Helsinki-3 Direct Estimate of Conjugation, Hyperconjugation and Aromaticity With an Energy Decomposition Analysis Gernot Frenking Fachbereich Chemie, Philipps-Universität

Helsinki-3

Direct Estimate of Conjugation, Hyperconjugation and Aromaticity With an Energy Decomposition Analysis

Gernot Frenking

Fachbereich Chemie, Philipps-Universität Marburg

Conjugation

What is conjugation?

“In a topological sense, the indication that each pair of multiple (double or triple) bonds in a polyunsaturated molecule is separated by one single bond.” Pure Appl. Chem. 1999, 71, 1919.

IUPAC Definition:

-carotene, the red pigment in carrots and other vegetables

“Conjugated compounds are usually more stable than bond-shifted isomers in which the double (triple) bonds are isolated from each other by more than on single one bond”

(a) isolated double bonds

(b) conjugated double bonds

Conjugation

Geometry

Reactivity

Properties

Short C–C distance: 1.453 Å

Hyperconjugation

What is hyperconjugation?

It is the interaction between orbitals having symmetry where at least one of the orbitals is located at an atom that does not have a multiple bond

(a')

(b')

(c') (d')

(a)

(b)

(c) (d)

π(sat

)

π(sat)π(sat)

π←π(sat)

π(sat)←π(sat)

+ H 2 + H 2

- 2 6 . 7 G 3

- 2 6 . 1 e x p t l

- 3 0 . 4 G 3

- 2 9 . 9 e x p t l ( 1 )

+ 2 H 2 + 2 H 2

- 7 0 . 6 G 3 - 7 0 . 4 G 3

- 6 9 . 5 e x p t l ( 2 )

+ +- 2 . 4 G 3

- 2 . 7 e x p t l ( 3 )

+- 4 . 9 G 3

- 4 . 7 e x p t l+

( 4 )

+ H 2 + H 2

- 2 4 . 3 - 3 2 . 8

( 5 )

+ 2 H 2 + 2 H 2

- 6 5 . 7 - 7 5 . 3

( 6 )

Energy Decomposition Analysis (EDA) Extended Transition State Method (ETS)K. Morokuma, J. Chem. Phys. 1971, 55, 1236 T. Ziegler, A. Rauk, Theor. Chim Acta 1977, 46, 1

A + B A-B

(A) + (B) [(A) + (B)](rA-B)

Eelstat

(A,B) =NÂ(A,B)

EPauli

NÂ

(A,B) (A-B)

EOrb

1.

2.

3.

1. + 2. + 3. = Eint

Eint + Eprep = E(BDE)

Three Steps:

(A-B)

(A-B)

T a b l e 1 . R e s u l t s o f t h e e n e r g y d e c o m p o s i t i o n a n a l y s i s . E n e r g y v a l u e s i n k c a l / m o l .

H C C - C C H H 2 C C H - C H C H 2 H C C - C H 3 H C C - C ( C H 3 ) 3 H 2 C C H - C H 3 H 2 C C H - C ( C H 3 ) 3 H C C - C H C H 2 ( C H 3 ) 3 C - C ( C H 3 ) 3 C H 3 - C H 3

S y m m e t r y D ? h C 2 h C 3 V C 3 V C S C S C S D 3 d D 3 d E i n t - 1 7 6 . 0 - 1 2 8 . 5 - 1 4 3 . 6 - 1 3 3 . 1 - 1 1 9 . 4 - 1 0 8 . 8 - 1 5 0 . 2 - 9 3 . 2 - 1 1 4 . 8 E P a u l i 1 6 1 . 8 2 6 8 . 4 1 7 6 . 5 2 1 9 . 1 2 2 8 . 9 2 6 7 . 9 2 0 9 . 4 2 5 3 . 6 2 0 0 . 8

E e l s t a ta - 1 1 4 . 6

( 3 3 . 9 % ) - 1 6 9 . 9

( 4 2 . 8 % ) - 1 2 5 . 5

( 3 9 . 2 % ) - 1 5 1 . 8

( 4 3 . 1 % ) - 1 4 7 . 5

( 4 2 . 4 % ) - 1 7 1 . 8

( 4 5 . 6 % ) - 1 4 3 . 1

( 3 9 . 8 % ) - 1 6 3 . 5

( 4 7 . 2 % ) - 1 3 1 . 3

( 4 1 . 6 % )

E O r ba - 2 2 3 . 3

( 6 6 . 1 % ) - 2 2 7 . 0

( 5 7 . 2 % ) - 1 9 4 . 6

( 6 0 . 8 % ) - 2 0 0 . 4

( 5 6 . 9 % ) - 2 0 0 . 7

( 5 7 . 6 % ) - 2 0 4 . 9

( 5 4 . 4 % ) - 2 1 6 . 4

( 6 0 . 1 9 % ) - 1 8 3 . 2

( 5 2 . 8 % ) - 1 8 4 . 2

( 5 8 . 4 % )

E b - 1 7 8 . 3 ( 7 9 . 8 4 % )

- 2 0 7 . 5 ( 9 1 . 4 % )

- 1 7 4 . 6 ( 8 9 . 6 8 % )

- 1 7 9 . 8 ( 8 9 . 7 % )

- 1 9 1 . 5 ( 9 5 . 3 8 % )

- 1 9 5 . 4 ( 9 5 . 3 7 % )

- 1 9 5 . 9 ( 9 0 . 5 % )

- 1 7 1 . 0 ( 9 3 . 3 % )

- 1 7 4 . 3 ( 9 4 . 5 8 % )

E b - 4 5 . 0 ( 2 0 . 1 5 % )

- 1 9 . 5 ( 8 . 5 9 % )

- 2 0 . 1 ( 1 0 . 3 2 % )

- 2 0 . 6 ( 1 0 . 2 8 % )

- 9 . 3 ( 4 . 6 1 % )

- 9 . 5 ( 4 . 6 3 % )

- 2 0 . 5 ( 9 . 5 % )

- 1 1 . 6 ( 6 . 3 5 % )

- 1 0 . 0 ( 5 . 4 1 % )

E p r e p 5 . 4 1 3 . 0 1 3 . 1 1 4 . 5 1 7 . 2 1 8 . 8 2 3 . 8 3 0 . 2 2 1 . 8 E ( = - D e ) - 1 7 0 . 6 - 1 1 5 . 6 - 1 3 0 . 6 - 1 1 8 . 6 - 1 0 2 . 2 - 9 0 . 0 - 1 2 6 . 4 - 6 3 . 0 - 9 3 . 0 r ( C - C ) [ Å ] 1 . 3 6 1 1 . 4 5 3 1 . 4 5 6 1 . 4 6 9 1 . 5 0 0 1 . 5 1 6 1 . 4 1 9 1 . 5 9 1 1 . 5 3 2

a T h e % a g e v a l u e s i n p a r e n t h e s e s g i v e t h e c o n t r i b u t i o n t o t h e t o t a l a t t r a c t i v e i n t e r a c t i o n s Δ E e l s t a t + Δ E o r b . b T h e % a g e v a l u e s i n p a r e n t h e s e s g i v e t h e c o n t r i b u t i o n t o t h e o r b i t a l i n t e r a c t i o n s Δ E o r b .

D. Cappel, S, Tüllmann, A. Krapp, F. Frenking, Angew. Chem. Int. Ed. 2005, 117, 3683.

Conjugation

BP86/TZ2P. Energy Values in kcal/mol

4 5 6 7 8 9 10

-19,5

-20,0

-20,5

-21,0

-21,5

-22,0

-22,5

-23,0

-23,5

Model: ExpGro1 Equation: y = A1*exp(x/t1) + y0 Chi^2/DoF = 0.00005R^2 = 0.99999 y0 -23.69 ±0.0127A1 24.05227 ±0.32081t1 -2.2579±0.01964E

/k

calm

ol-1

n C atoms

1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

9

10

Symmetry C2h C2h C2h C2h

Eint -128.5 -132.1 -133.0 -133.4

EPauli 268.4 271.3 272.4 273.0

Eelstat -169.9 (42.8%) -172.4 (42.7%) -173.0 (42.7%) -173.4 (42.7%)

EOrb -227.5 (57.2%) -231.1 (57.3%) -232.3 (57.3%) -233.0 (57.3%)

E -207.5 (91.4%) -209.0 (90.5%) -209.4 (90.1%) -209.6 (90.0%)

E

ΔE

-19.5 (8.6%)

-22.0 (9.5%)

-2.5

-23.0 (9.9%)

-1.0

-23.4 (10.0%)

-0.4

Eprep 13.0 13.4 13.6 13.7

E (=-De) -115.5 -118.7 -119.4 -119.7

r(C2−C3) / Å 1.453 1.444 1.441 1.439

200 220 240 260 280 300 320 340

-20

-21

-22

-23

Model: ExpGro1 Equation: y = A1*exp(x/t1) + y0 Chi^2/DoF = 0.00428R^2 = 0.99951 y0 -24.336±0.26037A1 101.43748 ±30.22802t1 -70.83613 ±8.01398

