The title compound, (C
12H
11N
3)
2[Mo
8O
26], was prepared by the hydrothermal method. The centrosymmetric β-octamolybdate anions are linked to form a three-dimensional structure by the 2-(4-pyridinio)benzimidazolium cations through N—H
O hydrogen bonds.
Supporting information
CCDC reference: 262251
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (C-C) = 0.009 Å
- R factor = 0.043
- wR factor = 0.114
- Data-to-parameter ratio = 15.0
checkCIF/PLATON results
No syntax errors found
Alert level C
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ?
PLAT125_ALERT_4_C No _symmetry_space_group_name_Hall Given ....... ?
PLAT199_ALERT_1_C Check the Reported cell_measurement_temperature 293
PLAT200_ALERT_1_C Check the Reported cell_ambient_temperature .... 293
PLAT220_ALERT_2_C Large Non-Solvent O Ueq(max)/Ueq(min) ... 3.49 Ratio
PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for Mo4
PLAT342_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ... 9
PLAT432_ALERT_2_C Short Inter X...Y Contact O2 .. C11 .. 2.97 Ang.
PLAT764_ALERT_4_C Overcomplete CIF Bond List Detected (Rep/Expd) . 1.17 Ratio
PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 2
C12 H11 N3
0 ALERT level A = In general: serious problem
0 ALERT level B = Potentially serious problem
10 ALERT level C = Check and explain
0 ALERT level G = General alerts; check
3 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
3 ALERT type 2 Indicator that the structure model may be wrong or deficient
1 ALERT type 3 Indicator that the structure quality may be low
3 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: CrystalClear (Rigaku Corporation, 2002); cell refinement: CrystalClear; data reduction: CrystalClear; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXL97; software used to prepare material for publication: SHELXTL (Sheldrick, 1995).
bis[2-(4-pyridinio)-1H-benzimidazolium] hexacosaoxooctamolybdenum(VI)
top
Crystal data top
(C12H11N3)2[Mo8O26] | F(000) = 1504 |
Mr = 1578.00 | Dx = 2.764 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
a = 11.304 (3) Å | Cell parameters from 5270 reflections |
b = 9.485 (3) Å | θ = 2.0–27.5° |
c = 17.835 (5) Å | µ = 2.66 mm−1 |
β = 97.434 (2)° | T = 293 K |
V = 1896.1 (9) Å3 | Prism, yellow |
Z = 2 | 0.20 × 0.10 × 0.10 mm |
Data collection top
Rigaku Mercury CCD diffractometer | 4335 independent reflections |
Radiation source: fine-focus sealed tube | 3867 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.033 |
Detector resolution: 14.6306 pixels mm-1 | θmax = 27.5°, θmin = 2.4° |
ω scan | h = −13→14 |
Absorption correction: multi-scan (CrystalClear; Rigaku, 2002) | k = −12→12 |
Tmin = 0.683, Tmax = 0.766 | l = −23→22 |
14344 measured reflections | |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.043 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.114 | H-atom parameters constrained |
S = 1.09 | w = 1/[σ2(Fo2) + (0.0575P)2 + 5.8052P] where P = (Fo2 + 2Fc2)/3 |
4335 reflections | (Δ/σ)max < 0.001 |
289 parameters | Δρmax = 1.87 e Å−3 |
0 restraints | Δρmin = −2.90 e Å−3 |
Special details top
Experimental. Both cell_measurement_temperature and cell_ambient_temperature are 293 K. |
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. The structure was solved by direct methods, and refined by the
full least-squares method against F2. All non-H atoms were
refined with anisotropic displacement parameters.
All calculations were performed
on a computer with SHELXTL-PC program package.
