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«SMALL QUANTUM DOTS OF DILUTED MAGNETIC III-V SEMICONDACTOR COMPOUNDS Liudmila A. Pozhar PermaNature, Birmingham, AL 35242 Home Address: 149 Essex ...»

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4. PRE-DESIGNED AND VACUUM MOLECULES In10As3V Virtual synthesis studies of In10As3V molecules are of significant importance both for practical purposes and for understanding a role of 3d AOs of V and Mn atoms in the development of positive MEP regions (delocalized holes) in InAs and GaAs zincblende bulk lattices containing a few percent of Mn or V atoms. Similar to the pre-designed In10As3Mn molecule, the predesigned In10As3V molecule has been developed by substitution of V atom instead of As one in the pyramidal symmetry element of the zincblende InAs lattice, and subsequent HF/ROHF minimization of the total energy of the atomic cluster so obtained in the case when spatial constraints were applied to the centers of mass of the cluster’s atoms. The corresponding vacuum molecule has been obtained upon the total energy minimization of the pre-designed cluster in the case when the spatial constraints applied to the centers of mass of its atoms were lifted, so the atoms could move. The structure of the molecules so obtained is detailed in Fig. 9. Visually these two molecules are indistinguishable, although in the vacuum molecule several atoms, including V and all As atoms have moved by several tens of Angstrom from their original positions in the pre-designed molecule. This motion also resulted in small changes to the angles between V, In and As atoms. For example, in the case of tetrafold-coordinated As atoms in the pre-designed

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Fig. 9. (Color online) The structure of the pre-designed [(a) to (c)] and vacuum [(d) to (f)] In10As3V molecules. Indium atoms are yellow, As red and V purple. In (a) and (d) atomic dimensions are reduced to show atomic positions; other dimensions are to scale. The radii of In atoms in (b), (c), (e) and (f) are somewhat smaller than their covalent radius, and those of As and V atoms are somewhat larger than the corresponding covalent radii of As and V atoms.

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Fig. 10. (Color online) The electron charge density distribution (CDD) of the pre-designed In10As3V molecule. Isosurfaces (golden) corresponds to the isovalues (a) 0.0005; (b) 0.01; (c) 0.05; (d) 0.075, (e) 0.075, and (f) 0.15. Indium atoms are yellow, As red and V purple. In (e) and (f) atomic dimensions are reduced to show the isosurface structure; other dimensions are to scale. The radii of In atoms in (a) to (d) are somewhat smaller than their covalent radius, and those of As and V atoms are somewhat larger than the corresponding covalent radii of As and V atoms.

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Fig. 11. (Color online) The electron charge density distribution (CDD) of the vacuum In10As3V molecule. Isosurfaces (golden) corresponds to the isovalues (a) 0.001; (b) 0.01; (c) 0.05; (d) 0.05, (e) 0.15, and (f) 0.25. Indium atoms are yellow, As red and V purple. In (e) and (f) atomic dimensions are reduced to show the isosurface structure; other dimensions are to scale. The radii of In atoms in (a) to (d) are somewhat smaller than their covalent radius, and those of As and V atoms are somewhat larger than the corresponding covalent radii of As and V atoms.

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Fig. 12. (Color online) The molecular electrostatic potential (MEP) of the pre-designed molecule In10As3V for several isosurfaces of the CDD calculated for the following fractions (isovalues) of the CDD maximum value 3.54328 (arbitrary units): (a) 0.01; (b) 0.05; (c) and (d) 0.075; (e) 0.15, and (f) 0.3. The color coding scheme for MEP surfaces is shown in each figure. In atoms are yellow, As red and V purple. All dimensions in (a) to (d) are to scale; atomic dimensions roughly correspond to the atoms’ covalent radii. In (d) to (f) atomic dimensions are reduced to show the MEP surface structure.

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Fig. 13. (Color online) The molecular electrostatic potential (MEP) of the vacuum molecule In10As3V for several isosurfaces of the CDD calculated for the following fractions (isovalues) of the CDD maximum value 3.264001 (arbitrary units): (a) 0.01; (b) 0.05; (c) and (d) 0.1; (e) 0.15, and (f) 0.25. The color coding scheme for MEP surfaces is shown in each figure. In atoms are yellow, As red and V purple. All dimensions in (a) and (b) are to scale; atomic dimensions roughly correspond to the atoms’ covalent radii. In (c) to (f) atomic dimensions are reduced to show the MEP surface structure.

molecule the In-As-In angles with the closest 4 In atoms are 113.0º, 113.0º, 105.7º and 105.7º, while in the case of the vacuum molecule those angles are 118.7º, 110.6º, 105.6º and 99.7º for two of the As atoms on the zincblende cube body diagonal opposite to that of the V atom, and

111.8º, 111.1º, 107.7º, and 107.0º for the As atom sharing the zincblende cube body diagonal with V atom. The vanadium atom has also been displaced from its original position in the predesigned molecule. Thus, the In-V-In angles in the small, tetrafold-coordinated V pyramid of the vacuum molecule are 118.4º, 111.0º, 105.4º and 99.6º. These small adjustments, however, are such that they do not affect V - As atomic coordination: both the distances between V and As atoms, and the angles remain the same as they are in the pre-designed molecule – 3.997 Å and

60.5º, respectively.

