Potassium p-nitro­phenyl sulfate

The crystal structure of the title compound, K⁺·C₆H₄NO₆S^-, is built up from p-nitro­phenyl sulfate anions and potassium cations. Adjacent anions form dimers, which are linked together in a three-dimensional network via short C-H...O contacts. The coordination sphere of the K⁺ ions may be described as a distorted square antiprism. The crystal structure is further stabilized by [pi]-[pi] stacking interactions between the aryl rings.

S1. Comment

p-Nitrophenyl sulfate (pNPS) is one of the synthetic compounds commonly used as a substrate in a wide range of biochemical assays (Dodgson et al., 1956) utilizing various hydrolase (EC 3.1) and sulfotransferase (EC 2.8.2) enzymes. In hydrolase assays, pNPS serves as a substrate for enzymes, mainly sulfatases (EC 3.1.6.1) (Suiko et al., 1996). It is also well recognized that pNPS can be hydrolyzed by numerous alkaline phosphatases (EC 3.1.3.1; O'Brien & Herschlag, 2001). This phenomenon, as well as the level of structural homology of the above mentioned enzymes (Bond et al., 1997; Lukatela et al., 1998), may support the thesis that both enzyme subclasses developed evolutionarily from a common ancestor. The activity of these hydrolases can be measured as a function of the release of free p-nitrophenol from the sulfate ester (Sinchaikul et al., 2002; Liu et al., 2000). In the case of sulfotransferase assays, the role of pNPS is rather to be a part of the PAPS regenerating system (PAPS is 3'-phosphoadenosine-5'-phosphosulfate; Chou et al., 1998; Frame et al., 2000). Sulfatases are enzymes involved in a huge number of biochemical processes and their physiological importance can be illustrated by the numerous disorders to which they are linked (Mehl & Jatzkewitz, 1964; Coughtrie et al., 1998; Parenti et al., 1997). Therefore, there have also been a significant number of papers devoted to the substrates of these enzymes, including various nitrophenyl esters (Jones et al., 1984a,b; Chapman et al., 2003). However, despite the importance of pNPS as a frequently used enzyme substrate, its crystal structure had remained unknown to date. Therefore, we undertook the present X-ray study of the title compound, (I), the potassium salt of pNPS, in order to acquire accurate and reliable data which can be used in molecular modelling enzyme–substrate interaction calculations. \sch

The molecular structure of the pNPS anion of (I) is shown in Fig. 1. A slight deviation from the coplanarity of the nitro group in relation to the plane of the aryl ring is observed, with an interplanar angle of 12.1 (3)°. The orientation of the sulfate group in relation to the phenyl ring is found to be -sc; the S—O1—C1—C2 torsion angle is −79.0 (2)°. The S—O1 ester bond length is 1.631 (2) Å, which corresponds well with the average value found for other aromatic sulfate esters (Popek, 1998). The values of the remaining S—O bond lengths are between 1.439 (2) and 1.442 (2) Å, which also correspond with those observed in other aromatic sulfate esters. Deformation from the ideal tetrahedral shape around the S atom is observed: the valence angles at the S atom range from 99.91 (9) to 115.66 (10)° (for O1—S—O2 and O2—S—O3, respectively). Conjugation between the π-system of the aromatic ring and the strongly electron-withdrawing nitro group in the para-position contributes to the significant shortening of the O1—C1 bond; the value of 1.390 (2) Å is the shortest among all known structures of sulfate monoesters (Popek, 1998). Selected geometric parameters of the anion in (I) are given in Table 1.

The coordination sphere of the K⁺ ion may be described as a distorted square antiprism composed of eight O atoms (Fig. 2), with six O atoms from four sulfate groups and two O atoms from two nitro groups. The K—O distances of the coordination sphere are given in Table 1.

