallel to the [100] direction (Fig. 3a). The anionic chains interconnect the cationic dimers by N—H···O hydrogen bonds, forming a three-dimensional hydrogen-bonded network (Fig. 3b). In the crystal structures of (Ic) and (Id), the dimeric cations form a stacking structure with a distance between the mean planes of the dimers of 3.71 (1) and 3.42 (1) Å, respectively.

This study illustrates the utility of 1-(diaminomethylene)thiourea in crystal engineering for developing a variety of supramolecular structures, namely layers, double layers and three-dimensional networks.

Related literature

For related literature, see: Abrahams (1956); Allen (2002); Allen et al. (1987, 1997); Bondi (1964); Doxiadi et al. (2003); Gillespie (1992); Janczak & Perpétuo (2008); Johnson et al. (1971); Pauling (1960); Perpétuo & Janczak (2008); Rowland & Taylor (1996).

S2. Experimental

Crystals of (Ia), (Ib), (Ic) and (Id) were obtained from 2-imino-4-thiobiuret (purchased from Aldrich, 99% purity) dissolved in 5% aqueous solutions of HCLO₄, H₂SO₄, H₃PO₄ and H₃AsO₄ acids, respectively [quantities of reagents?]. After several days at room temperature, suitable crystals were formed.

S3. Refinement

H atoms were located in difference Fourier maps and were refined with isotropic displacement parameters in all structures.

Computing details

For all compounds, data collection: CrysAlis CCD (Oxford Diffraction Poland, 2005); cell refinement: CrysAlis CCD (Oxford Diffraction Poland, 2005); data reduction: CrysAlis RED (Oxford Diffraction Poland, 2005); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg & Putz, 2006); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures

	Fig. 1. Views of (a) (Ia), (b) (Ib), (c) (Ic) and (d) (Id) with the atom-labelling scheme. Displacement ellipsoids are shown at the 50% probability level and H atoms as spheres of arbitrary radii. Dashed lines indicate hydrogen-bond contacts.
	Fig. 2. Views of the crystal packing of (Ia) and (Ib), showing hydrogen-bonded layers in (Ia) (a) and double layers in (Ib) (b). Dashed lines represent N—H···S hydrogen bonds in dimers of 1-(diaminomethylene)thiouron-1-ium and O—H···O bonds in dimers involving HSO4^-.
	Fig. 3. (a) A view of the anionic chains in the isomorphic structures of (Ic) and (Id), and (b) the crystal packing of (Id), showing the three-dimensional hydrogen-bonded network. Dashed lines represent N—H···S hydrogen bonds in dimers of 1-(diaminomethylene)thiouron-1-ium.

(Ia) 1-(diaminomethylene)thiouron-1-ium perchlorate

Crystal data

C2H7N4S^+·ClO4^−	Z = 2
Mr = 218.63	F(000) = 224
Triclinic, P1	Dx = 1.731 Mg m^−3 Dm = 1.73 Mg m^−3 Dm measured by flotation
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 5.8011 (9) Å	Cell parameters from 1038 reflections
b = 8.4511 (14) Å	θ = 3.7–29.5°
c = 9.430 (2) Å	µ = 0.69 mm^−1
α = 109.15 (2)°	T = 295 K
β = 91.441 (10)°	Paralellepiped, colourless
γ = 104.639 (11)°	0.37 × 0.22 × 0.14 mm
V = 419.59 (15) Å^3

Data collection

Kuma KM-4 diffractometer with CCD area detector	2110 independent reflections
Radiation source: fine-focus sealed tube	1516 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.016
Detector resolution: 1024x1024 with blocks 2x2 pixels mm^-1	θmax = 29.5°, θmin = 3.7°
ω–scan	h = −6→8
Absorption correction: analytical (face-indexed; SHELXTL; Sheldrick, 2008)	k = −11→11
Tmin = 0.785, Tmax = 0.910	l = −12→12
5108 measured reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.036	All H-atom parameters refined
wR(F^2) = 0.097	w = 1/[σ^2(Fo^2) + (0.0576P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.00	(Δ/σ)max < 0.001
2110 reflections	Δρmax = 0.29 e Å^−3
137 parameters	Δρmin = −0.35 e Å^−3
0 restraints	Extinction correction: SHELXL97
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.017 (5)

