Electronic structure calculations and properties of alkaline-earth molecular ions

219 Pages·2016·2.24 MB·English

by  Sandipan Banerjee

University of Connecticut
OpenCommons@UConn
Doctoral Dissertations University of Connecticut Graduate School
4-8-2013
Electronic structure calculations and properties of
alkaline-earth molecular ions
Sandipan Banerjee
University of Connecticut - Storrs, [email protected]
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Banerjee, Sandipan, "Electronic structure calculations and properties of alkaline-earth molecular ions" (2013).Doctoral Dissertations.
26.
https://opencommons.uconn.edu/dissertations/26
Electronic structure calculations and properties of
alkaline–earth molecular ions
Sandipan Banerjee, Ph.D.
University of Connecticut, 2013
Recent years have seen many advances in the study of ultracold molecular ions
[1, 2, 3]. Studies involving atom-ion scattering [4, 5], resonant charge transfer [6]
and charge mobility [7] at ultracold temperatures, are a few of the many emerging
fields of interest where an in-depth understanding of the underlying physics govern-
ing the interaction between atoms and ions is crucial. Alkaline-earth dimers are now
being used as new grounds for testing fundamental physics laws, precision measure-
ments [8] and quantum computation [9]. As a starting point for conducting such
studies, one needs a very good knowledge of the electronic structure, energetics and
long-range behavior of these molecular ions. In this thesis, we provide accurate ab
initio calculations for the ground and low-lying excited states of Be+, Mg+, Ca+ and
2 2 2
Sr+ molecular ions. We have also calculated the spectroscopic constants, electronic
2
transition dipole moments, polarizabilities and long-range dispersion coefficients for
the various alkaline-earth ionic dimers. We have extended our calculations to study
heteronuclear species of alkaline-earth molecular ions, like BeCa+, and mixed alkali
alkaline-earth species like NaCa+. We calculated photoassociation (PA) pathways
for the formation of cold molecular ions, and also studied corrections to the Born-
Oppenheimer Hamiltonian — non-adiabatic couplings and hyperfine structure due to
nuclear spins and electric quadrupoles. We believe this work will lay foundation for
new experiments in ultracold physics and chemistry.
Electronic structure calculations and properties of
alkaline–earth molecular ions
Sandipan Banerjee
B.Sc., University of Calcutta, Kolkata, India 2004
M.Sc., University of Calcutta, Kolkata, India 2006
M.S., University of Connecticut, Storrs, CT 2008
A Dissertation
Submitted in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy
at the
University of Connecticut
2013
(cid:13)c Copyright by
Sandipan Banerjee
2013
APPROVAL PAGE
Doctor of Philosophy Dissertation
Electronic structure calculations and properties of
alkaline–earth molecular ions
Presented by
Sandipan Banerjee
Major advisor
Robin Cˆot´e
Associate advisor
John A. Montgomery Jr.
Associate advisor
Jos´e A. Gasc´on
University of Connecticut
2013
ii
To my wife Jayita, and my parents Rathin and Dipti Banerjee;
without their love and support none of this would have been possible.
Thank you for always believing in me.
Acknowledgements
I would like to thank my major advisor Robin Coˆt´e, for all his help, and guid-
ance during my stay here at UConn. I have learned many things from him. I was
extremely blessed to have as my co-advisors John Montgomery, Jos´e Gasc´on and
Harvey Michels. They were instrumental in guiding me when I felt I was completely
lost. Several other members of the physics faculty played a significant role in my
graduate education – Edward Eyler, William Stwalley, Alexander Kovner, and Juha
Javanainen – I thank each one of you.
My life at UCONN would not have been easy without the help of the wonderful
staffmembersinthePhysicsdepartment. IwouldliketothankCarolArtacho-Guerra,
Kim Giard, David Perry, Michael Rapposch, Michael Rozman, Dawn Rawlinson, Ce-
cile Stanzione, and Barbara Styrczula for always being so helpful. I would like to
thank the former and present members of the Cˆot´e research group. I also thank the
members of the Gasco´n research lab in the Chemistry department for their warm
hospitality and support.
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I would like to express my gratitude to all of my fellow Physics graduate students
for establishing a collaborative educational environment. To my close friends J.C
Sanders and Nolan Samboy, thank you for helping me through all the rough times
and making the good times even better. I am grateful to my office-mates Han Chen,
SankaPiyadasaandFuChang-SunforcreatinganamazingworkatmosphereinP-210.
Finally I would like to thank my family for their unconditional love, and for ev-