The structure of the p-nitrophenyl sulfate anion of (I) is stabilized by short C—H···O intermolecular contacts and π–π stacking interactions. Two anions are linked by C—H···O contacts to form a centrosymmetrical head-to-head dimer [R₂²(12) ring], as shown in Fig. 3. Each dimer is linked to one other via two C—H.·O contacts, C2—H2.·O4(3/2 − x, y − 1/2, z) and C3—H3.·O4(3/2 − x, y − 1/2, z), with a bifurcated O4 acceptor (Fig. 4 and Table 2). Fig. 5 shows the π–π stacking interactions, which create a zigzag line along the a axis. The interplanar spacing between the centroids of parallel aryl rings is 3.58 (1) Å.

S2. Experimental

Colourless acicular crystals of potassium p-nitrophenyl sulfate were obtained by slow evaporation of a water solution of the commercial compound (Fluka Co.) at room temperature.

S3. Refinement

All H atoms were found in difference- Fourier maps and refined isotropically.

Computing details

Data collection: KM-4 Software (Kuma, 1995-1999); cell refinement: KM-4 Software; data reduction: KM-4 Software; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: XP in SHELXTL (Bruker, 1997); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. The molecular structure of the p-nitrophenyl sulfate anion of (I), showing the atom-labelling scheme. Displacement ellipsoids are drawn at the 30% probability level and H atoms are shown as small spheres of arbitrary radii.
	Fig. 2. The coordination sphere of the K^+ ion of (I). H atoms have been omitted for clarity.
	Fig. 3. A view of the crystal packing of (I), showing the centrosymmetric R2^2(12) dimer created by two anions placed head-to-head. Displacement ellipsoids are drawn at the 30% probability level and H atoms are shown as small spheres of arbitrary radii.
	Fig. 4. A packing diagram for (I), with the inter- and intradimeric C—H···O interactions shown as dashed lines.
	Fig. 5. A diagram showing the π–π stacking interactions in (I), marked as dotted lines, to illustrate the zigzags. The K^+ ions and all H atoms have been omitted for clarity. Displacement ellipsoids are drawn at the 30% probability level.

potassium p-nitrophenyl sulfate

Crystal data

K^+·C6H4NO6S^−	F(000) = 1040
Mr = 257.26	Dx = 1.989 Mg m^−3
Orthorhombic, Pbca	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2ab	Cell parameters from 66 reflections
a = 6.905 (3) Å	θ = 2.2–30.0°
b = 13.116 (5) Å	µ = 0.87 mm^−1
c = 18.969 (11) Å	T = 120 K
V = 1717.9 (14) Å^3	Needle, colourless
Z = 8	0.50 × 0.10 × 0.08 mm

Data collection

Kuma KM-4 κ-geometry diffractometer	Rint = 0.064
Radiation source: fine-focus sealed tube	θmax = 30.0°, θmin = 2.2°
Graphite monochromator	h = −9→9
ω–2θ scans	k = −18→18
12140 measured reflections	l = −26→26
2514 independent reflections	3 standard reflections every 100 reflections
1779 reflections with I > 2σ(I)	intensity decay: none

