Manuele Lamarra

Riccardo Tarroni
email: riccardo.tarroni@unibo.it

Ab initio structures and quartic force fields of phosphine oxide and phosphine sulphide Molecular Physics

Keywords: ab initio computations, spectroscopic parameters, anharmonic force field, anharmonic corrections, semi-experimental equilibrium structure ab initio computations, spectroscopic parameters, anharmonic force field, anharmonic corrections, semi-experimental equilibrium structure

Phosphine oxide, OPH 3 , and phosphine sulphide, SPH 3 have been studied ab initio using various combinations of theoretical methods (MP2, CCSD, CCSD(T)) and basis sets (cc-pV(X+d)Z, cc-pCVXZ, X=T,Q). For both molecules, high-level ab-initio full-quartic force fields have been calculated, and these have been used to predict the most important spectroscopic constants for several isotopologues. For OPH 3 , the semi-experimental equilibrium geometry and harmonic frequencies have been determined, by combining the theoretically calculated anharmonic corrections to the experimentally determined ground-state rotational constants and vibrational fundamentals. It is proved that, after applying anharmonic corrections, the unusually large disagreement between the experimental geometry and any high-level theoretical approach disappears.

All the ab-initio calculations have been performed with the ACES II suite of quantum chemistry programs, Mainz-Austin-Budapest version [START_REF] Stanton | the integral packages MOLECULE[END_REF]. The ground state equilibrium geometry and harmonic frequencies have been calculated by means of different combinations of theoretical methods and basis sets. The methods we used are the second order Møller-Plesset perturbation theory (MP2) [START_REF] Møller | [END_REF], the Coupled Cluster with Single and Double excitations (CCSD) [30] and the Coupled Cluster with Single and Double excitations with triples treated perturbatively [CCSD(T)] [22]. The bases, of triple and quadruple ζ quality, were chosen among the family of Dunning's correlation consistent sets. In particular we used the cc-pV(T+d)Z, cc-pV(Q+d)Z [31] bases, with only valence electrons correlated, and the cc-pCVTZ, cc-pCVQZ [32] bases, with all electrons correlated. These combinations of methods and bases were chosen since they are most commonly used in similar studies [23]. For each combination, the harmonic frequencies and the dipole moment have been calculated at the corresponding equilibrium geometry.

The CCSD(T)/cc-pCVQZ geometry was chosen as reference geometry for the calculation of the full quartic force field. The harmonic part of the force field was obtained analytically at the same level of the geometry optimization, while the complete set of cubic and quartic force constants, in Cartesian coordinates, were obtained from the finite differences of the analytical hessians evaluated at a lower level of theory (MP2/cc-pCVTZ). Such a hybrid approach relies on the smaller effects of basis set and electron correlation with increasing the order of the force fields [33]. The Cartesian geometries used in the finite differences procedure have been generated starting from the CCSD(T)/cc-pCVQZ equilibrium geometry, by increasing and decreasing the Cartesian coordinates with a step-size of 0.006 bohr, without taking into account symmetry relationships. 30 singly displaced and 210 doubly displaced structures are needed for a five atom molecule. The numerical stability of the procedure against the step size was checked by comparing the values of the F ijkl and F klij quartic force field elements in Cartesian coordinates. The maximum absolute differences was 0.03 aJ Å-n rad -m (m + n = 4).

The transformation of force constants from cartesian to normal coordinates and the computation of the spectroscopic constants [START_REF] Papousěk | Molecular vibrational spectra[END_REF][START_REF] Califano | Vibrational States[END_REF] have been performed with the SPECTRO program [START_REF] Gaw | SPECTRO -a program for derivation of spectroscopic constants from provided quartic force fields and cubic dipole fields[END_REF], while the transformation from cartesian to internal coordinates was performed with the INTDER program [33,[START_REF]INTDER2000 is a general program developed by W.D. Allen and co-workers which performs various vibrational analyses and higher order nonlinear transformations among force field representations[END_REF][START_REF] Allen | [END_REF]. In the transformation of the Cartesian force constants to internal coordinates, the small gradient term resulting from the choice of a non-stationary reference geometry was neglected, since the CCSD(T)/cc-pCVQZ and MP2/cc-pCVTZ geometries are almost coincident, differing at most 0.6 pm for the bond lengths and 0.3 degree for the angles.

Comparison of the ab initio methods

In Table 1 and 2 we compare the geometries, the dipole moments and the harmonic frequencies of OPH 3 and SPH 3 . The comparison is made, for OPH 3 , against semi-experimental equilibrium structures and harmonic frequencies, obtained from experimental B 0 [20] and anharmonic frequencies ν [18] after applying the theoretically calculated anharmonic corrections (see below).

We can see that in general the calculated r e (PO) overestimate the semi-empirical PO bond length, with larger deviations when only valence electrons are correlated. The smallest deviation (+0.04 pm) is found at the CCSD(T)/cc-pCVQZ level, indicating that an high level of correlation treatment, including core correlation, is needed to accurately describe the PO bond.

On the other hand, the calculated r e (PH) are much less sensitive to the combination of method and basis, with both positive and negative deviations with respect to the semi-experimental value.

The largest deviation is observed for the MP2/cc-pCVQZ approach, but it is less than 1 pm. Also OPH angle show little dependence on the method/basis combination, and they always overestimate the corresponding semi-empirical value by less than 0.5 degrees.

From the comparisons described above, it emerges that the best agreement with the semiexperimental equilibrium geometry is obtained at the CCSD(T)/cc-pCVQZ level. This "a posteriori" check validates its use as reference geometry for the calculation of the full quartic anharmonic force field and consequently of the anharmonic corrections which in turn are used to obtain the semi-experimental geometry itself, as described in the next section.

