The Evolution of Chemical Bonding over the Nuclear Transmutation Reaction Path
Matthew Timm,a,b Chérif F. Mattaa,b,*
(a) Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, NS, Canada; (b) Department of Chemistry, Dalhousie University, Halifax, NS, Canada.
* [email protected].
The University of Hong Kong (Friday, June 13, 2014)
The University of Hong Kong (Friday, June 13, 2014)
1
Professor Sun Kwok
Dr. Seyedabdolreza, Dr. Seyedabdolreza, Sadjadi
(Prof. Kwok
’s Group)
(Prof. Kwok’s Group)
Thank you for inviting me!
2
Matthew Timm
Matthew Timm
3
(posing with Chemistry Nobel Laurate Ada Yonath ‐ May 2014)
(posing with Chemistry Nobel Laurate
M. Timm, C. F. Matta; Primary Retention following M. Timm, C. F. Matta; Primary Retention following Nuclear Recoil in β‐Decay: Proposed Synthesis of a Nuclear Recoil in β‐Decay: Proposed Synthesis of a 38ArO
38ClO
Metastable
Metastable Rare Gas Oxide (
Rare Gas Oxide (38
ArO44) from (
) from (38
ClO44––) and ) and the Evolution of Chemical Bonding over the Nuclear the Evolution of Chemical Bonding over the Nuclear Transmutation Reaction Path; Applied Radiation and Transmutation Reaction Path; Applied Radiation and Isotopes, accepted 10 June 2014.
Isotopes, accepted 10 June 2014.
4
THE IDEA
THE IDEA
•• What happens to a chemical bond upon nuclear What happens to a chemical bond upon nuclear transmutation?
transmutation?
•• Would the compound survive?
Would the compound survive?
•• Will it take on new properties?
Will it take on new properties?
•• How does the electron density evolve following a How does the electron density evolve following a nuclear event?
nuclear event?
POSSIBLE SIGNIFICANCE
POSSIBLE SIGNIFICANCE
•• Nuclear transmutation as a synthetic “hot Nuclear transmutation as a synthetic “hot chemistry”
chemistry” route. route. •• Possible synthesis of thermodynamically metastable
Possible synthesis of thermodynamically metastable
compounds, generally difficult to synthesize.
compounds, generally difficult to synthesize.
•• Synthesis of compounds with unusual oxidation Synthesis of compounds with unusual oxidation states.
states.
5
•• Sheer intellectual curiosity!
Sheer intellectual curiosity!
Hot Atom Chemistry: An Obituary
H. Müller; The rise and fall of hot atom chemistry.
J. Radioanal. Nucl. Chem. 2000, 243, 165-168.
• Environmental movement.
• Rise of more fashionable fields.
• Moving away of PhD students to areas which can lead to attractive future employment.
• Lack of common language and appreciation between groups working on hot atom chemistry from different vantage points.
• Lack of funding.
6
Very thin literature on joint investigations of
hot atom chemistry & quantum chemistry
[1] J. A. Tossell; Does the calculated decay constant for 7Be vary significantly with chemical form and/or applied pressure? Earth Planet. Sci. Lett. 2002, 195, 131‐139.
[2] M. Defranceschi, G. Berthier; Molecular aspects of the β‐decay in Tc clusters. J. Nucl. Mater. 2002, 304, 212‐220.
[3] C. Jiang, C. R. Stanek, N. A. Marks, K. E. Sickafus, B. P. Uberuaga; Predicting from first principles the chemical evolution of crystalline compounds due to radioactive decay: The case of the transformation of CsCl to BaCl. Phys. Rev. B 2009, 79, 132110.
7
• Jaing et al.1 investigate radioactive decay as a possible synthetic route.
8
• This is the single example in the literature.
t1/2 = 30 years
When all Cs has been replaced by Ba, we find only a very small 0.03 eV/atom driving force for the rocksalt BaCl structure to phase separate 9
into a mixture of the orthorhombic structured BaCl2.
10
Hot atom synthesis of ArO44?
11
ArO44 is the last member of the N = 50 e–– isoelectronic
and isosteric series of ions: 4–, PO 3–
3–, SO 2–
2–, ClO ––. SiO444–
44
44
44
Å
Å
QCISD/6‐311+G(3df)
12
13
14
15
To this day, ArO44 remains to be synthesized.
