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Vanderbilt Chemistry
Determination of Molecular Stereochemistry Using
Chiroptical Spectroscopic Methods
Presented to
Synthetic community/ Chemical-Biology training programFebruary 15, 2011
Prasad L. PolavarapuDepartment of Chemistry
Vanderbilt UniversityNashville TN 37235 USA
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(1). Bromochlorofluoromethane, CHFClBr
(2). Molecules that are chiral solely due to isotopic substitution
How would you determine: (A). the absolute configuration of:
(3). Diastereomers of Natural Products
(B). The secondary structures of peptides/proteins
Food for thought
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Chiroptical Spectroscopic methods
ORD ECD
VCD
Optical Rotatory
dispersion
Electronic Circular Dichroism
Vibrational Circular
Dichroism
VROA
Vibrational Raman Optical Activity
Enantiomers of chiral molecules give oppositely signed chiroptical spectra and thus enable distinguishing enantiomers
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Optical Rotation: Experimental Measurement
Specific Rotation: []= /c l
is observed rotationc is concentration in g / mL
l is path length in dm
monochromator
Linear polarizer
Analyzer detector
Chiral sample
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Lack of a reliable method to correlate observed Specific rotation with molecular structure prevented optical rotation from becoming a structural tool for the most part of twentieth century.This status has changed now due to advances in quantum chemical theories and ever changing computer technology
Specific Rotation & Molecular structure
“Experimental determination of the absolute configuration of bromochlorofluoromethane is a challenge”.Wilen SH, Bunding KA, Kascheres CM, Weider MJ.
J Am Chem Soc 1985; 107:6997-6998
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Static method of Amos Chem. Phys. Lett. 1982; 87: 23-26
lim -1G’=-(h/) Im (s/F)|(s/B) 0
CPHF method implementedin CADPAC program
Calculations were done at Hartree-Fock level of theory using 6-31G*/DZP basis sets for 11 molecules
= -(1/3) -1[G’xx+ G’yy+ G’zz]
-1G’=-(4/h){[1/(2ns- 2)]Im{,snm,ns}}
[] = 13.43 x10-5 2/M(in deg.cc.dm-1.g-1)
Molecule Pred Expt(R)-methyloxirane 2 14(S)-methylthiirane -50 -51(R,R)-dimethyloxirane 70 59(S,S)-dimethylthiirane -248 -129
Using specific rotation at 589nm and Raman optical activity, absolute configuration of bromochlorofluoromethane was assigned as(S)-(+)/(R)-(-). Hecht L, Costante J, Polavarapu PL, Collet A, Barron LD. Angew. Chem. 1997; 36: 885-887; Chem. Eng. News, 1997
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Advanced theoretical methodsTime dependent density functional theory for specific rotation
(1). K. Yabana, G. F. Bertsch, Application of time-dependent densityfunctional theory to optical activity, Phys. Rev. A 60 (1999) 1271-1279; (2). J. R. Cheeseman, M. J. Frisch, F. J. Devlin, P. J. Stephens, Hartree-Fock and Density functional theory ab initio calculation of optical rotation using GIAOs: Basis set dependence, J. Phys. Chem. A.104 (2000) 1039-1046; (3). S. Grimme, Calculation of frequency dependent optical rotation using density functional response theory, Chem. Phys. Lett. 339 (2001) 380-388
(4).K. Ruud, T. Helgaker, Optical rotation studied by density functional and coupled-cluster methods, Chem Phys Lett. 352 (2002) 533-539.
(5). J. Autschbach, S. Patchkovskii, T. Ziegler, S. J. A. van Gisbergen, E. J. Baerends, Chiroptical properties from time-dependent density functional theory. II. Optical rotations of small to medium size organic molecules, J. Chem. Phys.117 (2002) 581-592.