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
Cl1	0.33875 (8)	0.76951 (6)	0.65728 (5)	0.03919 (17)
O1	0.2814 (4)	0.5916 (2)	0.5601 (2)	0.0906 (7)
O2	0.1475 (4)	0.7940 (3)	0.7455 (2)	0.0895 (7)
O3	0.5514 (3)	0.8099 (2)	0.7523 (2)	0.0810 (6)
O4	0.3649 (3)	0.88027 (19)	0.56864 (17)	0.0528 (4)
S1	0.65094 (9)	0.28351 (7)	0.92477 (6)	0.04618 (19)
C1	0.7894 (3)	0.4101 (2)	0.8318 (2)	0.0330 (4)
N1	0.9665 (3)	0.3752 (2)	0.73814 (18)	0.0350 (4)
H1	1.018 (4)	0.448 (3)	0.701 (2)	0.042 (6)*
N2	0.7399 (4)	0.5550 (2)	0.8389 (2)	0.0490 (5)
H21	0.812 (4)	0.611 (3)	0.795 (3)	0.053 (7)*
H22	0.644 (4)	0.590 (3)	0.892 (3)	0.054 (7)*
C2	1.0630 (3)	0.2376 (2)	0.7004 (2)	0.0359 (4)
N3	1.2312 (3)	0.2417 (3)	0.6086 (2)	0.0496 (5)
H31	1.298 (4)	0.160 (3)	0.587 (3)	0.053 (7)*
H32	1.267 (4)	0.320 (4)	0.580 (3)	0.058 (8)*
N4	0.9943 (4)	0.1105 (2)	0.7496 (3)	0.0535 (5)
H42	1.064 (4)	0.029 (3)	0.724 (3)	0.062 (7)*
H41	0.886 (6)	0.113 (4)	0.816 (3)	0.096 (10)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cl1	0.0538 (3)	0.0521 (3)	0.0679 (3)	0.0150 (2)	0.0159 (2)	0.0267 (2)
O1	0.0967 (19)	0.0368 (9)	0.0737 (13)	0.0236 (11)	−0.0041 (13)	0.0183 (9)
O2	0.0716 (13)	0.0936 (16)	0.0998 (17)	0.0381 (12)	0.0450 (12)	0.0584 (14)
O3	0.0564 (11)	0.0649 (12)	0.0737 (16)	0.0097 (9)	−0.0192 (11)	0.0292 (12)
O4	0.0671 (10)	0.0462 (8)	0.0617 (9)	0.0211 (7)	0.0230 (8)	0.0358 (8)
S1	0.0521 (3)	0.0442 (3)	0.0549 (3)	0.0201 (3)	0.0258 (3)	0.0280 (3)
C1	0.0312 (9)	0.0305 (9)	0.0347 (9)	0.0065 (7)	0.0046 (7)	0.0102 (7)
N1	0.0398 (9)	0.0295 (8)	0.0404 (8)	0.0113 (7)	0.0157 (7)	0.0169 (7)
N2	0.0569 (12)	0.0432 (10)	0.0658 (12)	0.0292 (9)	0.0337 (10)	0.0306 (10)
C2	0.0318 (9)	0.0312 (9)	0.0399 (10)	0.0100 (8)	0.0038 (8)	0.0060 (8)
N3	0.0484 (11)	0.0505 (11)	0.0560 (11)	0.0240 (9)	0.0236 (9)	0.0181 (10)
N4	0.0514 (11)	0.0412 (10)	0.0840 (15)	0.0261 (9)	0.0268 (11)	0.0320 (10)

Geometric parameters (Å, º)

