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
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
What do we want to do ?
And which are main the ingredients ?
yi(x)
electronelectron
RI
ion-ion
electron- ion
electron
- ion
Car-Parrinello Molecular Dynamics
• Solve the Euler-Lagrange equations of motion
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)| < C m1/2
(C > 0) if  0 

2 e
LUMO
e
HOMO

m 0
F.A. Bornemann and C. Schütte,
Numerische Mathematik vol.78, N. 3, p. 359-376 (1998)
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 < Ecut
R space
a G space
E1cut
E2cut > E1cut
G space
ci(G)
SG ci(G) G2 {Ek}
VNL(G) {ENL}
r(G)
R space
N*FFT
yi(x)
FFT
r (x)
Vloc (G) + VH(G) {Eloc+EH}
FFT
= VLH(G)
VLOC(G)ci(x)
+ VNL(G) + SG ci(G) G2
 E
 ci (G )
N*FFT
 Hˆ c i ( G )
Vxc(x) {Exc}
+ VLH(x)
= VLOC(x);
VLOC(x)yi(x)
 Hˆ y 
i
Practical implementation
• G=1,…,M (loop on reciprocal vectors) are distributed (via
MPI/OMP) in a parallel processing in bunches of M/(nproc)
• i=1,…,N (loop on electrons) is distributed (via MPI/OMP)
• I=1,…,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) M=basis set)
- http://www.cpmd.org
- http://www.cscs.ch/~aps/CPMD-pages/CPMD/Download
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): total=5120 AP
- a 16-GB main memory system (MS)
- a remote access control unit (RCU)
- an I/O processor.
MPI
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
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 F
• Time scale:  ~  mol e k T
D
*
B
F* ~ D
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.
V(s)
s
Set up collective variables {sa}
and parameters Ma, ka, Ds, A
F(s)
Perform few MD steps
under harmonic restraint
∙∙∙∙∙
F(s)+V(s, t)
Add a new Gaussian
t1
Update mean forces on {sa}
Update {sa}
脱出
t3
t2
t0
sa(t0)
The component of the force coming from the gaussians subtracts
from the “true” force the probability to visit again the same place
sa
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
√(kα/Mα) « ωI
History-dependent
potential
Collective (dynamical) variables
Velocity Verlet algorithm to solve the equations of motion
two contributions to the force
Beckmann rearrangement:
1.
2.
3.
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.html
http://es.epa.gov/p2pubs/techpubs/0/15650.html
4.
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
World wide production of e-caprolactam
Europe
USA
BASF 434
Honeywell 341
Bayer 155
BASF-USA 270 Toray
DOMO 100
DSM
UCHE
Evergreen 45 Mitsubishi 120
85
unit = 1000 ton/year
Japan
UBE
180
180
200 Sumitomo 160
Hydrogen-bond network in water
T=653 K
Supercritical water
r=0.73 g/cm3
Normal water
T = 300 K
r = 1.00 g/cm3
Continuous hydrogen-bond NW
Disrupted hydrogen-bond NW
Beckmann rearrangement reaction
proton
attack
to O
proton
attack
to N
in strong acid
and
supercritical H2O
hydrolysis in H2O
and
superheated H2O
Which are the important ingredients that make
water special at supercritical conditions ?
• Proton attack is the trigger (experimental outcome !)
High efficiency :
fast proton diffusion
High selectivity : difference in hydration
between O and N
~ 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
Acid catalyst ?
Efficient reaction in scH2Odue to fast
proton diffusion and acid properties of
the (broken) Eigen-Zundel complexes
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
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…
Proton diffusion：
normal water and supercritical water
Proton (structural defect) diffusion coefficient estimation in the 3 systems:
System
n-H2O
(normal water)
Superheated
H2O
scH2O
(supercritical water)
Diffusion constant
D (cm2/s)
Hydrogen bond
network
15.0 x 10-5
continuous
10-5
continuous
(fast switch)
62.0 x
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
Reaction selectivity ?
Selective reaction in scH2O due to
different solvation of O and N
Cyclohexanone-oxyme in scH2O (+ H+):
the selectivity
T = 673 K
H+
wet
dry
Cyclohexanone-oxyme in scH2O (+ H+)
R—C—R’
N—OH
H+
R—C—R’
+ H2O
N+
R—N＝C+—R’
A very small activation barrier
(about 1 kcal/mol) is required
for the N insertion process.
…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|
The last step:eventually the e-caprolactam
oxime
R—C—R’
R—C—R’
N—OH
+ H2O
N+
H+
H2O
H
H
O HO
H
R—N＝C—R’
HO
R—N＝C—R’
amide
H
O
R—N—C—R’
R—N＝C+—R’
The last step:eventually the e-caprolactam
Proton exchange in scH2O (metadynamics)
Free energy surface: a less rugged landscape
s1 = 0.5
s1 = 1.0
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)
Acknowledgements
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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