1. Effects of a Remote Binding Partner on the Electric Field and Electric Field Gradient at an Atom in a Weakly Bound Trimer: A Microwave Study of Kr-SO3 and Kr-SO3-CO
International Symposium on Molecular Spectroscopy
Rebecca Mackenzie
Brooke Timp, Yirong Mo, Ken Leopold
Department of Chemistry
University of Minnesota

2. Weakly Bound Complexes:
Dimers <-> pairwise interactions
Trimers <-> non-additive effects
To what extent can we treat large clusters as an aggregate of dimers?
Effect of remote molecules
The motivation for studying a complex like this, is obviously not for its natural abundance, but rather as a prototype for studying the effect of a remote molecule. For the general picture, if we’re considering monomers A and B and how they interact, but now C is introduced, begins to interact with B, we’re trying to better understand how this interaction would impact A. And this gets at the larger question of understanding clusters of molecules and whether they can be treated as a number of pairwise interactions, or to what extent do we have to consider third body interactions. And complexes with linear structures are ideal for studying the remote effect, compared to say a cyclical complex where all three are interacting spatially.
----- Meeting Notes (6/10/13 14:40) -----
add a little something on clusters
more gradiose
put linear stuff afterwards (in the Kr-SO3-CO slide)
three body interactions are usually thought of in terms of potential energy, of course, we can't do that, but by using microwave spectroscopy we can gain insight into those interactions with different physical parameters to understand the impact of a third body
----- Meeting Notes (6/11/13 16:09) -----
non-additive effects from trimers
long history of studying dimers to understand pairwise interactions and studying trimers to understand non-additive effects, with the understanding that what we're getting at is to what extent can we
to what extent can
----- Meeting Notes (6/11/13 16:16) -----
there's a long history of studying pairwise potentials using weakly bound complexes prototypes
the main question is whether we can treat clusters as the sum of pairwise interactions
----- Meeting Notes (6/11/13 16:19) -----
this is of course an important question for understanding the formation of condensed phases from the gas phase
Finish by talking about what microwave spectroscopy can contribute (since we can’t do energies) and use this to lead into what previous work has been done to provide a unique perspective (view it through a different lens) on these questions
Our group has done work on SO3 complexes and these systems provide a convenient geometry and simple spectroscopy for example… A B C

3. Previous Work on Ar-SO3-CO
Distances, dipole moments, and binding energies indicated the interactions on opposite sides of SO3 are independent
3.350(1) Å1
2.854(11) Å2 Ar
SO3
SO3 CO
0.2676(3) D1
0.8488(13)D2
2% increase in separation
no statistically significant change
To that end, Ken’s group has characterized similar linear structure complexes, moving from the dimer to a trimer. Ar-SO3-CO was characterized in 2003, where an analysis of the geometry shows that the CO has a slight impact on the Ar, since there is an increase of about 2% in the distance between Ar and S. Analysis of the dipole moments suggest that the complexation is additive, meaning that the two sides of the trimer do not impact each other since their dipole moments simple add together.
----- Meeting Notes (6/10/13 14:40) -----
start with ar-so3, then so3-co, then the trimer
add animations and ken's reference
----- Meeting Notes (6/11/13 14:40) -----
Add in binding energies from ab initio calculations
Change the animations on this
-Dimers first (with distances)
-Trimer (with distance)
-Dipole moments
Then make sure to say that the binding energies were consistent with this picture
THE DIPOLE MOMENT OF THE TRIMER WAS THE VECTOR SUM OF THE DIPOLE MOMENTS OF THE CONSTITUENT DIMERS
3.411(11) Å2
2.849(4) Å2 Ar
SO3 CO
0.602(15)D2
(1) K. H. Bowen, K. R. Leopold, K. V. Chance, W. Klemperer, J. Chem. Phys., 73, 137, 1980.
(2) M. B. Craddock, C. S. Brauer, K. J. Higgins, K. R. Leopold, J. Mol. Spec., 222, 63, 2003.

