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The Hydration Structure of Carbon Monoxide by Ab Initio Methods

The solvation of carbon monoxide (CO) in liquid water is important for understanding its toxicological effects and biochemical roles. In this paper, we use ab initio molecular dynamics (AIMD) and CCSD(T)-F12 calculations to assess the accuracy of the Straub and Karplus molecular mechanical (MM) model for CO(aq). The CCSD(T)-F12 CO--H2O potential energy surfaces show that the most stable structure corresponds to water donating a hydrogen bond to the C center. The MM-calculated surface it incorrectly predicts that the O atom is a stronger hydrogen bond acceptor than the C atom. The AIMD simulations indicate that CO is solvated like a hydrophobic solute, with very limited hydrogen bonding with water. The MM model tends to overestimate the degree of hydrogen bonding and overestimates the atomic radius of the C atom. The calculated Gibbs energy of hydration is in good agreement with experiment (9.3 kJ/mol calc. vs 10.7 kJ/mol exptl.). The calculated diffusivity of CO(aq) in TIP3P-model water was 5.19 x 10-5 cm2/s calc., more than double the experimental value of 2.32 x 10-5 cm2/s


Parameters and Simulation Cell
Calculations of the MM CO-H 2 O potential energy surfaces and the MD simulations structure of CO(aq) were performed using CHARMM c40b2. 34 The parameters for the Straub and Karplus model for CO are given in Table I. The water molecules were represented using the CHARMM variant of the TIP3P-model. 35,36 For the simulations of CO in bulk water, a cubic simulation cell was used with an average cell length of 30.8Å. Lennard-Jones interactions were scaled to zero using a switching function over the 10-12Å range. Electrostatic interactions were calculated using the Particle Mesh Ewald (PME) method using a 32 × 32 × 32 grid. 37 The simulation cell contained 995 water molecules and 1 CO molecule. The simulations to calculate the solvation energies and the radial distribution functions (rdf) used a Langevin thermostat (γ = 5 ps −1 ) and an Andersen-Hoover barostat. 38,39 The CHARMM input file is included in Supplementary Information.
The two states, denoted A and B, correspond to the states where the given solventsolute interaction is calculated or neglected, respectively. These states are coupled by the thermodynamic integration (TI) variable λ, through the definition of a linearly-interpolated potential, Here V A and V B are the potential energies of the A and B states.
The repulsive component of the Gibbs energy was calculated using a staged procedure where the repulsive component of the solvent-solute Lennard-Jones interaction potential was reduced to zero using a 9 stage free energy perturbation (FEP) approach. 40,41 For each TI or FEP simulation, the system was equilibrated for 1 ns followed by a 2 ns sampling simulation. The Gibbs energies were calculated using the Weighted Histogram Analysis Method (WHAM). 42 The reported Gibbs energy was calculated from an average of three independent simulations.

Diffusion Calculations
Simulations used to calculate the CO diffusion coefficient were performed with a Nosé thermostat with a response time of 0.1 ps. The systems were equilibrated for 1 ns before a 2 ns trajectory was collected. The reported diffusivity was calculated from an average of three independent simulations. The CO diffusion coefficient (D PBC ) under periodic boundary conditions was calculated using the Einstein relation, where r(t) is the position of the molecule at time, t. Yeh and Hummer found that the viscosity of a liquid simulated under periodic boundary conditions depends on the size of the system, which spuriously lowers the calculated diffusivities. 43 A correction was applied to our calculated diffusivities using, Here, η is the solvent viscosity and L is the length of the simulation cell.

C. AIMD Simulations
The AIMD simulations of aqueous CO were performed using CP2K version 2.6. 44 The MOLOPT-TZVP basis set was used for all atoms. 45 The PBE exchange-correlation functional was used 32 with the Grimme D3 correction for dispersion. 33 The simulation was initi-   Information.

A. Electric Properties
The models predict significantly different values for the electric moments of CO (Table   II)

C. Potential Energy Surfaces
Two-dimensional potential energy surfaces were calculated for the interaction between

D. Radial Distribution Functions
To examine CO-H 2 O interactions in bulk water, radial distribution functions were calculated from the AIMD and MM trajectories of CO(aq). Figure 5  The most significant difference between these two models is that the first peak of the C-O(H 2 ) rdf occurs at a 0.1Å larger distance than the AIMD value. This suggests that the Lennard-Jones radius of the monoxide carbon atom in the MM model is too large. This is consistent with the potential energy surfaces plotted in Figure 3, where the MM surface  Both models have very modest shoulders on the left-side of the first peak of the rdf for the distance between the monoxide C-atom and the water hydrogen ( Figure 5 (c)).
This indicates that neither model predicts that there are strong hydrogen bonds between the monoxide carbon and water molecules in aqueous solutions. This is apparent in the Wannier-localized orbitals, 56 which shows carbon-centered lone pair to be too distant from the water hydrogen atoms to serve as a strong hydrogen bond acceptor ( Figure 6).
The first peak of the MM RDF for the monoxide oxygen and water hydrogen distance ( Figure 5 (d)) has a shoulder on the left side between 1.9 and 2.1Å that is consistent with a water molecule donating a hydrogen bond to the monoxide oxygen. This shoulder is much more pronounced in the rdf calculated from the MM simulation and is a minor feature in the AIMD rdf. This is consistent with the QM potential energy surfaces, which show that the MM model overestimates the strength of hydrogen bonds where the monoxide oxygen is the acceptor.

E. Hydration Energy
To quantify how accurately this model predicts the CO-water interactions, the Gibbs energy of hydration of CO was calculated using alchemical FEP (Table III E These interactions are generally consistent with the hydration of a non-polar solute. 26

F. Diffusion Coefficient
The calculated diffusivity of CO in liquid water at 30 • C was calculated using the finitesize corrected Einstein relation (Eqn 3. A diffusivity of D = 5.19 ± 0.82 × 10 −5 cm 2 /s was calculated. This is considerably larger than the experimental value of D = 2.32±0.07×10 −5 cm 2 /s. 58 . The TIP3P water model predicts a viscosity that is significantly lower than the experimental value, so by the Stokes-Einstein equation, the diffusivity of the solutes is this medium will be overestimated. 59  bonds to the C atom are stronger. In comparison to the AIMD results, the atomic radius of the MM monoxide C atom model appears to be slightly too large by roughly 0.05Å. Despite these limitations, the ∆G • hydr of this model is in very good agreement with the experimental value (9 kJ mol −1 calc. vs 10 kJ mol −1 exptl.). The diffusivity the MM model is significantly higher than the experimental value (5.19 × 10 −5 cm 2 /s calc. vs 2.32 × 10 −5 cm 2 /s exptl.). An improved MM model could likely be designed by repositioning the off-center charge to be located in the place of the C-centered lone pair and changing the charges to reflect the actual electric moments. The Lennard-Jones radius of the C atom should also be increased.
Improving the diffusivity would require developing a model that can be used with a water model with an accurate viscosity.

SUPPLEMENTARY MATERIAL
See supplementary material for CP2K, CHARMM, and TURBOMOLE input files.