For what harmonic frequencies are concerned, the performance of the various approaches is ranked by calculating the root mean square deviation (RMSD) from the semi-experimental harmonic frequencies. These have been estimated by applying anharmonic corrections (see next section) to the observed fundamental frequencies obtained from rare-gas trapping experiments [18], as no gas-phase data was available at the time of writing. The largest RMSD (33.5 cm -1 ) is obtained for MP2/cc-pCVQZ and the smallest (10.7 cm -1 ) for CCSD(T)/cc-pCVQZ. The relatively high RMSD, even for the best theoretical treatment, probably reflects some frequency shifts of the fundamentals due to the solid state environment. It is then unlikely that higher levels of theory could markedly improve the RMSD with respect to these experimental data. The accuracy of the semi-experimental harmonic frequencies presented here is then affected by the unavoidable shifts due to the trapping matrix, which can be safely assumed to be about 1% of the frequency values [39] For SPH 3 the comparison is made against the values obtained from the CCSD(T)/cc-pCVQZ calculation, since experimental data are not currently available and this latter method has proved to perform very well for OPH 3 . Most methods tend to overestimate the SP bond length, with differences ranging from -2.54 pm (QCISD/6-311++G(d,p) [16,17] to +0.99 pm (MP2/cc-pCVQZ).

As for OPH 3 , the PH bond length and SPH bond angles are comparatively more stable, with a largest deviation of +0.47 pm (MP2/cc-pCVTZ) and 0.21 degrees (CCSD(T)/cc-pV(T+d)Z),

respectively.

For what frequencies are concerned, the QCISD/6-311++G(d,p) [16,17] is particularly unsatisfactory, with a RMSD of 36.0 cm -1 and a largest deviation of +61.6 cm -1 for ω 2 . In general, all MP2 approaches provide a poor description of the harmonic frequencies, with values always overestimated with respect to the CCSD(T)/cc-pCVQZ values and RMSD ranging from 24.3 cm -1 (MP2/cc-pV(T+d)Z) to 30.6 cm -1 (MP2/cc-pCVQZ) and a maximum deviation of +47.3 cm -1

for ω 4 (MP2/cc-pCVQZ).

Anharmonic force fields

The quadratic, cubic and quartic force fields transformation from cartesian to symmetry coordinates was done by means of the INTDER program [33,[START_REF]INTDER2000 is a general program developed by W.D. Allen and co-workers which performs various vibrational analyses and higher order nonlinear transformations among force field representations[END_REF][START_REF] Allen | [END_REF]. The definition of the symmetry coordinates is reported in Table 3. These are the same as in Ref. [5], but are reported also here for completeness.

The definition of the internal coordinates is also shown in Figure 1.

The harmonic, cubic and quartic force field of OPH 3 and SPH 3 in symmetry coordinates are reported in Tables 456. These have been used to calculate fundamental frequencies, anharmonicity constants, rotational and rotation-vibration constants for most common isotopologues, in order to assist future identification and analysis of gas-phase spectra. These values are reported in Table 7, together with the latest computed and experimental values.

The application of the vibration-rotation second order perturbation theory equations [START_REF] Papousěk | Molecular vibrational spectra[END_REF][START_REF] Califano | Vibrational States[END_REF] needed in this step, has been accomplished by means of the SPECTRO [START_REF] Gaw | SPECTRO -a program for derivation of spectroscopic constants from provided quartic force fields and cubic dipole fields[END_REF] code. Fermi resonances have been taken into account following Ref. [START_REF] Califano | Vibrational States[END_REF], by removing the divergent terms from the expression of the anharmonicity constants and explicitly diagonalizing the 2×2 matrix involving the resonant states. The effect of Coriolis resonances has been accounted by properly modifying the analytical expression of the vibration-rotation constants [START_REF] Papousěk | Molecular vibrational spectra[END_REF].

The listed spectroscopic constants have been finally used to calculate the anharmonic contribution to fundamental frequencies and to rotational constants, in order to estimate semi-experimental harmonic frequencies and equilibrium rotational constants. The semi-experimental harmonic frequencies ω se i have been obtained from the experimental fundamentals ν e i using the following equations, obtained from the vibrational term value expression for symmetric tops (see e.g. [START_REF] Papousěk | Molecular vibrational spectra[END_REF]):

ω se i = ν e i -2x ii - 1 2 s =i x si - t x ti non -degenerate modes (1)
ω se i = ν e i -3x ii -g ii - 1 2 s x si - t =i x ti degenerate modes (2)
where s denotes a non-degenerate and and t a degenerate mode. The semi-experimental harmonic frequencies for OPH 3 are reported in Table 1.

Semi experimental equilibrium rotational constants B se e for OPH 3 are obtained from the experimental B e 0 [20] by applying the following expression for all available isotopologues

B se e = B e 0 + i d i 2 α B i ( 3
)
where 1. As pointed out in the previous subsection, the CCSD(T)/cc-pCVQZ geometry is almost coincident with the semi-experimental one, hence settling this molecule for the apparent disagreement between theory and experiment.

d

Conclusions

Phospine oxide and phosphine sulphide have been studied ab-initio using different combinations of theoretical methods and basis sets. Among the various possibilities, we have chosen those most widely adopted for spectroscopic studies [23], that is MP2 (bases cc-pV(T+d)Z, cc-pV(Q+d)Z, cc-pCVTZ, cc-pCVQZ), CCSD (bases cc-pV(T+d)Z, cc-pV(Q+d)Z), and CCSD(T) (bases cc-pV(T+d)Z, cc-pV(Q+d)Z, cc-pCVTZ, cc-pCVQZ). For phosphine oxide, an almost perfect agreement with respect to the semi-experimental results is obtained only by taking into account core correlation. The same agreement is guessed also for phosphine sulphide, which unfortunately is completely lacking of experimental data.

