The document contains James Drewery's curriculum vitae. It details that he received a Master of Science in Mechanical Engineering and Applied Mechanics from the University of Pennsylvania, concentrating in heat transfer, fluid mechanics, and energy science engineering. He received a double Bachelor of Science in Mathematics and Physics with honors from Wake Forest University. The CV provides details on his relevant coursework from both undergraduate and graduate studies, including courses in calculus, differential equations, linear algebra, thermodynamics, and fluid mechanics. It also outlines his research experience, laboratory skills, publications, teaching experience, and awards.

1. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
James Lewis Drewery II
GRADUATE: UNIVERSITY OF PENNSYLVANIA – SCHOOL OF ENGINEERING AND APPLIED MECHANICS
Master of Science – Mechanical Engineering and Applied Mechanics
Concentration: Heat Transfer, Fluid Mechanics, and Energy Science Engineering
UNDERGRADUATE: WAKE FOREST UNIVERSITY
Double Bachelor of Science: Mathematics and Physics with Honors
Page 1 of 40

2. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
TABLE OF CONTENTS
Section Title Pages
Portfolio Cover.................................................................................................................. 1
Table of Contents .............................................................................................................. 2
Resume............................................................................................................................... 3
Relevant Coursework .................................................................................................. 4-11
Wake Forest University (Undergraduate) Transcript ............................................12-16
University of Pennsylvania (Graduate) Transcript...................................................... 17
References........................................................................................................................ 18
Writing Sample 1 of 2 – Graduate School Purpose Statement..............................19-20
Writing Sample 2 of 2 – WFU Physics Honors Thesis............................................21-40
Page 2 of 40

3. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
EDUCATION AND AWARDS
University of Pennsylvania, School of Engineering and Applied Science (SEAS) May 2017
Master of Science in Engineering in Mechanical Engineering and Applied Mechanics Philadelphia, PA
Concentration: Heat Transfer, Fluid Mechanics, and Energy Science
Wake Forest University May 2014
Bachelor of Science in Mathematics and Physics with Honors Winston-Salem, NC
Physics GPA: 3.44/4.00
GRE: 80th
% Quantitative; 90th
% Verbal; 98th
% Analytical Writing
Wake Forest Dean's Honor List: Spring 2014
John Council Joyner Sr. Merit Scholarship Recipient
Wake Forest Research Fellowship (WFRF): Summer 2013
RESEARCH EXPERIENCE
Organic Photovoltaic Research, Wake Forest Center for Nanotechnology and Molecular Materials Advisor: David L. Carroll
 Fabricated and characterized organic photovoltaic (OPV) solar cells Fall 2014-Summer 2015
 Collaborated directly with team of 8 graduate students, post-docs, and faculty to create automated system to Winston-Salem, NC
hermetically seal organic lighting and photovoltaic devices using 3-D printing
Scintillator Research, Wake Forest Center for Energy, Environment, and Sustainability (CEES) Advisor: Richard T. Williams
 Analyzed and modeled diffusion-limited, coupled rate equations for doped scintillators, e.g. CsI:Tl Fall 2014-Summer 2015
 Aided in construction of a Bridgman furnace system for use in crystal growth analysis Winston-Salem, NC
 Performed Z-scanning and laser shock peening experiments in doped and undoped compounds to observe
non-linear quenching, stress, and fatigue effects in semiconductor crystal growth
 Designed and machined a multi-stage Stirling engine in conjunction with a $2M Phase I Department of Energy research grant
Non-Linear Oscillations Research, Wake Forest University Mathematics Department Advisor: Stephen B. Robinson
 Explored solutions to non-linear, 2nd
order, boundary-value problems incorporating the Shooting Method Fall 2013-Spring 2014
 Investigated solution dependence and the behavior with variation of initial boundary conditions Winston-Salem, NC
Computational Materials Science Research, Wake Forest University Physics Department Advisor: Natalie A.W. Holzwarth
 Examined and modeled the energetic and structural properties of solid materials, including lithium Fall 2012-Fall 2014
phosphate dielectrics for use in battery technology Winston-Salem, NC
 Gained experience using WFU’s cluster computer for applications in materials science modeling
 Developed datasets for computational materials science explorations shared on the web at: pwpaw.wfu.edu
 Created open source database of files to run computer simulations for materials on the atomic level
LABORATORY AND TECHNICAL SKILLS
 Nanotechnology/Laser Laboratory: Scanning Electron Microscope (SEM) (1yr.), Cleanroom protocol (1yr.), LABstar N2 Glovebox
Workstation (1yr.), Imagine3D Printer (1yr.), Z-scanning (1yr.), Confocal Microscopy (< 1 yr.) and WFU Machine Shop
 Abaqus FEA (1 yr.), COMSOL Multiphysics (1 yr.), CorelCAD (1yr.), C++ (1yr.), HTML & CSS coding (1yr.), Labview (1yr.), Linux
Terminal (3yrs.), LaTeX (1yr.), Maple (1yr.), Mathematica (2yrs.), MatLab (2yrs.), Microsoft Office Suite (4yrs.), & SolidWorks (1yr.)
PUBLICATIONS AND PRESENTATIONS
 J. L. Drewery and S.B. Robinson, Understanding Non-Linear Oscillations in Boundary-Value Problems, Involve, 2016. (In Prep.)
 J. L. Drewery, Modeling Materials: A Comparison of Two Projector-Augmented Wave Datasets, Academic Honors Thesis, 2014.
 J. L. Drewery, “Shooting” To Understand Non-Linear Oscillations, WFU Mathematics Senior Project, Oral Presentation, 2014.
 J.L. Drewery and N. Holzwarth, Dataset Creation and Methodology for Atomic Structures, WFU Research Day, Poster, 2013.
TEACHING EXPERIENCE AND STUDENT ENRICHMENT
Teaching Assistant, WFU Physics Department Supervisor: Fred Salsbury
 Proctored tests, graded and logged scores for calculus-based General Physics I & II to 150 students Spring 2013-Summer 2015
Laboratory Instructor, WFU Physics Department Supervisor: Keith Bonin
 Taught laboratories for Introductory and General Physics courses to 80 students Spring 2013-Summer 2015
Facilities and Laboratory Manager, WFU Physics Department Supervisor: Eric Chapman
 Prepared and managed equipment for 8 instructional laboratory sections Fall 2013-Summer 2015
Physics Tutor, WFU Learning Assistance Center/Student-Athlete Services Supervisor: Donalee White
 Conducted individual and group tutoring sessions in areas of: Physics I & II, Modern, and Electronics Fall 2013-Summer 2015
Page 3 of 40

4. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 1 of 8
INTERNSHIPS - SPRING 2016
GRADUATE: UNIVERSITY OF PENNSYLVANIA – SCHOOL OF ENGINEERING AND APPLIED SCIENCE
Master of Science – Mechanical Engineering and Applied Mechanics
Concentration: Heat Transfer, Fluid Mechanics, and Energy Science Engineering
UNDERGRADUATE: WAKE FOREST UNIVERSITY
Double Bachelor of Science: Mathematics and Physics with Honors
Page 4 of 40

5. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 2 of 8
Page 1. Relevant Courses Outline Page 2-4. Course Descriptions Page 5. Extra Classes
 Graduate: Master of Science: Mechanical Engineering and Applied Mechanics – UPENN:
- Finite Element Methods & Analysis
- Engineering Mathematics
- Engineering Entrepreneurship
- Topics in Computational Science and Engineering
- Viscous Fluid Flow
- Performance & Design of Unmanned Aerial Vehicles (UAVs)
 Undergraduate: Bachelor of Science: Mathematics – Wake Forest University:
- Calculus of a Single Variable with Analytic Geometry I & II
- Multivariable Calculus
- Discrete Mathematics
- Linear Algebra
- Ordinary Differential Equations
- Partial Differential Equations
- Introductory Real Analysis of Numbers
- Modern Algebra I
- Numerical Linear Algebra
- Differential Geometry
- Research (2 semesters)
- Senior Seminar Presentation – “Shooting” to Understand Non-Linear Boundary Value Problems and
Oscillations
 Undergraduate: Bachelor of Science: Physics – Wake Forest University:
- Introductory Physics
- General Physics I & II
- Elementary Modern Physics
- Electronics
- Mechanics
- Analytical Mechanics
- Electricity and Magnetism
- Thermodynamics and Statistical Mechanics
- Quantum Mechanical Physics
- Intermediate Physics Laboratory (2 semesters)
- Research (4 semesters, 2 summers)
- Senior Academic Honors Thesis and Presentation – Modeling Materials: Comparison of Two Projector-
Augmented Wave (PAW) Datasets
Page 5 of 40

6. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 3 of 8
The relevant course descriptions as outlined by the UPENN 2015 Bulletin found here (MEAM) and here
(ENM).
1 of 3. Mechanical Engineering and Applied Mechanics (Master of Science):
Numerical and Finite Element Methods & Analysis
- The objective of this course is to equip students with the background needed to carry out finite elements-based
simulations of various engineering problems. The first part of the course will outline the theory of finite
elements. The second part of the course will address the solution of classical equations of mathematical physics
such as Laplace, Poisson, Helmholtz, the wave and the Heat equations. The third part of the course will consist
of case studies taken from various areas of engineering and the sciences on topics that require or can benefit
from finite element modeling. The students will gain hand-on experience with the multi-physics, finite element
package FemLab.
Engineering Entrepreneurship
- Engineers and scientists create and lead great companies, hiring managers when and where needed to help
execute their vision. Designed expressly for students having a keen interest in technological innovation, this
course investigates the roles of inventors and founders in successful technology ventures. Through case studies
and guest speakers, we introduce the knowledge and skills needed to recognize and seize a high-tech
entrepreneurial opportunity - be it a product or service - and then successfully launch a startup or spin-off
company. The course studies key areas of intellectual property, its protection and strategic value; opportunity
analysis and concept testing; shaping technology driven inventions into customer-driven products; constructing
defensible competitive strategies; acquiring resources in the form of capital, people and strategic partners; and
the founder's leadership role in an emerging high-tech company. Throughout the course emphasis is placed on
decisions faced by founders, and on the sequential risks and determinants of success in the early growth phase
of a technology venture.
Engineering Mathematics Foundations
- This is the first course of a two semester sequence, but each course is self-contained. Over the two semesters
topics are drawn from various branches of applied mathematics that are relevant to engineering and applied
science. These include: Linear Algebra and Vector Spaces, Hilbert spaces, Higher-Dimensional Calculus,
Vector Analysis, Differential Geometry, Tensor Analysis, Optimization and Variational Calculus, Ordinary and
Partial Differential Equations, Initial-Value and Boundary-Value Problems, Green's Functions, Special
Functions, Fourier Analysis, Integral Transforms and Numerical Analysis. The fall course emphasizes the study
of Hilbert spaces, ordinary and partial differential equations, the initial-value, boundary-value problem, and
related topics.
Topics in Computational Science and Engineering
- This course is focused on techniques for numerical solutions of ordinary and partial differential equations. The
content will include: algorithms and their analysis for ODEs; finite element analysis for elliptic, parabolic and
hyperbolic PDEs; approximation theory and error estimates for FEM. Background in ordinary and partial
differential equations; proficiency in a programming language such as MATLAB, C, or Fortran.
Page 6 of 40

7. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 4 of 8
Viscous Fluid Flow and Modern Applications
- This course is intended for juniors, seniors and graduate students from the Schools of Engineering and/or Arts
and Sciences that have a general interest in fluid dynamics and its modern applications. Students should have an
understanding of basic concepts in fluid mechanics and a good grasp on differential equations.
Performance and Design of Unmanned Aerial Vehicles (UAVs)
- Review of fluid kinematics and conservation laws; vorticity theorems; two-dimensional potential flow; airfoil
theory; finite wings; oblique shocks; supersonic wing theory; laminar and turbulent boundary layers. Additional
review of basic concepts of: pressure, density, velocity, forces. The standard atmosphere. Introduction to low
speed aerodynamics. Airfoils, wings, and other aerodynamic shapes. Aircraft performance. Aircraft stability and
control. Aircraft propulsion and sizing. Bernoulli’s principle. Angle of attack. Propeller analysis: Variable pitch
and variable speed. DC motors. IC engines and gas turbines. Multicopter near-hover performance. Longitudinal
moments. Non-symmetric flights and turns. Interactive deviation of range. Interactive design and analysis.
Seminar – Mechanical Engineering and Applied Mechanics
- The seminar course has been established so that students get recognition for their seminar attendance as well
as to encourage students to attend. Students registered for this course are required to attend weekly departmental
seminars given by distinguished speakers from around the world. There will be no quizzes, tests, or homework.
The course will be graded S/U. In order to obtain a satisfactory (S) grade, the student will need to attend more
than 70% of the departmental seminars. Participation in the seminar course will be documented and recorded on
the student’s transcript. In order to obtain their degree, doctoral students will be required to accumulate six
seminar courses and MS candidates (beginning in the Fall 2001) two courses.
Page 7 of 40

8. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 5 of 8
The relevant course descriptions as outlined by the WFU 2010 Bulletin found here.
2 of 3. Mathematics Degree (Bachelor of Science):
Calculus of a Single Variable with Analytic Geometry I & II
- (I). Functions, trigonometric functions, limits, continuity, differentiation, applications of derivatives,
introduction to integration, and the fundamental theorem of calculus.
- (II). Techniques of integration, indeterminate forms, improper integrals, transcendental functions, sequences,
Taylor's formula, and infinite series, including power series.
Multivariable Calculus
- The calculus of vector functions, including geometry of Euclidean space, differentiation, extrema, line
integrals, multiple integrals, Green's theorem, Stokes' theorem, and divergence theorem.
Discrete Mathematics
- Introduction to various topics in discrete mathematics applicable to computer science including sets, relations,
Boolean algebra, propositional logic, functions, computability, proof techniques, graph theory, and elementary
combinatorics.
Linear Algebra
- Vectors and vector spaces, linear transformations and matrices, determinants, eigenvalues, and eigenvectors.
Ordinary Differential Equations
- Linear equations with constant coefficients, linear equations with variable coefficients, and existence and
uniqueness theorems for first order equations.
Partial Differential Equations
- Detailed study of partial differential equations, including the heat equation, wave equation, and Laplace
equations, using methods such as separation of variables, characteristics, Green's functions, and the maximum
principle.
Introductory Real Analysis of Numbers
- Limits and continuity in metric spaces, sequences and series, differentiation and Riemann-Stieltjes integration,
uniform convergence, analytics functions, Cauchy sequences, Cauchy's theorem and its consequences, proof
techniques, power series and Fourier series, differentiation of vector functions, implicit and inverse function
theorems.
Modern Algebra I
- Introduction to modern abstract algebra through the study of groups, rings, integral domains, and fields.
Numerical Linear Algebra
- Numerical methods for solving matrix and related problems in science and engineering using a high-level
matrix-oriented language like MatLab. Topics include systems of linear equations, least squares methods, and
eigenvalue computations along with special emphasis given to applications.
Page 8 of 40

9. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 6 of 8
Differential Geometry
- Introduction to the theory of curves and surfaces in two and three dimensional space, including such topics as
curvature, geodesics, minimal surfaces, Fundamental Frenet and Bishop Frames, and the Theorema Egregium.
Research (2 semesters)
- Individual research conducted with a faculty member on which the student presents the WFU staff with in
completion of the major. (Required for all B.S majors)
Senior Seminar Presentation - Boundary/Initial Value Problems
- Preparation of a senior thesis paper followed by a one-hour oral presentation based upon work in a research
class. (My work was in the study of Non-Linear Oscillations in Boundary and Initial Value problems conducted
under Dr. Stephen Robinson)
Page 9 of 40

10. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 7 of 8
3 of 3. Physics Degree (Bachelor of Science):
Introductory Physics
- Conceptual, non-calculus one-semester survey of the essentials of physics, including mechanics, wave motion,
heat, sound, electricity, magnetism, optics, and modern physics.
General Physics I & II
- (I) Essentials of mechanics, wave motion, heat, and sound treated with some use of calculus.
- (II) Essentials of electricity, magnetism, optics, and modern physics related with some calculus.
Elementary Modern Physics
- Development of 20th-century physics and an introduction to quantum mechanical ideas.
Electronics
- Introduction to the theory and application of transistors and electronic circuits.
Mechanics
- Study of the equations of motion describing several kinds of physical systems: velocity-dependent forces;
damped and forced simple harmonic motion; orbital motion; inertial and non-inertial reference frames. Includes
extensive use of computers and software such as MatLab, Maple, and Mathematica.
Analytical Mechanics
- The Lagrangian and Hamiltonian formulations of mechanics with applications.
Electricity and Magnetism
- Electrostatics, magnetostatics, dielectric and magnetic materials, Maxwell's equations and applications to
radiation, relativistic formulations.
Thermodynamics and Statistical Mechanics
- Introduces classical and statistical thermodynamics and distribution functions.
Quantum Mechanical Physics (2 semesters)
- Basic quantum theory and applications including the time-independent Schrödinger equation, formalism and
Dirac notation, the hydrogen atom, spin, identical particles, and approximation methods. Perturbation theory
(Time independent and Time Dependent), Variational Principle, and WKB approximations.
Intermediate Physics Laboratory (2 semesters)
- Experiments on mechanics, modern physics, electronics, and computer simulations.
Research (3 semesters, 2 summers)
- Literature, conference, computation, and laboratory work performed on an individual basis. My project was in
Computational Materials Science under Dr. Natalie Holzwarth.
Page 10 of 40

11. James L. Drewery II
3600 Chestnut St, Philadelphia, PA 19104 Email: drjames@seas.upenn.edu Webpage: http://goo.gl/aEfa1B Phone: (704) 477-6423
Page 8 of 8
Additional Classes Taken (Undergraduate Credits)
These are several additional classes I have taken that show aptitudes in subjects besides
Mathematics and Physics disciplines.
United States History (AP Credit)—High School
Calculus AB (AP Credit) – High School
Freshman Writing Seminar
Elementary German
Health and Exercise Science I
Accessing Information in the 21st
Century
Fascism, Exile, and 20th
Century German Ideals
Intermediate German
Personality Psychology
Introductory Psychology
Lifestyles and Health
Western Civilization
Intro to Philosophical Ideas
Intro to German Short Fiction
Relational Communication
20th
Century Modern Dance History
Studies in British Literature
Page 11 of 40

12. Display Transcript 06183360 James L. Drewery
Jul 20, 2014 10:04 pm
This is NOT an official transcript. Courses which are in progress may also be included on
this transcript.
Transfer Credit Institution Credit Transcript Totals
Transcript Data
STUDENT INFORMATION
Name : James L. Drewery
***This is NOT an Official Transcript***
TRANSFER CREDIT ACCEPTED BY INSTITUTION -Top-
Summ
II
2010:
Advanced Placement Credit
Subject Course Title Grade Credit
Hours
Quality Points R
HST 150 United States
History
AP 3.000 0.000
MTH 111 Calculus/ Analytic
Geom I
AP 4.000 0.000
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 0.000 7.000 7.000 0.000 0.000 0.000
Unofficial Transcript
INSTITUTION CREDIT -Top-
Term: Fall 2010
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
ENG 111 UG Writing Seminar B- 4.000 10.680
GER 111 UG Elementary German B+ 4.000 13.320
HES 101 UG Exercise for Health A 1.000 4.000
LIB 100 UG Accessing Info in 21st Cent A 1.000 4.000
PHY 110 UG Introductory Physics A- 4.000 14.680
PHY 110L UG Intro Physics Lab NC 0.000 0.000
Page 12 of 40

13. PSY 151 UG Introductory Psychology B+ 3.000 9.990
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 17.000 17.000 17.000 17.000 56.670 3.333
Cumulative: 17.000 17.000 17.000 17.000 56.670 3.333
Unofficial Transcript
Term: Spring 2011
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
FYS 100 UG Fascism, Excile & 20th Cent B 3.000 9.000
GER 112 UG Elementary German B 4.000 12.000
HES 100 UG Lifestyles and Health A 1.000 4.000
MTH 112 UG Calculus / Analytic Geom II A- 4.000 14.680
PSY 255 UG Personality B+ 3.000 9.990
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 15.000 15.000 15.000 15.000 49.670 3.311
Cumulative: 32.000 32.000 32.000 32.000 106.340 3.323
Unofficial Transcript
Term: Fall 2011
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
GER 153 UG Intermediate German B 4.000 12.000
MTH 113 UG Multivariable Calculus C+ 4.000 9.320
MTH 121 UG Linear Algebra I B 3.000 9.000
PHY 113 UG General Physics I B 4.000 12.000
PHY 113L UG General Physics Lab NC 0.000 0.000
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 15.000 15.000 15.000 15.000 42.320 2.821
Cumulative: 47.000 47.000 47.000 47.000 148.660 3.162
Unofficial Transcript
Term: Spring 2012
Subject Course Level Title Grade Credit Quality R
Page 13 of 40

