«SMALL QUANTUM DOTS OF DILUTED MAGNETIC III-V SEMICONDACTOR COMPOUNDS Liudmila A. Pozhar PermaNature, Birmingham, AL 35242 Home Address: 149 Essex ...»
molecule, with some small deviations. As a rule, 3d AOs of its V atom bond 4p AOs of the nearest 4 Ga atoms. Four or 3 of these Ga atoms bond another 4 or 3 Ga atoms (Ga-Ga 4p – 4p bonding), where the 3 Ga are bonded to all 3 As atoms (Ga-As 4p – 4p bonding). In some cases the Ga atom bonded to V and positioned in the pyramid vertex closest to the V atom may be only weakly bonded to the Ga-As portion of the entire hybrid MO. Such MOs provide for the vacuum molecule being a robust ROHF triplet with a large OTE and a deep energy minimum of its ground state (Table II). The Ga-V bond length in this molecule takes only 2 values: 2.505 Å and
2.998 Å. The bond length of the ligand Ga-Ga bonding also takes two values: 4.046 Åand 4.532 Å, while Ga-As bonding is more flexible, so the Ga-As bond may be 2.487 Å, 2.519 Å and 2.835 Å. Similar to the case of the pre-designed molecule, in the vacuum molecule vanadium and arsenic atoms do not bond directly.
Compared to InAs-based molecules with one V atom that are pre-designed ROHF nonet and vacuum ROHF pentet, GaAs-based ones are more stable, being ROHF triplets. This phenomenon is due to extraordinary stability of bonding MOs of this molecule that possess a large π-type Ga-ligand (122) and Ga-As bonding contributions.
Being ROHF triplets, both Ga10As3V molecules have “ferromagnetic” arrangement of aligned uncompensated spins (Fig. 22) contributed by electrons in 3d AOs of Ga atoms, with a very small contribution of V atoms and even smaller contributions of As atoms. The SDD values of these molecules are about an order of magnitude smaller than those of the InAs-based molecules with one V atom discussed in Sec. 4, that are higher ROHF spin multiplets.
Correspondingly, the magnetic moment of the GaAs-based molecules with one V atom is
Fig. 22. Isosurfaces of the spin density distribution (SDD) of the pre-designed [(a) to (c)] and vacuum [(d) to (f)] Ga10As3V molecules corresponding to the fractions (a) 0.0005, (b) 0.0007, (c) 0.001, and (d) 0.0007, (e) 0.0005, (f) 0.001 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.
significantly smaller (3 µB) than the smallest of the magnetic moments of InAs-based molecules 5 µB) with one V atom. Thus, for DMS applications with an emphasis on the large magnetic moment In10As3V molecules may be a better choice.
6. InAs - AND GaAs - BASED MOLECULES WITH TWO VANADIUM
Pre-designed and vacuum In10As2V2 and Ga10As2V2 molecules have been virtually synthesized using the same procedures utilized for virtual synthesis of In10As2V and Ga10As2V molecules (see Sections 1, 4 and 5 of this Chapter), with the only difference that this time two As atoms have been replaced by two V atoms in each of the pre-designed In10As4 and Ga10As4 tetrahedral pyramids (see Chapter 4) of the zincblende InAs and GaAs lattices. After the replacement, the In10As2V2 and Ga10As2V2 pyramidal structures were optimized while the centers of mass of their atoms were constrained to the same positions in space. The result of this optimization is two predesigned molecules In10As2V2 and Ga10As2V2. Then the initial structures were optimized again, this time when the constraints applied to the atomic positions were lifted, producing two socalled vacuum molecules In10As2V2 and Ga10As2V2. The structure of all four molecules is pictured in Fig. 23. Because of the spatial constraints applied to the atomic positions, both of the pre-designed molecules (Figs. 23a and 23d) retain their pyramidal shape. When the constrains are lifted, only the vacuum Ga10As2V2 molecule (Figs, 23e and 23f) appears pyramidal, while the vacuum In10As2V2 molecules loses any resemblance to the tetrahedral pyramid of its parent structure. These phenomena, of course, follow from the relative sizes of the participating atoms and the number of electrons they possess. Thus, the V atom is smaller and has fewer electrons
Fig. 23. (Color online) The pre-designed (a) and vacuum [(b) and (c)] In10As2V2 molecules, and the pre-designed (d) and vacuum [(e) and (f)] Ga10As2V2 molecules, respectively. Atomic dimensions approximately correspond to the atoms’ covalent radii. In the In10As2V2 molecules In atoms are yellow, As red and V blue. In the Ga10As2V2 molecules Ga atoms are blue, As brown, and V yellow.