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(1). K. Ruud, T. Helgaker, Optical rotation studied by density-functional and coupled-cluster methods, Chem Phys Lett. 352 (2002) 533-539.(2). Ruud K, Stephens PJ, Devlin FJ, Taylor PR, Cheeseman JR, Frisch MJ. Coupled cluster calculations of optical rotation, Chem. Phys. Lett. 2003; 373:606-614.(3). Tam MC, Russ NJ, Crawford TD, Coupled cluster calculation of optical rotatory dispersion of (S)-methyloxirane, J. Chem. Phys. 2004; 121:3550-3557.(4). Pedersen TB, Sanchez de Meras AMJ, Koch H. Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decomposition. J. Chem. Phys. 2004; 120: 8887-8897.(5). Kongsted J, Pedersen TB, Strange M, Osted A, Hansen AE, Mikkelsen KV, Pawlowski F, Jorgensen P, Hattig C. “Coupled cluster calculations of optical rotation of S-propylene oxide in gas phase and solution”, Chem. Phys. Lett. 2005; 401:385-392
Advanced theoretical methodsCoupled cluster theory for specific rotation
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Predicted withB3LYP/aug-cc-pVTZFor (S)-CHFClBr
Optical rotatory dispersion in bromochlorofluoromethane
Experimental data from: Canceill J, Lacombe L, Collet A., J Am Chem Soc 1985; 107: 6993-6996.
Hecht L, Costante J, Polavarapu PL, Collet A, Barron LD. Angewandte Chemie 1997; 36: 885-887P. L.Polavarapu, Angewandte Chemie Int. Ed 41(23),4544-4546 (2002).
Absolute configuration of Bromochlorofluoromethane
0
1
2
3
4
350 450 550 650
nm)
Spec
icic
Rot
atio
n
(S)-(+)-CHFClBrin C6H12
neat liquid
B3LYP/aug-cc-pVTZ
ClBrF C
H
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Summary forOptical rotatory dispersion
Remarkable advances in calculation of specific rotations. ORD can now be calculated through resonant regions using sophisticated levels of theory
Optical rotation at a single wavelength should never be used for establishingMolecular structure“Protocols for the analysis of theoretical optical rotations”, P. L. Polavarapu, Chirality 2006; 18: 348-356
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However need a significant culture changein reporting
Experimental solution phase optical rotations
Errors are not usually reported for optical rotation measurements in liquid solutions
Significant errors can arise from (a). Preparing solutions with smaller amount (~mg) of samples(b). Preparing smaller volume (~ mL) solutions(c). Measuring small (<0.01) optical rotation values
Optical rotation measurements of organometallic compounds: Caveats and recommended procedures. Dewey MA, Gladysz JA. Organometallics 1993, 12, 2390-2392.
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AL-AR
0
1
Vibrational ground stateFirst Vibrational excited state
Excited electronic state
Ground electronic state
Electronic Circular Dichroism (ECD)
ECD technique is more than 100 yrs old
Gained a new life, in the last decade, with the advent of reliable quantum chemical theories
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Measurement of Electronic Circular Dichroism
sample
Detector
Experimental
AbsorbanceA= - log(I/I0)
Circular DichroismA=AL-AR
Theoretical
Dipole StrengthD01=|<0||1>|2
Rotational StrengthR01=Im[<0||1>•<1|m|0>]
Visible light source
CircularlyPolarized light
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A typical ECD spectrum
(aS)- 3,3'-diphenyl-[2,2'-binaphthalene]-1,1'-diol
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Empirical rules: Octant rule etc[Lightner, D. A.; Gurst, J. E. Organic Conformational Analysis and Stereochemistry from Circular Dichroism Spectroscopy, John Wiley & Sons: New York, 2000.]
Semi-classical models: Devoe’s Polarizability model[Superchi, S.; Giorgio, E.; Rosini, A. Structural determinations by circular dichroism spectra analysis using coupled oscillator methods: An update of the applications of the DeVoe polarizability model, Chirality, 2004, 16, 422-451]
ECD and Molecular Structures… the Old Way
Exciton coupling model[Harada, N.; Nakanishi, K. Circular Dichroism Spectroscopy: Exciton coupling in Organic Stereochemistry; University Science Books: Mill Valley, CA, 1983.; ]
Vanderbilt ChemistryECD and Molecular Structures… the Modern Way
For ith electronic transition, calculate rotational strength, Ri. ooo
iR siis mIm
heDm
f iiei 2
2
38
Corresponding absorption intensity as dipole strength, Di=|<s||i>|2or dimensionless oscillator strength, fi.
Peak intensity of Lorentzian band: 400, 10
94.228.3298
i
iii
R
Lorentzian band intensity distribution: 22
2
0, )()(
ii
iii
Early Quantum chemical calculations with Random phase approximation:Hansen AE, Bouman TD, Natural chiroptical spectroscopy: Theory and computations, Adv Chem Phys 1980;44:545–644.Hansen AE, Voigt B, Rettrup S, Large-scale RPA calculations of chiroptical properties of organic molecules: Program RPAC, Int J Quantum Chem 1983;23:595–611.