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 | x | y | z | Uiso*/Ueq | |
Mo1 | 0.08527 (4) | 0.20725 (5) | 0.11005 (3) | 0.02921 (13) | |
Mo2 | −0.07505 (4) | 0.14690 (5) | −0.04739 (2) | 0.02545 (13) | |
Mo3 | −0.15054 (4) | −0.01806 (5) | 0.11830 (3) | 0.02886 (13) | |
Mo4 | −0.31705 (5) | −0.07244 (7) | −0.04252 (3) | 0.04438 (17) | |
C1 | −0.4557 (5) | 0.1538 (7) | −0.5952 (4) | 0.0399 (14) | |
C2 | −0.5482 (6) | 0.1996 (8) | −0.6487 (4) | 0.0511 (18) | |
H2A | −0.6090 | 0.2573 | −0.6359 | 0.061* | |
C3 | −0.5445 (7) | 0.1548 (9) | −0.7211 (4) | 0.060 (2) | |
H3A | −0.6054 | 0.1819 | −0.7585 | 0.073* | |
C4 | −0.4535 (7) | 0.0705 (8) | −0.7410 (4) | 0.0543 (18) | |
H4A | −0.4552 | 0.0429 | −0.7912 | 0.065* | |
C5 | −0.3611 (7) | 0.0267 (7) | −0.6891 (4) | 0.0488 (16) | |
H5A | −0.2995 | −0.0288 | −0.7026 | 0.059* | |
C6 | −0.3645 (5) | 0.0695 (6) | −0.6150 (3) | 0.0346 (12) | |
C7 | −0.3309 (5) | 0.1043 (6) | −0.4917 (3) | 0.0313 (11) | |
C8 | −0.2761 (5) | 0.0923 (5) | −0.4127 (3) | 0.0317 (11) | |
C9 | −0.1731 (6) | 0.0122 (7) | −0.3965 (3) | 0.0413 (14) | |
H9A | −0.1397 | −0.0323 | −0.4352 | 0.050* | |
C10 | −0.1211 (6) | −0.0008 (7) | −0.3231 (4) | 0.0459 (16) | |
H10A | −0.0521 | −0.0541 | −0.3115 | 0.055* | |
C11 | −0.2691 (7) | 0.1387 (7) | −0.2816 (4) | 0.0485 (16) | |
H11A | −0.3016 | 0.1792 | −0.2414 | 0.058* | |
C12 | −0.3243 (6) | 0.1573 (7) | −0.3545 (4) | 0.0426 (14) | |
H12A | −0.3925 | 0.2125 | −0.3642 | 0.051* | |
N1 | −0.4317 (4) | 0.1727 (6) | −0.5173 (3) | 0.0399 (12) | |
H1A | −0.4747 | 0.2206 | −0.4901 | 0.048* | |
N2 | −0.2888 (4) | 0.0437 (5) | −0.5492 (3) | 0.0345 (10) | |
H2B | −0.2241 | −0.0048 | −0.5462 | 0.041* | |
N3 | −0.1702 (5) | 0.0634 (5) | −0.2686 (3) | 0.0436 (13) | |
H3B | −0.1361 | 0.0557 | −0.2228 | 0.052* | |
O1 | −0.4517 (4) | −0.0113 (9) | −0.0827 (3) | 0.089 (2) | |
O2 | −0.1654 (4) | 0.0796 (5) | 0.1958 (2) | 0.0452 (11) | |
O3 | 0.0564 (4) | 0.2433 (5) | 0.1990 (2) | 0.0429 (10) | |
O4 | 0.1123 (4) | 0.3670 (4) | 0.0713 (3) | 0.0481 (11) | |
