Galen Sedo, Jane Curtis, Kenneth R. Leopold Department of Chemistry, University of Minnesota The Dipole Moment of the Sulfuric Acid Monomer

Galen SedoGalen Sedo, Jane Curtis, Kenneth R. Leopold, Jane Curtis, Kenneth R. Leopold

Department of Chemistry, University of MinnesotaDepartment of Chemistry, University of Minnesota

The Dipole Moment of the The Dipole Moment of the Sulfuric Acid MonomerSulfuric Acid Monomer

Sulfuric Acid Aerosols• A principle source of sulfate-containing

atmospheric particles

• High affinity for water and a high rate of nitrogen species uptake

Investigating Sulfuric Acid SystemsInvestigating Sulfuric Acid Systems

Nucleation Theory• Homogeneous and Heterogeneous particle growth

• Ion-induced and ion-mediated nucleation theory

• Charge-dipole interactions

H2SO4b

2.725(15) D

H2SO4-H2Oa

3.052(17) D

a) Brauer, C. S.; Sedo, G.; Leopold, K. R. Geophys. Res. Lett. 33 (2006) L23805, doi:10.1029/2006GL028110.

b) Kuczkowski, R. L.; Suenram, R. D.; Lovas, F. J. Journal of the American Chemical Society 1981, 103, 2561.

Previous Dipole Moment WorkPrevious Dipole Moment Work

H2SO4b

2.725(15) D

2.817 D

H2SO4-H2Oa

3.052(17) D

2.147 D



c) Al Natsheh, A; Nadykto, A. B.; Mikkelsen, K. V.; Yu, F.; Ruuskanen, J. J. Phys. Chem. A 2004, 108, 8914.


PW91PW91/TZPc

0.905 D(29.7 %)

-0.092 D(-3.4 %)

H2SO4b

2.725(15) D

2.817 D

3.147 D

H2SO4-H2Oa

3.052(17) D

2.147 D

2.965 D



c) Al Natsheh, A; Nadykto, A. B.; Mikkelsen, K. V.; Yu, F.; Ruuskanen, J. J. Phys. Chem. A 2004, 108, 8914.


PW91PW91/TZPc

0.905 D(29.7 %)

-0.092 D(-3.4 %)

0.087 D(2.9 %)

-0.692 D(-25.4 %)

MP2/aug-cc-pVQZa

Mirror

Antenna

Argon passed over a sample of polymerized SO3

Backing Pressure 25 psig

Microwave

Electronics

Computer

14732.5 14733 14733.5 14734 14734.5 14735

Frequency (MHz)Spectrum

Fabry-Perot Cavity

Diffusion Pump

Pulsed

Nozzle

Mirror

The Pulsed Nozzle FTMW Spectrometer

Mirror

Antenna

Argon passed over a sample of polymerized SO3

Backing Pressure 25 psig

Microwave

Electronics

Computer

14732.5 14733 14733.5 14734 14734.5 14735

Frequency (MHz)Spectrum

Fabry-Perot Cavity

Diffusion Pump

Pulsed

Nozzle

Mirror


Series 9PulsedSolenoidValve

Needle Adaptor

• Stainless Steal Needle Dimensions ID = 0.016" Length = 0.205"

• Argon bubbled through H2O at a rate of 10 sccm.

Diffusion Pump

Fabry-Perot Cavity


Mirror

Fabry-Perot Cavity

Diffusion Pump

Mirror

Diffusion Pump

Fabry-Perot Cavity


1. A potential of up to 10,000 V(5,000 V/plate)

2. Calibrated the plate spacing before and after collecting data using the Ar-SO3 complex [ = 0.2676(3) D]

• Checked the calibration method using OCS

lit = 0.7152(2) D

obs = 0.7157(16) D

DM = 0

y = 1.1674E-04x - 7.7449E-04

R2 = 1.0000E+00

0.0

0.5

1.0

1.5

2.0

0 5000 10000 15000

e2 (V

2/cm

2)

Dn

(MH

z)Zero Field and 37 Stark-shifted Frequencies

The The DDM = 0 Stark Component of theM = 0 Stark Component of the

111010 ← 0 ← 00000 Transition Transition

10184.250 10184.750 10185.250 10185.750 10186.250 10186.750

10184.250 10184.750 10185.250 10185.750 10186.250 10186.75010184.250 10185.250 10186.250

Frequency [MHz]

e = 0 V/cm

e = 76.5 V/cm

Dnmax = 1.749 MHz

emax = 122.3 V/cm

D|M| = 1

y = 5.1046E-05x - 5.8754E-04

R2 = 1.0000E+00

0.0

0.5

1.0

1.5

2.0

0 10000 20000 30000

e2 (V2/cm2)