CDDs (Figs. 10 and 11) and MEPs (Figs. 12 and 13) of both molecules retain a general appearance of tetrahedral symmetry. However, detailed analysis reveals tetrahedral symmetry breaking in both cases. Comparing these CDD and MEP isosurfaces to those of In10As3Mn molecules one can see that in the latter case the electron charge is pushed further into the space surrounding the molecules with Mn atom. In the case of molecules containing V atom the electronic charge are about twice as closer to the molecular “surfaces” for the same isosurface values. The vanadium atoms in these molecules accumulate electronic charge (Figs. 10d and 11d). The MEP values are positive near the “surfaces” of both molecules (Figs. 12d and 13d) and in the immediate vicinity of the “surfaces” on the inner side of the molecules (Figs. 12 e to 12f, and 13e to 13f). The “shell” of positive MEP values surrounding molecular surfaces is less distinctive and the MEP values are lesser in the case of the pre-designed In10As3V molecule (Figs. 10 and 12) than those in the case of its vacuum counterpart. To a degree, this may be a consequence of the fact that the pre-designed molecule is a ROHF nonet (its spin multiplicity M is 9). Such high excited states are beyond applicability of the ROHF approximation (see the corresponding discussion in Chapter 3), indicating that this molecule may not be stable. In contrast, the vacuum vanadium-containing molecule is a ROHF pentet, and therefore is expected to be much more stable. Correspondingly, its “shell” of positive MEP values is much more distinctly defined and contains regions in the immediate outer vicinity of the molecular “surface”, and much thicker regions near that “surface” from inside of the molecule. Using the “hole” terminology, one can expect the hole mediated by V atom to be contained inside the 14atomic tetrahedral symmetry element of the zincblende InAs structure containing a vanadium substitution defect, while in the case of Mn-mediated “holes” of In10As3Mn molecules such “holes” are delocalized about a larger region containing the corresponding pyramidal element.





The volume of that region is about twice as large as the region of delocalization of V-mediated “holes” in In10As3V molecules. The observation that the V-mediated charge hole delocalized in a pyramidal symmetry element of the InAs zincblende lattice containing the vanadium atom is more localized than the corresponding Mn-mediated hole steams from the fact that a vanadium atom has smaller number of 3d-electrons (2, as opposed to 5 3d-electrons of a Mn atom), and those electrons are closer to the V nucleus. Therefore, more ligand electron charge of In atoms can be kept “inside” of In10As3V molecules (Figs. 12e and 13e) compared to the case of In10As3Mn molecules (Figs. 3e and 4e). In practical terms this means that the semiphenomenological band theory of semiconductors and its extensions and modifications designed to embrace a realm of DMS should work better for InAsV systems than for InAsMn ones.

Analysis of MOs of In10As3V molecules provides detailed information on electron charge configuration, a role of the vanadium atom in stabilization of these molecules and the development of regions of positive MEP values (“holes”). Several such MOs in the HOMOLUMO regions of these molecules are depicted in Figs. 14 and 15. Similar to the case of In10As3Mn molecules, the major contributions to MOs of In10As3V molecules in the HOMOLUMO region come from 5p AOs of In atoms, 3d AOs of V atom and 4p AOs of As atoms hybridized in various proportions, and some contributions from 4d AOs of In atoms (this latter contributions must be ascertained by further CI, MCSCF and MP-2 studies). In the case of the pre-designed ROHF nonet, HOMO 121 (Figs. 14a and 14b) contains both bonding and nonbonding regions mediated by 3dxy AOs of V atom that orchestrates In ligand bonding via their 5p AOs, with a significant contribution of 4p AOs of As atoms. HOMOs 122 and 123 are bonding MOs with the major contributions from 3dz2 AOs of the vanadium atom hybridized with both 5p and 4d AOs of several In ligand atoms (Figs. 14c to 14f). Only 4p AOs of one As atom contribute to bonding in the case of HOMO 122 (Fig. 14d), while all As atoms significantly contribute to bonding in the case of HOMO 123 (Figs. 14e and 14f). LUMOs 124 and 126 of this molecule (Figs, 14g and 14i, respectively) are bonding MOs where the In ligand bonding is mediated by 3dz2 AOs of the vanadium atom, while LUMO 125 contains both non-bonding and bonding regions all mediated by 3dxy AOs of the vanadium atom. In contrast to In10As3Mn molecules, all MOs in the HOMO-LUMO region of the pre-designed In10As3V molecule exhibit significant contributions from ligand bonding with 4 or more participating In atoms. Both 5p some 4d AOs of In atoms contribute to this bonding, in agreement with the corresponding CDD picture indicating that in the case of V-containing molecules electron charge of In atoms is more effectively redistributed inside the molecules, and less of this charge is pushed outside of the molecular “surfaces”.