O5 | −0.0442 (4) | 0.3071 (4) | −0.0798 (2) | 0.0419 (10) | |
O6 | 0.2408 (3) | 0.1304 (5) | 0.1290 (2) | 0.0377 (9) | |
O7 | −0.1765 (4) | −0.1853 (5) | 0.1438 (3) | 0.0457 (11) | |
O8 | −0.2291 (3) | 0.1276 (4) | −0.0751 (2) | 0.0361 (9) | |
O9 | −0.2928 (3) | 0.0231 (5) | 0.0521 (2) | 0.0377 (9) | |
O10 | −0.0293 (3) | 0.0259 (4) | −0.12942 (19) | 0.0268 (7) | |
O11 | 0.0986 (3) | 0.0833 (4) | −0.00075 (19) | 0.0255 (7) | |
O12 | −0.0808 (3) | 0.1821 (4) | 0.0588 (2) | 0.0281 (8) | |
O13 | −0.3462 (6) | −0.2377 (6) | −0.0121 (3) | 0.0775 (19) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Mo1 | 0.0299 (3) | 0.0288 (2) | 0.0278 (2) | −0.00825 (18) | −0.00072 (18) | −0.00357 (17) |
Mo2 | 0.0245 (2) | 0.0249 (2) | 0.0259 (2) | 0.00281 (17) | −0.00101 (17) | 0.00143 (15) |
Mo3 | 0.0214 (2) | 0.0380 (3) | 0.0269 (2) | −0.00321 (18) | 0.00246 (17) | −0.00148 (17) |
Mo4 | 0.0251 (3) | 0.0731 (4) | 0.0350 (3) | −0.0183 (3) | 0.0041 (2) | −0.0125 (3) |
C1 | 0.030 (3) | 0.047 (3) | 0.041 (3) | −0.003 (3) | −0.001 (2) | 0.015 (3) |
C2 | 0.031 (3) | 0.072 (5) | 0.048 (4) | 0.006 (3) | −0.003 (3) | 0.024 (3) |
C3 | 0.050 (4) | 0.070 (5) | 0.054 (4) | −0.013 (4) | −0.020 (4) | 0.027 (4) |
C4 | 0.069 (5) | 0.047 (4) | 0.043 (4) | −0.010 (4) | −0.008 (3) | 0.007 (3) |
C5 | 0.058 (4) | 0.045 (4) | 0.040 (3) | 0.003 (3) | −0.006 (3) | −0.001 (3) |
C6 | 0.037 (3) | 0.032 (3) | 0.033 (3) | −0.001 (2) | −0.003 (2) | 0.007 (2) |
C7 | 0.028 (3) | 0.033 (3) | 0.031 (3) | 0.002 (2) | 0.000 (2) | 0.007 (2) |
C8 | 0.036 (3) | 0.024 (2) | 0.034 (3) | −0.001 (2) | −0.001 (2) | 0.005 (2) |
C9 | 0.043 (3) | 0.047 (3) | 0.032 (3) | 0.012 (3) | −0.004 (3) | 0.002 (2) |
C10 | 0.049 (4) | 0.046 (4) | 0.038 (3) | 0.008 (3) | −0.008 (3) | −0.001 (3) |
C11 | 0.061 (4) | 0.054 (4) | 0.030 (3) | 0.011 (3) | 0.007 (3) | −0.001 (3) |
C12 | 0.042 (3) | 0.046 (4) | 0.039 (3) | 0.011 (3) | 0.005 (3) | 0.002 (3) |
N1 | 0.030 (2) | 0.056 (3) | 0.033 (3) | 0.016 (2) | 0.005 (2) | 0.012 (2) |
N2 | 0.033 (2) | 0.033 (2) | 0.035 (2) | 0.007 (2) | −0.006 (2) | 0.0033 (19) |
