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THz-TDS Studies of Low Frequency Modes in Organic Molecular Crystals and Progress
Toward THz Vibrational Optical Activity
Charles A. Schmuttenmaer
Department of Chemistry, Yale University225 Prospect St., New Haven, CT 06520-8107
Schmuttenmaer LabBecky Milot, Michael WilliamsDan AschaffenburgRebecca Allred, Stafford Sheehan
Solar Energy CollaborationVictor Batista, et al. Theory
Gary Brudvig, et al. Biophysical & PSII
Bob Crabtree, et al. Inorganic & Catalysis
Coworkers and $$$
http://thz.yale.edu
THz Time-Domain Spectroscopy(THz-TDS)
Advantages:
Very sensitive to intermolecular interactions (H-bonding, Coulombic forces, etc.).
Most sensitive broadband far-infrared method at frequencies below 33 cm-1.
Many opaque substances (in the visible or infrared) are transparent in the far-IR.
Absorption coefficient and refractive index are obtained “automatically”.
Kramers-Kronig analysis is not required.
Opens up largely unexplored region of the spectrum: 0.2 to 4 THz (6 to 130 cm-1).
Disadvantages:
Somewhat limited spectral coverage compared to Raman or Fourier Transform-IR.
P. U. Jepsen and S. J. Clark, "Precise ab-initio prediction of terahertz vibrational modes in crystalline systems," Chem. Phys. Lett. 442, 4-6 275-280 (2007).
THz Spectra of OMCs are Rich
Possible Spectroscopic Measurements
THz spectraRaman spectraTemperature dependencePressure dependenceSingle crystal orientation dependenceIsotope dependenceFamily of related compoundsTHz optical activityX-ray diffraction & powder XRD
Theoretical ConsiderationsLevel of theory: Empical, semi-empirical, ab initio, DFTDFT: Plane-wave vs. atom-centeredvan der Waals interactions: R-6 term vs. vdW functionalUnit cell relaxation (or not)Anharmonicity0 K
To Obtain…Vibrational frequencies and intensitiesIntensities along a, b, and c crystallographic axesPressure dependenceTemperature dependence (not really)VCD & VORDIsotope dependence
1. THz Studies of Organic Molecular Crystals1. Range of interactions2. Experimental considerations3. Calculations4. Describing vibrational modes5. Comparing calculations with measurements
2. THz Optical Activity1. CD and ORD2. Experimental considerations3. Spirals4. Molecules (future studies…)
Outline
L-valine crystal lattice
Isolated L-valine molecule
THz-TDS of Molecular Crystals
+ --
---
-
-- -
--
-
+ +
+++
+ ++
+ ++ +
+---
Types of Interactions in a Molecular Crystal
Molecules We Have Studied Over the Years
Materials are purchased from Sigma and used as received. They are polycrystalline “powders” –polarizing microscope. They are pressed into pellets (~2 – 5 mm thick). Typically, no filler material is used.
Experimental Schematic & Representative Data
General ApproachUse THz spectroscopy, Raman scattering, powder XRD, and ab initio (DFT) calculations to fully understand THz spectra of organic molecular crystals (OMCs): Which modes correspond to which peaks???1. Measure THz and Raman spectra of L, D, and DL-racemates of polycrystalline amino acids.
2. Verify polymorph using XRD.
3. Assign low frequency intermolecular phonon modes.- If crystal structure is known: Calculate modes. - If not: Determine it ourselves, and then calculate modes.
4. Understand the different phonon modes in the different crystals.
5. Verify interpretation with isotope substitution, temperature dependence, pressure dependence, and THz vibrational optical activity.
Frequency (THz)0.0 0.5 1.0 1.5 2.0 2.5P
ower
abs
orpt
ion
coef
. (cm
-1)
0
50
100
150
200
250
D-histidine L-histidine DL-histidine
Frequency (THz)0.0 0.5 1.0 1.5 2.0 2.5
0
50
100
150
200
250a) b)
Frequency (THz)0.0 0.5 1.0 1.5 2.0 2.5
Pow
er a
bsor
ptio
n co
ef. (
cm-1
)
020406080
100120140160 c)
Polymorphism
As received Recrystallized
Recrystallized (same data as part b)
50/50 linear combination of D- and L-histidine in part (a).