Vanderbilt ChemistryAutschbach, J.; Ziegler T.; van Gisbergen SJA.; Baerends EJ. Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules, J. Chem. Phys. 2002; 116: 6930-6940.
Diedrich C.; Grimme S. Systematic Investigation of Modern Quantum Chemical Methods to Predict Electronic Circular Dichroism Spectra, J. Phys. Chem. A. 2003, 107, 2524-2539;
Pecul M.; Ruud K.; Helgaker T. Density functional theory calculation of electronic circular dichroism using London orbitals, Chem. Phys. Lett. 2004; 388: 110-119;
Stephens PJ, McCann DM, Devlin FJ, Cheeseman JR, Frisch MJ. Determination of the absolute configuration of [3(2)](1,4) barrelenophanedicarbonitrile using concerted time-dependent density functional theory calculations of optical rotation and electronic circular dichroism. J Am Chem Soc 126 (2004) 7514-7521.
Modern Quantum chemical calculations:Density functional theoretical method for ECD
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Pedersen TB.; Koch H.; Ruud K. Coupled cluster response calculation of natural chiroptical spectra, J. Chem. Phys. 1999; 110: 2883-2892;
Crawford TD.; Tam MC.; Abrams ML. The current state of ab initio calculations of optical rotation and electronic circular dichroism spectra. J. Phys. Chem. 2007, 111, 12057-12068
Modern Quantum chemical calculations:Coupled Cluster theoretical method for ECD
Vanderbilt Chemistry
Molecular stereochemistry:(+)-P-Ni3[(C5H5N)2N]4Cl2
Daniel W. Armstrong, , F. Albert Cotton, Ana G. Petrovic, Prasad L Polavarapu, and Molly M. WarnkeInorg. Chem. 2007, 46, 1535-1537
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-450
0
450
200 400 600 800
Experimental
BHLYP/LANL2DZ
Ni3[(C5H5N)2N]4Cl2
Electronic circular dichroism and
Molecular Stereochemistry(+)-P-Ni3[(C5H5N)2N]4Cl2
Daniel W. Armstrong, , F. Albert Cotton, Ana G. Petrovic, Prasad L Polavarapu, and Molly M. WarnkeInorg. Chem. 2007, 46, 1535-1537
(+)-P- absolute configuration was also confirmed using ORD and VCD
Vanderbilt ChemistrySummary for ECD
Remarkable advances in calculation of ECD using sophisticated levels of quantum chemical theory
But that does not mean redundancy•ECD in the UV-Vis range cannot be measured in solvents such as DMSO but ORD can still be measured in DMSO in the long wavelength region.•Experimental ORD may show more sensitivity than what can bededuced for accessible experimental ECD spectrum•If ECD is predicted correctly and ORD is not (or vice versa) thenthat reflects on the inadequacy of theoretical level used.
ECD and ORD are not independent methods(can be transformed into each other using Kramers-Kronig transform)
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(A). The absolute configurations of:
(1). Diastereomers of natural products that have same signed ORD and ECD?
(2). Molecules that are chiral solely due to isotopic substitution
How would you determine:
(B). Secondary Structures of Peptides and Proteins confidently
But ……………….
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Diastereomeric Natural Products
ECD
ECD and ORD may not be able to discriminate diastereomers
ORD
OO
H
COOCH3
HOCOOCH3
Garcinia acid dimethyl ester (GADE)
Garcinia acid is extracted from the dried rind of the fruit of G.cambogia (tamarind fruit)
Hibiscus acid dimethyl ester (HADE)
Hibiscus acid is extracted from the Rosella plant
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(A). Vibrational Circular Dichroism (VCD)(B). Vibrational Raman Optical Activity (ROA)
(1). All (3N-6) vibrations of a chiral molecule can exhibit VCD/ROAFor a 10 atom molecule, there will be 24 vibrations
Thus, unlike in ECD, no chromophore is needed to observe VCD/ROA
(2). Chiral hydrocarbons do not exhibit measurable ECD/ORD spectra, but they do give large VCD/ROA spectra
(3). Through isotope labeling, site specific structure can de determined
(4). VCD is a ground electronic state property.Thus, quantum chemical predictions of VCD are more reliable
and less time consuming(5). Some of the literature ECD interpretations of absolute configurations and
protein secondary structures are now being corrected in light of VCD studies(6). Some of the literature crystal structure determinations of absolute
configurations are now being corrected in light of VCD studies
New Chiroptical Spectroscopic methods
What are the advantages?