N3 | 0.054 (3) | 0.039 (3) | 0.033 (3) | 0.000 (2) | −0.012 (2) | 0.004 (2) |
O1 | 0.026 (2) | 0.186 (7) | 0.052 (3) | 0.002 (3) | −0.004 (2) | −0.036 (4) |
O2 | 0.036 (2) | 0.062 (3) | 0.038 (2) | 0.000 (2) | 0.0049 (18) | −0.011 (2) |
O3 | 0.046 (2) | 0.046 (2) | 0.035 (2) | −0.008 (2) | 0.0019 (19) | −0.0088 (18) |
O4 | 0.057 (3) | 0.036 (2) | 0.050 (3) | −0.017 (2) | 0.001 (2) | 0.0001 (19) |
O5 | 0.050 (3) | 0.031 (2) | 0.044 (2) | 0.0047 (19) | 0.004 (2) | 0.0079 (17) |
O6 | 0.027 (2) | 0.054 (3) | 0.030 (2) | −0.0095 (18) | −0.0035 (16) | −0.0059 (17) |
O7 | 0.044 (2) | 0.051 (3) | 0.042 (2) | −0.013 (2) | 0.004 (2) | 0.0086 (19) |
O8 | 0.0259 (19) | 0.044 (2) | 0.036 (2) | 0.0088 (17) | −0.0036 (16) | 0.0018 (17) |
O9 | 0.0200 (18) | 0.054 (3) | 0.039 (2) | 0.0002 (17) | 0.0033 (16) | −0.0056 (18) |
O10 | 0.0232 (18) | 0.0319 (18) | 0.0242 (17) | −0.0002 (15) | −0.0004 (14) | 0.0001 (14) |
O11 | 0.0222 (17) | 0.0262 (17) | 0.0275 (18) | −0.0028 (14) | 0.0012 (14) | 0.0000 (13) |
O12 | 0.0270 (18) | 0.0302 (18) | 0.0266 (18) | 0.0021 (15) | 0.0014 (15) | −0.0027 (14) |
O13 | 0.099 (4) | 0.075 (4) | 0.067 (4) | −0.062 (3) | 0.043 (3) | −0.027 (3) |
Geometric parameters (Å, º) top
Mo1—O3 | 1.695 (4) | C3—C4 | 1.385 (12) |
Mo1—O4 | 1.709 (4) | C3—H3A | 0.9300 |
Mo1—O6 | 1.893 (4) | C4—C5 | 1.368 (9) |
Mo1—O12 | 1.993 (4) | C4—H4A | 0.9300 |
Mo1—O11 | 2.321 (3) | C5—C6 | 1.387 (9) |
Mo1—O10i | 2.338 (4) | C5—H5A | 0.9300 |
Mo1—Mo2 | 3.1906 (9) | C6—N2 | 1.382 (7) |
Mo2—O5 | 1.679 (4) | C7—N2 | 1.317 (7) |
Mo2—O8 | 1.757 (4) | C7—N1 | 1.340 (7) |
Mo2—O12 | 1.932 (4) | C7—C8 | 1.468 (7) |
Mo2—O10 | 1.980 (4) | C8—C9 | 1.389 (8) |
Mo2—O11 | 2.118 (3) | C8—C12 | 1.379 (8) |
Mo2—O11i | 2.374 (4) | C9—C10 | 1.369 (8) |
Mo3—O7 | 1.687 (4) | C9—H9A | 0.9300 |
Mo3—O2 | 1.689 (4) | C10—N3 | 1.327 (9) |
Mo3—O9 | 1.909 (4) | C10—H10A | 0.9300 |
Mo3—O10i | 2.018 (4) | C11—N3 | 1.321 (9) |
Mo3—O11i | 2.333 (4) | C11—C12 | 1.378 (9) |
Mo3—O12 | 2.360 (4) | C11—H11A | 0.9300 |
Mo4—O13 | 1.705 (6) | C12—H12A | 0.9300 |
Mo4—O1 | 1.698 (5) | N1—H1A | 0.8600 |