14. Hours Points
HST 101 UG Western Civ. to 1700 B- 3.000 8.010
MTH 117 UG Discrete Mathematics B- 4.000 10.680
PHI 112 UG Intro to Phil Ideas C+ 3.000 6.990
PHY 114 UG General Physics II B- 4.000 10.680
PHY 114L UG General Physics II Lab NC 0.000 0.000
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 14.000 14.000 14.000 14.000 36.360 2.597
Cumulative: 61.000 61.000 61.000 61.000 185.020 3.033
Unofficial Transcript
Term: Fall 2012
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
GER 212 UG Intro to German Short Fiction B 3.000 9.000
MTH 251 UG Ordinary Differential Equation B- 3.000 8.010
MTH 311 UG Introductory Real Analysis I F 3.000 0.000 E
PHY 215 UG Elementary Modern Physics A- 3.000 11.010
PHY 265 UG Intermediate Laboratory B+ 1.000 3.330
PHY 301 UG Physics Seminar P 0.500 0.000 I
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 13.500 10.500 10.500 10.000 31.350 3.135
Cumulative: 74.500 71.500 71.500 71.000 216.370 3.047
Unofficial Transcript
Term: Spring 2013
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
COM 113 UG Relational Communication B- 3.000 8.010
MTH 321 UG Modern Algebra I B- 3.000 8.010
MTH 334 UG Differential Geometry C 3.000 6.000
PHY 230 UG Electronics B 3.000 9.000
PHY 262 UG Mechanics B+ 3.000 9.990
PHY 266 UG Intermediate Laboratory A 1.000 4.000
PHY 301 UG Physics Seminar P 0.500 0.000 I
PHY 381 UG Research A 1.500 6.000 I
Page 14 of 40

15. Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 18.000 18.000 18.000 17.500 51.010 2.914
Cumulative: 92.500 89.500 89.500 88.500 267.380 3.021
Unofficial Transcript
Term: Fall 2013
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
DCE 203 UG 20th C Mod Dance History A 3.000 12.000
MTH 311 UG Introductory Real Analysis I B+ 3.000 9.990 I
MTH 326 UG Numerical Linear Algebra C 3.000 6.000
MTH 391 UG Senior Seminar Preparation D 1.000 1.000
PHY 337 UG Analytical Mechanics A 1.500 6.000
PHY 339 UG Electricity and Magnetism A 1.500 6.000
PHY 343 UG Quantum Physics C+ 3.000 6.990
PHY 381 UG Research A 3.000 12.000 I
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 19.000 19.000 19.000 19.000 59.980 3.156
Cumulative: 111.500 108.500 108.500 107.500 327.360 3.045
Unofficial Transcript
Term: Spring 2014
Additional Standing: *Dean's List
Subject Course Level Title Grade Credit
Hours
Quality
Points
R
ENG 165 UG Studies in British Literature A- 3.000 11.010
MTH 352 UG Partial Differential Equations B- 3.000 8.010
MTH 392 UG Senior Seminar Presentation A 1.000 4.000
PHY 340 UG Electricity and Magnetism A 3.000 12.000
PHY 341 UG Statistical Physics B 3.000 9.000
PHY 344 UG Quantum Physics A 3.000 12.000
PHY 381 UG Research A 3.000 12.000 I
Term Totals (Undergraduate)
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Current Term: 19.000 19.000 19.000 19.000 68.020 3.580
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16. Cumulative: 130.500 127.500 127.500 126.500 395.380 3.125
Unofficial Transcript
TRANSCRIPT TOTALS (UNDERGRADUATE) -Top-
Attempt
Hours
Passed
Hours
Earned
Hours
GPA
Hours
Quality
Points
GPA
Total Institution: 130.500 127.500 127.500 126.500 395.380 3.125
Total Transfer: 0.000 7.000 7.000 0.000 0.000 0.000
Overall: 130.500 134.500 134.500 126.500 395.380 3.125
Unofficial Transcript
RELEASE: 8.4.1
Page 16 of 40

17. 1/18/2016 Unofficial Transcript and GPA
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Unofficial Transcript and GPA
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Unofficial Transcript as of: 01/18/16 17:22:12 PM
AT THE GRADUATE LEVEL IN ENGINEERING
* * * * * * * * * * ACADEMIC PROGRAM * * * * * * * * * * *
School: ENGINEERING & APPLIED SCIENCE
Division: ENGINEERING & APPLIED SCIENCE MASTERS
Degree Program: MASTER OF SCIENCE IN ENGINEERING
Major: MECHANICAL ENGR & APPLIED MECHANICS
* * * * * UNIVERSITY OF PENNSYLVANIA COURSE WORK * * * * * *
Fall 2015 ENGINEERING & APPLIED SCIENCE MASTERS
EAS 545 ENG ENTREPRENEURSHIP I 1.00 CU A
ENM 510 FNDATIONS OF ENG MATH I 1.00 CU C+
MEAM 527 NUM & FIN ELE MTHDS 1.00 CU B‐
Term Statistics: 3.00 CU GPA 3.00
Cumulative: 3.00 CU GPA 3.00
Spring 2016 ENGINEERING & APPLIED SCIENCE MASTERS
ENGR 503 ENG IN OIL,GAS&COAL (1.00) CU NR
ENM 511 FNDATIONS OF ENG MATH II (1.00) CU NR
MEAM 642 ADVANCED FLUID MECHANICS (1.00) CU NR
Term Statistics: 0.00 CU
Cumulative: 3.00 CU GPA 3.00
* * * * * * * NO ENTRIES BEYOND THIS POINT * * * * * * * *
Page 17 of 40

18. JAMES L. DREWERY II
3600 Chestnut Street
Philadelphia, PA 19104-6106
(704) 477-6423
drjames@seas.upenn.edu
https://sites.google.com/site/dreweryiijames/
https://www.linkedin.com/pub/james-drewery/99/915/663/
REFERENCES:
1. Dr. Natalie A.W Holzwarth
Professor - Physics
300 Olin Physical Laboratory
Wake Forest University
P.O. Box 7507
1834 Wake Forest Road
Winston-Salem, NC 27109-7507
(336) 758-5510 - Work
(336) 749-9457 - Cell
natalie@wfu.edu
http://users.wfu.edu/natalie/
Relationship: Employer, Physics Professor,
Research Advisor, and mentor at Wake
Forest University from 2011–2015.
Employer: Wake Forest University Physics
Department.
2. Dr. Richard Williams
Reynolds Professor
212 Olin Physical Laboratory
Wake Forest University
P.O Box 7507
1834 Wake Forest Road
Winston-Salem, NC 27109-7507
(336) 758-5132 – Work
(910) 759-5132 – Cell
williams@wfu.edu
http://physics.wfu.edu/people/williams.html
https://sites.google.com/a/wfu.edu/williams/
Relationship: Employer, Physics Professor,
Research Advisor, and mentor at Wake
Forest University from 2014-2015.
Employer: Wake Forest University Center
for Energy, Environment, and Sustainability
(CEES).
3. Dr. David Carroll
Associate Professor
214 Olin Physical Laboratory
Wake Forest University
P.O. Box 7507
1834 Wake Forest Road
Winston-Salem, NC 27109-7507
(336) 727-1806 - Work
(336) 403-2289 - Cell
carroldl@wfu.edu
http://users.wfu.edu/carroldl/Prof._Carroll.html
http://nanotech.wfu.edu/Welcome.html
Relationship: Employer, Physics Professor,
Research Advisor, and mentor at Wake
Forest University from 2013-2015.
Employer: Wake Forest University Center
for Nanotechnology and Molecular Materials
(CNMM).
Page 18 of 40

