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Electronic structure calculations and X-ray emission spectra of some metal phosphides
Solid State Communications, Vol. 83, No. 6, pp. 447-450, 1992. Printed in Great Britain.
0038-1098/92 $5.00 + .00 Pergamon Press Ltd
ELECTRONIC STRUCTURE CALCULATIONS AND X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES P. Alemany and S. Alvarez* Departament de Quimica Inorgfinica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
(Received 11 November 1991; in final form 13 April 1992 by P.H. Dederichs) The contribution of different atomic orbitals to the density of states (DOS) of CdP 4 and CUP2, calculated with the Extended Hiickel Tight Binding approximation, are compared to the previously known X-ray emission spectra. The calculated data are in good qualitative agreement with the spectra in (a) the composition of the levels near the Fermi energy, (b) the number of bands in each spectrum, (c) the relative positions of the bands in the different emission spectra of the same compound, and (d) their relative intensities. It is found that the phosphorus 3s spectra of compounds with isolated phosphide ions (p3-) must present a single band, whereas, in those with p4- pairs, (P-)o~ chains or phosphorus layers the 3s band is split in two components. THE USE of a basis of atomic orbitals for electronic band structure calculations, allows simple population analysis from which one can plot out the contributions of different atomic orbitals to the total density of states (DOS) [1, 2]. On the other hand, the X-ray emission spectra provide the energies and densities of the states associated with a particular set of atomic orbitals, relative to that of an inner core level [2-4]. However, comparison of the theoretical results at the semiempirical extended Hfickel level and experimental spectra is not common, and we found it was worthwhile exploring the degree of agreement between theory and experiment for several metal phosphides. We have recently reported band electronic structure calculations of the extended Hiickel type for several metal phosphides [5], from which we will here comment only on the DOS curves. The calculated DOS of CdP4 and the contributions of several atomic orbitals are shown in Fig. 1 (left). For comparison, schematic representations of the X-ray emission spectra reported by Domashevskaya et al. [6, 7] are presented side by side with the DOS contributions after some adjustments: (i) the original energy scales of the spectra have been inverted, since the largest energy of the emitted radiation corresponds to the Fermi level (relative zero of energy); (ii) the beginning of the spectral band is matched with the highest occupied band level in the DOS curve. In Fig. 1(a) is represented the Lfl2,15 spectrum of Cd in CdP4, which corresponds to emissions
produced after ionization of a cadmium 2p electron. According to the selection rule ( A I = 4-1), only emissions from s or d levels may appear in such a spectrum. An intense peak is assigned to the 4d levels [6], and the tail at higher energies assigned to the 5s ones. The structure present in that tail has its correspondence in the calculated DOS contribution. The contribution of the 4d orbitals is not shown because these orbitals were not included as valence orbitals of Cd in our calculations. The phosphorus L2,3 spectrum (Fig. lb) corresponds to the phosphorus 3p orbitals. The large contribution of these atomic orbitals near the Fermi level found in the DOS is confirmed by the spectrum, which also shows some structure and a low intensity tail at lower energies. The phosphorus K~ spectrum (Fig. lc) corresponds to the 3s levels of phosphorus. It is more intense at lower energies, showing a split band (A and A'), with a less intense band at higher energy, in good qualitative agreement with the appropriate projection of the DOS. The K~(P) and L2,3(P) spectra [7-9] of CuP2 (Fig. 2) and AgP 2 (not shown but very similar to those of CUP2) are analogous to those of CdP4 (Fig. 1), with minor differences probably due to the different interactions with the metal atoms, while important differences are evident in the metal contributions. This fact could be expected given that the 2D phosphorus networks of CdP4 and CuP2 are essentially identical. The Ka spectrum (P 3p orbitals) of CuP2 shows less structure than for CdP4, with two
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Fig. 1. Left: Density of states diagrams for CdP4, showing the contributions of the Cd 5s (a), phosphorus 3p (b), and phosphorus 3s orbitals (c). Right: Schematic representations of the cadmium L#215 (a), phosphorus K# (b), and phosphorus L2,3 (c)'X-ray emission spectrum [6], referred to the same energy scale.