than As and Ga atoms, so after the replacement of 2 As atoms by 2 V atoms in the original Ga10As4 pyramid (see Chapter 3 for details on this structure) the pre-designed molecule Ga10As2V2 is somewhat loose. When spatial constraints on atomic positions are lifted, the atoms move from their original positions, but only by several tenths of Angstrom. Thus, visually, the vacuum Ga10As2V2 molecule appears pyramidal. In the case of In10As2V2, the V atom is much smaller and has much fewer electrons that the In atom. After the replacement of two As atoms by two V ones the original In10As4 structure becomes too loose, as the absence of 20 electrons that occur after the replacement creates a large charge and mass distribution imbalance. Thus, when the constraints applied to atomic positions are lifted, atoms in the original structure adjust dramatically in response to the charge imbalance. As a result, the vacuum In10As2V2 molecule assumes entirely a shape entirely different from that of its parent pyramidal structure and becomes a stable ROHF singlet. In contrast, its pre-designed counterpart has spin multiplicity 11, and thus is an unstable molecule (see Table II) in the framework of ROHF approximation used here. The CDDs and MEPs of the studied molecules with two V atoms reflect characteristic features of their composition and shape (Figs. 24 and 25).
Comparison of MEP surfaces of the pre-designed and vacuum In10As2V2 molecules in Fig. 24 obtained for similar CDD isovalues reveals strikingly different electrostatics of these molecules. Thus, the MEP surface values of the pre-designed molecule for the CDD isovalue
0.001 ran from highly negative to positive ones (Fig. 24a), while for the close CDD isovalue
0.0007 the MEP values of the vacuum molecule are uniformly close to 0 (Fig. 24d). Thus, in the case of the pre-designed molecule, at large distances from the molecular “surface” there still exists large MEP fluctuations that reflect instability of this molecule. In contrast, the vacuum molecule is stable exhibiting text-book MEP values for large separations from the molecular “surface”. Similar conclusions follow from comparison of MEP values in Figs. 24b and 24e for the same CDD isovalue 0.01, and those in Figs. 24c and 24f for close CDD isovalues 0.08 and 0.1, respectively. Comparison of the ground state energy values of these molecules reveals that
Fig. 24. (Color online) The molecular electrostatic potential (MEP) of the pre-designed [(a) to (c)] and vacuum [(d) to (f)] In10As3V2 molecules for several isosurfaces of the corresponding CDDs calculated for the following fractions (isovalues) of the CDD maximum values 3.44417 and 3.01378 (in arbitrary units), respectively: (a) 0.001, (b) 0.01, (c) 0.08, (d) 0.0007, (e) 0.01, and (f) 0.1. The color coding scheme for MEP surfaces is shown in each figure. In the pre-designed molecule [(a) to (c)] In atoms are yellow, As red and V purple. In the vacuum molecule [(d) to (f)] In atoms are blue, As brown and V yellow. In (a) to (e) atomic dimensions of In atoms are somewhat smaller than those defined by the In atom’s covalent radius. In (a) to (c) the dimensions of V and As atoms are enlarged. In (f) all atomic dimensions are significantly reduced to show the MEP surface structure. In (d) to (f) MEP surfaces are semi-transparent to reveal the structure.
the ground state energy values differ by about 1 H (Table II). This difference lies at the limit of the best total energy evaluation accuracy of the RHF-ROHF approximation method. The dipole moment of the pre-designed molecule is also somewhat larger than that of the vacuum one (Table II). These facts indicate that the pre-designed molecule that realizes a local minimum of the total energy of the In10As2V2 atomic cluster (corresponding to the tetrahedral symmetry spatial constraints applied to the cluster’s atoms) is not stable and may not be realizable experimentally.
