Acceleration of Quantum Chemistry and Chemical Similarity
calculations on GPGPU architecture towards faster virtual screening
Yuki Furukawa, Ryota Koga : X-Ability Co.,Ltd. Koji Yasuda : Nagoya Univ Naoki Nariai : Tohoku Univ
E-mail : rkoga@x-ability.jp

Results & Discussion

Background
1. Biologically important macromolecules, such as proteins, arewithin the scope of electronic-structure calculation by using
FMO because of the improvement of computational resources.
2. LINGO [Vidal et al. 2005] is a computational method tomeasure chemical similarity by comparing SMILESrepresentations of two molecules.
3. GPGPU is successfully applied for many kinds of problems
in high performance computation.

Purpose of this ResearchFirst, based on Yasuda [2008], we develop XA-CUDA-QM toaccelerate famous QM softwares (GAMESS-US etc) by mainly using
NVIDIA GPU. We show the excellent FMO performance by XACUDA-QM. Second, we develop a LINGO similarity calculation
method to utilize multiple CPUs and GPUs at the same time, basedon SIML [Haque et al. 2010] originally developed to accerelate
LINGO similarity calculations by using GPGPU.

Coding Policy
1. Total energy and the gradient of under FMO approximation.
2. Most time-consuming steps (the evaluation of Coulomb, HartreeFock exchange, and exchange-correlation matrices…) are
executed on GPUs. Remaining parts are calculated on CPUs.
3. Use single precision arithmetic as much as possible for the sakeof effective speedup, without degradation of accuracy.
4. Take special care for task scheduling and host-GPU
communication time to keep as many CPUs and GPUs busy.
5. Modify LINGO original-code for multi-CPUs/multi-GPUs.

Residue E(CPU)ΔE(GPGPU)

1(GLY)-442.916776617

0.000000005

1. The value of dipole moment isexactly the same.

2(VAL)-308.573606501

0.000000009

2. Total Monomer Energy3(GLU)-457.046042916

0.000000011

E(Original) : -21635.4488652520

4(GLN)-437.255799945

0.000000002

E(GPGPU) : -21635.4488649211

5(CYS)-1254.889732125

0.000000004

ΔE

6(CYS)
7(THR)
8(SER)
9(ILE)-1254.930631919-344.327645726-305.393476307-347.549172133

0.000000003
0.000000007
0.000000004
0.000000010

Electrostatic potential (Coulomb or J-matrix) :The two-electron integrals and the J-matrix in terms of primitiveHermite Gaussian basis are evaluated by GPU (Direct J Engine).
pJ ab   (ab | cd ) Dcd   Eab  ( p | q ) Dq
cdpq

Schwarz upper bounds are used to reduce the number of ERIs to becalculated, but we don’t use integral symmetry ( e.g. (p|q)=(q|p) ).
The McMurchie-Davidson algorism is used to evaluate Hermite ERIs.
The communication time between CPU and GPU to send / receivep, q, Dq , J p was only about 10 % of GPU computation time.
 log | ( p | q) Dq |The upper bound of each ERI is
first evaluated and ERIs which aresmall in magnitude are calculated
on GPU with single-precision. Therests (10% of total count of ERIs)
are calculated on GPU with double
precision.
Fig 1. Valinomycin(x 108 , converged D)s,sp,p,dJ-matrix algorithm is reused.
GPU(DP) GPU(SP) unnecessary
This is the mainly timef or moreconsuming step of FMO.
CPUunnecessary
LINGO algorithm on multi-CPUs and multi-GPUs:

Original algorithm implemented in SIML [Haque et al. 2010] is based on asingle-CPU and single-GPU architecture. We have modified the sourcecode so that LINGO algorithm can run parallel on multi-CPUs and multiGPUs at the same time. In our implementation, calculation workload is
divided into each set of CPU-GPU process with utilizing MPI.

: 3.31×10-7 a.u.

3. Calculation Time (sec) :Original : 3279.944
GPGPU : 790.527

Intel Core i7-3930K @3.2GHz (6 core) , GTX580 x 2, 32GB, CUDA 4.0+ same CPU, mem, compiler + GTX580 x 4 (2 nodes parallel)

Table 1-2 : FMO environmental electrostatic potential
and total acceleration rate of Insulin(2HIU)
Basis set / method/ GPU
6-31G / FMO2, Single Point / GTX680
6-31G*/GMO2, Single Point / GTX680
6-31G / FMO3, Single Point / GTX680
6-31G / FMO2, Gradient / GTX680
6-31G / FMO2, Single Point / GTX580

ESPTotal
13.8
4.11
16.6
4.43
19.5
3.74
10.6
2.55
14.1
4.20

Intel Core i7-3930K @3.2GHz (6 core) , GTX580 x 2, 32GB, CUDA 4.0

The calculation of ESP consumes predominant time (over 75%)
so that FMO2 accelerates so much. The direct SCF method is
unfavorable for them because fragments are so small that we
can store all ERIs in a host memory.
Table 2 : LINGO Similarity calculation time (16,384 x 16,384
chemical compounds all-to-all)
Time(msec)

Algorithms

Environmental Electrostatic
Potential (ESP):

Table 1-1 : FMO2 monomer energies of eachresidue of Insulin(2HIU) by GAMESS (FMORHF/6-31G, a.u.)

Speed up

1CPU53,488x1.00

4CPU

14,097x3.79

60CPU (*)

2,640x20.26

1CPU+1GPU

1,980x27.01

2CPU+2GPU

1,010x52.96

3CPU+3GPU

713x75.02

4CPU+4GPU529x101.11

Intel Core i7-3930K @3.2GHz (6 core) , GTX580 x 2, 32GB, CUDA 4.0(*) Only 60 CPU by Intel Quad Core XeonE5450 3.0GHz (many core), 32GB

Summary
The total energy of FMO and the dipole moments were essentiallythe same. GPGPU calculation of ESP becomes about 20 times
faster than multi-core CPUs calculation.
LINGO calculation method that utilizes 4CPUs and 4GPUsimproves calculation speed by more than 100 times compared tothe speed calculated by one CPU. The calculation results were allcoincident.

Future Theme
1. GPGPU acceleration of ERI with higher basis (metal protein).
2. Combination with molecular dynamics method
3. Massive parallelization on GPGPU cluster
4. LINGO similarity calculations on millions of compounds(*) The super-computing resource was provided by Human Genome Center, Institute ofMedical Science, University of Tokyo
http://sc.hgc.jp/shirokane.html