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.036	All H-atom parameters refined
wR(F^2) = 0.085	w = 1/[σ^2(Fo^2) + (0.0472P)^2 + 0.329P] where P = (Fo^2 + 2Fc^2)/3
S = 1.04	(Δ/σ)max = 0.001
2514 reflections	Δρmax = 0.42 e Å^−3
153 parameters	Δρmin = −0.43 e Å^−3
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0014 (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
K	0.85348 (6)	0.35353 (3)	0.47032 (2)	0.01419 (11)
S	0.65970 (7)	0.61196 (3)	0.56001 (2)	0.01058 (11)
O1	0.4906 (2)	0.56250 (11)	0.60936 (8)	0.0139 (3)
O2	0.5421 (2)	0.65770 (11)	0.50573 (8)	0.0166 (3)
O3	0.7815 (2)	0.52899 (11)	0.53763 (8)	0.0177 (3)
O4	0.7623 (2)	0.68404 (13)	0.60360 (9)	0.0232 (4)
C1	0.5440 (3)	0.50551 (15)	0.66800 (11)	0.0123 (4)
C2	0.6045 (3)	0.40525 (15)	0.65984 (10)	0.0123 (4)
H2	0.627 (4)	0.380 (2)	0.6120 (14)	0.014 (6)*
C3	0.6444 (3)	0.34741 (15)	0.71925 (10)	0.0130 (4)
H3	0.682 (4)	0.282 (2)	0.7180 (15)	0.026 (7)*
C4	0.6160 (3)	0.39100 (16)	0.78505 (10)	0.0125 (4)
C5	0.5517 (3)	0.49063 (16)	0.79346 (11)	0.0144 (4)
H5	0.536 (4)	0.514 (2)	0.8359 (15)	0.018 (7)*
C6	0.5183 (3)	0.54896 (16)	0.73438 (10)	0.0141 (4)
H6	0.470 (5)	0.621 (2)	0.7372 (15)	0.022 (7)*
N	0.6511 (3)	0.32929 (14)	0.84804 (9)	0.0160 (3)
O5	0.7355 (3)	0.24697 (12)	0.84089 (9)	0.0229 (4)
O6	0.5948 (3)	0.36222 (15)	0.90491 (8)	0.0262 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K	0.01029 (18)	0.0148 (2)	0.0175 (2)	0.00077 (16)	−0.00045 (16)	−0.00194 (15)
S	0.0081 (2)	0.0102 (2)	0.0135 (2)	−0.00049 (17)	0.00010 (17)	0.00041 (16)
O1	0.0081 (6)	0.0178 (7)	0.0158 (6)	0.0015 (5)	0.0005 (5)	0.0049 (5)
O2	0.0126 (7)	0.0193 (7)	0.0180 (7)	0.0021 (6)	0.0002 (6)	0.0055 (6)
O3	0.0156 (7)	0.0156 (7)	0.0219 (7)	0.0041 (6)	0.0058 (6)	0.0022 (6)
O4	0.0204 (8)	0.0203 (8)	0.0291 (8)	−0.0080 (7)	−0.0044 (7)	−0.0046 (7)
C1	0.0067 (8)	0.0154 (9)	0.0148 (9)	−0.0026 (7)	0.0001 (7)	0.0018 (7)
C2	0.0096 (8)	0.0159 (9)	0.0113 (8)	−0.0012 (6)	0.0012 (6)	−0.0014 (7)
C3	0.0107 (8)	0.0123 (9)	0.0160 (8)	−0.0004 (7)	0.0010 (7)	−0.0003 (7)
C4	0.0090 (8)	0.0164 (9)	0.0120 (8)	−0.0036 (7)	−0.0001 (6)	0.0027 (7)
C5	0.0108 (9)	0.0188 (10)	0.0135 (9)	−0.0017 (7)	0.0008 (7)	−0.0036 (7)
C6	0.0107 (9)	0.0152 (9)	0.0166 (9)	0.0005 (7)	0.0009 (7)	−0.0021 (7)
N	0.0116 (8)	0.0214 (8)	0.0150 (8)	−0.0069 (7)	−0.0025 (6)	0.0038 (6)
O5	0.0261 (9)	0.0188 (7)	0.0238 (8)	−0.0037 (7)	−0.0062 (7)	0.0080 (6)
O6	0.0268 (9)	0.0400 (10)	0.0119 (7)	−0.0048 (8)	0.0005 (6)	0.0034 (7)

Geometric parameters (Å, º)