Cl1—O3	1.4044 (17)	N2—H21	0.78 (3)
Cl1—O2	1.4198 (17)	N2—H22	0.81 (3)
Cl1—O1	1.4283 (18)	C2—N4	1.283 (3)
Cl1—O4	1.4304 (14)	C2—N3	1.322 (3)
S1—C1	1.6656 (19)	N3—H31	0.85 (2)
C1—N2	1.308 (2)	N3—H32	0.78 (3)
C1—N1	1.396 (2)	N4—H42	0.86 (3)
N1—C2	1.364 (2)	N4—H41	0.90 (3)
N1—H1	0.81 (2)
O3—Cl1—O2	109.83 (14)	C1—N2—H21	118.6 (18)
O3—Cl1—O1	109.43 (13)	C1—N2—H22	121.4 (17)
O2—Cl1—O1	108.83 (14)	H21—N2—H22	120 (2)
O3—Cl1—O4	110.59 (10)	N4—C2—N3	121.6 (2)
O2—Cl1—O4	108.40 (10)	N4—C2—N1	122.37 (18)
O4—Cl1—O4	109.73 (10)	N3—C2—N1	116.0 (2)
N2—C1—N1	112.58 (18)	C2—N3—H31	117.5 (16)
N2—C1—S1	122.50 (16)	C2—N3—H32	119 (2)
N1—C1—S1	124.92 (14)	H31—N3—H32	123 (2)
C2—N1—C1	130.08 (17)	C2—N4—H42	118.5 (17)
C2—N1—H1	115.6 (14)	C2—N4—H41	120 (2)
C1—N1—H1	114.3 (14)	H42—N4—H41	121 (3)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1^i	0.81 (2)	2.40 (2)	3.159 (3)	156.5 (19)
N2—H21···O2^i	0.78 (2)	2.32 (3)	3.050 (3)	156 (2)
N2—H22···S1^ii	0.80 (3)	2.63 (3)	3.434 (2)	177 (2)
N3—H31···O4^iii	0.85 (2)	2.44 (3)	3.245 (3)	158 (2)
N3—H31···O4^iv	0.85 (2)	2.50 (2)	3.104 (2)	129 (2)
N3—H32···O1^i	0.78 (3)	2.35 (3)	3.082 (3)	159 (3)
N4—H42···O2^iii	0.86 (3)	2.22 (3)	3.014 (3)	153 (2)
N4—H41···S1	0.90 (3)	2.25 (3)	2.981 (2)	138 (3)

Symmetry codes: (i) x+1, y, z; (ii) −x+1, −y+1, −z+2; (iii) x+1, y−1, z; (iv) −x+2, −y+1, −z+1.

(Ib) 1-(diaminomethylene)thiouron-1-ium hydrogen sulfate

Crystal data

C2H7N4S^+·HO4S^−	Z = 2
Mr = 216.24	F(000) = 224
Triclinic, P1	Dx = 1.783 Mg m^−3 Dm = 1.78 Mg m^−3 Dm measured by flotation
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 7.8371 (11) Å	Cell parameters from 1225 reflections
b = 8.103 (2) Å	θ = 3.2–27.9°
c = 8.104 (2) Å	µ = 0.65 mm^−1
α = 60.88 (1)°	T = 295 K
β = 65.99 (1)°	Paralellepiped, colourless
γ = 87.54 (2)°	0.37 × 0.27 × 0.22 mm
V = 402.85 (17) Å^3

Data collection

Kuma KM-4 diffractometer with CCD area detector	1917 independent reflections
Radiation source: fine-focus sealed tube	1731 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.005
Detector resolution: 1024x1024 with blocks 2x2 pixels mm^-1	θmax = 27.9°, θmin = 3.2°
ω–scan	h = −10→10
Absorption correction: analytical (face-indexed; SHELXTL; Sheldrick, 2008)	k = −10→10
Tmin = 0.796, Tmax = 0.871	l = −10→10
4199 measured reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.029	All H-atom parameters refined
wR(F^2) = 0.070	w = 1/[σ^2(Fo^2) + (0.0341P)^2 + 0.2478P] where P = (Fo^2 + 2Fc^2)/3
S = 1.01	(Δ/σ)max = 0.001
1917 reflections	Δρmax = 0.52 e Å^−3
134 parameters	Δρmin = −0.49 e Å^−3
0 restraints	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.101 (6)

