video for 2013 Sigma Xi Student Research Showcase

1. Model Core
Potentials Studies of
HRnX Molecules in
Confinement
Amelia Fitzsimmons
23 February, 2013
Sigma Xi Student Research Showcase

2. Presentation Outline
Presentation Outline
• Introduction
• Noble Gas Chemistry
• Role of Computational Chemistry in Noble Gas Chemistry
• Model Core Potentials: Basis Sets for Large or Heavy Systems
• Radon: The Next Frontier
• Research Goals
• Computational Methods
• Confinement Models
• Results
• Results of Preliminary Stage
• Effect of relativistic basis set vs. non relativistic basis set on quality of results inside
harmonic confinement
• Effect of confinement on transition state structure
• Additional Research Goals
• Results of Stage 1
• Effect of relativistic basis set vs. non relativistic basis set on quality of results inside
harmonic confinement
• Effect of confinement on transition state structure
• Effect of confinement on electron density
• Conclusion: Does confinement stabilize the transition state?
• Future Directions 2
• Acknowledgements

3. Radon Gas is Often Found in
Basement Air
• Radon is produced as a α β
daughter nucleus in the α-
decay chain of both 238U and
235U. Consequently, soils in
areas with natural uranium
Introduction
deposits often contain radon
α β
gas.
• Saskatchewan is one such
area.
• As the radon gas is produced,
it rises through the soil and
α
leaks into the air above the
uranium deposit. If homes
are built in a uranium-rich α
area, radon may be present
in the air of the lowest floor
of such homes. 3
Picture Source: http://en.wikipedia.org/wiki/File:Wheat_harvest.jpg

4. Radon: The Next Frontier
• Due to radon’s confirmed
carcinogenic activity1 and presence in
residential basement air it is
imperative to find ways to sequester
radon within molecules to facilitate
its removal.
• Periodic trends hint that radon may
Introduction
behave in a chemically similar
manner to xenon.
• Radon is directly below xenon on
the periodic table, indicating that
it should react under the same
conditions but more strongly.
• Xenon chemistry is therefore a
launching point for exploration of
radon chemistry.
(1) Quoted on the American Lung Association website “Radon-American Lung Association”. 4
http://www.lung.org/healthy-air/home/resources/radon.html (accessed January 10, 2013) from: "Health
Risks | Radon | U.S. EPA." U.S. Environmental Protection Agency.
http://www.epa.gov/radon/healthrisks.html (accessed September 14, 2009). (2) Picture Credit:
http://www.factmonster.com/dk/science/encyclopedia/periodic-table.html

5. HRnF: A World of Possibility
!
H!+!Rg!+!X!
• Molecules of the type
HRgX (Rg=Xe, Rn;
HRgX!TS!
X=halogen) have been DE1!
shown to be
DETS!
metastable1,2. HRgX!
DE3!
Introduction
• HRgX molecules decay
spontaneously into HX +
Rg, but the kinetics of DE2!
this mechanism are
Rg!+!HX!
unknown.
• Many small, heavy-rare Any investigation into the
gas containing molecules kinetic stability of HRgX
have been synthesized in molecules must take the
solid rare gas matrices effects of the rare gas matrix
environment into account. 5
(1) Lundell, J.; Chaban, G. M.; Gerber, R. B. Chem. Phys. Lett. 2000, 331, 308-316. (2) Fitzsimmons, A.; Klobukowski,
M. J. Phys. Chem. A 2010, 114, 8786. Figure Credit: Fitzsimmons; A.; Klobukowski, M. Can. J. Chem., 2013, in press.

6. Computational Chemistry’s
Contribution to Noble Gas
Chemistry • The radioactivity and
short half life of radon
(3.8 days) limit
Introduction
experimental
investigation of radon
chemistry.
• Advantage of
computational study:
select for radon
compounds predicted
to have higher stability
prior to experimental
study 6

