An oxygen-centered titanium square embedded in a cuboctahedron of iodine in the salt K4[{Ti4O}I12]

Angewandte Chemie - International Edition

Volumn 43, Issue 24, 2004, Pages 3183-3185

  Jongen, Liesbet ^a   Mudring, Anja Verena ^a   Möller, Angela ^a   Meyer, Gerd ^a  

^a UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Cluster compounds; Electronic structure; Iodine; Titanium

Indexed keywords

BONDING; OPTIMIZATION;

ANTIBONDING; CUBOCTAHEDRON;

TITANIUM;

IODINE; OXYGEN; SODIUM CHLORIDE; TITANIUM; TITANIUM DERIVATIVE;

ARTICLE; CALCULATION; CHEMICAL BOND; CHEMICAL INTERACTION; CRYSTAL STRUCTURE; DENSITY FUNCTIONAL THEORY; QUANTUM MECHANICS; X RAY ANALYSIS;

EID: 4544270651     PISSN: 14337851     EISSN: None     Source Type: Journal    
DOI: 10.1002/anie.200453739     Document Type: Article

References (30)

1. T. Gloger, Dissertation, Universität zu Köln, 1998.
2. A. Lachgar, D. S. Dudis, J. D. Corbett, Inorg. Chem. 1998, 37, 2242.
3. B. Krebs, G. Henkel, Z. Anorg. Allg. Chem. 1981, 474, 149.
4. J. Zhang, R.-I. Qi, J. D. Corbett, Inorg. Chem. 1991, 30, 4794.
5. D. J. Hinz, G. Meyer, T. Dedecke, W. Urland, Angew. Chem. 1995, 107, 97; Angew. Chem. Int. Ed. Engl. 1995, 34, 71.
6. D. J. Hinz, G. Meyer, T. Dedecke, W. Urland, Angew. Chem. 1995, 107, 97; Angew. Chem. Int. Ed. Engl. 1995, 34, 71.
7. D. J. Hinz, G. Meyer, J. Chem. Soc. Chem. Commun. 1994, 125.
8. Ka radiation, (cell parameters at 150 K refined from powder data: a = 1369.1(4) pm, c = 808.8(3) pm).
9. 0)]. The data were processed with the program systems SHELX-97 [G. M. Sheldrick, SHELX-97, Universität Göttingen, 1997]. Scattering factors were taken from the International Tables for Crystallography, Volume C [A. J. C. Wilson, International Tables for Crystallography, Vol. C, Kluwer Dordrecht, the Netherlands, 1995]. Numerical absorption correction after crystal shape optimization was performed using the programs XRED and XSHAPE [Stoe, XRED 1.01 and XSHAPE 1.01, Darmstadt, 1996]. Further details on the crystal structure investigations may be obtained from the Fachinfortnationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49) 7247-808-666; e-mail: crysdata@fiz-karlsruhe.de), on quoting the depository numbers CSD-413504 and CSD-413505.
10. 0)]. The data were processed with the program systems SHELX-97 [G. M. Sheldrick, SHELX-97, Universität Göttingen, 1997]. Scattering factors were taken from the International Tables for Crystallography, Volume C [A. J. C. Wilson, International Tables for Crystallography, Vol. C, Kluwer Dordrecht, the Netherlands, 1995]. Numerical absorption correction after crystal shape optimization was performed using the programs XRED and XSHAPE [Stoe, XRED 1.01 and XSHAPE 1.01, Darmstadt, 1996]. Further details on the crystal structure investigations may be obtained from the Fachinfortnationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49) 7247-808-666; e-mail: crysdata@fiz-karlsruhe.de), on quoting the depository numbers CSD-413504 and CSD-413505.
11. 0)]. The data were processed with the program systems SHELX-97 [G. M. Sheldrick, SHELX-97, Universität Göttingen, 1997]. Scattering factors were taken from the International Tables for Crystallography, Volume C [A. J. C. Wilson, International Tables for Crystallography, Vol. C, Kluwer Dordrecht, the Netherlands, 1995]. Numerical absorption correction after crystal shape optimization was performed using the programs XRED and XSHAPE [Stoe, XRED 1.01 and XSHAPE 1.01, Darmstadt, 1996]. Further details on the crystal structure investigations may be obtained from the Fachinfortnationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49) 7247-808-666; e-mail: crysdata@fiz-karlsruhe.de), on quoting the depository numbers CSD-413504 and CSD-413505.
12. W. Klemm, L. Grimm, Z. Anorg. Allg. Chem. 1942, 249, 198.
13. W. R. Robinson, J. Solid State Chem. 1974, 9, 255.
14. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
15. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
16. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
17. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
18. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
19. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
20. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
21. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
22. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
23. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
24. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
25. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
26. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
27. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
28. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R.
29. 4- cluster. Mulliken overlap populations [R. S. Mulliken, J. Chem. Phys. 1955, 23, 1397] are given for selected interactions. For graphical display of the cluster valence orbitals Hyperchem [HyperChem, Hypercube Inc., Gainesville, Florida, USA, 2001] was used. Density functional studies were performed with the Stuttgarter LMTO program [R. W. Tank, O. Jepsen, A. Burckhardt, O. K. Andersen, TB-LMTO-ASA Program, Vers. 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1998] based on the linear-muffin-tin approximation using the local density functional LDA as the exchange-correlation functional and the atomic sphere approximation ASA [H. L. Shriver, The LMTO Method, Springer, Berlin, 1984; O. Jepsen, M. Snob, O. K. Andersen, Linearized Band-Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Note, Springer, Berlin, 1987; O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571]. Interstitial spheres are introduced to achieve space filling. The ASA radii as well as the positions and radii of additional empty spheres are calculated automatically. Reciprocal-space integrations are carried out using the tetrahedron method [O. K. Andersen, O. Jepsen, Solid State Commun. 1971, 9, 1763; P. Blöchl, O. Jepsen, O. K. Andersen, Phys. Rev. B 1994, 34, 16223] The basis set of short ranged, atom-centered TB-LMTOs contained for O 3s, 2p, 3d, for I 6 s, 5p, 5d, and 4f, for K 4s, 4p, 3d, and 4f and for Ti 4s, 4p, and 3d. For O the 3s and 3d, for I the 6s, 5d, and 4f, for K the 4p, 3d, and 4f and for Ti 4s, 4p, and 3d orbitals were treated with the downfolding technique [W. R. L. Lambrecht, O. K. Andersen, Phys. Rev. B 1986, 34, 2439; O. Jepsen, O. K. Andersen, Z. Phys. B 1995, 97, 35; G. Krier, O. Jepsen, O. K. Andersen, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, unpublished] The crystal orbital Hamiltonian population (COHP) method is used for bond analysis [R. Dronskowski, P. Blöchl, J. Phys. Chem. 1993, 97, 8617]. Note that the values are negative for bonding and positive for antibonding interactions, the reverse of the signs used in crystal orbital overlap population (COOP; [S. Wijeyesekera, R. Hoffmann, Organometallics 1984, 3, 949]) diagrams in the semi-empirical Hückel treatment. This discrepancy emerges because, to obtain the COOP the DOS gets multiplied by the overlap population while for weighting the DOS in case of the COHP the corresponding element of the Hamiltonian is used.
30. M. Kriener, V. Kataev, A. Freimuth, unpublished results.