Dn

(MH

z)Zero Field and 54 Stark-shifted Frequencies

Dnmax = 1.721 MHz

emax = 183.5 V/cm10184.250 10184.750 10185.250 10185.750 10186.250 10186.750

10184.250 10184.750 10185.250 10185.750 10186.250 10186.750

e = 0 V/cm

e = 76.5 V/cm

10184.250 10185.250 10186.250

Frequency [MHz]

The The D|D|M| = 1 Stark Component of theM| = 1 Stark Component of the

111010 ← 0 ← 00000 Transition Transition

a) Kuczkowski, R. L.; Suenram, R. D.; Lovas, F. J. “Microwave Spectrum, Structure, and Dipole Moment of Sulfuric Acid.” Journal of the American Chemical Society 1981, 103, 2561-2566.

Sulfuric Acid Molecular ConstantsSulfuric Acid Molecular Constantsaa

a) Kuczkowski, R. L.; Suenram, R. D.; Lovas, F. J. “Microwave Spectrum, Structure, and Dipole Moment of Sulfuric Acid.” Journal of the American Chemical Society 1981, 103, 2561-2566.

Sulfuric Acid Transition FrequenciesSulfuric Acid Transition Frequenciesaa

H = Hrot + HQ + He

He = -• e

c = tot = 2.9643(67) D

H = Hrot + HQ + He

He = -• e

110 ← 000

c = tot = 2.9643(67) D

643 ← 533

c = tot = 2.725(15) D

Dn = (ac + bcM2)e2c2

ac = 2.4048 x 10-8

bc = -3.8759 x 10-6

A 5160.5951(36)B 5024.5405(33)C 4881.025(13)D

J 0.002522(27)D

JK -0.00516(86)D

K 0.005214(74)d

J -0.000413(17)d

K 0.003099(65)

Molecular Constants for the H2SO4 Monomer.

(a) All values are in MHz.

643 ← 533

c = tot = 2.725(15) D

664343 ← 5 ← 53333 Stark Coefficients Stark Coefficients

M = 1

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 5000 10000 15000 20000 25000

e2 [V/cm]

Dn

[MH

z]

y = -3.3742E-05x – 4.6141E-04

R2 = 1.0000

M = 0

0.000

0.001

0.002

0.003

0.004

0.005

0 5000 10000 15000 20000 25000

e2 [V/cm]

Dn [

MH

z]

y = 2.112E-07x – 5.694E-05

R2 = 1.000

643 ← 533

c = tot = 2.725(15) D

ac = 2.4048 x 10-8

bc = -3.8759 x 10-6

110 ← 000

c = tot = 2.9643(67) D

ac = 2.4032 x 10-8

bc = -3.8640 x 10-6

Error AnalysisError Analysis

Three Primary Sources of Experimental Error

1. Least Squares Analysis ls = 2.96434 D

Dls = 0.00023 D



Dls = 0.00023 D

2. Plate Spacing dplate = 32.702 cm

Dplate = 0.064 cm


22

D

DD

plate

plate

ls

lslstotal d


Dd SOAr

SOAr

plate

plate

ls

lslstotal 0067.0

222

3

3

D

D

DD



Dls = 0.00023 D

2. Plate Spacing dplate = 32.702 cm

Dplate = 0.064 cm

3. Calibration Standard Ar-SO3 = 0.2676 D

DAr-SO3 = 0.0003 D

This Work 2.9643(67) D

Kuczkowski, Suenram, & Lovas 2.725(15) D0.239 D

Comparison of the Experimental and Comparison of the Experimental and Theoretical Dipole MomentsTheoretical Dipole Moments

PW91PW91/aug-cc-pV(Q+d)Z 2.9520 D

MP2/aug-cc-pV(Q+d)Z 3.4416 D

0.0

5.0

10.015.0

20.0

25.0

30.0

HF MP2 B3LYP PW91

Theory/aug-cc-pVTZ

|% E

rror

|

This Work

Literature

Comparison of the Experimental and Comparison of the Experimental and Theoretical Dipole MomentsTheoretical Dipole Moments

This Work 2.9643(67) DPW91PW91/aug-cc-pV(Q+d)Z 2.9520 DMP2/aug-cc-pV(Q+d)Z 3.4416 D

Brauer et al. 3.052(17) DPW91PW91/aug-cc-pVQZ 2.407 DMP2/aug-cc-pVQZ* 2.965 D

H2SO4

H2SO4-H2O

* Single-point calculation done at the aug-cc-pVTZ geometry, taken from Brauer et al.

0.0

5.0

10.0

15.0

20.0

25.0

HF MP2 B3LYP PW91

Theory/aug-cc-pVTZ

|% E

rror

|

Sulfuric Acid

Monohydrate

ConclusionsConclusions

1. The dipole moment of the sulfuric acid monomer has been refined using Fourier transform microwave spectroscopy.

• 91 Stark-shifted frequencies were collect for the 110 ← 000 rotational transition.

