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CBS Methods

The following method keywords specify various Complete Basis Set (CBS) methods of Petersson and coworkers for computing very accurate energies [Nyden81, Petersson88, Petersson91, Petersson91a, Montgomery94, Ochterski96, Montgomery99, Montgomery00]:

  • CBS-4M
  • CBS-QB3

The keywords refer to the modified version of CBS-4 [Ochterski96, Montgomery00], CBS-Q//B3 [Montgomery 99, Montgomery00] and CBS-APNO [Ochterski96] methods, respectively. No basis set should be specified with any of these keywords. The RO prefix may be added to CBS-QB3 to request the ROCBS-QB3 method [Wood06].

These methods are complex energy computations involving several pre-defined calculations on the specified system. All of these distinct steps are performed automatically when one of these keywords is specified, and the final computed energy value is displayed in the output.

Either of the Opt=Maxcyc=n, QCISD=Maxcyc=n or CCSD=Maxcyc=n keywords may be used in conjunction with any of the these keywords to specify the maximum number of optimization, QCISD, or CCSD cycles, respectively.


Do only a single-point energy evaluation using the specified compound model chemistry. No zero-point or thermal energies are included.


Perform the frequencies and single-point energy calculation for the specified model chemistry at the input geometry. Freq=TProjected is implied. This option is not meaningful or accepted for methods such as G1, which use different geometries for the frequencies and the single-point steps. StartFreq is a synonym for NoOpt.


This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor and/or isotopes—298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.

Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 

0 1

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.
isotope mass for atom 1  
isotope mass for atom 2  
isotope mass for atom n  

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared in the molecule specification section. If integers are used to specify the atomic masses, the program will automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18O, and Gaussian uses the value 17.99916).

Energies only.

CBS-4M and CBS-QB3 are available for first and second row atoms; CBS-APNO is available for first row atoms only.

RO may be combined with CBS-4M and CBS-QB3.

The original CBS-4 model chemistry has been updated with both the new localization procedure and improved empirical parameters [Montgomery00]. The new version, CBS-4M, (M referring to the use of Minimal Population localization) is recommended for new studies.

The output from each step of a CBS method calculation is included in the output file. The final section of the file contains a summary of the results of the entire run.

CBS Summary Output. Here is the output from a CBS-QB3 calculation on CH2 (triplet state):

 Complete Basis Set (CBS) Extrapolation:
 M. R. Nyden and G. A. Petersson, JCP 75, 1843 (1981)
 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)
 J. A. Montgomery, J. W. Ochterski, and G. A. Petersson, JCP 101, 5900 (1994)

 Temperature=          298.150000 Pressure=                   1.000000
 E(ZPE)=                 0.016991 E(Thermal)=                 0.019855
 E(SCF)=               -38.936447 DE(MP2)=                   -0.114761
 DE(CBS)=               -0.011936 DE(MP34)=                  -0.018720
 DE(CCSD)=              -0.002759 DE(Int)=                    0.004204
 DE(Empirical)=         -0.006404
 CBS-QB3 (0 K)=        -39.069832 CBS-QB3 Energy=           -39.066969
 CBS-QB3 Enthalpy=     -39.066025 CBS-QB3 Free Energy=      -39.088192

The temperature and pressure are given first, followed by the components terms of the CBS-QB3 energy. The second-to-last line gives the CBS-QB3 energy values (reading across): at 0 K and at the specified temperature (298.15 K by default). The final line gives the CBS-QB3 enthalpy (including the thermal correction for the specified temperature) and the Gibbs free energy computed via the CBS-QB3 method (i.e., the CBS-QB3 energy including the frequency job free-energy correction). All of the energies are in Hartrees.

Rerunning the Calculation at a Different Temperature. The following two-step job illustrates the method for running a second (very rapid) CBS calculation at a different temperature. This job computes the CBS-QB3 energy at 298.15 K and then again at 300 K:

The energy labels thus have the following meanings (CBS-QB3 is used as an example):

CBS-QB3 (0 K)    Zero-point-corrected electronic energy: E0 = Eelec + ZPE
CBS-QB3 Energy    Thermal-corrected energy: E = E0 + Etrans + Erot + Evib
CBS-QB3 Enthalpy    Enthalpy computed using the CBS-QB3 predicted energy: H = E + RT
CBS-QB3 Free Energy    Gibbs Free Energy computed using the CBS-QB3 predicted energy: G = H – TS
# CBS-QB3 Test
CBS-QB3 on formaldehyde
0 1
molecule specification
# CBS-QB3(Restart,ReadIso) Geom=AllCheck Test
300.0 1.0
isotope specifications

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