Chemistry Reference
In-Depth Information
electrons. Besides, the use of molecular orbital calculations in intermolecular
problems was severely limited by the Hartree-Fock approach, with its inadequate
treatment of electron correlation. Both problems are nowadays less critical, if
not completely solved: benchmark ab initio calculations of top quality including
dispersion effects can be carried out for intermolecular dimers of chemical sig-
nificance, like aromatic ring-stacking or hydrogen-bonding [
34
-
36
], or DNA base
pairs [
37
] or other biomolecular binding motifs [
38
,
39
]. Nowadays, systems with
about 30-50 second-row atoms are tractable [
34
]. The dimerization energies thus
obtained are reliable beyond doubt, and much more reliable than the scarce and
uncertain experimental values. This is a case in which theoretical chemistry is
ahead of experimental chemistry. These calculations still require highly sophisti-
cated computer resources, but computing times are quickly decreasing. Moreover,
this benchmarking provides a safe way to the parameterization of much more cost-
efficient semiempirical methods.
In typical organic crystals, molecular pairs are easily sorted out and ab initio
methods that work for gas-phase dimers can be applied to the analysis of molecular
dimers in the crystal coordination sphere. The entire lattice energy can then be
approximated as a sum of pairwise molecule-molecule interactions; examples are
crystals of benzene [
40
], alloxan [
41
], and of more complex aziridine molecules
[
42
]. This obviously neglects cooperative and, in general, many-body effects,
which seem less important in hard closed-shell systems. The positive side of this
approach is that molecular coordination spheres in crystals can be dissected
and bonding factors can be better analyzed, as examples in the next few sections
will show.
The proper way of dealing with periodic systems, like crystals, is to periodicize the
orbital representation of the system. Thanks to a periodic exponential prefactor, an
atomic orbital becomes a periodic multicenter entity and the Roothaan equations for
the molecular orbital procedure are solved over this periodic basis. Apart from an
exponential rise in mathematical complexity and in computing times, the con-
ceptual basis of the method is not difficult to grasp [
43
]. Software for performing
such calculations is quite easily available to academic scientists (see, e.g., CASTEP at
www.castep.org
; CRYSTAL at
www.crystal.unito.it
; WIEN2k at
www.wien2k.at
)
.
There is, of course, a range of accuracy, inversely proportional to human and
computational cost. To summarize, quantum chemical methods for intermolecular
energy calculations are, in descending order of complexity and cost (each of these
methods can be applied in a nonperiodic or a periodic-orbital approach):
- Full ab initio electron-correlation methods, fromMP2 to CCSD(T) (the acronyms
refer to increasing complexity in the treatment of correlation, with increasing
computational cost); include polarization and dispersion contributions and apply
to any molecular system. Accuracy depends on the size of the basis set, but
so-called complete set limit calculations can nowadays be carried out.
- High-quality, large basis set Hartree-Fock calculations; may be reliable for
highly polar molecular systems (typically, amino acids) where Coulombic
energies play the major role [
44
].
