OC-IV

1. OC-IV Orbital Concepts and Their Applications in Organic Chemistry Klaus Müller Script ETH Zürich, Spring Semester 2010 Chapter 3 s-Character balancing for central atom hAO’s Ligand geometries around central atoms

2. In principle, sp3 hAO‘s is a good starting point for a tetrahedrally coordinated central atom, even if the ligand geometry deviates somewhat from an ideal tetrahedral geometry. There may be various reasons for he observation of ligand geometries that deviate markedly from ideal tetrahedral coordination: - steric interactions between the ligands - electronic interactions between the ligands other than steric - non-tetrahedral valence angle(s) when ligands are involved in rings - different electronegativities of the ligands electropositive ligand the s-LMO is polarized towards the central atom; the coefficient cs at the central atom for this s-LMO is comparatively large; electronic energy lowering by shifting s-character from low-amplitude hAO domain to high-amplitude hAO domain hence, any change in s-character of the hAO of the central atom will be strongly felt by this s-LMO electronegative ligand the s-LMO is polarized towards the ligand; the coefficient cs at the central atom for this s-LMO is comparatively small; Bent‘s rule: a central atom increases the s-character of its hAOs oriented towards electropositive ligands at the expense of s-character in hAO‘s towards electronegative ligands, i.e., hence, any change in s-character of the hAO of the central atom will be little felt by this s-LMO a central atom does not waste s-character towards electronegative ligands

3. 112.1° 114.7° 115.9° 106.7° 103.8° 102.4° hypothetical ligand of zero electronegativity s-LMO polarized towards central atom; any gain in s-character of center hAO results in marked energy gain of s-LMO s-LMO in the extreme becomes a lonepair orbital s-LMO polarized towards electronegative ligand atom; any change in s-character of center hAO has little effect on energy of s-LMO valence electron sextett 108.4° 120.0° 110.5° hypothetical ligand of infinite electronegativity s-LMO polarized towards electronegative ligand atom; any change in s-character of center hAO has little effect on energy of s-LMO s-LMO in the extreme becomes an empty hAO; no s-character is wasted for empty orbital: hence, empty orbital is pure p-AO; → planar geometry s-LMO polarized towards central atom; any gain in s-character of center hAO results in marked energy gain of s-LMO three s-LMO‘s receive all s-character in symmetrical case: three sp2-hAO‘s; geometry is trigonal planar

4. y g f2 x f1 g 180° 170° 160° 1 150° 1 - 2 140° cp 130° 120° 2 - cs 110° 2 1 - cs 100° 90° hAO p-character 50% 60% 70% 80% 80% 100% hAO s-character 50% 40% 30% 20% 10% 0% sp sp2 sp3 sp5 p relationships between s- and p-character of two equivalent hAO‘s and the interorbital axis angle g 2 2 f1 = cs.s + cp.px normalization : cs + cp = 1 2 2 f2 = cs.s + cp. (cosg.px + sing.py) orthogonality : cs + cp.cosg = 0 2 2 hence : 1 - cp + cp.cosg = 0 1 2 p-character : cp= 1 - cosg -cosg 2 s-character : cs= 1 - cosg g from p-character : cosg= g from s-character : cosg=

5. alkyl 108.4° ± 2.6° 109.6° ± 1.8° 111.3° ± 2.0° 112.7° ± 0.2° 108.1° ± 2.2° 109.1° ± 2.0° 111.0° ± 1.5° 110.9° ± 0.2° 104.5° 92.1° 90.6° 90.3° 111.7° 98.9° 96.2° 106.6 92.2 87.8 1.714 1.855 1.362 .. .. 0.14 - 0.20 Å q = 67° q q = 3.5° ± 3.7° q ~ 70°! X-ray of 1-benzyl- phosphole (BZPHOS10) pyrroles essentially planar p-conjugation pays for lone pair spx→ p promotion

6. + + 106.7° 109.8° 119.7° 110.9° 107.1° 102.4° 93.3° 98.9° 101.7° 113.0° q q q q q = 59.1° ± 3.4° q = 49.3° ± 3.5° q = 46.3° ± 6.5° q = 49.1° ± 5.7° 0.66 ± 0.04 Å 0.51 ± 0.04 Å 0.43 ± 0.06 Å 0.44 ± 0.05 Å h (pyr.height) ~ 19 kcal/mol ~ 10 kcal/mol ~ 8 kcal/mol ~ 8 kcal/mol N inversion barrier e- hn IP1 9.9 eV 9.0 eV 8.8 eV 8.7 eV 8.0 11.3 11.3 11.1 pKa(R=H) 7.9 - 10.3 10.1 pKa(R=CH3) amine basicity (in H2O) 215.7 kcal/mol 222.7 224.3 225.4 kcal/mol PA (R=H) 221.5 kcal/mol - 227.8 228.8 kcal/mol PA (R=CH3) proton affinity in gas-phase