K—O3	2.678 (2)	N—O6	1.225 (3)
K—O1^i	3.024 (2)	S—K^iii	3.4403 (16)
K—O2^i	2.773 (2)	S—K^vi	3.5974 (13)
K—O2^ii	2.751 (2)	S—K^i	3.6183 (16)
K—O3^iii	2.958 (2)	O1—K^i	3.0236 (17)
K—O4^iii	3.041 (2)	O2—K^vi	2.7511 (18)
K—O5^iv	2.903 (2)	O2—K^i	2.773 (2)
K—O6^v	2.897 (2)	O3—K^iii	2.9580 (19)
K—S^iii	3.4403 (16)	O4—K^iii	3.041 (2)
K—S^ii	3.5974 (13)	C1—C2	1.388 (3)
K—S^i	3.6183 (16)	C1—C6	1.393 (3)
K—K^iii	4.4860 (16)	C2—C3	1.386 (3)
S—O1	1.631 (2)	C2—H2	0.98 (3)
S—O2	1.442 (2)	C3—C4	1.387 (3)
S—O3	1.439 (2)	C3—H3	0.90 (3)
S—O4	1.442 (2)	C5—C6	1.377 (3)
O1—C1	1.390 (2)	C5—H5	0.87 (3)
C4—C5	1.389 (3)	C6—H6	1.00 (3)
C4—N	1.463 (3)	O5—K^vii	2.903 (2)
N—O5	1.234 (3)	O6—K^viii	2.897 (2)
O3—K—O2^ii	137.26 (6)	O3^iii—K—K^iii	35.15 (3)
O3—K—O2^i	77.57 (5)	O1^i—K—K^iii	99.67 (4)
O2^ii—K—O2^i	99.71 (4)	O4^iii—K—K^iii	82.01 (4)
O3—K—O6^v	71.55 (6)	S^iii—K—K^iii	59.241 (16)
O2^ii—K—O6^v	71.73 (5)	S^ii—K—K^iii	130.32 (3)
O2^i—K—O6^v	115.78 (6)	S^i—K—K^iii	111.99 (2)
O3—K—O5^iv	137.83 (5)	O2—S—O1	99.91 (9)
O2^ii—K—O5^iv	81.73 (5)	O3—S—O1	106.66 (9)
O2^i—K—O5^iv	80.68 (5)	O4—S—O1	106.45 (10)
O6^v—K—O5^iv	150.48 (5)	O3—S—O2	115.66 (10)
O3—K—O3^iii	74.63 (6)	O4—S—O2	114.42 (10)
O2^ii—K—O3^iii	105.99 (5)	O3—S—O4	112.20 (11)
O2^i—K—O3^iii	151.09 (5)	O3—S—K^iii	58.62 (7)
O6^v—K—O3^iii	62.03 (5)	O4—S—K^iii	61.95 (7)
O5^iv—K—O3^iii	115.62 (5)	O2—S—K^iii	112.09 (7)
O3—K—O1^i	77.26 (5)	O1—S—K^iii	147.97 (6)
O2^ii—K—O1^i	131.92 (5)	O3—S—K^vi	122.77 (7)
O2^i—K—O1^i	47.72 (5)	O4—S—K^vi	72.91 (8)
O6^v—K—O1^i	147.79 (5)	O2—S—K^vi	44.09 (6)
O5^iv—K—O1^i	61.46 (5)	O1—S—K^vi	127.13 (6)
O3^iii—K—O1^i	117.02 (5)	K^iii—S—K^vi	80.199 (15)
O3—K—O4^iii	121.40 (5)	O3—S—K^i	128.31 (7)
O2^ii—K—O4^iii	74.49 (5)	O4—S—K^i	119.36 (8)
O2^i—K—O4^iii	157.87 (5)	O2—S—K^i	44.19 (6)
O6^v—K—O4^iii	83.17 (6)	O1—S—K^i	55.94 (6)
O5^iv—K—O4^iii	77.37 (5)	K^iii—S—K^i	156.04 (2)
O3^iii—K—O4^iii	46.96 (5)	K^vi—S—K^i	77.871 (14)
O1^i—K—O4^iii	120.94 (5)	C1—O1—K^i	143.54 (11)
