continuous symmetry and chirality measures david avnir institute of chemistry the hebrew university...
TRANSCRIPT
![Page 1: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/1.jpg)
Continuous Symmetry and Chirality Measures
David Avnir
Institute of ChemistryThe Hebrew University of Jerusalem
Harvard, Boston, January 28, 2013
![Page 2: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/2.jpg)
![Page 3: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/3.jpg)
![Page 4: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/4.jpg)
![Page 5: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/5.jpg)
![Page 6: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/6.jpg)
![Page 7: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/7.jpg)
“Near” C2 symmetry: HIV Protease mutant V82A complexed with A77 inhibitor
What, quantitatively, is the C2 symmetry content of that protein?
![Page 8: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/8.jpg)
Gradual changing chirality and C2-ness in aggregates
Is it possible to quantify these changes?
![Page 9: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/9.jpg)
![Page 10: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/10.jpg)
Since achirality relates to symmetry, similar questions pop up also in the context of chirality:
“By how much is one molecule more chiral than the other?”
![Page 11: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/11.jpg)
In fact, asymmetry and chirality are very common:
Given a sufficiently high resolution in space or time it is quite difficult to find a fully symmetric, achiral molecule.
Consider watching methane on a vibrational time-scale:
Only one in zillion frames will show the following:
![Page 12: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/12.jpg)
Given a sufficiently high resolution in space or time it is quite difficult to find a fully symmetric, achiral molecule
Spatial resolutions:
Often, symmetry is lost at the condensed phase:
# An adsorbed molecule
# A matrix-entrapped molecule
# A molecule packed in the crystal
# A molecule in the glassy state
# A molecule within a cluster
![Page 13: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/13.jpg)
A methodology is needed in order to quantify the degree of symmetry and the degree of chirality:
#Comparing different molecules
#Following changes within a single molecule
![Page 14: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/14.jpg)
The proposed methodology for a symmetry-measure design:
Find the minimal distance between the original structure, and the one obtained after the G point-group symmetry is operated on it.
![Page 15: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/15.jpg)
The continuous symmetry measure
* The scale is 0 - 1 (0 - 100):
The larger S(G) is, the higher is the deviation from G-symmetry
N
1k
2
2ˆ1
min100 kk QQNd
)S(G
kQ
kQצ
: The original structure
: The symmetry-operated structure
N : Number of vertices
d : Size normalization factor
H. Zabrodsky
![Page 16: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/16.jpg)
E
C3
C32
Measuring the degree of C3-ness (S(C3)) of a triangle
Ch. Dryzun
![Page 17: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/17.jpg)
All three triangles are superimposed. The set of 9 points is C3-symmetric. Its blues average is a C3-symmetric triangle
The measure is the collection of distances between the blue and the (original) red
![Page 18: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/18.jpg)
G: The achiral symmetry point group which minimizes S(G)
Achiral molecule: S(G) = 0
The more chiral the molecule is, the higher is S(G)
S(G) as a continuous chirality measure
N
1k
2
2ˆ1
min100 kk QQNd
)S(G
![Page 19: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/19.jpg)
The Continuous Shape Measure
S. Alvarez, P. Alemany
* The CSM estimates the distance to an a-priori unknown shape with the desired symmetry
* The Shape Measure estimates the minimal distance to a specific pre-selected shape (any shape)
* For ML6:
# Shape: What is the degree of ML6-
octahedricity (S(L6-Oh))?
# Symmetry: What is the degree of Oh-ness
(S(Oh))? D4h-ness (S(D4h)? And of S(D2h)?
