CPMD:%20design%20and%20characterization%20of%20innovative%20materials

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CPMD design and characterization of innovative
materials

• Mauro Boero
• Institut de Physique et Chimie des Matériaux de
  Strasbourg, UMR 7504 CNRS-UDS, 23 rue du Loess,
  BP 43, F-67034 Strasbourg, France and CREST,
  Japan Science and Technology Agency, Kawaguchi,
  Saitama 332-0012, Japan, and JAIST, Hokuriku,
  Ishikawa, Japan

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Outline

• CPMD a quick overview of the basics of the code
  and advanced tools for simulating reactive
  processes reaction
• Synthetic organic reactions - e-Caprolactam
  (Nylon-6) production without using acid
  catalysts
• - Catalytic properties of water above the
  critical point
• - Tuning the efficiency and selectivity of the
  reaction

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What do we want to do ? And which are main the
ingredients ?
yi(x)
electron- electron
electron - ion
RI
ion-ion
electron- ion
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Car-Parrinello Molecular Dynamics

• Solve the Euler-Lagrange equations of motion

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BO surface
CP trajectory BO trajectory
The difference between the CP trajectories
RICP(t) and the Born-Oppenheimer (BO) ones
RIBO(t) is bound by RICP(t) -
RIBO(t) lt C m1/2 (C gt 0) if
F.A. Bornemann and C. Schütte, Numerische
Mathematik vol.78, N. 3, p. 359-376 (1998)

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Plane wave basis set yi(x) SG ci(G) eiGx
For each electron i 1,,N , G 1,,M are the
reciprocal space vectors. The Hilbert space
spanned by PWs is truncated to a cut-off Gcut2/2
lt Ecut
R space a G space
E1cut
E2cut gt E1cut
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G space R space
NFFT
ci(G)
yi(x)
SG ci(G) G2 Ek VNL(G)
ENL r(G)
FFT
r (x)
Vloc (G) VH(G) ElocEH VLH(G)
Vxc(x) Exc VLH(x) VLOC(x) VLOC(x)yi(x)
FFT
NFFT
VLOC(G)ci(x) VNL(G) SG ci(G) G2
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Practical implementation

• G1,,M (loop on reciprocal vectors) are
  distributed (via MPI/OMP) in a parallel
  processing in bunches of M/(nproc)
• i1,,N (loop on electrons) is distributed (via
  MPI/OMP)
• I1,,K (loop on atoms) generally does not
  require parallelization (vectorized and
  distributed via OMP)
• The scaling of the algorithm is O(NM)for the
  kinetic term,
• O(NM logM) for the local potential and
  O(N2M) for the
• non-local term and orthogonalization
  procedure (all other quantum chemical methods
  scale as O(MN3) Mbasis set)
• - http//www.cpmd.org
• - http//www.cscs.ch/aps/CPMD-pages/CPMD/Downloa
  d

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ES system configuration

• Parallel vector supercomputer system with 640
  processor nodes (PNs) connected by 640x640
  single-stage crossbar switches.
• Each PN is a system with a shared memory,
  consisting of
• 8 vector-type arithmetic processors (APs)
  total5120 AP
• a 16-GB main memory system (MS)
• a remote access control unit (RCU)
• an I/O processor.

MPI
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ES system single processor node (PN)

• The overall MS is divided into 2048 banks
• The sequence of bank numbers corresponds to
  increasing addresses of locations in memory.

OMP
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From reactants A to products B we have to climb
the mountain minimizing the time

• A general chemical reaction starts from reactants
  A and goes into products B
• The system spends most of the time either in A
  and in B
• but in between, for a short time, a barrier is
  overcome and atomic and electronic modifications
  occur
• Time scale

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Escaping the local minima of the FES In one
dimension, the system freely moves in a potential
well (driven by MD). Adding a penalty potential
in the region that has been already explored
forces the system to move out of that region, but
always choosing the minimum energy path, i.e. the
most natural path that brings it out of the well.
Providing a properly shaped penalty potential,
the dynamics is guaranteed to be smooth and
therefore the systems explores the whole well,
until it finds the lowest barrier to escape.
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Set up collective variables sa and parameters
Ma, ka, Ds, A
Perform few MD steps under harmonic restraint
Add a new Gaussian
Update mean forces on sa
Update sa
The component of the force coming from the
gaussians subtracts from the true force the
probability to visit again the same place
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How to plug all this in CPMD ?We simply write a
(further) extended Lagrangean including the new
degrees of freedom
Fictitious kinetic energy
Restrain potential coupling fast and slow
variables v(ka/Ma) ?I
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Collective (dynamical) variables
Velocity Verlet algorithm to solve the equations
of motion
two contributions to the force
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Beckmann rearrangement

