Supplemental Material
Communication: Vibrational spectroscopy of atmospherically relevant
acid cluster anions – bisulfate versus nitrate core structures
Tara I. Yacovitch, Nadja Heine, Claudia Brieger, Torsten Wende, Christian Hock,
Daniel M. Neumark, Knut R. Asmis
FULL CITATION FOR GAUSSIAN 09
Gaussian 09, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji,
H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J.
L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.;
Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.;
Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi,
R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi,
M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.;
Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.;
Cioslowski, J.; Fox, D. J.; Gaussian, Inc.: Wallingford CT, 2010.
1
SIMULATED SPECTRA
1a
1b
1c
FIG. S1. Comparison between experimental IRMPD spectrum
for cluster 1 and simulated IR intensities calculated at the
B3LYP/6-311++G(2df,2pd) level of theory. Simulated line
spectra are convoluted with a Gaussian of FWHM=15 cm-1.
Theoretical isomers are labeled according to their relative
energy, which includes ZPE.
2
1d
2a
2b
2c
2d
2e
2g
FIG. S2. Comparison between experimental IRMPD
spectrum for cluster 2 and simulated IR intensities
calculated at the B3LYP/6-311++G(2df,2pd) level of
theory. Simulated line spectra are convoluted with a
Gaussian of FWHM=15 cm-1. Theoretical isomers are
labeled according to their relative energy, which includes
ZPE.
2j
2l
3
3a
3b
3d
3f
3g
FIG. S3. Comparison between experimental IRMPD
spectrum for cluster 3 and simulated IR intensities
calculated at the B3LYP/6-311++G(2df,2pd) level of
theory. Simulated line spectra are convoluted with a
Gaussian of FWHM=15 cm-1. Theoretical isomers are
labeled according to their relative energy, which includes
ZPE.
3h
3i
4
4a
FIG. S4. Comparison between experimental IRMPD spectrum for HSO 4¯ and simulated IR intensities calculated at
the B3LYP/6-311++G(2df,2pd) level of theory. Simulated line spectra are convoluted with a Gaussian of
FWHM=15 cm-1.
5
PEAK POSITIONS AND ASSIGNMENTS
TABLE SI. Summary of experimental peaks and assignments. Selected unscaled harmonic frequencies, simulated
at the B3LYP/6-311++G(2df, 2pd) level, are given next to an approximate description of the normal mode.
Experimental
peak (cm-1)
Theoretical
peak (cm-1)
Theoretical
structure
Approximate normal mode description.a
Cluster 1: HSO4¯·HNO3
890
900
1a
942
990
1b
1031
1186
944
1164
1316
1a
1b
1b
(H2SO4): symmetric SOH wags
(HNO3): NO3 symmetric stretch, (HSO4¯):
symmetric SO3 stretch
(H2SO4): symmetric SOH wags
(HSO4¯): SOH bend and S=O stretch
(HSO4¯): SOH bend and S=O stretch, (HNO3):
NOH bend and N-O stretch
/
out-of-phase version of the same vibration
(HNO3): NOH bend
(NO3¯): N=O stretch, H2SO4: SOH bends
(HNO3): NOH bend and N=O stretch
1310
/
1338
1400
1478
1483
1462
1621
1652
Cluster 2: HSO4¯·H2SO4·HNO3
590
575
875
911
934
974
1045
1030
1155
1168
/
1b
1b
1a
1b
2a
2a
2a
2a
2a
2a
2a
2a
(HSO4¯): SO2 bend
(H2SO4): antisymmetric S-OH stretch
(HNO3): symmetric NO3 stretch
(HSO4¯): symmetric SO3 stretch
(H2SO4): symmetric SO2 stretch, (HSO4¯): SOH
bend and S=O stretch
/
(HSO4¯): antisymmetric SO2 stretch
(HSO4¯): SOH bend and S=O stretch, SO and
NO stretches on other moieties
(HSO4¯): SOH bend, (HNO3): symmetric N-OH
stretch
(HNO3): antisymmetric NO3 stretch, (HSO4¯):
SOH bend
(H2SO4): SOH wags
(HNO3): NOH bend
(HNO3): NOH bend and N=O stretch
3a
3a
(HNO3): symmetric NO3 stretch
(H2SO4): symmetric SO2 stretch
/
1171
/
2a
1224
1206
2a
1300
1318
2a
1338
1350
2a
1399
1388
1443
1427
1660
1687
Cluster 3: NO3¯·H2SO4·HNO3
945
978
1116
1185
6
1297
1322
3a
1349
1339
3a
1399
3a
1412
/
1415
/
3a
1650
Ion 4:
1131
1198
1244
1689
HSO4¯
1137
1224
1280
3a
(HNO3): NOH bend and antisymmetric NO3
stretch, NO and SO stretches on other moieties
(H2SO4): antisymmetric SO2 stretch and SOH
wags, (HNO3): antisymmetric stretch
(NO3¯): antisymmetric stretch, stretches and
wags on other moieties
/
(NO3¯): antisymmetric stretch, stretches and
wags on other moieties
(HNO3): NOH bend and N=O stretch
4a
4a
4a
SOH bend
Antisymmetric S=O stretch
SOH bend and S=O stretch
a. Descriptions of cluster normal modes are given in terms of the moieties where vibration occurs. A normal mode
involving motion of two moieties would be described thusly: (Moiety1): description of the vibrations of moiety 1,
(Moiety2): description of the vibrations of moiety 2. A forward slash “/” is used to separate different normal modes.