7. Model Core Potentials: Basis Sets
for Large or Heavy Systems
• Large, relativistic basis sets provide the most complete description
of molecules, especially those that contain heavy atoms with many
electrons.
• However, such basis sets are computationally inefficient, requiring
extensive amounts of time for computations.
Introduction
• Efficiency can be improved by replacing the core electrons in a
heavy atom with a potential which models their behaviour.1
5d radial function of Au
1
AE
0.8
P(r) = rR(r) (in a.u.)
MCP
0.6 ECP
0.4 VMCP: The Model Core Potential,
0.2 which replaces the core
0 electrons and approximates the
-0.2 shape of their radial distribution
-0.4 functions, as illustrated by the 7
-0.6 green and red lines on the
0 1 2 3 4 5
graph.
r (in a.u.)
(1) Model Core Potentials: Theory and Applications. Klobukowski, M.; Huzinaga, S.; Sakai, Y. Computational
Chemistry: Reviews of Current Trends, 1999, 3. Picture Credit: Ph.D. Thesis, Tao Zeng, University of Alberta, 2011.

8. Research Goals
• Synthesis of HRgX occurs via photodissociation of HX inside a Rg-
Research Goals
doped rare gas matrix1:
• Given that small, xenon-containing molecules have already been
synthesized inside rare-gas matrices at low temperatures and the
periodic relationship between xenon and radon, will:
• A basis set containing relativistic effects be necessary to effectively
model this system?
• Confinement stabilize an HRgX species as compared to free atoms in
the gas phase?
• HRnX demonstrate superior stability inside either rare-gas matrix or a
harmonic confining potential? 8
(1) Bihary, Z.; Chaban, G. M.; Gerber, R. B. J. Chem. Phys. 2003, 119, 11278-11284.

9. Computational Methods
Computational Methods
Stage of Study Method Basis Set Confinement
Preliminary RHF iMCP-NR1 Harmonic Potential
iMCP-NR2
iMCP-SR1
iMCP-SR2
Stage 1 RHF iMCP-SR2 Planar Helium Lattice
• Details: Stage 1
• Details: Preliminary Stage • Planar lattice of non-interacting helium atoms
Harmonic Potential of the form:
• He atoms represented explicitly with a
contracted, 8s locally-developed basis set
W = w å[za - w0 ]2 • HRgX transition state described with the iMCP-
a SR2 basis set.
Potential Strength governed by the constant ω. • At each 10 degree increment along the angle
made by the transition state, the bond lengths
Eight different values of ω used: 0.00, 0.05, 0.10, r(Rg-X) and r(Rg-H) and the total energy of the
0.15, 0.20, 0.25, 0.30. molecule were optimized.
Four MCP basis sets of the improved-Model Core Graphical depictions of each type
Potential family were used to describe HRgX
transition states. of confinement are shown on the
At each 10 degree increment along the angle made following slide. 9
by the transition state, the bond lengths r(Rg-X)
and r(Rg-H) and the total energy of the molecule
were optimized.

10. Computational Methods
Confinement Models
Harmonic Potential 8x8 Planar Helium Lattice
z
H 2.5Å
X H
1.7Å y
x R R X
n 2.2Å n
Confined Region
10

11. Quantum Theory of Atoms in
Computational Methods
Molecules (QTAIM) Analysis
• QTAIM was developed by Dr. Richard Bader as a
mathematically rigorous method for defining which regions of
space within a molecule belong to component atoms1.
• This division is based on the topology of the electron density.
• Critical points in the electron density are characterized by
their rank, ω, and signature, ς and can be one of four types:
• Bond Critical Point (BCP): a local maximum in one dimension
between to nuclei.
• Ring Critical Point (RCP): A local minimum in one dimension
between two BCPs.
• Cage Critical Point (CCP): A local minimum in all three
dimensions.
• Nuclear Critical Point (NCP): A local maximum on the electron
density in all three dimensions. 11
(1) The Quantum Theory of Atoms in Molecules. Edited by Chérif Mata and Russell Boyd. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA,
Weinheim ISBN: 978-3-527-30748-7

12. Effect of Basis Set on HRnF Transition
Results-Preliminary Stage
State-A Classic Variational Question
Results of Basis Set
Examination:
• Nonrelativistic basis sets
(NR1 & NR2) display blue
shifted transition state
geometries
• Scalar Relativistic basis
sets (SR1 & SR2) have
lower overall energies.
• As the RHF method is
variational, SR2 results
are by definition closer 12
to the true energies of
the HRgF molecules.

