From Excited Charge Dynamics to Cluster Diffusion

308 Pages·2017·7.32 MB·English

by  Shree Ram Acharya

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Electronic Theses and Dissertations
2018
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Shree Ram Acharya
University of Central Florida
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of Techniques Beyond DFT and KMC" (2018). Electronic Theses and Dissertations. 5837.
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FROM EXCITED CHARGE DYNAMICS TO CLUSTER DIFFUSION: DEVELOPMENT
AND APPLICATION OF TECHNIQUES BEYOND DFT AND KMC

by

SHREE RAM ACHARYA
B.Sc., Tribhuvan University, 2004
M.Sc., Tribhuvan University, 2007

A dissertation submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
in the Department of Physics
in the College of Sciences
at University of Central Florida
Orlando, Florida

Spring Term
2018

Major Professor: Talat S. Rahman
©2018 Shree Ram Acharya

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ABSTRACT
This dissertation focuses on developing reliable and accurate computational techniques
which enable the examination of static and dynamic properties of various activated phenomena
using deterministic and stochastic approaches. To explore ultrafast electron dynamics in
materials with strong electron-electron correlation, under the influence of a laser pulse, an ab
initio electronic structure method based on time-dependent density functional theory (TDDFT)
in combination with dynamical mean field theory (DMFT) is developed and applied to: 1)
single-band Hubbard model; 2) multi-band metal Ni; and 3) multi-band insulator MnO. The
ultrafast demagnetization in Ni reveal the importance of memory and correlation effects,
leading to much better agreement with experimental data than previously obtained, while for
MnO the main channels of charge response are identified. Furthermore, an analytical form of
the exchange-correlation kernel is obtained for future applications, saving tremendous
computational cost. In another project, size-dependent temporal and spatial evolution of homo-
and hetero-epitaxial adatom islands on fcc(111) transition metals surfaces are investigated
using the self-learning kinetic Monte Carlo (SLKMC) method that explores long-time
dynamics unbiased by apriori selected diffusion processes. Novel multi-atom diffusion
processes are revealed. Trends in the diffusion coefficients point to the relative role of adatom
lateral interaction and island-substrate binding energy in determining island diffusivity.
Moreover, analysis of the large data-base of the activation energy barriers generated for
multitude of diffusion processes for variety of systems allows extraction of a set of descriptors
that in turn generate predictive models for energy barrier evaluation. Finally, the kinetics of
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the industrially important methanol partial oxidation reaction on a model nanocatalyst is
explored using KMC supplemented by DFT energetics. Calculated thermodynamics explores
the active surface sites for reaction components including different intermediates and
energetics of competing probable reaction pathways, while kinetic study attends to the
selectivity of products and its variation with external factors.

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To my daughter, Sophia Acharya