![Page 20: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/20.jpg)
* The measure is a global structural parameter: It takes into account all bond angles and bond lengths
* A full profile of symmetry and chirality values is obtained
* All values are comparable either within the same molecule or between different ones
* The computational tools are efficient
* Analytical solutions have been obtained for many types of symmetry
* The shape of the nearest symmetric object is an outcome
* The measure is well behaved, and its correlations with physical/chemical parameters agree with intuition
Some properties of the symmetry measure
![Page 21: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/21.jpg)
Planar square – D4h
The CSM values of an AB4 species
with respect to tetrahedricity and planar-squareness
Distorted tetrahedron
S(Td) = 0
S(D4h) = 33.3
S(Td) = 10.6
S(D4h) = 7.84
S(Td) = 33.3
S(D4h) = 0
Perfect tetrahedron - Td
![Page 22: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/22.jpg)
0 10072.22
Td
D4h
C3v
Cv
33.33 65.73
0 1
S(Td)
The full scale of the CSM
![Page 23: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/23.jpg)
![Page 24: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/24.jpg)
S(TP)
[Ta(CCSitBu3)6]- [Ti2(-SMe)3(SMe)6]2-[Zr(SC6H4-4-OMe)6]2-
1.88
18.8°
1.67
8.27
5.51
1.34
33.3°
4.45
3.94
2.16
30.4°
5.09
S(chir)
S(Oh)
The most chiral monodentate complex
![Page 25: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/25.jpg)
![Page 26: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/26.jpg)
Trends within families and classifications
Symmetry maps
![Page 27: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/27.jpg)
The symmetry map of 13,000 transition metal ML4 complexes
S. Alvarez, P. Alemany, JACS 2004
![Page 28: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/28.jpg)
0
5
10
15
20
25
30
0 5 10 15 20 25 30
CuCl42-: The tetrahedral to planar-square symmetry map and pathway
S(Td)
S(D
4h)
S. Keinan
![Page 29: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/29.jpg)
Several possible pathways for this transformation
Spread
Twist
Compression
70o
110o
![Page 30: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/30.jpg)
0
5
10
15
20
25
30
0 5 10 15 20 25 30
The tetrahedral to planar-square transformation
Spread
Twist
Compression
CuCl42-
S(Td)
S(D
4h)
![Page 31: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/31.jpg)
30
25
20
15
10
5
035302520151050
-2033.20-2033.15-2033.10-2033.05-2033.00-2032.95
d
JS(D
)
S(T )
-2033.15-2033.10
-2033.05
-2033.00
(136.8 kcal/mol)(105.4 kcal/mol)(74.1 kcal/mol)(42.67 kcal/mol)(11.29 kcal/mol)
J -2033.168 (0 Kcal/mol)
Spread simulation
Energy in Hartree (relative energy in kcal/mol)
Minimal energy and minimal symmetry values coincide
•S
( D4 h
)
![Page 32: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/32.jpg)
Tetracoordinated Bis-Chelate Metal Complexes
M(L-L')2: The [M(bipy)2] family
L-M-L bond angles:
# Spread From 90° to 109.4°
#Two Twist pathways: The bidentate nature is introduced by keeping the two opposite L-M-L bond angles constant at typical 82 and 73°
70o
110o
Twist
![Page 33: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/33.jpg)
We (mainly S. Alvarez) analyzed similarly all MLn families with n from 4 to 10
4 Chem. Eur. J., 10, 190-207 (2004).
5 J. Chem. Soc., Dalton Trans., 3288-3303 (2000).
6 New J. Chem., 26, 996-1009 (2002).
7 Chem. Eur. J., 9, 1281-1295 (2003).
8 Chem. Eur. J., 11, 1479 (2005).
9 Inorg. Chem., 44, 6939-6948 (2005).
10 Work in progress
![Page 34: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/34.jpg)
Symmetry or chirality as reaction coordinates
![Page 35: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/35.jpg)
Stone-Wales Enantiomerizations in Fullerenes
Y. Pinto, P. Fowler (Exeter)
![Page 36: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/36.jpg)
Hückel energy changes along the enantiomerization
![Page 37: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/37.jpg)
The sensitivity of energy/chirality dependence on the size of the fullerene
![Page 38: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/38.jpg)
Temperature and pressure effects
on symmetry and chirality
![Page 39: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/39.jpg)
Cl
NH3+
150
200
250
300
0.34 0.35 0.36 0.37 0.38 0.39
Tem
p (o K
)
S(Oh)
Data: Wei, M. & Willett, R.D. Inorg. Chem. (1995) 34, 3780. Analysis: S. Keinan
Changes in the degree of octahedricity
with temperature
CuCl64-
![Page 40: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/40.jpg)
Low QuartzSiO2, P3221
Temperature and pressure effects on the chirality and symmetry of extended materials:
Quartz
![Page 41: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/41.jpg)
The building blocks of quartz
SiO4 Si(OSi)4
SiSi4-O(SiO3)4-
![Page 42: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/42.jpg)
Combining temperature and pressure effects through symmetry analysis
b
0
0.5
1
1.5
2
2.5
3
3.5
4
120 130 140 150SiOSi angle
C2
A
B
C
D
T
S(C2) of a four tetrahedra unit:
A measure of helicity
A correlation between global and specific geometric parameters
![Page 43: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/43.jpg)
0 5 10 15
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15Pressure (GPa)
Te
tra
he
dri
city
GeO4
SiO4
GeO4
SiO4
a
b
20 SiO2
GeO2
SiO2
GeO2
20
GeGe4
SiSi4
0 5 10 15
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15Pressure (GPa)
Te
tra
he
dri
city
GeO4
SiO4
GeO4
SiO4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15Pressure (GPa)
Te
tra
he
dri
city
GeO4
SiO4
GeO4
SiO4
GeO4
SiO4
a
b
20 SiO2
GeO2
20 SiO2
GeO2
SiO2
GeO2
20 SiO2
GeO2
20 SiO2
GeO2
20 SiO2
GeO2
20
GeGe4
SiSi4
GeO
SiO
4
4
4
4
4
4
Predicting the high pressure symmetry behavior of quartz based on the isostrucutral GeO2
D. Yogev-Einot , D. Avnir; Acta Cryst. (2004) B60 163-173
![Page 44: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/44.jpg)
The building blocks of quartz: All are chiral!