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AL-AR0
1
Vibrational ground state
First Vibrational excited state
Excited electronic state
Ground electronic state
Vibrational Circular Dichroism (VCD)
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Measurement of Vibrational Circular Dichroism
sample
Detector
Infrared light source
CircularlyPolarized light
Infrared circular dichroim of C-H and C-D stretching vibrations: ObservationsHolzwarth G.; Hsu EC.;Mosher HS.; Faulkner TR; Moscowitz AJ Am Chem Soc 1974, 96: 252-253
First measured in 1974
Remarkable developments in instrumentation and theory have occurred in 1980s and 1990s
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Measurement of Vibrational Circular Dichroism: Fourier Transform instruments
Moving Mirror
Fixed Mirror
Polarizer
PEM
Sample
Lens
Detector
IACLA
BS
FT
FT
IDC
S
Filter
MI
Moving Mirror
Fixed Mirror
Polarizer
PEM
Sample
Lens
Detector
IACLA
BS
FT
FT
IDC
S
Filter
MI
1. Liquid samples Routine2. Gas samples Samples with high vapor pressure3. Films (dried solutions) became possible recently
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A typical VCD spectrum [(+)-vanol]
VCD magnitudes are of the order of 10-4 absorbance units
100 times smaller than ECD magnitudes
Vanderbilt ChemistryDensity functional theoretical method
J. R. Cheeseman, M. J. Frisch, F. J. Devlin, P. J. Stephens, Ab initio calculation of atomic axial tensors and vibrational rotational strengths using density functional theory, Chem. Phys. Lett. 252 (1996) 211-220.
Computer Programs:
Freeware: DALTON program [www.kjemi.uio.no/software/dalton/ ]
Commercial: Gaussian 09 [www.gaussian.com]; Turbomole [www.turbomole.com]; ADF [www.scm.com]
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Diastereomeric Natural ProductsO
O
H
COOCH3
HOCOOCH3
ECD ORD
VCD can discriminate diastereomers better than ECD/ORD
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Diastereomeric Natural ProductsO
O
H
COOCH3
HOCOOCH3
VCD is much more powerful than ECD/ORD for discriminating diastereomers
Vanderbilt ChemistrySummary for VCD
VCD provides an independent reliable approach from ECD/ORD for molecular structure determination
Are there any disadvantages of VCD ?(1). Higher concentrations than those needed for ECD/ORD
VCD measurements require ~1-20 mg/100 L(2). Sample should be soluble in IR transparent solvents
(CCl4, CHCl3, CD2Cl2, CD3CN, D2O, DMSO-d6 etc)
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Natural products whose structures have been determined/confirmed using VCD
Carboxylic acids (1-4)Monoterpenes (5-14)
Alkaloids Cinchonidine
Schizozygane alkaloids (15-19)
Iso-schizozygane alkaloids(20-21)
Tropane alkaloids(22-28)
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Natural products whose structures have been determined/confirmed using VCD
Tropane alkaloids(22-28)Montanine-type alkaloids
(29-30)Iridoids (31-34)Meroditerpenoids (35-38)Verticillane diterpenoids(39)Sesquiterpenes (40-46)
