Chirped-Pulse Fourier Transform Microwave Spectroscopy with

Real-Time Digitizers Steven Shipman

Assistant Professor of Physical Chemistry

Division of Natural Sciences New College of Florida

Rotational Spectroscopy at Elevated Temperatures

High T spectra give access to excited vibrational and conformational states.

Spectra are more crowded and much weaker at elevated temperature.

Collecting spectra rapidly is straightforward; analysis is more complicated!

Chirped Pulse Spectroscopy

• A chirped pulse is a linear frequency sweep.

• Can have multiple frequencies in one pulse.

E(t) = E0 e i(0t + (t))‏

Electric Field:

Instantaneous Frequency: = 0 + t, = sweep rate

(t) = (/2) t2

1) 500 ns sweep (0.1 – 4.9 GHz) generated

by AWG and mixed with PLDRO.

2) A sideband is amplified and sent into

sample cell.

3) Molecular FID is amplified and mixed

with PLDRO.

4) Downconverted FID (0.1 – 4.9 GHz) is

detected with oscilloscope.

NCF Spectrometer

Real-time Digitizers Acquiris U1084A (Agilent)

Guzik ADC 6082 (formerly Guzik, now Agilent)

Current scope: Tektronix TDS 6154C

Bandwidth Averaging? Real-time? Rep. Rate*

Current scope

15 GHz Yes No 50 Hz

U1084A 1.5 GHz Yes Yes 2900 Hz

ADC 6082 8 GHz By mid-April Yes 2140 Hz†

* Rep. Rate normalized for bandwidth (8 GHz) and record length (50k points). † Majority of time spent writing data to disk due to lack of on-board averaging.

o-fluorotoluene, 10 mTorr

-20 °C, 16 ms FID

S/N ~ 70:1

Nitromethane, 2.5 mTorr

-20 °C, 6 ms FID

S/N ~ 140:1

Acquiris U1084A

1M shots, 83 seconds

1.5 GHz bandwidth

Guzik ADC 6082 25k shots, 28 seconds

8 GHz bandwidth

RT Digitizer Data

Guzik digitizer currently does not average. Repetition rate is mainly due to data transfer (2.8 GB for 25k shots). Averaging should be implemented by mid-April. Expecting roughly 60-fold speed enhancement over existing digitizer! Spectral assignment problem will only get worse.

En

erg

y

Frequency

Inte

nsi

ty

5

1 2

4

6

3

1 2 3 5 4 6

Procedure: • Construct H and TD matrix from molecular parameters. • Diagonalize H to get energy levels (eigenvalues). • Use eigenvectors of H to transform TD. • |TD element|2 = prob. of transition (peak height), DE gives peak position.

Forward Prediction is Easy…

Severely over-determined – 8 parameters determine position of ~ 103 lines.

Acceptable fits require convergence of some parameters to ~ 1 part in 105.

Very rough landscape; minute changes completely change predictions.

…But Assignment is Hard!

Frequency

Inte

nsi

ty

5

1 2

4

6

3 En

erg

y

1 2 3 5 4 6

(Assignment: labeling a peak with upper and lower state quantum numbers)

1

2

3

1 + 2 + 3

Conformers Don’t Help!

Erel = 0 cm-1 Erel = 82 cm-1 Erel = 165 cm-1 Erel = 226 cm-1 Erel = 133 cm-1

Tt Tg Gg’ Gt Gg

Name E (cm-1) Frac. Pop.*

Tt 0 18%

Tg 82 24%

Gt 133 18%

Gg 165 23%

Gg’ 226 18%

Conformers of n-propylamine

* Includes 2-fold degeneracy for gauche conformers

Durig, J.R. et al., J Raman Spectrosc. 43, 1329-1336 (2012).

1M averages 1777 peaks above 3:1 S/N

1) Get initial guess from ab initio

2) Tentatively assign a few lines

3) Non-linear least squares fit on selected parameters

4) Forward prediction with new parameters. Better or worse?

5) Loop until satisfied.

Severe issues with line density (conformers, excited vibrational states).

No‏“close”‏fits‏– very frustrating (easy to spend hours with no progress).

10 12 14 16 18

Frequency (GHz)

2-methylfuran

3 million averages

3091 peaks above 3:1 S/N

Typical Approach

Triples Fitting Method

A, B, C are much larger than rest

Three equations and three unknowns = perfect fit!

Procedure:

• Choose three experimental peaks, assign to three transitions

• Fit to A, B, C

• Predict additional peaks, score based on how close to experiment

• Iterate over all combinations of three peaks

• Best score should correspond to something actually present!

Rotational constants

A (MHz) 9769.6435

B (MHz) 868.84083

C (MHz) 818.52411

DJ (kHz) 0.04171

DJK (kHz) -0.778

DK (kHz) 26.06

dJ (kHz) 3.59

dk (kHz) -2.36

Hexanal Conformers < 300 cm-1

Hexanal Spectrum

Noise is ~2x10-5 units. S/N on tallest peak in spectrum is 20,000:1.