For both molecules, high-level ab-initio full-quartic force fields have been also calculated. These have been used to both predict the most important spectroscopic constants for several isotopologues and to estimate, for OPH 3 , the anharmonic corrections needed to obtain the semi-experimental equilibrium geometry and harmonic frequencies. The large disagreement between the experimental geometry and any high-level theoretical approach, as pointed out by some authors [15,20], is then completely eliminated. Work is in progress to solve an analogous problem observed for the OPH 2 Table 6: Calculated MP2/cc-pCVTZ quartic anharmonic force fields of OPH 3 and SPH 3 in symmetry coordinates, as defined in Table 3. Units are in aJ Å-n rad -m where n is the number of stretches and m the number of bendings in the definition of the force constants. For the quartic force field m + n = 4. Only force constants independent and non-zero by symmetry are reported Fermi resonances of the second type between ν 1 and ν 2 +ν 3 , and between ν 4 and ν 2 +ν 5 , taken into account. b Fermi resonance of the first type between ν 1 and 2ν 3 taken into account c Fermi resonance of the first type between ν 1 and 2ν 2 taken into account d From Ref. [18] e MP2/6-311** calculation from ref. [7]. The scaling factor of 0.943 has been removed f QCISD/6-311+G(d,p) calculation from Ref. [17] g From Ref. [6] h From Ref. [20] i Coriolis resonances between ν 2 and ν 5 , and between ν 3 and ν 5 taken into account l Coriolis resonance between ν

)/ √ 3 S 2 (K∆α 1 + K∆α 2 + K∆α 3 -∆β 1 -∆β 2 -∆β 3 )/ √ 3 + K 2 S 3 ∆R S 4a (2∆r 1 -∆r 2 -∆r 3 )/ √ 6 S 4b (∆r 2 -∆r 3 )/ √ 2 S 5a (2∆α 1 -∆α 2 -∆α 3 )/ √ 6 S 5b (∆α 2 -∆α 3 )/ √ 2 S 6a (2∆β 1 -∆β 2 -∆β 3 )/ √ 6 S 6b (∆β 2 -∆β 3 )/ √ 2 a r = r P H , R = r P X , α = (
OPH 3 SPH 3 i j k l f ijkl f ijkl 1 1

  Figure captions

Figure 1 . 3 Page

 13 Figure 1.Internal coordinates used for the definition of the symmetry coordinates of OPH 3 and SPH 3

3 and ν 5

 5 taken into account m Coriolis resonance between ν 2 and ν 5 taken into account Internal coordinates used for the definition of the symmetry coordinates of OPH3 and SPH3 102x131mm (96 x 96 DPI) Page 22 of 22 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics

  i is 1 for non-degenerate and 2 for degenerate modes. The vibrational corrections to the ground state rotational constants turned out to be 107.586, 83.738 and 97.157 MHz, for the 16 OPH 3 , 16 OPD 3 and 18 OPH 3 isotopologues, respectively. By applying these corrections to the experimental B e 0 values [20], one obtains the semi-experimental B se e : 17534.2077, 14683.5899 and 16355.8216 MHz. Finally, by fitting the symmetric top geometrical parameters to these values, by means of the STRFIT program [40], we obtained the best estimate of the experimental r e structure of OPH 3 : r e (PO) = 1.4703 Å, r e (PH) = 1.4043 Å and HPO = 116.72 o , which is also reported in Table

Table 1 :

 1 Computed equilibrium geometries, dipole moments and harmonic vibrational frequencies of OPH 3 . Bond lengths in Angstrom, bond angles in degrees, dipole moments in Debye and vibrational frequencies in cm -1

	Method	r e (PO) r e (PH) OPH µ e	ω 1	ω 2	ω 3	ω 4	ω 5	ω 6 RMSD
	MP2/6-311G** a	1.4855 1.4061 117.68 3.473 2531	1327	1203	2505	1181	893	47.1
	MP2/cc-pV(T+d)Z b	1.4785 1.4039 117.18 3.502 2503.6 1299.2 1182.5 2488.1 1165.6 867.3 27.2
	MP2/cc-pV(Q+d)Z b	1.4781 1.4027 116.86 3.628 2510.6 1283.8 1174.0 2498.0 1161.3 863.5 27.9
	MP2/cc-pCVTZ c	1.4767 1.4014 117.16 3.516 2513.0 1300.3 1182.9 2499.6 1167.2 867.3 33.2
	MP2/cc-pCVQZ c	1.4733 1.3989 116.87 3.627 2516.9 1288.6 1177.3 2505.5 1164.2 866.7 33.5
	CCSD/cc-pV(T+d)Z CCSD(T)/cc-pCVTZ c	1.4749 1.4064 117.15 3.523 2463.9 1292.0 1173.3 2448.7 1149.8 859.3 16.9
	CCSD(T)/cc-pCVQZ c	1.4707 1.4040 116.88 3.633 2469.8 1283.4 1168.1 2456.6 1145.9 860.0 10.7
	Experimental d,e	1.4703 1.4043 116.72	2472.4 1261.1 1164.9 2475.1 1140.6 864.3	-
	harmonic contribution (see text)

b 1.4707 1.4058 117.04 3.611 2480.6 1307.5 1189.0 2463.1 1160.6 872.3 23.2 CCSD/cc-pV(Q+d)Z b 1.4688 1.4046 116.75 3.726 2490.2 1298.1 1181.4 2475.1 1155.9 870.8 20.0 CCSD(T)/cc-pV(T+d)Z b 1.4767 1.4085 117.17 3.512 2455.2 1289.4 1171.9 2438.4 1147.7 858.5 20.9 CCSD(T)/cc-pV(Q+d)Z b 1.4754 1.4074 116.86 3.638 2464.6 1277.1 1163.5 2450.6 1142.5 856.0 11.1

a From Ref.

[7]

. To facilitate the comparison with the present data, the empirical scaling factor of 0.943 has been removed. A recent high level structure calculation [CCSD(T)/cc-pVQZ] is reported also in ref

[15]

b Only valence electrons correlated c All electrons correlated d Semi-experimental r e structure obtained from the experimental B 0 of Ref.

[20]

, corrected by the anharmonic contribution (see text).

e Semi-experimental harmonic frequencies obtained from the fundamentals of Ref.