Powder XRD: Histidines
angle (2)10 15 20 25 30
log
inte
nsity
0
1
2
3
Recrystallized L-histidine (both phases)50/50 linear combination of D & L
a) L-histidine, as received
b) Calculated, orthorhombic
c) D-histidine, as received
d) Calculated, monoclinic
e) 50/50 linear combination of D & L
angle (2)10 15 20 25 30
Log
inte
nsity
0
5
10
15
e)
d)
c)
b)
a)
D- and L-histidine can exist in two stable polymorphs: orthorhombic and monoclininc.
P. U. Jepsen and S. J. Clark, Chem. Phys. Lett. 442, 275-280 (2007).
Alp
ha (c
m-1
)
050
100150200250
Frequency (THz)0.5 1.0 1.5 2.0 2.5
Alp
ha (c
m-1
)
0
50
100
150
200D-tyrosineL-tyrosine
DL-tryosine
CHARMM(empirical)
Karen Siegrist,† Christine R. Bucher,† Idan Mandelbaum,† Angela R. Hight Walker,† Radhakrishnan Balu,‡ Susan K. Gregurick,‡ and David F. Plusquellic*,† J. AM. CHEM. SOC. 2006, 128, 5764-5775
THz spectroscopy definitely reveals interesting absorption features. These low-frequency vibrations are strongly influenced by intermolecular interactions.
But what are they?
Harmonic frequencies are calculated which means they are WRONG!
Pote
ntia
l Ene
rgy
r
Anharmonicity: Diatomic MoleculeRed-shifts at higher temperatures.
Urea calculations
Mode v1:
Harmonic frequency: 30.44 cm-1 (shown in gray)
Anharmonic:0 1: 62.9 cm-1
1 2: 82.9 cm-1
2 3: 93.1 cm-1
It is significantly anharmonicand blue-shifts at higher temperatures.
(shown in blue)
NH2H2N
O
Name AC vs. PW Price vdW functional?
Crystal09 Atom-centered $$$ ?DMol3 Plane Waves $$$ ??VASP Plane Waves $$$ ??GPAW Plane Waves Free ?ABINIT Plane Waves Free ?CASTEP Plane Waves $$$ ?SIESTA Atom-centered Free YESGaussian Atom-centered $$$ No
and many, many, many more…http://dft.sandia.gov/Quest/DFT_codes.html
Density Functional Theory (DFT) Calculations
Begin calculation with experimental XRD coordinates.
1200 eV 0.35 Å
Plane wave
s
p
d
f
Atom-centered
Basis functions
Korter et al., J. Phys. Chem. A 113, 13013 (2009).
Comparing different DFT calculationsCurrently, people compare calculated spectra to experimental ones, and use their judgment to decide which is the “best” fit.
1. Quantify vibrational mode character.
2. Vibrational mode eigenvector projection.
We need a way to more rigorously compare different calculations.
Experiment & CalculatedL-leucine
L-valine
L-isoleucine
DL-leucine
DL-valine
DL-isoleucine
L-enantiomers: High line density DL-racemates: Low line density
Small Molecules
Describing vibrations
Michael Denk, http://131.104.156.23/Lectures/CHEM_207/vibrational_spectroscopy
Medium Sized Molecules (alanine)
27-carbon CH stretch
33OH stretch
1 3
Medium Sized Molecules (alanine)
Large Molecules and/or Organic Molecular Crystals
Tim Korter, Syracuse University, Department of Chemistry
Quantifying Intermolecular Vibrational Character
4 molecules per unit cell
For each molecule in unit cell:
= Total displacement
Displace along vibrational mode eigenvector:
2rms
1
1TotalN
i ii
mN
where i is displacement vector for each atom and 1, 0,i i ir r
Quantifying Intermolecular Vibrational Character
Calculate C.O.M. displacement:
= Translational Component
2rms rms 0, , 1, ,
1
1Trans TotalN
i com i com ii
m r rN
Finally:
Intermolecular = Total – Intra
Rotational = Inter - Trans
We obtain:
Total displacement
Intramolecular
IntermolecularRotationalTranslational
Overlap C.O.M.s. & Rotatefor maximum overlap.