O3—K—S^iii	98.51 (4)	S—O1—K^i	97.51 (7)
O2^ii—K—S^iii	84.69 (4)	S—O2—K^vi	114.52 (8)
O2^i—K—S^iii	175.48 (4)	S—O2—K^i	114.56 (8)
O6^v—K—S^iii	64.49 (5)	K^vi—O2—K^i	110.35 (5)
O5^iv—K—S^iii	101.10 (4)	S—O3—K	153.98 (10)
O3^iii—K—S^iii	24.55 (3)	S—O3—K^iii	96.84 (8)
O1^i—K—S^iii	129.51 (4)	K—O3—K^iii	105.37 (6)
O4^iii—K—S^iii	24.73 (3)	S—O4—K^iii	93.32 (8)
O3—K—S^ii	121.78 (5)	C1—O1—S	118.9 (2)
O2^ii—K—S^ii	21.39 (3)	C2—C1—O1	120.0 (2)
O2^i—K—S^ii	81.42 (3)	C3—C4—N	118.9 (2)
O6^v—K—S^ii	70.30 (4)	C5—C4—N	118.7 (2)
O5^iv—K—S^ii	89.60 (5)	O1—C1—C6	118.0 (2)
O3^iii—K—S^ii	120.29 (4)	O5—N—C4	118.2 (2)
O1^i—K—S^ii	122.50 (3)	O6—N—C4	118.1 (2)
O4^iii—K—S^ii	95.59 (4)	O6—N—O5	123.7 (2)
S^iii—K—S^ii	102.689 (17)	C2—C1—C6	121.77 (19)
O3—K—S^i	77.68 (4)	C3—C2—C1	119.17 (18)
O2^ii—K—S^i	114.35 (4)	C3—C2—H2	122.6 (16)
O2^i—K—S^i	21.25 (3)	C1—C2—H2	118.0 (16)
O6^v—K—S^i	133.50 (4)	C2—C3—C4	118.57 (18)
O5^iv—K—S^i	69.36 (4)	C2—C3—H3	124.0 (18)
O3^iii—K—S^i	139.57 (4)	C4—C3—H3	117.4 (18)
O1^i—K—S^i	26.55 (3)	C3—C4—C5	122.43 (18)
O4^iii—K—S^i	143.26 (4)	C6—C5—C4	118.88 (19)
S^iii—K—S^i	156.04 (2)	C6—C5—H5	122.2 (18)
S^ii—K—S^i	99.241 (17)	C4—C5—H5	118.9 (18)
O3—K—K^iii	39.48 (4)	C5—C6—C1	119.1 (2)
O2^ii—K—K^iii	128.33 (4)	C5—C6—H6	122.4 (16)
O2^i—K—K^iii	116.66 (4)	C1—C6—H6	118.4 (16)
O6^v—K—K^iii	60.12 (4)	N—O5—K^vii	115.89 (13)
O5^iv—K—K^iii	136.69 (4)	N—O6—K^viii	152.61 (15)
O3—S—O1—C1	56.4 (2)	S^ii—K—O3—S	−95.9 (2)
O4—S—O1—C1	−63.6 (2)	S^i—K—O3—S	−2.6 (2)
O2—S—O1—C1	177.1 (2)	K^iii—K—O3—S	147.7 (2)
K^iii—S—O1—C1	−0.5 (2)	O2^ii—K—O3—K^iii	97.09 (7)
K^vi—S—O1—C1	−144.33 (12)	O2^i—K—O3—K^iii	−172.01 (6)
K^i—S—O1—C1	−178.24 (17)	O6^v—K—O3—K^iii	65.10 (6)
O3—S—O1—K^i	−125.36 (8)	O5^iv—K—O3—K^iii	−111.38 (8)
O4—S—O1—K^i	114.66 (9)	O3^iii—K—O3—K^iii	0.0
O2—S—O1—K^i	−4.62 (8)	O1^i—K—O3—K^iii	−123.04 (6)
K^iii—S—O1—K^i	177.77 (7)	O4^iii—K—O3—K^iii	−4.39 (7)
K^vi—S—O1—K^i	33.91 (8)	S^iii—K—O3—K^iii	5.70 (5)