16
Proposed synthesis of 38ArO4 from 38ClO4‐
38Cl is ideal because:
• t1/2 (38Cl Æ38Ar+β) = 37.24±0.05 min[1] • readily produced:[2] 37Cl‐ (aq) + n → 38Cl–(aq) + γ
[1] G. Audi, et al.; Nucl. Phys. A 2003, 729, 3‐128. [2] H. V. A. Briscoe, A. A. Eldridge, G. M. Dyson; Mellor's Comprehensive Treatise on Inorganic and Theoretical Chemistry (Supplement II, Part I.); Longman, London, 1956.
17
NaCl+3H 2 O → NaClO3 +3H 2
−
3
ClO (aq) + H 2 O(l)
−
4
→ ClO (aq) + H 2 (g)
38
−
4
ClO (aq) →
38
ArO 4 (aq) + β
18
−
38
−
4
ClO (aq) →
38
ArO 4 (aq) + β
−
• But how about the recoil? (from 0 Æ~ 5 MeV)
• Would ArO4 survive?
19
α‐decay spectrum
Ground state of a parent nucleus Æ excited or ground state of a daughter nucleus & α‐particle. The change in energy of the nucleus is shared as K.E. by the α-particle and the recoiling daughter nucleus ∆E according to the principles of conservation of momentum and of energy. This requires the α-particle and the daughter nucleus to move in opposite directions with the same magnitude of p Æ Sharp p.
20
http://www.ohio.edu/people/piccard/radnotes/alphabeta.html
β‐decay spectrum
End point energy
In β‐decay there are 3 products: The daughter nucleus, the β‐e‐, & an antineutrino (ṽ). Thus, conservation of momentum and of energy do not suffice to determine the K.E. of a β‐particle, there are too many unknowns. The spectrum of β‐K.E. is a broad curve. By conservation of momentum and energy, there will be a maximum K.E. of a β‐particle at the limit as the momentum and energy given to the neutrino approach zero. In this case the momentum and energy of only two particles need to be taken into account, giving us the same algebra as alpha decay.
21
http://www.ohio.edu/people/piccard/radnotes/alphabeta.html
β‐emission spectrum of 38Cl with 3 “end points”
22
Langer, L. M. 1950. The beta‐spectra of Cl38. Phys. Rev.; 77: 50‐53.
Estimation of the yield of primary retention
precoil =
pe =
precoil =
Erecoil
p + pν + 2 pe pν cos θ
2
e
2
Ee2 + 2 Ee me c 2
c2
Eν
pν =
c
Ee2 + 2 Ee me c 2 Eν2
Ee2 + 2 Ee me c 2 Eν
+ 2 +2
cos θ
2
2
c
c
c
c
Ee2 + 2 Ee me c 2 + Eν2 + 2 Eν Ee2 + 2 Ee me c 2 cos θ
=
2 Mc 2
An. N. Nesmeyanov Radiochemistry (English Translation); Mir Publishers: Moscow, 1974.
23
which can be simplified by expressing energies in MeV
(1 kcal/mol = 4.336×10–8 MeV) and masses in atomic mass units (a.m.u.):
Erecoil
(
5.36 ×102 2
Ee + 1.02 Ee + Eν2 + 2 Eν Ee2 + 1.02 Ee cos θ
=
M
Erecoil = Recoil energy of transmuted atom (in MeV)
M = Mass of transmuted atom (in a.m.u.)
Ee = Kinetic energy of ejected β‐ particle (in MeV)
Eν = Kinetic energy of ejected antineutrino (in MeV)
θ = Angle between ejected β‐ particle and antineutrino
An. N. Nesmeyanov Radiochemistry (English Translation); Mir Publishers: Moscow, 1974.