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
S2	0.76851 (5)	0.01455 (5)	0.33072 (6)	0.02512 (12)
O1	0.69633 (16)	0.19365 (15)	0.28570 (19)	0.0336 (3)
O2	0.97036 (17)	0.04752 (19)	0.2646 (2)	0.0451 (3)
O3	0.68035 (18)	−0.11706 (16)	0.57480 (18)	0.0335 (3)
H3	0.561 (4)	−0.161 (4)	0.628 (4)	0.059 (7)*
O4	0.7104 (2)	−0.08542 (19)	0.2500 (2)	0.0449 (3)
S1	0.45743 (6)	0.60771 (7)	0.16711 (9)	0.04241 (15)
N1	0.11009 (18)	0.70288 (18)	0.2241 (2)	0.0263 (3)
H1	0.046 (3)	0.789 (3)	0.225 (3)	0.032 (5)*
C1	0.2893 (2)	0.7335 (2)	0.2114 (2)	0.0250 (3)
C2	0.0226 (2)	0.5553 (2)	0.2314 (2)	0.0249 (3)
N2	0.3173 (2)	0.8791 (2)	0.2346 (3)	0.0368 (3)
H21	0.234 (3)	0.943 (3)	0.258 (3)	0.039 (5)*
H22	0.433 (3)	0.908 (3)	0.217 (3)	0.046 (6)*
N3	−0.1488 (2)	0.5632 (2)	0.2417 (3)	0.0385 (3)
H31	−0.206 (3)	0.467 (3)	0.252 (3)	0.048 (6)*
H32	−0.204 (3)	0.654 (3)	0.248 (3)	0.045 (6)*
N4	0.1035 (2)	0.4111 (2)	0.2324 (3)	0.0373 (3)
H41	0.225 (3)	0.415 (3)	0.218 (3)	0.048 (6)*
H42	0.042 (3)	0.324 (4)	0.237 (4)	0.055 (6)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
S2	0.02383 (19)	0.02176 (18)	0.0340 (2)	0.00638 (13)	−0.01303 (15)	−0.01719 (15)
O1	0.0596 (8)	0.0404 (7)	0.0520 (7)	0.0089 (6)	−0.0284 (6)	−0.0327 (6)
O2	0.0339 (6)	0.0436 (7)	0.0509 (8)	0.0089 (5)	−0.0153 (5)	−0.0252 (6)
O3	0.0342 (6)	0.0304 (6)	0.0340 (6)	0.0061 (5)	−0.0183 (5)	−0.0127 (5)
O4	0.0344 (6)	0.0221 (5)	0.0444 (6)	0.0095 (4)	−0.0183 (5)	−0.0168 (5)
S1	0.0387 (2)	0.0433 (3)	0.0631 (3)	0.01779 (18)	−0.0243 (2)	−0.0427 (2)
N1	0.0255 (6)	0.0238 (6)	0.0364 (7)	0.0093 (5)	−0.0153 (5)	−0.0192 (5)
C1	0.0263 (7)	0.0242 (6)	0.0276 (7)	0.0040 (5)	−0.0124 (5)	−0.0149 (6)
C2	0.0260 (7)	0.0243 (6)	0.0245 (6)	0.0035 (5)	−0.0121 (5)	−0.0117 (5)
N2	0.0350 (7)	0.0357 (7)	0.0558 (9)	0.0098 (6)	−0.0214 (7)	−0.0337 (7)
N3	0.0313 (7)	0.0357 (7)	0.0583 (9)	0.0085 (6)	−0.0254 (7)	−0.0266 (7)
N4	0.0359 (7)	0.0336 (7)	0.0566 (10)	0.0093 (6)	−0.0270 (7)	−0.0288 (7)

Geometric parameters (Å, º)

S1—C1	1.6615 (16)	N3—H31	0.87 (2)
N1—C2	1.3685 (19)	N3—H32	0.85 (2)
N1—C1	1.3902 (18)	N4—H41	0.91 (2)
N1—H1	0.84 (2)	N4—H42	0.84 (2)
C1—N2	1.3212 (19)	S2—O2	1.4380 (13)
C2—N4	1.303 (2)	S2—O4	1.4427 (12)
C2—N3	1.313 (2)	S2—O1	1.4633 (11)
N2—H21	0.83 (2)	S2—O3	1.5571 (15)
N2—H22	0.89 (2)	O3—H3	0.84 (2)
C2—N1—C1	129.74 (13)	C2—N3—H32	121.3 (15)
C2—N1—H1	114.9 (13)	H31—N3—H32	121 (2)
C1—N1—H1	115.3 (13)	C2—N4—H41	118.1 (14)
N2—C1—N1	112.97 (14)	C2—N4—H42	117.7 (15)
N2—C1—S1	121.75 (12)	H41—N4—H42	124 (2)
N1—C1—S1	125.27 (11)	O2—S2—O4	113.95 (9)
N4—C2—N3	121.22 (15)	O2—S2—O1	111.09 (8)
N4—C2—N1	121.83 (14)	O1—S2—O4	111.90 (8)
N3—C2—N1	116.94 (14)	O2—S2—O3	104.43 (9)
C1—N2—H21	123.1 (15)	O4—S2—O3	108.00 (8)
C1—N2—H22	115.2 (14)	O1—S2—O3	106.90 (8)
H21—N2—H22	122 (2)	S2—O3—H3	111.5 (14)
C2—N3—H31	116.9 (15)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···O1^i	0.86 (3)	1.83 (3)	2.6714 (19)	166 (2)
N1—H1···O2^ii	0.84 (2)	2.29 (2)	3.073 (2)	155.2 (17)
N2—H21···O2^ii	0.83 (2)	2.19 (2)	2.963 (2)	154.0 (19)
N2—H22···O4^iii	0.89 (2)	2.30 (2)	3.164 (2)	166 (2)
N3—H31···O1^iv	0.87 (2)	2.23 (2)	3.080 (2)	168 (2)
N3—H32···O4^ii	0.85 (2)	2.19 (2)	3.031 (2)	168 (2)
N4—H41···S1	0.92 (2)	2.22 (2)	2.9798 (18)	140.4 (19)
N4—H41···O3^i	0.92 (2)	2.47 (2)	3.029 (2)	119.6 (17)
N4—H42···O2^iv	0.85 (3)	2.22 (3)	3.021 (2)	159 (2)

