Inorganic Chemistry Cheatsheet

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Biological Inorganic Chemistry 1. Metalloenzymes Enzymes containing a bound metal ion cofactor essential for catalytic activity. Metal ion (e.g., Fe, Cu, Zn, Mo) in active site, acts as Lewis acid, facilitates e-transfer, stabilizes transition states. Examples: Carbonic Anhydrase ($\text{Zn}^{2+}$), Cytochrome c Oxidase (Fe, Cu). 2. Role of Molybdenum in Xanthine Oxidase Mo (as Moco) is the site of catalysis. Catalyzes oxidation of hypoxanthine to xanthine, and xanthine to uric acid. Mo cycles between $\text{Mo}(\text{VI})$ and $\text{Mo}(\text{IV})$ oxidation states, accepting/donating electrons. 3. Role of Cobalt in Vitamin B$_{12}$ Cobalt (Co) ion in corrin ring (typically $\text{Co}(\text{III})$ or $\text{Co}(\text{I})$). Facilitates formation of reactive Co-C bond, which undergoes homolytic cleavage to generate a deoxyadenosyl radical. Radical catalyzes rearrangements and methyl transfer reactions. 4. Rubredoxin vs Ferredoxin Feature Rubredoxin (Rd) Ferredoxin (Fd) Structure Mononuclear Fe center, $\text{Fe}^{3+/2+}$ coordinated by 4 Cys thiolate groups. Di- or polynuclear Fe-S clusters (e.g., [2Fe-2S], [4Fe-4S]), Fe coordinated by inorganic $\text{S}^{2-}$ and Cys. Electron Transfer Mediates one-electron transfer. Generally mediates one-electron transfer. Reduction Potential Higher reduction potentials. Lower reduction potentials. 5. Why is Gadolinium used in MRI? $\text{Gd}^{3+}$ is a paramagnetic ion with seven unpaired f-electrons ($4f^7$). High magnetic moment alters relaxation times ($T_1$, $T_2$) of water protons. Enhances contrast between tissues. Chelation (e.g., Gd-DTPA) prevents toxicity. 6. Applications of cis-platin Widely used anticancer drug for testicular, ovarian, and bladder cancers. Mechanism: Loses chloride ligands inside cells, active Pt species coordinates to N7 of guanine in DNA. Forms intra- and inter-strand DNA cross-links, triggering apoptosis in cancer cells. 7. Chelation Therapy Medical procedure to treat heavy metal poisoning (e.g., Pb, Hg, Fe overload). Chelating agent binds to toxic metal, forming a stable, water-soluble complex. Complex is safely excreted from the body. Use: $\text{CaNa}_2\text{EDTA}$ for lead poisoning; Deferoxamine for iron overload. 1. Structure and Mechanism of Carbonic Anhydrase (CA) Function: Extremely fast enzyme vital for $\text{pH}$ regulation and $\text{CO}_2$ transport. Catalyzes reversible hydration of $\text{CO}_2$ to $\text{HCO}_3^-$ and $\text{H}^+$. $$ \text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{H}^+ $$ Structure: Metalloenzyme with a single $\text{Zn}^{2+}$ ion at its active site, located in a hydrophobic pocket. $\text{Zn}^{2+}$ is tetrahedrally coordinated by three histidine imidazole nitrogen atoms (His-94, His-96, His-119) and one water molecule or hydroxide ($\text{OH}^-$). The $\text{Zn}^{2+}$ acts as a strong Lewis acid. Mechanism (Catalytic Cycle): Water Ionization: $\text{Zn}^{2+}$ significantly lowers the $\text{pK}_{\text{a}}$ of coordinated $\text{H}_2\text{O}$ ($\approx 15.7 \to \approx 7$), facilitating rapid deprotonation to nucleophilic $\text{Zn}-\text{OH}^-$. A nearby buffer residue (e.g., His-64) shuttles the released proton away. $\text{CO}_2$ Binding and Attack: $\text{CO}_2$ enters the active site. The $\text{Zn}-\text{OH}^-$ attacks the electrophilic carbon of $\text{CO}_2$. Product Formation: This attack forms a zinc-bound bicarbonate ion ($\text{Zn}-\text{HCO}_3^-$). Water Displacement and Regeneration: A solvent $\text{H}_2\text{O}$ displaces the $\text{HCO}_3^-$ product, re-coordinates to $\text{Zn}^{2+}$, regenerating the initial $\text{Zn}-\text{H}_2\text{O}$ species. Cycle repeats. 