24
)
Erecoil
(
5.36 ×102 2
Ee + 1.02 Ee + Eν2 + 2 Eν Ee2 + 1.02 Ee cos θ
=
M
From this equation, the extreme values of the recoil energy occur for θ = 0 (max) and θ = π (min), leading to:
θ = 0o
Erecoil
(
5.36 ×102 2
Ee + 1.02 Ee + Eν2 ± 2 Eν Ee2 + 1.02 Ee
=
M
θ=π
25
)
)
ṽ
Forbidden
β‐e‐
Allowed
θcritical
θ critical
threshold
⎧ ⎛ M × Erecoil
⎞
2⎫
2
− Ee − 1.02 Ee − [ max( Ee ) − Ee ] ⎪
⎪⎜
2 ⎟
⎪ ⎝ 5.36 ×10 ⎠
⎪
= arccos ⎨
⎬
2
2 [ max( Ee ) − Ee ] Ee + 1.02 Ee
⎪
⎪
⎪⎩
⎪⎭
• θcritical = Anglular deviation from colinearity between β‐
particle and ṽ resulting in a given Erecoil. threshold
• For Erecoil ≤ Erecoil
Æ θ ≤ θcritical.
• max(Ee) = Maximum energy of an ejected β‐‐particle (the 26
end‐point or cut‐off value of the bell curved spectrum).
We now impose the energy threshold of recoil (below which the recoil energy is insufficient to cause the dissociation of the daughter molecule).
Set the upper bound for the recoil energy as:
E
thresh.
recoil
= max( Erecoil ) =
20 kcal/mol ≈ 9.1 ×10–7 MeV (gas‐phase).
In other words: This is the highest recoil energy that will leave the ArO4 molecule intact after the β‐decay event. 27
28
(= E
threshold
recoil
29
)
(= E
threshold
recoil
30
)
threshold
(= Erecoil
)
31
β‐emission spectrum of 38Cl
30.8%
53.4%
15.8%
32
Langer, L. M. 1950. The beta‐spectra of Cl38. Phys. Rev.; 77: 50‐53.
The yield from primary retention of ArO4
• Applying the derived Eq. over all possible β‐ energies gives proportion of ejected β‐ Particles & antineutrinos whose K.E. cancels within the chosen threshold, giving “acceptable” recoil energy less than the threshold and hence insufficient to break the daughter molecule.
• Applying proportions to beta spectrum percentages gives rough percent yield.
retention gas phase (%) = 0.6 × 0.534
+ 1.0 × 0.158 + 1.9 × 0.308 = 1.1%
retention solid phase (%) = 4.1× 0.534
+ 6.7 × 0.158 + 14.1× 0.308 = 7.633%
The 20 kcal/mol threshold
34
PES of ArO3—O bond dissociation (U)MP2/6‐311+G*
35
PES of ArO3—O bond dissociation (U)MP2/6‐311+G*
36
PES of ArO3—O bond dissociation • ArO44 exists at a local minimum.
• Negative BDE of ≈ 30 kcal/mol.
• Barrier ≈ 22 kcal/mol.
(U)MP2/6‐311+G*
37
The sudden approximation The increase in Z from 17(Cl)Æ18 (Ar) causes a sudden change in the total energy of the system equivalent to a hypothetical X‐
ray photon of 4.4×1017 Hz.
Solving the relativistic K.E. equation for the β‐particle:
v = c 1 − ⎡⎣( K .E./ me c ) + 1⎤⎦
2
−2
we find that ~ 50% of all ejected e‐ have speeds of > 0.95 c.
• At these speeds, a β‐e‐ crosses 1Å in ~ 3.5×10–19 s, > 2 orders of magnitude faster than the period of this photon. 38
The nuclear transmutation reaction path
38
−β−
→38 ArO4 ⎡⎣@geom(ClO4− )⎤⎦ → 38 ArO4 [@geom(ArO4 )]
ClO ⎯⎯⎯
−
4
(‐)
Å
Å
QCISD/6‐311+G(3df)
39
The nuclear transmutation reaction path
38
−β−
→38 ArO4 ⎡⎣@geom(ClO4− )⎤⎦ → 38 ArO4 [@geom(ArO4 )]
ClO ⎯⎯⎯
−
4
Å
Å
QCISD/6‐311+G(3df)
40
The nuclear transmutation reaction path
38
−β−
→38 ArO4 ⎡⎣@geom(ClO4− )⎤⎦ → 38 ArO4 [@geom(ArO4 )]
ClO ⎯⎯⎯
−
4
Å
Å
QCISD/6‐311+G(3df)
41
Evolution of QTAIM properties along the nuclear transmutation reaction path:
Bond Properties
QCISD/6‐311+G(3df)
42
Evolution of QTAIM properties along the nuclear transmutation reaction path:
Atomic Properties
QCISD/6‐311+G(3df)
43
How can the formation of ArO4 be monitored?