E

/ kca

lmo

l-1

Wavelength / nm

Conjugation


1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

9

10

Symmetry C2h C2h C2h C2h

Eint -128.5 -278.9 -429.9 -581.3

Eint(extra) - -21.9 -22.5 -22.9

EPauli 268.4 501.0 737.2 976.1

Eelstat -169.9 (42.8%) -340.2 (43.6%) -512.5 (43.9%) -686.0 (44.0%)

EOrb -227.5 (57.2%) -439.7 (56.4%) -654.6 (56.1%) -871.4 (56.0%)

E -207.5 (91.4%) -398.3 (90.6%) -589.8 (90.1%) -782.1 (89.7%)

E

E

-19.5 (8.6%)

-19.5

-41.4 (9.4%)

-21.9

-64.9 (9.9%)

-23.5

-89.3 (10.2%)

-24.4

Eprep 13.0 17.4 22.7 27.8

E (=-De) -115.5 -261.1 -407.2 -553.5

r(C−C) 1.453 1.444 C2-C3: 1.441

C4-C5: 1.432

C2-C3: 1.439

C4-C5: 1.428

Conjugation


n 0 1 2 3 4

Symmetry D∞h D∞h D∞h D∞h D∞h

Eint -176.0 -360.9 -547.4 -734.8 -922.8

EPauli 162.1 310.0 462.6 618.8 777.2

Eelstat -114.7 -228.0 -342.6 -458.3 -574.6

(33.9%) (34.0%) (33.9%) (33.9%) (33.8%)

EOrb -223.4 -443.0 -667.4 -895.3 -1125.4

(66.1%) (66.0%) (66.1%) (66.1%) (66.2%)

E -178.4 -346.7 -515.7 -685.6 -856.0

(79.8%) (78.3%) (77.3%) (76.6%) (76.1%)

E -45.0 -96.3 -151.7 -209.7 -269.4

(20.2%) (21.7%) (22.7%) (23.4%) (23.9%)

E -45.0 -51.3 -55.4 -58.0 -59.7

Eprep 5.4 9.1 13.5 18.3 23.4

E (=-De) -170.6 -351.8 -533.9 -716.5 -899.4

r(C–C)/Å 1.361 1.349 C2-C3: 1.345 C2-C3: 1.343 C2-C3: 1.342

C4-C5: 1.334 C4-C5: 1.329 C4-C5: 1.327

C2-C3: 1.345 C2-C3: 1.343 C6-C7: 1.324

H Hn

4 6 8 10 12

-44

-46

-48

-50

-52

-54

-56

-58

-60

H Hx

Equation: y = A1*exp(x/t1) + y0

Chi^2/DoF = 0.00025R^2 = 1 y0 -62.76918 ±0.04952A1 42.76372 ±0.13518t1 -4.5555±0.02673

E

/ kca

lmo

l-1

n of C atoms

Conjugation


H2Si SiH H2Si

SiH2

H2Si Si

H

CH2

H2Si

HSi

H2C

HSi

SiH

CH2

trans cis 1 2 3 3’ 4 5 6 Symmetry C2h C2v Cs Cs C2h Cs Cs C2h

Eint -128.5

-125.7 -131.3 -102.5 -135.7 -134.6 -110.8 -98.8 -79.5

EPauli 268.4 257.4 263.8 176.9 263.9 244.0 177.5 172.4 107.2

Eelstat[a] -169.9 -163.1 -160.4 -128.5 -152.9 -144.0 -125.6 -120.9 -88.8

(42.8%) (42.6%) (40.6%) (46.0%) (38.3%) (38.0%) (43.6%) (44.6%) (47.5%)

EOrb[a] -227.5 -220.0 -234.6 -150.9 -246.7 -234.6 -162.7 -150.3 -98.0

(57.2%) (57.4%) (59.4%) (54.0%) (61.7%) (62.0%) (56.4%) (55.4%) (52.5%)

E[b] -207.5 -202.7 -209.9 -138.9 -213.9 -205.1 -146.4 -136.9 -89.2

(91.4%) (92.2%) (89.5%) (92.1%) (86.7%) (87.4%) (89.9%) (91.1%) (91.0%)

E[b] -19.5 -17.2 -24.8 -12.0

-32.8 -29.5 -16.4 -13.4 -8.8 (8.6%) (7.8%) (10.5%) (7.9%) (13.3%) (12.6%) (10.1%) (8.9%) (9.0%)

Eprep 13.0 14.2 17.7 8.2 2.6 21.9 11.5 8.3 2.9

E (=-De) -115.5 -111.5 -113.6 -94.3 -133.1 -112.7 -99.3 -90.5 -76.6

r(X−X’)[c] 1.453 1.469 1.442 1.844 1.424 1.453 1.817 1.845 2.299

Conjugation


H2C

HSi

SiH

CH2

H2Si

HSi

SiH

SiH2

H2Si

HSi SiH

SiH2

trans cis 6 trans-7 cis-7 Symmetry C2h C2v C2h C2h C2v

Eint -128.5

-125.7 -79.5 -79.0 -77.8

EPauli 268.4 257.4 107.2 109.3 105.6

Eelstat[a] -169.9 -163.1 -88.8 -81.9 -78.6

(42.8%) (42.6%) (47.5%) (43.5%) (42.9%)

EOrb[a] -227.5 -220.0 -98.0 -106.4 -104.8

(57.2%) (57.4%) (52.5%) (56.5%) (57.1%)

E[b] -207.5 -202.7 -89.2 -93.7 -93.0

(91.4%) (92.2%) (91.0%) (88.1%) (88.7%)

E[b] -19.5 -17.2 -8.8 -12.6 -11.8

(8.6%) (7.8%) (9.0%) (11.9%) (11.3%)

Eprep 13.0 14.2 2.9 3.1 3.3

E (=-De) -115.5 -111.5 -76.6 -75.9 -74.5

r(X−X’)[c] 1.453 1.469 2.299 2.274 2.284

Conjugation


O

R

R=H R=Me R=OH R=NH2 R=F R=Cl R=Br R=I

NH

(E) Symmetry C2h Cs Cs Cs Cs Cs Cs Cs Cs Cs

Eint -128.5 -104.9 -101.4 -111.7 -102.4 -114.0 -104.8 -101.1 -95.3 -111.7

EPauli 268.4 324.3 317.8 296.2 302.7 295.4 310.1 316.8 327.1 316.3

Eelstat[a] -169.9

(42.8%)

-186.9

(43.5%)

-186.1

(44.4%)

-176.6

(43.3%)

-178.7

(44.1%)

-173.6

(42.4%)

-171.5

(41.3%)

-168.3

(40.3%)

-167.2

(39.6%)

-187.6

(43.8%)

EOrb[a] -227.5

(57.2%)

-242.3

(56.5%)

-233.2

(55.6%)

-231.3

(56.7%)

-226.4

(55.9%)

-235.7

(57.6%)

-243.3

(58.7%)

-249.6

(59.7%)

-255.2

(60.4%)

-240.4

(56.2%) E

[b] -207.5

(91.4%)

-221.8

(91.6%)

-215.1

(92.3%)

-212.9

(92.1%)

-210.8

(93.1%)

-215.1

(91.3%)

-222.2

(91.3%)

-228.2

(91.4%)

-233.8

(91.6%)

-220.3

(91.7%) E

[b] -19.5

(8.6%)

-20.5

(8.4%)

-18.0

(7.7%)

-18.4

(7.9%)

-15.6

(6.9%)

-20.6

(8.7%)

-21.1

(8.7%)

-21.4

(8.6%)

-21.4

(8.4%)

-20.1

(8.3%) Eprep 13.0 7.6 9.0 9.1 9.1 8.7 9.1 9.4 10.3 10.2

E (=-De) -115.5 -97.2 -92.4 -102.6 -93.3 -105.3 -95.7 -91.7 -85.1 -101.5

r(C−C)[c] 1.453 1.474 1.489 1.480 1.495 1.471 1.474 1.474 1.475 1.465

Conjugation

-0,6 -0,4 -0,2 0,0 0,2-15

-16

-17

-18

-19

-20

-21

-22

I

Cl

Br

FH

CH3

OH

R SD-0,97055 0,54405

E

/ kca

l mo

l-1

p

NH2

O

R

Conjugation

R H Me OH NH2 F CHO CO2H CN NO2

Eint -219.7 -229.0 -237.0 -251.7 -223.6 -211.8 -214.6 -209.5 -204.8

EPauli 293.3 293.1 288.5 290.4 286.2 289.1 290.1 285.5 284.2

Eelstata -172.0 -174.4 -174.0 -181.2 -166.5 -161.5 -164.7 -155.7 -154.6

(33.5%) (33.4%) (33.1%) (33.4%) (32.7%) (32.2%) (32.6%) (31.4%) (31.6%)

Eorba -341.0 -347.7 -351.5 -360.1 -343.3 -339.4 -331.9 -339.3 -334.5

(66.5%) (66.6%) (66.9%) (66.6%) (67.3%) (67.8%) (67.4%) (68.6%) (68.4%)