[18]

, corrected by the an-

Table 2 :

 2 Computed equilibrium geometries, dipole moments and harmonic vibrational frequencies of SPH 3 . Bond lengths in angstrom, bond angles in degrees, dipole moments in debye and vibrational frequencies in cm-1

	Method	r e (PS) r e (PH)	SPH µ e	ω 1	ω 2	ω 3	ω 4	ω 5	ω 6 RMSD
	QCISD/6-311++G(d,p) a 1.9507 1.4053 117.55 -	2503	1205	641	2482	1129	742	36.0
	MP2/cc-pV(T+d)Z b	1.9258 1.4025 117.79 3.569 2501.1 1165.0 749.1 2488.6 1153.0 703.6 24.3
	MP2/cc-pV(Q+d)Z b	1.9225 1.4017 117.58 3.583 2507.6 1157.0 748.9 2496.3 1148.3 706.4 26.5
	MP2/cc-pCVTZ c	1.9220 1.4002 117.81 3.567 2509.9 1165.5 703.6 2499.3 1154.6 748.3 29.1
	MP2/cc-pCVQZ c	1.9154 1.3981 117.63 3.565 2513.2 1159.7 708.8 2502.8 1151.4 750.7 30.6
	CCSD/cc-pV(T+d)Z b	1.9336 1.4042 117.67 3.702 2479.6 1159.1 740.5 2464.8 1147.9 680.4 11.1
	CCSD/cc-pV(Q+d)Z b	1.9286 1.4032 117.44 3.737 2489.7 1151.8 743.4 2476.2 1143.7 686.2 13.8
	CCSD(T)/cc-pV(T+d)Z b 1.9363 1.4070 117.83 3.582 2453.7 1148.8 731.2 2438.6 1134.8 677.8 10.1
	CCSD(T)/cc-pV(Q+d)Z b 1.9317 1.4061 117.59 3.628 2463.3 1139.6 732.8 2449.9 1129.5 682.7	4.1
	CCSD(T)/cc-pCVTZ c	1.9330 1.4048 117.83 3.584 2462.4 1150.2 678.5 2448.9 1136.9 731.4	6.0
	CCSD(T)/cc-pCVQZ c	1.9253 1.4028 117.62 3.615 2468.2 1143.4 686.0 2455.5 1133.0 735.6	-

a Ref.

[16,17]

, EPAPS document No. E-JCPSA6-127-302742 b Only valence electrons correlated c All electrons correlated Page 14 of 22 URL: http://mc.manuscriptcentral.com/tandf/tmph

Table 3 :

 3 Definition of symmetry coordinates for OPH 3 and SPH 3 according to ref.[5]

	Coordinate Definition a
	S 1	(∆r 1 + ∆r 2 + ∆r 3

Table 4 :

 4 Calculated CCSD(T)/cc-pCVQZ harmonic force fields of OPH 3 and SPH 3 in symmetry coordinates, as defined in Table3. Units are in aJ Å-n rad -m where n is the number of stretches and m the number of bendings in the definition of the force constants. For the harmonic force field m + n = 2. Only force constants independent and non-zero by symmetry are reported. Previous theoretical values reported in ref.[5] are shown in parentheses.

	Molecular Physics

HPH) (101.16 for OPH 3 , 100.23 for SPH 3 ), β = (HPX) (116.88 for OPH 3 , 117.62 for SPH 3 ) b K = -3 sin β cos β/ sin α Page 15 of 22 URL: http://mc.manuscriptcentral.com/tandf/tmph URL: http://mc.manuscriptcentral.com/tandf/tmph

Table 5 :

 5 Calculated MP2/cc-pCVTZ cubic anharmonic force fields of OPH 3 and SPH 3 in symmetry coordinates, as defined in Table3. Units are in aJ Å-n rad -m where n is the number of stretches and m the number of bendings in the definition of the force constants. For the cubic force field m + n = 3. Only force constants which are independent and non-zero by symmetry are reported

		OPH 3	SPH 3		OPH 3 SPH 3
	i j k	f ijk	f ijk	i j k	f ijk	f ijk
	1 1 1 -10.226 -10.270
	1 1 2	-0.111	-0.115
	1 1 3	-0.143	-0.005
	1 2 2	-0.168	-0.099
	1 2 3	0.162	0.094
	1 3 3	-0.327	-0.332
	2 2 2	0.361	0.254
	2 2 3	-0.368	-0.325
	2 3 3	0.304	0.425
	3 3 3 -62.034 -23.705
	1 4 4	-9.962 -10.088
	1 4 5	0.089	0.078
	1 4 6	0.004	0.011
	1 5 5	-0.302	-0.306
	1 5 6	0.053	0.023
	1 6 6	-0.193	-0.079
	2 4 4	0.050	0.056
	2 4 5	0.139	0.142
	2 4 6	0.027	-0.031
	2 5 5	-0.507	-0.479
	2 5 6	0.089	0.077
	2 6 6	0.090	0.063

Table 7 :

 7 Calculated spectroscopic parameters of 16 OPH 3 , 16 OPD 3 , 18 OPH 3 , 18 OPD 3 , 32 SPH 3 , 32 SPD 3 , 34 SPH 3 and 34 SPD 3 . All values are in cm -1 . Experimental values are shown in parentheses, while most recent theoretical values are reported in square brackets