Several MEP surfaces of Ga10As2V2 molecules for several CDD isovalues are shown in Fig. 25. In contrast to those of the In10As2V2 molecules, the MEP surfaces of Ga10As2V2 ones are very similar. This is a consequence of the fact that both Ga10As2V2 molecules are close ROHF spin multiplets (see Table II). On the other hand, both the pre-designed ROHF Ga10As2V2 septet and vacuum Ga10As2V2 nonet are higher excited states, and are not typical for the ground state of the majority of small stable molecules. Moreover, the pre-designed septet is more stable than the vacuum nonet, indicating that the calculated minimum of the total energy in the case of the vacuum nonet may not be a global minimum. Indeed, comparing for example, MEP surfaces of these molecules depicted in Figs. 25 c and 25f, one can see that the pre-designed molecule has larger areas of delocalized electron charge shared between Ga, V and As atoms than the predesigned one. Most likely, the vacuum nonet is a realization of a local minimum of energy of Ga10As2V2 atomic cluster. This consideration is further supported by comparison of the ground state energies of these molecules (Table II) that are lying within the error brackets of the RHFROHF approximation. Indeed, the difference in the ground state energy values of these molecules is only 0.055 H, while the best possible total energy evaluation accuracy of the used
Fig. 25. (Color online) The molecular electrostatic potential (MEP) of the pre-designed [(a) to (c)] and vacuum [(d) to (f)] Ga10As3V2 molecules for several isosurfaces of the corresponding CDDs calculated for the following fractions (isovalues) of the CDD maximum values 9.46923 and 10.37640 (in arbitrary units), respectively: (a) 0.007, (b) 0.01, (c) 0.08, (d) 0.005, (e) and (f): 0.1. The color coding scheme for MEP surfaces is shown in each figure. Ga atoms are blue, As brown and V yellow. In (a), (c), (d) and (f) atomic dimensions roughly correspond to those defined by the atoms’ covalent radii. In (b) to (e) all atomic dimensions are reduced to show the MEP surface structure. In all cases but (c) MEP surfaces are semitransparent to reveal the structure.
calculation method is a few Hartrees. The dipole moment of the vacuum molecule is considerably smaller than that of the pre-designed one (Table II). This further supports the conclusion that the vacuum nonet is a local minimum of the total energy of the unconstrained Ga10As2V2 cluster that correspond to a more uniform electron charge distribution than that specific to the local minimum of the constrained pre-designed molecule.
Molecular orbitals of the molecules with two V atoms are shown in Figs. 26 and 27. In support of the conclusion regarding instability of the pre-designed In10As2V2 molecule discussed above, MOs of this molecule in the near HOMO-LUMO region (Figs. 26a and 26b) feature antibonding parts contributed to by 3d AOs of In and V atoms, and bonding sp - type portions due to As-In bonding, and π-type portions of In ligand bonding. The LUMO (Fig. 26c) of this molecule is a bonding orbital realized via hybrid type pd-type In-V, p-type In-As, and π-type InIn bonding. MOs of the vacuum In10As2V2 molecule in its HOMO-LUMO region (Figs. 26d to 26f) are bonding hybrid MOs with significant portions of pd In-V bonding, and As-mediated πtype In ligand bonding.
In the case of Ga10As2V2 molecules (Fig. 27), all MOs in the HOMO region and the LUMOs are bonding hybrid MOs contributed to by (1) pd-type Ga-V bonding due to 3d AOs of V and 4p AOs of Ga, (2) 4p-type As-Ga bonding, and (3) π-type Ga ligand bonding.
Magnetic properties of the studied InAs- and GaAs-based molecules are illustrated in Fig.
28. An important finding is that replacement of an As atom by the second vanadium one in the studied In10As3V and Ga10As3V molecules does not ensure an increase in the magnetic moment of the obtained molecules, because it generally destabilizes the original molecules. At this point in studies, it seems that the pre-designed Ga10As2V2 septet (Figs. 28c and 28d) may be
Fig. 26. (Color online) 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. The pre-designed In10As2V2 molecule: (a) HOMO 127, isovalue 0.01; (b) HOMO 128, isovalue 0.001; (c) LUMO 129, isovalue 0.015. The vacuum In10As2V2 molecule: (d) HOMO 122, isovalue 0.015; (e): HOMO 123, isovalue 0.01; (f): LUMO 124, isovalue 0.015. Indium atoms are yellow, As red and V purple. Atomic dimensions are reduced to reveal the isosurface structure.
Fig. 27. (Color online) 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. The pre-designed Ga10As2V2 molecule: (a) HOMO 125, isovalue 0.008; (b) HOMO 126, isovalue 0.01; (c) LUMO 127, isovalue 0.008. The vacuum Ga10As2V2 molecule: (d) HOMO 126, isovalue 0.01; (e): HOMO 127, isovalue 0.01; (f): LUMO 128, isovalue 0.01. Ga atoms are blue, As brown and V yellow. In (a) to (d) Atomic dimensions are reduced to reveal the isosurface structure. In (e) and (f) the atomic dimensions are reduced only slightly. Isosurfaces are semi-transparent to reveal the structure.