Eb -219.8 -228.7 -226.9 -226.9 -227.2 -227.6 -228.0 -226.6 -226.8

(64.4%) (65.8%) (64.5%) (62.9%) (66.2%) (67.1%) (67.1%) (66.8%) (67.8%)

Eb -119.4 -119.0 -124.6 -133.9 -116.1 -111.8 -112.0 -112.7 -107.8

(35.6%) (34.2%) (35.4%) (37.1%) (33.8%) (32.9%) (32.9%) (33.2%) (32.2%)


-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8-105

-110

-115

-120

-125

-130

-135

H2C R

H

NO2

CNCHO

CO2H

F

CH3

OH

NH2

E

/ kca

l mo

l-1

p Hammett

r = 0.95, r = 0.95, SD=2.60SD=2.60

-1,5 -1,0 -0,5 0,0 0,5 1,0-105

-110

-115

-120

-125

-130

-135

H2C R

CHOCO

2H CN

NO2

H

F

CH3

OH

E

/ kca

l mo

l-1

+

p Hammett

NH2

r = 0.97, r = 0.97, SD=2.15SD=2.15

Conjugation



Eint -176.3 -174.7 -171.9 -164.5 -178.0 -205.4 -202.4 -202.0 -214.4

EPauli 310.8 309.6 302.7 300.9 304.4 320.9 319.4 316.6 318.1

Eelstat -197.1 -194.7 -192.8 -187.0 -197.7 -211.6 -209.2 -210.2 -214.4 (40.5%) (40.2%) (40.6%) (40.2%) (41.0%) (40.2%) (40.1%) (40.5%) (40.3%)

EOrb -290.1 -289.6 -281.8 -278.4 -284.6 -314.7 -312.6 -308.5 -318.0 (59.5%) (59.8%) (59.4%) (59.8%) (59.0%) (59.8%) (59.9%) (59.5%) (59.7%)

E -220.2 -220.0 -216.2 -214.9 -216.5 -224.4 -223.4 -222.1 -221.5 (76.0%) (75.9%) (76.7%) (77.2%) (76.1%) (71.3%) (71.5%) (72.0%) (69.7%)

E -69.9 -69.7 -65.7 -63.5 -68.2 -90.3 -89.2 -86.4 -96.5 (24.0%) (24.1%) (23.3%) (22.8%) (23.9%) (28.7%) (28.5%) (28.0%) (30.3%)

-0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

-95

-90

-85

-80

-75

-70

-65

-60

H2C R

NO2

CN

CHOCO2H

E

/ kca

l mo

l-1

-

p Hammett

NH2

OH

CH3

H

F

r = 0.98, r = 0.98, SD=2.92SD=2.92

Conjugation in Cyanoethynylethenes, CEEs, Conjugation in Cyanoethynylethenes, CEEs, (Diederich)(Diederich)

151,0 151,5 152,0 152,5 153,0 153,5

-30

-32

-34

-36

-38

-40

E

/ kca

lmo

l-1

ipso

/ ppm

17

r = 0.99, SD= r = 0.99, SD= 0.430.43

NMe2D =


o

Cipso

NMe2D =o

Cmeta

1 7

r = 0.98, SD= r = 0.98, SD= 0.620.62

CN

CN

D

NC

CN

D

NC

R

CN

D

NC

R

CN

D

NC

D

DD

CN

CNNC

R

CN

D

NC

D

NC

RD

R

CN

RD

R

DD

R R

19 16 SiMe3R=

15 SiMe3R=

17 22 SiiPr3R=

18 (E)-12 SiiPr3R=

(Z)-12 SiiPr3R=

13 SiiPr3R=

ipso 153.41 152.58 152.28 151.98 151.51 151.42 151.14 151.06 150.95

meta 136.38 135.58 135.37 135.03 134.49 133.93 133.95 133.79 133.37

E -39.52 -35.62 -35.40 -31.29 -33.01 -31.59 -31.83 -31.21 -30.97

r 0.04201 0.03868 0.03854 0.03508 0.03691 0.3477 0.3526 0.03485 0.03447

r = 0.99, SD= r = 0.99, SD= 0.360.36

NMe2D =a

a'

b

b'

c

c'Calculated quinoid character: r = (((c + c’)/2 – (b + b’)/2) + ((a + a’)/2 – (b + b’)/2))/2.

D

A

D

A

DA

9a 9b 10

NMe2,D = NO2A =

ipsoa 150.69 150.76 150.60

Eb -31.37 -30.96 -29.08

rc 0.03477 0.03491 0.03315

I. Fernández, G. Frenking, Chem. Commun. 2006, 5030.

Hyperconjugation

X=H X=CH3 X=SiH3 X=F X=Cl

Symmetry Cs Cs Cs Cs Cs

Eint -119.4 -108.8 -107.9 -113.8 -102.7

E (a”) -9.3

(4.6%)

-9.5

(4.6%)

-14.4

(6.7%)

-11.6

(5.4%)

-14.7

(6.2%) E (a”) -4.0 -4.3 -5.8 -7.6 -8.9

E (a”) -6.0 -6.2 -9.7 -5.2 -6.9

E (=-De) -102.2 -90.0 -87.8 -103.4 -87.1

r(C−C) / Å 1.500 1.516 1.512 1.496 1.496

X=H X=CH3 X=SiH3 X=F X=Cl

Symmetry C3v C3v C3v C3v C3v

Eint -143.6 -133.1 -133.6 -130.4 -120.8

E -20.1

(10.3%)

-20.6

(10.3%)

-33.0

(14.6%)

-23.0

(11.1%)

-32.5

(13.3%) E -9.3 -10.4 -14.7 -17.2 -22.4

E -12.8 -12.6 -21.4 -9.8 -14.4

E (=-De) -130.5 -118.6 -117.5 -122.9 -108.1

r(C−C) / Å 1.456 1.469 1.446 1.456 1.435

H2C=CH–CX3

HC≡C–CX3


(H2C=CH)→*(CX3)

*(H2C=CH)←(CX3)

(H2C≡CH)→*(CX3)

*(H2C≡CH)←(CX3)

No clear correlation between No clear correlation between hyperconjugation and Chyperconjugation and C–C bond –C bond

distancesdistances

Hyperconjugation


Me O

R

Me R = H R=Me R=OH R=NH2 R=F R=Cl R=Br R=I

Me NH

(E)

Symmetry Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs

Eint -119.4 -97.8 -95.6 -107.2 -98.5 -109.4 -99.4 -95.4 -89.3 -104.0

EPauli 228.9 439.4 434.2 435.6 427.4 440.9 416.3 405.6 394.4 439.4

Eelstat -147.5

(42.4%)

-167.5

(31.2%)

-167.9

(31.7%)

-159.3

(29.4%)

-163.1

(31.0%)

-156.9

(28.5%)

-155.9

(30.2%)

-153.3

(30.6%)

-152.2

(31.6%)

-166.1

(30.6%)

EOrb -200.7

(57.6%)

-369.6

(68.8%)

-361.9

(68.3%)

-383.3

(70.6%)

-362.7

(68.9%)

-393.4

(71.5%)

-359.9

(69.8%)

-347.8

(69.4%)

-331.0

(68.4%)

-377.3

(69.4%)

E -191.5

(95.4%)

-358.5

(97.0%)

-351.9

(97.2%)

-373.1

(97.4)

-354.0

(97.6%)

-382.1

(97.1%)

-348.1

(96.7%)

-335.8

(96.6%)

-318.9

(96.3%)

-367.1

(97.3%)

E -9.3

(4.6%)

-11.1

(3.0%)

-10.0

(2.8%)

-10.1

(2.6%)

-8.8

(2.4%)

-11.3

(2.9%)

-11.8

(3.3%)

-12.0

(3.4%)

-12.1

(3.7%)

-10.2

(2.7%)

Eprep 17.2 11.5 12.4 12.8 12.7 12.3 12.0 12.0 12.6 14.0

E (=-De) -102.2 -86.3 -83.2 -94.4 -85.5 -97.1 -87.4 -83.4 -76.7 -90.0

r(C−C) 1.500 1.505 1.520 1.507 1.523 1.496 1.500 1.500 1.501 1.504

Hyperconjugation

-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4-12,5

-12,0

-11,5

-11,0

-10,5

-10,0

-9,5

-9,0

-8,5

Br

Cl

I

F

OH

H

OH

NH2

E

/ kca

l mo

l-1

p

r = 0.97, SD= r = 0.97, SD= 0.290.29

Hyperconjugation


X3C–CY3

X=H

Y=CH3

X=H

Y=SiH3

X=H

Y=F

X=H

Y=Cl

X=CH3

Y=SiH3

X=CH3

Y=F

X=CH3

Y=Cl

X=SiH3

Y=F

X=SiH3

Y=Cl

X=F

Y=Cl

Symmetry[c] Td C3v C3v C3v C3v C3v C3v C3v C3v C3v

Eint -104.6 -100.9 -113.4 -100.2 -91.6 -103.4 -91.9 -102.2 -91.3 -81.7

EPauli 243.8 228.7 444.0 418.6 243.0 282.2 299.4 288.2 319.9 285.3

Eelstat -156.8

(45.0%)

