by timm reumann prof. dr. k. k. baldridge

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By Timm Reumann Prof. Dr. K. K. Baldridge Organic Chemistry Institute, University of Zürich, Switzerland Scaled Hypersphere Search Method

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Scaled Hypersphere Search Method. By Timm Reumann Prof. Dr. K. K. Baldridge Organic Chemistry Institute, University of Zürich, Switzerland. Potentail Energy (Hyper-) Surface (PES). PES: Potential Energy Surface. Potential Energy (Hyper-) Surface (PES). Energy. TS 2. TS 1. GS 1. GS 0. - PowerPoint PPT Presentation

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Page 1: By Timm Reumann  Prof. Dr. K. K. Baldridge

By Timm Reumann

Prof. Dr. K. K. Baldridge

Organic Chemistry Institute, University of Zürich, Switzerland

Scaled Hypersphere Search Method

Page 2: By Timm Reumann  Prof. Dr. K. K. Baldridge

PES: Potential Energy Surface

Potentail Energy (Hyper-) Surface (PES)

Page 3: By Timm Reumann  Prof. Dr. K. K. Baldridge

Energy

Reaction Coordinate

GS0

TS1

GS2

TS2

GS1

Molecule in Ground State (GS): Stable Equilibrium of Forces

Molecule in Transition State (TS): Instable Equilibrium of Forces,

2 directions downwards

Reaction Path: Valley on PES connecting 2 GSs

Potential Energy (Hyper-) Surface (PES)

Page 4: By Timm Reumann  Prof. Dr. K. K. Baldridge

Chemical Bond and Electron CloudsShape of Molecule => Energy?

1. Bond Stretching: 2. Angle Bending:

Electrostatic Interaction between Electrons (--) => Repulsion Electrostatic Interaction between Atomic Cores (++) => Repulsion Electrostatic Interaction between Electrons and Atomic Cores (-+) => Repulsion Overlap Interaction => Attraction (usually)

Page 5: By Timm Reumann  Prof. Dr. K. K. Baldridge

E.g. Water: some few ones

Page 6: By Timm Reumann  Prof. Dr. K. K. Baldridge

Motivation:

Finding all (relevant) reaction pathways for a given molecule (e.g. catalyst)

e.g.:

modifying a catalyst to favor a specific reaction

unfortunately also a side reaction favored now

survey over

Prioritizing reaction pathways

Without Specific Knowledge about given System (e.g. Initial Guess)

Page 7: By Timm Reumann  Prof. Dr. K. K. Baldridge

But:

• Initial guess of TS or Pathway or further GS still required by established methods (e.g. nudged elastic band and string methods1)

• OR: systematic exploration of all possible reaction pathways starting at one GS

1. No general formula for energy of a molecule available (esp. at TS) Iteration on single electron clouds and their total charge distribution electron clouds of minimal energy and energy itself (Self-Consistent-Field-Proc, SCF)

2. Calculations of 1st and 2nd derivatives of energy on atoms to follow reaction path requires converged electron clouds => SCF-Procedure beforehand

(esp. 2nd derivates computationally expensive)

3. Changing one coordinate affects dependency of energy on another coordinate

(Energy coupling between coordinates)

Page 8: By Timm Reumann  Prof. Dr. K. K. Baldridge

Harmonic Approximation of Energy (computationally cheap)

Instead of 1st and 2nd Derivatives

Describing Chemical Bond as a Spring:

F = -kf (x – x0) => Eharm = -0.5 kf (x – x0)2

E

GS TS

Eharm

ESCFΔE

GS

Dissociation

x

x0 x

Eharm ∞ for x ∞

unbreakable bonds

no chemical reaction

Downwards Deviation (ΔE) of “true” energy (ESCF) from harmonic energy (Eharm)

potential reaction path

Since Chemical Bonds ARE breakable:

0

Page 9: By Timm Reumann  Prof. Dr. K. K. Baldridge

Nd SCF-Energy Calculations required

Etot = E(X1, …, Y2, …, Z3) + E(X2, …, Y3 ) + …

Etot = E(L1, ϕ1) + E(ϕ1, L1,L2) + … + E(φ1, ϕ1, L1, L2, L3, …) + … L : Bond Length ; ϕ, φ : Bending, Torsion Angle

For example:

• Stretching a bond

Weaker bond

Bending that bond now easier

H

O

H

Real

Spa

ce C

oord

. 1

Real Space Coord. 2

Exploration of PES in Normal Coordinates IIInstead of Real Space Coordinates

Energy Coupling between Real Space Coordinates:

Page 10: By Timm Reumann  Prof. Dr. K. K. Baldridge

Etot ≈ e1 n12 + e2 n2

2 + … + en nn2

Only Nd Sample Points Necessary at least around Ground State

Nor

mal

Coo

rd. 1

Normal Coord. 2

• smart combinations of basic atomic displacements

compensating each others’ influences on energy terms

• each mode represented by basis vector ni in

normal coordinate space

Decoupling in Normal Coordinates

Of Vibrational Modes:

n1

n2

n3

HO

H

4080

1960

4080

ei

Exploration of PES in Normal Coordinates IIInstead of Real Space Coordinates

Maeda, S.; Ohno, K.; Chemical Physics Letters, 2003, 381, 177

Page 11: By Timm Reumann  Prof. Dr. K. K. Baldridge

E

GS TS

Eharm

ESCFΔE

GS

Dissociation

q

Overall Procedure

Yes

No

GS Molecule G

Vibrational Modes + Eigenvalues

Radius of Hypersphere:Rk = Rk-1 + ΔR

Transition States

New GS Molecules

Exploration of Spherical PES

Points of locally lowest ΔE

TS region reached? G

Checking dE/dx, d2E/dx2

Optimization to TS GDownhill Walks G

G Done with GAMESS-US

Comparison with old GS Molecules

Really New GS Molecules

Deformed Molecules on Reaction Paths

Page 12: By Timm Reumann  Prof. Dr. K. K. Baldridge

Scaling qi = vi ei

0.5

Q = {q1, …, qn}T

Scaled Normal Coordinate Space Real Coordinate Space

n2

n1

n3

xi = Q-1 n + xGS

Points on Hypersphere

e.g.: Deformations of GS xi

e.g.:

X Y ZO 0.09 -1.02 0.00H -2.46 -2.70 0.00 H 5.66 -2.60 0.00

e.g.:

Generation of Grid

Exploration of Spherical PES

GS Geometry xGS

Radius Rk Vibrational Modes vi

Energy Values ei

Page 13: By Timm Reumann  Prof. Dr. K. K. Baldridge

SCF Runs

ΔE = ESCF - Eharm

Points with ΔE-Values

e.g.: n1

n2

n3

ΔE > 0ΔE < 0

ESCF

Interpolation of ΔE

Local Minima of ΔE Deformed Molecules xi

on Reaction Paths

xi = Q-1 n + x0

Scaled Normal Coordinate Space Real Coordinate Space

Eharm = 0.5 Rk2

Page 14: By Timm Reumann  Prof. Dr. K. K. Baldridge

Everything much Easier NowOr???

Number of Sample Point for Molecules *

Molecule ♯ of Vib. Modes ♯ in Real Space ♯ in norm. Coord. Space

Water, 3 atoms 3 103 630

Methanal, 4 atoms 6 106 60630

* Maeda, S.; Ohno, K.; Chemical Physics Letters, 2003, 381, 177

Vibrational Modes calculated at the GS only valid for the GS Going away from GS (deforming molecule) Vibrational Modes more and more invalid increasing energy coupling between normal coordinates

Complete SCF-energy calculation for each point necessary Computational Time: few seconds for simple molecules (e.g. water) few hours for big ones (e.g. Organic Platinum-Komplex)