19. James L. Drewery II
When I was a sophomore at Wake Forest University (WFU), I attended a physics seminar
regarding energy harvesting methods. While most of this lecture focused on the physics of this topic, there
was a substantial discussion about the global consequences of not addressing this problem. Having grown
up on a family farm I knew there was high demand for energy, but I had never realized the magnitude of
the circumstances. If the energy crisis is not solved in the coming years, future generations will struggle
with a lack of resources and poor environmental conditions. Needless to say, when I walked out of that
lecture hall, both my curiosity and concern for the future were ignited. Since that day, I have dedicated
myself to finding a solution for this problem.
One of the most important things I have learned about energy is that the United States (US) relies
heavily upon the non-renewable hydrocarbon resources of other countries. As a major consumer of energy,
this dependence makes the US highly vulnerable to both the whims of foreign countries and the
environment itself. Fortunately, however, the US has the answer to this problem right at home; its lands are
adorned with bountiful sunlight and natural resources, such as wind, water, and natural gas. The US needs
to focus on how to use these resources to implement clean, cost-effective, and renewable energy
technologies in order to develop a long-term, sustainable energy infrastructure.
It is my hope that I can help solve this problem by studying Mechanical Engineering with a
specialization in energy conversion, energy development, and/or in the manufacturing of energy-related
devices at the University of Pennsylvania (UPENN). I believe that this education will provide me with the
skillset necessary to contribute to the efficient development of the US’s energy infrastructure.
As an undergraduate captivated by physics, I sought to answer a simple question– how will
mankind address the ever-increasing demand for energy? This curiosity was sparked by Dr. Natalie
Holzwarth, a physics professor at WFU. Her research on battery technology involving the application of
computational materials science to energy storage greatly interested me. Fascinated by the idea of creating
more efficient, high-capacity, and low-cost energy storage devices, I joined her Computational Modeling
research group in 2012. I have since conducted computational physics and mathematical research for five
undergraduate semesters and worked one year as a full-time experimental laboratory research assistant.
With Dr. Holzwarth, I performed a first principles computational analysis of atomic and crystalline
lattice structures for elementary and binary compounds. I generated projector-augmented wave (PAW)
pseudopotential datasets. These incorporate detailed atomic information into ab initio electronic structure
calculations for elements on the periodic table. I used the WFU high-performance cluster to compare
independent computational methods. I tested the accuracy of binding energy vs. lattice constant curves. The
summer of my junior year, WFU awarded me a Research Fellowship, which allowed me to continue the
project, as well as to perform a comparison analysis between our pseudopotentials and those of our
collaborators. This accuracy testing, along with considerations of computational expenses and choice of
electron states, formed the basis for my academic Honors Thesis in Physics. Our group used these
molecular dynamics simulation methods to study ionic conductivity in solid electrolytes. The simulations
provide insight into the effects of atomic-level events on the macroscopic behavior of solid electrolyte
materials. One application of the project involved using these datasets to model the lithium thiophosphate
electrolyte (Li4P2S6) as a possible solid electrolyte material in lithium-ion batteries. Additionally, I
optimized our group webpage using HTML and CSS programming skills. I wrote a series of BASH scripts
that ran simulations for the datasets to make sharing our updated research quicker and more efficient. This
project taught me how computational research and modeling can be used in conjunction with experimental
research to provide the foundation for novel technology and innovation.
During my senior year, I researched nonlinear oscillations in boundary value problems (BVPs)
with Dr. Stephen Robinson. I observed the behavior of certain types of second-order, nonlinear BVPs.
Incorporating principles from real analysis and differential equations, we made conjectures as to the
existence and number of solutions. Experiments using Maple and the shooting method showed a
dependence on the choice of initial slope and integer-constant sign in the differential equation. Results were
formally presented in the spring of 2014 and are currently in preparation for submission to Involve, an
undergraduate research journal. I learned to rigorously test a hypothesis and write methodically, as is
Page 19 of 40

20. expected in a graduate level research position. The engineering mathematics offered at UPENN will
provide me with the meticulous understanding of mechanical systems needed to improve energy research.
My successes and interests in science and engineering earned me a dual appointment at the WFU
Center for Energy, Environment, and Sustainability (CEES) under Dr. Richard Williams and at the WFU
Center for Nanotechnology and Molecular Materials (CNMM) under Dr. David Carroll. These
experimental research projects complement my computational physics and modeling backgrounds to make
me a well-rounded student. These opportunities have allowed me to further my pursuits into energy-related
devices research.
In Dr. Williams’ optics group, we are working to improve scintillation detectors with promising
new materials. By observing dopant effects in Yttrium Aluminum Perovskite (YAP), we are attempting to
model the linearity, or proportionality, of the material’s light yield with particle energy. This involves
measuring materials’ related electrical and optical properties for input to the model. To simulate energetic
particle tracks, I am testing an in-house code that models exciton formation and recombination rates in
semiconductors. As the code incorporates values determined in other papers, I learned to develop a
methodical literature review, a skill which will benefit me greatly at UPENN and as a future engineer. I
performed interband Z-scan light-yield experiments to analyze nonlinear quenching effects in the doped
materials. Aiding in the construction of a Bridgman furnace for in-house crystal growth, I designed the
fume hood apparatus to control heat dispersion. I performed laser shock peening experiments to study the
mutual interaction of intense pulsed laser light, strain, and temperature in brittle crystals. The initial work
consisted of nanosecond pulses of Nd:YAG in the 4th
and 5th
harmonic. For a joint DOE research grant, I
designed and machined a multi-stage Stirling engine to work with a linear Fresnel solar concentrator as the
heat source. This project correlates directly with my goals to understand how energy is harnessed.
To further supplement my computationally-based experience, I began experimental research under
Dr. Carroll studying organic photovoltaics (OPV) and thermoelectrics. I worked on different levels of OPV
development and device fabrication. I used a 3-D printer to hermetically seal the lighting and OPV devices
within a N2 glove box setting. This allows for more precision during the epoxy layer application. Doing so
systematically creates more control and uniformity in the final stages of the solar cell fabrication process.
The project enriched my understanding of experimental design and how to solve problems by
implementing practical solutions. In addition, I have grown in my knowledge of each iteration of the
manufacturing process, which I will apply in the production of energy-related devices.
My future aspirations in energy and sustainability are the direct result of the research opportunities
I received at WFU. During the last four years, I have worked in three research groups comprised of highly
dedicated and passionate individuals. My experiences endowed me with an intimate knowledge which will
be used to contribute to the innovation and advancement of the fields of energy conversion, storage, and
sustainability at UPENN. As a researcher, my success will depend, in part, on a close-knit scientific
community. I strive to be a part of cross-disciplinary research where collaboration among colleagues and
students facilitates a focused, yet eclectic, approach to solving energy-related problems. The Penn Center
for Energy Innovation, or Pennergy, and similar green-campus initiatives address important energy-related
concepts and constitutes why I find UPENN so desirable.
I am compelled to contribute to solving the contemporary issue of depleting energy sources and
finding a clean, renewable, and accessible alternative through scientific research. My strong work ethic,
coupled with a devotion and passion for research, has facilitated my understanding of the fundamental
principles of physics and mathematics. My interactions with scientists and engineers who have developed
on theory and applied findings to solve contemporary problems have uniquely exposed me to the
possibilities in energy research. My ultimate career goal as an engineer is to improve efficiency in energy
development and pursue alternative clean energy sources such as solar, thermal, wind, and hydroelectric
energy. This requires the development of a certain technical skillset and understanding of energy, both of
which I am confident I will acquire at UPENN. It is with these skills that I hope to explore the complexities
of Mechanical Engineering, energy conversion, storage, and sustainability to one day find myself leaving a
significant impact on the world. I look forward to my future as a graduate student at the esteemed UPENN.
Page 20 of 40