Symmetry codes: (i) −x+1, −y, −z+1; (ii) x−1, y+1, z; (iii) x, y+1, z; (iv) x−1, y, z.

(Ic) 1-(diaminomethylene)thiouron-1-ium dihydrogen phosphate

Crystal data

C2H7N4S^+·H2O4P^−	Z = 2
Mr = 216.16	F(000) = 224
Triclinic, P1	Dx = 1.654 Mg m^−3 Dm = 1.65 Mg m^−3 Dm measured by flotation
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 4.5229 (8) Å	Cell parameters from 1257 reflections
b = 8.3241 (11) Å	θ = 3.0–28.0°
c = 11.574 (2) Å	µ = 0.54 mm^−1
α = 88.160 (12)°	T = 295 K
β = 86.191 (11)°	Paralellepiped, colourless
γ = 87.359 (10)°	0.38 × 0.18 × 0.17 mm
V = 434.15 (13) Å^3

Data collection

Kuma KM-4 diffractometer with CDD area detector	2067 independent reflections
Radiation source: fine-focus sealed tube	1757 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.012
Detector resolution: 1024x1024 with blocks 2x2 pixels mm^-1	θmax = 28.0°, θmin = 3.0°
ω–scan	h = −5→5
Absorption correction: analytical (face-indexed; SHELXTL; Sheldrick, 2008)	k = −10→10
Tmin = 0.812, Tmax = 0.909	l = −15→15
4924 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.027	Hydrogen site location: difference Fourier map
wR(F^2) = 0.072	All H-atom parameters refined
S = 1.00	w = 1/[σ^2(Fo^2) + (0.0412P)^2 + 0.0855P] where P = (Fo^2 + 2Fc^2)/3
2067 reflections	(Δ/σ)max < 0.001
145 parameters	Δρmax = 0.27 e Å^−3
0 restraints	Δρmin = −0.26 e Å^−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
P1	0.28127 (7)	0.65855 (4)	0.60758 (3)	0.02430 (11)
O1	0.4070 (2)	0.49667 (11)	0.64587 (8)	0.0298 (2)
O2	0.01641 (19)	0.71967 (12)	0.68229 (9)	0.0310 (2)
O3	0.1843 (2)	0.65850 (13)	0.48022 (9)	0.0375 (3)
H3	0.305 (4)	0.600 (2)	0.4396 (18)	0.050 (5)*
O4	0.5195 (2)	0.78877 (12)	0.60441 (11)	0.0403 (3)
H4	0.675 (6)	0.759 (3)	0.625 (2)	0.084 (8)*
S1	−0.34160 (11)	0.23701 (5)	0.97068 (4)	0.04931 (14)
C1	−0.1533 (3)	0.35003 (17)	0.87071 (12)	0.0315 (3)
N1	0.0335 (3)	0.29052 (14)	0.78114 (11)	0.0323 (3)
H1	0.131 (4)	0.364 (2)	0.7380 (16)	0.039 (5)*
C2	0.0998 (3)	0.13590 (16)	0.74954 (12)	0.0311 (3)
N2	−0.1685 (4)	0.50789 (16)	0.87172 (13)	0.0404 (3)
H21	−0.086 (4)	0.562 (2)	0.8152 (16)	0.035 (4)*
H22	−0.269 (4)	0.557 (2)	0.9211 (18)	0.049 (5)*
N3	0.2781 (4)	0.11737 (19)	0.65666 (14)	0.0473 (4)
H31	0.332 (4)	0.027 (2)	0.6361 (16)	0.041 (5)*
H32	0.324 (4)	0.202 (3)	0.6131 (18)	0.057 (6)*
N4	−0.0002 (4)	0.01142 (16)	0.80830 (14)	0.0461 (4)
H42	0.041 (4)	−0.083 (2)	0.7754 (16)	0.041 (5)*
H41	−0.114 (4)	0.024 (2)	0.8625 (17)	0.043 (5)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P1	0.02301 (17)	0.02320 (17)	0.02656 (19)	0.00039 (12)	−0.00156 (13)	−0.00079 (13)
O1	0.0312 (5)	0.0243 (5)	0.0334 (5)	0.0025 (4)	−0.0025 (4)	0.0008 (4)
O2	0.0240 (5)	0.0339 (5)	0.0348 (6)	0.0007 (4)	0.0008 (4)	−0.0047 (4)
O3	0.0392 (6)	0.0396 (6)	0.0330 (6)	0.0121 (5)	−0.0060 (5)	−0.0029 (5)
O4	0.0319 (5)	0.0365 (5)	0.0528 (8)	−0.0015 (4)	−0.0082 (5)	0.0058 (5)
S1	0.0682 (3)	0.0338 (2)	0.0429 (2)	−0.00430 (19)	0.0194 (2)	0.00190 (17)
C1	0.0391 (8)	0.0287 (7)	0.0273 (7)	−0.0019 (6)	−0.0059 (6)	−0.0006 (5)
N1	0.0424 (7)	0.0227 (6)	0.0308 (6)	−0.0017 (5)	0.0034 (5)	0.0021 (5)
C2	0.0369 (7)	0.0255 (6)	0.0309 (7)	0.0016 (5)	−0.0051 (6)	0.0007 (5)
N2	0.0586 (9)	0.0277 (6)	0.0334 (7)	−0.0008 (6)	0.0076 (6)	−0.0019 (6)
N3	0.0531 (10)	0.0381 (7)	0.0468 (8)	0.0067 (7)	0.0174 (7)	0.0027 (6)
N4	0.0589 (10)	0.0337 (7)	0.0437 (8)	−0.0041 (6)	0.0137 (8)	−0.0018 (6)