44
QCISD/6‐311+G(3df)
ClO4‐
1152.9
643.7
45
QCISD/6‐311+G(3df)
ArO4
982.5
573.2
∆ν = ‐70.5
∆ν = ‐170.4
46
Referees’ Reports
• Reviewer #1:
This is an interesting study on a possible way of making the strongly endothermic but metastable molecule.
..........
Summing up, this is a good paper, that should be published after minor changes. No need to re‐referee.
Applied Radiation and Isotopes, accepted 10 June 2014.47
Referees’ Reports
• Reviewer #2: What an original work! Seldomly, I had the pleasure to read such a paper full of original and interesting ideas. Although this is a theoretical study (better: theoretical suggestion or prediction) and it is not fully obvious whether it will be possible to realize the proposed experiment, it is a very interesting piece of work that deserves publication. Applied Radiation and Isotopes, accepted 10 June 2014.48
Referees’ Reports
• Reviewer #2: (Cont’d)
The value of the paper is three‐fold. First, it proposes an interesting transmutation reaction to generate the meta‐
stable, but yet unknown argon tetroxide from an isolectronic
perchlorate precursor. Next, it applies QTAIM concepts to study the change in chemical bonding during such a transmutation process, which allows one to relate the known prototypical perchlorate with the unknown and much less stable argon tetroxide. Finally, significant mathematical modelling is done for the assessment of the viability of the transmutation reaction.
Applied Radiation and Isotopes, accepted 10 June 2014.49
Referees’ Reports
• Reviewer #2: (Cont’d)
This paper is theoretical chemistry at its best: Rather than descriptive post factum calculations, the authors exploit the full predictive power of the quantum chemical approach. It is my pleasure to recommend this paper for publication.
Applied Radiation and Isotopes, accepted 10 June 2014.50
Summary highlights
• Starting from the principle of conservation of momentum, a theoretical framework has been developed to provide quantitative estimates of primary retention yields from the hot‐atom chemistry of the β‐decay.
• ArO4 have very unusual properties: Negative BDE
Metastable (bound kinetically)
• ArO4 may have other than theoretical interest since it can conceivably be: (a) a powerful oxidizer (b) perhaps an energy storage compound 51
ACKNOWLEDGEMENTS
I have benefited from discussions with (in alphabetical order):
• Axel D. Becke (Dalhousie) • Lou Massa (City University of New York)
• Mark Obrovac (Dalhousie) • Pekka Pyykkö (Helsinki)
• Josef Zwanzinger (Dalhousie)
The University of Hong Kong (Friday, June 13, 2014)
The University of Hong Kong (Friday, June 13, 2014)
52
ACKNOWLEDGEMENTS
Financial support
The University of Hong Kong (Friday, June 13, 2014)
The University of Hong Kong (Friday, June 13, 2014)
53
Thank You
The University of Hong Kong (Friday, June 13, 2014)
The University of Hong Kong (Friday, June 13, 2014)
54
Extra Slides for Possible Questions
The University of Hong Kong (Friday, June 13, 2014)
The University of Hong Kong (Friday, June 13, 2014)
55
ArO 4 (aq) + 4H 2 O → Ar + 4H 2 O 2 ?
56
•• KClO
KClO44 crystallizes crystallizes without water of without water of crystallization.
crystallization.
•• 4 molecules per 4 molecules per unit cell.
unit cell.
57
β‐decay spectrum
Unlike the sharp momentum spectra of α‐decay, β‐decay 58
exhibits continuous momentum / K.E. spectra.
Realizing that
Eν = max( Ee ) − Ee
then substituting into (*)
Erecoil
(
5.36 ×102 2
Ee + 1.02 Ee + Eν2 + 2 Eν Ee2 + 1.02 Ee cos θ
=
M
(*)
and solving for θ we obtain the following expression for the critical angle:
59
)
Technical details of the calculations
•QCISD/6‐311+G(3df) for geometry optimizations, harmonic vibrational
frequencies, and electron densities.
•(U)MP2/6‐311+G* for PES scans.
•Programs:
o Gaussian 09 Rev.B01
o AIMAll/AIMStudio
60