7
THERMODYNAMIC CALCULATIONS
TABLE SII details relative energetics of structures 1a and 1b with and without inclusion
of zero point energy. Thermodynamic corrections for enthalpy and entropy are also included at
two different conditions: 298.15K / 1atm and 15.0K / 4·10-4atm. At trap temperatures, inclusion
of enthalpy or free energy does not much impact the realtive energetics and even at 298K,
structure 1a remains energetically favorable by all measures. However, at STP, the free energy
of 1b lies only 14.0 kJ/mol
above 1a.
Not included in this calculation is the entropy
contribution from internal rotations. We expect this contribution to be negligible for 1a but
significant for 1b: both the nitric acid and free OH bond in 1b are free to rotate while the
presence of two H-bonds limits such motion in 1a. We estimate that this contribution could
further decrease the free energy by around 2 kJ/mol for 1b at 298.15K (method of Pitzer and
Gwinn1-3). Thus, entropy effects lower the relative free energy of 1b at higher temperatures.
TABLE SII. Relative energies (kJ/mol) for the two lowest energy structures of cluster 1 calculated at the
B3LYP/6-311++G(2df,2pd) level.a The relative electronic energy (Eelec) is shown along with corrections due to zero
point energy (ZPE), enthalpy (ΔH) and free energy (ΔG). The dissociation energy of the clusters relative to their
geometry optimized fragments is also calculated.
1a
0.00
0.00
0.00
0.00
0.00
0.00
101
Eelec
Eelec + ZPE
Eelec + ΔH15K
Eelec + ΔG15K
Eelec + ΔH298K
Eelec + ΔG298K
D0
1b
28.3
24.3
24.4
24.2
27.0
14.0
175
a. Thermodynamic quantities were calculated at the following conditions: 15 K and 4.0·10 -4 atm; 298.15K and 1.00
atm. D0 includes ZPE. ΔH and ΔG include internal energies (ZPE, rotational and translational) but do not account
for internal rotations within the cluster.
8
POTENTIAL ENERGY SURFACE SCANS
A potential energy surface scan was done to investigate the rotation of the HNO 3 moiety
in structure 1b by scanning the S-O-O-N dihedral angle (Fig. S5). At ~100° there is a small
barrier before acessing the deep attractive well of the second hydrogen bond (a structure which
would converge to 1a), and at ~330° there is a high barrier due to repulsion from a bisulfate
oxygen. The lowest of these two barriers is ~2.5 kJ/mol and corresponds to a kT temperature of
297 K. This is significantly higher than the trap temperature and likely higher than the
evaporating droplet temperature in the He filled ion guide. Thus, we expect that most clusters
formed on this shallow HSO4¯·HNO3 surface can relax during ion guide or ion trap collisions
down to structure 1b, but perhaps not to the minimum energy structure 1a.
FIG. S5. Rigid scan of the SOON dihedral angle of the
HSO4¯·HNO3 cluster 1b. Calculations were done at the
B3LYP/6-311++G(2df,2pd) level. Energies in kJ/mol are
relative to the 1a global minimum and do not include zero
point energies.
9
REFERENCES
(1) Pitzer, K. S.; Gwinn, W. D. J. Chem. Phys. 1942, 10, 428.
(2) Pitzer, K. S. J. Chem. Phys. 1946, 14, 239.
(3) Janz, G. J. Thermodynamic Properties of Organic Compounds: Estimation Methods,
Principles and Practice; Revised ed.; Academic Press: New York, 1967.
10