Fig. 2. Density of states diagrams for CuP 2 (left), showing the contributions of all the Cu atomic orbitals (a), phosphorus 3p (b), and phosphorus 3s orbitals (c). Schematic representations of the copper L~ (a), phosphorus K# (b), and phosphorus L2,3 (c) X-ray emission spectra [7] (right), referred to the same energy scale.
peaks (B and/iv in Fig. 2b) and a shoulder, in good agreement with the calculated phosphorus 3p contributions. In both the phosphorus 3s DOS and the L2,3 spectrum (Fig. 2c), the phosphorus 3s band is split in two components (A and A') in the same way as found for CdP4. Finally, both the copper 3d contribution to the DOS and the Cu-L~ spectrum (Fig. 2a) correspond to the highest occupied levels and show similar structures. In summary, the emission spectra of CdP4 compare well with the calculated contributions to the DOS in their main qualitative aspects: (i) the number of peaks, (ii) their approximate energies relative to the Fermi level, and (iii) their relative intensities. A feature common to these compounds is the
splitting of the low energy band (A, A' in Figs. lc and 2c) of the phosphorus 3s levels, neatly reproduced by the calculations. This splitting has also been found in the P-K# spectrum of elemental phosphorus [7] and phosphides of cadmium and zinc [6-10]. The analysis of the wavefunctions corresponding to such bands should allow us to rationalize the splitting and may help in establishing some rule for the interpretation of analogous spectra. The splitting in the emission spectra has been often attributed to the formation of P - P bonds. Let us consider a P2 pair. The 3s orbitals form combinations Crg and n (Fig. 3) at -22.0 and -17.0eV, respectively, at the extended HiJckel level
Vol. 83, No. 6
X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES
Fig. 3. Bonding (ag) and non-bonding (n) combinations of the phosphorus 3s orbitals in a P2 unit. with P-P = 2.3 A. Hence the bands formed from crg and n in a crystal with P2 pairs should be approximately centered at -22 and - 17 eV. Furthermore, the low energy band should have P - P bonding character and the upper one should be P - P nonbonding [11]. In contrast, the analysis of the COOP curves of CdP 4 and CuP2 (not shown here) tells that both bands, centered at -24.5 and -21.0eV, have a clear P - P bonding character. We must go one step further and consider the formation of phosphorus chains (P-)o~. ZnP2 (tetragonal modification) and CdP2, having such chains [6-10], present the same splitting in their P-K# spectra. Let us recall that the phosphorus layers in CdP4 and CuP2 are formed by the fusion of parallel helical chains. It is then reasonable to explore the behaviour of the DOS curves of such (P-)~ chains. Different chain structures [12, 13] are shown in (Fig. 4). Structure a in Fig. 4 is found in SrP2, BaP2 and EuP2; structure b appears in LiP, NaP, KP, ZnP 2 (tetragonal form) and CdP2, and e in GdPS. DOS and COOP calculations for the three structures shown in Fig. 4 present a split band centered approximately at -24 and -21 eV, both with P - P bonding character. The fact that there are four P atoms per unit cell in the chains gives rise to two bands built up from the orbitals shown in Fig. 5. In summary, a single P-3s band should be expected for compounds with isolated p3- ions [12, 14], as found in the spectra [9, 10] of TiP, GaP or Cu3P. For compounds with p4- pairs, the band is split and the two components appear at ca. -17 and
Fig. 5. Combinations of the phosphorus 3s orbitals contributing to the lowest P - P bonding bands of the (P-)o~ chains in structure e (Fig. 4). eV, whereas, for compounds with (P-)~ chains or phosphorus layers the two components appear at lower energies (ca. -21 and -24 eV), as found [6-10] for chains of the type b present in the structures [13c, d] of ZnP2 and CdP2 or in the layers [15] of CdP 4 and CUP2. The bands at -21 and -24eV are P-P bonding, hence its position may allow comparisons of the P - P bond strength among different compounds with related structures. Acknowledgements - Financial support f o r this research work was generously given by DGICYT through grant PB89-0268. The authors thank F. Vilardell for the drawings and a referee for his suggestions. P. Alemany thanks the Ministerio de Educaci6n y Ciencia for a fellowship of the Plan Nacional de Nuevos Materials. REFERENCES 1. 2. 3. 4. 5.
6.
7.
8. a
b
c
Fig. 4. Different conformations of (P-)~ chains found in the experimental structures.
449
9.
