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G. A. Landrum, YaeHMOP: Yet Another extended Hückel Molecular Orbital Package
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b) G. A. Landrum, YaeHMOP: Yet Another extended Hückel Molecular Orbital Package.
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53349137588
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6 from Ref. [2c] were used throughout this work. 2κ 4s, 4p, 3d and 2s, 2p basis sets for Ca and C, respectively, were used for the expansion of valence states, while the Ca 3s, 3p states were treated as semicore states. In the interstitial region, the pseudo-LMTOs were expanded in plane waves up to 75.64, 109.5, and 156.5 eV for the Ca 4s, 4p, and 3d shells, and 533.3, 776.8 eV for C 2s and 2p shells, respectively, while the potential and charge density in the interstitial region were expanded in plane waves up to 2250.9 eV, corresponding to 17752 plane waves. 4237 and 13 independent k points for the valence and semicore states, respectively, were used in the self-consistent calculations.
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6 from Ref. [2c] were used throughout this work. 2κ 4s, 4p, 3d and 2s, 2p basis sets for Ca and C, respectively, were used for the expansion of valence states, while the Ca 3s, 3p states were treated as semicore states. In the interstitial region, the pseudo-LMTOs were expanded in plane waves up to 75.64, 109.5, and 156.5 eV for the Ca 4s, 4p, and 3d shells, and 533.3, 776.8 eV for C 2s and 2p shells, respectively, while the potential and charge density in the interstitial region were expanded in plane waves up to 2250.9 eV, corresponding to 17752 plane waves. 4237 and 13 independent k points for the valence and semicore states, respectively, were used in the self-consistent calculations.
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53349125789
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Orbital compositions for some representative Fermi states: ψ (pd,1, 15.1%Eg (Ca dxy, Ca d x2-y2, 14.7% Eg (Ca dxz, Ca dyz, 64.9% A2u C pz; ψ(sd,2, 60.9% A1g Ca s, 15.6% A1g Ca d z2, ψ (pd,3, 30.0% Eg (Ca d xz, Ca dyz, 68.9% A2u C p z; ψ (sd,4, 22.7% A1g Ca s, 66.3% A 1g Ca dz2, ψ(sd,5, 37.1% A1g Ca s, 51.2% A1g Ca dz2, ψ(sd,6, 63.4% A 1g Ca s, 32.2% A1g Ca dz2; ψ(sd,7, 49.9% A1g Ca s, 23.9% A1g Ca dz2, 11.3% A2u C pz; ψ(pd,8, 30.4% Eg Ca dxy+Ca dx2
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z. The contributions below 10% are omitted for brevity. The orbitals are grouped according to their symmetry in the corresponding point group of R̄m.
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53349083847
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Γ-F(x) = α + 2β + 2γ + 4δ + (4β + 4γ) cos(2πx) + 2δcos(4πx), where α is the on-site energy of the sd hybrid, β, γ, δ are the hopping integrals for 1st , 2nd, and 3rd nearest neighbors for a sd hybrid, respectively, and χ is a parameter ranging between 0 and 1/2. In deriving the above formula, it is assumed that there is no hybridization between the sd hybrids and other states, and a cutoff for such interactions to the 3rd nearest neighbors is taken.
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Γ-F(x) = α + 2β + 2γ + 4δ + (4β + 4γ) cos(2πx) + 2δcos(4πx), where α is the on-site energy of the sd hybrid, β, γ, δ are the hopping integrals for 1st , 2nd, and 3rd nearest neighbors for a sd hybrid, respectively, and χ is a parameter ranging between 0 and 1/2. In deriving the above formula, it is assumed that there is no hybridization between the sd hybrids and other states, and a cutoff for such interactions to the 3rd nearest neighbors is taken. Global fitting to the first-principles sd band was not attempted; instead, the parameters α, β, γ, δ are extracted with the eigenvalues at the special points Γ, L, Z, and F. The obtained values are 27.651, -0.2655, -0.0555, and -0.0747 eV for α, β, γ, δ, respectively.
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53349095219
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i are the reciprocal lattice vectors corresponding to the primitive basis vectors of the direct lattice. By choosing k in this way, the anisotropy of the structure is implicitly considered.
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i are the reciprocal lattice vectors corresponding to the primitive basis vectors of the direct lattice. By choosing k in this way, the anisotropy of the structure is implicitly considered.
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Springer, New York
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A. S. Hedayat, N. J. A. Sloane, J. Stufken, Orthogonal Arrays: Theory and Applications, Springer, New York, 1999.
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Hedayat, A.S.1
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53349136526
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Optimized EH parameters for Ca in this work: H4s (eV): -9.5, ζs: 1.6; H4p: -2.5, ζp: 1.6, H3d: -7.0, ζ1,3d: 2.74, c1:0.413, ζ2,3d: 1.13, c2: 0.7228; standard parameters: H4s (eV): -7.0, ζs: 1.2; H4p: -4.0, ζp: 1.2.
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Optimized EH parameters for Ca in this work: H4s (eV): -9.5, ζs: 1.6; H4p: -2.5, ζp: 1.6, H3d: -7.0, ζ1,3d: 2.74, c1:0.413, ζ2,3d: 1.13, c2: 0.7228; standard parameters: H4s (eV): -7.0, ζs: 1.2; H4p: -4.0, ζp: 1.2.
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53349137590
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xc,...)]: (Equation Presented)
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xc,...)]: (Equation Presented)
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31
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3543090314
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In this work, the real-space hopping integrals and orbital coefficients are all extracted from FP-LMTO calculations
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