Handbook of Solvents - George Wypych - ChemTech - Ventech!

478 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
(non-Euclidean geometry has to be considered) are expected to decrease as the system increases,
so that in the case of solutes of large size, “spherical boundary conditions” are expected
to be a noticeable method for simulating bulk liquids. In this case, boundary
conditions can be obtained by inserting the spherical cell into a large sphere and then by performing
a simulation of a lower computational level in the extended region. However, recent
versions of the method tend to replace the second portion of the liquid, described at a
molecular level, with a description by means of continuum models (see Section 8.7.3),
which can be easily extended up to r=∞.
Turning attention to the accuracy gained in the calculation of liquids properties by molecular
simulations, it turns out that certain properties can be calculated more accurately
than others. For example, the mean potential energy can be obtained with an uncertainty less
than 1%; larger errors are associated with the calculation of thermodynamic properties,
such as, the specific heat, that are linked to fluctuations in a microscopic variable. Typically,
an uncertainty of the order of 10% is expected. 42
The dynamical properties of liquids can be generally computed by calculating the
time-correlation functions. They provide a quantitative description of the microscopic dynamics
in liquids. Here, computer simulations play a key role, since they give access to a
large variety of correlation functions, many of which are not measurable by laboratory experiments.
In a MD simulation, the value of the correlation function CAB(t) at time t is calculated
by averaging the product A(t+s)B(s) of two dynamical variables, A(t) and B(t) over
many choices of the time origin s. It has been shown that the uncertainty in time correlations
between events separated by an interval τ increases as τ 1/2 . In addition, the correlated motion
of large numbers of particles determines many dynamical properties. These collective properties
are usually subjected to larger errors than in the case of single particle properties, and
their calculation is very demanding from a computational point of view. 42
QM/MM
As final remark of this section, we would like to briefly mention the so-called QM/MM
method. 78,79
In this approach, a part of the system (the solute M) is treated explicitly by a quantum
mechanical (QM) method, while another part (the bulk solvent S) is approximated by a standard
Molecular Mechanics (MM) force field. It is clear that such a method takes advantage
of the accuracy and generality of the QM treatment, and of the computational efficiency of
the MM calculation.
Using the BO approximation and assuming that no charge transfer occurs between S
and M, the Hamiltonian of the system can be separated into three terms:
H� = H� + H� + H�
[8.112]
M MS SS
where the first term is the Hamiltonian of the solute in vacuo, the second one represents the
QM/MM solute-solvent interaction and couples solvent effects into QM calculations. It can
be separated in an electrostatic term, a van der Waals terms and a polarization term, i.e.:
� � el
H H H�vdW H�
pol
= + + [8.113]
MS MS
MS
MS