See, e..g., R. Hoffmann, Solids and Surfaces. A Chemist's View of Bonding in Extended Structures. VCH Publishers, New York (1988). P.A. Cox, The Electronic Structure and Chemistry of Solids, Oxford University Press, Oxford (1987). P. Day (Editor), Emission and Scattering Techniques, D. Reidel, Dordrecht (1981). F.J. Berry & D.J. Vaughan, Chemical Bonding and Spectroscopy in Mineral Chemistry, Chapman and Hall, London (1985). VP4: S. Alvarez, J. Fontcuberta & M.-H. Whangbo, Inorg. Chem. 27, 2702 (1988); CUP2: P. Alemany & S. Alvarez, Inorg. Chem. 31, 119 (1992); CdP4, RuP4: P. Alemany, Tesi Doctoral, Universitat de Barcelona (1991). E.P. Domashevskaya, V.A. Terekhov & L.N. Marshakova, Fiz. Tverd. Tela (Leningrad) 20, 2675 (1978); Soy. Phys. Solid State 20, 1545 (1978). E.P. Domashevskaya, V.A. Terekhov, L.N. Marshakova, Y.A. Ugai, Izv. Akad. Nauk. SSSR, Set. Fiz. 38, 567 (1974); Bull. Acad. Sci. USSR, Phys. Set. 38, 119 (1974). E.P. Domashevskaya, V.I.Nefedov, Y.V. Salyn, N.P. Sergushin, V.A. Terekhov, L.N. Marshakova & Y.A. Ugai, Izv. Akad. Nauk. SSSR, Ser. Fiz. 4t), 389(1976); Bull. Acad. Sci. USSR, Phys. Set. 40, 145 (1976). E.P. Domashevskaya, V.A. Terekhov, Y.A. Ugai, V.I. Nefedov, N.P. Sergushin & G.N.
450
10. 11. 12. 13.
14.
15.
16. 17.
X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES Dolenko, Fiz. Tverd. Tela (Leningrad) 19, 3610 (1977); Sov. Phys. Solid State 19, 2109 (1977). V.I. Nefedov, Y.V. Salyn, E.P. Domashevskaya, Y.A. Ugai & V.A. Terekhov, J. Electron Spectrosc. Rel. Phenom. 6, 231 (1975). For a more detailed theoretical study of compounds with p4- groups see: R. Hoffmann & C. Zheng, J. Phys. Chem. 89, 4175 (1985). H.-G. von Schnering & W. H6nle, Chem. Rev. 88, 243 (1988). (a) LiP: W. H6nle & H.-G. von Schnering, Z. Krist. 155, 307 (1981); (b) NaP, KP: H.-G. von Schnering & W. H6nle, Z. Anorg. Allgem. Chem. 456, 194 (1979); (c) ZnP2: tetragonal modification, J.G. White, Acta Cryst. 18, 217 (1965); monoclinic form, M.E. Fleet & Th.A. Mowles, Acta Cryst. Sect. C C40, 1778 (1984); (d) CdP2: J. Goodyear & G.A. Steigmann, Acta Cryst. Sect B B25, 2371 (1969); O. Olofsson & J. Gullman, Acta Cryst. Sect. B B26, 1883 (1970)); J. Horn, Bull. Acad. Polon. Sci. 17, 69 (1969); (e) GdPS: F. Hulliger, R, Schmelczer & D. Swarzenbach, J. Solid State Chem. 21, 371 (1977). (a) GaP: A. Addamiano, Acta Cryst. Sect. 13, 505 (1960); (b) CuaP: H. Schlenger, H. Jacobs & R. Juza, Z. Anorg. Allgem. Chem. 385, 177 (1971). (a) CUP2: O. Olofsson, Acta Chem. Scand. 19, 299 (1965); M.H. M611er & W. Jeitschko, Z. Anorg. Allgem. Chem. 491, 225 (1982); (b) CdP4: H. Krebs, K.H. Miiller & G. Ziirn, Z. Anorg. Allgem. Chem. 285, 15 (1956). R. Hoffmann, J. Chem. Phys. 39, 1397 (1963); R. Hoffmann & W.N. Lipscomb, J. Chem. Phys. 36, 2179, 2872, 3489 (1962). M.H. Whangbo & R. Hoffmann, J. Am. Chem. Soc. 100, 6093 (1978).
18. 19. 20. 21. 22.
23.
