Finding the Order in Complexity: The Electronic Structure of 14-1-11 Zintl Compounds

Yb14MnSb11 and Yb14MgSb11 have rapidly risen to prominence as high-performing p-type thermoelectric materials for potential deep space power generation. However, the fairly complex crystal structure of 14-1-11 Zintl compounds renders the interpretation of the electronic band structure obscure, making it difficult to chemically guide band engineering and optimization efforts. In this work, we delineate the valencebalanced Zintl chemistry of A14MX 11 compounds (A = Yb, Ca; M = Mg, Mn, Al, Zn, Cd; X = Sb, Bi) using molecular orbital theory analysis. By analyzing the electronic band structures of Yb14MgSb11 and Yb14AlSb11, we show that the conduction band minimum is composed of either an antibonding molecular orbital originating from the (Sb3) 7− trimer, or a mix of atomic orbitals of A, M, and X. The singly degenerate valence band is comprised of non-bonding Sb pz orbitals primarily from the Sb atoms in the (MSb4) mtetrahedra and the of isolated Sb atoms distributed throughout the unit cell. Such a chemical understanding of the electronic structure enables strategies to engineer electronic properties (e.g., the band gap) of A14MX 11 compounds.

The X atom can be any of the pnictides (Sb 15 , As 24 or Bi 16 ).
From detailed experimental and theoretical analysis of the high zT compositions Yb 14 MnSb 11 and Yb 14 MgSb 11 and related compounds it has been shown 15,23,[25][26][27][28] that the valence bands are essentially the same for the Sb compounds. The valence bands contain a simple, light valence band with a second heavier valence band close in energy that has high valley degeneracy which provides additional conduction paths, contributing to a high electrical conductivity, while maintaining a large thermopower 5,6 .
The electronic structure and chemical tunability of Yb 14 M Sb 11 can be generally explained using Zintl Chemistry 7 . Zintl compounds can be described as a network of covalently bonded complex anions with charge balanced by cations donating their valence electrons 29 . Thus, the valence of an atom can be defined as follows: where V represents the valence, e is the number of valence electrons, and b is the number Another way to understand the chemistry of the Zintl compounds is to combine the Zintl concept with molecular orbital analysis 32 . This method has been successfully applied to half-Heusler compounds to interpret band structures based on the characteristics of molecular In this study, we will focus on interpreting the computed band structures of two This difference can be attributed to the M cation in A 14 M X 11 . In Yb 14 M Sb 11 compounds, the conduction bands are separated into those that are purely of (Sb 3 ) 7− character (i.e., the σ * bands) and those that are higher in energy. The latter group of conduction bands have partial M character, meaning that the bands will be lower in energy in Yb 14 AlSb 11 than in Yb 14 MgSb 11 due to the higher electronegativity of Al. We also do not expect the absolute energies of the σ * bands to differ significantly between the two compounds, as the (Sb 3 ) 7− The (Sb 3 ) 7− linear trimer unit is isoelectronic to the triiodide ion I − 3 and therefore has similar molecular orbitals (Figure 4a). 24,32,45 The relative phases of the Sb-p orbitals in (Sb 3 ) 7− lead to distinct molecular orbital energies based on whether the neighboring interactions are bonding, antibonding, or nonbonding, as well as their configurations (i.e., whether they are σ-or π-oriented, see Figure 4a). When the p-orbitals of all three Sb atoms align in-phase along the axis of the trimer unit, the lowest-energy σ bonding state will form. However, if the neighboring interactions are out-of-phase instead, then the highest-energy σ * antibonding state will form. Due to the linear structure of the (Sb 3 ) 7− trimer, there is only one σ bonding state and one σ * antibonding state. Additionally, the p-orbitals of the Sb atoms can align perpendicular to the axis of the trimer unit, forming doublet π bonding and doublet π * antibonding states. The π and π * states are closer in energy than the σ and σ * states, as π-bonds are typically weaker than σ-bonds 32 . Moreover, there are nonbonding states both in the σ and π configurations. In total, each (Sb 3 ) 7− trimer unit contributes nine bands (two σ-type, four π-type, and three nonbonding) to the electronic structure of Yb 14 M Sb 11 , of which eight are filled with two electrons each. The one unfilled state, the σ * molecular orbital, should appear in the conduction bands of Yb 14 M Sb 11 . As a matter of fact, the σ * molecular orbital in Figure 4a corresponds precisely to the σ * bands in Figure 3a: the four σ * bands come from the four (Sb 3 ) 7− trimer units per primitive cell of Yb 14 M Sb 11 , and the charge density distribution of the σ * bands indicate antibonding character.
The molecular orbital diagram of the (AlSb 4 ) 9− tetrahedral unit (Figure 4b) is constructed following the methodology of Toriyama et al. 46 The bonding a 1 state of (AlSb 4 ) 9− is a molecular orbital in which the a 1 state of the Sb 4 complex, which appears as dumbbell-like orbitals at each corner of the tetrahedron oriented towards the central Al atom, interferes constructively with the s-orbital of the central Al atom. Due to the constructive interference, we expect the charge density for the a 1 state to be high between the central Al atom and the surrounding Sb 4 complex, as in the charge density shown in Figure 3b. On the other hand, the destructive interference leads the formation of a * 1 state. Moreover, we expect from molecular orbital theory that the a 1 bonding state of (AlSb 4 ) 9− consists of Al-s, Sb-s, and Sb-p character by symmetry, all of which are reflected in the a 1 peaks in the orbitaldecomposed DOS in Figure 2b

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.