GPUAM Graphics Processing Units for Atoms and Molecules Jorge Garza - - PowerPoint PPT Presentation

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GPUAM Graphics Processing Units for Atoms and Molecules Jorge Garza - - PowerPoint PPT Presentation

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GPUAM Graphics Processing Units for Atoms and Molecules Jorge Garza Departamento de Qu mica Area de Fisicoqu mica Te orica Universidad Aut onoma Metropolitana-Iztapalapa. April 6th, 2016 Reactive sites in a molecule

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GPUAM Graphics Processing Units for Atoms and Molecules

Jorge Garza

Departamento de Qu´ ımica ´ Area de Fisicoqu´ ımica Te´

  • rica

Universidad Aut´

  • noma Metropolitana-Iztapalapa.

April 6th, 2016

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Reactive sites in a molecule

Characterization of reactive sites in a molecule

Jorge Garza (UAMI) GPUAM April, 2016 2 / 32

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Reactive sites in a molecule

Characterization of reactive sites in a molecule Electron density

Jorge Garza (UAMI) GPUAM April, 2016 2 / 32

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Reactive sites in a molecule

Characterization of reactive sites in a molecule

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Reactive sites in a molecule

Characterization of reactive sites in a molecule Electrostatic potential

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Reactive sites in a molecule

Characterization of reactive sites in a molecule

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Reactive sites in a molecule

Characterization of reactive sites in a molecule Electron density plus electrostatic potential

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Interaction between two systems

Characterization of molecular interactions from first principles

Jorge Garza (UAMI) GPUAM April, 2016 5 / 32

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Interaction between two systems

Characterization of molecular interactions from first principles

Jorge Garza (UAMI) GPUAM April, 2016 6 / 32

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Interaction between two systems

Characterization of molecular interactions from first principles Non-covalent interactions index

Jorge Garza (UAMI) GPUAM April, 2016 6 / 32

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Electron density

For wave-function methods or density functional theory the electron density is obtained from ρ( r) =

  • cc
  • i=1

ωiψ∗

i (

r)ψi( r)

Jorge Garza (UAMI) GPUAM April, 2016 7 / 32

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Electron density

For wave-function methods or density functional theory the electron density is obtained from ρ( r) =

  • cc
  • i=1

ωiψ∗

i (

r)ψi( r) For atoms, molecules or extended systems, in general, the orbitals are represented in a basis set functions ψi( r) =

K

  • µ=1

c(i)

µ fµ(

r) {fµ} : basis set functions. {cµ} : coefficients obtained from a quantum chemistry method. K : number of the basis functions.

Jorge Garza (UAMI) GPUAM April, 2016 7 / 32

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Gaussian functions

Gaussian functions used as basis set fµ( r) = (x − X)mµ(y − Y )lµ(z − Z)nµe−ζr2 with r2 = (x − X)2 + (y − Y )2 + (z − Z)2 (X, Y, Z): coordinates of a center (nucleus). There are several codes where gaussian functions are used to describe orbitals or electron density for atoms, molecules or solids.

Jorge Garza (UAMI) GPUAM April, 2016 8 / 32

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Semiempirical methods

Additionally to the codes based on gaussian functions, there are codes which are implented using Slater Type Orbitals. For example, semiempirical methods use this kind of basis set fµ( r) = (x − X)mµ(y − Y )lµ(z − Z)nµe−ζr with r =

  • (x − X)2 + (y − Y )2 + (z − Z)2

(X, Y, Z): coordinates of a center (nucleus). These methods use only valence orbitals.

Jorge Garza (UAMI) GPUAM April, 2016 9 / 32

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Semiempirical methods

Semiempirical methods present an important challenge!! In these methods the number of atoms in the molecule is large, and consequently the number of basis set functions to be used could be huge.

Jorge Garza (UAMI) GPUAM April, 2016 10 / 32

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Visualization of quantum chemistry scalar fields

In quantum chemistry, scalar fields are evaluated typically on a mesh to be displayed

  • n a screen by using

the marching cubes algorithm.

Jorge Garza (UAMI) GPUAM April, 2016 11 / 32

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Computing and rendering of scalar fields on GPUs

Graphics Processing Units for Atoms and Molecules GPUAM Orbitals Electron density Laplacian of orbitals or electron density Reduced gradient Electron localization function Non-covalent interactions index Electrostatic potential

Jorge Garza (UAMI) GPUAM April, 2016 12 / 32

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Evaluation of quantum chemistry scalar fields on GPUs

  • Quantum. Chem.

Calculation NWChem, G09, GAMESS WFX or WFN files Molecular Orbitals Electron Density Gradient Laplacian

  • Red. Grad.

Dens.

  • Kin. Ener.

Dens. ELF Localized Orb. Locator Electrostatic Potential Non-covalent Int. Index

Jorge Garza (UAMI) GPUAM April, 2016 13 / 32

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Evaluation of quantum chemistry scalar fields on GPUs

One thread is associated to each point on the mesh Mesh for the scalar field Mesh on the GPU

Jorge Garza (UAMI) GPUAM April, 2016 14 / 32

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Evaluation of the electrostatic potential

  • ρ(r′)

|r′ − r|dr′ =

  • i
  • µν

ωicµicνi gµ(r′; α, A, a)gν(r′; β, B, b) |r − r′| dr′, gµ(r; α, A, a) = e−α|r−A|2

3

  • j=1

(xj − Aj)aj. For the product of two Gaussian functions

  • ρ(r′)

|r′ − r|dr′ =

  • µν

˜ Gµν 1 P(t2)e−qt2|Q−r|2dt with P(t2) =

3

  • j=1

ηj(aj, bj; t), GPUAM uses a Gauss-Legendre quadrature with different points.