Voi. 83, No. 6
M.H. Whangbo, R. Hoffmann & R.B. Woodward, Proc. Roy. Soc. London, Set. A 366, 23 (1979). J.H. Ammeter, H.-B. Bfirgi, J.C. Thibeault & R. Hoffmann, J. Am. Chem. Soc. 100, 3686 (1978). R. Ramirez & M.C. B6hm, Int. J. Quantum Chem. 34, 571 (1988); 30, 391 (1986). P.J. Hay, J.C. Thibeault & R. Hoffmann, J. Am. Chem. Soc. 97, 4884 (1975). R. Munita & J.R. Letelier, Theoret. Chim. Acta (Berl.) 58, 167 (1981); E. Clementi & C. Roetti, Atomic Data Nucl. Data Tables 14, 454 (1974). R.H. Summerville & R. Hoffmann, J. Am. Chem. Soc. 98, 7240 (1976).
APPENDIX: COMPUTATIONAL DETAILS The qualitative theoretical discussions in this paper are based on molecular orbital [16] and tight-binding band calculations [17, 18] of the extended Hfickel type with a modified Wolfsberg-Helmholz formula [19], using the atomic parameters shown in Table 1. Experimental structural data was used for CuP2 and CdP4. In calculations for phosphide chains all P - P bond distances were taken as 2.3 A, bond angles as 120°, and torsion angles of 0, 120 and 120 (Fig. 4, a), 60, 60 and 60 (Fig. 4, b) and 0 and 180 (Fig. 4, c) degrees. DOS and COOP diagrams were obtained by averaging throughout the Brillouin zone using a set of 48 k-points chosen according to the geometrical method of Ramirez and B6hm [20].
Table 1. Atomic parameters for extended Hfickel calculations. Hii's are the orbital ionization energies, 6ij the Slater exponents and cj the coefficients in the double-( expansion of the d orbitals
Atom
Orbital
Hii
~il
Cu
4s 4p 3d 5s 5p 3s 3p
- 11.40 -6.06 - 14.00 - 11.80 -8.20 - 18.60 - 14.00
2.20 2.20 5.95 1.64 1.60 1.75 1.30
Cd P
(cl)
~i2
(c2)
Reference [21]
(0.5933)
2.30
(0.5744) [22] [23]
0038-1098/92 $5.00 + .00 Pergamon Press Ltd
ELECTRONIC STRUCTURE CALCULATIONS AND X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES P. Alemany and S. Alvarez* Departament de Quimica Inorgfinica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
(Received 11 November 1991; in final form 13 April 1992 by P.H. Dederichs) The contribution of different atomic orbitals to the density of states (DOS) of CdP 4 and CUP2, calculated with the Extended Hiickel Tight Binding approximation, are compared to the previously known X-ray emission spectra. The calculated data are in good qualitative agreement with the spectra in (a) the composition of the levels near the Fermi energy, (b) the number of bands in each spectrum, (c) the relative positions of the bands in the different emission spectra of the same compound, and (d) their relative intensities. It is found that the phosphorus 3s spectra of compounds with isolated phosphide ions (p3-) must present a single band, whereas, in those with p4- pairs, (P-)o~ chains or phosphorus layers the 3s band is split in two components. THE USE of a basis of atomic orbitals for electronic band structure calculations, allows simple population analysis from which one can plot out the contributions of different atomic orbitals to the total density of states (DOS) [1, 2]. On the other hand, the X-ray emission spectra provide the energies and densities of the states associated with a particular set of atomic orbitals, relative to that of an inner core level [2-4]. However, comparison of the theoretical results at the semiempirical extended Hfickel level and experimental spectra is not common, and we found it was worthwhile exploring the degree of agreement between theory and experiment for several metal phosphides. We have recently reported band electronic structure calculations of the extended Hiickel type for several metal phosphides [5], from which we will here comment only on the DOS curves. The calculated DOS of CdP4 and the contributions of several atomic orbitals are shown in Fig. 1 (left). For comparison, schematic representations of the X-ray emission spectra reported by Domashevskaya et al. [6, 7] are presented side by side with the DOS contributions after some adjustments: (i) the original energy scales of the spectra have been inverted, since the largest energy of the emitted radiation corresponds to the Fermi level (relative zero of energy); (ii) the beginning of the spectral band is matched with the highest occupied band level in the DOS curve. In Fig. 1(a) is represented the Lfl2,15 spectrum of Cd in CdP4, which corresponds to emissions
