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 – , India.

Abstract We have performed Car-Parrinello molecular dynamics (CPMD) simulations of scCO 2 at K and at the density of 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 CO 2 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 scCO 2. 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 6.1x 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 CO 2 molecule. CPMD & classical MD calculations of ethanol in scCO 2 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 CO 2.

Motivation Green Solvents scCO 2, Room Temperature Ionic Liquids scCO 2, an alternative to CFCs for dissolving PTFE Recent alternative is scCO 2 ; non-toxic and does not remove flavour Initial decaffeination of coffee using Methylene Chloride ---> hazardous for humans and environment; may cause Cancer Reaction medium for chemical synthesis Ethanol in scCO 2 enhances the solvation properties Polymerization and Polymer processing

Methodology Car-Parrinello Molecular Dynamics (CPMD) Kohn-Sham formulation of DFT using LDA, CPMD code Vanderbilt ultrasoft pseudopotential,Plane wave cutoff = 25 Ry, NVT condition, T = K, Nose-Hoover chain, 32 molecules CO 2, Cubic boxlength = . 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 months Number of electrons = 512 Classical Molecular Dynamics (MD) EPM2 model, PINY-MD code, Coulombic + Lennard-Jones potential, 100 molecules CO 2, Boxlength = 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) =  C k i exp(ik.r) Snapshot of CO 2 molecules

Radial Distribution Function

Solvent structure in scCO 2 Top view Side view Density isosurfaces of oxygen atoms that belong to molecules in the first coordination shell of CO 2 in supercritical carbon dioxide Angle Distribution O O Oa Ob C2 C1 P

MSD & VACF Mean Square DisplacementVelocity Auto-Correlation D CPMD = 2.29 x cm 2 /sec, D MD = 2.17 x cm 2 /sec D CPMD = 2.50 x cm 2 /sec, D MD = 2.62 x cm 2 /sec D exp = 2.02 x cm 2 /sec C v (t)

Power spectrum 628 (667) (1338) Bending Symmetric stretch Asymmetric stretch 2309 (2349) Numbers in brackets are for ‘ISOLATED’ CO 2. Splitting in symmetric stretch is due to ‘FERMI RESONANCE’

Distribution of coordination no. and intramolecular angle Coordination no. P Intramolecular angle 

Z X Y Multipole moment calculation 0 Dipole moment calculation  = dipole moment of i-th molecule Quadrupole moment calculation Q mn = quadrupole moment component r c = 1.3 A; z c = 2.8 A

Multipole moment distribution Instantaneous Quadrupole momentInstantaneous Dipole moment from CPMD calculation=0.85 D from CPMD = 6.1x esu Experimental value = 4.1x esu Geometry optimized value for isolated molecule from CPMD = 4.26x esu

2 d-Ethanol in CO 2 (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 = K, Nose-Hoover chain, 64 CO 2 molecules + Ethanol (C 2 D 5 OD) molecule, Cubic box length = 19.0A. Time step = 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 potential A CO 2 molecules+205 Ethanol molecules, boxlen =63A B. 64 CO 2 +1C 2 H 5 OH,boxlen =19A, Cubic Box, NVT condition Time step = 4.0 fs, Total run length = 1.08 ns, Analysis run length =120 ps, No electronic degrees of freedom

Near neighbour arrangement of CO 2 around C 2 H 5 OH ++  64 CO C 2 H 5 OH (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) = C(t) = 64 CO CH 3 CH 2 OH (Classical MD) h(t) = 1, if a pair of atoms are bonded at time t, nmii= 0, otherwise H(t) = 1, if a pair of atoms are bonded between time 0 to time t, nmii= 0, otherwise C(t) Hydrogen bond  S(t) = ps  C(t) = ps

Conclusions  Well defined solvent structure in neat scCO 2.  Red shift in the frequencies of modes, relative to isolated CO 2 molecule.  Splitting in symmetric stretch modes, due to FERMI RESONANCE, was observed.  Existence of Dipole Moment  Non-linear structure of CO 2 molecule. The instantaneous intramolecular OCO angle is o  Intramolecular bond lengths are unequal. References :  M. Saharay and S. Balasubramanian, J. Chem. Phys. 120 (2004)  M. Saharay and S. Balasubramanian, ChemPhysChem 5 (2004)  Ethanol behaves as a co-solvent in scCO 2  Lewis acid-base interaction is energetically more favorable than hydrogen Iiibonded interaction between CO 2 and C 2 H 5 OH.

  Hydrogen bond

Radial Distribution Function 64 CO C 2 H 5 OH

Ethanol-Ethanol pair interaction energy Frequency 3000 CO C 2 H 5 OH (Classical MD)

Clustering of C 2 H 5 OH molecules in scCO CO ethanol

Radial Distribution Function 3000 CO C 2 H 5 OH (Classical MD)

Near neighbour arrangement of CO 2 around C 2 H 5 OH 3000 CO C 2 H 5 OH (Classical MD)

Conclusions Well defined solvent structure in neat scCO 2 Existence of instantaneous Dipole Moment Non-linear structure of CO 2 molecule. The instantaneous intramolecular OCO angle is o Intramolecular bond lengths are unequal Enhanced Quadrupole moment - Well defined solvent structure around ethanol - Reduction of eth_H-CO 2 _O coordination number with increasing concentration of C 2 H 5 OH 1.54% of C 2 H 5 OH N(r) = at 2.5 A from MD N(r) = 1.12 at 3.08 A from CPMD } N(r) = 0.24 at 2.4 A from MD, 6.4% of C 2 H 5 OH - Clustering of ethanol molecules in higher concentration Hydrogen bond life time important in solvating other species Lewis acid-base interactions are also being probed

Solvent structure in scCO 2 Top viewSide view Density isosurfaces of oxygen atoms that belong to molecules in the first coordination shell of CO 2 in supercritical carbon dioxide Angle Distribution O OOa Ob C2 C1 P