4. Similar Results for HCN-SO3-CO
Similar distances
Vector addition of dipole moments
Additive binding energies
The HCN-SO3-CO complex was characterized, with significant change in the geometry when moving from the dimer to trimer for both parts of the trimer. So, here there was some significant indication that the two outer moieties were affecting each other, but the final piece of information we’d like to get out of this work was on the electronic structure before and after complexation. And while nitrogen has a non-zero nuclear quadrupole moment, because it is molecular, detailed information on the electronic structure was lost in the spectra due to the vibrational motion of the molecule within the complex. So this is where our recent work on Kr-SO3-CO comes into provide a unique perspective on the interactions within a trimer.
----- Meeting Notes (6/10/13 14:40) -----
do analogous animations for this slide
and while these results show the effect of CO as a remote binding partner on the structure of the complex, because of the large amplitude vibrations of HCN, specific information on the electronic structure of the complex could not be derived from the hyperfine structure from the nuclear quadrupole moment of the nitrogen. Thus, we’d d like to have insight on how it impacts the electronic structure of the complex
“difficult to separate the effects of large amplitude vibrations from genuine changes in the electronic structure”
C.S. Brauer, M.R. Craddock, K.J. Higgins, K.R. Leopold, Molecular Physics, 105, 613, 2006.

5. Kr-SO3-CO Kr SO3 SO3 CO eQq ? Kr SO3 CO 83Kr nucleus has a spin of 9/2
Kr 83 has a spin of 9/2 and because it is atomic rather than molecular, all the splitting in the spectra can be accounted for by changes in the electronic structure.
----- Meeting Notes (6/10/13 14:40) -----
emphasize the linear structure of the molecule and how CO impacts it
emphasize that the dimer was studied first then the trimer to gain insight on the change brought on by CO
83Kr nucleus has a spin of 9/2
Measure the change in electronic structure as CO is introduced

6. Experimental Dimer Trimer Four major isotopes of Kr with predicted B
11.5% Kr in Ar
BP- 25 psig
SO3 reservoir
Trimer
0.9% CO, 11.5% Kr in Ar
BP- 35 psig
Four major isotopes of Kr with predicted B
82 (~12%), 934 MHz
83 (~12%), 929 MHz
84 (~57%), 924 MHz
86 (~17%), 914 MHz Ar Kr d CO
SO3
Our experimental setup was straight forward. Using our FTMW, we pulsed in a mixture of Kr and Ar through a bubbler of SO3 and into the cavity. For the trimer we simply added CO into our gas mixture. We were looking for the four major isotopes of Kr, which I have here along with their predicted rotational constants. Kr 83 is the only isotope that will yield hyperfine, making it easy to identify which isotope we’re looking at.
----- Meeting Notes (6/12/13 15:52) -----
mixes with the vapor of polymerized sulfur trioxide
resevoir instead of bubbler
FTMW

7. Data Trimer Dimer 82,84,86Kr-32SO3-12/13CO species
82,84,86Kr-32/34SO3 species
J 1->2, K=0
J 2->3, K=0
83Kr-32SO3
Hyperfine for J 1->2 and 2->3
Trimer
82,84,86Kr-32SO3-12/13CO species
J 3->4, K=0,3
J 4->5, K=0,3
J 5->6, K=0,3
83Kr-32SO3-12/13CO
Hyperfine structure of Kr was found for J 3->4 for K=0
84Kr-SO3-C0
J 4->5
K=3
K=0
83Kr-SO3-C0
J 3->4, K=0
13/2->15/2
15/2->17/2
11/2->13/2
Cavity
----- Meeting Notes (6/10/13 14:42) -----
look back at that spectra, how many components did you see and what did we actually look for?
----- Meeting Notes (6/12/13 15:52) -----
off handed comment, K=1,2 are not present because of the oxygen nuclear spin statistics
oxygen are spinless bosons

8. Spectroscopic Constants
ν=2B(J+1)-4DJ(J+1)3-2DJK(J+1)K2
In total, we collected and determined rotational constants for 6 different isotopologues for the dimer and 8 for the trimer. First, I’ll bring your attention to the rotational constants and the process we went through to determine our complex geometry from them.