Mo4—O9 | 1.904 (4) | N2—H2B | 0.8600 |
Mo4—O6i | 1.941 (4) | N3—H3B | 0.8600 |
Mo4—O8 | 2.253 (4) | O6—Mo4i | 1.941 (4) |
Mo4—O11i | 2.492 (3) | O10—Mo3i | 2.018 (4) |
C1—C2 | 1.391 (8) | O10—Mo1i | 2.338 (4) |
C1—N1 | 1.392 (8) | O11—Mo3i | 2.333 (4) |
C1—C6 | 1.385 (9) | O11—Mo2i | 2.374 (4) |
C2—C3 | 1.366 (11) | O11—Mo4i | 2.492 (3) |
C2—H2A | 0.9300 | | |
| | | |
O3—Mo1—O4 | 105.4 (2) | O1—Mo4—O11i | 160.5 (3) |
O3—Mo1—O6 | 101.4 (2) | O9—Mo4—O11i | 73.86 (14) |
O4—Mo1—O6 | 101.7 (2) | O6i—Mo4—O11i | 73.17 (14) |
O3—Mo1—O12 | 99.75 (18) | O8—Mo4—O11i | 70.24 (12) |
O4—Mo1—O12 | 97.34 (19) | C2—C1—N1 | 132.5 (7) |
O6—Mo1—O12 | 146.48 (16) | C2—C1—C6 | 121.6 (6) |
O3—Mo1—O11 | 160.13 (18) | N1—C1—C6 | 105.9 (5) |
O4—Mo1—O11 | 94.02 (18) | C3—C2—C1 | 116.1 (7) |
O6—Mo1—O11 | 78.21 (15) | C3—C2—H2A | 122.0 |
O12—Mo1—O11 | 73.15 (14) | C1—C2—H2A | 122.0 |
O3—Mo1—O10i | 87.94 (18) | C2—C3—C4 | 122.4 (6) |
O4—Mo1—O10i | 164.61 (18) | C2—C3—H3A | 118.8 |
O6—Mo1—O10i | 82.65 (16) | C4—C3—H3A | 118.8 |
O12—Mo1—O10i | 72.41 (14) | C5—C4—C3 | 121.9 (7) |
O11—Mo1—O10i | 72.26 (12) | C5—C4—H4A | 119.0 |
O3—Mo1—Mo2 | 134.71 (15) | C3—C4—H4A | 119.0 |
O4—Mo1—Mo2 | 85.07 (15) | C4—C5—C6 | 116.3 (7) |
O6—Mo1—Mo2 | 119.78 (12) | C4—C5—H5A | 121.8 |
O12—Mo1—Mo2 | 35.01 (10) | C6—C5—H5A | 121.8 |
O11—Mo1—Mo2 | 41.57 (8) | N2—C6—C5 | 131.8 (6) |
O10i—Mo1—Mo2 | 80.01 (8) | N2—C6—C1 | 106.6 (5) |
O5—Mo2—O8 | 103.9 (2) | C5—C6—C1 | 121.6 (6) |
O5—Mo2—O12 | 102.47 (19) | N2—C7—N1 | 108.9 (5) |
O8—Mo2—O12 | 97.77 (18) | N2—C7—C8 | 124.3 (5) |
O5—Mo2—O10 | 100.64 (19) | N1—C7—C8 | 126.8 (5) |
O8—Mo2—O10 | 94.37 (17) | C9—C8—C12 | 119.3 (5) |
O12—Mo2—O10 | 150.39 (15) | C9—C8—C7 | 118.8 (5) |
O5—Mo2—O11 | 99.79 (18) | C12—C8—C7 | 122.0 (5) |
O8—Mo2—O11 | 156.21 (16) | C10—C9—C8 | 119.6 (6) |
O12—Mo2—O11 | 79.14 (14) | C10—C9—H9A | 120.2 |
O10—Mo2—O11 | 78.91 (14) | C8—C9—H9A | 120.2 |
O5—Mo2—O11i | 174.52 (18) | N3—C10—C9 | 119.3 (6) |
O8—Mo2—O11i | 81.50 (16) | N3—C10—H10A | 120.3 |
O12—Mo2—O11i | 77.57 (14) | C9—C10—H10A | 120.3 |