20, , 1, ,
1
N
i com i com ii
m r r
U
2rms 0, , 1, ,
1
1IntraN
i com i min com ii
m r rN
U
Quantifying Intermolecular Vibrational Character
Remaining displacements:= Intramolecular Component
Rigorous Convergence in DL-Valine Calculations
Calculation methods have a plenitude of settings
How to check convergence?
Energy
Calculated Vibrations
Character of the Modes
DL-Valine: Fixed vs. Optimized Unit Cell
Begin calculation with experimental XRD coordinates. Calculation is at 0 K, crystal structure is not. Therefore, one should NOT fix unit cell dimensions at experimental values.
DL-Valine: Fixed vs. Optimized Unit Cell
L-valine
Atomic coordinates are optimized (otherwise, imaginary frequencies are obtained). So why not unit cell parameters as well?
If unit cell remains fixed, then it is under an indeterminate amount of stress during the calculation. Therefore, one should NOT fix unit cell dimensions at experimental values.
DL-Valine Frozen Unit Cell
Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode character.
DL-Valine Fixed vs. Optimized Unit Cell
DL-Valine Frozen Unit Cell
Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode character.
DL-Valine Fixed vs. Optimized Unit Cell
DL-Valine Frozen Unit Cell
Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode characters.
DL-Valine Fixed vs. Optimized Unit Cell
DL-Valine Frozen Unit Cell
Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode character.Phys. Chem. Chem. Phys. 13, 11719 (2011)
DL-Valine Fixed vs. Optimized Unit Cell
??
Looking at Convergence (again)
Vibrational mode eigenvector projection.
56
6
5
789
9
8
7
Looking at Convergence (again)Vibrational mode eigenvector projections from one calculation onto another. 6-31G(d,p) is considered the best basis set (that we used), so express the eigenvectors of the other calculations as linear combinations of the 6-31G(d,p) results.
6-31G(d) is converged
DL-Valine Fixed vs. Optimized Unit Cell
DL-Valine Fixed vs. Optimized Unit Cell
SIESTA DZDP is Converged
Double ZetaTriple Zeta
Need to use a van der Waals functional!
The Perdew–Burke–Ernzerhof (PBE) functional does NOT treat dispersion, i.e., van der Waals interactions.
c
Compare Gaussian and SIESTA Results
No vdW No vdW No vdW vdW No vdWvdW
NH3+-O2C
CHH
H3C CH3
L-Valine
DL-valine (triclinic)
1
2
3
4
5
6
7
8
9
10
11
12
Tx Ty Tz RA RB RC O1-C1 -
O2O1-C
1 -C2
O2-C1 -
C2N1-C
2 -C1
N1-C2 -
C3C1-C
2 -C3
C2-C3 -
C4C2-C
3 -C5
C4-C3 -
C5O1-C
1 -C2 -
N1
O1-C1 -
C2 -C3
O2-C1 -
C2 -N1
O2-C1 -
C2 -C3
N1-C2 -
C3 -C4
N1-C2 -
C3 -C5
C1-C2 -
C3 -C4
C1-C2 -
C3 -C5
DL-leucine
1
2
3
4
5
6
7
8
9
10
11
12
Tx Ty Tz RA RB RC O1-C1 -
O2O1-C
1 -C2
O2-C1 -
C2N1-C
2 -C1
N1-C2 -
C3C1-C
2 -C3
C2-C3 -
C4C3-C
4 -C5
C4-C3 -
C6
O1-C1 -
C2 -N1
O1-C1 -
C2 -C3
O2-C1 -
C2 -N1
O2-C1 -
C2 -C3
N1-C2 -
C3 -C4
C1-C2 -
C3 -C4
C2-C3 -
C4 -C5
C2-C3 -
C4 -C6
C4-C3 -
C6
1. Isotope Substitution2. Temperature Dependence3. Pressure Dependence4. Selection Rules (Raman vs. IR)5. Related Molecules6. THz Optical Activity (VCD & VORD)
Experimental Variables
Isotope Substitution
Another way to verify that calculation is correct. Even if the frequencies are not perfect, they should shift in correct direction.