SiO4 Si(OSi)4
SiSi4-O(SiO3)4-
![Page 45: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/45.jpg)
M. Pinsky et al, “Statistical analysis of the estimation of distance measures” J. Comput. Chem., 24, 786–796 (2003)
How small can the measure be and still indicate chirality?
The error bar
# Typical limit: In quartz, S(Chir) of SiO4 = 0.0007
# For S values near zero, the error bar is not symmetric: The + and - are different.
# If the lower bound of S touches 0.00000, then the molecule is achiral.
![Page 46: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/46.jpg)
0.97
1.02
1.07
1.12
1.17
98 298 498 698 898 1098
Temperature (°K)
Le
Cha
teli
er
t
The optical rotation of quartz
Le Chatelier, H. Com. Rend de I'Acad Sciences 1889, 109, 264.
![Page 47: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/47.jpg)
0.97
1.02
1.07
1.12
1.17
98 298 498 698 898 1098
Temperature ( K)
0.54
0.56
0.58
0.6
0.62
0.64
Temperature (°K)
Le
Cha
teli
er
t
Ch
irality, SiSi4
Chirality t
115 years later: Interpretation and exact match with quantitative chirality changes
Crystallography: Kihara, 1990. Analysis: D. Yogev-Einot
SiSi4
![Page 48: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/48.jpg)
Correlations between continuous symmetry and spectral properties
![Page 49: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/49.jpg)
7000
8000
9000
10000
11000
12000
13000
14000
15000
0 5 10 15 20 25 30 35S(Td)
max d-d
(c
m-1)
Jahn-Teller effects and symmetry:
The d-d splitting in Cu complexes
Data: Halvorson, 1990. Analysis: S. Keinan
![Page 50: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/50.jpg)
Changes in transition probability as a function of octahedricity
CuN4O2 Chromophores:
S(Oh)
N
Cu NN
N
O2N
H
HH
H
(a)
(c) (b)
50
100
150
200
250
1 2 3 4 5 6 7
a=b=c=(CH2)3
a=b=c=(CH2)2
a=c=(CH2)3; b=(CH2)2
a=c=(CH2)2; b=(CH2)3
[c
m-1M
-1]
Data: P. Comba, 1999
+2H2O
![Page 51: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/51.jpg)
Degree of allowedness of ESR transition
as a function of the degree of tetrahedricity
![Page 52: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/52.jpg)
z
x
y
z
x
y
Maximal and minimal shielding in AB4 species
Symmetry effects on NMR chemical shielding
![Page 53: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/53.jpg)
Current wisdom:
But how does the shielding change when the symmetry changes continuously?
![Page 54: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/54.jpg)
350
0 10 20 30 40
0
50
100
150
200
250
300C
SA
(ppm
)
S(D4h) – deviation from planarity
CSA vs. S(D4h)200 randomly distorted SiH4
All 29Si NMR properties were calculated using Gaussian98, B3LYP/6-31G* and GIAO
A. Steinberg, M. Karni
![Page 55: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/55.jpg)
0
50
100
150
200
250
300
350
RandomSpread: Maximal de-shielding
0 10 20 30 40
S(D4h) – deviation from planarity
CSA
(ppm
)
CSA vs. S(D4h)
If you de le te a
parag raphmark, the
follow ing
![Page 56: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/56.jpg)
Correlation between symmetry/chirality
and chemical recognition
* Chromatography
* Catalysis
* Enzymatic activity
![Page 57: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/57.jpg)
The pioneering work of Gil-Av on
chiral separations of helicenes
E. Gil-Av, F. Mikes, G. Boshart, J. Chromatogr, 1976, 122, 205
A pair of enantiomers of a [6]-helicene
Silica derivatized with a chiral silylating agent
![Page 58: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/58.jpg)
Enantioselectivity of a chiral chormatographic column
towards helicenes
Is there a relation between this behavior and the degree of chirality of helicenes?