-139.2

(42.2%)

-160.0

(28.7%)

-165.1

(31.8%)

-149.7

(44.7%)

-177.4

(45.9%)

-174.3

(44.5%)

-168.7

(43.2%)

-173.1

(42.1%)

-157.7

(43.0%)

EOrb -191.6

(55.0%)

-190.4

(57.8%)

-397.4

(71.3%)

-353.7

(68.2%)

-184.9

(55.3%)

-208.9

(54.1%)

-217.1

(55.5%)

-221.7

(56.8%)

-238.1

(57.9%)

-209.2

(57.0%)

E (a1) -180.2

(94.1%)

-176.4

(92.7%)

-382.7

(96.3%)

-336.5

(95.1%)

-169.6

(91.7%)

-191.8

(91.8%)

-197.2

(90.8%)

-197.3

(89.0%)

-207.9

(87.3%)

-192.0

(91.8%)

a2) <-0.1 <-0.1 <-0.1 <-0.1 -0.6 (0.3%) -0.3 (0.1%) -0.5 (0.2%) -0.3 (0.1%) -0.5 (0.2%) -0.2 (0.1%)

E (e) -11.3

(5.9%)

-13.9

(7.3%)

-14.6

(3.7%)

-17.2

(4.9%)

-14.7

(8.0%)

-16.8

(8.0%)

-19.5

(9.0%)

-24.1

(10.9%)

-29.7

(12.5%)

-17.0

(8.1%)

Eprep 22.3 23.3 14.1 18.6 33.0 16.6 24.9 21.9 31.8 10.1

E (=-De) -82.3 -77.6 -99.3 -81.6 -58.6 -86.8 -67.0 -80.3 -59.5 -71.6

r(C−C) / Å 1.539 1.562 1.504 1.515 1.601 1.534 1.563 1.512 1.523 1.570

Hyperconjugation


X3C–CY3 (* deleted)

X

Y H CH3 SiH3 F Cl

H -10.0

(-5.6)

-11.3

(-6.4; -6.7)

-13.9

(-8.2; -7.7)

-14.6

(-5.9; -11.2)

-17.2

(-7.3;-12.2)

CH3 -11.6

(-6.8)

-14.7

(-8.7; -8.3)

-16.8

(-8.2; -11.7)

-19.5

(-9.3; -13.1)

SiH3 -17.5

(-9.8)

-24.1

(-10.4; -17.4)

-29.7

(-12.6; -20.8)

F -12.9

(-7.9)

-17.0

(-10.1; -10.2)

Cl -20.9

(-12.1)

blue: (X3C)→*(CY3)

red: * (X3C)←CY3)

black: total hyperconj

the relative donor strengths of two groups may be inverted depending on the acceptor moiety

C–H > C–C

C–C > C–H

Molecule

1.314

1.522

1.314

1.522

1

2

3

4

5

6

7

8

Symmetry D6h D6h D6h D3h D3h C2h

Eint -996.7

-513.3 -353.7 -977.8 -487.6 -489.5

EPauli 1573.7 1180.0 538.7 1531.8 919.2

1064.9

Eelstata -1072.1

(41.7%) -540.4

(31.9%) -358.7

(40.2%) -1036.8 (41.3%)

-420.0 (29.8%)

-512.5 (33.0%)

EOrba -1498.3

(58.3%)

-1152.8 (68.1%)

-533.7 (59.8%)

-1472.8 (58.7%)

-986.8 (70.2%)

-1041.9 (67.0%)

Eb -1280.6

(85.5%) -1045.2 (90.7%)

-460.2 (86.2%)

-1250.6 (84.9%)

-931.8 (94.4%)

-976.7 (93.7%)

Eb -217.7

(14.5%)

-107.7 (9.3%)

-73.5 (13.9%)

-222.2 (15.1%)

-55.1 (5.6%)

-65.2 (6.3%)

r(C−C)/Å 1.397 1.397 1.397 1.314/1.552 1.314/1.552 C1-C2: 1.348 C2-C3: 1.441 C3-C4: 1.361 C4-C5: 1.432

ASEc

42.5

Fragmentsd 6 CH q 3 C2H2 os C4H4os+ C2H2os

6 CH q 3 C2H2 os short

2 C2H3d + 2 C2H2 os

Molecule N N P P As As Sb Sb Bi Bi

HN

HBNH

BH

NH

HB

HN

HBNH

BH

NH

HB

Symmetry C2v C2v C2v C2v C2v D3h Eint -938.7

-495.0

-886.3 -464.7 -862.9 -453.2 -839.0 -440.0 -824.1 -431.5 -1059.5 -485.6

EPauli 2427.4 1356.2 1536.8 1169.9 1481.1 1120.4 1422.5 1070.5 1396.2 1044.0

1521.3 867.5

Eelstata -1101.3

(32.7%) -563.0

(30.4%) -1029.6 (42.5%)

-517.1 (31.6%)

-1011.1 (43.1%)

-504.1 (32.0%)

-982.7 (43.5%)

-489.2 (32.4%)

-964.5 (43.4%)

-478.0 (32.5%)

-1038.4 (40.2%)

-525.8 (38.9%)

EOrba -2264.9

(67.3%)

-1288.2 (69.6%)

-1393.4 (57.5%)

-1117.5 (68.4%)

-1332.9 (56.9%)

-1069.4 (68.0%)

-1278.9 (56.5%)

-1021.3 (67.6%)

-1255.8 (56.6%)

-995.5 (67.5%)

-1542.4 (59.8%)

-827.3 (61.1%)

Eb -1965.4

(86.8%) -1174.7 (91.2%)

-1193.8 (85.7%)

-1016.2 (90.9%)

-1144.4 (85.9%)

-971.6 (90.8%)

-1101.4 (86.1%)

-926.5 (90.7%)

-1083.8 (86.3%)

-901.9 (90.6%)

-1411.3 (91.5%)

-756.9 (91.5%)

Eb -299.4

(13.2%)

-113.5 (8.8%)

-199.6 (14.3%)

-101.3 (9.1%)

-188.5 (14.1%)

-97.8 (9.2%)

-177.5 (13.9%)

-94.8 (9.3%)

-172.0 (13.7%)

-93.6 (9.4%)

-131.1 (8.5%)

-70.4 (8.5%)

r(X−Y)/Å N-C1: 1.342 C1-C2: 1.397 C2-C3: 1.395

P-C1: 1.748 C1-C2: 1.393 C2-C3: 1.398

As-C1: 1.870 C1-C2: 1.390 C2-C3: 1.400

Sb-C1: 2.068 C1-C2: 1.388 C2-C3: 1.403

Bi-C1: 2.162 C1-C2: 1.386 C2-C3: 1.405

N-B: 1.433

ASEc 45.7 36.9 34.9 31.1 29.4 11.6

Fragmentsd 5 CH q + N q

2 C2H2os +NCHos

5 CH q + P q

2 C2H2os + PCHos

5 CH q + As q

2 C2H2os +AsCHos

5 CH q + Sb q

2 C2H2os +SbCHos

5 CH q + Bi q

2 C2H2os +BiCHos

3 BHt + 3 NHt

3 BNH2

os

Molecule N

H NH O O S S

Symmetry D5h C2v C2v C2v Eint -853.3

-532.5

-845.3 -519.0 -772.5 -444.6 -727.9 -400.8

EPauli 1476.3 1188.4 1501.6 1178.7 1528.5 1170.7 1348.8 961.1

Eelstat

a -868.7 (37.3%)

-550.5 (32.0%)

-822.7 (35.1%)

-493.8 (29.1%)

-811.8 (35.3%)

-472.3 (29.2%)

-795.8 (38.3%)

-450.8 (33.1%)

EOrb

a -1460.9 (62.7%)

-1170.4 (68.0%)

-1524.2 (64.9%)

-1203.9 (70.9%)

-1489.2 (64.7%)

-1143.0 (70.8%)

-1280.9 (61.7%)

-911.1 (66.9%)

E

b -1217.4 (83.3%)

-1016.3 (86.8%)

-1320.3 (86.6%)

-1105.9 (91.9%)

-1297.9 (87.2%)

-1065.3 (93.2%)

-1097.3 (85.7%)

-833.5 (91.5%)

E

b -243.5 (16.7%)

-154.1 (13.2%)

-203.9 (13.4%)

-98.0 (8.1%)

-191.3 (12.8%)

-77.7 (6.8%)

-183.6 (14.3%)