THz Optical Activity:
Optical activity in an artificial chiral media: a terahertz time-domain investigation of Karl F. Lindman’s 1920 pioneering experiment.
A. Y. Elezzabi* and S. Sederberg, 13 April 2009 / Vol. 17, No. 8 / OPTICS EXPRESS 6600.
Circular Dichroism (CD) & Optical Rotatory Dispersion (ORD) areRelated through Kramers-Kronig
http://www.answersingenesis.org/images/chirality-rgb.jpg
http://www.georgehart.com/rp/chiral-2-layer-sphere.html http://www.georgehart.com/rp/rp.html
http://scienceblogs.com/pharyngula/upload/2009/04/nodal_spiral.jpeg
http://www.nanotech-now.com/images/nanotube-chiral-large.jpg
Chirality makes it all possible.
Polarized Light
http://en.wikipedia.org/wiki/File:Linear_polarization_schematic.png
http://en.wikipedia.org/wiki/File:Circular_polarization_schematic.png
http://en.wikipedia.org/wiki/File:Elliptical_polarization_schematic.png
Linear Circular Elliptical
Also, Linear = RCP ± LCP
http://commons.wikimedia.org/wiki/File:Circular_dichroism.png http://www.imb-jena.de/ImgLibDoc/cd/images/lucepolarizzata3.jpg
Time = t a little later
Circular Dichroism
On average, VCD spectrum is 300 / 5000 times weaker than UV CD spectrum.
A (1/.
Circular Dichroism
http://www.nsm.buffalo.edu/~jochena/research/opticalactivity.html
Hexahelicene (M)HexahelieceneCD spectrum of (M)-Hexahelicene.Green: Experiment, Red: Computed
http://www.brukeroptics.com/uploads/pics/enantiom1_02.jpg
Vibrational Circular Dichroism (VCD)
http://www.chem.uic.edu/takgroup/Research/Warwick/Slide91.JPG
Optical Rotatory (Dispersion)Analogous to birefringence (no & ne)
http://www.star.le.ac.uk/~rw/courses/lect4313_fig48.jpghttp://sirius.ucsc.edu/demoweb/images/optics/birefrigent.jpg
nLCP > nRCP (or vice versa)
http://chemed.chem.purdue.edu/genchem/topicreview/bp/1organic/graphics/24_19.gif
Making Circularly Polarized THz LightLinear Quarter wave-plate with optic axis @ 45o
PCA-40-05-10-800-0
Frequency (THz)
0 1 2 3 4 5 6
Spe
ctra
l Am
plitu
d (a
rb. u
nits
)
1
10
100
1000
10000
/4 /2 /4 /4
SampleInput pulse(vertically polarized)
DetectorRotatablePolarizerat 45o
Si prism inducesπ/2 phase shift
Making Circularly Polarized THz Light
Fresnel Rhombhttp://spie.org/Images/Graphics/Publications/FG05_P49_f1.jpg
Phase Shift upon total internal reflection in Si (n = 3.417)(c = 17 degrees)
Reflection angle (degrees)40 41 42 43 44 45
Pha
se s
hift
betw
een
p- a
nd s
-pol
ariz
atio
ns (d
egre
es)
86
88
90
92
94
20 30 40 5050
70
90
110
2 2 2tan 2 cos sin 1 / sinn n
(Masahiko Tani, Fukui University)
“XY-antenna” to generate THz pulse
at 45o
Electronically Rotating THz Linear Polarization (Faster than Mechanical)
Use lockin amplifier to Either measure ARCP – ALCP(With either mechanical or electronic modulation).
