determination of molecular stereochemistry using ... · optical rotatory dispersion remarkable...

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


(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


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


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


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


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


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.


(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


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


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


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.


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


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


A typical ECD spectrum

(aS)- 3,3'-diphenyl-[2,2'-binaphthalene]-1,1'-diol


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


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


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


-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)


(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 ……………….


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


(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?


AL-AR0

1

Vibrational ground state

First Vibrational excited state



Vibrational Circular Dichroism (VCD)


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


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


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]


Diastereomeric Natural ProductsO

O

H

COOCH3

HOCOOCH3

ECD ORD

VCD can discriminate diastereomers better than ECD/ORD


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)


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)



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.



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)



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)


Vibrational Raman Optical Activity (VROA)


Measurement of Vibrational Raman Optical Activity (VROA)

IR-IL

0

1

Vibrational ground state

First Vibrational excited state


Virtual state


Scattered lightIncident light

sample

laser

IR-ILFirst Measured in 1973L. D. Barron, M. P. Bogaard and A. D. Buckingham, JACS. 95, 603 (1973)


Hartree-Fock Numerical differentiation approach using Amos’ static method for G tensor

Quantum Chemical predictions of ROA


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.


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)-(+)


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


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


Secondary Structures of Peptides and Proteins

How about……………….


-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


-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


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


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


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


Funding over the years

National Institute of HealthNational science FoundationNational center for Supercomputing Applications

Acknowledgments

determination of molecular stereochemistry using ... · optical rotatory dispersion remarkable...

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