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Fig. 14. (Color online) The pre-designed In10As3V molecule. Isosurfaces of the positive (green) and negative (orange) parts of the highest occupied and lowest unoccupied molecular orbits (HOMOs and LUMOs, respectively) corresponding to several isovalues. (a) and (b): HOMO 121, isovalue 0.01; (c) and (d): HOMO 122, isovalue 0.01; (e) and (f): HOMO 123, isovalue 0.015; (g), (h) and (i): LUMO 124, 125 and 126, isovalues 0.0150.01, 0.01 and 0.02, respectively. Indium atoms are yellow, As red and V purple. Atomic dimensions are reduced to show the isosurface structure; other dimensions are to scale.

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Fig. 15. (Color online) The vacuum In10As3V molecule. Isosurfaces of the positive (green) and negative (orange) parts of the highest occupied and lowest unoccupied molecular orbits (HOMOs and LUMOs, respectively) corresponding to several isovalues. (a) to (c): HOMO 118, 119 and 120, isovalue 0.01, respectively; (d) and (f): HOMO 121, isovalue 0.01; (g) and (h): LUMO 122 and 123, isovalue 0.015, respectively; and (i) LUMO 124, isovalue 0.015. Indium atoms are yellow, As red and V purple. In all figures except for (d) atomic dimensions are reduced to show the isosurface structure; other dimensions are to scale. In (d) atomic dimensions are roughly defined by the atoms’ covalent radii.

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Fig. 16. Isosurfaces of the spin density distribution (SDD) of the pre-designed [(a) to (c)] and vacuum [(d) to (f)] In10As3V molecules corresponding to the fractions (a) 0.001, (b) 0.005, (c) 0.01, and (d) 0.001, (e) 0.003, (f) 0.005 of the respective SDD maximum values (not shown). Indium atoms are yellow, As red and Mn blue. All atomic dimensions are reduced to show the SDD surface structure.

All MOs in the HOMO-LUMO region of the vacuum In10As3V molecule shown in Fig.

15 are bonding orbits. The 3dz2 AO of the vanadium atom provide the major contribution to all MOs except for LUMO 124, in which case the contribution due to this AO of the vanadium atom are small and all bonding is mediated by 4p AOs of 3 As atoms. All MOs of this molecule exhibit two large areas of shared charge: one is a delocalized charge of 4 to 6 In ligand atoms mediated by V, and the other a delocalized charge of 3 In atoms mediated by one to three As atoms. These two portions of the MO are bonded to each other through one of the In ligand atoms. Once again, this type of bonding violates the octet rule and is the major means of stabilization of the studied non-stoichiometric molecules.

The In ligand bond length in the case of the pre-designed molecule is defined entirely by the geometry and is 4.284 Å, which is also the distance between any two In neighbours. In the vacuum molecule the ligand bond length is flexible taking several values between 4.272 Å and

4.999 Å. The In-As bond length is flexible in both cases and allows for several values in the ranges from 2.220 Å to 2.934 Å (the pre-designed molecule) and 2.346 Å to 2.895 Å (the vacuum molecule). The arsenic and vanadium atoms bond directly only to In ones. In the case of the pre-designed molecule the length of the V - In bond can take 4 values: 2.220 Å, 2.717 Å,

2.934 Å and 4.695 Å. The first 3 values are the same as those of the In - As bond in this

molecule. In the case of the vacuum molecule the length of V - In bond takes only 3 values:

2.340 Å, 2.706 Å and 2.907 Å.

Both In10As3V molecules are ROHF spin multiplets with “ferromagnetic” arrangement of uncompensated spins (Fig. 16). The spin of these molecules are primarily contributed to by spin components of delocalized 4d electrons of In atoms, with a very small contribution coming from electrons of the V atom. AOs of arsenic atoms do not contribute to SDDs. SDD values of the predesigned molecule (which is a “ferromagnetic” ROHF nonet with the uncompensated magnetic moment 9µB, Figs. 16a to 16c) are about 3 times larger than those of the vacuum one, which is a ”ferromagnetic” ROHF pentet with the uncompensated magnetic moment 5µB, Figs. 16d to 16i.



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