Compounds 40-43: P. J. Stephens, D. M. McCann, F. J. Devlin, A. B. Smith,
J. Nat. Prod. 2006, 69, 1055-1064.
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Natural products whose structures have been determined/confirmed using VCD
Halogenated sesquiterpenes (47-51)
Endoperoxides (52)Furochromones (53-56)Eremophilanoids (57-59)Eudesamanolides (60)Presilphiperfolanes (61-63)Longipinane derivatives (64-66)Cruciferous phytoalexins (67-73)
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Natural products whose structures have been determined/confirmed using VCD
Furanones (74-80)Furanocoumarins (81)Klaivanolide (82)Pheromones(83-84)Norlignan(85-86)TaxolGinkgolidesPeptides
(pexiganan, cyclosporins)Axially chiral natural products
Dicurcuphenol B (87)Dicurcuphenol C (88)Gossypol (90)Cephalochromin (91)
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Vibrational Raman Optical Activity (VROA)
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Measurement of Vibrational Raman Optical Activity (VROA)
IR-IL
0
1
Vibrational ground state
First Vibrational excited state
Excited electronic state
Virtual state
Ground electronic state
Scattered lightIncident light
sample
laser
IR-ILFirst Measured in 1973L. D. Barron, M. P. Bogaard and A. D. Buckingham, JACS. 95, 603 (1973)
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Hartree-Fock Numerical differentiation approach using Amos’ static method for G tensor
Quantum Chemical predictions of ROA
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Advances in Quantum mechanical predictions
Numerical differentiation methodsHartree-Fock Numerical differentiation with Dynamic method and London orbitalsT Helgaker, K. Ruud, K. L. Bak, P. Jorgensen, J. Olsen. Farad Disc 1994, 99,165-1802000s Density functional numerical differentiation methodK. Ruud, T. Helgaker, P. Bour, J. Phys. Chem. A. 106, 7448 (2002)
Analytical methods2000sTime-dependent Hartree–Fock schemes for analytical evaluation of the Raman Intensities, Quinet, O.; Champagne, B. J. Chem. Phys. 2001, 115, 6293-6299.TDHF Evaluation of the Dipole−Quadrupole Polarizability and Its Geometrical Derivatives, Quinet, O.; Liegeois, V.; Champagne, B. J. Chem. Theory Comput. 2005, 1, 444-452An analytical derivative procedure for the calculation of vibrational Raman opticalactivity spectra, Liegeois, V.; Ruud K.; Champagne, B. J. J. Chem. Phys. 2007; 127, 204105.
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Absolute configuration of
BromochlorofluoromethaneComparison of experimental ROA of (-) CHFClBr with predictions for (R)-CHFClBr
Absolute Configuration of Bromochlorofluoromethane from Experimental and Ab Initio Theoretical Vibrational Raman Optical Activity. Hecht L, Costante J, Polavarapu PL, Collet A, Barron LD. Angewandte Chemie 1997; 36: 885-887
HF(or MP2)/DZP
Experiment B3LYP/6-311++G(2d,2p)Freq(cm-1) zx104 Freq(cm-1) zx104
3022 -0.7 3173 -0.31305 -2.4 1321 0.51206 -2.8 1212 -1.01062 -4.5 1065 -0.2774 -5.1 744 -4.9662 5.9 634 3.2427 10.2 417 1.1315 -2.1 305 0.0218 -1.9 218 -0.3
The Absolute Configuration of Bromochlorofluoromethane.P L. Polavarapu, Angewandte Chemie, 41(23),4544-4546 (2002).
ClBrF
Absolute configuration
of CHFClBr is
(S)-(+)
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Absolute configuration of chirally deuterated neopentane, J. Haesler, I. Schindelholz, E. Riguet, C. G. Bochet & W. Hug, Nature 446, 526-529 (2007)
Absolute configuration of chirally deuterated neopentane:(R)-[2H1, 2H2, 2H3]-neopentane
Boltzmann population weightedSpectrum
Vanderbilt ChemistrySummary for ROA
ROA provides an independent and reliable approach to determineChiral molecular structures
Well suited for biological molecules in aqueous solutions
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How Can You Benefit From
These New Developments
There are three independent methods, fully developed and ready to be used.
VCDECD and ORD ROA
These two should be viewed as one
No need for crystallization, unlike X-rayNo need for derivatization with shift reagents,
unlike in NMRExperimental measurements done for solutions or
for film samples
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Secondary Structures of Peptides and Proteins
How about……………….
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-10
-5
0
5
10
15
200 220 240 260Wavelength (nm)
Mol
ar E
llipt
icity
218
-Sheet
-4.5
-3
-1.5
0
1.5
200 220 240 260
Wavelength (nm)
Mol
ar E
llipt
icity
217
230
200
-turn
ECD has been widely used for determining Secondary structuresPeptides and proteins:
ECD spectra-structure correlations
-30
-20
-10
0
10
190 210 230 250
Mol
ar E
llipt
icity
Wavelength (nm)
196
222
collagen
Polyproline II
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-6
-4
-2
0
2
4
6
14001500160017001800Frequency (cm-1)
A1
05 16281666 1516
1628
16621516
Ovalbumin
Trypsin
-Helix + -Sheet
-10
-5
0
5
160017001800
Wavenumber (cm-1)
AX
105
1686
1662
-turn
-4
-2
0
2
4
6
14001500160017001800Frequency (cm-1)
A1
05
1640
1662
1662
1516
1643
1512
BSA
Hemoglobin
-Helix
-3
-2
-1
0
1
2
3
4
5
14001500160017001800Frequency (cm-1)
A1
05
1632
1632 1516
1520
Pepsin
Chymotrypsin
-Sheet
Peptides and proteins: VCD spectra-structure correlations
-2
-1
0
1
2
14501550165017501850
Wavenumber (cm-1)
A
104
1636
1670
Polyproline II (PPII)collagen
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Secondary Structures of peptides and ProteinsVP1 peptide: Domain IV of Calpain enzyme
Time dependent structural transition of VP1
VP1: GTAMRILGGVI
TEM image
Ganesh Shanmugam, Nsoki Phambu, Prasad L Polavarapu, BioPhysChem.
