Experimental data discussion

Experimental data discussion

What properties can we measure?

Properties of what molecules should be targeted?

MRS argues that nonbondeds and charging schemes (which should probably involve fewer parameters than one for every atom) should involve parameterization to small molecule thermodynamic data. A isopropyl group should be have roughly the same parameters no matter the chemical context. Any parameterization scheme should avoid when possible making separate protein/DNA/lipid forces. Adjusting torsions on a molecule-by-molecule basis may not be possible to avoid, especially when joining residues.

MRS would also argue that getting mixture properties right is essential.

X-ray scattering data of liquids

A nice review is here: http://www.hindawi.com/journals/isrn.materials.science/2012/852905/ For water: http://www.hindawi.com/journals/isrn/2013/279463/

What sort of QM should be used?

One question is whether one should use QM to calculate bond lengths and angles. A fundamental issue is whether the bond lengths and angles in a vapor phase system are the same as the bond lengths and angles in a fluid. For example, for methanol we get (http://cccbdb.nist.gov/) for

                            C-O              O-H  

CCSD(T)/6-31G* 1.4268 0.9722

CCSD(T)=FULL/aug-cc-pVTZ 1.4205 0.9586

For experimental liquids, then we get for different diffraction studies.

a. Narten and Habenschuss 1.437 +/- 0.002^a 0.9451 +/- 0.003^b (20 C)

b. Tomberli et al 1.450 +/- 0.005^c (25 C)

a. Narten A H and Habenschuss A 1984 J. Chem. Phys. 80 3387

b. Lees R M and Baker J G 1968 J. Chem. Phys. 48 5299

c. B Tomberli, P A Egelstaff, C J Benmore and J Neuefeind, 2001 J. Phys.: Condens. Matter 13 11405

For water, See discussions of temperature + solvent effects. From http://www1.lsbu.ac.uk/water/molecule.html

"The experimental values for gaseous water molecule are O-H length 0.95718 Å, H-O-H angle 104.474° These values are not maintained in liquid water, where ab initio (O-H length 0.991 Å, H-O-H angle 105.5°) and diffraction studies (O-H length 1.01 Å, O-D length 0.98 Å ; O-H length 0.990 Å, O-D length 0.985 Å; O-D length 0.970 Å, D-O-D angle 106°) suggest slightly greater values, which are caused by the hydrogen bonding weakening the covalent bonding and reducing the repulsion between the electron orbitals. These bond lengths and angles are likely to change, due to polarization shifts, in different hydrogen-bonded environments and when the water molecules are bound to solutes and ions."

What experimental properties are available already?

NIST ThermoLit reporter has a database of thermodynamic information, searchable by mixture composition and property type. There is a lot of existing data, though not always well-curated.

http://trc.nist.gov/thermolit/main/home.html#help

The NIST Standard Reference Database 103b has a large amount of experimental data for binary, ternary, and pure fluids (5 million points), but is not free.

http://www.nist.gov/srd/nist103b.cfm

This is accessible through the ThermoData Engine, again not free ($9000!)

http://trc.nist.gov/tde.html.

They claim to have 80% of the physical data that has ever been generated for organic compounds. http://wtt-pro.nist.gov/wtt-pro/help/source.html

There's a fair amount of experimental data that is stored in the ThermoML format, an XML format for standard storage of thermophysical data.

http://trc.nist.gov/ThermoML.html

How much flexibility in the functional form should there be?

Is LJ 6-12 sufficiently flexible/physical, or should we move to something else? How would we prove that we need to move to something else?

Is fixed charge sufficient, or would we need to move to something else? Is a direct polarization model sufficient? How would we prove it?

In my mind, one simple right way would be do 1) parameterize to binary mixtures, and then see 2) whether ternary mixtures properties were righ.

What properties are sufficient to characterize the thermodynamics?

All thermodynamic properties are functions of the free energy (usually, Gibbs free energy is the easiest to work with, though sometimes, it’s Helmholtz). To eliminate size-extensive quantities, for pure compounds we deal with the molar free energy (g, which is just the chemical potential). For mixtures, it’s the chemical potential of the species as a function of concentration.

Examples for pure properties:

$V = -dg/dP$

$H = -T^2 d(G/T)/dT$

$C_p = (dS/dT)_P = d^2 G/d^2 T$

$\beta_T = -1/V (dV/dP) = -(dP/dG)^(-1) dG^2/dP^2$ (isothermal compressibility)

$\alpha_V = 1/V dV/dT = -(dP/dG)^(-1) dG^2/dPdT$

And so forth. Some of these are a bit easier noting that if $f = \beta G$ and u = \beta H then $u = dg/dT$. Note that it’s usually the derivatives that are the experimental quantities.

For a pure fluid, since $G(T,P)$, a function of only two variables, knowledge of the responses of the free energy to T and P is enough to characterize the macroscopic behavior of the molecule, so knowledge of those properties at T and P is sufficient to describe the fluid.

Fitting directly to the G(T,P) surface even when available can be problematic, however, since small errors in G(T,P) can head to larger errors in the derivative properties, which are the experimentally determined properties.

For composition, where $\vec{x}$ is the vector of compositions, then $G(vec{x}) = N\sum \mu_i x_i$

And all of the various properties of interest can be computed from this.

partial molar volume = $dV/dN_i = dG/dPdN_i

partial molar enthapy = $dH/dN_i = df/dTdN_i

chemical potential = $dG/dN_i$

Some of these, such as partial molar volume as a function of composition, are very easy to measure.

Usually chemical potentials are tabulated in terms of activity coefficients, the deviations of the chemical potential from ideal solution:

Ideal solution:

$\mu(T,P,x) = \mu(T,P) - RT \ln x_i

Non ideal solution:

$\mu(T,P,x) = \mu(T,P) - RT \ln x_i\gamma(T,P,\vec{x})

And so forth.

Some more reading:

http://en.wikipedia.org/wiki/Partial_molar_property