21. Page 1 of 20
Modeling Materials: Comparison of Two Projector-Augmented Wave (PAW) Datasets
A paper presented to the faculty of the Department of Physics of Wake Forest University in
partial fulfillment of the requirements for graduation with Honors in Physics
James Lewis Drewery II
May 9, 2014
Approved by:
______________________________________________
Dr. Natalie Holzwarth
______________________________________________
Dr. Timo Thonhauser
______________________________________________
Dr. Freddie Salsbury Jr.
Page 21 of 40

22. Page 2 of 20
Table Of Contents
1. Introduction
1.1 Motivation
1.2 Computational Requirements
1.3 Road to Thesis
2. Computational Methods
2.1 Basic Formalism
2.1.1 Pseudopotentials and PAW
2.2 Software
2.2.1 ATOMPAW
2.2.2 ABINIT
2.2.3 WIEN2K
2.2.4 Brief Summary of Code Usage
2.2.5 Binding Energy and Lattice Constant
3. Thesis Components
3.1 Atomic Configuration
3.2 Matching Radius Selection
4. Tools For Comparison
4.1 Wavefunction Analysis and Logderivatives
4.2 Projector Wave Functions
5. Problems
5.1 Ghost States
6. Conclusions
6.1 Delta Factor
7. Acknowledgments and Collaborators
8. References
Page 22 of 40