![Page 59: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/59.jpg)
The chiral separation of helicenes on Gil-Av’s column is dictated by their degree of chirality
O. Katzenelson Tetrahedron-Asymmetry, 11, 2695 (2000)
Gil-Av
Quantitative chirality
![Page 60: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/60.jpg)
Catalysis
![Page 61: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/61.jpg)
N
OO
CH2
Cu N
X X
ON
O O
O N
OO
n
X = OTf
1 n = 12 n = 23 n = 34 n = 4
1-4
5 6
Catalytic Chiral Diels-Alder Reaction
Data: Davies, 1996. Analysis: Lipkowitz, Katzenelson
![Page 62: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/62.jpg)
The nearest symmetry plane of the catalyst
n = 1
![Page 63: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/63.jpg)
The enantiomeric excess of the product
as a function of the degree of chirality of the catalyst
Lipkowitz, JACS 123 6710 (2001)
![Page 64: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/64.jpg)
N
Cu
N
O O
C C
CC
SS
S1 S2
CC C
N
Cu
N
CC
O O
C
C
C
C
SO
O
CF
F F
SO
O
CF
F F
C C
CC
CC
N
Cu
N
O O
C
C
C
C
S
CF
F F
S
CF
F F
C
CC C
C
C
Sb Sg
Which smallest fragment carries the essential chirality?
S. Alvarez
![Page 65: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/65.jpg)
The smallest fragment which carries
the essential chirality for catalysis
![Page 66: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/66.jpg)
Prediction 1: Replace the exocyclic ring with C=O or C=CH2 to get good homologue catalysts
![Page 67: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/67.jpg)
Prediction 2: Increase the twist angle
![Page 68: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/68.jpg)
Enzymatic activity
![Page 69: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/69.jpg)
Trypsin inhibitors
S. Keinan JACS 98
![Page 70: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/70.jpg)
Attempt to find a correlation between the inhibition constant and the chirality of the whole inhibitor
No correlation; but…
![Page 71: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/71.jpg)
The correlation follows the degree of chirality but not the length of the alkyl chain
Correlation between inhibition
and the chirality of the pharmacophor
![Page 72: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/72.jpg)
Inhibition of acetylcholine esterase by chiral organophosphates
![Page 73: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/73.jpg)
Ala82Asn83
Ile84
Gly50
HIV protease complexed
with A77 inhibitor
HIV protease-drug complex C2-symmetric color map
![Page 74: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/74.jpg)
F
FF
FFF
FF
FF
F
J
E
-16000
-15000
-14000
-13000
-12000
-11000
-10000
-9000
-8000
-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0
G [
Kcal/
mol]
[S(C )]2
F: Native HIV-protease inhibitors
E: Native HIV-protease inhibitor A77
J: V82A mutant HIV-protease inhibitor A77
Free energy of inhibitors binding vs. their C2-symmetry change
![Page 75: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/75.jpg)
Given a sufficiently high resolution in space or in time, nothing is symmetric, everything is chiral
![Page 76: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/76.jpg)
Our web-site (beta)
http://chirality.ch.huji.ac.il/ or http://www.csm.huji.ac.il/
![Page 77: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/77.jpg)
![Page 78: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/78.jpg)
![Page 79: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/79.jpg)
![Page 80: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/80.jpg)
![Page 81: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/81.jpg)
![Page 82: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/82.jpg)
![Page 83: Continuous Symmetry and Chirality Measures David Avnir Institute of Chemistry The Hebrew University of Jerusalem Harvard, Boston, January 28, 2013](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649d205503460f949f583c/html5/thumbnails/83.jpg)
The J. Am. Chem. Soc. Series:
114, 7843 (1992)115, 8278 (1993)117, 462 (1995)120, 6152 (1998)122, 4378 (2000)123, 6710 (2001)125, 4368 (2003)126, 1755 (2004)
Literature
Recent:
A. Steinberg et al, "Continuous Symmetry Analysis of NMR Chemical Shielding Anisotropy”, Chem. Eur. J., 12, 8534 – 8538 (2006)
D. Yogev-Einot et al, "The temperature-dependent optical activity of quartz: from Le Chaˆtelier to chirality measures”, Tetrahedron: Asymmetry 17, 2723 – 2725 (2006)
Mark Pinsky et al, "Symmetry operation measures”, J. Comput. Chem., 2007