4. Cytochrome P450 — Structure, Catalytic Cycle & Function Function: Superfamily of heme-containing monooxygenases crucial for metabolism of endogenous compounds (steroids) and xenobiotics (drugs, toxins) in the liver. Catalyze monooxygenation: one $\text{O}$ atom inserted into substrate ($\text{RH}$), other reduced to $\text{H}_2\text{O}$. $$ \text{RH} + \text{O}_2 + 2\text{e}^- + 2\text{H}^+ \to \text{ROH} + \text{H}_2\text{O} $$ Structure: Contain a single iron-porphyrin prosthetic group (heme) at the active site. Iron usually in $\text{Fe}(\text{III})$ state. Heme iron is coordinated by four pyrrole N atoms of the porphyrin ring and a fifth ligand: a thiolate group (sulfur) from a conserved cysteine residue. This axial thiolate ligand gives $\text{P}450$ its characteristic Soret band absorption at $450\ \text{nm}$ when $\text{Fe}(\text{II})$ is bound to $\text{CO}$. Catalytic Cycle: Substrate Binding: Substrate ($\text{RH}$) binds, displacing axial $\text{H}_2\text{O}$ ligand, changing $\text{Fe}(\text{III})$ from low-spin to high-spin. First Reduction: One electron reduces $\text{Fe}(\text{III})$ to $\text{Fe}(\text{II})$. $\text{O}_2$ Binding: Molecular oxygen ($\text{O}_2$) binds to $\text{Fe}(\text{II})$, forming an $\text{Fe}(\text{II})-\text{O}_2$ complex. Second Reduction and Protonation: A second electron and two protons are added. This cleaves the $\text{O}-\text{O}$ bond, releasing one $\text{H}_2\text{O}$ molecule. Reactive Intermediate: Highly reactive Compound I is formed ($\text{Fe}(\text{IV})$ oxo species coupled with a porphyrin $\pi$-cation radical, formally $\text{Fe}(\text{V})=\text{O}$). Oxygen Transfer: Compound I abstracts a hydrogen atom from $\text{RH}$, forming an $\text{R}\cdot$ radical and an $\text{Fe}(\text{IV})-\text{OH}$ species. The hydroxyl group recombines with $\text{R}\cdot$ to form hydroxylated product ($\text{ROH}$). Product Release: $\text{ROH}$ dissociates, enzyme returns to initial $\text{Fe}(\text{III})$ state. 8. Cis-platin: Clinical Use, Mechanism & DNA Binding Clinical Use: Cornerstone chemotherapeutic agent for testicular, ovarian, bladder, and head/neck cancers. Administered intravenously, often in combination regimens. Mechanism of Action: Prodrug activated by chloride concentration differences. Uptake & Activation: Neutral $\text{cis}-\text{Pt}$ complex enters cell. In low $\text{Cl}^-$ cytoplasm/nucleus ($\approx 3-20\ \text{mM}$), chloride ligands are displaced by water (aquation), forming active, positively charged $\text{cis}-[\text{Pt}(\text{NH}_3)_2(\text{H}_2\text{O})_2]^{2+}$. Targeting DNA: The active electrophilic platinum complex binds to nucleophilic N atoms of DNA bases. DNA Binding: Primary therapeutic target is DNA. Activated Pt binds covalently to the $\text{N}7$ atoms of purine bases, specifically guanine (G). Most crucial lesions ($\approx 90\%$ of adducts) are intra-strand cross-links between adjacent bases on the same DNA strand: $\text{GG}$ Adduct: Cross-link between two adjacent guanines (d(GpG)). $\text{AG}$ Adduct: Cross-link between adjacent adenine and guanine (d(ApG)). This $\text{Pt}-\text{DNA}$ cross-link causes severe local kinking and unwinding of the double helix, distorting DNA structure. Distortion recognized by cellular repair/transcription proteins, preventing DNA replication and RNA transcription. If DNA damage is irreparable, it triggers cell apoptosis, destroying the cancer cell. Organometallic Chemistry 8. Organometallic Compounds and Classification Compounds with at least one direct M-C bond (metal/metalloid to carbon). Classification by M-C Bond Character: Main Group OMCs: Ionic/polar covalent (e.g., RLi, RMgX). Covalent OMCs: Predominantly covalent M-C bonds (e.g., $\text{ZnMe}_2$, $\text{SnEt}_4$). Transition Metal OMCs: Covalent, $\sigma$ and/or $\pi$ bonding (e.g., Ferrocene, $\text{RhCl}(\text{PPh}_3)_3$). 9. Hapticity ($\eta$) Number of ligand atoms simultaneously bonded to a central metal atom. Denoted by $\eta^n$ (n = number of atoms). Example: In ferrocene, $\text{C}_5\text{H}_5$ ligand is $\eta^5$. Formula: $\text{Fe}(\eta^5-\text{C}_5\text{H}_5)_2$. 10. The 18-Electron Rule Guideline for stability of transition metal organometallic complexes. Stable diamagnetic complexes often have 18 electrons (metal d-electrons + ligand electrons). Corresponds to filling of metal's valence orbitals (1s, 3p, 5d = 9 orbitals $\times$ 2 e- = 18e-). 11. Effective Atomic Number (EAN) Total electrons around metal nucleus (metal's own + donated by ligands). $\text{EAN} = (\text{Atomic Number of Metal}) - (\text{Oxidation State}) + (\text{Total electrons donated by all ligands})$. If EAN = atomic number of next noble gas, the 18e- rule is satisfied. 12. $\beta$-Elimination Crucial decomposition pathway for alkyl/hydride complexes. Transfer of H from $\beta$-carbon to metal center, forming M-H bond. Requires empty coordination site. Results in elimination of an alkene. Contributes to instability of many alkyl-transition metal complexes. 13. Main-Group vs Transition-Metal Organometallics Feature Main-Group OMCs Transition-Metal OMCs Metal Groups 1, 2, 12-16 (Li, Mg, Al, Sn) Groups 3-11 (Fe, Rh, Pt) Bonding Ionic or highly polar covalent ($\sigma$ bonds). Covalent ($\sigma$ and $\pi$ bonds, often synergic). Reactivity Highly reactive (strong bases/nucleophiles), air/water sensitive. Diverse reactivity, often used in catalysis. Stability Rule No simple electron count rule. Often obey 18-electron rule. Ligands Simple alkyls/aryls (e.g., MeLi). Wide variety of $\pi$-acid/donor ligands (CO, $\text{PR}_3$, alkenes). 14. Tertiary Phosphine Ligands ($\text{PR}_3$) Versatile ligands due to adjustable electronic and steric properties. Electronic Effects: Generally $\sigma$-donors (P lone pair) and $\pi$-acceptors (backbonding into $\text{P}-\text{C}$ $\sigma^*$ or d-orbitals). Electron-withdrawing R groups (e.g., $\text{P}(\text{OPh})_3$) enhance $\pi$-acidity. Electron-donating R groups (e.g., $\text{PMe}_3$) enhance $\sigma$-donating ability. Steric Effects: Size of R groups determines cone angle ($\theta$), influencing coordination number, geometry, and reaction pathways. 