Page 15: By Timm Reumann  Prof. Dr. K. K. Baldridge

Submission of Jobs

Folder of Input Files

Cluster 1

Grid Interface

Resource Requests♯of Cores, Memory, Wall Time

Grid Interface

Folder of Output Files

Cluster 3 Cluster 2 Cluster 4

Page 16: By Timm Reumann  Prof. Dr. K. K. Baldridge

GAMESSGeneral Atomic and Molecular Electronic Structure System 2 Versions of GAMESS: GAMESS-US (free) and GAMESS-UK (commercial) multipurpose Quantum Chemistry Package

Energies, Forces, Vibrational Modes on various theory levels,

Properties of Molecules … used here: Optimization of GS and TS Molecules,

Calculation of Vibrational Modes and SCF-Energies

Distributed Data Interface (DDI): communication layer for parallel execution of GAMESS manages dynamic memory allocation and data exchange between single cores and processes does I/O-operations for each single calculation process

Page 17: By Timm Reumann  Prof. Dr. K. K. Baldridge

SCF-Procedure

Optimal Electron Clouds

Total Charge Distribution

Summing upOptimizationEigenvector Determination

Initial Electron Clouds

optimizing shapes of electron clouds => lowest energy energy of single cloud depends on shapes

of all other clouds due to electrostatic interaction

(and exchange interaction) Knowledge about all other clouds required to

determine each single one

ΔE or ΔChargeDist.Below predefined value

No

YesDone

Page 18: By Timm Reumann  Prof. Dr. K. K. Baldridge

Problems with SCF-Runs on large Number of Jobs (e.g. 2000)

2) Prediction of Resource Requirements:

Memory, Number of CPUs e.g.: 3 - 25 MB per Core, 16 Cores

Harddisk Space e.g.: 6 – 30546 MB

Wall Clock Time e.g.: 1 – 17 sec

very small molecules (4 – 20 atoms)

1) Automated Error Treatment:

inappropriate input parameters

allocated resources exceeded

node / cluster crashed

convergence problems of SCF-Procedure

Page 19: By Timm Reumann  Prof. Dr. K. K. Baldridge

Automated Error Treatment1. Separation of Jobs

(successful, failure type 1, 2, …)

Inspection of output files for (error-) messages

e.g.:

---------------------------------------- ddikick.x: exited gracefully.

real 0m8.210suser 0m0.003ssys 0m0.006sfinish time: Mon Jul 11 22:14:07 CEST 2011

Read from remote host compute-1-412: Connection reset by peerFailed creating /state/partition1/grid027/121792 on compute-1-412

Sorting them according to found messages

Page 20: By Timm Reumann  Prof. Dr. K. K. Baldridge

II,JST,KST,LST =318 1 1 1 NREC = 3768 INTLOC = 5381 PWRT: NODE 0 ENCOUNTERED I/O ERROR WRITING UNIT 8 EXECUTION OF GAMESS TERMINATED -ABNORMALLY- AT Wed Jul 13 10:08:36 2011 4613448 WORDS OF DYNAMIC MEMORY USED CPU 0: STEP CPU TIME= 28.41 TOTAL CPU TIME= 57.7 ( 1.0 MIN) TOTAL WALL CLOCK TIME= 95.6 SECONDS, CPU UTILIZATION IS 60.40% DDI Process 0: error code 911 ddikick.x: application process 0 quit unexpectedly. ddikick.x: Fatal error detected. The error is most likely to be in the application, so check for input errors, disk space, memory needs, application bugs, etc. ddikick.x will now clean up all processes, and exit...

Initiating 16 compute processes on 7 nodes to run the following command: /share/apps/gamess-2010R1-ethernet-gfortran//gamess.00.x INP00018

ddikick.x: Timed out while waiting for DDI processes to check in. ddikick.x: Fatal error detected. The error is most likely to be in the application, so check for input errors, disk space, memory needs, application bugs, etc. ddikick.x will now clean up all processes, and exit...

