Code author: Lori A. Burns
Section author: Lori A. Burns
Function to define a multistage energy method from combinations of basis set extrapolations and delta corrections and condense the components into a minimum number of calculations.
Aliases :  cbs() 

Returns:  (float) – Total electronic energy in Hartrees 
Psi variables: 
Caution
Some features are not yet implemented. Buy a developer a coffee.
As represented in the equation below, a CBS energy method is defined in several sequential stages (scf, corl, delta, delta2, delta3, delta4, delta5) covering treatment of the reference total energy, the correlation energy, a delta correction to the correlation energy, and a second delta correction, etc.. Each is activated by its stage_wfn keyword and is only allowed if all preceding stages are active.
Here, is an energy or energy extrapolation scheme, and the following also hold.
A translation of this ungainly equation to example [5] below is as follows. In words, this is a double and triplezeta 2point Helgakerextrapolated CCSD(T) coupledcluster correlation correction appended to a triple and quadruplezeta 2point Helgakerextrapolated MP2 correlation energy appended to a SCF/augccpVQZ reference energy.
The presence of a stage_wfn keyword is the indicator to incorporate (and check for stage_basis and stage_scheme keywords) and compute that stage in defining the CBS energy.
The cbs() function requires, at a minimum, name='scf' and scf_basis keywords to be specified for referencestep only jobs and name and corl_basis keywords for correlated jobs.
The following energy methods have been set up for cbs().





Parameters: 


Currently, the basis set set through set commands have no influence on a cbs calculation.
Parameters: 


Transformations of the energy through basis set extrapolation for each stage of the CBS definition. A complaint is generated if number of basis sets in stage_basis does not exactly satisfy requirements of stage_scheme. An exception is the default, 'highest_1', which uses the best basis set available. See Extrapolation Schemes for all available schemes.
Parameters: 


Examples : 
>>> # [1] replicates with cbs() the simple model chemistry scf/ccpVDZ: set basis ccpVDZ energy('scf')
>>> cbs('scf', scf_basis='ccpVDZ')
>>> # [2] replicates with cbs() the simple model chemistry mp2/junccpVDZ: set basis junccpVDZ energy('mp2')
>>> cbs('mp2', corl_basis='junccpVDZ')
>>> # [3] DTQzeta extrapolated scf reference energy
>>> cbs('scf', scf_basis='ccpV[DTQ]Z', scf_scheme=scf_xtpl_helgaker_3)
>>> # [4] DTzeta extrapolated mp2 correlation energy atop a Tzeta reference
>>> cbs('mp2', corl_basis='ccpv[dt]z', corl_scheme=corl_xtpl_helgaker_2)
>>> # [5] a DTzeta extrapolated coupledcluster correction atop a TQzeta extrapolated mp2 correlation energy atop a Qzeta reference
>>> cbs('mp2', corl_basis='augccpv[tq]z', corl_scheme=corl_xtpl_helgaker_2, delta_wfn='ccsd(t)', delta_basis='augccpv[dt]z', delta_scheme=corl_xtpl_helgaker_2)
>>> # [6] a Dzeta ccsd(t) correction atop a DTzeta extrapolated ccsd cluster correction atop a TQzeta extrapolated mp2 correlation energy atop a Qzeta reference
>>> cbs('mp2', corl_basis='augccpv[tq]z', corl_scheme=corl_xtpl_helgaker_2, delta_wfn='ccsd', delta_basis='augccpv[dt]z', delta_scheme=corl_xtpl_helgaker_2, delta2_wfn='ccsd(t)', delta2_wfn_lesser='ccsd', delta2_basis='augccpvdz')
>>> # [7] cbs() coupled with database()
>>> database('mp2', 'BASIC', subset=['h2o','nh3'], symm='on', func=cbs, corl_basis='ccpV[tq]z', corl_scheme=corl_xtpl_helgaker_2, delta_wfn='ccsd(t)', delta_basis='sto3g')
>>> # [8] cbs() coupled with optimize()
>>> optimize('mp2', corl_basis='ccpV[DT]Z', corl_scheme=corl_xtpl_helgaker_2, func=cbs)
At the beginning of a cbs() job is printed a listing of the individual energy calculations which will be performed. The output snippet below is from the example job [2] above. It shows first each model chemistry needed to compute the aggregate model chemistry requested through cbs(). Then, since, for example, an energy('ccsd(t)') yields CCSD(T), CCSD, MP2, and SCF energy values, the wrapper condenses this task list into the second list of minimum number of calculations which will actually be run.
Naive listing of computations required.
scf / augccpvqz for SCF TOTAL ENERGY
mp2 / augccpvtz for MP2 CORRELATION ENERGY
mp2 / augccpvqz for MP2 CORRELATION ENERGY
ccsd(t) / augccpvdz for CCSD(T) CORRELATION ENERGY
ccsd(t) / augccpvtz for CCSD(T) CORRELATION ENERGY
mp2 / augccpvdz for MP2 CORRELATION ENERGY
mp2 / augccpvtz for MP2 CORRELATION ENERGY
Enlightened listing of computations required.
mp2 / augccpvqz for MP2 CORRELATION ENERGY
ccsd(t) / augccpvdz for CCSD(T) CORRELATION ENERGY
ccsd(t) / augccpvtz for CCSD(T) CORRELATION ENERGY
At the end of a cbs() job is printed a summary section like the one below. First, in the components section, are listed the results for each model chemistry available, whether required for the cbs job (*) or not. Next, in the stages section, are listed the results for each extrapolation. The energies of this section must be dotted with the weightings in column Wt to get the total cbs energy. Finally, in the CBS section, are listed the results for each stage of the cbs procedure. The stage energies of this section sum outright to the total cbs energy.
==> Components <==

