OC-IV

1. OC-IV Orbital Concepts and Their Applications in Organic Chemistry Klaus Müller Script ETH Zürich, Spring Semester 2009 Lecture assistants: Deborah Sophie MathisHCI G214 – tel. 24489mathis@org.chem.ethz.ch Alexey FedorovHCI G204 – tel. 34709 fedorov@org.chem.ethz.ch

2. Chapter 2 hybrid atomic orbitals (hAO’s) and their use in qualitative LMO pictures see also document:“Basic Features of MO Theory” on http://www.chen.ethz.ch/course/

3. 1/2 s + √3/2 pz √3/2 = 1/2 s - 1/√2 px - 1/√6 py - √3/6 pz = 1/2 s + √2/√3 py - √3/6 pz) = 1/2 s + 1/√2 px - 1/√6 py - √3/6 pz hAO’s for tetrahedral centers for an atom with a tetrahedral configuration, 4 equivalent valence sp3 hybrid-AO’s are used sp3 sp3 sp3 sp3 (1) (2) (3) (4) - sp3-hAO’s have 25% s-character and 75% p-character; hence the squared mixing coefficients for the s-AO and p-AO components are, 1/4 and 3/4, respectively, and the linear mixing coefficients are 1/2 and . - proper vector components for the px, py, pz-AO’s ensure that the sp3-hAO’s are correctly oriented and remain orthogonal and normalized: example: z sp3 (1) = 1/2 s + √3/2 (√8/3 (- √3/2 px - 1/2 py) - 1/3 pz) g = tetrahedral; cos g = -1/3 sin g = √8/3 sp3 (4) y 1/2 s + √3/2 (√8/3 py - 1/3 pz) x 1/2 s + √3/2 (√8/3 (+ √3/2 px - 1/2 py) - 1/3 pz) sp3 (2) sp3 (3)

4. / √2 √3 z z z 1/√3 y y y x x x 1/√3 s + √2/√3 (-1/2 py + √3/2 px) sp2(1) sp2(3) = 1/√3 s + √2/√3 py = 1/√3 s - 1/√6 py - 1/√2 px hAO’s for trigonal planar centers for an atom with a planar trigonal configuration, 3 equivalent valence sp2 hybrid-AO’s are defined sp2 sp2 sp2 p (1) (2) (3) (4) • since two orthogonal p-AO’s span a plane, it is convenient to choose the coordinate • system in such a way that two p-AO’s lie in the plane of the trigonal bond vectors; • this leaves a third p-AO unused, which is orthogonal to the plane,. • from the s-AO and two p-AO’s, three equivalent sp2-HAO’s can be formed, which • are mutually orthogonal and have 1/3 s-character and 2/3 p-character; hence, the squared mixing coefficients for the s-AO and p-AO components are 1/3 and 2/3, respectively, and the linear coefficients and , accordingly. - proper vector components for the px, py-AO’s ensure that the sp2-hAO’s are correctly oriented and remain mutually orthogonal and normalized; this is illustrated below for the case where the three sp2-HOA’s are defined in the (xy)-plane; the pz-AO remains unused: sp2 sp2 sp2 (1) (2) (3) 1/√3 s + √2/√3 (-1/2 py - √3/2 px) sp2(2) = 1/√3 s - 1/√6 py + 1/√2 px

5. sp(1) sp(2) = 1/√2 s + 1/√2 py = 1/√2 s - 1/√2 py hAO’s for centers with linear double coordination for an atom with a linear arrangement of two bonds, 2 equivalent valence sp Hybrid-AO’s are defined sp sp p p (1) (2) (3) (4) • it is convenient to orient the coordinate system so that one coordinate axis coincides with the linear coordination of the center. One p-AO along the linear • bond axis can then combine with the s-AO to generate two orthonormal sp-hAO’s; • the other two p-AO’s are orthogonal to this coordination axis and remain unused. • both sp-hAO’s have ½ s-character and ½ p-character; the squared mixing • coefficients on the two orthonormal sp-hAO’s are thus both ½, and the linear coefficients are ±1/√2. z z y y x x sp sp (1) (2)

