by timm reumann prof. dr. k. k. baldridge organic chemistry institute, university of zürich,...
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By Timm Reumann
Prof. Dr. K. K. Baldridge
Organic Chemistry Institute, University of Zürich, Switzerland
Scaled Hypersphere Search Method
PES: Potential Energy Surface
Potentail Energy (Hyper-) Surface (PES)
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)
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)
E.g. Water: some few ones
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)
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)
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
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:
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
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
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
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
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)
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
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
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
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
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
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:
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 (?)
Automated Error TreatmentConvergence Problems
How to make the computer recognizing Convergence Problems?
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
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
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
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?
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)
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
Thank you for your Attention
Suggestions?
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