23. Page 3 of 20
1. Introduction
1.1 Motivation: Why Model Materials
Materials science has become one of the most predominantly studied areas of physics today.
Simulating atomic interactions may provide physicists with an experimental advantage. The use of
computational modeling provides a quick and efficient means of analyzing properties of materials on
the atomic level. Computational modeling of materials is an important tool in the development of
new technologies. A potential focus of this technology is in energy storage. The simulation of new and
innovative ways of designing batteries may lead to a cleaner and more efficient world. Although it is
unlikely that perfect battery designs will be a result of this simulation process alone, it may provide
experimentalists with a foundation as to what may in fact yield possible results.
1.2 Computational Requirements
The simulation of materials requires initial data input, or datasets, for each constituent atom. Each
dataset contains all of the important information needed to represent the atom that figures in the
simulation of materials containing that atom. Upon coming to work with Professor Holzwarth, the
creation of these initial datasets was the main focus of my research. With the help of Marc Torrent’s
user guide for the ATOMPAW computer program, and the watchful eye of my mentor, I came to
understand how the physics I had been exposed to until this point reflects in a legitimate research
endeavor. Fresh out of PHY 215, the capabilities of applying Modern Physics to our research was
amazing. Understanding quantum numbers, electron configurations and placement, atomic radii, and
more were things that were at the heart of my research in the beginning. Cameron Kates and myself
worked together to update an online database of these atomic inputs. Our process was systematic in
nature. We hoped to find an approach that for any given element, we could create a particularly
effective atomic input that would work with several materials simulation software packages.
1.3 Road to Thesis
Initially, my work with Dr. Holzwarth consisted solely in the creation of the aforementioned datasets,
together with Cameron Kates, Zachary Pipkorn, and Chaochao Dun. This research encompassed my
final semester Junior year and the following summer during the Wake Forest Research Fellowship.
At the end of the summer, one Dr. Holzwarth’s French collaborators, Francois Jollet, compiled a similar
database of atomic inputs (Jollet, Torrent, and Holzwarth).
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24. Page 4 of 20
Jollet had a very eclectic approach in his dataset creation. It was in the testing and comparison of
these two databases of atomic datasets that my thesis was based. I began testing the French datasets
with the ones that we had created and found some very interesting conclusions. I was successful in
the comparison of many compound materials. From these comparisons, I was able to draw several
conclusions as to what parameters were most likely more pertinent in the atomic simulations.
Additionally, a hypothesis was made about which method was more effective in creating these inputs.
I found that with a more liberal choice of valence state electrons, versus core state electrons, that our
results were generally more similar to what we took as our standard. In choosing more valence state
electrons, we found a general trend in that our datasets were better than Jollet’s, but at a price. The
computational cost of including more valence states was something that Jollet was able to work
around and still yield results very to ours, and at times better. Also, his process of using many formats
and approaches to build his database showed striking contrast to our systematic approach and raises
questions as to which is in fact a better method. Ideally, a universally accepted approach would greatly
benefit computational material science research. As a possible step toward this, I offer a detailed
analysis of the differences found between our dataset results and that of Jollet’s.
2. Computational Methods
2.1 Basic Formalism
The starting point of the simulations is the self-consistent electronic structure of an atom within the
framework of Density Functional Theory (DFT) (Hohenberg and Kohn). The idea is that we can model
an atom by incorporating First Principles calculations. This means that we are using only established
laws of physics and we are not taking into account any outside or predetermined experimental data.
First Principles simulations of materials are an important tool for basic research and the development
of new techniques. Additionally, because we will want to model elements that will actually have many
electrons, we incorporate Mean-Field approximations and also Density Functional Theory (DFT).
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25. Page 5 of 20
With this First Principles basis and use of DFT for our calculations, we are able to illustrate what how
the wave function will behave for the all-electron case. To illustrate this, first recall the Schrödinger
Equation,
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1: 𝐻𝜓 = 𝐸𝜓
and that the Hamiltonian represents the kinetic energy plus the potential energy. Here, the
Hamiltonian of the atom is defined such that,
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2: 𝐻(𝑟) 𝑎𝑡𝑜𝑚 = −
ℏ2
2𝑚
∇2
−
𝑍𝑒2
𝑟
+ 𝑉𝑒𝑒(𝑟) + 𝑉𝑋𝐶(𝜌(𝑟)) .
The first term represent the kinetic energy of the electron, the second term represents the Coulomb
interaction of an electron with the nucleus of charge Z in cgs units, or 𝑒
2
𝑟, 𝑉𝑒𝑒(𝑟) is the electron-
electron potential, and 𝑉𝑋𝐶(𝑟) is the exchange correlation due to the DFT calculation. This is the
effective Hamiltonian that acts on each electron. With respect to DFT, we assume a local-density
approximation (LDA) for our calculations (Perdew and Wang). Mean-Field Theory and DFT are figure
prominently in our research as they provide the basis for our calculations. This is simply how our
software code is designed to find the All-Electron wave functions for which we are trying to more
smoothly approximate with our Pseudowave functions. The main take away from these two theories
is rather simple. For Mean-Field theory, we suppose that each electron sees an average of all the
others. As such, we replace the individual electrons instead by an electron charge density.
2.1.1 Pseudopotentials and PAW
The All-Electron case takes into account both core and valence state electrons. However, in materials
modeling, the important contributions come from the valence electrons only. Pseudopotentials were
invented to further approximate the valence electrons so that they may be numerically well
represented in solid simulations. The Projector Augmented Wave scheme (PAW) was developed by
Peter Bloechl is a more accurate and efficient Pseudopotential method (Blöchl).
We need to create the PAW dataset to represent the valence electron properties for each atom.
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26. Page 6 of 20
2.2 Software
2.2.1 ATOMPAW
ATOMPAW is a computer program that we used in the creation of atomic projector and basis functions
for our electronic structure calculations (Holzwarth, Tackett, and Matthews). This code incorporates
the PAW method as previously mentioned. ATOMPAW is the first code which we run to create our
datasets. The resultant output from running the code yields the datasets that are used to model the
solid materials. These datasets include the All-Electron and Pseudo basis functions and corresponding
Projector functions. In addition, the datasets include Pseudopotential functions and matrix elements
for each atom.
2.2.2 ABINIT
ABINIT is a program that allows us to use our Pseudo functions to test for the total energy, charge
density, and electronic structure of our electronic structure (Gonze et al.). After running ATOMPAW,
we take our “ideal” cases and we can test them by running them on the ABINIT software. The main
point of this program is to check that ATOMPAW outputs or datasets can reliably describe the
properties of materials made of those atoms. In particular, our main focus was to compute the
Binding Energy versus lattice constant for simple binary compounds and elemental solids with an
LAPW standard.
2.2.3 WIEN2k
The WIEN2k plot is derived using a Linearized Plane Wave method, or LAPW (Schwarz and Blaha). This
is another technique for generating Binding Energy vs. Lattice constant curves. The WIEN2k software
is what we consider to be our “standard” by which we compare both our results and those of the
generated datasets by Jollet. We take this to be a standard because it is another process for finding
the exact same results, a Binding Energy vs. Lattice Constant plot, using a method completely
independent of the use of Pseudopotentials. My main source of research of the Pseudopotential
approach came from reading Electronic Structure: Basic Theory and Practical Methods (Martin).
2.2.4 Brief Summary of Code Usage
The use of the two previously described codes is to find the best suited Pseudopotential wave function
that smoothly approximates the All-Electron case. In the dataset generation phase, one is yielded with
many results given the range of input parameters.
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27. Page 7 of 20
Taking this range and finding the case with minimum error between the Pseudo case and the All-
Electron case yields the choice of input parameters for ABINIT. Running this final code yields a Binding
Energy vs. Lattice Constant curve that we can compare to our standard which is the Wien2k, or LAPW,
plot.
2.2.5 Binding Energy and Lattice Constant
The result that will be of most importance to our analysis will be that of the Binding Energy vs. Lattice
Constant plot. It is important to describe what each of these parameters represents. The minimum of
the Binding Energy curve occurs at the equilibrium lattice constant and the curvature represents the
bulk modulus (“Binding Energy (physics) -- Britannica Online Encyclopedia”). The Lattice Constant is a
degree of proximity between the atoms in the unit cell of our calculations. We wanted to test our
datasets to see if they accurately modeled the near-equilibrium properties of materials containing the
atoms in question. Our process was to make these graphs and see if the ABINIT and WIEN2k curves
visually coincided. We wanted to keep the calculations simple so we chose several elemental
materials and binary compounds for the comparison. We also had to specify the structure of the cell
for each compound before we ran ABINIT and WIEN2k. The structures mostly consisted of simple
cubic, Body-Centered Cubic, Face-Centered Cubic, Zinc-blende, and Diamond orientations (given in
order by Figure 1).
Figure 1: Showing possible cell structures in which we incorporated into our calculations (SC, BCC, FCC,
ZB, D ( Van Zeghbroeck, B.)
3. Thesis Components
It is very important that a clear distinction is made on the comparison between the Jollet’s datasets
and ours. Jollet incorporated many schemes and approaches in his database development. This is in
contradiction of our adherence to a strict process by which we created our datasets. The differences
and similarities to follow may provide insight as to the efficiency of either approach.
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28. Page 8 of 20
Additionally, it is noteworthy to mention just how many parameters there are to consider in
comparing these datasets. It is not simply “change parameters X and Y to see how Z is affected.” It
would be more appropriately to describe it such that one is to “change parameters A, B, C… and Y to
see how Z is affected.” There were many parameters that I handled differently than did Jollet and it
is with analyzing these distinctions that may provide insight as to what is the better method. The
parameters involved were choice of pseudization schemes, matching radii, valence state choices,
basis function energies, and others.
3.1 Atomic Configuration
A primary component of the dataset is in regards to the distribution of the electrons of the atomic
element. At times, the delegation of electrons was quite easy. We could simply follow the choice of
electron configuration given by the periodic table and this would yield really good results with smooth
wavefunctions. However, many times this approach would fail and we had to be a bit clever with the
electron states. At times, we could add in additional partially occupied, or even unoccupied, electron
states. Doing this would give an additional valence electron state and a bit more flexibility when
looking for bound states of the Schrödinger equation. An instance where such a technique is
employed is shown in Figure 2. As illustrated there were at times vast differences in the choice of
electron distribution. To make sense of this, the description of Jollet’s Barium dataset may prove
beneficial. There are 56 electrons total. The first line of the first box gives the maximum of each
quantum number for the material. The dataset reads max S is 6, max P is 5, and max D is 5. The next
