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

GPUAM Graphics Processing Units for Atoms and Molecules Jorge Garza Departamento de Qu´ ımica ´ Area de Fisicoqu´ ımica Te´ orica Universidad Aut´ onoma Metropolitana-Iztapalapa. April 6th, 2016

Reactive sites in a molecule Characterization of reactive sites in a molecule Jorge Garza (UAMI) GPUAM April, 2016 2 / 32

Reactive sites in a molecule Characterization of reactive sites in a molecule Electron density Jorge Garza (UAMI) GPUAM April, 2016 2 / 32

Reactive sites in a molecule Characterization of reactive sites in a molecule Jorge Garza (UAMI) GPUAM April, 2016 3 / 32

Reactive sites in a molecule Characterization of reactive sites in a molecule Electrostatic potential Jorge Garza (UAMI) GPUAM April, 2016 3 / 32

Reactive sites in a molecule Characterization of reactive sites in a molecule Jorge Garza (UAMI) GPUAM April, 2016 4 / 32

Reactive sites in a molecule Characterization of reactive sites in a molecule Electron density plus electrostatic potential Jorge Garza (UAMI) GPUAM April, 2016 4 / 32

Interaction between two systems Characterization of molecular interactions from first principles Jorge Garza (UAMI) GPUAM April, 2016 5 / 32

Interaction between two systems Characterization of molecular interactions from first principles Jorge Garza (UAMI) GPUAM April, 2016 6 / 32

Interaction between two systems Characterization of molecular interactions from first principles Non-covalent interactions index Jorge Garza (UAMI) GPUAM April, 2016 6 / 32

Electron density For wave-function methods or density functional theory the electron density is obtained from occ � ω i ψ ∗ ρ ( � r ) = i ( � r ) ψ i ( � r ) i =1 Jorge Garza (UAMI) GPUAM April, 2016 7 / 32

Electron density For wave-function methods or density functional theory the electron density is obtained from occ � ω i ψ ∗ ρ ( � r ) = i ( � r ) ψ i ( � r ) i =1 For atoms, molecules or extended systems, in general, the orbitals are represented in a basis set functions K � c ( i ) ψ i ( � r ) = µ f µ ( � r ) µ =1 { f µ } : basis set functions. { c µ } : coefficients obtained from a quantum chemistry method. K : number of the basis functions. Jorge Garza (UAMI) GPUAM April, 2016 7 / 32

Gaussian functions Gaussian functions used as basis set r ) = ( x − X ) m µ ( y − Y ) l µ ( z − Z ) n µ e − ζr 2 f µ ( � with r 2 = ( 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

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 r ) = ( x − X ) m µ ( y − Y ) l µ ( z − Z ) n µ e − ζr f µ ( � with ( x − X ) 2 + ( y − Y ) 2 + ( z − Z ) 2 � r = ( X, Y, Z ): coordinates of a center (nucleus). These methods use only valence orbitals. Jorge Garza (UAMI) GPUAM April, 2016 9 / 32

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

Visualization of quantum chemistry scalar fields In quantum chemistry, scalar fields are evaluated typically on a mesh to be displayed on a screen by using the marching cubes algorithm. Jorge Garza (UAMI) GPUAM April, 2016 11 / 32

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

Evaluation of quantum chemistry scalar fields on GPUs Quantum. Chem. NWChem, G09, Calculation GAMESS WFX or WFN files Molecular Electron Gradient Electrostatic Non-covalent Int. Orbitals Density Laplacian Potential Index Red. Grad. Kin. Ener. Localized Orb. ELF Dens. Dens. Locator Jorge Garza (UAMI) GPUAM April, 2016 13 / 32

Evaluation of quantum chemistry scalar fields on GPUs One thread is associated to each point on the mesh Mesh on the GPU Mesh for the scalar field Jorge Garza (UAMI) GPUAM April, 2016 14 / 32

Evaluation of the electrostatic potential � g µ ( r ′ ; α, A , a ) g ν ( r ′ ; β, B , b ) ρ ( r ′ ) � | r ′ − r | d r ′ = � � d r ′ , ω i c µi c νi | r − r ′ | i µν 3 g µ ( r ; α, A , a ) = e − α | r − A | 2 � ( x j − A j ) a j . j =1 For the product of two Gaussian functions � 1 ρ ( r ′ ) � | r ′ − r | d r ′ = P ( t 2 ) e − qt 2 | Q − r | 2 dt � ˜ G µν 0 µν with 3 � P ( t 2 ) = η j ( a j , b j ; t ) , j =1 GPUAM uses a Gauss-Legendre quadrature with different points. Jorge Garza (UAMI) GPUAM April, 2016 15 / 32

Computing critical points on GPUs Graphics Processing Units for Atoms and Molecules GPUAM Critical Points Laplacian of the Electron Density Electron Density Jorge Garza (UAMI) GPUAM April, 2016 16 / 32

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

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

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

Grid-based methods Electron density: ρ ∂ρ ∂x i ∂ 2 ρ ∂x 2 i Jorge Garza (UAMI) GPUAM April, 2016 19 / 32

Grid-based methods Laplacian of ρ ( � r ): Electron density: ∇ 2 ρ ρ ∂ 3 ρ ∂ρ ∂x 3 ∂x i i ∂ 2 ρ ∂ 4 ρ ∂x 2 ∂x 4 i i Jorge Garza (UAMI) GPUAM April, 2016 19 / 32

AIM on GPUs Critical points of the electron density Jorge Garza (UAMI) GPUAM April, 2016 20 / 32

AIM on GPUs: Total time in seconds CPU H 2 O-H 2 O C 8 H 8 (H 2 O) 12 CH 4 Xe E5-2670 v2 16 04 200 27170 GPU H 2 O-H 2 O C 8 H 8 (H 2 O) 12 CH 4 Tesla K80 1 00 11 880 2 08 553 4 08 350 Jorge Garza (UAMI) GPUAM April, 2016 21 / 32

AIM on GPUs Jorge Garza (UAMI) GPUAM April, 2016 22 / 32

AIM on GPUs Mixing ρ , NCI and critical points Jorge Garza (UAMI) GPUAM April, 2016 23 / 32

AIM on GPUs Critical points of the laplacian of ρ Jorge Garza (UAMI) GPUAM April, 2016 24 / 32

AIM on GPUs Critical points of the laplacian of ρ No all codes find all critical points! Jorge Garza (UAMI) GPUAM April, 2016 25 / 32

Semiempirical methods Semiempirical MOPAC Calculation MGF file Molecular Electron Gradient Non-covalent Int. Orbitals Density Laplacian Index Red. Grad. Localized Orb. Critical Dens. Locator Points Jorge Garza (UAMI) GPUAM April, 2016 26 / 32

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

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

Semiempirical methods 6179 nuclei, 15588 STOs, 17306 electrons Jorge Garza (UAMI) GPUAM April, 2016 28 / 32

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

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

Conclusions GPUAM G raphics P rocessing U nits at U niversidad A ut´ onoma M etropilitana Jorge Garza (UAMI) GPUAM April, 2016 30 / 32