Ab initio and Classical Molecular Dynamics Simulations of Supercritical Carbon Dioxide

1. 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.

2. Abstract We 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.

3. Motivation Green Solvents scCO2, Room Temperature Ionic Liquids scCO2, an alternative to CFCs for dissolving PTFE Initial decaffeination of coffee using Methylene Chloride ---> hazardous for humans and environment; may cause Cancer Recent alternative is scCO2; non-toxic and does not remove flavour Polymerization and Polymer processing Reaction medium for chemical synthesis Ethanol in scCO2 enhances the solvation properties

4. 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 = 318.15K, Nose-Hoover chain, 32 molecules CO2, Cubic boxlength = 14.956 A. 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 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.

5. Density functional theory Yi (r) = S Cki exp(ik.r) Kohn-Sham energy functional Norm-Conserving Pseudopotentials Equations of motion Snapshot of CO2 molecules

6. Radial Distribution Function

7. Solvent structure in scCO2 Density isosurfaces of oxygen atoms that belong to molecules in the first coordination shell of CO2 in supercritical carbon dioxide Angle Distribution P O Top view Side view Oa C1 C2 O Ob

8. MSD & VACF Mean Square Displacement Velocity Auto-Correlation Cv (t) 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

9. Power spectrum 628 (667) 1319 (1338) 1228 Bending Asymmetric stretch 2309 (2349) Symmetric stretch Numbers in brackets are for ‘ISOLATED’ CO2. Splitting in symmetric stretch is due to ‘FERMI RESONANCE’

10. Distribution of coordination no. and intramolecular angle Coordination no. Intramolecular angle q P

11. Multipole moment calculation Dipole moment calculation Z mi = dipole moment of i-th molecule Quadrupole moment calculation 0 X Y Qmn = quadrupole moment component rc = 1.3 A; zc = 2.8 A

12. Multipole moment distribution Instantaneous Quadrupole moment Instantaneous Dipole moment <m> from CPMD calculation=0.85 D <Q> from CPMD = 6.1x10-26 esu Geometry optimized value for isolated molecule from CPMD = 4.26x10-26 esu Experimental value = 4.1x10-26 esu

13. d-Ethanol in CO2 (Methodology) 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 Classical Molecular Dynamics TraPPe potential parameters, PINY-MD code, Coulombic + Lennard-Jones potential A. 3000 CO2 molecules+205 Ethanol molecules, boxlen =63A B. 64 CO2+1C2H5OH,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

14. Near neighbour arrangement of CO2 around C2H5OH 64 CO2 + 1 C2H5OH (Classical MD) Potential of Mean Force W(r) g(r) = exp{-bW(r)} Scaled g(r) Lewis acid Comparison between CPMD & CMD +d Density distribution of CO2 carbon with respect to ethanol oxygen -d Lewis base

15. Hydrogen bond life time 64 CO2 + 1 CH3CH2OH (Classical MD) tS(t) = 0.127 ps tC(t) = 0.302 ps C(t) Hydrogen bond S(t) = <h(t)H(t+t)> h(t) = 1, if a pair of atoms are bonded at time t,nmii= 0, otherwise <h> H(t) = 1, if a pair of atoms are bonded between time 0 to time t,nmii= 0, otherwise C(t) = <h(t)h(t+t)> <h>

16. 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 Moment • Non-linear structure of CO2 molecule. The instantaneous intramolecular OCO angle is 174.4o • Intramolecular bond lengths are unequal. • Ethanol behaves as a co-solvent in scCO2 • Lewis acid-base interaction is energetically more favorable than hydrogen Iiibonded interaction between CO2 and C2H5OH. References : • M. Saharay and S. Balasubramanian, J. Chem. Phys. 120 (2004) 9694. • M. Saharay and S. Balasubramanian, ChemPhysChem 5 (2004) 1442.

17. Hydrogen bond +d -d

18. Radial Distribution Function 64 CO2 + 1 C2H5OH

19. Ethanol-Ethanol pair interaction energy 3000 CO2 + 205 C2H5OH (Classical MD) Frequency

20. Clustering of C2H5OH molecules in scCO2 3000 CO2 + 205 ethanol

21. Radial Distribution Function 3000 CO2 + 205 C2H5OH (Classical MD)

22. Near neighbour arrangement of CO2 around C2H5OH 3000 CO2 + 205 C2H5OH (Classical MD)

23. Conclusions Well defined solvent structure in neat scCO2 Existence of instantaneous Dipole Moment Non-linear structure of CO2 molecule. The instantaneous intramolecular OCO angle is 174.5o Intramolecular bond lengths are unequal Enhanced Quadrupole moment Reduction of eth_H-CO2_O coordination number with increasing concentration of C2H5OH - } N(r) = 0.689 at 2.5 A from MD 1.54% of C2H5OH N(r) = 1.12 at 3.08 A from CPMD N(r) = 0.24 at 2.4 A from MD, 6.4% of C2H5OH Well defined solvent structure around ethanol - Clustering of ethanol molecules in higher concentration - Hydrogen bond life time important in solvating other species Lewis acid-base interactions are also being probed

24. Solvent structure in scCO2 Density isosurfaces of oxygen atoms that belong to molecules in the first coordination shell of CO2 in supercritical carbon dioxide Angle Distribution P O Top view Side view C1 Ob C2 O Oa