erything they have done for me. It was not easy for me to leave my parents and
relatives in India, and travel halfway across the globe to pursue my graduate educa-
tion. I thank my parents and parent-in-laws for always being extremely supportive of
everything. I would like to thank my close friends Swastik Ghoshdastidar and Piyal
Das for always encouraging me to achieve even the farthest dreams; I miss you guys
everyday. I was fortunate enough to have family members in US, I thank Saikat and
Debjani Ray-Majumder my brother-in-law and sister-in-law for being so loving and
caring, and of course their amazing kids Rishi and Arjun. I thank my cousin brother
Siddhartha (Jubin) for telling me that life is not all about taking stress, it is about
having fun too. Last but not the least, I would like to thank my lovely wife Jayita.
Without her, my accomplishments would be nowhere near as fulfilling or satisfying.
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Table of Contents
Page
Acknowledgements....................................................iv
List of Tables ......................................................... x
List of Figures ....................................................... xii
Chapter
1. Introduction ....................................................... 1
1.1 Motivations......................................................1
1.2 Overview of ab initio methodology ..................................3
1.2.1 Born-Oppenheimer approximation ............................4
1.2.2 Commonly used methods – Configuration Interaction and
Coupled Cluster.........................................7
1.2.3 Basis sets .................................................9
1.3 Outline of the Thesis.............................................11
2. The prototype example of Be+ .................................... 12
2
2.1 Ground X 2Σ+ and B 2Σ+ states ..................................12
u g
2.2 Computational Details ...........................................15
2.3 Results and Discussions ..........................................22
2.3.1 Potential Curves and Spectroscopic Constants.................22
2.3.2 Transition Moments and Lifetimes...........................25
2.3.3 Long-Range Coefficients....................................30
2.4 Concluding Remarks .............................................31
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3. Excited States in Be+ dimer — An application to
2
Photoassociation............................................... 32
3.1 Low lying asymptotes in Be+......................................32
2
3.2 Ab inito curves for Excited States..................................33
3.3 Theoretical background on photoassociation (PA) ....................36
3.4 PA scheme via the A2Π state.....................................40
u
3.5 Transition moment and Long-range expansion coefficients .............41
3.6 Photoassociation Rates ...........................................45
3.7 Concluding Remarks .............................................47
4. Other homonuclear alkaline-earth systems
— Ca+, Sr+ and Mg+ .......................................... 48
2 2 2
4.1 Motivations.....................................................48
4.2 Ca+ molecular ion ...............................................49
2
4.2.1 Computational Methods ...................................49
4.2.2 Potential Curves and Spectroscopic Constants.................55
4.2.3 Electronic dipole transition moments.........................59
4.2.4 Polarizabilities and long-range coefficients ....................62
4.3 Sr+ molecular ion................................................64
2
4.3.1 Computational Methods ...................................64
4.3.2 Potential Curves and Spectroscopic Constants.................65
4.3.3 Electronic dipole transition moments.........................68
4.3.4 Polarizabilities and long-range coefficients ....................68
4.4 Mg+ molecular ion...............................................71
2
4.4.1 Computational Methods ...................................71
4.4.2 Potential Curves and Spectroscopic Constants.................72
4.4.3 Electronic dipole transition moments.........................73
4.4.4 Polarizabilities and long-range coefficients ....................73
4.5 Beyond the Born-Oppenheimer (BO) regime –
Non-Adiabatic Corrections.....................................80
4.6 A comparative study of all homonuclear alkaline-earth dimers .........86
4.7 Long-Range — Inclusion of Exchange energy ........................91
4.8 Concluding Remarks .............................................94
5. Heteronuclear alkaline-earth molecular ions — BeMg+, BeCa+
and MgCa+ .................................................... 95
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