Geometric parameters (Å, º)

P1—O1	1.5034 (10)	N1—H1	0.890 (19)
P1—O2	1.5086 (11)	C2—N4	1.303 (2)
P1—O4	1.5612 (12)	C2—N3	1.309 (2)
P1—O3	1.5656 (12)	N2—H21	0.855 (19)
O3—H3	0.84 (2)	N2—H22	0.81 (2)
O4—H4	0.79 (2)	N3—H31	0.81 (2)
S1—C1	1.6800 (16)	N3—H32	0.88 (2)
C1—N2	1.3130 (19)	N4—H42	0.893 (19)
C1—N1	1.3827 (19)	N4—H41	0.790 (19)
N1—C2	1.3639 (18)
O1—P1—O2	114.17 (6)	C1—N1—H1	115.5 (11)
O1—P1—O4	111.37 (6)	N4—C2—N3	120.67 (15)
O2—P1—O4	107.58 (6)	N4—C2—N1	123.09 (14)
O1—P1—O3	111.95 (6)	N3—C2—N1	116.22 (14)
O2—P1—O3	107.03 (6)	C1—N2—H21	119.4 (12)
O4—P1—O3	104.12 (7)	C1—N2—H22	122.0 (14)
P1—O3—H3	109.9 (13)	H21—N2—H22	118.3 (18)
P1—O4—H4	115.4 (18)	C2—N3—H31	120.2 (13)
N2—C1—N1	112.91 (14)	C2—N3—H32	119.3 (13)
N2—C1—S1	122.04 (12)	H31—N3—H32	120.2 (19)
N1—C1—S1	125.04 (11)	C2—N4—H42	115.3 (12)
C2—N1—C1	130.34 (13)	C2—N4—H41	119.9 (14)
C2—N1—H1	114.2 (11)	H42—N4—H41	123.9 (18)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···O1^i	0.84 (2)	1.76 (2)	2.5994 (17)	171.0 (19)
O4—H4···O2^ii	0.79 (2)	1.73 (3)	2.5123 (15)	171 (3)
N1—H1···O1	0.890 (19)	1.948 (19)	2.8273 (18)	169.3 (16)
N2—H21···O2	0.855 (19)	2.035 (19)	2.874 (2)	166.4 (16)
N2—H21···O2	0.855 (19)	2.035 (19)	2.874 (2)	166.4 (16)
N2—H22···S1^iii	0.81 (2)	2.68 (2)	3.4677 (19)	163.3 (18)
N4—H42···O2^iv	0.893 (19)	2.00 (2)	2.8682 (19)	162.9 (16)
N4—H41···S1	0.790 (19)	2.36 (2)	3.0028 (19)	138.9 (17)
N3—H31···O4^iv	0.81 (2)	2.16 (2)	2.964 (2)	171.0 (17)
N3—H32···O1	0.88 (2)	2.55 (2)	3.234 (2)	136.2 (17)
N3—H32···O4^i	0.88 (2)	2.57 (2)	3.182 (2)	127.8 (17)