					OPH 3 SPH 3		OPH 3 SPH 3
				i j k l	f ijkl	f ijkl	i j k l	f ijkl	f ijkl
	1 1	24.340 24.554	2 2 4 5 -0.104 -0.095	2 5 5 6	0.227	0.181
	1 1 1 2	-0.065 -0.161	2 2 4 6	0.021 -0.035	2 5 6 6	-0.317 -0.250
	1 1 1 3	-0.063 -0.114	2 2 5 5	0.112	0.052	2 6 6 6	0.316	0.328
	1 1 2 2	-0.163 -0.145	2 2 5 6	0.012	0.003	3 4 4 4	-0.247 -0.168
	1 1 2 3	-0.002	0.077	2 2 6 6	0.115	0.035	3 4 4 5	0.068	0.079
	1 1 3 3	0.349	0.232	2 3 4 4 -0.022	0.060	3 4 4 6	-0.060 -0.103
	1 2 2 2	-0.097	0.016	2 3 4 5 -0.025 -0.025	3 4 5 5	0.025	0.021
	1 2 2 3	0.248	0.097	2 3 4 6 -0.225 -0.021	3 4 5 6	-0.058 -0.067
	1 2 3 3	-0.329 -0.238	2 3 5 5	0.135	0.121	3 4 6 6	0.341	0.147
	1 3 3 3	1.546	0.789	2 3 5 6 -0.028	0.007	3 5 5 5	-0.088 -0.016
	2 2 2 2	1.108	0.670	2 3 6 6 -0.283 -0.253	3 5 5 6	0.266	0.280
	2 2 2 3	-0.465 -0.409	3 3 4 4	0.401	0.198	3 5 6 6	-0.309 -0.306
	2 2 3 3	0.201	0.316	3 3 4 5	0.019	0.058	3 6 6 6	0.797	0.717
	2 3 3 3	-0.955 -0.292	3 3 4 6	0.707	0.545	4 4 4 4	36.972 37.200
	3 3 3 3 332.850 95.180	3 3 5 5	0.134	0.124	4 4 4 5	0.219	0.211
	1 1 4 4	24.429 24.587	3 3 5 6 -0.069 -0.024	4 4 4 6	-0.042	0.018
	1 1 4 5	0.061	0.069	3 3 6 6	0.247	0.484	4 4 5 5	-0.269 -0.301
	1 1 4 6	-0.067 -0.023	1 4 4 4 17.166 17.298	4 4 5 6	0.074	0.054
	1 1 5 5	0.018 -0.010	1 4 4 5	0.122	0.115	4 4 6 6	-0.258 -0.181
	1 1 5 6	0.032	0.030	1 4 4 6	0.021	0.042	4 5 5 5	-0.253 -0.229
	1 1 6 6	-0.127 -0.094	1 4 5 5	0.041	0.046	4 5 5 6	0.154	0.134
	1 2 4 4	-0.092 -0.155	1 4 5 6 -0.034 -0.007	4 5 6 6	-0.122 -0.057
	1 2 4 5	-0.043 -0.020	1 4 6 6 -0.045 -0.037	4 6 6 6	0.227	0.006
	1 2 4 6	0.082	0.027	1 5 5 5 -0.081 -0.095	5 5 5 5	1.376	1.241
	1 2 5 5	0.098	0.078	1 5 5 6	0.075	0.036	5 5 5 6	-0.789 -0.667
	1 2 5 6	-0.032 -0.042	1 5 6 6 -0.112 -0.071	5 5 6 6	0.804	0.638
	1 2 6 6	0.024	0.081	1 6 6 6	0.176	0.033	5 6 6 6	-1.324 -1.013
	1 3 4 4	-0.268 -0.178	2 4 4 4 -0.144 -0.196	6 6 6 6	2.224	1.686
	1 3 4 5	-0.012	0.004	2 4 4 5	0.235	0.227	4a 4a 5b 5b -0.733 -0.750
	1 3 4 6	-0.008 -0.115	2 4 4 6	0.047	0.014	4a 4a 5b 6b	0.076	0.044
	1 3 5 5	-0.009 -0.054	2 4 5 5	0.082	0.092	4a 4a 6b 6b -0.079 -0.055
	1 3 5 6	-0.091 -0.032	2 4 5 6 -0.021 -0.024	4a 5a 6b 6b -0.048 -0.031
	1 3 6 6	0.544	0.237	2 4 6 6 -0.009	0.035	4a 6a 5b 6b -0.037 -0.013
	2 2 4 4	-0.274 -0.234	2 5 5 5 -0.372 -0.431	5a 5a 6b 6b	0.553	0.440

Table 9 :

 9 Table 7 continued

		16 OPH 3	16 OPD 3	18 OPH 3	18 OPD 3	32 SPH 3	32 SPD 3	34 SPH 3	34 SPD 3
	A 0	3.51115	1.76314	3.51101	1.76311 3.60893 1.80634 3.60893 1.80634
	B 0	0.58078 (0.58128953) h (0.48699864) h (0.54233067) h 0.48647 0.54186	0.45568 0.24682 0.21725 0.23971 0.21099
	α A 1 × 10 3	34.548 [29.071] g	13.200	34.546	13.192	33.453	12.790	33.453	12.790
	α B 1 × 10 3	0.649 [0.469] g	3.846	0.576	2.952	0.075	0.243	0.070	0.231
	α A 2 × 10 3	-3.128 [-2.472] g	0.178	-6.588	0.059	-15.998	-5.385	-15.998	-5.443
	α B 2 × 10 3	2.778 i [0.122] g	2.553	2.018 i	2.313	0.288 m	0.307 m	0.279 m	0.289 m
	α A 3 × 10 3	-10.948 [-10.795] g	-5.610	-7.530	-5.503	1.343	-0.089	1.323	-0.041
	α B 3 × 10 3	1.188 i [-1.062] g	0.372 l	1.562 i	0.325 l	1.573	0.852	1.457	0.815
	α A 4 × 10 3	21.099 [16.046] g	7.657	21.114	7.659	20.069	7.286	20.069	7.286
	α B 4 × 10 3	0.665 [0.416] g	-0.801	0.583	-0.467	0.008	0.091	0.005	0.086
	α A 5 × 10 3	14.862 [13.570] g	2.509	15.040	2.839	19.885	6.730	19.887	6.735
	α B 5 × 10 3	-0.946 i [5.727] g	-1.175 l	-0.822 i	-1.003 l	-0.112 m -0.188 m -0.105 m -0.176 m
	α A 6 × 10 3	-2.331 [-5.673] g	1.689	-2.359	1.391	-9.462	-3.369	-9.432	-3.357
	α B 6 × 10 3	1.562 [1.567] g	1.384	1.402	1.222	0.367	0.405	0.380	0.392
	a


Sandra Bornand

Is Otherness Represented in Songhay-Zarma society ? A case study of the 'Tula' story

Introduction

Both in Africa and Europe, concerns about Otherness and its counterpart, Identity, have been and are -more than ever -at the heart of politics. However, although they are presented as facts, Identity and Otherness are really imaginary social constructs.