Michael Johnston, Oxford University
Experimental Apparatus and Sample(Measure CD and ORD simultaneously)
cos cosA A
Sample rotates light by , polarizer angle is .
cos cosA A
cos( ) cos( ) cos( ) sin( ) sin( ) cos( )xA A sin( )yA A
2cos ( ) cos( )sin( )x yA A A
cos 2 cos2 2A AA
2 2
2tan 2 ( ) cosx y
x y
A AA A
cos sinixe x i x cos 1 2 ix ixx e e
Can Analyze Data in Frequency Domain…
Rotation angle
Sample rotates light by , polarizer angle is .
D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient Measurement of Broadband Terahertz Optical Activity.” J. Appl. Phys., 100, 241114 (2012). DOI: 10.1063/1.4729148
2 2 2 2 2
2 2 2 2 2
cos sin 2 cos cos sin
sin cos 2 cos cos sinx y x y
x y x y
a A A A A
b A A A A
Or Time Domain
Rotation angle only Rotation angle and ellipticity
2 2 2cos 2 cos2 2f f fA AA f t
Thanks to Diyar Talbayev!!
Axcos()cos(-) for -180 <= <= 0
2f (phase angle of lockin, in degrees, when detecting second harmonic)
-180-150-120 -90 -60 -30 0 30 60 90 120 150 180
THz
Am
plitu
de (a
rb. u
nits
)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Axcos()cos(-) for 0 <= <= 180
2f (phase angle of lockin, in degrees, when detecting second harmonic)
-180-150-120 -90 -60 -30 0 30 60 90 120 150 180TH
z A
mpl
itude
(arb
. uni
ts)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
= 2f
o o
* *0
* *1
2 45 45
3
1
cos 2 cos 2
2 cos cos 2 sin 2
2 sin sin 2
x y x x y y
x y x x y y
x y
RHCP LHCP x y
S I I A A A A
S I I A A A A
S I I A A
S I I A A
Stokes Parameters
1. Tiny metal helices (watch springs, other ideas?)THz Vibrational Optical Activity
2. Hexahelicene (hard to obtain material… )Intramolecular modes shown.Intermolecular could be even stronger.
Frequency (cm-1)0 200 400 600 800 1000
(c
m-1
)
0
500
1000
1500
2000
IR absorption coefficient
Frequency (cm-1)0 200 400 600 800 1000
(cm
-1)
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
VCD “absorption coefficient”
Can be positive or negative!
3. (R)-(+)-1,1′-bi-2-naphtholThings to Study (cont.)
Claire Niezborala and Francois Hache, J. AM. CHEM. SOC. 2008, 130, 12783–12786
P. Fischer, F. W. Wise, and A. C. Albrecht, J. Phys. Chem. A 2003, 107, 8232-8238
$100 for 5 g (S enantiomer).
Hexahelicene
$467 for 2 mg!
Things to Study (cont.)
P. U. Jepsen and S. J. Clark, "Precise ab-initio prediction of terahertz vibrational modes in crystalline systems," Chem. Phys. Lett. 442, 4-6 275-280 (2007).
Alp
ha (c
m-1
)
050
100150200250
Frequency (THz)0.5 1.0 1.5 2.0 2.5
Alp
ha (c
m-1
)
0
50
100
150
200D-tyrosineL-tyrosine
DL-tryosine
CHARMM(empirical)
3. Organic molecular crystals (help assign spectrum)
Things to Study (cont.)4. Helix-rich proteins (albumin and hemoglobin )
Albumin
THz CD will (hopefully) be more sensitive to tertiary structure than CD in the visible/UV or VCD in the infrared.
Hemoglobin
General Approach in Summary
1. Measure THz and Raman spectra of L, D, and DL-racemates of polycrystalline amino acids.
2. Verify polymorph using XRD.
3. Assign low frequency intermolecular phonon modes.- If crystal structure is known: Calculate modes. - If not: Determine it ourselves, and then calculate modes.
4. Understand the different phonon modes in the different crystals.
5. Verify interpretation with isotope substitution, temperature dependence, pressure dependence, and THz vibrational optical activity.
Use THz spectroscopy, Raman scattering, powder XRD, and ab initio (DFT) calculations to fully understand THz spectra of organic molecular crystals (OMCs): Which modes correspond to which peaks???