O3—S—O2—K^vi	−111.54 (10)	S^ii—K—O3—K^iii	116.43 (4)
O4—S—O2—K^vi	21.18 (12)	S^i—K—O3—K^iii	−150.24 (5)
O1—S—O2—K^vi	134.46 (8)	O3—S—O4—K^iii	31.26 (9)
K^iii—S—O2—K^vi	−46.91 (9)	O2—S—O4—K^iii	−103.07 (9)
K^i—S—O2—K^vi	128.96 (12)	O1—S—O4—K^iii	147.59 (6)
O3—S—O2—K^i	119.50 (10)	K^vi—S—O4—K^iii	−87.82 (5)
O4—S—O2—K^i	−107.78 (10)	K^i—S—O4—K^iii	−152.67 (3)
O1—S—O2—K^i	5.50 (10)	S—O1—C1—C2	−79.0 (2)
K^iii—S—O2—K^i	−175.87 (4)	S—O1—C1—C6	106.5 (2)
K^vi—S—O2—K^i	−128.96 (12)	K^i—O1—C1—C2	103.9 (2)
O4—S—O3—K	178.86 (19)	K^i—O1—C1—C6	−70.5 (3)
O2—S—O3—K	−47.4 (2)	O1—C1—C2—C3	−175.59 (18)
O1—S—O3—K	62.7 (2)	C6—C1—C2—C3	−1.4 (3)
K^iii—S—O3—K	−148.7 (2)	C1—C2—C3—C4	2.1 (3)
K^vi—S—O3—K	−97.7 (2)	C2—C3—C4—C5	−0.8 (3)
K^i—S—O3—K	3.2 (3)	C2—C3—C4—N	177.84 (18)
O4—S—O3—K^iii	−32.44 (10)	C3—C4—C5—C6	−1.2 (3)
O2—S—O3—K^iii	101.29 (9)	N—C4—C5—C6	−179.93 (18)
O1—S—O3—K^iii	−148.64 (6)	C4—C5—C6—C1	2.0 (3)
K^vi—S—O3—K^iii	50.97 (8)	C2—C1—C6—C5	−0.7 (3)
K^i—S—O3—K^iii	151.92 (4)	O1—C1—C6—C5	173.60 (17)
O2^ii—K—O3—S	−115.3 (2)	C3—C4—N—O5	12.1 (3)
O2^i—K—O3—S	−24.4 (2)	C3—C4—N—O6	−167.8 (2)
O6^v—K—O3—S	−147.2 (2)	C5—C4—N—O5	−169.2 (2)
O5^iv—K—O3—S	36.3 (2)	C5—C4—N—O6	10.9 (3)
O3^iii—K—O3—S	147.7 (2)	O6—N—O5—K^vii	−9.7 (3)
O1^i—K—O3—S	24.6 (2)	C4—N—O5—K^vii	170.38 (13)
O4^iii—K—O3—S	143.3 (2)	O5—N—O6—K^viii	−64.3 (4)
S^iii—K—O3—S	153.4 (2)	C4—N—O6—K^viii	115.6 (3)

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) −x+3/2, y−1/2, z; (iii) −x+2, −y+1, −z+1; (iv) x, −y+1/2, z−1/2; (v) x+1/2, y, −z+3/2; (vi) −x+3/2, y+1/2, z; (vii) x, −y+1/2, z+1/2; (viii) x−1/2, y, −z+3/2.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
C2—H2···O2^i	0.98 (3)	2.57 (3)	3.401 (3)	143 (2)
C2—H2···O4^ii	0.98 (3)	2.69 (3)	3.225 (3)	115 (2)
C3—H3···O4^ii	0.90 (3)	2.55 (3)	3.134 (3)	123 (2)
C6—H6···O5^ix	1.00 (3)	2.63 (3)	3.443 (3)	138 (2)

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) −x+3/2, y−1/2, z; (ix) −x+1, y+1/2, −z+3/2.