15. Metallocenes Organometallic compounds with a metal "sandwiched" between two cyclopentadienyl (Cp, $\text{C}_5\text{H}_5$) rings. General formula $\text{M}(\eta^5-\text{C}_5\text{H}_5)_2$. Cp rings $\pi$-bonded with $\eta^5$ hapticity. High thermal and chemical stability. Examples: Ferrocene ($\text{Fe}(\eta^5-\text{C}_5\text{H}_5)_2$) - 18e- complex. Nickelocene ($\text{Ni}(\eta^5-\text{C}_5\text{H}_5)_2$) - 20e- complex. 16. TON vs TOF Used to evaluate catalyst efficiency. Turnover Number (TON): Total moles of substrate converted per mole of catalyst before deactivation. Measure of productivity/lifetime. Turnover Frequency (TOF): Moles of substrate converted per mole of catalyst per unit time. Measure of intrinsic activity/speed. 17. CO Stretching Frequency Decrease Upon Coordination $\nu_{\text{CO}}$ decreases when CO coordinates to a metal compared to free CO ($2143\ \text{cm}^{-1}$). Due to synergic bonding ($\sigma$-donation and $\pi$-backbonding): $\sigma$-Donation: CO donates electron density from its HOMO to the metal. $\pi$-Backbonding: Metal donates electron density from a filled d-orbital into CO's $\pi^*$-antibonding LUMO. Backbonding populates $\pi^*$-antibonding orbital, weakening C$\equiv$O bond, lengthening C-O bond, and decreasing $\nu_{\text{CO}}$. Magnitude of decrease indicates strength of $\pi$-backbonding. $\pi$-Acid Complexes & Carbonyls 18. $\pi$-Acid Ligands Ligands with empty $\pi^*$ or d orbitals that accept electron density from metal d-orbitals. Process ( $\pi$-backbonding) stabilizes metal center, especially in low oxidation states (e.g., M(0), M(-1)). Examples: Carbon Monoxide (CO), Nitrosyl (NO), isocyanides (CNR), phosphines ($\text{PR}_3$), alkenes/alkynes. 19. Synergic Bonding in CO Complexes Mutually reinforcing interaction between metal and CO ligand, stabilizing the complex. Components: $\sigma$-Donation: CO donates electron density from its C lone pair to an empty d-orbital on the metal. $\pi$-Backdonation: Electron-rich metal harmonizes by donating electron density from its filled d-orbitals back to CO's empty $\pi^*$-antibonding orbitals. This reciprocal donation strengthens M-C bond and weakens C-O bond. 20. IR Spectral Features of Metal Carbonyls IR $\nu_{\text{CO}}$ is a powerful tool for determining metal oxidation state and CO coordination mode. Characteristic $\nu_{\text{CO}}$ ranges: Free CO: $\approx 2143\ \text{cm}^{-1}$ Terminal CO ($\text{M}-\text{C}\equiv\text{O}$): $2125 - 1850\ \text{cm}^{-1}$ Bridging CO ($\text{M}-(\mu_2-\text{CO})-\text{M}$): $1850 - 1750\ \text{cm}^{-1}$ Triply Bridging CO ($\mu_3-\text{CO}$): $1750 - 1620\ \text{cm}^{-1}$ Lower $\nu_{\text{CO}}$ indicates stronger $\pi$-backbonding and lower metal oxidation state. 21. Linear and Bent NO Bonding Feature Linear NO ($\nu_{\text{NO}} > 1650\ \text{cm}^{-1}$) Bent NO ($\nu_{\text{NO}} Geometry M-N-O angle $\approx 180^{\circ}$. M-N-O angle $\approx 120^{\circ}$. Formal Count $\text{NO}^{+}$ (Nitrosylium) is a 3-electron donor. $\text{NO}^{-}$ (Nitroso) is a 1-electron donor. Formal Charge N is formally positive. N is formally negative. These represent extremes of a continuum of resonance structures. 