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x+1, y, z; (iii) −x−1, −y+1, −z+2; (iv) x, y−1, z.

(Id) 1-(diaminomethylene)thiouron-1-ium dihydrogen arsenate

Crystal data

C2H7N4S^+·H2AsO4^−	Z = 2
Mr = 260.11	F(000) = 260
Triclinic, P1	Dx = 1.914 Mg m^−3 Dm = 1.91 Mg m^−3 Dm measured by flotation
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 4.7250 (8) Å	Cell parameters from 1287 reflections
b = 8.4071 (10) Å	θ = 3.0–28.0°
c = 11.3841 (19) Å	µ = 3.98 mm^−1
α = 89.402 (11)°	T = 295 K
β = 86.840 (12)°	Paralellepiped, colourless
γ = 88.871 (14)°	0.38 × 0.14 × 0.12 mm
V = 451.41 (12) Å^3

Data collection

Kuma KM-4 diffractometer with CCD area detector	2149 independent reflections
Radiation source: fine-focus sealed tube	1927 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.013
Detector resolution: 1024x1024 with blocks 2x2 pixels mm^-1	θmax = 28.0°, θmin = 3.0°
ω–scan	h = −6→6
Absorption correction: analytical (face-indexed; SHELXTL; Sheldrick, 2008)	k = −11→11
Tmin = 0.513, Tmax = 0.642	l = −15→14
4770 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.041	Hydrogen site location: difference Fourier map
wR(F^2) = 0.109	All H-atom parameters refined
S = 1.01	w = 1/[σ^2(Fo^2) + (0.0863P)^2] where P = (Fo^2 + 2Fc^2)/3
2149 reflections	(Δ/σ)max < 0.001
136 parameters	Δρmax = 1.02 e Å^−3
0 restraints	Δρmin = −0.93 e Å^−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
As1	0.26918 (5)	0.65723 (3)	0.60563 (3)	0.02854 (14)
O1	0.3995 (5)	0.4836 (3)	0.6521 (2)	0.0338 (5)
O2	−0.0076 (4)	0.7238 (3)	0.6864 (2)	0.0337 (5)
O3	0.1745 (5)	0.6532 (3)	0.4633 (2)	0.0450 (6)
H3	0.289 (13)	0.618 (8)	0.423 (6)	0.10 (2)*
O4	0.5174 (5)	0.8017 (3)	0.6031 (3)	0.0446 (6)
H4	0.657 (12)	0.763 (7)	0.627 (4)	0.067 (15)*
S1	−0.3455 (3)	0.23998 (12)	0.97557 (9)	0.0543 (3)
C1	−0.1611 (8)	0.3520 (4)	0.8756 (3)	0.0362 (7)
N1	0.0297 (6)	0.2922 (3)	0.7906 (3)	0.0362 (6)
H1	0.111 (8)	0.356 (5)	0.753 (3)	0.030 (10)*
C2	0.0922 (8)	0.1389 (4)	0.7590 (3)	0.0367 (7)
N2	−0.1802 (8)	0.5071 (4)	0.8752 (3)	0.0416 (7)
H21	−0.118 (10)	0.566 (6)	0.817 (4)	0.054 (13)*
H22	−0.290 (9)	0.550 (5)	0.924 (4)	0.042 (11)*
N3	0.2708 (9)	0.1196 (4)	0.6664 (3)	0.0546 (9)
H31	0.368 (12)	0.030 (7)	0.646 (5)	0.073 (16)*
H32	0.306 (13)	0.213 (9)	0.634 (5)	0.09 (2)*
N4	−0.0123 (9)	0.0163 (4)	0.8138 (3)	0.0525 (9)
H41	−0.150 (9)	0.031 (5)	0.871 (4)	0.050 (12)*
H42	0.019 (10)	−0.063 (6)	0.769 (4)	0.051 (12)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
As1	0.01797 (19)	0.0306 (2)	0.0371 (2)	0.00060 (12)	−0.00229 (12)	−0.00070 (13)
O1	0.0299 (11)	0.0347 (11)	0.0366 (11)	0.0054 (9)	−0.0040 (8)	−0.0017 (8)
O2	0.0203 (9)	0.0374 (11)	0.0432 (12)	−0.0004 (8)	0.0006 (8)	−0.0076 (9)
O3	0.0345 (13)	0.0569 (15)	0.0435 (14)	0.0138 (11)	−0.0087 (10)	−0.0021 (11)
O4	0.0192 (10)	0.0337 (12)	0.0818 (19)	−0.0032 (9)	−0.0094 (11)	0.0041 (12)
S1	0.0714 (7)	0.0427 (5)	0.0464 (5)	−0.0061 (5)	0.0201 (5)	0.0008 (4)
C1	0.0391 (17)	0.0381 (17)	0.0315 (15)	−0.0051 (13)	−0.0041 (12)	0.0002 (12)
N1	0.0437 (15)	0.0276 (13)	0.0371 (14)	−0.0010 (11)	0.0014 (12)	0.0008 (10)
C2	0.0420 (17)	0.0319 (15)	0.0364 (16)	0.0033 (13)	−0.0074 (13)	−0.0018 (12)
N2	0.0545 (18)	0.0386 (15)	0.0300 (14)	−0.0025 (13)	0.0103 (13)	−0.0039 (12)
N3	0.063 (2)	0.0394 (17)	0.059 (2)	0.0075 (16)	0.0208 (17)	0.0031 (15)
N4	0.070 (2)	0.0326 (16)	0.053 (2)	−0.0065 (15)	0.0153 (17)	−0.0054 (13)