-100
-50
0
50
195 215 235 255 275
CD
(mde
g)
Wavelenth (nm)
ECD
Double minima indicate -helical structure
0
0.3
0.6
0.9
15751625167517251775Wavenumber (cm-1)
Abs
orba
nce
16741620
1697
-5
-3
0
3
5
AX1
05
1624
1670
1609
1682 1640
0
0.3
0.6
0.9
15751625167517251775Wavenumber (cm-1)
Abs
orba
nce
16741620
1697
-5
-3
0
3
5
AX1
05
1624
1670
1609
1682 1640
VCD
VCD band at 1609 indicates -sheet structure possibly fibril formation
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Do not bet your life if using ECD !!
Verify your conclusions using VCD/ROA
Secondary structures of peptides and proteins
Vanderbilt ChemistryGlobal Summary
Older methods of structural interpretations using ECD and ORDhave been replaced with much more reliable modern quantum chemical methods
Two new chiroptical spectroscopic methods, VCD and ROA, have emerged in the last two decades as powerful techniques for chiral molecular structure determination
Combined applications of these methods yield a reliable meansof chiral molecular structure determination
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Coming this year ……August 2011
Comprehensive Chiroptical SpectroscopyEds, N. Berova, P. L. Polavarapu, K. Naksnishi, R. W. Woody (John Wiley)
Volume 1: Instrumentation, Methodologies, and Theoretical Simulations
Volume 2: Applications in Stereochemical Analysis of Synthetic Compounds, Natural Products, and Biomolecules
More than 50 chapters and 1000 pages !!
Vanderbilt ChemistryAcademic Collaborators
Sergio Abbate (Italy)Daniel Armstrong (Texas)Brian Bachman (Vanderbilt)P Balaram (India)Laurence Barron (Glasgow)Nina Berova (Columbia Univ)James Birch (UK)F. A. Cotton (Texas)Jeanne Crassous (France)Carlo De Micheli (Italy)Jozef Drabowicz (Poland)Helmut Duddeck (Germany)Carl Ewig (Vanderbilt)Joe Gal (Denver)B. A. Hess (Vanderbilt)Ibrahim Ibnusaud (India)
Tibor Kurtan (Hungary)Tingyu Li (Vanderbilt)Zsuzsa Majer (Hungary)Larry Nafie (Syracuse)Koji Nahanishi (Columbia Univ)Bruce Novak (North Carolina)Arvi Rauk (Calgary)Carmelo Rizzo (Vanderbilt)Gabrielle Roda (Italy)Kenneth Ruud (Tromso)William Salzman (Arizona)Larry Schaad (Vanderbilt)Volker Schurig (Germany)Howard Smith (Vanderbilt)Gerald Stubbs (Vanderbilt)William Wulff (Michigan)
Vanderbilt ChemistryGraduate StudentsDarlene BackT. M. BlackP. K. BoseS. T. PickardD. K. ChakrabortyT. ChandramoulyZ. DengJ. HeJ. McBrideA. PetrovicP. ZhangF. WangC. Zhao
Research AssociatesP. K. BoseG. ChenB. GalabovD. HendersonD. MichalskaR. S. PandurangiG. ShanmugamK. Srinivasan
Undergraduate studentsS. R. ChatterjeeS. ChawlaP. ChenA DehlaviJ. Goring K. HammerNeha JeirathSheng LinA.G. PetrovicR. Reddy A. SchwaabS. E. Vick Sheena Walia
Coworkers
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Funding over the years
National Institute of HealthNational science FoundationNational center for Supercomputing Applications
Acknowledgments
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