9. Structure Determination
COMcomplex
COMCO C3 r1
RKrS
RCS O C R1 R2 R3 χ γ Kr S O O
Variables: R1 R2 R3 χ and γ
Use nonlinear regression analysis to solve for the best RKrS and RCS distances
Here we have the moment of inertia for our complex as defined by R1, R2, and R3 as well as chi and gamma, which define the off-axis angles of the two molecules within the complex. R1, R2, and R3 are defined by the center of mass of the complex, so we’ll redefine our distances in terms of isotopically invariant distances, RKrS, RCS, and r1. Substituting these into our moment of inertia equation, and using the moments of inertia collected for the various isotopes, we can go through a nonlinear regression analysis to solve for the geometry of our complex.
----- Meeting Notes (6/10/13 14:48) -----
allowed for out of plane bending using angle estimates from related systems
make an extra
----- Meeting Notes (6/12/13 15:52) -----
chi and gamma represent the instantaeous vibrational amplitudes and were taken to be similar to those in previous characterized dimers and have a very small effect on the results and were taken into account when determining error bars
REWRITE not REDEFINE

10. Results and Conclusions
3.438(3) Å
2.854(11) Å Kr
SO3
SO3 CO
no statistically significant change
1% increase in separation
3.488(6) Å
2.871(9)Å Kr
SO3 CO
Taking a look at those results, we get results that are in line with the results for the Ar-SO3-CO complex. There was no statistical change in the carbon sulfur distance and a very slight change in the krypton sulfur distance. But now to further analyze the impact of the carbon monoxide on the krypton, we’ll return to the table of rotational constants, but this time, focus on the eQqs for the two complexes.
----- Meeting Notes (6/10/13 14:54) -----
trimer bond lengths are nearly identical to those in their constituent dimers
van der waals bond lengths do not change signficantly upon complexation
----- Meeting Notes (6/10/13 14:56) -----
separate dimer and trimer images
remove kr-so3-co complex from top
Trimer bond lengths are nearly identical to those in their constituent dimers

11. Spectroscopic Constants
ν=2B(J+1)-4DJ(J+1)3-2DJK(J+1)K2
So here, we see that the eQq changed significantly upon complexation with carbon monoxide.

12. Results and Conclusions
eQq = MHz
3.438(3) Å
2.854(11) Å Kr
SO3
SO3 CO
3.488(6) Å
2.871(9)Å Kr
SO3 CO
SO bringing those values back into our overall picture of the complex, we see that the eQq decreased by 18%, showing that the eQq is a very sensitive measure of Cos impact on Kr.
----- Meeting Notes (6/10/13 15:13) -----
change distance point to whatever you have on the other slide
cut out eqq is a sensitive measure- and say that we wanted to investigate that
eQq = MHz
Trimer bond lengths are nearly identical to those in their constituent dimers
Upon addition of CO, the eQq decreased by ~18%

13. Comparison of 83Kr eQq Complex eQq (83Kr), MHz KrHCN 7.457(50)1 KrHF
10.227(71)2
KrSO3CO
16.646(156)
KrSO3
(129)
KrAgF
(16)3
KrAuF
(46)3
eQq of weakly bound,
van der Waal complexes
eQq of strongly bound complexes,
provided evidence for a weak chemical bond
To put these numbers in perspective, here are our numbers compared to the eQqs for some other complexes.
----- Meeting Notes (6/10/13 15:13) -----
a change of 18% seems to be more than what would be suggested by the change in structure, so we'd like to understand what else could be physically causing that change
(1) E.J. Campbell, L.W. Buxton, A.C. Legon, J. Chem. Phys. 78, 3483, 1983.
(2) E.J. Campbell, M.R. Keenan, L.W. Buxton, T.J. Balle, P.D. Soper, A.C. Legon, W.H. Flygare, Chem. Phys. Letters, 70, 420, 1980
(3) J.T. Thomas, N.R. Walker, S.A. Cooke, M.C. L. Gerry, J. Am. Chem. Soc. 126, 1235, 2004