-77.6 (8.5%)

r(X−C)/Å N-C1: 1.376

C1-C2: 1.381 C2-C3: 1.425

O-C1: 1.371 C1-C2: 1.363 C2-C3: 1.434

S-C1: 1.727 C1-C2: 1.373 C2-C3: 1.424

ASEc

3.1 21.1 16.2 21.9

Fragmentsd 4 CH q 1CH- os

2C2H2os 1CH- os

4 CHq 1NHos

2C2H2os 1NH os

4 CH q 1 O os

2C2H2os 1O os

4 CH q 1 S os

2C2H2os 1S os

Molecule

1

2

3

4

5

6

1

2

3

4

5

6

7

8

1

23

4

5 1

2

3

4 5

6

Symmetry D6h C2h C2h D5h C2v C2v Eint -513.3 -308.7 -489.5 -532.5

-337.2 -530.1

EPauli 1180.0 688.9 1064.9 1188.4 808.6 1170.5 Eelstat

a -540.4 (31.9%)

-340.2 (34.1%)

-512.5 (33.0%) -550.5 (32.0%)

-392.5 (34.3%)

-572.5 (33.7%)

EOrba -1152.8

(68.1%) -657.3

(65.9%) -1041.9 (67.0%) -1170.4

(68.0%)

-753.3 (65.7%)

-1128.1 (66.3%)

E

b -1045.2 (90.7%)

-615.8 (93.7%)

-976.7 (93.7%) -1016.3 (86.8%)

-643.3 (85.4%)

-977.0 (86.6%)

Eb -107.7

(9.3%) -41.5

(6.3%) -65.2 (6.3%)

-154.1

(13.2%)

-109.9 (14.6%)

-151.0 (13.4%)

r(C−C)/Å 1.397 C1-C2: 1.347

C2-C3: 1.444 C3-C4: 1.357

C1-C2: 1.348 C2-C3: 1.441 C3-C4: 1.361 C4-C5: 1.432

C1-C2: 1.383 C2-C3: 1.412

C1-C2: 1.374 C2-C3: 1.418 C3-C4: 1.397

ASEc

42.5 66.2

3.1 44.2

Fragmentsd 3 C2H2 os

2 C2H3d + C2H2 os

2 C2H3d + 2 C2H2 os

2C2H2os 1CH- os

2 C2H3d + + 1CH- os

2 C2H3d + 1 C2H2 os + 1CH- os

Molecule

1

4

2

3

1

4

2

3

1

4

2

3

1

4

2

3

1

4

2

3

5

1

4

2

3

5

1

4

2

3

5

1

4

2

3

5 singlet triplet singlet triplet singlet triplet

Symmetry C2v C2v C2v h C2v C2v C2v Eint -406.8

-249.2 -486.7 -326.1 -715.4 -386.0 -890.0 -563.2 -1085.1 -606.8 -1231.3 -747.7

EPauli 885.6 600.3 813.2 369.8

1572.3 1018.4 1241.3 934.6 2132.0 1646.9 1908.6 1276.3

Eelstata -471.0

(36.4%) -312.6

(36.8%) -391.3

(30.1%) -240.0

(34.5%)

-829.8 (36.3%)

-460.2 (32.8%)

-816.9 (38.3%)

-480.3 (32.1%)

-1307.8 (40.7%)

-731.2 (32.4%)

-1239.0 (39.5%)

-660.8 (32.6%)

EOrba -821.4

(63.6%)

-536.8 (36.8%)

-908.6 (69.9%)

-455.9 (65.5%)

-1457.9 (63.7%)

-944.1 (67.2%)

-1314.4 (61.7%)

-1017.5 (67.9%)

-1909.2 (59.3%)

-1522.5 (67.6%)

-1900.9 (60.5%)

-1363.2 (67.4%)

Eb -680.8

(82.9%) -476.1

(88.7%) -817.2

(89.9%) -429.1

(94.1%)

-1314.5 (90.2%)

-906.0 (96.0%)

-1137.9 (86.6%)

-943.1 (92.7%)

-1663.6 (87.1%)

-1387.6 (91.1%)

-1660.1 (87.3%)

-1258.2 (92.3%)

Eb -140.5

(17.1%)

-60.8 (11.3%)

-91.4 (10.1%)

-26.8 (5.9%)

-143.4 (9.8%)

-38.1 (4.0%)

-176.5 (13.4%)

-74.4 (7.3%)

-245.6 (12.9%)

-134.9 (8.9%)

-240.9 (12.7%)

-105.0 (7.7%)

r(C−C)/Å C1-C2: 1.328 C2-C3: 1.426

C1-C2: 1.329 C2-C3: 1.454

C1-C2: 1.512 C2-C3: 1.342 C3-C4: 1.537

C1-C2: 1.427 C2-C3: 1.377 C3-C4: 1.483

C1-C2: 1.425 C2-C3: 1.402 C3-C4: 1.389 C4-C5: 1.403

C1-C2: 1.391 C2-C3: 1.384 C3-C4: 1.453 C4-C5: 1.366

ASEc 3.8

-40.1 -44.4 -22.0 23.8 -18.7

Fragmentsd 2 CH q C os

C2H2os C os

2 CH q C t

C2H2 os C t

4 CH q 1 Cos

2C2H2 os 1 C os

4 CH q 1 C t

2C2H2os 1 Ct

6 CH q C s

3C2H2os C s

6 CH q C t

3C2H2os C t

Molecule

1

2 3

4

1

2

3

4

56

1

2

3

4

56

1

2

3 4

5

1

2

3 4

5

1

2 3

1

2 3

Symmetry C2v C2v C2v C2v C2v D2h Eint -230.3 -264.6

-291.7 -456.1 -290.6 -435.9 -276.3 -600.4 -570.4 -242.3

EPauli 362.7 444.6

441.8 944.0 399.1 967.8 420.4 1206.1 836.5 353.3

Eelstata -213.2

(36.0%) -277.3

(39.1%)

-302.2 (41.2%)

-460.3 (32.9%)

-268.9 (39.0%)

-455.8 (32.5%)

-270.2 (38.8%)

-606.0 (33.5%)

-563.8 (40.0%)

-219.6 (36.9%)

EOrba -379.8

(64.0%) -432.0

(60.9%)

-431.2 (58.8%)

-939.8 (67.1%)

-420.9 (61.0%)

-947.9 (67.5%)

-426.5 (61.2%)

-1200.5 (66.5%)

-843.1 (60.0%)

-376.0 (63.1%)

Eb -365.7

(96.3%) -412.0

(95.4%)

-412.7 (95.8%)

-904.4 (96.2%)

-399.6 (95.0%)

-906.5 (95.6%)

-407.4 (96.3%)

-1147.7 (95.6%)

-730.0 (86.6%)

-366.4 (97.4%)

Eb -14.0

(3.7%) -20.0

(4.6%)

-18.6 (4.2%)

-35.4 (3.8%)

-21.3 (5.0%)

-41.4 (4.4%)

-19.1 (3.7%)

-52.8 (4.4%)

-113.1 (13.4%)

-9.6 (2.6%)

r(C−C)/Å

C1-C2: 1.XX C2-C3: 1.514

C1-C2: 1.344 C2-C3: 1.519 C3-C4: 1.574

C1-C2: 1.465 C2-C3: 1.343 C3-C4: 1.510 C4-C5: 1.560

C1-C2: 1.503 C2-C3: 1.354 C3-C4: 1.465

C1-C2: 1.511 C2-C3: 1.347 C3-C4: 1.458 C4-C5: 1.354

C1-C2: 1.331 C2-C3: 1.581

ASEc

-2.9 3.5 -1.5 4.2 -6.5 -31.9

Fragments6 C2H2os + CH2os

C2H2os + C2H4os

C4H4os + C2H4os

2 C2H2os + C2H4os

C4H4os + CH2os

2 C2H2os + CH2os

C6H6os + CH2os

3 C2H2os + CH2os

4 CH q 2 C2H2os

1

2

3

4*

5*

dyz

dxz

D.L. Thorn, R. Hoffmann, Nouv. J. Chim. 1979, 3, 39.