Some more Examples:

Page 21: By Timm Reumann  Prof. Dr. K. K. Baldridge

Automated Error Treatment2. Case Specific Treatment

1) Successful Job Extraction of SCF-Energy

2) Inappropriate input parameters correction by human being e.g.: “ILLEGAL …” in output file

3) Allocated Resources exceeded Resubmission of Job with larger Resources

How to avoid repetition of entire computation (e.g. SCF-Procedure)?

4) node / cluster crashed Resubmission of Job on another cluster (?)

Page 22: By Timm Reumann  Prof. Dr. K. K. Baldridge

Automated Error TreatmentConvergence Problems

How to make the computer recognizing Convergence Problems?

Page 23: By Timm Reumann  Prof. Dr. K. K. Baldridge

Prediction of Resource Requirements1. Memory and Number of Cores

Using several cores to accumulate

enough total memory:

MEMshared + MEMreplic < available MEMCore

MEMshared = total MEMshared / NCores

SCF-Run SCF-Run

DDI-Process

Core 1 Core 2Allocated for each Core:

Memory for Replicated Data (MEMreplic)

Memory for Shared Data (MEMshared)

Node

HDD

more cores faster run

fewer cores memory overflow

available MEMCore = total MEMCore – MEMGAMESS+OS

e.g. : MEMGAMESS+OS ≈ 50 MB + 25 MB

Page 24: By Timm Reumann  Prof. Dr. K. K. Baldridge

Prediction of Resource Requirements2. Speed up with Number of Cores

Communication limits linear speed up:

NCores

1 / W

all C

lock

Tim

e SCF-Energy for Molecule with paired electrons

Vibrational Modes for Molecule with unpaired electrons

Waiting time in Queuing System

Page 25: By Timm Reumann  Prof. Dr. K. K. Baldridge

Prediction of Resource Requirements3. Hard Disk Storage (HD):

Each node with its own HD (2 TB) accumulating HD space for single job using more nodes, i.e. cores if HD space exceeded on 1 node entire job crashes - in the best case

Mainly Overlap- and Interaction Integrals of electron clouds of isolated atoms (at least in energy calculations)

required HD ≈ NInt BytesInt

max Nint = 1/sym 1/8 NBasisfunctions

But: Lots of Integrals almost =0 and neglected by GAMESS

actual NInt << max NInt

fraction of ignored Integrals strongly depends on molecule

Otherwise System crashes, if GAMESS is not restricted to a Scratch Partition

Page 26: By Timm Reumann  Prof. Dr. K. K. Baldridge

Prediction of Resource RequirementsCheck-Run Modus of GAMESS:

Input File with all SettingsOne additional: Exetyp = Check

GAMESS

Output File with Estimates ofMEMreplic , total MEMshared , actual Nint

And some more stuff

Reliability not assessed yet

How to test Check-Run Mode of GAMESS systematically?

Page 27: By Timm Reumann  Prof. Dr. K. K. Baldridge

Prediction of Resource Requirements4. Wall Clock Time:

Depends on:

Level of Theory (RHF ≤ DFT < MP2 < CC… << Full-CI)

Size of Basis Set constituting the Electron Clouds

Number and Size of Atoms in Molecule

And:

Number of required SCF-Cycles for given Molecule

(almost) impossible to predict

Benchmarks necessary to obtain Empirical Function for Wall Clock Time:

WCT = f(input parameters)

Page 28: By Timm Reumann  Prof. Dr. K. K. Baldridge

2 Problems for you

Predicting Memory-, Core- and HD-Space Requirements:

Testing Check-Run Mode of GAMESS systematically

Automated Recognition of Convergence Problems

in SCF-Energy Calculation

Page 29: By Timm Reumann  Prof. Dr. K. K. Baldridge

Thank you for your Attention

Suggestions?