O10—Mo2—O11i | 77.67 (14) | N3—C11—C12 | 120.2 (6) |
O11—Mo2—O11i | 74.79 (14) | N3—C11—H11A | 119.9 |
O5—Mo2—Mo1 | 91.21 (15) | C12—C11—H11A | 119.9 |
O8—Mo2—Mo1 | 134.05 (14) | C11—C12—C8 | 118.6 (6) |
O12—Mo2—Mo1 | 36.28 (11) | C11—C12—H12A | 120.7 |
O10—Mo2—Mo1 | 125.55 (10) | C8—C12—H12A | 120.7 |
O11—Mo2—Mo1 | 46.65 (9) | C7—N1—C1 | 108.9 (5) |
O11i—Mo2—Mo1 | 85.65 (8) | C7—N1—H1A | 125.5 |
O7—Mo3—O2 | 104.8 (2) | C1—N1—H1A | 125.5 |
O7—Mo3—O9 | 101.4 (2) | C7—N2—C6 | 109.7 (5) |
O2—Mo3—O9 | 103.2 (2) | C7—N2—H2B | 125.1 |
O7—Mo3—O10i | 98.46 (19) | C6—N2—H2B | 125.1 |
O2—Mo3—O10i | 98.36 (18) | C11—N3—C10 | 123.0 (5) |
O9—Mo3—O10i | 145.67 (16) | C11—N3—H3B | 118.5 |
O7—Mo3—O11i | 93.79 (19) | C10—N3—H3B | 118.5 |
O2—Mo3—O11i | 160.66 (19) | Mo1—O6—Mo4i | 117.7 (2) |
O9—Mo3—O11i | 77.76 (15) | Mo2—O8—Mo4 | 118.03 (19) |
O10i—Mo3—O11i | 73.21 (13) | Mo4—O9—Mo3 | 117.6 (2) |
O7—Mo3—O12 | 163.35 (19) | Mo2—O10—Mo3i | 107.75 (16) |
O2—Mo3—O12 | 90.07 (19) | Mo2—O10—Mo1i | 109.73 (16) |
O9—Mo3—O12 | 81.99 (16) | Mo3i—O10—Mo1i | 103.83 (15) |
O10i—Mo3—O12 | 71.52 (13) | Mo2—O11—Mo1 | 91.78 (13) |
O11i—Mo3—O12 | 70.83 (12) | Mo2—O11—Mo3i | 92.91 (13) |
O13—Mo4—O1 | 104.4 (4) | Mo1—O11—Mo3i | 162.03 (17) |
O13—Mo4—O9 | 99.6 (2) | Mo2—O11—Mo2i | 105.21 (14) |
O1—Mo4—O9 | 103.2 (2) | Mo1—O11—Mo2i | 97.77 (13) |
O13—Mo4—O6i | 96.7 (2) | Mo3i—O11—Mo2i | 97.72 (13) |
O1—Mo4—O6i | 103.2 (2) | Mo2—O11—Mo4i | 164.61 (17) |
O9—Mo4—O6i | 144.23 (16) | Mo1—O11—Mo4i | 85.88 (11) |
O13—Mo4—O8 | 165.1 (3) | Mo3i—O11—Mo4i | 85.01 (11) |
O1—Mo4—O8 | 90.3 (3) | Mo2i—O11—Mo4i | 90.18 (11) |
O9—Mo4—O8 | 79.03 (17) | Mo2—O12—Mo1 | 108.71 (18) |
O6i—Mo4—O8 | 77.14 (17) | Mo2—O12—Mo3 | 110.94 (16) |
O13—Mo4—O11i | 95.1 (2) | Mo1—O12—Mo3 | 103.85 (15) |
Symmetry code: (i) −x, −y, −z. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1A···O13ii | 0.86 | 2.07 | 2.764 (7) | 138 |
N2—H2B···O4iii | 0.86 | 1.85 | 2.674 (7) | 160 |
N3—H3B···O10 | 0.86 | 1.95 | 2.794 (6) | 168 |
Symmetry codes: (ii) −x−1, y+1/2, −z−1/2; (iii) −x, y−1/2, −z−1/2. |