(Color online) Small Co–Pt clusters, complexes 1–13; three different configurations for the bonding of onto a triangular complex, adducts 14–16, and onto an almost flattened tetrahedron (7), adducts 17–19—the latter result upon optimization of the adducts obtained from 14–16, respectively, by expanding the complex to a tetrahedron complex; cluster representing the surface, complex 20, and cluster modeling the adsorption of onto complex 20, adduct 21; triangular Pt cluster with bonded onto it almost parallel to one of its sides, 22; and a configuration for the bonding of onto a tetrahedron, 23. The most stable adduct is 14 (the relative energy of 15 is and that of 16 is ), whereas the most stable adduct is 18 (the relative energy of 17 is and that of 19 is ). Co–Pt clusters without are also denoted complexes, those with are also termed adducts. Atoms are colored as follows: Co (blue), Pt (yellow), and O (red). Most lines connecting atoms are a visual help for the eye.
(Color online) Unit cell of the cubic phase of (left) and its (111) derivative (right). Pt (yellow), Co (blue).
(Color) DOS per unit cell for majority and minority spins of the bulk phase of (a). Spin- and site-projected DOS of , , , and characters for Co [(b) and (c)], respectively, and Pt [(d) and (e)]. Left panels [(b) and (d)] are for the majority spin states and right panels [(c) and (e)], are for the minority spin states. In all panels, the vertical dashed line at zero-energy marks the Fermi level.
(Color online) Top view of and adducts.
(Color online) -orbital resolved DOS of triplet (a), and stacked partial DOS of Co and Pt in complex 3 (b). -orbital resolved partial DOS for molecule in 14 (c), 15 (e), 16 (g), 17 (d), 18 (f), and 19 (h). The Fermi energy is taken as the zero-energy point in all panels without exception. For and each adduct, this point is set to the mid-point of its HOMO-LUMO gap. The lower panels of (a)–(h) indicate the discrete energy levels of the corresponding clusters; the DOSs have been obtained from these discrete sets by convoluting them with Gaussian functions having full width at half maximum (FWHM) of . The purple lines denote LUMO energies, the gray, HOMO energies. In panels (c)–(h), the shaded green area gives the contribution of the orbitals of Co and Pt to the total DOS of the corresponding adducts.
(Color online) Isosurface of the difference electron densities (left) and spin density (difference between and densities; right) for adducts 14–19 and 21. In the electron density spectra, charge flows from the green into the red regions. The spin density of the isolated is also shown as a reference. Pt atoms are shown in yellow, Co atoms in blue, and O atoms in red.
(Color online) Frontier orbitals , HOMO, LUMO, and of 14, 15, and 16 together with their corresponding energies. Their HOMO-LUMO gaps are 2.99, 3.01, and , respectively. The molecular orbitals correspond to isovalues of
(Color online) -orbital resolved partial DOS for molecule in 14 (a), 15 (c), 16 (d), 17 (b), 18 (e), and 19 (f) supported on a surface of bulk . The Fermi energy of bulk is taken as the zero-energy point in all panels. Each DOS has been computed in two ways: in the first, (red curves), each Co and Pt atom has been assigned the orbital-projected DOS of bulk averaged over a unit cell; in the second, (blue curves), each Co and Pt atom has been assigned the average over a unit cell of the orbital-projected DOS of bulk onto Co and Pt atoms, respectively. The band of bulk (green curve) is shown as a reference.
(Color online) P-orbital resolved partial DOS for the oxygen molecule in 21. In (a) 21 is considered as a finite cluster, in (b) it is considered as forming part of an on bulk system. The zero-energy point in (a) is set to the mid-point of the HOMO-LUMO gap of 21, in (b), it is set to the Fermi energy of bulk . The lower panel of (a) displays the discrete energy levels of 21: the purple bars denote LUMOs energies, gray bars HOMOs energies. The DOS in the upper panel has been obtained from this discrete set by convoluting the energy levels with Gaussian functions having FWHM of . The shaded green area gives the contribution of the orbitals of Co and Pt to the total DOS of 21. The DOS in (b) has been computed in two ways: in the first, , each Co and Pt atom has been assigned the orbital-projected DOS of the bulk averaged over a unit cell; in the second, , each Co and Pt atom has been assigned the average over the unit cell of the orbital-projected DOS of the bulk onto Co and Pt atoms, respectively. The band of bulk (green) is shown as a reference.
(Color online) (a) Projected density of states of onto the orbitals of O in adducts, (a) 22 and (b) 22, when considered as a fragment in an on Pt(111) system, (c) 23 and (d) 23, when considered as a fragment in an on Pt(111) system. The band of bulk Pt is shown in green. The set of bars in the bottom panels of (a) and (b) displays the energy levels of 22, that in the bottom panel of (c) and (d) displays the energy levels of 23. Blue and purple lines correspond to occupied and unoccupied states, respectively. The HOMO-LUMO gap of 22 is ; that of 23 is .
Structure and energies for Co–Pt complexes and adducts using the B3PW91 functional with the LANL2DZ basis set and effective core potentials for Co and Pt, and the basis set for O. is the multiplicity, , with the total electron spin of the molecule. The bond length between atoms and is denoted by , the angle between bonds and is denoted by , and the dihedral angle between the two planes defined by atoms , , and , , is denoted by .
Mulliken populations, O–O bond lengths , vibration frequencies , and binding energies of per oxygen atom for adducts 14–19 and 21–23. Atom labels are defined in Fig. 1.
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