Jorge Garza (UAMI) GPUAM April, 2016 15 / 32

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Computing critical points on GPUs

Graphics Processing Units for Atoms and Molecules GPUAM Critical Points Electron Density Laplacian of the Electron Density

Jorge Garza (UAMI) GPUAM April, 2016 16 / 32

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Critical points: Grid-based methods

Atoms in Molecules (AIM) approach ∇f( r) = 0 All points that satisfy this condition are known as critical points.

Jorge Garza (UAMI) GPUAM April, 2016 17 / 32

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Grid-based methods

For the AIM analysis the critical points searching is a challenge, in particular when the size of the system and the number of functions in the basis set are large!

Jorge Garza (UAMI) GPUAM April, 2016 18 / 32

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Grid-based methods

For the AIM analysis the critical points searching is a challenge, in particular when the size of the system and the number of functions in the basis set are large! Molecule immersed in a grid Newton-Raphson method within each cube of the grid Stop if f( r) < ǫ or if a critical point is found Unique critical points Characterization of critical points

Jorge Garza (UAMI) GPUAM April, 2016 18 / 32

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Grid-based methods

Electron density: ρ

∂ρ ∂xi ∂2ρ ∂x2

i Jorge Garza (UAMI) GPUAM April, 2016 19 / 32

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Grid-based methods

Electron density: ρ

∂ρ ∂xi ∂2ρ ∂x2

i

Laplacian of ρ( r): ∇2ρ

∂3ρ ∂x3

i

∂4ρ ∂x4

i Jorge Garza (UAMI) GPUAM April, 2016 19 / 32

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AIM on GPUs

Critical points of the electron density

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AIM on GPUs: Total time in seconds

CPU H2O-H2O C8H8 (H2O)12CH4 Xe E5-2670 v2 16 04 200 27170 GPU H2O-H2O C8H8 (H2O)12CH4 Tesla K80 1 00 11 880 2 08 553 4 08 350

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AIM on GPUs

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AIM on GPUs

Mixing ρ, NCI and critical points

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AIM on GPUs

Critical points of the laplacian of ρ

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AIM on GPUs

Critical points of the laplacian of ρ No all codes find all critical points!

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Semiempirical methods

Semiempirical Calculation MOPAC MGF file Molecular Orbitals Electron Density Gradient Laplacian

  • Red. Grad.

Dens. Localized Orb. Locator Critical Points Non-covalent Int. Index

Jorge Garza (UAMI) GPUAM April, 2016 26 / 32

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Evaluation of the electron density for poly-(Ala)n from semiempirical methods

n Atoms Func. Orb. Points Time (s) K80 CPU 4 43 106 60 313,632 1 26 5 53 131 74 373,248 2 45 10 103 256 144 958,800 7 446 15 153 381 214 1,953,504 24 1999 20 203 506 284 3,369,600 54 6112 30 303 756 424 8,276,400 349 33007 35 353 881 494 10,365,264 509 56533

Jorge Garza (UAMI) GPUAM April, 2016 27 / 32

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Evaluation of the electron density for poly-(Ala)n from semiempirical methods

n Atoms Func. Orb. Points Time (s) K80 CPU 4 43 106 60 313,632 1 26 5 53 131 74 373,248 2 45 10 103 256 144 958,800 7 446 15 153 381 214 1,953,504 24 1999 20 203 506 284 3,369,600 54 6112 30 303 756 424 8,276,400 349 33007 35 353 881 494 10,365,264 509 56533 40 403 1006 564 13,893,120 1009 45 453 1131 634 19,077,120 1537 50 503 1256 704 24,135,552 2171 60 603 1506 844 39,387,256 5691 70 703 1756 984 57,189,888 10509

Jorge Garza (UAMI) GPUAM April, 2016 27 / 32

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Semiempirical methods

6179 nuclei, 15588 STOs, 17306 electrons

Jorge Garza (UAMI) GPUAM April, 2016 28 / 32

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Conclusions

Code on GPUs to evaluate scalar and vector fields in quantum chemistry. Wave function from NWChem, G09, GAMESS or MOPAC. Critical points searching based on grid-methods for large systems. Stable code and tested over several GPUs.

Jorge Garza (UAMI) GPUAM April, 2016 29 / 32

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Conclusions

GPUAM

Jorge Garza (UAMI) GPUAM April, 2016 30 / 32

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Conclusions

GPUAM Graphics Processing Units at Universidad Aut´

  • noma Metropilitana

Jorge Garza (UAMI) GPUAM April, 2016 30 / 32

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Collaborators and acknowledgments

Raymundo Hern´ andez-Esparza Luis Antonio Soriano-Agueda Sol Milena Mej´ ıa-Chica Apolinar Mart´ ınez-Melchor Andy D. Zapata-Escobar

  • Dr. Rubicelia Vargas (UAMI)
  • Dr. Julio Manuel Hern´

andez-P´ erez (BUAP)

  • Dr. Raquel V´

aldez (UAMI)

  • M. C. Oscar Ya˜

nez (UAMI)

Jorge Garza (UAMI) GPUAM April, 2016 31 / 32

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Collaborators and acknowledgments

CONACYT www.fqt.izt.uam.mx jgo@xanum.uam.mx

Jorge Garza (UAMI) GPUAM April, 2016 32 / 32