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Electronic Structures and Chemical Bonding of Minerals and Complexes II. Multielectronic Atoms, Bonding and Molecules Physical Chemistry of Minerals and Aqueous Solutions DM Sherman, University of Bristol Electronic Configurations: Pauli Exclusion Principle We can approximate the electronic structures of multielectronic atoms as electronic configurations over one-electron (hydrogen-like) orbitals. The Pauli Exclusion principle states that no two electrons in an atom can have the same four quantum numbers. Hence, we can only put two electrons (one spin-up and one spin-down) in each nlm orbital. The Quantum Numbers and the Periodic Table of the Elements Stable Electronic Configurations Atoms like to adopt closed-shell configurations. To do this, they may gain or lose electrons to become ions Na0 : open shell Na: open shell Na+: closed shell Na+: closed shell Stable Electronic Configurations (Cont.) The most stable ionization state of Si is the Si4+ ion. The semiclosed shell Si2+ ion does exist in interstellar gas, however. Si0: open shell Si4+: closed shell Stable Electronic Configurations (Cont.) Iron cannot adopt a closed-shell configuration... Fe0: open shell Fe3+: open shell Crystal Field Theory Tetrahedral Octahedral eg t2 10Dq e t2g Multiplet States One-electron orbitals: t2g (= xy,yz,xz), eg (= x2-y2, z2) Electronic Configuration: (t2g)2(eg)1 Slater Determinants: Spectroscopic States: |xy,yz,x2-y2|, |xy,xz,x2-y2|, |xy,yz,z2|, |xy,xz,z2|, |yz,xz,z2| 4T 2g + 4T1g Ions and Electronic Configurations Whether an atom will gain electrons to become an anion or lose electrons to become a cation depends on its electronegativity relative to other atoms. Atoms with high electronegativity tend to become anions. More precisely, if two neutral atoms come together, the more electronegative atom will receive electrons and become the anion. Mg + O → Mg2+ + O2- Electronegativity Stable Ions and Oxidation states The full ionic charge is only realized in completely ionic compounds. Otherwise it is only the formal oxidation state. Chemical bonding: ionic vs. covalent When electrons are completely transferred between atoms to yield cations and anions, the atoms will be held together by ionic bonds. If atoms have similar electronegativities, they adopt closed-shell configurations by sharing electrons with each other; the atoms are held together by covalent bonds. The chemical bond between two different elements is intermediate between the ionic and covalent extremes. The %ionic character is determined from the difference in electronegativity. Molecular Orbital Theory Linear Combination of Atomic Orbitals (LCAO) The quantum states of a molecule are molecular orbitals (ψi). These are constructed by taking linear combinations of atomic orbitals (φi) to yield bonding molecular orbitals " = c1#1 + c2#2 ! + + + = ! ! + ! and antibonding molecular orbitals ! " = c1#1 $ c2#2 ! ! + - + ! = + ! + ! Molecular Orbital Theory: π vs σ bonds ! + ! "-antibonding + #-antibonding + ! ! + ! + + ! ! + + + ! ! ! py px #-bonding + ! ! + + "-bonding Molecular Orbital Theory of Si-O bond Si Atomic Levels In quartz, the Si-O bond is partially covalent: electrons are shared by the O(2p) and Si(3p) orbitals. O Atomic Levels 2p " ! Energy The “core” atomic orbitals (e.g., Si 1s, 2s, 2p and O 1s) are highly localized and do not participate in bonding; they retain their atomic character. 3p !* "* 3s !* ! 2p 2s 1s 2s 1s Molecular orbitals involving d-orbitals # + !-antibonding (eg symmetry) # + + # + # + # + # !-bonding (eg symmetry) # # # # # + + # # + + # + + # # + # # + # + + "-antibonding (t2g symmetry) + # + # + + + # + # + "-bonding (t2g symmetry) # + Chemical Bonding: Theoretical Pictures Ionic Approximation (Crystal Field Theory) Localized electrons MgO (Fe,MgO) Molecular Orbital Theory Band Theory (solids) FeO Delocalized electrons FeS Electronic Structures of Fe-Mn Oxides The d-orbitals can be viewed as antibonding molecular orbitals. The crystal-field splitting results from σ− vs. π− antibonding.
