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