produced after ionization of a cadmium 2p electron. According to the selection rule ( A I = 4-1), only emissions from s or d levels may appear in such a spectrum. An intense peak is assigned to the 4d levels [6], and the tail at higher energies assigned to the 5s ones. The structure present in that tail has its correspondence in the calculated DOS contribution. The contribution of the 4d orbitals is not shown because these orbitals were not included as valence orbitals of Cd in our calculations. The phosphorus L2,3 spectrum (Fig. lb) corresponds to the phosphorus 3p orbitals. The large contribution of these atomic orbitals near the Fermi level found in the DOS is confirmed by the spectrum, which also shows some structure and a low intensity tail at lower energies. The phosphorus K~ spectrum (Fig. lc) corresponds to the 3s levels of phosphorus. It is more intense at lower energies, showing a split band (A and A'), with a less intense band at higher energy, in good qualitative agreement with the appropriate projection of the DOS. The K~(P) and L2,3(P) spectra [7-9] of CuP2 (Fig. 2) and AgP 2 (not shown but very similar to those of CUP2) are analogous to those of CdP4 (Fig. 1), with minor differences probably due to the different interactions with the metal atoms, while important differences are evident in the metal contributions. This fact could be expected given that the 2D phosphorus networks of CdP4 and CuP2 are essentially identical. The Ka spectrum (P 3p orbitals) of CuP2 shows less structure than for CdP4, with two
447
448
X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES Spectrum
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Fig. 1. Left: Density of states diagrams for CdP4, showing the contributions of the Cd 5s (a), phosphorus 3p (b), and phosphorus 3s orbitals (c). Right: Schematic representations of the cadmium L#215 (a), phosphorus K# (b), and phosphorus L2,3 (c)'X-ray emission spectrum [6], referred to the same energy scale.
Fig. 2. Density of states diagrams for CuP 2 (left), showing the contributions of all the Cu atomic orbitals (a), phosphorus 3p (b), and phosphorus 3s orbitals (c). Schematic representations of the copper L~ (a), phosphorus K# (b), and phosphorus L2,3 (c) X-ray emission spectra [7] (right), referred to the same energy scale.
peaks (B and/iv in Fig. 2b) and a shoulder, in good agreement with the calculated phosphorus 3p contributions. In both the phosphorus 3s DOS and the L2,3 spectrum (Fig. 2c), the phosphorus 3s band is split in two components (A and A') in the same way as found for CdP4. Finally, both the copper 3d contribution to the DOS and the Cu-L~ spectrum (Fig. 2a) correspond to the highest occupied levels and show similar structures. In summary, the emission spectra of CdP4 compare well with the calculated contributions to the DOS in their main qualitative aspects: (i) the number of peaks, (ii) their approximate energies relative to the Fermi level, and (iii) their relative intensities. A feature common to these compounds is the
splitting of the low energy band (A, A' in Figs. lc and 2c) of the phosphorus 3s levels, neatly reproduced by the calculations. This splitting has also been found in the P-K# spectrum of elemental phosphorus [7] and phosphides of cadmium and zinc [6-10]. The analysis of the wavefunctions corresponding to such bands should allow us to rationalize the splitting and may help in establishing some rule for the interpretation of analogous spectra. The splitting in the emission spectra has been often attributed to the formation of P - P bonds. Let us consider a P2 pair. The 3s orbitals form combinations Crg and n (Fig. 3) at -22.0 and -17.0eV, respectively, at the extended HiJckel level