In many African societies, including the Songhay-Zarma of Niger that I will focus on here, oral literature is one of the major vehicles for dissemination of these social representations understood as "knowledge that is socially produced and shared, having a practical aim and contributing to the shaping of a common reality in a social group." (Jodelet 1989: 53, my translation). This concept of social representations requires us to take two things into account:

-On the one hand, Otherness can not be studied without considering what constitutes Identity, because as the Other speaks, so he shapes himself ; or as Sabria puts it he "shapes himself by constant evaluation of his own being, and of whether or not to be the Other." (1999: 16, my translation). -On the other hand, enunciation plays a central role in the development of self-image. "The way a speaker says things says much more about him than anything he can say about himself" (Charaudeau & Maingueneau, 2002: 238-239, following Ducrot, my translation). But beyond the development of his own image, the speaker shapes his spoken word according to the image he has of the person he is speaking to (his narratee).

Using an example from Songhay-Zarma oral literature, I will analyze how Identity and Otherness are represented in Jasare narratives (Jasares are griots who are genealogists and historians). From this, we can decipher how the perception of Songhay-Zarma identity fits into a changing world, and to draw out what group ("ethnic", "class", religious) these notions are founded on.

Thus, through the analysis of Jasare stories, we can ask the following questions:

-How is Otherness defined (and lived) in the Songhay-Zarma territory? -What forms can it take? -How is it put into words? -Are some more "Other" than others, that is to say, are there different hierarchical categories of Otherness? -Robic-Diaz states that "Shaping ones identity on a form of Otherness is the same as identifying, at least partially, with the Other, the logic being that one can not compare elements of the same 'nature '." (2005: 27, my translation). Given that what is totally Other can not be described, how does the narrator go about evoking an Otherness whose form would be a priori completely foreign?

Otherness and utterance-based linguistics

Before illustrating these theoretical considerations, I would like to clarify one point:

To designate the "Other" and describe "Difference" we must pass through the experience and awareness of self, an unavoidable egocentricity which, in turn, is the source of ethnocentricity. So Otherness and Identity form an inseparable and analytically indissociable couple. And they are obviously a couple with problems. (Deuber, Ziegler & Perret 2005: 32, my translation).

A proverb offers us an initial indication of Songhay-Zarma world-view:

No matter how long the log stays in the water, it will never become a crocodile.

1

This proverb questions notions of Identity and Otherness. It tells us that if you ever mistake a log for a crocodile, it is simply a confusion; a log remains, substantially and despite its age, a log. Likewise, a foreigner who is immersed in the lives of villagers remain different (in spite of illusions to the contrary) and will never be the same as a local person.

The proverb tells us that the passage of time has no influence on the definition that we have of ourselves and of each other. But the Jasare stories relativize this rigid conception of Otherness. Narrative analysis shows the evolution of our view of Otherness and Identity to the extent that "for a story to happen, you need a minimum sequence of events occurring in a time t and t + n" (Adam, 1992: 46). This time dimension allows the narrator to stage not only the development of the plot but also the representations he disseminates, especially those of Otherness and Identity in the case of Tula.

The story, by adding a time dimension to representations of Identity and Otherness as developed by language, allows us to deconstruct the ideological process that is at the heart of representations of Self and Others in a given society, and to dissect the linguistic mechanisms responsible for these representations and the mechanisms of appropriation and exclusion.

Case study

Tula's story, which is analyzed here, was narrated by a Jasare to the descendants of the heroine's family [on 16 December 2006]. It is a story about a girl called Tula who was sacrificed by her maternal uncle, Biyey Koy, to the spirit of the local pond in exchange for a heavy rainy season which would ensure the survival of his people. Tula is now a dangerous spirit who haunts the pond, and is liable to kill anyone approaching it who is not descended from the sisters of her mother.

If the question of perspective is essential, it will not be developed here for a question of time.

Who is the Other, who is the Same?

Through the enunciation of a genealogy presented in reverse chronological order (v. 14-36), starting with the narratee and going back in time to Askia Mohammed, the ancestor of the Mayga Muslim dynasty, the narrator defines who is truly Songhay and who is not, from his point of view and that of the narratee. Indeed, after enumerating a list of ancestors, the narrator concludes with the following:

He who is not descended from these Songhay ancestors / is not Songhay / It is not millet / [...] / This is Songhay and its boundaries (v. 37-41) He takes up the same conclusion later on

You are the gold of Songhay / He who is not descended from Mamar / Is nothing 2 This genealogy thus excludes a large number of people designated as « Songhay » by the colonial and post-colonial administrators :

-Slaves (Bannya) and descendants of slaves; -Freemen, called Burcin, who are not descended from Askia Mohammed. In this way, the narrator reduces Songhay identity to the aristocracy. -But not only so, because -and here I'm simplifying -he also excludes the descendants of the non-Muslim Songhay dynasty of Si that preceded the Mayga (Muslim) dynasty.

This exclusion is reinforced by the use of metaphors intended to confer prestige on those, says the narrator, who are the real Songhay:

-the image of millet, the staple diet indispensible to the survival of the people; -the image of gold. This is even more the case, because anyone who doesn't trace their ancestry to Askia Muhammad is utterly disparaged ("is nothing"). In this way, exclusion is reinforced by negation and disqualification. So the real Songhay is defined by his aristocratic origins that bind him to the founder of the Mayga dynasty. This exclusion of certain people who are usually considered to be "Songhay" has as its corollary their characterization as "Others" and their assimilation with other people groups mentioned in the narrative: -the Bella -the Fulani Three different people groups are straightaway mentioned as living in the Tareygorou area where the story takes place:

[Biyey Koy] used to lead the Bella / The Songhay and the Fulani 3 Two of them are immediately understood as being different from Songhay to which the chief belongs : Bella and Fulani.