7. ‡ DGN-inv ~ 8 kcal/mol 13-16 kcal/mol 26-30 kcal/mol very slow at RT very fast at RT fast at RT rates (RT) ~ 107 sec ~ 103 – 101 sec ~ 10-6 – 10-9 sec t1/2 (RT) ~ 10-7 sec ~ 10-3 – 10-1 sec ~ 106 – 109 sec ~ 10d– 10y first diastereomeric cis- and trans- N-methoxy isoxazolidin derivatives isolated by K. Müller & A.Eschenmoser, Helv.Chim.Acta 52, 1823 (1969) ‡ DGN-inv ~ 18-20 kcal/mol 25-28 kcal/mol >32 kcal/mol very slow at RT fast at RT very slow at RT first diastereomeric cis- and trans- N-Cl-aziridine derivatives isolated by A.Eschenmoser & D. Felix, Angew. Chem IE 7, 224 (1968) ‡ DGN-inv ~ 28-32 kcal/mol ~ 26-28 kcal/mol very slow at RT very slow at RT

8. kB.T DG# . e k = RT h t1/2 = ln2 / k T k (sec-1) -80°C 0°C 25°C 100°C DG# 5 9.106 6.108 1.109 9.109 kcal/mol 10 2.101 6.104 3.105 1.107 5.10-5 7.101 6.100 1.104 15 1.10-10 20 6.10-4 2.10-2 2.101 7.10-8 25 3.10-16 3.10-6 2.10-2 6.10-22 7.10-12 30 8.10-10 2.10-5 t1/2 (sec) T -80°C 0°C 25°C 100°C DG# 5 7.10-8 1.10-9 5.10-10 7.10-11 kcal/mol 10 1.10-5 2.10-6 6.10-8 3.10-2 15 ~4h 1.10-1 1.10-2 5.10-5 20 5.101 4.10-2 ~200y ~20min ~108y 3.101 25 ~120d ~2d ~8h 30 ~1013y ~3000y ~30y

9. z z z y y y x x x hAO2 = csss + csp (cosj (- py + px) – sinj pz) hAO3 = csss + csp (cosj (- py - px) – sinj pz) 2 2 cns + 3 css = 1 (1 valence s-AO available, eq 2) 2 2 2 cnpz + 3 csp sin j = 1 (1 valence pz-AO, eq 3) 2 2 1 3 3 3 2 2 3 csp cos j = 2 (2 valence px,y-AO‘s, eq 4) 2 2 cns + cnpz = 1 (n-HAO normalized, eq 1) 1 1 √3 √3 2 2 2 2 2 2 csp = csp = 2 2 2 cnpz = css = cns = quantitative relationships between hAO s- and p-characters for a trigonal pyramidal center with a lone pair as a function of ligand geometry r r j j r g r d 1 lonepair spn hybrid-AO pojnting along z-axis 3 equivalent spm hybrid-AO‘s pojnting along axes of trigonal pyramid relationship between out-of-plane angle j and valence bond angle g d2 = 2r2 – 2r2 cos g d2 = 2r2 – 2r2 cos 120° r= r cosj cos2j = (1 – cosg) hAOn = cnss + cnpzpz hAO1 = csss + csp (cosj py – sinj pz) contraints and normalization: 1 1 (from eq 4) hence: cos j 1 - cosg 2 - 3 cosg 2 2 cnpz = 1 – 2 tg j (from eq 3) 1 - cosg 1 + 2 cosg 2 2 cns = 2 tg j (from eq 1) 1 - cosg - cosg 2 2 css = (1 - 2 tg j) (from eq 2) 1 - cosg