Vol. 83, No. 6
X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES
Fig. 3. Bonding (ag) and non-bonding (n) combinations of the phosphorus 3s orbitals in a P2 unit. with P-P = 2.3 A. Hence the bands formed from crg and n in a crystal with P2 pairs should be approximately centered at -22 and - 17 eV. Furthermore, the low energy band should have P - P bonding character and the upper one should be P - P nonbonding [11]. In contrast, the analysis of the COOP curves of CdP 4 and CuP2 (not shown here) tells that both bands, centered at -24.5 and -21.0eV, have a clear P - P bonding character. We must go one step further and consider the formation of phosphorus chains (P-)o~. ZnP2 (tetragonal modification) and CdP2, having such chains [6-10], present the same splitting in their P-K# spectra. Let us recall that the phosphorus layers in CdP4 and CuP2 are formed by the fusion of parallel helical chains. It is then reasonable to explore the behaviour of the DOS curves of such (P-)~ chains. Different chain structures [12, 13] are shown in (Fig. 4). Structure a in Fig. 4 is found in SrP2, BaP2 and EuP2; structure b appears in LiP, NaP, KP, ZnP 2 (tetragonal form) and CdP2, and e in GdPS. DOS and COOP calculations for the three structures shown in Fig. 4 present a split band centered approximately at -24 and -21 eV, both with P - P bonding character. The fact that there are four P atoms per unit cell in the chains gives rise to two bands built up from the orbitals shown in Fig. 5. In summary, a single P-3s band should be expected for compounds with isolated p3- ions [12, 14], as found in the spectra [9, 10] of TiP, GaP or Cu3P. For compounds with p4- pairs, the band is split and the two components appear at ca. -17 and
Fig. 5. Combinations of the phosphorus 3s orbitals contributing to the lowest P - P bonding bands of the (P-)o~ chains in structure e (Fig. 4). eV, whereas, for compounds with (P-)~ chains or phosphorus layers the two components appear at lower energies (ca. -21 and -24 eV), as found [6-10] for chains of the type b present in the structures [13c, d] of ZnP2 and CdP2 or in the layers [15] of CdP 4 and CUP2. The bands at -21 and -24eV are P-P bonding, hence its position may allow comparisons of the P - P bond strength among different compounds with related structures. Acknowledgements - Financial support f o r this research work was generously given by DGICYT through grant PB89-0268. The authors thank F. Vilardell for the drawings and a referee for his suggestions. P. Alemany thanks the Ministerio de Educaci6n y Ciencia for a fellowship of the Plan Nacional de Nuevos Materials. REFERENCES 1. 2. 3. 4. 5.
6.
7.
8. a
b
c
Fig. 4. Different conformations of (P-)~ chains found in the experimental structures.
449
9.
See, e..g., R. Hoffmann, Solids and Surfaces. A Chemist's View of Bonding in Extended Structures. VCH Publishers, New York (1988). P.A. Cox, The Electronic Structure and Chemistry of Solids, Oxford University Press, Oxford (1987). P. Day (Editor), Emission and Scattering Techniques, D. Reidel, Dordrecht (1981). F.J. Berry & D.J. Vaughan, Chemical Bonding and Spectroscopy in Mineral Chemistry, Chapman and Hall, London (1985). VP4: S. Alvarez, J. Fontcuberta & M.-H. Whangbo, Inorg. Chem. 27, 2702 (1988); CUP2: P. Alemany & S. Alvarez, Inorg. Chem. 31, 119 (1992); CdP4, RuP4: P. Alemany, Tesi Doctoral, Universitat de Barcelona (1991). E.P. Domashevskaya, V.A. Terekhov & L.N. Marshakova, Fiz. Tverd. Tela (Leningrad) 20, 2675 (1978); Soy. Phys. Solid State 20, 1545 (1978). E.P. Domashevskaya, V.A. Terekhov, L.N. Marshakova, Y.A. Ugai, Izv. Akad. Nauk. SSSR, Set. Fiz. 38, 567 (1974); Bull. Acad. Sci. USSR, Phys. Set. 38, 119 (1974). E.P. Domashevskaya, V.I.Nefedov, Y.V. Salyn, N.P. Sergushin, V.A. Terekhov, L.N. Marshakova & Y.A. Ugai, Izv. Akad. Nauk. SSSR, Ser. Fiz. 4t), 389(1976); Bull. Acad. Sci. USSR, Phys. Set. 40, 145 (1976). E.P. Domashevskaya, V.A. Terekhov, Y.A. Ugai, V.I. Nefedov, N.P. Sergushin & G.N.
450
10. 11. 12. 13.
14.
15.
16. 17.
