The design and development of GPU accellerated Algorithms for AB Initio integrals and integral

224 Pages·2016·6.38 MB·English

THE DESIGN AND DEVELOPMENT OF GPU ACCELERATED
ALGORITHMS FOR AB INITIO INTEGRALS AND INTEGRAL
DERIVATIVES ILLUSTRATED ON AB INITIO QUANTUM AND
HYBRID QM/MM DYNAMICS
CARINA ALICIA RENISON
SUPERVISOR: PROFESSOR KEVIN J. NAIDOO
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A THESIS SUBMITTED IN ACCORDANCE WITH THE REQUIREMENTS FOR
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THE DEGREE OF
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DOCTOR OF PHILOSIPeHY
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SCIENTIFIC iCOMPUTING RESEARCH UNIT
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iTHE DEPARTMENT OF CHEMISTRY
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UNIVERSITY OF CAPE TOWN
APRIL 2016
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The copyright of this thesis vests in the author. No
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quotation from it or information derived from it is to be

published without full acknowledgeement of the source.
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The thesis is to be used for private study or non-
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commercial research purposes only.

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Published by the Universit y of Cape Town (UCT) in terms
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of the non-exclusive license granted to UCT by the author.
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ABSTRACT

THE DESIGN AND DEVELOPMENT OF GPU ACCELERATED ALGORITHMS
FOR AB INITIO INTEGRALS AND INTEGRAL DERIVATIVES ILLUSTRATED
ON AB INITIO QUANTUM AND HYBRID QM/MM DYNAMICS

CARINA ALICIA RENISON

Graphical Processing Units (GPUs) are highly parallel, programmable accelerators boasting
high peak floating point performance. Over the last couple of years the use of GPUs for
general purpose computing have revolutionized quantum chemistry. The computational
bottleneck in an ab-initio quantum method is the calculation of a large number of two-
electron integrals. To date, a number of GPU accelerated two-electron integral
implementations have been developed significantly improving the performance of a static
quantum mechanical (QM) calculation.

However, when performing an ab-initio QM gradient calculation, optimization, QM or Hybrid
Quantum Mechanical/Molecular Mechanical (QM/MM) dynamics simulation the two-
electron integral derivatives arise as an additional bottleneck. Hybrid QM/MM methods
particularly dynamics methods are commonly used to study large chemical/biological
systems. These methods are a popular choice used for studying reaction mechanisms,
conformational and configurational structures important in glycobiology. Usually a semi-
empirical QM method is used however, these have shown variable accuracy for the study of
carbohydrate conformation and prevents an analytical investigation of electronic structure.
The use of a higher level of theory, such as an ab initio method, is desirable however this
comes at a much greater computational cost. Together with the bottlenecks above this cost
results from the polarization of the QM region within an electrostatic embedding scheme,
which requires the calculation of a large number of one-electron integral derivatives. Thus
for QM/MM calculations the one-electron integral derivatives becomes a third bottleneck
together with the two mentioned above. Recently, the above bottlenecks have become
popular GPU acceleration targets.

This thesis describes an extension of the GPU based Quantum Supercharger Library (QSL) to
perform the above calculations/simulations. In contrast to GPU packages developed from
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the ground up, the QSL is a library of routines aimed at accelerating legacy codes, such as
GAMESS-UK, GAMESS-US and NWChem, used in electronic structure calculations. Algorithms
are presented for accelerating the one- and two-electron integral derivatives on a GPU. In
addition to the derivatives, the one-electron integral calculation was ported to the GPU in
order to remove a small additional cost arising for large QM/MM systems. Furthermore, the
use of automatic code generation for generating GPU kernels was explored and compared to
the original approach.

Using the QSL library implemented in GAMESS-UK several benchmark calculations and
simulations were performed. These were performed in double precision on a single GPU
(Kepler K20) and compared to a single CPU using the 6-31G basis set. A speedup of up to
9.3X is achieved for an ab initio gradient calculation compared to the CPU running an
optimized serial version of GAMESS-UK using the Schlegel method. For a single point
QM/MM calculation of cellobiose in different sized water spheres (3267-24843 point
charges) speedups of between 13X and 34X is achieved. QSL/GAMESS-UK coupled to the
CHARMM molecular dynamics package was then used in order to perform accelerated
molecular dynamics simulations. Benchmark QM and QM/MM molecular dynamics
simulations were performed on cellobiose in vacuo and in a water sphere (45 QM atoms and
24843 point charges respectively). The QSL is able to perform 9.7 ps/day of ab initio QM
dynamics and 6.4 ps/day of QM/MM dynamics. Testing of the auto-generated version of the
QSL showed better performance for lower angular momentum classes but reduced
performance for higher angular momentum classes.