22. Isolobal Analogy Conceptual tool relating bonding of organic fragments to organometallic fragments. Two fragments are isolobal if their frontier molecular orbitals (HOMO/LUMO) have same symmetry, electron count, shape, and energy. Use: Predict structures/reactivity of organometallic/cluster compounds based on organic molecules. Example: $\text{CH}_3$ radical is isolobal with $\text{Mn}(\text{CO})_5$ radical. 23. M-M Bond Order in $\text{Mn}_2(\text{CO})_{10}$ Total Valence Electrons (TVE): Mn (Group 7): $7 \times 2 = 14$ e- CO (2-e donor): $10 \times 2 = 20$ e- TVE = $14 + 20 = 34$ e- Required Electrons for 18e- Rule: $18 \times 2 = 36$ e- (for two Mn atoms). Electron Deficit (for M-M bond): $36 - 34 = 2$ e-. M-M Bond Order: A deficit of 2 electrons means one Mn-Mn single bond. Bond order = 1. Molecular Symmetry 24. Symmetry Elements and Operations Symmetry Element: A geometrical entity (point, line, or plane) for symmetry operations. Symmetry Operation: A movement leaving the molecule in an indistinguishable arrangement. Element Operation Symbol Center of Inversion Inversion $i$ Plane of Symmetry Reflection $\sigma$ Proper Axis of Rotation Rotation $C_n$ Improper Axis of Rotation Rotation-Reflection $S_n$ Identity Do nothing $E$ 25. Difference Between $\sigma_v$, $\sigma_h$, and $\sigma_d$ $\sigma_h$ (Horizontal): Plane of symmetry perpendicular to the principal ($C_n$) rotation axis. $\sigma_v$ (Vertical): Plane of symmetry that contains the principal ($C_n$) rotation axis. $\sigma_d$ (Dihedral): A type of $\sigma_v$ that bisects the angle between two adjacent $C_2$ axes perpendicular to the principal $C_n$ axis. Found in $D_{nd}$ point groups. 26. Improper Rotation Axis $S_n$ Symmetry element corresponding to the Improper Rotation ($S_n$) operation. Operation: Rotation by $360^{\circ}/n$ about the axis ($C_n$). Reflection in a plane perpendicular to the axis ($\sigma_h$). Final position must be indistinguishable from initial. Example: Methane ($\text{CH}_4$) has three $S_4$ axes. 27. Equivalent Combination of Operations to $S_n$ $S_n$ operation is a combination of a proper rotation ($C_n$) and a horizontal reflection ($\sigma_h$). $S_n = C_n \times \sigma_h$ (or $\sigma_h \times C_n$). Note: If $n$ is even, $S_n^n = E$. If $n$ is odd, $S_n^n = \sigma_h$ and $S_n^{2n} = E$. 28. Subgroup, Group, and Class Group: Set of symmetry operations for a molecule satisfying closure, associativity, identity, and inverse criteria. Subgroup: A subset of a larger group's operations that itself satisfies group criteria. Class: Collection of symmetry operations within a group that are conjugate to one another ($B = X^{-1}AX$). Operations in the same class have same characteristics. 29. Assign Point Groups to $\text{H}_2\text{O}$ / $\text{NH}_3$ $\text{H}_2\text{O}$ (Water): Principal axis: $C_2$ (bisects H-O-H angle). Planes: Two $\sigma_v$ planes (one molecular, one bisecting H-H). No perpendicular $C_2$. No $i$. Point Group: $C_{2v}$ $\text{NH}_3$ (Ammonia): Principal axis: $C_3$ (along N-H bond bisector). Planes: Three $\sigma_v$ planes (each containing N and one H). No perpendicular $C_2$. No $\sigma_h$. Point Group: $C_{3v}$ 30. Full Form of FTIR Fourier-Transform Infrared.