Ab initio and Classical Molecular Dynamics

Simulations of Supercritical Carbon Dioxide

Moumita Saharay and S. Balasubramanian

Jawaharlal Nehru Center for Advanced Scientific Research,Chemistry and Physics of Materials Unit,

Jakkur, Bangalore – 560064, India.

AbstractWe have performed Car-Parrinello molecular dynamics (CPMD) simulations of scCO2 at 318.15 K and at the density of 0.073 g/cc in order to understand its microscopic structure and dynamics. Atomic pair correlation functions and structure factors have been obtained and good agreement has been found with experiments. Analyses of angle distributions between near neighbour molecules reveal the existence of configurations with pairs of molecules in the distorted T-shaped geometry. The intramolecular vibrations of CO2 have also been examined through an analysis of the velocity autocorrelation function of the atoms. These reveal a red shift in the frequency spectrum relative to that of an isolated molecule, consistent with experiments on scCO2. The distribution of the magnitude of dipole and quadrupole moments of individual molecules were obtained, and were found to be asymmetric with long tails. The mean dipole and quadrupole moments were 0.85 Debye and 6.1x10-26 esu respectively. Long tails in these distributions are likely to be due to an asymmetry in the distribution of the number of neighbours around a given CO2 molecule.

CPMD & classical MD calculations of ethanol in scCO2 have also been performed to study the nature of its solvation. We have investigated the lifetime of the ephemeral hydrogen bond and Lewis acid-base interaction between ethanol and CO2.

Motivation

Green SolventsscCO2, Room Temperature Ionic LiquidsscCO2, an alternative to CFCs for

dissolving PTFE

Recent alternative is scCO2; non-toxic and does not remove flavour

Initial decaffeination of coffee usingMethylene Chloride ---> hazardous for humans and environment; may cause Cancer

Reaction medium for chemical synthesisEthanol in scCO2 enhances the solvation properties

Polymerization and Polymer processing

Methodology

Car-Parrinello Molecular Dynamics (CPMD)Kohn-Sham formulation of DFT using LDA, CPMD codeVanderbilt ultrasoft pseudopotential,Plane wave cutoff = 25 Ry, NVT condition, T = 318.15K, Nose-Hoover chain, 32 molecules CO2, Cubic boxlength = 14.956 .Time step = 0.12 fs, Total run length = 15 ps, Analysis time length = 12 ps, Equilibration length = 3 ps, Computational wall clock time using 24 processors in Param Padma supercomputer = 2.5 monthsNumber of

electrons = 512Classical Molecular Dynamics (MD)

EPM2 model, PINY-MD code, Coulombic + Lennard-Jones potential, 100 molecules CO2, Boxlength = 21.866 A, NVT Conditions.Time step = 0.5 fs, Total run length = 120 ps, Analysis time length = 20 ps, Equilibration length = 100 ps, No electronic degrees of freedom.

Density functional theory

Kohn-Sham energy functional

Norm-Conserving Pseudopotentials

Equations of motion

i (r) = Cki

exp(ik.r)

Snapshot of CO2 molecules

Radial Distribution Function

Solvent structure in scCO2

Top view Side view

Density isosurfaces of oxygen atoms that belong to molecules in the first coordination shell of CO2 in supercritical carbon dioxide

Angle Distribution

O

O

Oa

Ob

C2C1

P

MSD & VACF

Mean Square Displacement

Velocity Auto-Correlation

DCPMD = 2.29 x 10-4 cm2/sec,

DMD = 2.17 x 10-4 cm2/sec

DCPMD = 2.50 x 10-4 cm2/sec,

DMD = 2.62 x 10-4 cm2/sec

Dexp = 2.02 x 10-4 cm2/sec

Cv (

t)

Power spectrum

628 (667) 1228

1319(1338)

Bending

Symmetric stretch

Asymmetric stretch 2309 (2349)

Numbers in brackets are for ‘ISOLATED’ CO2. Splitting in symmetric stretch is due to ‘FERMI RESONANCE’

Distribution of coordination no. and intramolecular angle

Coordination no.