Molecule RhCl

Cl

PH3

PH3 Symmetry C2v

Eint -338.3 -295.1 -209.4 EPauli 399.5 405.7 329.6 Eelstat

a -465.1 -391.6 -242.7 (63.0%) (55.9%) (45.0%)

EOrba -272.7 -309.2 -296.2

(37.0%) (44.1%) (55.0%)

Eσ(a1)b -71.5 (26.2%) -40.2 (13.0%) -119.2 (40.2%)

Eπ(a2)b -14.6 (5.3%) -14.5 (4.7%) -10.3 (3.5%)

Eπ(b1)b -31.0 (11.4%) -53.2 (17.2%) -52.3 (17.7%)

Eσ(b2)b -155.7 (57.1%) -201.3 (65.1%) -114.5 (38.6%)

Fragmentsc C5H5- s +

[Rh]+ s C5H5

+ s + [Rh]- s

C5H5 q + [Rh] q

I. Fernandez, G. Frenking, Chem. Eur. J., 2007, 13, 5873.

Molecule Os

CO

I

PH3

PH3

OsCO

I

PH3

PH3

1

2

3

4

5 6

7OsOC I

PH3

PH3

OsCO

CO

PH3

PH3

OsCO

CO

PH3

PH3

1

2

3

4

5 6

7OsOC CO

PH3

PH3

Eint -883.7 -423.6 -393.4 -911.6 -452.0 -419.9

EPauli 1915.7 1038.2 977.8 1428.8 1016.2 956.0

Eelstat -1051.8

(37.6%) -519.7

(35.6%) -508.5

(37.1%) -1013.6 (43.3%)

-507.6 (34.6%)

-493.2 (35.8%)

EOrb -1747.6

(62.4%)

-942.1 (64.4%)

-862.6 (62.9%)

-1326.8 (56.7%)

-960.6 (65.4%)

-882.7 (64.2%)

E -1512.6

(86.6%) -862.7

(91.6%) -803.3

(93.1%) -1118.4 (84.3%)

-863.2 (89.9%)

-802.8 (91.0%)

E -235.0 (13.4%)

-79.4 (8.4%)

-59.3 (6.9%)

-208.4 (15.7%)

-97.5 (10.1%)

-79.9 (9.0%)

ASE 20.1 17.6

Fragments 5 CH q + [Os] q

2 C2H2os +[Os]−CHos

5 CH q + [Os] q 2 C2H2os +[Os]+−CHos

Molecule IrCO

PH3

PH3

IrCO

PH3

PH3

1

2

3

4

5 6

7IrOC PH3

PH3

Ir

PH3

PH3

PH3

Ir

PH3

PH3

PH3

1

2

3

4

5 6

7IrH3P PH3

PH3

Eint -875.7 -441.1 -399.8 -873.5 -432.3 -393.6

EPauli 1499.1 1022.4 974.1 1523.4 1030.4 1005.7

Eelstat -1067.4

(45.0%) -514.3

(35.1%) -498.3

(36.3%) -1082.6 (45.2%)

-516.5 (35.3%)

-506.1 (36.8%)

EOrb -1307.4

(55.0%)

-949.2 (64.9%)

-875.6 (63.7%)

-1314.3 (54.8%)

-946.2 (64.7%)

-893.2 (63.8%)

E -1125.3

(86.1%) -867.2

(91.4%) -816.8

(93.3%) -1130.4 (86.0%)

-863.6 (91.3%)

-832.9 (93.2%)

E -182.1 (13.4%)

-82.0 (8.6%)

-58.8 (6.7%)

-183.8 (14.0%)

-82.7 (8.7%)

-60.3 (6.8%)

ASE 23.2 22.4

Fragments 5 CH q + [Ir] q

2 C2H2os +[Ir]−CHos

5 CH q + [Ir] q 2 C2H2os +[Ir]−CHos

Conjugation and Hyperconjugation

CONCLUSIONSCONCLUSIONS

The calculated E values taken from the EDA can be used to estimate the strength of the relative contributions of interactions that come from conjugation/hyperconjugation

The EDA method has a predictive value. The trend of the calculated E values is in very good agreement with NMR chemical shifts and experimentally derived Hammett constants.

The comparison of E values of cyclic system with a suitable reference compound makes it possible to estimate the stabilization due to aromaticity.

Bond energies and lengths should not be used as indicators of the strength of hyperconjugation because the effect of interactions and electrostatic forces may compensate for the hyperconjugative effect.

Acknowledgement

Dipl. Chem. Andreas Krapp Dr. Israel Fernandez Lopéz Dr. Matthias Lein Dipl. Chem. Robin Haunschild Dipl. Chem. Ralf Tonner Takayasu Shimizu, M. Sc. Cand. Chem. Philip Mörschel Stefan Reuter €: Deutsche Forschungsgemeinschaft

Molecule X1

2

3

4

5 6

7

B

NB

NB

NB

N1

2

3

4

5

6

78

H

H

H

H

H

H

H

H

H

H

X N P As Sb Bi

Symmetry Cs Cs Cs Cs Cs Cs Eint -456.0

-426.0 -415.4 -404.4 -397.2 -501.1

EPauli 1194.9 993.6 955.5 923.4 906.6

880.3

Eelstata -565.5

(34.2%) -502.2

(35.4%)

-484.9 (35.4%)

-471.4 (35.5%)

-461.2 (35.4%)

-523.8 (37.9%)

EOrba -1085.4

(65.8%)

-917.4 (64.6%)

-886.0 (64.6%)

-856.5 (64.5%)

-842.6 (64.6%)

-857.6 (62.1%)

Eb -1017.5

(93.8%) -853.0

(93.0%)

-823.1 (92.9%)

-792.8 (92.6%)

-778.5 (92.4%)

-798.8 (93.1%)

Eb -67.8

(6.2%)

-64.4 (7.0%)

-62.9 (7.1%)

-63.7 (7.4%)

-64.2 (7.6%)

-58.8 (6.9%)

r(X−X)/Å C1-C2: 1.347 C2-C3: 1.442 C3-C4: 1.359 C4-C5: 1.435 C5-N: 1.297 N-C6: 1.386 C6-C7: 1.344

C1-C2: 1.349 C2-C3: 1.438 C3-C4: 1.366 C4-C5: 1.426 C5-P: 1.710 P-C6: 1.807 C6-C7: 1.345

C1-C2: 1.350 C2-C3: 1.437 C3-C4: 1.370 C4-C5: 1.419 C5-As: 1.831 As-C6: 1.936 C6-C7: 1.342

C1-C2: 1.352 C2-C3: 1.434 C3-C4: 1.374 C4-C5: 1.413 C5-Sb: 2.035 Sb-C6: 2.142 C6-C7: 1.341

C1-C2: 1.353 C2-C3: 1.433 C3-C4: 1.377 C4-C5: 1.409 C5-Bi: 2.133 Bi-C6: 2.245 C6-C7: 1.339

B1-N2: 1.414 N2-B3: 1.447 B3-N4: 1.426 N4-B5: 1.441 B5-N6: 1.426 N6-B7: 1.443 B7-N8: 1.409

Molecule X1

2

3

4 5

6 X CH- NH O S

Symmetry C2v Cs Cs Cs Eint -530.1

-495.1

-419.7 -370.7

EPauli 1170.5 1134.1 1116.9 951.1

Eelstat

a -572.5 (33.7%)

-505.3 (31.0%)

-479.6 (31.2%)

-436.2 (33.0%)

EOrb

a -1128.1 (66.3%)

-1124.0 (69.0%)

-1057.0 (68.8%)

-885.6 (67.0%)

Eb -977.0

(86.6%) -1047.1 (93.2%)

-995.5 (94.1%)

-829.8 (93.7%)

E

b -151.0 (13.4%)

-76.9 (6.7%)

-61.5 (5.5%)

-55.7 (6.3%)

r(X−X)/Å C1-C2: 1.374

C2-C3: 1.418 C3-C4: 1.397

C1-C2: 1.346 C2-C3: 1.441 C3-C4: 1.356 C4-N: 1.377 N-C5: 1.383 C5-C6: 1.344

C1-C2: 1.346 C2-C3: 1.445 C3-C4: 1.345 C4-O: 1.369 O-C5: 1.373 C5-C6: 1.332

C1-C2: 1.347 C2-C3: 1.445 C3-C4: 1.352 C4-S: 1.751 S-C5: 1.761 C5-C6: 1.338

Molecule 1

23

singlet

1

23

triplet

1

2

3

4

5

6

7

singlet

1

2

3

4

5

6

7

triplet

1

2

3

4

5

6

7

8

9

singlet

1

2

3

4

5

6

7

8

9

triplet

Symmetry C2v C2v Cs Cs Cs Cs Eint -234.6 -394.4 -418.0 -578.1 -600.6 -761.8

EPauli 960.1 797.6 1327.0 1044.5 1513.6 1481.2

Eelstata -385.4

(32.3%) -353.6

(29.7%) -557.3

(31.9%) -528.9

(32.6%) -732.0

(34.6%) -707.1

(31.5%)

EOrba -809.3

(67.7%) -838.4

(70.3%) -1188.0 (68.1%)

-1093.7 (67.4%)

-1382.2 (65.4%)

-1535.8 (68.5%)

Eb -752.3

(93.0%) -771.5

(92.0%) -1105.4 (93.0%)

-997.3 (91.2%)

-1271.1 (92.0%)

-1412.1 (92.0%)

Eb -57.0

(7.0%) -66.9

(8.0%) -82.5

(7.0%)

-96.4 (8.8%)

-111.1 (8.0%)

-123.7 (8.0%)

r(C−C)/Å C1-C2: 1.355 C2-C3: 1.443

C1-C2: 1.368 C2-C3: 1.390

C1-C2: 1.349 C2-C3: 1.438 C3-C4: 1.372 C4-C5: 1.428 C5-C6: 1.443 C6-C7: 1.355

C1-C2: 1.359 C2-C3: 1.423 C3-C4: 1.392 C4-C5: 1.371 C5-C6: 1.398 C6-C7: 1.362

C1-C2: 1.349 C2-C3: 1.438 C3-C4: 1.365 C4-C5: 1.424 C5-C6: 1.378 C6-C7: 1.423 C7-C8: 1.443 C8-C9: 1.355


Molecule 1

23

1

2

3

4 1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

1

2

3

4

5

6

7

8

9

1

2

3

4 Symmetry C2v Cs Cs Cs Cs C2h

Eint -245.3 -272.5 -451.2 -423.8 -604.0 -308.7

EPauli 615.0 615.2 978.5 1000.5 1294.8 688.9

Eelstata -300.7

(35.0%) -311.0

(35.0%) -479.0

(33.5%) -468.6

(32.9%) -639.4

(33.7%) -340.2

(34.1%)