6. - - + + - + qualitative LMO‘s from hAO‘s, 1sH AO‘s, and residual p-AO‘s A B A H approximate sAB-LMO approximate s*AB-LMO approximate sAH-LMO approximate s*AH-LMO The linear combination of two spx hAO‘s oriented along the connection axis of two adjacent atoms results in a bonding s-LMO and an antibonding s*-LMO. In the case of bonds to hydrogen atoms, the s- and s*-LMO are formed by linear combinations with the 1s-AO of the hydrogen atom. Although such linear combinations are only crude approximations to the LMO‘s obtained from rigorous LCAO MO SCF calculations, followed by a chemically unbiased orbital localization procedure, the results are in many cases remarkably close. Positive and negative linear combinations of p-AO‘s orthogonal to a given bond axis between adjacent atoms, can create, respectively, a bonding p-LMO and an antibonding p*-LMO, provided the p-AO axes on the adjacent atoms are properly aligned in a common p-plane. p-AO‘s twisted p plane reduction of p-p overlapand hence p-p interaction; p- and p*-LMO‘s with reduced bonding and antibonding character, resp. B A p-AO‘s 90° twisted p-p overlap and interaction vanish by symmetry; no bonding p-LMO and no antibonding p*-LMO can be formed. approximate pAB-LMO approximate p*AB-LMO

7. spx-hAO‘s or p-AO‘s for which no suitable partner orbital at an adjacent atom is available, remain as nonbonding n-LMO‘s. If electronically doubly occupied, these orbitals generally represent reasonable approximations to nonbonding lone pair orbitals as also obtained from rigorous LCAO MO SCF calculations followed by a chemically unbiased localization procedure. If electronically unoccupied, they represent vacant n-LMO‘s at an electron-deficient atom center. e.g.: B N Interactions between localized MO‘s Under which conditions do LMO‘s interact significantly? Rule 1: The interaction between two LMO‘s situated at neighboring atoms is related to the overlap integral between the LMO‘s. hence: - the interaction between two LMO‘s is attenuated rapidly with increasing spatial separation of the neighboring atom centers. Rule 2: The interactions between two LMO‘s situated at the same atom center is generally quite significant. hence: - for atoms in a saturated structural environment, local interactions between geminal LMO‘s are the largest interactions, followed by interactions between vicinal LMO‘s. Rule 3: There are no interactions between LMO‘s that are orthogonal by symmetry, i.e., either symmetrical or antisymmetrical with respect to global or even local symmetry elements. hence: - there are no (or essentially no) interactions between s-type and p-type LMO‘s pertaining to a local unsaturated structural unit, independently of the symmetry of the whole molecule.

8. Qualitative considerations of geminal and vicinal orbital interactions interactions between geminal LMO‘s in saturated systems geminal (n-s*)-interactions small geminal (s-s)-interactions large geminal (n-s)-interactions large geminal (s-s*)-interactions small interactions between vicinal LMO‘s in saturated systems vicinal synplanar n-s interactions significant; increasing with increasing pp components in n- and s-LMO LMO axes twisted by 90° vicinal n-s interactions small, decreasing withincreasing pp componentsin n- and s-LMO vicinal antiplanar n-s interactions small; more significant with increasing pp components in n- and s-LMO antiplanar vicinal n-s*-interaction more significant since phase change in s*-LMO opposite to large lobe of n-LMO; interaction increasing with increasing pp-character of s*-LMO vicinal synplanar n-s*-interactions comparatively small due to phase change in s*

9. Qualitative considerations of geminal and vicinal orbital interactions geminal interactions between pp n-LMO and s-LMO vanish for symmetry reasons geminal interactions between p-LMO and s-LMO vanish for symmetry reasons geminal interactions between p*-LMO and s-LMO vanish for symmetry reasons dominant interaction dominant interaction n-LMO n-LMO n-LMO p-LMO p-LMO p-LMO vicinal interaction between pp n-LMO and p-LMO significant if pp-orbitals properly aligned vicinal interaction between spx n-LMO and p-LMO reduced, but significant if pp-components properly aligned; increasing with increasing pp-component in n-LMO orbital axes of pp n-LMO and p-LMO twisted by 90°; (n-p)-orbital interaction vanishes for symmetry reasons similar arguments for vicinal interaction between n-LMO and p*-LMO dominant interaction dominant interaction vanishing interaction for symmetry reasons n-LMO n-LMO n-LMO p*-LMO p*-LMO p*-LMO