P

Intramolecular angle

Z

XY

Multipole moment calculation

0

Dipole moment calculation

= dipole moment of i-th molecule

Quadrupole moment calculation

Qmn = quadrupole moment component

rc = 1.3 A; zc = 2.8 A

Multipole moment distribution

Instantaneous Quadrupole moment Instantaneous Dipole moment

<> from CPMD calculation=0.85 D<Q> from CPMD = 6.1x10-26 esu

Experimental value = 4.1x10-26 esu

Geometry optimized value for isolated molecule from CPMD = 4.26x10-26 esu

d-Ethanol in CO22 (Methodology)

Classical Molecular Dynamics

Car-Parrinello Molecular Dynamics (CPMD)Kohn-Sham formulation of DFT using GGA, CPMD code

Plane wave cutoff = 70 Ry, NVT condition, T = 318.15K, Nose-Hoover chain, 64 CO2 molecules + Ethanol (C2D5OD) molecule, Cubic box length = 19.0A.Time step = 0.096 fs, Total run length (till now) = 3 ps, Computational wall clock time using 10 P4 processors for 1ps = 20 days. Number of electrons = 1045

TraPPe potential parameters, PINY-MD code, Coulombic + Lennard-Jones potentialA. 3000 CO2 molecules+205 Ethanol molecules, boxlen =63A B. 64 CO2+1C2H5OH,boxlen =19A, Cubic Box, NVT conditionTime step = 4.0 fs, Total run length = 1.08 ns, Analysis run length =120 ps , No electronic degrees of freedom

Near neighbour arrangement of CO2 around C2H5OH

+

64 CO2 + 1 C2H5OH (Classical MD)

Comparison between CPMD & CMD

Potential of Mean Force W(r)g(r) = exp{-

W(r)}Scaled g(r)

Density distribution of CO2 carbon with respect to ethanol oxygen

Lewis acid

Lewis base

Hydrogen bond life time

S(t) = <h()H(t+)><h>

C(t) = <h()h(t+)><h>

64 CO2 + 1 CH3CH2OH (Classical MD)

h(t) = 1, if a pair of atoms are bonded at time t, nmii= 0, otherwiseH(t) = 1, if a pair of atoms are bonded between time 0 to time t, nmii= 0, otherwise

C(t

)

Hydrogen bond

S(t) = 0.127

ps

C(t) =

0.302 ps

Conclusions

Well defined solvent structure in neat scCO2.Red shift in the frequencies of modes, relative to

isolated CO2 molecule.Splitting in symmetric stretch modes, due to FERMI RESONANCE, was observed.Existence of Dipole

MomentNon-linear structure of CO2 molecule. The instantaneous intramolecular OCO angle is 174.4oIntramolecular bond lengths are

unequal.

References :M. Saharay and S. Balasubramanian, J. Chem. Phys. 120 (2004) 9694.M. Saharay and S. Balasubramanian,

ChemPhysChem 5 (2004) 1442.

Ethanol behaves as a co-solvent in scCO2Lewis acid-base interaction is energetically more

favorable than hydrogen Iiibonded interaction between CO2 and C2H5OH.

Hydrogen bond

Radial Distribution Function 64 CO2 + 1 C2H5OH

Ethanol-Ethanol pair interaction energy

Fre

qu

en

cy3000 CO2 + 205 C2H5OH (Classical MD)

Clustering of C2H5OH molecules in scCO2

3000 CO2 + 205 ethanol

Radial Distribution Function3000 CO2 + 205 C2H5OH (Classical MD)

Near neighbour arrangement of CO2 around C2H5OH3000 CO2 + 205 C2H5OH (Classical MD)

ConclusionsWell defined solvent structure in neat scCO2Existence of instantaneous Dipole MomentNon-linear structure of CO2 molecule. The instantaneous intramolecular OCO angle is 174.5o

Intramolecular bond lengths are unequalEnhanced Quadrupole moment

-- Well defined solvent structure around ethanol

-- Reduction of eth_H-CO2_O coordination number with increasing concentration of C2H5OH

1.54% of C2H5OH

N(r) = 0.689 at 2.5 A from MDN(r) = 1.12 at 3.08 A from

CPMD}

N(r) = 0.24 at 2.4 A from MD, 6.4% of C2H5OH

-- Clustering of ethanol molecules in higher concentrationHydrogen bond life

timeimportant in solvating other speciesLewis acid-base interactions are also

being probed

Solvent structure in scCO2

Top view Side view

Density isosurfaces of oxygen atoms that belong to molecules in the first coordination shell of CO2 in supercritical carbon dioxide

Angle Distribution

O

O Oa

ObC2

C1

P