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ACKNOWLEDGMENTS
I would like to thank my advisor Dr. Talat S. Rahman for providing continuous guidance,
support, and encouragement throughout the work. Her approach to have something new to
justify every work lead me to explore more in each of the projects. This exploration extend my
horizon even out of basic physical concepts and develop confidence to handle problem in
physics and beyond. I really appreciate her approach to update herself and fellow students on
the ongoing novice approaches in the scientific community and provide necessary environment
to motivated researchers. I am benefited on my writing skill from her approach to look for
simplified explanation to seemingly complicated scenario and critical analysis. I feel lucky to
get in a scientific environment where one can explore range of problems in a guided way and
can explore more without boundary. Her professional and personal support help me to get my
dream come true.
I am most grateful to the members of my committee, Dr. Lee Chow, Dr. Sergey Stolbov,
and Dr. Annie Wu for their time, valuable suggestions, and expertise throughout this study. I
am grateful to department of physics, UCF for providing me an opportunity for graduate study
to pursue Ph.D.
My deep appreciation goes to my collaborator Dr. Volodymyr Turkowski for his invaluable
assistance and guidance to understand complicated physics concepts and collaborating on
design and implementation of mathematical formulations to extract material properties. I
collaborate with him on the work reported on chapter 3, 4, and 5. I would like to extend sincere
thanks to collaborator Dr. Sampyo Hong and Dr. Takat Rawal for useful discussions. I
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collaborate with them in the work reported in chapter 8. My thanks goes to collaborator Dr.
Syed Islamuddin Shah for his inputs during initial phase of my research work to understand
the SLKMC package. I collaborate with him in the work reported in chapter 6. I would like to
sincerely thank to Dr. Duy Le for his valuable inputs and for assisting to fix computational
issues. I am grateful with Dr. Lyman Baker for his help on writing manuscripts with critical
analysis that help to improve manuscript and endowed with points to consider while writing
manuscript. I would like to thank my groupmates, Dr. Maral Aminpour, Dr. Neha Nayyar, Dr.
Alamgir Kabir, Dr. Ghazal Sadatshafaie, Zahra Hoosmand Gharebagh, Naseem Ud Din, Tao
Jiang, Mahboob Ur Rehman, and Andre Childs for their inputs during presentation and beyond
and creating friendly environment.
I am especially thankful to my family, grandmother, parents, wife Nisha, daughter Sophia,
brother Prakash, sister Bindu, sister-in-law Asmita, and brother-in-law Krishna, who always
encourage, maintain good academic environment, and keep their dream upon me. I am
especially grateful to my wife and daughter who always support and sacrifice their interests to
come our dream true. I am indebted of motivation and caring of my late grandfather and
grandmother. I am thankful to my classmates at UCF, NSA-UCF, and NCCO members at
Orlando, physics departments of Tribhuvan University, and my relatives for their cooperation.
I thank Govinda Prasad Adhikari, Pawan, Navin, and Baral family, Dr. Suresh Subedi, Kalpana
Dhakal, Bishnu Baral, Narayan Baral, Dhurba Bhandari, Narayan Acharya, Prem Acharya,
Shiva Acharya, Rabin Acharya, and Bal Ram Acharya for their support.
Shree Ram Acharya
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TABLE OF CONTENTS
LIST OF FIGURES ........................................................................................................... xiv
LIST OF TABLES ............................................................................................................ xxii
CHAPTER 1: INTRODUCTION ........................................................................................ 1
CHAPTER 2: THEORETICAL METHODS ...................................................................... 8
2.1 Electronic Structure Calculation of Static System ...................................................... 8
2.1.1 Density Functional Theory ................................................................................ 12
2.1.1.1 Hohenberg-Kohn Theorems ....................................................................... 12
2.1.1.2 Kohn-Sham Equations ................................................................................ 14
2.1.2 Beyond Standard DFT: the Case of Strong Electron-Electron Correlation ....... 16
2.1.2.1 The Hubbard Model .................................................................................... 18
2.1.2.2 The DMFT Solution ................................................................................... 22
2.1.2.3 Real Systems: The DFT+DMFT Solution .................................................. 28
2.1.2.3.1 Analytical Continuation .................................................................................... 29
2.1.2.3.2 Calculation of electronic structures ................................................................ 29
2.2 Electronic Properties Calculation of System out-of-Equilibrium ............................. 32
2.2.1 Time-Dependent Density-Functional Theory .................................................... 34
2.2.1.1 The Case of Linear Response: Exchange-Correlation (XC) Kernel ........... 38
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2.2.1.2 Calculation of XC Kernel ........................................................................... 41
2.2.1.3 Bound States (Exciton) ............................................................................... 43
2.3 Atomic Properties Calculation of Static System ...................................................... 45
2.3.1 Models for Total Energy .................................................................................... 46
2.3.2 Methods to Calculate Activation Energy Barrier .............................................. 47
2.3.2.1 Barrier Calculation Based on Interaction Potential .................................... 48
2.3.2.1.1 Drag Method ....................................................................................................... 49
2.3.2.1.2 Nudged Elastic Band Method .......................................................................... 50
2.3.2.2 Barrier Calculation Based on Predictive Data-driven Approaches ............ 50
2.3.2.2.1 Linear Approach: Multivariate Linear Regression (MLR) ........................ 51
2.3.2.2.2 Non-linear Approach: Neural Network (NN) ............................................... 53
2.4 Atomic Properties Calculation of Evolving Systems ............................................... 55
2.4.1 Molecular Dynamics .......................................................................................... 55
2.4.2 Kinetic Monte Carlo .......................................................................................... 56
2.4.2.1 KMC for Chemical Reaction ...................................................................... 59
2.4.2.2 Self-Learning KMC for Island Diffusion ................................................... 64
2.4.2.2.1 Structural Model and Nomenclature .............................................................. 67
2.4.2.2.2 Pattern Recognition Scheme ............................................................................ 72
2.4.2.2.3 Process Finder and Barrier Calculation Scheme .......................................... 73
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