10. Interaction effects in the 2-LMO system An interaction between two LMO’s results in characteristic energy shifts (‘splitting’) and mixing effects as illustrated below for the degenerate and non-degenerate case: antibonding linear combination ‘orbital splitting due to orbital interaction’ DE = 0 bonding linear combination n-LMO n-LMO weakly antibonding linear combination ‘orbital splitting and mixing effects due to interaction between n-LMO and p*-LMO p*-LMO DE >0 weakly bonding linear combination n-LMO The orbital splitting and mixing effects - increase with increasing magnitude of the orbital interaction The orbital splitting and mixing effects - are maximal if the interacting orbitals are degenerate; - and decrease with increasing energy gap between the interacting orbitals

11. Conjugative stabilization in the 2-orbital-system with 2-electrons unoccupied energetically higher-lying orbital f2 doubly occupied energetically lower-lying orbital electron pair is stabilized by deb due to orbital interaction between LMO’s f1 and f2 f1 deb examples for conjugatively stabilized 2-electron 2-orbital systems: carbenium ion in a-position to ether oxygen carboxamide 1,3-butadiene N O O p-LMO doubly occupied p*-LMO unoccupied n-LMO (p-AO) unoccupied in valence sextett n-LMO (p-AO) doubly occupied n-LMO (pN-AO) doubly occupied p*CO-LMO unoccupied p*-LMO unoccupied p-LMO doubly occupied

12. Conjugative destabilization in the 2-orbital-system with 4-electrons 2 electrons are destabilized by deab due to the interaction between the LMO’s f1 and f2 deab f2 both LMO’s doubly occupied f1 2 electrons are stabilized by deb due to the interaction between the LMO’s f1 and f2 deb note that: deab ≥ deb hence, the net effect of the orbital interaction is a conjugative destabilization of the 4-electron 2-orbital system. → “Pauli exclusion principle repulsion” → “overlap repulsion” examples for conjugatively destabilized 4-electron 2-orbital systems: cyclopropenyl anion ethane ecliptic conformation hydrazine N N nN-LMO doubly occupied nN-LMO doubly occupied pCC-LMO doubly occupied sCH-LMO doubly occupied sCH-LMO doubly occupied n-LMO (pC-AO) doubly occupied

13. Qualitative aspects of conjugative stabilization for conjugated systems. Two structural subunits are said to be ‘conjugated’ if at least one LMO of one subunit interacts (significantly) with at least one LMO of the other subunit. The total ‘conjugative effect’ for two conjugated structural subunits can be approximated by the sum of conjugative effects for all individual two-orbital interaction systems between the two subunits. conjugative stabilization in the 2-orbital 2-electron system; DEn,p* ‘small enough’ to produce significant p-conjugative stabilization, resulting in net conjugative stabilization of the full system. N p* O conjugative destabilization in the 2-orbital 4-electron system N nN O p N O conjugative effects in empty 2-orbital system are not relevant for the discussion of conjugative effects in the electronic ground state of the full system. p* p* conjugative stabilization in both 2-orbital 2-electron systems, small net conjugative stabilization of the full system. p p conjugative destabilization in the 2-orbital 4-electron system s* s* conjugative effects in empty 2-orbital system are not relevant for the discussion of conjugative effects in the electronic ground state of the full system. conjugative stabilization in both 2-orbital 2-electron systems, very small conjugative stabilization due to weak interaction and large DE gap conjugative destabilization in the 2-orbital 4-electron system dominates, resulting in small net destabilization of the full system. s s

14. conditions for significant net conjugative stabilization effects are • strong orbital interaction between • occupied and unoccupied orbitals - small energy gap between these interacting orbitals schematic illustrations s* s* s* p* p* p* DE DE n n n DE DE DE DE DE DE n n n DE .. p p p .. s s s ..