EOrba -559.6

(65.0%) -576.7

(65.0%) -950.7

(66.5%) -955.7

(67.1%) -1259.4 (66.3%)

-657.3 (65.9%)

Eb -542.8

(97.0%) -560.2

(97.1%) -913.8

(96.1%) -918.5

(96.1%) -1200.1 (95.3%)

-615.8 (93.7%)

Eb -16.9

(3.0%) -16.5

(2.3%) -36.9

(3.9%) -37.2

(3.9%) -59.3

(4.7%) -41.5

(6.3%)

r(C−C)/Å C1-C2: 1.335 C2-C3: 1.513

C1-C2: 1.335 C2-C3: 1.511 C3-C4: 1.534

C1-C2: 1.344 C2-C3: 1.450 C3-C4: 1.346 C4-C5: 1.506 C5-C6: 1.534 C6-C7: 1.511 C7-C8: 1.335

C1-C2: 1.344 C2-C3: 1.450 C3-C4: 1.346 C4-C5: 1.508 C5-C6: 1.513 C6-C7: 1.334


C1-C2: 1.347 C2-C3: 1.444 C3-C4: 1.357

+ H 2 + H 2

- 2 6 . 7 G 3

- 2 6 . 1 e x p t l

- 3 0 . 4 G 3

- 2 9 . 9 e x p t l ( 1 )

+ 2 H 2 + 2 H 2

- 7 0 . 6 G 3 - 7 0 . 4 G 3

- 6 9 . 5 e x p t l ( 2 )

+ +- 2 . 4 G 3

- 2 . 7 e x p t l ( 3 )

+- 4 . 9 G 3

- 4 . 7 e x p t l+

( 4 )

+ H 2 + H 2

- 2 4 . 3 - 3 2 . 8

( 5 )

+ 2 H 2 + 2 H 2

- 6 5 . 7 - 7 5 . 3

( 6 )

T a b l e 1 . R e s u l t s o f t h e e n e r g y d e c o m p o s i t i o n a n a l y s i s . E n e r g y v a l u e s i n k c a l / m o l .

H C C - C C H H 2 C C H - C H C H 2 H C C - C H 3 H C C - C ( C H 3 ) 3 H 2 C C H - C H 3 H 2 C C H - C ( C H 3 ) 3 H C C - C H C H 2 ( C H 3 ) 3 C - C ( C H 3 ) 3 C H 3 - C H 3

S y m m e t r y D ? h C 2 h C 3 V C 3 V C S C S C S D 3 d D 3 d E i n t - 1 7 6 . 0 - 1 2 8 . 5 - 1 4 3 . 6 - 1 3 3 . 1 - 1 1 9 . 4 - 1 0 8 . 8 - 1 5 0 . 2 - 9 3 . 2 - 1 1 4 . 8 E P a u l i 1 6 1 . 8 2 6 8 . 4 1 7 6 . 5 2 1 9 . 1 2 2 8 . 9 2 6 7 . 9 2 0 9 . 4 2 5 3 . 6 2 0 0 . 8

E e l s t a ta - 1 1 4 . 6

( 3 3 . 9 % ) - 1 6 9 . 9

( 4 2 . 8 % ) - 1 2 5 . 5

( 3 9 . 2 % ) - 1 5 1 . 8

( 4 3 . 1 % ) - 1 4 7 . 5

( 4 2 . 4 % ) - 1 7 1 . 8

( 4 5 . 6 % ) - 1 4 3 . 1

( 3 9 . 8 % ) - 1 6 3 . 5

( 4 7 . 2 % ) - 1 3 1 . 3

( 4 1 . 6 % )

E O r ba - 2 2 3 . 3

( 6 6 . 1 % ) - 2 2 7 . 0

( 5 7 . 2 % ) - 1 9 4 . 6

( 6 0 . 8 % ) - 2 0 0 . 4

( 5 6 . 9 % ) - 2 0 0 . 7

( 5 7 . 6 % ) - 2 0 4 . 9

( 5 4 . 4 % ) - 2 1 6 . 4

( 6 0 . 1 9 % ) - 1 8 3 . 2

( 5 2 . 8 % ) - 1 8 4 . 2

( 5 8 . 4 % )

E b - 1 7 8 . 3 ( 7 9 . 8 4 % )

- 2 0 7 . 5 ( 9 1 . 4 % )

- 1 7 4 . 6 ( 8 9 . 6 8 % )

- 1 7 9 . 8 ( 8 9 . 7 % )

- 1 9 1 . 5 ( 9 5 . 3 8 % )

- 1 9 5 . 4 ( 9 5 . 3 7 % )

- 1 9 5 . 9 ( 9 0 . 5 % )

- 1 7 1 . 0 ( 9 3 . 3 % )

- 1 7 4 . 3 ( 9 4 . 5 8 % )

E b - 4 5 . 0 ( 2 0 . 1 5 % )

- 1 9 . 5 ( 8 . 5 9 % )

- 2 0 . 1 ( 1 0 . 3 2 % )

- 2 0 . 6 ( 1 0 . 2 8 % )

- 9 . 3 ( 4 . 6 1 % )

- 9 . 5 ( 4 . 6 3 % )

- 2 0 . 5 ( 9 . 5 % )

- 1 1 . 6 ( 6 . 3 5 % )

- 1 0 . 0 ( 5 . 4 1 % )

E p r e p 5 . 4 1 3 . 0 1 3 . 1 1 4 . 5 1 7 . 2 1 8 . 8 2 3 . 8 3 0 . 2 2 1 . 8 E ( = - D e ) - 1 7 0 . 6 - 1 1 5 . 6 - 1 3 0 . 6 - 1 1 8 . 6 - 1 0 2 . 2 - 9 0 . 0 - 1 2 6 . 4 - 6 3 . 0 - 9 3 . 0 r ( C - C ) [ Å ] 1 . 3 6 1 1 . 4 5 3 1 . 4 5 6 1 . 4 6 9 1 . 5 0 0 1 . 5 1 6 1 . 4 1 9 1 . 5 9 1 1 . 5 3 2

a T h e % a g e v a l u e s i n p a r e n t h e s e s g i v e t h e c o n t r i b u t i o n t o t h e t o t a l a t t r a c t i v e i n t e r a c t i o n s Δ E e l s t a t + Δ E o r b . b T h e % a g e v a l u e s i n p a r e n t h e s e s g i v e t h e c o n t r i b u t i o n t o t h e o r b i t a l i n t e r a c t i o n s Δ E o r b .

D. Cappel, S, Tüllmann, A. Krapp, F. Frenking, Angew. Chem. Int. Ed. 2005, 117, 3683.

Conjugation


Eint -219.7 -229.0 -237.0 -251.7 -223.6 -211.8 -214.6 -209.5 -204.8

EPauli 293.3 293.1 288.5 290.4 286.2 289.1 290.1 285.5 284.2

Eelstata -172.0 -174.4 -174.0 -181.2 -166.5 -161.5 -164.7 -155.7 -154.6

(33.5%) (33.4%) (33.1%) (33.4%) (32.7%) (32.2%) (32.6%) (31.4%) (31.6%)

Eorba -341.0 -347.7 -351.5 -360.1 -343.3 -339.4 -331.9 -339.3 -334.5

(66.5%) (66.6%) (66.9%) (66.6%) (67.3%) (67.8%) (67.4%) (68.6%) (68.4%)

Eb -219.8 -228.7 -226.9 -226.9 -227.2 -227.6 -228.0 -226.6 -226.8

(64.4%) (65.8%) (64.5%) (62.9%) (66.2%) (67.1%) (67.1%) (66.8%) (67.8%)

Eb -119.4 -119.0 -124.6 -133.9 -116.1 -111.8 -112.0 -112.7 -107.8

(35.6%) (34.2%) (35.4%) (37.1%) (33.8%) (32.9%) (32.9%) (33.2%) (32.2%)


-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8-105

-110

-115

-120

-125

-130

-135

H2C R

H

NO2

CNCHO

CO2H

F

CH3

OH

NH2

E

/ kca

l mo

l-1

p Hammett

r = 0.95, r = 0.95, SD=2.60SD=2.60

-1,5 -1,0 -0,5 0,0 0,5 1,0-105

-110

-115

-120

-125

-130

-135

H2C R

CHOCO

2H CN

NO2

H

F

CH3

OH

E

/ kca

l mo

l-1

+

p Hammett

NH2

r = 0.97, r = 0.97, SD=2.15SD=2.15

I. Fernández, G. Frenking, J. Org. Chem. 2006, 71, 2251.

Conjugation in Cyanoethynylethenes, CEEs, Conjugation in Cyanoethynylethenes, CEEs, (Diederich)(Diederich)