X-RAY EMISSION SPECTRA OF SOME METAL PHOSPHIDES Dolenko, Fiz. Tverd. Tela (Leningrad) 19, 3610 (1977); Sov. Phys. Solid State 19, 2109 (1977). V.I. Nefedov, Y.V. Salyn, E.P. Domashevskaya, Y.A. Ugai & V.A. Terekhov, J. Electron Spectrosc. Rel. Phenom. 6, 231 (1975). For a more detailed theoretical study of compounds with p4- groups see: R. Hoffmann & C. Zheng, J. Phys. Chem. 89, 4175 (1985). H.-G. von Schnering & W. H6nle, Chem. Rev. 88, 243 (1988). (a) LiP: W. H6nle & H.-G. von Schnering, Z. Krist. 155, 307 (1981); (b) NaP, KP: H.-G. von Schnering & W. H6nle, Z. Anorg. Allgem. Chem. 456, 194 (1979); (c) ZnP2: tetragonal modification, J.G. White, Acta Cryst. 18, 217 (1965); monoclinic form, M.E. Fleet & Th.A. Mowles, Acta Cryst. Sect. C C40, 1778 (1984); (d) CdP2: J. Goodyear & G.A. Steigmann, Acta Cryst. Sect B B25, 2371 (1969); O. Olofsson & J. Gullman, Acta Cryst. Sect. B B26, 1883 (1970)); J. Horn, Bull. Acad. Polon. Sci. 17, 69 (1969); (e) GdPS: F. Hulliger, R, Schmelczer & D. Swarzenbach, J. Solid State Chem. 21, 371 (1977). (a) GaP: A. Addamiano, Acta Cryst. Sect. 13, 505 (1960); (b) CuaP: H. Schlenger, H. Jacobs & R. Juza, Z. Anorg. Allgem. Chem. 385, 177 (1971). (a) CUP2: O. Olofsson, Acta Chem. Scand. 19, 299 (1965); M.H. M611er & W. Jeitschko, Z. Anorg. Allgem. Chem. 491, 225 (1982); (b) CdP4: H. Krebs, K.H. Miiller & G. Ziirn, Z. Anorg. Allgem. Chem. 285, 15 (1956). R. Hoffmann, J. Chem. Phys. 39, 1397 (1963); R. Hoffmann & W.N. Lipscomb, J. Chem. Phys. 36, 2179, 2872, 3489 (1962). M.H. Whangbo & R. Hoffmann, J. Am. Chem. Soc. 100, 6093 (1978).
18. 19. 20. 21. 22.
23.
Voi. 83, No. 6
M.H. Whangbo, R. Hoffmann & R.B. Woodward, Proc. Roy. Soc. London, Set. A 366, 23 (1979). J.H. Ammeter, H.-B. Bfirgi, J.C. Thibeault & R. Hoffmann, J. Am. Chem. Soc. 100, 3686 (1978). R. Ramirez & M.C. B6hm, Int. J. Quantum Chem. 34, 571 (1988); 30, 391 (1986). P.J. Hay, J.C. Thibeault & R. Hoffmann, J. Am. Chem. Soc. 97, 4884 (1975). R. Munita & J.R. Letelier, Theoret. Chim. Acta (Berl.) 58, 167 (1981); E. Clementi & C. Roetti, Atomic Data Nucl. Data Tables 14, 454 (1974). R.H. Summerville & R. Hoffmann, J. Am. Chem. Soc. 98, 7240 (1976).
APPENDIX: COMPUTATIONAL DETAILS The qualitative theoretical discussions in this paper are based on molecular orbital [16] and tight-binding band calculations [17, 18] of the extended Hfickel type with a modified Wolfsberg-Helmholz formula [19], using the atomic parameters shown in Table 1. Experimental structural data was used for CuP2 and CdP4. In calculations for phosphide chains all P - P bond distances were taken as 2.3 A, bond angles as 120°, and torsion angles of 0, 120 and 120 (Fig. 4, a), 60, 60 and 60 (Fig. 4, b) and 0 and 180 (Fig. 4, c) degrees. DOS and COOP diagrams were obtained by averaging throughout the Brillouin zone using a set of 48 k-points chosen according to the geometrical method of Ramirez and B6hm [20].
Table 1. Atomic parameters for extended Hfickel calculations. Hii's are the orbital ionization energies, 6ij the Slater exponents and cj the coefficients in the double-( expansion of the d orbitals
Atom
Orbital
Hii
~il
Cu
4s 4p 3d 5s 5p 3s 3p
- 11.40 -6.06 - 14.00 - 11.80 -8.20 - 18.60 - 14.00
2.20 2.20 5.95 1.64 1.60 1.75 1.30
Cd P
(cl)
~i2
(c2)
Reference [21]
(0.5933)
2.30
(0.5744) [22] [23]