Hi,
Could
you please help me to understand the "double slash" notation that I
see in quantum chemical literature? The notation
is:
method/basis set//method/basis
set
What is the convention -- if any -- for the order
of the calculations, (a) or (b)?
(a)
Is the calculation before the "//" performed first, while the
calculation after the "//" is performed second? In other words,
"do this [left], then that [right]"?
(b) Or
is it the other way around, meaning that the left-hand calculation is
performed ON the output of the right-hand calculation? In other words,
somewhat like an operator acting on a wave function; "do this [left] on the
output of that [right]."
Below are two examples
from the literature. I try to reason through the notation based on these
examples:
(1) Maxwell, Tirado-Rives, and Jorgensen. J.
Comput. Chem. 1995, 16, 984-1010 (
https://doi.org/10.1002/jcc.540160807 ). In this
paper, ab initio calculations were performed to determine torsional
parameters for organic molecules and ions. From the abstract, "The
rotational energy profiles were obtained at the
HF/6-31G*//HF/6-31G*." In certain cases, they also used
MP2/6-31G*//RHF/6-31G* or MP2/6-31G*//MP2/6-31G*. I think this means an
initial, unconstrained geometry optimization of the entire molecule/ion was
performed first, followed by a geometry optimization at each selected,
constrained value of the torsional angle. In the case of MP2//RHF, then,
is MP2 used for the initial optimization and RHF for the scan? Because RHF
is less expensive, I think, that would probably make sense. Based on this,
I would say that MP2//RHF means that MP2 is performed first and RHF is performed
second; in other words, the "double slash" notation is read from left
to right. So interpretation (a) above is
correct.
(2) Liptak and Shields, J. Am. Chem. Soc.
2001, 123, 7314-7319 (
https://doi.org/10.1021/ja010534f ). In this paper,
the free energy of solvation, DeltaG_s, is calculated using an implementation of
the polarizable conductor model (CPCM) -- see the third page (p. 7316) of this
paper. Near the top left-hand side of that page, it says, "The CPCM
calculations were performed as SPCs (single-point calculations) using the
6-31G(d) and 6-31+G(d) basis sets on the HF/6-31G(d) and HF/6-31+G(d) geometries
for each of the six systems." Based on that description, the HF
geometry optimization was performed first and the CPCM single-point calculation
was performed second. So, if my reasoning from example (1) above is
correct (i.e., interpretation (a) above), I'd expect the "double
slash" notation in the paper to be HF//CPCM. But, in fact, it's
not. In the Results section near the bottom of the left-hand side of the
third page (p. 7316), the authors state, "CPCM/6-31G(d)//HF/6-31G(d),
CPCM/6-31+G(d)//HF/6-31G(d), and CPCM/6-31+G(d)//HF/6-31+G(d) are denoted S1,
S2, and S3 [in Table 1]." This, I think, implies that
interpretation (b) above is correct. The strange thing, though, is
that at the bottom of Table 1 on the fourth page [p. 7317], the definitions of
S1, S2, and S3 are different from those stated in the text, by an
"extra" "HF" to the left of the "//"; there, they
state, "S1: CPCM/HF/6-31G(d)//HF/6-31G(d). S2:
CPCM/HF/6-31+G(d)//HF/6-31G(d). S3:
CPCM/HF/6-31+G(d)//HF/6-31+G(d)."
It's
entirely possible, then, that there is no set convention for "double slash
notation" in quantum chemistry (or that I'm misinterpreting these
papers). Could anyone shed some light on this, since I'm not a quantum
chemist?
Thanks so much for any insight you can
provide,
Andrew
Andrew DeYoung,
PhD
Carnegie Mellon University