13. HRnF in Harmonic Confinement
Results-Preliminary Stage
• Relative energies shown on the graph are computed as: (Eangle + Elinear)
• Difference of energies at the transition state angle ( 95o) between the strongest 13
(ω=0.30) and weakest (ω=0.00) confining potentials is 9.9 kJ/mol
• Increasing confinement strength does not alter the angle at which the transition
state occurs.

14. HRnCl in Harmonic Confinement
Results-Preliminary Stage
• As in the previous figure, relative energies shown on the graph are computed as
(Eangle + Elinear).
• Difference of energies at the transition state angle ( 95o) between the strongest 14
(ω=0.30) and weakest (ω=0.00) confining potentials is 10.5 kJ/mol
• Increasing confinement strength does not alter the angle at which the transition
state occurs.

15. Preliminary Conclusions
Conclusions-Preliminary Stage
• Research goals addressed in the Preliminary Stage:
• Will a basis set containing relativistic effects be necessary to
effectively model this system?
• Yes: the relativistic basis set is necessary for two reasons.
• First, it shifted the angle at which the transition state occurs from
100o to 95o for both HRnF and HRnCl.
• Second, it resulted in a lower relative energy at the transition
state by 3.9% for HRnF and by 9.9% for HRnCl.
• Does confinement stabilize an HRgX species?
• Yes: the strongest harmonic potential has a minute stabilizing
effect on the energy barrier to decomposition into HX + Rg:
• Erelative is increased by 9.9 kJ/mol for HRnF and by 10.5 kJ/mol for
HRnCl.
• No: the presence or absence of the confining potential does not
affect the geometry of the transition state. 15
• Neither ∠HRnF nor ∠HRnCl are altered by the confining potential.

16. Research Goals Added as a
Additional Research Goals
Result of the Preliminary Stage
• In the Preliminary Stage, it was determined that confinement
inside the harmonic potential well did not alter the geometry
of the transition state.
• Consequently, the following research goal will also be
investigated in Stage 1 of the study:
• Does confinement inside of the helium lattice alter the geometry
of the transition state?
• Based on the increase in Erelative for HRnF and HRnCl observed
in the harmonic potential confinement:
• Will confinement in the helium lattice further stabilize HRnX?
16

17. Stage 1-Helium Lattice
17

18. Effect of Confinement in He lattice
on Erelative of HRnX
Results-Stage 1
• Confinement in the helium lattice decreases the angle of the
transition state compared to the angle of the unconfined 18
transition state.
• Relative energies of HRnX are decreased in the He-sheet
confinement.

19. Molecular Graph of Linear HRnF
• Gray Spheres: He
atoms
• Neon green sphere:
Cl atom
• White sphere: H
Results-Stage 1
atom
• Teal sphere: Rn
atom
• Dashed lines: bond
paths
• Green dots: BCPs
BCP ρ@ L(ρ) @
o Values of ρ @ BCP indicate the magnitude
BCP BCP
of the electron density at the specified BCP.
Rn-H 0.1331 -0.0301 o Meanings of L(ρ) @ BCP values:
• Rn-H BCP: density is locally
Rn-F 0.0767 0.2236 concentrated:: covalent bonding.
• Rn-F BCP: density is locally depleted:: 19
strongly polar bond.
Picture Credit: This molecular graph and all following QTAIM-related figures were generated by A. Fitzsimmons using
AIMAll (Version 12.06.03) by Todd. A. Keith, TK Gristmill Software, Overland Park, KS, USA, 2012(aim.tkgristmill.com)

20. Continued QTAIM Analysis of
HRnF in He
Results-Stage 1
BCP Ellipticity @ BCP (ε) Meaning of ε @ BCP
Rn-H 0.0192 If ε=0, a bond is cylindrically symmetric; this
bond is nearly cylindrically symmetric, lacking
significant π-character as expected from the ς
Molecular Orbitals (MOs) in this region of the
molecule.
Rn-F 0.0201 This bond is less cylindrically symmetric; this is 20
also reasonable due to the strong polarity of
fluorine.

21. Molecular Graph of HRnF
Transition State
Results-Stage 1
• The value of ρ @ BCP for the Rn-F BCP has decreased,
BCP ρ @ L(ρ) @ indicating a weakening of the Rn-F interaction as the
BCP BCP molecule prepares to dissociate.
• Values of L(ρ) @ BCP retain the same sign as values of
Rn-H 0.1568 -0.1858 L(ρ) @ BCP of the linear compound; the nature of the
interaction is not changing: merely the strength. 21
Rn-F 0.0425 0.1439 • Thick blue lines describe the interatomic surfaces (IAS)
belonging to the HRnF transition state; note that the
upper boundaries of these are defined by the He lattice.