The evocation of these two populations refers not only to local realities [since the Bella and Fulani live in this region], but also to opposing stereotypes and ethnotypes:

-The first are the Tuareg slaves who dominated the region in the nineteenth century. They are seen as "the most despised of ethnic groups or social categories, and are victims of all the racist ethnotypes (thieves, filth, liars, savages...)" (Olivier de Sardan 1982: 65, my translation). They are represented as sub-humans, with the behavior of slaves. But they also inspire fear, because they used to abduct women and children who were isolated in the bush and sell them. -The Fulani are considered better : they are, most often, respected and admired, because they are viewed as being "more" noble than anyone else. But sometimes they are also ridiculed because of their reputation for being deceitful and their different lifestyle : like the Bella, they are nomadic shepherds,4 whereas the Songhay are settled farmers.

But whether Bella or Fulani, in this instance there is no difference, for all are characterised by their submission to Biyey Koy. The only elements that vary are what is conveyed implicitly by the evocation of stereotypes, and the fact that even the "most noble" are under the orders of the Songhay chief which can only enhance his status. By restricting their role to that of being subjugated, the narrator denies them their ethnic identity as it were, and more or less equates them with other social groups that depend on chiefdom.

The reference to the Songhay people is surprising for two reasons. First, the term "Songhay" is rarely used in popular language, which refers more often to subgroups (Kado, Wogo, etc.). This generic term is usually employed exogenously, by the colonial administration or in scientific literature. So the narrator's use of the term "Songhay" has strong connotations and expresses his willingness to highlight the dominance of Biyey Koy not only over a single sub-group, but over the entire Songhay population. Secondly, the Songhay are first and foremost the people from whom Biyey Koy came, and to see his name inserted between the words "Bella" and "Fulani" is surprising. From a linguistic point of view, he is put on the same level as the two "ethnic" groups (which is confirmed by the use of the coordinating conjunction nda "and"), positioning him as an Other rather than as an Identity. This is in contrast to Biyey Koy, who is no longer considered to be a simple Songhay, but a Mayga. 5 The kind of Otherness defined here is not really that of people groups, but that which exists between a dominant group and the peoples who are subjugated to it.

This interpretation is confirmed further on too, when the narrator presents Songhay (here referred to as Kaado6 ) and Bella on an equal footing, because Biyey Koy sacrifices the same number of each to the spirit in the version told out of context],7 he also mentions the same number of Fulani):

He told her he would offer / Ten Bella-s to redeem his people He told her he would offer / Ten Kaado-s to redeem his people 8

The term kaado comes from Fulani and means "foreign, pagan." It refers not only to slaves and to groups of diverse backgrounds who have assimilated to the Songhay people over the years, but also to the ruling aristocracy (composed of Mayga or Si descendants). The comparison to the Bellaslaves of the Tuareg -suggests that we are dealing here with "common people".

In this way, the Songhay populations really are perceived as "Others", just like the Fulani and the Bella, because of their common exclusion from power. So initial representations of Otherness are presented here in terms of exclusion from political power and relationships between the dominant and the dominated. So-called "ethnic Otherness" is therefore reduced to "class Otherness."

Along with this deconstruction of the "Songhay ethnic group", there is the shaping of a new Songhay identity, that of the Mayga aristocracy:

-First, the story is intended for the Mayga aristocratic lineage, dating back to the sixteenth century. Their power, as we have seen, holds sway in Songhay territory.

7

-Secondly, he assigns a double religious identity to this dynasty. Two superimposed religious features characterize this lineage: the reference to Askia Mohammed, his ancestor, identifies him with Islam, since the Mayga dynasty is Muslim. But at the same time it implies a special relationship with the water spirits: the story of Askia Mohammed that follows the story of Tula in the narrative studied here reminds us that Askia Muhammad's father is a water djinn 9 who gave him powers so that he could topple the chief, his maternal uncle Sonni Ali Ber. The eulogy also designates the Mayga as "chief of the magician-crocodiles" and "guardian of the fetish.

10 " 11 The term kaara koy comes from the association of the name kaara (a Songhay subgroup closely associated with water, belonging to the Kaado, and whose origin is probably kaare, "crocodile") and the suffix -koy designating "one who possesses." We can state two hypotheses regarding the origin of the cult of Tula, the young girl who became a spirit. The first places it in the continuity of the primeval ties that bind Mayga and the water spirit. The second defines it as the Songhay's continuation of ancient Gourmantche 12 cults. This refers to the double origin of the Kaado: Gourmantche and Songhay, Muslim (for the Askia dynasty) and pre-Islamic. The term kanga koy, for its part, comes from the association of the verb kanji (infinitive kanjiyaη "to fix, to drive into the ground") and the suffix -koy. It recalls the fact that a stake planted in the ground [kangari: "what is planted"] was, before modern-day Islamicisation, the "object used for magical and propitiatory practices" (Olivier de Sardan 1982: 249, my translation). So we find, in the eulogy directed both to the narratee and to Biyey Koy (his ancestor), a link to the fetishes and the water spirit. This contributes to the shaping of their identity as a "mythical" aristocracy, linked to supernatural powers, and therefore increasing their prestige.

9 A Muslim spirit refering back to a pre-Islamic practice.

10 A "fetish" or "idol" is an object or a place "where supernatural forces dwell (spirits, ancestors…), and to whom one addresses prayers and sacrifices" (de Sardan 1982 : 358, my translation).

11 Mayga Kaara koy kanga koy.

12 According to de [START_REF] Olivier De Sardan | Concepts et conceptions songhay-zarma[END_REF], the cult of the crocodile-spirit or the snake-spirit is probably of Gourmanche origin.

What about gender Otherness?

In this story, the sister and the mother are defined as being close to Biyey Koy and since they are related, they are the Same.