The efficiency of the integral and derivative routines within the QSL library was tested on a
computationally intense realistic glycobiological condensed phase free energy computation.
Ab-initio pucker free energy surfaces/volumes of !-Ribofuranose and !-Glucopyranose in
vacuum and in water were computed. These are the first converged Hartree-Fock/MM free
energy simulations for these carbohydrates performed in solution. The value of the ab initio
Free energy surfaces/volumes was demonstrated through an analysis of solvent polarization
effects that are evident through a comparison of the vacuum and solution minimum free
energy pathways. In particular the water structure around the pucker conformers, analysis
of the primary alcohol distribution as well as analysis of the electronic structure of these
conformers reveals that water significantly affects the free energy pathways, primary
alcohol distribution and the barriers for inter-conversion between pucker conformers.
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UBLICATIONS
While this thesis describes my own work performed under the guidance of my supervisor
Prof. Kevin J. Naidoo, aspects of the work have been published. My own work represents all
aspects related to a) the 1-electron integral algorithm and code development, b) 1-electron
integral derivatives algorithm and code development and c) 2-electron integral derivatives
algorithm and code development.

Sections of this work have been published in:

1. C. Alicia Renison, Kyle, D. Fernandes and Kevin J. Naidoo, J. Comput. Chem. 2015,
36, 1410-1419

In this paper only development work performed by me is reported. This was
combined with the HF QSL plugged into GAMESS-UK to be reported in Mr.
Fernandes’ thesis (a doctoral student under Prof. Naidoo’s supervision). The entire
QSL was needed to perform optimization and QM/MM simulations. Hence Mr.
Fernandes in addition to his helpful discussions is a co-author on this paper.

2. Kyle, D. Fernandes, C. Alicia Renison and Kevin J. Naidoo, J. Comput. Chem. 2015,
36, 1399-1409

In this paper the development work of the HF QSL performed by Mr. Fernandes and
the 1-electron integral development performed by me are reported.

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ECLARATION
I, Carina Alicia Renison, hereby declare that the work on which this thesis is based is
my original work (except where acknowledgements indicate otherwise) and that
neither the whole work nor any part of it has been, is being, or is to be submitted for
another degree in this or any other university. I authorise the University to
reproduce for the purpose of research either the whole or any portion of the
contents in any manner whatsoever.

CARINA ALICIA RENISON
APRIL 2016

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CKNOWLEGEMENTS

I am thankful for financial support provided by the University of Cape Town, the South
African Research Chairs Initiative (SARChI) and the National Research Foundation (NRF). I
would like to thank the Nvidia Professor Partnership Program to Kevin J. Naidoo for a
generous donation of equipment used in this study and for the usage of their development
cluster. In addition I would like to thank Mark Berger from Nvidia for always keeping me
updated on all the latest in the GPU world.

Thank you to my supervisor Prof. Kevin Naidoo for allowing me the opportunity to work with
you. In addition I would like to thank all the members of the Scientific Computing Research
Unit who helped me at some point during my stay and with whom I shared interesting
discussions. In particular I would like to thank Kyle Fernandes for all the things he taught me,
especially about GPU computing and for sharing the joys and frustrations of being a PhD
student. I would also like to thank Dr. Chris Barnett for lots of discussions about puckering
and other random topics over a cup or two of coffee.

My sincere thanks goes to my husband Martin for supporting me with my studies over
several years. Thank you for all your encouragement and understanding. Last but not least I
would like to thank the rest of my family for all their support during the last couple of years.

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BBREVIATIONS

ALU: Arithmetic Logic Unit
AM1: Austin Model 1
API: Application Programming Interface
ATP: Adenosine triphosphate
CP: Cremer and Pople method
CPU: Central Processing Unit
CUDA: Compute Unified Device Architecture
DFT: Density Functional Theory
DNA: Deoxyribonucleic acid
ERI: Electron Repulsion Integral
FEARCF: Free Energy from Adaptive Reaction Coordinate Forces
FPGA: Field Programmable Gate Array
GPU: Graphical Processing Unit
HF: Hartree Fock
ILP: Instruction Level Parallelism
IUPAC: International Union of Pure and Applied Chemistry
LJ: Lennard Jones
MD: Molecular Dynamics
MM: Molecular Mechanics
NMR: Nuclear Magnetic Resonance Spectroscopy
NVT: Canonical ensemble
PM3: Parametric Method Number 3
PMF: Potential of Mean Force
ps: picosecond
QM: Quantum Mechanics
QM/MM: Hybrid Quantum Mechanics/Molecular Mechanics
QSL: Quantum Supercharger Library
RNA: Ribonucleic acid
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SCF: Self Consistent Field
SIMD: Single Instruction Multiple Data
SM/SMX: Streaming Multiprocessor
STO: Slater-type orbital
GTO: Gaussian-type orbital
TIP3P: Transferrable Intermolecular Potential 3P
VVER: Velocity Verlet method
VV2: New Velocity Verlet method
WHAM: Weighted Histogram Analysis Method

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