two lines below actually tell how many electrons are allotted to that specific quantum number. In
essence, this tells the program the cutoff of the number of electrons present. Here, Jollet has chosen
for the 5D state to have 2 electrons and for the 6S state to have zero electrons.
This choice of parameter is very different from what we chose on the right, as we stuck to a more
basic and straightforward assortment of the electrons. I predict that his choice of adding in the
unoccupied 6S state introduced a degree of flexibility that was not present in ours. As illustrated, the
choice of electron configuration we have from the summer adheres strictly to that of the periodic
table. However, Jollet’s file puts 2 electrons in the 5D state and uses an unoccupied 6S state. In doing
so, he introduces 2 additional valence electron states. Upon comparing the Binding Energy vs. Lattice
Constant curves, it is obvious that the French dataset is in fact a better choice. This conclusion is
supported by the fact that the choice of matching radius for the pseudofunction to the all-electron
function was very close together with a difference of only 0.2 atomic units.
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29. Page 9 of 20
It is of mention to note that our compound BaS, where the Sulfur atomic datasets were identical, was
one of the only instances in which Jollet’s results were vastly better than our own. I also would
mention that I did not personally have a hand in our Barium dataset creation. However, it does
illustrate the difference in electron placement while explicitly representing the effect of allowing
additional valence states.
Figure 2: Showing differences of electron distribution in either dataset.
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30. Page 10 of 20
Figure 3: Binding Energy vs. Lattice Constant curve for BaS.
In Figure 3, we show the Binding Energy curve from Jollet’s dataset compared with LAPW and our
summer result. It is worth noting that Jollet’s more successful dataset did not use the 4D state as
valence, but included a bound 5D state. This may be responsible for the better result. With the
example of Jollet’s dataset, we see how to improve our own initial dataset. As such, we chose not to
publish the data on the web. However, the fact that Jollet’s dataset very accurately represents the
WIEN2k plot gives us something to study in future endeavors.
3.2 Matching Radius Selection (along with Electron Distribution)
It may be the case that our choice of matching radius between the Pseudofunction and the All-
Electron function may play a role in the final result. Initially, it is at times difficult to determine a good
choice for the initial radius of the atom with which we are concerned. To get a relative idea, we
consulted a copy of Quantum Theory and Molecular Solids to find approximate values for the radius
value (Slater). Again, this just gets us a range to work with and the true value for the matching radius
should be determined from refining the ATOMPAW outputs. The choice of the radius value may have
important consequences when comparing our files with those of our French collaborators.
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31. Page 11 of 20
Figure 4: Atomic inputs for Gallium highlighting Electron Distribution and Radius difference.
In Figure 4, representing the case of Gallium, we see that there is a vast difference in the parameter
of matching radius (arrow 3). Jollet’s choice of radius was nearly 50% times our choice. This vast
difference in the radius may be a potential reason for the difference in results. This larger radius in
Jollet’s dataset may have caused issues with the presence of excess room between the atoms when
ABINIT was executed. Additionally, it is again pertinent to observe the choice of the electrons. We
have many more valence state allocations than does Jollet this may either overshadow the difference
in radii or it may also complement an inherently better choice. Again, it is really hard to pinpoint just
exactly where the certain parameters contribute to better results. Generally, Jollet’s results were very
similar to our own, even if ours were consistently more precise to the LAPW plot. However, the
amount of processing power each method requires may be the more important variable to consider
when one is considering the best approach for dataset creation.
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32. Page 12 of 20
Figure 5: Binding Energy vs. Lattice Constant for Gallium-Arsenide.
Figure 5 shows the Binding Energy curve results to have a slightly better result for our choice of
parameters than those of Jollet. It is an important observation to see that the lowest binding energy
occurs at the same lattice constant value as the LAPW.
4. Tools for Comparison
4.1 Wavefunction Analysis and Logderivatives
The fundamental aspect of the PAW method is the creation of the Pseudofunction to more smoothly
represent the All-Electron wave function. This relationship between the two functions is shown in the
transition between Figure 5 and Figure 6. It is important to understand that there is two distinct
Wavefunctions that we are dealing with. The All-Electron Wavefunction (Red) should be the very
similar for both Jollet’s dataset and our dataset. There may be very small differences, but this is only
if the electron configuration is different as in the Barium case. This had better be the case because
there should be the same total number of electrons in for both inputs. The Pseudo Wavefunction
(Green) is, however, subject to change and may vary with our differing choice of parameters.
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33. Page 13 of 20
A fundamental difference between the two datasets was the choice of basis functions in creating the
Pseudofunction.
Figure 6: Graph of the All-Electron Wavefunction.
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34. Page 14 of 20
Figure 7: Graph of the All-Electron Wavefunction with the newly created Pseudo Wavefunction.
Mostly, Jollet used polynomial functions in creation of his Pseudopotentials whereas we used Bessel
functions. Now after we have the Pseudofunctions created, we must be sure that they accurately
represent the All-Electron Wavefunction past the choice of matching radius. The Pseudofunction does not
model the behavior of the All-Electron case until after the matching radius (see Figure 6). After this point,
we hope the Pseudofunction accurately describes the All-Electron case. However, we need a means to
test the accuracy between the two wavefunctions. We do this by looking at the logderivatives of both
functions simultaneously:
Equation 3: Logderivative ≡
(
𝑑𝑅
𝑑𝑟
)
𝑅
| 𝑟𝑐
.
Notice the nature of this calculation is exactly that of how one takes derivatives of logarithmic functions.
Doing this calculation for both the All-Electron wavefunction and the Pseudo-wavefunctions should give
very similar results. We expect this at least to some degree as for later states, there may be a bit of
disagreement, but the thing we are most interested in is using this as a tool for analysis. We may look the
logderivatives of the S, P, D, etc. state and see if there is any huge disagreement between the two
functions.
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35. Page 15 of 20
If there is, then perhaps this specific state is where we need to refocus our attention and alter the dataset
accordingly. For a case in which the functions show little logderivative error, or disagreement, can be seen
in Figure 8.
Figure 8: Showing the All-Electron logderivatives are in red, while the Pseudofunction logderivatives are
shown as green dots.
4.2 Projector Wave Functions
Another key component in analyzing our datasets was by looking at the projector wavefunctions
associated with our Pseudofunction and All-Electron Wavefunction. It was important that these
projectors be smooth and go to zero after the matching radius value.
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36. Page 16 of 20
Figure 9: Graph showing all Wavefunctions for Francois Jollet’s Arsenic dataset.
In Figure 9, the All-Electron wavefunction is shown in red, the Pseudofunction in green, and projector
shown in blue (pink represents the line y=0). I observed these wavefunctions for both our cases and
Jollet simultaneously to get a better idea about how our inputs related to each other. As such, I found
that much of the time, the wavefunctions resembled each other, with differences in amplitude being
the main difference. Predominantly speaking, I found that our results were better and the most likely
reason is due to the more liberal placement of valence states in the dataset. As such, I observed
smoother functions in general, especially the projectors, for our datasets compared to Jollet’s.
Although, I found our results were only better by a small margin.
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5. Problems
5.1 Ghost States
The presence of “Ghost States” was perhaps the most problematic occurrence in my research. A
“ghost state” occurs when the computing software finds numerical solutions to the Schrödinger
Equation where there should not be solutions. In such cases, the self-consistent field step would not
converge. When this happened, we would end up using inaccurate data when running ABINIT. This
would result in a divergent trial, even though our chosen data was supposedly the optimum choice.
However, sometimes we were able graph the logderivatives and find where the problem arose.
Figure 10: Presence of a “Ghost State” in the logderivative plot.
Notice how it is the Pseudofunction (green) that is causing the problem here. The asymptote shown
in the blue circle in Figure 10 represents a bound state that is not reflected by the All-Electron
Wavefunction (Red). This was the main cause of problems for us this summer as it was particularly
difficult to pinpoint the cause of such behavior.
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6. Conclusions
In summary, we focused on several interesting relationships between our datasets and that of Jollet’s.
These relationships were determined by choice of initial parameters of the either input file. While
each party had their own means of dataset creation, there seems to be agreement between the
results. Although our datasets were found to yield more precise results, our data runs were generally
more computationally expensive. This is a reasonable consequence of our choice of liberal assignment
of valence states in the datasets. However, a question may be posed as to whether this extra
computational cost is legitimate. After all, we are using a series of approximations to model how one
may expect these materials to behave. Perhaps the extra precision is not necessary. If so, then Jollet’s
datasets that generally incorporate less valence states may in fact be a more efficient approach.
Another honorable mention of this research is that it was the first time Jollet’s datasets were tested
in compound form. All of his other trials were dealing with elemental calculations. The fact that we
saw such agreement between his datasets and ours, even though he only dealt with singular elements,
speaks to the efficiency of both methods. Additionally, the agreement found between our final results,
given that, at times, our initial datasets were greatly different, leads one to believe that there may in
fact be a range of “acceptable” input parameters that may yield good results. Perhaps with the study
and refinement of these input parameters, and debugging of the computer codes, one may eventually
come to an acceptable hypothesis as to the best format in which to computationally model materials.
This research was very important because we must always test datasets to ensure that they will
comply in computational modeling applications.
6.1 Delta Factor
In our work, we have used the Binding Energy curve qualitatively to distinguish and test our
calculations. More recently, there has been a development to make this analysis more quantitative.
The idea comes with this notion of a Delta Factor. This measurement is found by integrating the
difference between the standard Binding Energy curve and any other calculation result (Lejaeghere
et al.). Jollet’s datasets were designed to have small Delta Factors. Up until now, this Delta Factor has
only been used with elemental materials.
However, the authors are now enhancing the features of the Delta factor such that it modifies the
comparison to include binary compounds. If we computed the Delta Factor for the materials we did
this summer, we expect them to be very small. This new comparison may provide a standard that we
can very easily use based on our previous work.
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Acknowledgements and Collaborators:
Supported by Dr. Holzwarth’s NSF Grant DMR-1105485, WFU DEAC Cluster computer and support
staff, Dr. Natalie Holzwarth, Cameron Kates, Zachary Pipkorn, Chaochao Dun from Wake Forest
University and Francois Jollet and Marc Torrent- CEA, France.
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