The status of Tula, the principal female in the story, on the other hand, is more ambiguous: it is presented to us as being half-way between the Same and the absolutely Other. The Tula story tells us about the transformation of the eponymous character, defined as the nearest possible relationship (the chief's preferred uterine niece) to the absolutely Other (a spirit living in the pond in the guise of a serpent), giving an interesting perspective on the relationship between Identity and Otherness. In this case, the Other stems from the close relationship, as if an irreducible proximity still existed in the absolutely Other. It is this process of transformation that I will attempt to explain here. We will see how it is shown as an (admittedly radical) metaphor for a young girl's change of status when she marries: as daughter of the family, she becomes a stranger to it when she leaves the parental home.

Metamorphosis is a component of her Otherness. Tula, having become a spirit, in effect changes into a woman whose incredible beauty is henceforth simply a lure to attract her victims. Yet -so the story tells us -"In the rainy season she becomes a white water lily"

13 whose properties are metaphorically those of the Tula spirit: both live in still waters (ponds, backwaters, etc..), and both show their loveliest apparel on the surface: the water-lily's flowers, and Tula's long hair (in the out-of-context version) and breasts.

Tula's metamorphosis, in addition to being an enticement, demonstrates the elusiveness of her being. We might also wonder whether this inability to grasp her form, and therefore to describe it, is not the only way to evoke her as absolutely Other. How can we describe that for which there are no words?

The part of her that appears on the surface of the water is presented as being identical to the human body (with the use of terms such as headsometimes with hair -arms, breasts). But the story does not describe what is below,14 as if it lacked words to express this Otherness. The silence of the narrative on this subject is closer to that of Tula herself, and seems to emphasis that absolute Otherness manifests itself primarily by the inability to say or be said.

As the uterine niece, Tula is the blood relative to whom Biyey Koy is most attached. Presented first as a passive object, she only becomes a proactive subject (witness the verbs used: to want, to be able to, to do) once recognized by her mother, that is once she accepts her Otherness: having been offered to the spirit, she has become different from her mother. The origin of this differentiation refers to the bonds of alliance, an alliance symbolized here by the uncle's negotiation with the spirit. To truly become a proactive subject, Tula must be distinguished from her nearest and dearest, that is her mother and her maternal uncle.

Yet this process of distancing and individualization brings Tula close to the process that every bride experiences. In a patrivirilocal society, the wife leaves her parent's home to join her husband and her settling into this new family makes her in some way a stranger to her own blood family.

So women, because of their potential as wives, are Other ; and this Otherness is manifested in the misfortunes for which she is responsible. Do not the Songhay-Zarma say that behind the fall of every hero there is always a woman? The Other does not reveal herself through words, but appears veiled, manifesting herself through the evils she causes. Is it not the spirit who is responsible when a drought ravages the region? Is it not the spirit who (through a stranger, an old Gourmantche man) demands that Biyey Koy sacrifices the person who is dearest to him in the world? And finally, is not Tula, once sacrificed, who is responsible for the numerous drownings that happen in Tareygorou pool, and in other pools elsewhere? ( 5'?)

Conclusion

At a time when Songhay-Zarma society and [the whole country of] Niger are rapidly changing under the constant pressures of Islam and the West, the Jasare reminds the audience -through his story -what he claims are the "real" values of Songhay society. So we witness a redefining of Songhay identity by the spokesman of a once totally dominant ideology, that of the aristocracy. This has two consequences:

-First, it excludes a whole segment of society that the colonial and postcolonial administrators define as "Songhay". -Secondly, it highlights the predominance of the social over what might be called the "ethnic". -Third, From the perspective of gender relations, narrator and narratee join and offer a full representation of women as "Other" and therefore dangerous. These representations are not really different from those of modern power and are not necessarily in conflict with them, The analysis of enunciation devices in the Tula narrative lets us examine the relationship between Identity and Otherness and how the narrative forms particular images of it. It also shows that one is faced with a vivid, dynamic relationship between Self and Other, the "we", symbol of social identity, bringing the narrator sometimes towards or sometimes away from the narratee. We note that this conception of Otherness as a dynamic and moving category is also seen in the recurring image of metamorphosis.

  [Taking into account the enunciative dimension of oral literature narratives, this analysis makes it possible to highlight the process of shaping the relationship between Identity and Otherness and the discursive strategies and processes established by the enunciators in defense of their different points of view.] Bibliography Adam, Jean-Michel 1992: Les Textes : types et prototypes. Récit, description, argumentation, explication et dialogue ; Paris, Nathan. Adam, Jean-Michel 1999: Linguistique textuelle. Des genres de discours aux textes ; Paris, Nathan. Badjé, Djéliba, 1998 and 2006: Le récit de Toula. Benveniste, Emile 1974: Problèmes de linguistique générale II ; Paris, Gallimard. Bornand, Sandra 2002: « Images de soi : le griot zarma (Niger) tel qu'il se représente dans les récits qu'il raconte aux nobles » in Aktuelle Forschungen zu afrikanischen Sprachen; Köln, Koeppe, p.275-289. Bornand, Sandra 2005: Le discours du griot généalogiste chez les Zarma du Niger ; Paris, Karthala.

Ba bundu ga gay hari ra a si bare ga te kaaray.

Araη ga ti Soηay wura / Bora kaη mana fun Maamar ga / Bora manti hari kulu (v.

[332][333][334] 3 Nga no ga Balley / Da Soηey da Fulaηey kulu dabari(v. 57-58)

Even though many Fulani have been sedentary for a long time, the stereotype of the Fuluni nomad is still very real in Songhay-Zarma territory.

A true Songhay as the narrator says in verses 37-41.

This term, more restrictive than "Songhay", designates a sub-group, but the narrator's earlier reference to "Songhay" leads the listener to continue the synecdoche.

See also Hamidou Yayé's account of the story of his ancestors.

A ne a se to nga ga no / Kaado way ga nga laabo fansa(v. 101-102)

. Kaydiya mo bolooli no a ga te (v. 301). Bolooli : nymphea lotus, white water lily or nymphea alba, pond lily.

It could be that what is hidden is a metaphor for taboo: the part of Tula's body that should not be shown in public because of its sexual connotations (breasts are not associated with sex in Songhai-Zarma society).