151,0 151,5 152,0 152,5 153,0 153,5

-30

-32

-34

-36

-38

-40

E

/ kca

lmo

l-1

ipso

/ ppm

17

r = 0.99, SD= r = 0.99, SD= 0.430.43

NMe2D =


o

Cipso

NMe2D =o

Cmeta

1 7

r = 0.98, SD= r = 0.98, SD= 0.620.62

CN

CN

D

NC

CN

D

NC

R

CN

D

NC

R

CN

D

NC

D

DD

CN

CNNC

R

CN

D

NC

D

NC

RD

R

CN

RD

R

DD

R R

19 16 SiMe3R=

15 SiMe3R=

17 22 SiiPr3R=

18 (E)-12 SiiPr3R=

(Z)-12 SiiPr3R=

13 SiiPr3R=

ipso 153.41 152.58 152.28 151.98 151.51 151.42 151.14 151.06 150.95

meta 136.38 135.58 135.37 135.03 134.49 133.93 133.95 133.79 133.37

E -39.52 -35.62 -35.40 -31.29 -33.01 -31.59 -31.83 -31.21 -30.97

r 0.04201 0.03868 0.03854 0.03508 0.03691 0.3477 0.3526 0.03485 0.03447

I. Fernández, G. Frenking, Chem. Commun. 2006, 5030

Molecule

1.314

1.522

1.314

1.522

1

2

3

4

5

6

7

8

Symmetry D6h D6h D6h D3h D3h C2h

Eint -996.7

-513.3 -353.7 -977.8 -487.6 -489.5

EPauli 1573.7 1180.0 538.7 1531.8 919.2

1064.9

Eelstata -1072.1

(41.7%) -540.4

(31.9%) -358.7

(40.2%) -1036.8 (41.3%)

-420.0 (29.8%)

-512.5 (33.0%)

EOrba -1498.3

(58.3%)

-1152.8 (68.1%)

-533.7 (59.8%)

-1472.8 (58.7%)

-986.8 (70.2%)

-1041.9 (67.0%)

Eb -1280.6

(85.5%) -1045.2 (90.7%)

-460.2 (86.2%)

-1250.6 (84.9%)

-931.8 (94.4%)

-976.7 (93.7%)

Eb -217.7

(14.5%)

-107.7 (9.3%)

-73.5 (13.9%)

-222.2 (15.1%)

-55.1 (5.6%)

-65.2 (6.3%)

r(C−C)/Å 1.397 1.397 1.397 1.314/1.552 1.314/1.552 C1-C2: 1.348 C2-C3: 1.441 C3-C4: 1.361 C4-C5: 1.432

ASEc

42.5

Fragmentsd 6 CH q 3 C2H2 os C4H4os+ C2H2os

6 CH q 3 C2H2 os short

2 C2H3d + 2 C2H2 os

Molecule N N P P As As Sb Sb Bi Bi

HN

HBNH

BH

NH

HB

HN

HBNH

BH

NH

HB

Symmetry C2v C2v C2v C2v C2v D3h Eint -938.7

-495.0

-886.3 -464.7 -862.9 -453.2 -839.0 -440.0 -824.1 -431.5 -1059.5 -485.6

EPauli 2427.4 1356.2 1536.8 1169.9 1481.1 1120.4 1422.5 1070.5 1396.2 1044.0

1521.3 867.5

Eelstata -1101.3

(32.7%) -563.0

(30.4%) -1029.6 (42.5%)

-517.1 (31.6%)

-1011.1 (43.1%)

-504.1 (32.0%)

-982.7 (43.5%)

-489.2 (32.4%)

-964.5 (43.4%)

-478.0 (32.5%)

-1038.4 (40.2%)

-525.8 (38.9%)

EOrba -2264.9

(67.3%)

-1288.2 (69.6%)

-1393.4 (57.5%)

-1117.5 (68.4%)

-1332.9 (56.9%)

-1069.4 (68.0%)

-1278.9 (56.5%)

-1021.3 (67.6%)

-1255.8 (56.6%)

-995.5 (67.5%)

-1542.4 (59.8%)

-827.3 (61.1%)

Eb -1965.4

(86.8%) -1174.7 (91.2%)

-1193.8 (85.7%)

-1016.2 (90.9%)

-1144.4 (85.9%)

-971.6 (90.8%)

-1101.4 (86.1%)

-926.5 (90.7%)

-1083.8 (86.3%)

-901.9 (90.6%)

-1411.3 (91.5%)

-756.9 (91.5%)

Eb -299.4

(13.2%)

-113.5 (8.8%)

-199.6 (14.3%)

-101.3 (9.1%)

-188.5 (14.1%)

-97.8 (9.2%)

-177.5 (13.9%)

-94.8 (9.3%)

-172.0 (13.7%)

-93.6 (9.4%)

-131.1 (8.5%)

-70.4 (8.5%)

r(X−Y)/Å N-C1: 1.342 C1-C2: 1.397 C2-C3: 1.395

P-C1: 1.748 C1-C2: 1.393 C2-C3: 1.398

As-C1: 1.870 C1-C2: 1.390 C2-C3: 1.400

Sb-C1: 2.068 C1-C2: 1.388 C2-C3: 1.403

Bi-C1: 2.162 C1-C2: 1.386 C2-C3: 1.405

N-B: 1.433

ASEc 45.7 36.9 34.9 31.1 29.4 11.6

Fragmentsd 5 CH q + N q

2 C2H2os +NCHos

5 CH q + P q

2 C2H2os + PCHos

5 CH q + As q

2 C2H2os +AsCHos

5 CH q + Sb q

2 C2H2os +SbCHos

5 CH q + Bi q

2 C2H2os +BiCHos

3 BHt + 3 NHt

3 BNH2

os

I, Fernández, G. Frenking, Faraday Discuss., 2007, 135, 403

Molecule Os

CO

I

PH3

PH3

OsCO

I

PH3

PH3

1

2

3

4

5 6

7OsOC I

PH3

PH3

OsCO

CO

PH3

PH3

OsCO

CO

PH3

PH3

1

2

3

4

5 6

7OsOC CO

PH3

PH3

Eint -883.7 -423.6 -393.4 -911.6 -452.0 -419.9

EPauli 1915.7 1038.2 977.8 1428.8 1016.2 956.0

Eelstat -1051.8

(37.6%) -519.7

(35.6%) -508.5

(37.1%) -1013.6 (43.3%)

-507.6 (34.6%)

-493.2 (35.8%)

EOrb -1747.6

(62.4%)

-942.1 (64.4%)

-862.6 (62.9%)

-1326.8 (56.7%)

-960.6 (65.4%)

-882.7 (64.2%)

E -1512.6

(86.6%) -862.7

(91.6%) -803.3

(93.1%) -1118.4 (84.3%)

-863.2 (89.9%)

-802.8 (91.0%)

E -235.0 (13.4%)

-79.4 (8.4%)

-59.3 (6.9%)

-208.4 (15.7%)

-97.5 (10.1%)

-79.9 (9.0%)

ASE 20.1 17.6

Fragments 5 CH q + [Os] q

2 C2H2os +[Os]−CHos

5 CH q + [Os] q 2 C2H2os +[Os]+−CHos

I. Fernández, G. Frenking, Chem. Eur. J., in print.

Molecule IrCO

PH3

PH3

IrCO

PH3

PH3

1

2

3

4

5 6

7IrOC PH3

PH3

Ir

PH3

PH3

PH3

Ir

PH3

PH3

PH3

1

2

3

4

5 6

7IrH3P PH3

PH3

Eint -875.7 -441.1 -399.8 -873.5 -432.3 -393.6

EPauli 1499.1 1022.4 974.1 1523.4 1030.4 1005.7

Eelstat -1067.4

(45.0%) -514.3

(35.1%) -498.3

(36.3%) -1082.6 (45.2%)

-516.5 (35.3%)

-506.1 (36.8%)

EOrb -1307.4

(55.0%)

-949.2 (64.9%)

-875.6 (63.7%)

-1314.3 (54.8%)

-946.2 (64.7%)

-893.2 (63.8%)

E -1125.3

(86.1%) -867.2

(91.4%) -816.8

(93.3%) -1130.4 (86.0%)

-863.6 (91.3%)

-832.9 (93.2%)

E -182.1 (13.4%)

-82.0 (8.6%)

-58.8 (6.7%)

-183.8 (14.0%)

-82.7 (8.7%)

-60.3 (6.8%)

ASE 23.2 22.4

Fragments 5 CH q + [Ir] q

2 C2H2os +[Ir]−CHos

5 CH q + [Ir] q 2 C2H2os +[Ir]−CHos

Documents

Helsinki-3 Direct Estimate of Conjugation, Hyperconjugation and Aromaticity With an Energy Decomposition Analysis Gernot Frenking Fachbereich Chemie, Philipps-Universität