The absolute entropy of a system can be defined through the use of statistical mechanics (see an undergraduate physical chemistry text--McQuarrie, if you are well-versed in calculus). Using Boltzmann statistics, one introduces, W, the weight of configuration. This is defined as the most probable configuration of a system. I find this to be utterly abstract for all but the most simplistic systems. It is easier to look at things instead using, q, the partition function (the wikipedia page on this topic is fairly informative: http://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics
). Using this formalism, one can derive the relationship of entropy with temperature:
This is the general form with which entropy can be computed. As far as the absolute enthalpy and free energy, if one introduced the Maxwell relations, we can attain these using classical thermodynamic relations (taking internal energy and entropy to be known quantities which are obtained from earlier derivations). Chiefly, we must find an expression for the pressure of a system as a function of the partition function. Using a relationship gained from deriving the Maxwell relations we know that:
, where Q is the more general molecular partion function. From classical thermodynamics we know that H=U+PV, and we know all of the quantities in question and can obtain the absolute enthalpy as a function of the partition function:
Clearly, at this point we can put together H and S and form the aformentioned G. Using the farmiliar relation: G=H-TS. doing so, we get:
Where I've used the more tractable expressions for A, the Helmholtz energy, and p, the pressure, and also the relationship:
The absolute Gibbs Free energy can be obtained exactly (in theory, although the partition functions required for analysis are rarely exact except for the most ideal systems eg. monatomic ideal gas, ideal diatomic gas...). Approximate partition functions are used in the absence of exact ones and most electronic structure packages have the ability to compute the absolute entropy, enthalpy and free energy after calculating the vibrational frequencies. From there theoretical entropies, enthalpies and free energies of reaction or activation (using transition state structures) can be postulated.
Hope this helps!