(13C at 1.07%, 18O at 0.205%)

Hexanal Spectrum (x70) (x1400)

3074 lines above 3:1 between 6.5 and 18 GHz – density of 27 lines / 100 MHz.

531,441 triples (813) to evaluate for typical 300 MHz search window.

Found 8 conformers using ab initio constants, dipoles with triples fitter (300 MHz).

Found 10 conformers with traditional methods.

High Temperature Spectra

Caminati, W. et al., Chemical Physics 110, 67-82 (1986).

Conclusions • New instrumentation is making assignment bottleneck worse, as ALMA and

EVLA cause the great data flood – estimates are > 1 TB / day in 2013.

• Automated data analysis will be critical; additional benefit is making it easier for undergraduate researchers to make more progress during the semester.

Credit: Image courtesy of NRAO/AUI and Computer Graphics by ESO

Acknowledgments Former Students Noah Anderson (‘12) Ian Finneran (‘11) Kaitlin Lovering (’11) Ben Reinhold (‘10)

Current Students Lauren Bernier (‘14) Brittany Gordon (‘13) Erin Kent (‘14) Sophie Lang (‘14) Morgan McCabe (‘14) Christian Metzger (‘13) Maria Phillips (’13) Ben Rooks (‘13)

Funding

New College of Florida National Science Foundation Office of Naval Research

Collaborators Pat McDonald (New College) Brooks Pate (University of Virginia) Susanna Widicus Weaver (Emory University)

“Embarrassingly‏parallel”.‏‏Linear‏scaling‏with‏number‏of‏processors.

Typical benchmark is about 500,000 triples per hour (4 core machine, 2.5 GHz)

Written in Python (adapted from

Pate lab MathCAD script)

Fitting done with SPFIT (spectral

fitting program from JPL)

Generally evaluates 106 – 107

candidates per run

Triples Fitting Method

Triples Fitter Test: Hexanal (C6H12O)

D1

D2

D3

D4

Dihedrals distinguish conformers.

81 potential possibilities (some are

identical by symmetry).

Inexpensive, good vapor pressure and dipole moment, multiple conformers.

Performed ab initio calculations on all possible minima with B3LYP, MP2,

and M06-2X methods using 6-311++G(d,p) basis set.

Found 8 conformers using ab initio constants, dipoles with triples fitter (300 MHz). Found 10 conformers with traditional methods. ‚Missing conformers‛ • one due to strangeness with calculations (below) • one due to broad potential well (next slide)

B3LYP M06-2X MP2 Exp’t

A (MHz) 4832.4 4614.9 4554.1 4827.9152

B (MHz) 1211.3 1308.8 1310.9 1240.83816

C (MHz) 1134.4 1214.3 1213.9 1159.91719

B3LYP M06-2X MP2

Hexanal Results

1-D Torsional Potential and Expectation Values

At Minimum A: 3778 MHz B: 1535 MHz C: 1230 MHz

Expectation Value <A>: 4044 MHz <B>: 1323 MHz <C>: 1112 MHz

Experimental A: 3961 MHz B: 1400 MHz C: 1158 MHz

Scan is of C=O dihedral FWHM of wavefunction is ~0.4 radians (23 degrees)! With broad wells, may need to use averaged rotational constants.

# E (cm-1) A (MHz)

B (MHz)

C (MHz)

|mA| (D)

|mB| (D)

|mC| (D)

1 0.0 5399 1158 1040 0.3 2.4 1.1

2 85.5 9812 874 823 1.3 2.4 0.0

3 156.8 4760 1336 1182 0.4 2.6 0.1

4 157.5 6057 1191 1079 0.2 2.4 0.8

5 171.0 4849 1419 1360 1.3 2.2 0.5

6 190.7 9157 942 901 2.0 1.8 0.8

7 192.8 5407 1188 1133 1.9 0.2 2.1

8 194.5 5928 1069 957 0.9 2.6 0.6

9 216.1 4615 1309 1214 0.5 1.9 1.8

10 275.5 4038 1543 1395 1.3 2.6 0.1

11 278.9 3981 1557 1273 0.1 1.8 1.8

12 288.6 3781 1536 1230 0.4 2.9 0.1

13 289.1 5423 1068 945 1.8 2.4 0.7

14 297.0 3335 2057 1501 0.5 2.3 1.2

Hexanal Conformers

Data in black, fit results in red. Fits initiated with triples fitter and refined. There are many, many possible fits of 15 peaks to 1-2 MHz fit error…

High Temperature Spectra

2-methylfuran

8.7 – 960 GHz from NCF and Emory (Widicus Weaver lab) 100 kHz point spacing GS: 19k transitions v = 1: 6k transitions Collected in 2 weeks Analyzed in 3 months All for one molecule!