_{2}solvation free energy using quasi-chemical theory

^{1}and Susan B. Rempe

^{1,a)}

### Abstract

Accumulation of greenhouse gases, especially carbon dioxide, is believed to be the key factor in global climate change. To develop effective ways to remove CO_{2} from the atmosphere, it is helpful to understand the mechanism of CO_{2} solvation first. Here we investigate the thermodynamics of CO_{2} hydration using quasi-chemical theory. Two approaches for estimating hydration free energy are carried out. Both agree reasonably well with experimental measurements. Analysis of the free energy components reveals that the weak hydration free energy results from a balance of unfavorable molecular packing and favorable chemical association.

This work was supported by Sandia's LDRD program. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

I. INTRODUCTION

II. METHODS

A. Molecular dynamics simulations

B. Quasi-chemical theory for hydration free energy calculations

C. Direct approach

D. Cluster approach

III. RESULTS AND DISCUSSION

A. Thermodynamic integration molecular dynamics

B. Direct approach

1. Defining an inner shell

2. Solvation free energy calculation

3. Choice of inner-shell radius

C. Cluster approach

1. Inner-shell gas phase calculation

2. Outer-shell contribution

IV. CONCLUSION

### Key Topics

- Carbon dioxide
- 127.0
- Free energy
- 75.0
- Solvents
- 36.0
- Electrostatics
- 25.0
- Water vapor
- 13.0

## Figures

The simulation box with CO_{2} solvated in water. CO_{2} is displayed in ball-and-stick form while water molecules are shown in licorice representation. The three overlapping spherical volumes represent the inner-shell region with R_{o} = 3.3 Å (radius of the sphere centered on oxygen atoms) and R_{c} = 3.925 Å (radius of the sphere centered on the carbon atom).

The simulation box with CO_{2} solvated in water. CO_{2} is displayed in ball-and-stick form while water molecules are shown in licorice representation. The three overlapping spherical volumes represent the inner-shell region with R_{o} = 3.3 Å (radius of the sphere centered on oxygen atoms) and R_{c} = 3.925 Å (radius of the sphere centered on the carbon atom).

Radial distribution function (RDF), g(r), of CO_{2} and water oxygen atoms. Blue line depicts the RDF of CO_{2} carbon and water oxygens. Green and red lines represent the RDFs of two CO_{2} oxygens and water oxygens. The shoulder of the CO_{2} carbon-water RDF is presumably due to the uneven distribution of the water molecules in the first hydration shell caused by the existence of the two CO_{2} oxygens.

Radial distribution function (RDF), g(r), of CO_{2} and water oxygen atoms. Blue line depicts the RDF of CO_{2} carbon and water oxygens. Green and red lines represent the RDFs of two CO_{2} oxygens and water oxygens. The shoulder of the CO_{2} carbon-water RDF is presumably due to the uneven distribution of the water molecules in the first hydration shell caused by the existence of the two CO_{2} oxygens.

Inner-shell free energy contribution based on corrdination number distribution (RT lnx_{n}) with the inner-shell boundary at R_{c} = 3.925 Å (R_{o} = 3.3 Å). The red line with squares gives the observed data points while the black line is the extra/interpolation of a second-order polynomial function.

Inner-shell free energy contribution based on corrdination number distribution (RT lnx_{n}) with the inner-shell boundary at R_{c} = 3.925 Å (R_{o} = 3.3 Å). The red line with squares gives the observed data points while the black line is the extra/interpolation of a second-order polynomial function.

Packing contribution to the solvation free energy in terms of radius. Red squares are the observed points. The solid black line represents the extrapolation of a polynomial function.

Packing contribution to the solvation free energy in terms of radius. Red squares are the observed points. The solid black line represents the extrapolation of a polynomial function.

Decomposition of solvation free energy of CO_{2} with respect to the radius of the inner shell. Blue diamonds represent the inner-shell chemical contribution; red squares represent the packing term; green triangles are the long-range contributions including electrostatics and van der Waals terms. The sum gives the total solvation free energy, denoted in purple crosses.

Decomposition of solvation free energy of CO_{2} with respect to the radius of the inner shell. Blue diamonds represent the inner-shell chemical contribution; red squares represent the packing term; green triangles are the long-range contributions including electrostatics and van der Waals terms. The sum gives the total solvation free energy, denoted in purple crosses.

Coordination number distributions, p(n), for various inner-shell radii ranging from 2.7 to 3.3 Å. The most probable number of water molecules surrounding CO_{2} in liquid water ranges from *n* = 1 to *n* = 7, depending on the inner-shell observation volume.

Coordination number distributions, p(n), for various inner-shell radii ranging from 2.7 to 3.3 Å. The most probable number of water molecules surrounding CO_{2} in liquid water ranges from *n* = 1 to *n* = 7, depending on the inner-shell observation volume.

QM-optimized structures of CO_{2}-water clusters with various numbers of water ligands from *n* = 1 to *n* = 6.

QM-optimized structures of CO_{2}-water clusters with various numbers of water ligands from *n* = 1 to *n* = 6.

## Tables

Van der Waals parameters for CO_{2} and water interactions. The parameters were determined using the combination rule (Ref. 41) from the AMBER force field. ε_{ ij } is the well depth of the potential while σ_{ ij } is the radius. Ow represents the oxygen atom of water.

Van der Waals parameters for CO_{2} and water interactions. The parameters were determined using the combination rule (Ref. 41) from the AMBER force field. ε_{ ij } is the well depth of the potential while σ_{ ij } is the radius. Ow represents the oxygen atom of water.

Hydration free energies of CO_{2} in terms of coordination number using the cluster approach. Individual terms are listed. *μ* _{ IS }, the total inner-shell contribution, includes the gas-phase binding free energy Δ*G* ^{(0)}, anharmonicity correction *G* ^{anharm}, inner-shell dispersion effects, , the density term *μ* ^{ den } = nRTln1354, the entropic penalty and the probability term RTlnp(n). The outer-shell components consist of the long-range electrostatic interaction, ; long-range van der Waals interaction, ; and molecular packing term, Δμ^{ pac }. μ^{ ex } is the total solvation free energy.

Hydration free energies of CO_{2} in terms of coordination number using the cluster approach. Individual terms are listed. *μ* _{ IS }, the total inner-shell contribution, includes the gas-phase binding free energy Δ*G* ^{(0)}, anharmonicity correction *G* ^{anharm}, inner-shell dispersion effects, , the density term *μ* ^{ den } = nRTln1354, the entropic penalty and the probability term RTlnp(n). The outer-shell components consist of the long-range electrostatic interaction, ; long-range van der Waals interaction, ; and molecular packing term, Δμ^{ pac }. μ^{ ex } is the total solvation free energy.

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