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 - -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 ?

electron-electron

ion-ion

electron- ion

electron- ion

i(x)

RI

Car-Parrinello Molecular Dynamics

• Solve the Euler-Lagrange equations of motion

BO surface

CP trajectory

BO trajectoryThe difference between the CP trajectories RI

CP(t) and the Born-Oppenheimer (BO) ones RI

BO(t) is bound by

| RICP(t) - RI

BO(t)| < C 1/2

(C > 0) if 020 HOMOLUMO

F.A. Bornemann and C. Schütte, Numerische Mathematik vol.78, N. 3, p. 359-376 (1998)

R space G space

Plane wave basis set: i(x) = G 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 Gcut

2/2 < Ecut

E2cut > E1

cut

E1cut

G space R spaceci(G) i(x)

G ci(G) G2 {Ek} VNL(G) {ENL} (G)

N*FFT

FFT (x)

Vloc (G) + VH(G) {Eloc+EH} = VLH(G)

Vxc(x) {Exc}+ VLH(x)= VLOC(x); VLOC(x)i(x)

FFT

N*FFTVLOC(G)ci(x)

+ VNL(G) + G ci(G) G2

iii

HcHc

E

ˆ)(ˆ)(

GG

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

• Time scale:

Tk

F

molBe

*

~ ~*F

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

t0

t1t2

脱出

F(s)

F(s)+V(s, t)

ss(t0)

t3

∙∙∙∙∙

Set up collective variables {s} and parameters M, k, s, A

Perform few MD steps under harmonic restraint

Add a new Gaussian

Update mean forces on {s}

Update {s}

The component of the force coming from the gaussians subtractsfrom the “true” force the probability to visit again the same place

How to plug all this in CPMD ?We simply write a (further) extended Lagrangean including

the new degrees of freedom

History-dependent potential

Fictitious kinetic energy

Restrain potential: coupling fast and slow variables√(kα/Mα) « ωI

Collective (dynamical) variables

Velocity Verlet algorithm to solve the equations of motion

two contributions to the force

Beckmann rearrangement:1. Commercially important for production of synthetic fibers2. Known to be catalyzed only by strong acids in conventional

non-aqueous systems

3. 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

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 -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

Hydrogen-bond network in water

T = 300 K = 1.00 g/cm3

T=653 K=0.73 g/cm3

Continuous hydrogen-bond NW Disrupted hydrogen-bond NW

Normal water

Supercritical water

Beckmann rearrangement reaction

in strong acid and

supercritical H2O

hydrolysis in H2Oand

superheated H2O

proton attack to O

proton attack to N

Which are the important ingredients that make water special at supercritical conditions ?

• Proton attack is the trigger (experimental outcome !)

fast proton diffusion

difference in hydration between O and N

High efficiency :

High selectivity :

~ 0.9 ps in scH2O

~ 5.2 ps in n-H2O

Contrary to normalliquid water, scH2Oaccelerates selectivelythe formation of the first intermediate

Proton attack to N:Cycrohexanon(byproduct) formation

Efficient reaction in scH2Odue to fast proton diffusion and acid properties of the (broken) Eigen-Zundel complexes

Acid catalyst ?

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

Is the proton diffusion slowed down in scH2O ? Not really…

• Hydrogen bond network is disrupted in SCW.

Proton diffusion ：normal water and supercritical water

Proton (structural defect) diffusion coefficient estimation in the 3 systems:

SystemDiffusion constant

D (cm2/s)Hydrogen bond

network

n-H2O(normal water)

15.0 x 10-5 continuous

Superheated

H2O62.0 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

Selective reaction in scH2O due to different solvation of O and N

Reaction selectivity ?

H+

T = 673 K

wet

dry

Cyclohexanone-oxyme in scH2O (+ H+): the selectivity

Cyclohexanone-oxyme in scH2O (+ H+)

R—C—R’N—OH

H+

R—C—R’

N+

+ H2O

R—N ＝ C+—R’

A very small activation barrier (about 1 kcal/mol) is requiredfor the N insertion process.

…and now the second step: C-O bond formation

E = 5.9 kcal/molF = 5.1 kcal/mol

Approach of an H2O molecule, = |Owat-C|

+ 　 H2OR—C—R’

N+

H+

R—N ＝ C—R’

HO

R—N ＝ C—R’

HOOH

H

R—C—R’

N—OH

oxime

R—N—C—R’

OHamide

H2O

R—N ＝ C+—R’

OH

－

H

The last step:eventually the -caprolactam

The last step:eventually the -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 -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

• 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