Subject: CBS references, was G94 Accurate Methods?

From: [email-masked] (Joe Ochterski)
Date: Wed, 12 Apr 1995 06:49:40 -0400

>  What I am not familiar with is the complete basis set methods (CBS) 
>  called CBS-4, CBS-q. CBS-Q and CBS-APNO [in GAUSSIAN 94].

These methods were developed by George Petersson (Wesleyan Univ.) and
several collaborators.  The CBS-Q model produces better results than
either G2 or G2(MP2), and is comparable in speed to G2(MP2). CBS-4 is
considerably faster and gives results accurate to ~2 kcal/mol. CBS-APNO
is accurate to about 0.5 kcal/mol. Here is a brief description of the
CBS models:

With the development of accurate correlation methods like CCSD(T),
QCISD(T), etc., the largest errors in ab initio thermochemical
calculations come from basis set truncation.  The CBS models use the known
 asymptotic convergence of pair natural orbital expansions to
extrapolate finite basis calculations to an estimated complete basis set
(CBS) limit (see references below).

These CBS extrapolation techniques have been used by Ochterski,
Petersson, and Montgomery to construct a family of CBS model chemistries
(CBS-4, CBS-q, CBS-Q and CBS-APNO). Like G2 theory, we obtain the CBS
energy via a series of calculations. Our analysis shows that the order
by order contributions to chemical energy differences generally decrease
with order of perturbation theory, while the computational expense
increases rapidly.  The CBS models take advantage of these complimentary
trends by using progressively smaller basis sets for the higher orders
of perturbation theory.

The CBS-Q model starts with a geometry optimization at the MP2 level of
theory. It then uses a large basis set MP2 calculation as a base energy,
and a CBS extrapolation to correct the energy through second order. Two
calculations are used to approximate higher order contributions. We use
MP4(SDQ)/6-31+(d,p) with extra polarization functions on sulfur
phosphorous and chlorine to approximate the higher order effects of
polarization functions, and QCISD(T)/6-31+G* for still higher order
effects.  This model also has corrections for zero-point energy and spin
contamination and a size-consistent higher order correction.  The CBS-Q
model improves the treatment at every level of theory, and the CBS-APNO
improves it still further. The CBS-APNO model improves the treatment at
every level of theory. We developed the CBS-4 model in a similar way to
treat substantially larger systems, althought somewhat less accurately.

All the models have been found to reproduce the 125 experimental
energy differences in the G2 test set with relatively small errors (63
differences were used for CBS-APNO):

                      Accuracy of Models (kcal/mole)
              CBS-4    CBS-q     CBS-Q    G2(MP2)     G2    CBS-APNO
Mean Abs Dev   2.0       1.7      1.0       1.6       1.2     0.5
RMS Dev        2.5       2.2      1.3       2.0       1.5     0.7
Maximum        7.0       5.4      3.8       6.3       5.1     1.5

                           Relative Speed Up
Molecule              CBS-4      CBS-Q     G2(MP2)       G2
--------              -----      -----     -------      ----
water                  3.8        1.4        1.3         1.0
acetylene              5.9        2.1        2.1         1.0                 
propane               25.3        6.0        2.3         1.0
F2C=O                 25.9        3.1        2.5         1.0
SiF4                  59.0        9.6        5.1         1.0
benzene               23.8        1.8        1.0

CBS-Q offers better accuracy and speed than the G2 family of models.
Molecules with many hydrogens fare particularly well. CBS-4 can be
used to treat much larger systems. CBS-APNO is suitable for systems
where accuracy is critical.

General Complete Basis Set (CBS) Extrapolation References:
 M. R. Nyden and G. A. Petersson, JCP 75, 1843 (1981)
 G. A. Petersson, A. Bennett, T. G. Tensfeldt, M. A. Al-Laham, W. A.
   Shirley and J. Mantzaris, J. Chem. Phys. 89, 2193 (1988).
 G. A. Petersson and M. A. Al-Laham, JCP 94, 6081 (1991)
 G. A. Petersson, T. Tensfeldt, and J. A. Montgomery, JCP 94, 6091 (1991)
CBS-APNO:
 J. A. Montgomery, J. W. Ochterski, and G. A. Petersson, JCP 101, 5900 (1994)
CBS-4, CBS-q, CBS-Q
 J. W. Ochterski, G. A. Petersson and J. A. Montgomery, Jr., submitted
  to J. Chem. Phys.

A PostScript version of the CBS-4 paper is available via anonymous FTP to
dali.chem.wesleyan.edu, file name:/pub/cbs-4.paper.ps.

It is also available on WWW. The URL is:

http://dali.chem.wesleyan.edu/papers/paper.950120.ps 

If neither of these options is available to you, please ask Gaussian,
Inc. for a printed copy. They can be reached at [email-masked] or
(412)279-6700.

Joe Ochterski
[email-masked]