Geometric parameters (Å, º)

As1—O2	1.649 (2)	N1—H1	0.80 (5)
As1—O1	1.666 (2)	C2—N4	1.292 (5)
As1—O4	1.704 (2)	C2—N3	1.322 (5)
As1—O3	1.706 (3)	N2—H21	0.84 (4)
O3—H3	0.78 (5)	N2—H22	0.83 (5)
O4—H4	0.81 (5)	N3—H31	0.91 (6)
S1—C1	1.686 (4)	N3—H32	0.86 (6)
C1—N2	1.305 (5)	N4—H41	0.91 (5)
C1—N1	1.378 (4)	N4—H42	0.84 (5)
N1—C2	1.364 (4)
O2—As1—O1	113.83 (11)	C1—N1—H1	115 (3)
O2—As1—O4	107.10 (12)	N4—C2—N3	120.0 (3)
O1—As1—O4	111.59 (11)	N4—C2—N1	123.8 (3)
O2—As1—O3	107.43 (11)	N3—C2—N1	116.2 (3)
O1—As1—O3	113.10 (12)	C1—N2—H21	123 (3)
O4—As1—O3	103.05 (14)	C1—N2—H22	118 (3)
As1—O3—H3	112 (5)	H21—N2—H22	117 (4)
As1—O4—H4	107 (4)	C2—N3—H31	126 (3)
N2—C1—N1	113.5 (3)	C2—N3—H32	109 (4)
N2—C1—S1	122.0 (3)	H31—N3—H32	124 (5)
N1—C1—S1	124.5 (3)	C2—N4—H41	119 (3)
C2—N1—C1	130.4 (3)	C2—N4—H42	107 (3)
C2—N1—H1	115 (3)	H41—N4—H42	129 (4)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···O1^i	0.78 (5)	1.83 (5)	2.599 (3)	169 (5)
O4—H4···O2^ii	0.81 (5)	1.76 (5)	2.555 (3)	166 (6)
N1—H1···O1	0.80 (5)	2.03 (5)	2.806 (4)	166 (4)
N2—H21···O2	0.84 (4)	2.06 (4)	2.897 (4)	173 (5)
N2—H22···S1^iii	0.83 (5)	2.66 (5)	3.449 (3)	160 (4)
N3—H31···O4^iv	0.91 (6)	2.08 (6)	2.974 (4)	168 (5)
N3—H32···O1	0.86 (6)	2.35 (6)	3.133 (4)	150 (5)
N4—H41···S1	0.91 (5)	2.28 (5)	3.007 (4)	136 (4)
N4—H42···O2^iv	0.84 (5)	2.05 (6)	2.867 (4)	164 (5)

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x+1, y, z; (iii) −x−1, −y+1, −z+2; (iv) x, y−1, z.