10. 120 110 3 2 cosg = 1 - cos j 2 100 90 2 2 80 cos j cos j 70 - 2 3 cosq = 60 √ 4 - 3 50 40 30 20 10 0 q j g 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 j e(p) e(s-hAO) e(sp3) e(sp2) e(n-hAO) e(s) for extreme pyramidalities, the poor s-orbital overlap of a p-AO with the ligand hAO, results in a destabilization of the s-LMOs e(s-LMO) in this domain, the s-LMO‘s show a rather flat energy response to the rehybridization of the hAO‘s at the central atom; this response is the weaker the more the s-LMO‘s are polarized towards electronegative ligands; hence, in this domain, the energy of the doubly occupied lone pair orbital dictates the geometry by pulling as much s-character as possible from the hAO‘s involved in the s-LMO‘s trig tet tet q = tet/2

11. quantitative relationships between hAO s- and p-characters for a tetrahedral center with two different sets of ligands z z z y y y x x x 2 2 sin gA/2 = 1 – cos gA 2 2 2 csA + 2 csB = 1 2 2 2 2 2 cpB sin gB/2 = 1 2 cpA sin gA/2 = 1 2 2 2 2 csB + cpB = 1 csA + cpA = 1 1 1 2 cpA = = 2 2 sin gA/2 1 - cos gA - cos gA 1 2 csA = 1 - = 1 - cos gA 1 - cos gA 2 1 – 2 csA 1 + cos gA 2 csB = = 2 2 (1 - cos gA) _ _ _ 1 + cos gA cos gB = = – + + + 1 - 3 cos gA 2 2 1 – 3 cos gA cpB = 1 – csB = 2 (1 - cos gA) 2 2 cpB - 1 cpB - 1 2 2 ≈ cos gAd cpB cpB + 2 2 √2 √2 3 3 √2 2 equivalent spm hAO‘s along Z-A axes A A A A A A gA B B B gB 2 equivalent spn hAO‘s along Z-B axes B B B hAOA1,2 = csA s + cpA (cos gA/2 pz± sin gA/2 py) gA given; gB = f(gA) hAOB3,4 = csB s + cpA (- cos gB/2 pz± sin gB/2 px) contraints and normalization: (1 s-valence AO, eq 1) (1 py-valence AO, eq 2) (1 px-valence AO, eq 3) (normalization, eq 4) (normalization, eq 5) (from eq 2) hence: (from eq 4) (from eq 1) (from eq 5) (from eq 3) angular deviation: gA = (tet) ± d cos (gA ± d) = cos gA cos d sin gA sin d 1+ cos gAd 1 + cos gA 1 d cos gB = = – ≈ = (1 ) hence: 3 1 – 3 cos gA 2 opening of gA results in closing of gB and vice versa; and hence: increase in s-character in hAOA‘s and decrease in s-character in HAOB‘s

12. 1 + cos gA 1 + cos gA cos gB = – cos gB = – 1 – 3 cos gA 1 – 3 cos gA Search in Cambridge Structural DatabaseA = {Ctet} B = {N, O, F, P, S, Cl} all bonds acyclic at central C results in 253 X-ray structures: gB 108.3° gA 113.7° gB 1 + cos gA cos gB = – 1 – 3 cos gA gB = tet gB = 107.5° ± 3.2° gA-gB scattergram gA gA = tet gA = 115.4° ± 3.0° Search in Cambridge Structural DatabaseA = {C, N, O, F) all bonds acyclic at central C results in 12‘624 X-ray structures: gB gB gA 1 + cos gA cos gB = – 1 – 3 cos gA gB = tet gA-gB scattergram gA gA = tet

13. 114.7° ± 4.6° 109.9° ± 4.1° 108.5° ± 4.0° 108.0° ± 3.4° 113.2° ± 1.5° 110.4° ± 1.2° 108.1° ± 2.0° 107.6° ± 1.1° 115.9° ± 2.0° 110.6° ± 1.3° 110.9° ± 3.5° 109.7° ± 1.9° no equivalent orthonormal spx hAOs possible for bond vectors of < 90° interbond angle equivalent orthonormal spx hAOs along bond vectors of 90° interbond angle would be pure p-AOs resulting in poor s-LMOs and unacceptable angle (180°!) for exocyclic (sp) hAOs two equivalent spx hAOs (ca. sp5) defined by equivalent hAOs (ca. sp2) along exocyclic bond axes; two equivalent spx hAOs (ca. sp3) defined by equivalent hAOs along exocyclic bond axes sp5 hAO axes deviate ca.20° from CC bond axes of cyclopropane; off-axis hAOs result in significantly bent s-LMOs (s*-LMOs) sp3 hAO axes deviate only ca.10° from CC bond axes of cyclobutane; off-axis hAOs result in only slightly bent s-LMOs (s*-LMOs)