Method / Basis Rqd Energy [H] Variable

scf / augccpvqz * 1.11916375 SCF TOTAL ENERGY
mp2 / augccpvqz * 0.03407997 MP2 CORRELATION ENERGY
scf / augccpvdz 1.11662884 SCF TOTAL ENERGY
mp2 / augccpvdz * 0.02881480 MP2 CORRELATION ENERGY
ccsd(t) / augccpvdz * 0.03893812 CCSD(T) CORRELATION ENERGY
ccsd / augccpvdz 0.03893812 CCSD CORRELATION ENERGY
scf / augccpvtz 1.11881134 SCF TOTAL ENERGY
mp2 / augccpvtz * 0.03288936 MP2 CORRELATION ENERGY
ccsd(t) / augccpvtz * 0.04201004 CCSD(T) CORRELATION ENERGY
ccsd / augccpvtz 0.04201004 CCSD CORRELATION ENERGY

==> Stages <==

Stage Method / Basis Wt Energy [H] Scheme

scf scf / augccpvqz 1 1.11916375 highest_1
corl mp2 / augccpv[tq]z 1 0.03494879 corl_xtpl_helgaker_2
delta ccsd(t) / augccpv[dt]z 1 0.04330347 corl_xtpl_helgaker_2
delta mp2 / augccpv[dt]z 1 0.03460497 corl_xtpl_helgaker_2

==> CBS <==

Stage Method / Basis Energy [H] Scheme

scf scf / augccpvqz 1.11916375 highest_1
corl mp2 / augccpv[tq]z 0.03494879 corl_xtpl_helgaker_2
delta ccsd(t)  mp2 / augccpv[dt]z 0.00869851 corl_xtpl_helgaker_2
total CBS 1.16281105

Scheme for total or correlation energies with a single basis or the highest zetalevel among an array of bases. Used by complete_basis_set().
Extrapolation scheme for reference energies with two adjacent zetalevel bases. Used by complete_basis_set().
Extrapolation scheme for reference energies with three adjacent zetalevel bases. Used by complete_basis_set().
Extrapolation scheme for correlation energies with two adjacent zetalevel bases. Used by complete_basis_set().
When a particular composite method or its functional form is going to be reused often, it is convenient to define an alias to it. A convenient place for such Python code to reside is in psi4/lib/python/aliases.py (source location) or psi4/share/psi/python/aliases.py (installed location). No recompilation is necessary after defining an alias. Some existing examples are below.
Function to call the quantum chemical method known as ‘Gold Standard’ in the Sherrill group. Uses complete_basis_set() to evaluate the following expression. Twopoint extrapolation of the correlation energy performed according to corl_xtpl_helgaker_2().
>>> # [1] singlepoint energy by this composite method
>>> energy('sherrill_gold_standard')
>>> # [2] finitedifference geometry optimization
>>> optimize('sherrill_gold_standard')
>>> # [3] finitedifference geometry optimization, overwriting some predefined sherrill_gold_standard options
>>> optimize('sherrill_gold_standard', corl_basis='ccpV[DT]Z', delta_basis='321g')
Function to call Wes Allenstyle Focal Point Analysis. JCP 127 014306. Uses complete_basis_set() to evaluate the following expression. SCF employs a threepoint extrapolation according to scf_xtpl_helgaker_3(). MP2, CCSD, and CCSD(T) employ twopoint extrapolation performed according to corl_xtpl_helgaker_2(). CCSDT and CCSDT(Q) are plain deltas. This wrapper requires Kallay’s MRCC code.
>>> # [1] singlepoint energy by this composite method
>>> energy('allen_focal_point')
>>> # [2] finitedifference geometry optimization embarrasingly parallel
>>> optimize('allen_focal_point', mode='sow')