• Commercially important for production of
  synthetic fibers
• Known to be catalyzed only by strong acids in
  conventional non-aqueous systems
• Formation of byproducts (ammonium sulfate,
  (NH4)2SO4) of low commercial value in acid
  catalyst byproducts 1.7 products (in
  weight). See (e.g.)http//www.clarkson.edu/ochem
  /Spring01/CM244/caprolactam.htmlhttp//es.epa.gov
  /p2pubs/techpubs/0/15650.html
• Environmentally harmful acid wastes are produced
• Points 2, 3 and 4 and related problems can
  be eliminated in scH2O no acid required no
  byproducts.
• See Y. Ikushima et al. J. Am. Chem. Soc.
  122, 1908 (2000)
  

Work done on collaboration with Michele
Parrinello, Kiyoyuki Terakura, Tamio Ikeshoji and
Chee Chin Liew
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World wide production of e-caprolactam
Europe USA Japan
BASF 434 Honeywell 341 UBE 180
Bayer 155 BASF-USA 270 Toray 180
DOMO 100 DSM 200 Sumitomo 160
UCHE 85 Evergreen 45 Mitsubishi 120
unit 1000 ton/year
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Hydrogen-bond network in water
T653 K r0.73 g/cm3
Supercritical water
Normal water
T 300 K r 1.00 g/cm3
Continuous hydrogen-bond NW
Disrupted hydrogen-bond NW
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Beckmann rearrangement reaction
proton attack to O
in strong acid and supercritical H2O
hydrolysis in H2O and superheated H2O
proton attack to N
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Which are the important ingredients that make
water special at supercritical conditions ?

• Proton attack is the trigger (experimental
  outcome !)

High efficiency
fast proton diffusion
difference in hydration between O and N
High selectivity
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0.9 ps in scH2O
Contrary to normal liquid water,
scH2O accelerates selectively the formation of
the first intermediate
5.2 ps in n-H2O
Proton attack to N Cycrohexanon (byproduct)
formation
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Acid catalyst ?
Efficient reaction in scH2Odue to fast proton
diffusion and acid properties of the (broken)
Eigen-Zundel complexes
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Cyclohexanone-oxyme in scH2O

• The energy barrier seems rather high and the
  reaction pathway not unique
• The reaction is generally acid catalyzed, hence
  protons are expected to be essential in
  triggering the process
• At supercritical conditions, however, the Kw of
  water increase, hence H and OH- can be around in
  the solvent in non-negligible concentration
• And small amounts of weak acids greatly enhance
  reaction rates

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Proton diffusion in ordinary liquid and
supercritical water

• Hydrogen bond network is disrupted in SCW.

Is the proton diffusion slowed down in scH2O ?
Not really
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Proton diffusionnormal water and supercritical
water
Proton (structural defect) diffusion coefficient
estimation in the 3 systems
System Diffusion constant D (cm2/s) Hydrogen bond network
n-H2O(normal water) 15.0 x 10-5 continuous
Superheated H2O 62.0 x 10-5 continuous (fast switch)
scH2O (supercritical water) 55.0 x 10-5 disrupted
In scH2Othe network is disrupted and the motion
occurs in sub-networks that join and break apart
rapidly due to density fluctuations two
diffusion regimes are cooperating hydrodynamics
(vehicular) and Grotthus
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Reaction selectivity ?
Selective reaction in scH2O due to different
solvation of O and N
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Cyclohexanone-oxyme in scH2O ( H) the
selectivity
T 673 K
H
wet
dry
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Cyclohexanone-oxyme in scH2O ( H)
RNCR
A very small activation barrier (about 1
kcal/mol) is required for the N insertion process.
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and now the second step C-O bond formation
DE 5.9 kcal/mol DF 5.1 kcal/mol
Approach of an H2O molecule, x Owat-C
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The last stepeventually the e-caprolactam
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The last stepeventually the e-caprolactam Proton
exchange in scH2O (metadynamics)
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Free energy surface a less rugged landscape
s1 0.5
s1 1.0
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Conclusions and perspectives

• The H diffusion in scH2O occurs in sub-networks
  that join and break rapidly due to density
  fluctuations two diffusion regimes are present.
• Destabilization of Eigen (Zundel) complex makes
  scH2O an acid-like environment able to trigger
  chemical reaction
• The selectivity of the cyclohexanone-oxyme to
  e-caprolactam reaction could be understood
• The role of the H-bond in differentiating the
  solvation features of the solute has been
  evidenced
• A new green chemistry perspective has been
  explored.
• Related Publications
• M.B. et al., Phys. Rev. Lett. 85, 3245
  (2000) J. Chem. Phys. 115, 2219 (2001)
• Phys. Rev. Lett. 90, 226403 (2003) J. Am.
  Chem. Soc. 126, 6280 (2004) ChemPhysChem 6, 1775
  (2005)

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Acknowledgements

• Michele Parrinello, ETHZ-USI and Pisa University
• Roberto Car, Princeton University
• Kiyoyuki Terakura, JAIST, AIST and Hokkaido
  University
• Michiel Sprik, Cambridge University
• Pier Luigi Silvestrelli, Padova University
• Alessandro Laio, SISSA, Trieste
• Jürg Hutter, Zurich University
• Marcella Iannuzzi, Zurich Univeristy
• Carlo Massobrio, IPCMS