• The newly measured value, 2.9643(67) D, represents an increase of approximately 0.24 D over the previously published value.

2. The dipole moments of the sulfuric acid monomer and mono-hydrate were calculated using both ab initio and Density Functional Theory.

• The calculated dipole moments show convergence with increasing basis set size.

• The agreement between the measured experimental values and those of theory various drastically with the method employed.

• Dr. Kenneth Leopold

• Jane Curtis

• Dr. Carolyn Brauer

Acknowledgements

Funding

• National Science Foundation (NSF)

• Petroleum Research Fund (PRF)

• Minnesota Supercomputing Institute (MSI)

http://www.umn.edu/

http://www.nsf.gov/home/news.html

J' K-1' K+1' J" K-1" K+1" nobs

ncalc

nobs-ncalc

AssignedError n

obs-ncalcc

1 1 0 0 0 0 10185.126 10185.127 -0.001 0.005 -----6 3 3 5 2 3 60668.59 60668.65 -0.06 0.15 -0.066 4 2 5 3 2 60861.50 60861.43 0.07 0.15 0.066 1 5 5 0 5 60935.35 60934.87 0.48 0.15 0.476 3 4 5 2 4 60939.80 60940.06 -0.26 0.15 -0.276 2 5 5 1 5 60946.00 60945.72 0.28 0.15 0.276 4 3 5 3 3 61060.32 61060.53 -0.21 0.15 -0.226 5 1 5 4 1 61317.72 61317.35 0.37 0.15 0.346 5 2 5 4 2 61353.12 61353.36 -0.24 0.15 -0.278 3 5 7 2 5 81056.65 81056.47 0.18 0.15 0.188 5 3 7 4 3 81066.90 81066.92 -0.02 0.15 -0.028 4 5 7 3 5 81212.24 81212.14 0.10 0.15 0.09

10 5 5 9 4 5 101080.17 101080.21 -0.04 0.15 -0.0510 6 4 9 5 4 101267.30 101267.42 -0.12 0.15 -0.1110 4 6 9 3 6 101294.00 101294.46 -0.46 0.15 -0.4610 5 6 9 4 6 101475.20 101475.32 -0.12 0.15 -0.1210 3 7 9 2 7 101480.86 101480.71 0.15 0.15 0.1510 4 7 9 3 7 101503.07 101503.44 -0.37 0.15 -0.3710 6 5 9 5 5 101574.71 101574.86 -0.15 0.15 -0.1610 1 9 9 0 9 101594.99 101595.07 -0.08 0.15 -0.0910 7 3 9 6 3 101775.30 101775.42 -0.12 0.15 -0.1210 7 4 9 6 4 101852.61 101852.67 -0.06 0.15 -0.0710 8 2 9 7 2 102221.46 102221.32 0.14 0.15 0.1310 8 3 9 7 3 102227.85 102227.76 0.09 0.15 0.0810 10 1 9 9 1 103008.75 103008.82 -0.07 0.15 -0.0911 6 5 10 5 5 111209.35 111209.35 0.00 0.15 0.0011 5 6 10 4 6 111268.10 111267.94 0.16 0.15 0.1611 4 7 10 3 7 111533.90 111533.79 0.11 0.15 0.1211 5 7 10 4 7 111612.31 111612.29 0.02 0.15 0.0211 7 4 10 6 4 111617.32 111617.21 0.11 0.15 0.1211 6 6 10 5 6 111629.15 111629.04 0.11 0.15 0.1011 3 8 10 2 8 111661.00 111660.40 0.60 0.15 0.6111 4 8 10 3 8 111667.05 111667.42 -0.37 0.15 -0.3711 1 10 10 0 10 111757.44 111757.51 -0.07 0.15 -0.0511 7 5 10 6 5 111817.39 111817.21 0.18 0.15 0.1811 8 3 10 7 3 112126.95 112126.89 0.06 0.15 0.0711 8 4 10 7 4 112156.53 112156.62 -0.09 0.15 -0.0811 10 1 10 9 1 112937.95 112938.13 -0.18 0.15 -0.2011 11 1 10 10 1 113327.41 113327.29 0.12 0.15 0.12

(b) All transition assignments and frequencies, except the 110 ← 000, are those reported by Kuczkowski et al .(c) Original nobs - ncalc values reported by Kuczkowski et al .

Rotational Transitions for the H2SO4 monomer.a,b

(a) All frequencies are in MHz.

Documents

Galen Sedo, Jane Curtis, Kenneth R. Leopold Department of Chemistry, University of Minnesota The Dipole Moment of the Sulfuric Acid Monomer