22. Molecular Graph of HRnCl
Transition State
Results-Stage 1
• Dashed lines: bond paths
• Gray Spheres: He atoms • Green dots: bond critical points; indicating
• Neon green sphere: Cl atom regions of accumulated electron density 22
• White sphere: H atom between atoms
• Teal sphere: Rn atom • Pink spheres: Non-nuclear attractor critical
points (NNACPs)

23. QTAIM Analysis of HRnCl
Transition State
• IAS lines depict the volume of the
HRnCl molecule: this region is
clearly confined by the sheet of
He atoms above and below it.
Results-Stage 1
• NNACPs occurring around the Cl
atom are artifacts of the MCP,
and as such additional electron
density functions are required.
BCP ρ@ L(ρ) @ Meaning of L(ρ) @ BCP
BCP BCP
Rn-H 0.1565 -0.1964 Local concentration of electron density, nearly
identical in magnitude to that of ρ@ BCP (Rn-H)
for the HRnF transition state, indicating that
strength of this interaction is minimally affected by
the substitution of a heavier halogen. 23
Rn-Cl midpoint 0.0242 0.0739 The presence of the NNACPs around Cl makes
these L(ρ) values devoid of chemical meaning.
Rn-Cl near Cl 0.2654 -1.5614

24. Conclusions
• The Preliminary Stage addressed the research goals related to the
design of the study, and found that:
• A basis set containing relativistic effects is necessary to reliably
model HRnX systems.
• Confinement inside of a harmonic potential well increased the
Conclusions
energy barrier to decomposition for HRnX, thereby stabilizing it.
• Confinement in a harmonic potential well did not affect the
geometry of the transition state.
• The computations in Stage 1 addressed new research goals born out
of the results from the Preliminary Stage, and addressed the original
research goals related to the chemical properties of the HRnX
molecules, finding that:
• Confinement inside the He lattice decreases ∠HRnX of the transition
state.
• The He sheet actively confines the IAS belonging to the component
atoms of HRnX, as evinced by the IAS paths.
• Accurate computation of BCPs and other QTAIM properties around Cl 24
atoms require additional electron density functions.

25. Future Directions
• Stage 2: Post Hartree-Fock methods and expansive basis sets for HRgX
• Method: the Møller-Plesset second order (MP2)1 perturbation method
includes effects of electron correlation at a higher level than the
Restricted Hartree-Fock method, and will therefore provide higher-quality
Future Directions
results. The necessary additional electron density functions will also be
added at this stage.
• The Model Core Potentials basis set aug-MCP-tzp has been demonstrated
to be of high quality in previous studies2 while retaining a high level of
computational efficiency.
• Stage 3: Other small compounds of rare gases
• HRgOH has been shown to be metastable at room temperature3
• A transition state for HRnOH has been located at the RHF/ims2 level4
• Confinement studies of this molecule will elucidate stability in real-life
conditions
• Stage 4: Intrinsic Reaction Coordinate (IRC) computations
• IRC is an extremely reliable method for confirming a decomposition
mechanism for a transition state: this would be valuable for all HRgX and
HRgOH. 25
(1)Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618-622. (2) Miyoshi, E. et al., J. Chem. Phys. 2005, 122, 074101. (3)
Tsivion, E.; Gerber, R.B. Phys. Chem. Chem. Phys. 2010, 12, 11791-11794. (4) Unpublished
Computations, Fitzsimmons.

26. Acknowledgements
Acknowledgements
Many thanks to the University of Alberta Department of Chemistry
(pictured above) located in the Gunning-Lemieux Chemistry Centre
and the Centennial Centre for Interdisciplinary Science; to Dr.
Mariusz Klobukowski; to fellow graduate students and 26
undergraduate students in the theoretical chemistry research
groups at the University of Alberta.
Picture Credit: http://www.chemistry.ualberta.ca/AboutUs.aspx

27. The end
Thank you for your attention! If you have any questions or 27
comments, I would be happy to address them in the comments
section of this post.