14. Theoretical Results Yirong Mo, Western Michigan University
PBE-D/cc-PVTZ
M06-2X/cc-PVTZ qualitatively similar
Binding energies were additive:
Kr-SO3-CO (5.18 kcal/mol) ≈ Kr-SO3 (1.38 kcal/mol) + SO3-CO (4.16 kcal/mol)
Parameter
Experiment
Theory
%Error
Kr-SO3
RKrS (Å)
3.438(3)
3.495
+1.7%
eQq (MHz)
(45)
21.96
+8.6%
Kr-SO3-CO
3.488(6)
3.572
+2.4%
RSC (Å)
2.871(9)
2.742
-4.5%
16.646(57)
15.69
-5.7%
----- Meeting Notes (6/10/13 15:13) -----
mention M06 calculations were done, with the same qualitative results, but PBE-D had the better quantitative results
put binding energies into the table and color animate so it'll be easier to talk through the slides
Add in comparison of change between the eqq for dimer and trimer

15. Block-localized Wavefunction Computations
Over a series of events Ez and Ez were calculated
Geometrical distortion
Electrostatic interaction
Polarization
Electron transfer
----- Meeting Notes (6/12/13 15:52) -----
have a sentence on block-localized wavefunctions
decomposition method allowing for the calculation to be broken into physically meaningful events

16. Ez During Kr-SO3-CO Complexation
0.0060
0.0012
0.0014
0.0016
0.0018
0.0020
Kr-SO3-CO
Distortion
Electrostatic
Polarization ET
Optimized
Kr-SO3
0.0050
Electrostatic
0.0040
Polarization
Ez(a.u.)
0.0030
Optimized
Kr-SO3
0.0020
----- Meeting Notes (6/10/13 15:13) -----
CO damps the effect of the SO3
Electron Transfer
Optimized
Kr-SO3-CO
0.0010 Kr
Kr-SO3
Kr-SO3-CO

17. Ez During Kr-SO3-CO Complexation
16.0
18.0
20.0
22.0
Kr-SO3-CO
Distortion
Electrostatic
Polarization ET
Optimized
Kr-SO3
14.0
Optimized
Kr-SO3
20.0
Electron Transfer
Optimized
Kr-SO3-CO
15.0
10.0
eQq (MHz)
Polarization
5.0
0.0
Electrostatic
-5.0 Kr
Kr-SO3
Kr-SO3-CO

18. Conclusions
The eQq of 83Kr indicated a significant impact of CO on the electronic structure of the Kr
Provides a more sensitive picture than
Structural changes
Dipole moments
Binding energies
BLW computations illustrate the complexity of the changes in the electric field and electric field gradient

19. Acknowledgments Dr. Ken Leopold Dr. Brooke Timp Dr. Yirong Mo
Dr. Chris Dewberry

20. Structure Determination cont.
Kr-SO3 (angles from Ar-SO3)
Different values of χ changed the R(Kr-S) distance more than the error
x->
10.8
15.6
18.9
R(Kr-S)
(5)
(3)
(2)
Kr-SO3-CO (angles from SO3-CO)
Error in the values was greater than the change introduced by different angles
R(Kr-S)
x y 5
6.5 8
1.3
3.490(7)
11.4
3.488(6)
15.8
3.486(5)
R(S-C)
2.872(11)
2.871(9)
2.872(9)
2.871(8)