cbs

psi4.driver.cbs(func, label, **kwargs)[source]

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:complete_basis_set()
Returns:(float) – Total electronic energy in Hartrees
PSI variables:

Caution

Some features are not yet implemented. Buy a developer a coffee.

  • No way to tell function to boost fitting basis size for all calculations.
  • Need to add more extrapolation schemes

As represented in the equation below, a CBS energy method is defined in several sequential stages (scf, corl, delta1, delta2, … ) 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, or as a field in the `cbs_metadata` list, and is only allowed if all preceding stages are active.

\[E_{\text{total}}^{\text{CBS}} = \mathcal{F}_{\textbf{scf_scheme}} \left(E_{\text{total},\; \text{SCF}}^{\textbf{scf_basis}}\right) \; + \mathcal{F}_{\textbf{corl_scheme}} \left(E_{\text{corl},\; \textbf{corl_wfn}}^{\textbf{corl_basis}}\right) \; + \delta_{\textbf{delta_wfn_lesser}}^{\textbf{delta_wfn}} \; + \delta_{\textbf{delta2_wfn_lesser}}^{\textbf{delta2_wfn}} \; + \delta_{\textbf{delta3_wfn_lesser}}^{\textbf{delta3_wfn}} \; + \delta_{\textbf{delta4_wfn_lesser}}^{\textbf{delta4_wfn}} \; + \delta_{\textbf{delta5_wfn_lesser}}^{\textbf{delta5_wfn}}\]

Here, \(\mathcal{F}\) is an energy or energy extrapolation scheme, and the following also hold.

\[\delta_{\textbf{delta_wfn_lesser}}^{\textbf{delta_wfn}} \; = \mathcal{F}_{\textbf{delta_scheme}} \left(E_{\text{corl},\; \textbf{delta_wfn}}^{\textbf{delta_basis}}\right) - \mathcal{F}_{\textbf{delta_scheme}} \left(E_{\text{corl},\; \textbf{delta_wfn_lesser}}^{\textbf{delta_basis}}\right)\]
\[\delta_{\textbf{delta2_wfn_lesser}}^{\textbf{delta2_wfn}} \; = \mathcal{F}_{\textbf{delta2_scheme}} \left(E_{\text{corl},\; \textbf{delta2_wfn}}^{\textbf{delta2_basis}}\right) - \mathcal{F}_{\textbf{delta2_scheme}} \left(E_{\text{corl},\; \textbf{delta2_wfn_lesser}}^{\textbf{delta2_basis}}\right)\]
\[\delta_{\textbf{delta3_wfn_lesser}}^{\textbf{delta3_wfn}} \; = \mathcal{F}_{\textbf{delta3_scheme}} \left(E_{\text{corl},\; \textbf{delta3_wfn}}^{\textbf{delta3_basis}}\right) - \mathcal{F}_{\textbf{delta3_scheme}} \left(E_{\text{corl},\; \textbf{delta3_wfn_lesser}}^{\textbf{delta3_basis}}\right)\]
\[\delta_{\textbf{delta4_wfn_lesser}}^{\textbf{delta4_wfn}} \; = \mathcal{F}_{\textbf{delta4_scheme}} \left(E_{\text{corl},\; \textbf{delta4_wfn}}^{\textbf{delta4_basis}}\right) - \mathcal{F}_{\textbf{delta4_scheme}} \left(E_{\text{corl},\; \textbf{delta4_wfn_lesser}}^{\textbf{delta4_basis}}\right)\]
\[\delta_{\textbf{delta5_wfn_lesser}}^{\textbf{delta5_wfn}} \; = \mathcal{F}_{\textbf{delta5_scheme}} \left(E_{\text{corl},\; \textbf{delta5_wfn}}^{\textbf{delta5_basis}}\right) - \mathcal{F}_{\textbf{delta5_scheme}} \left(E_{\text{corl},\; \textbf{delta5_wfn_lesser}}^{\textbf{delta5_basis}}\right)\]

A translation of this ungainly equation to example [5] below is as follows. In words, this is a double- and triple-zeta 2-point Helgaker-extrapolated CCSD(T) coupled-cluster correlation correction appended to a triple- and quadruple-zeta 2-point Helgaker-extrapolated MP2 correlation energy appended to a SCF/aug-cc-pVQZ reference energy.

\[E_{\text{total}}^{\text{CBS}} = \mathcal{F}_{\text{highest_1}} \left(E_{\text{total},\; \text{SCF}}^{\text{aug-cc-pVQZ}}\right) \; + \mathcal{F}_{\text{corl_xtpl_helgaker_2}} \left(E_{\text{corl},\; \text{MP2}}^{\text{aug-cc-pV[TQ]Z}}\right) \; + \delta_{\text{MP2}}^{\text{CCSD(T)}}\]
\[\delta_{\text{MP2}}^{\text{CCSD(T)}} \; = \mathcal{F}_{\text{corl_xtpl_helgaker_2}} \left(E_{\text{corl},\; \text{CCSD(T)}}^{\text{aug-cc-pV[DT]Z}}\right) - \mathcal{F}_{\text{corl_xtpl_helgaker_2}} \left(E_{\text{corl},\; \text{MP2}}^{\text{aug-cc-pV[DT]Z}}\right)\]
  • Energy Methods

    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 reference-step only jobs and name and corl_basis keywords for correlated jobs.

    The following energy methods have been set up for cbs().

    • scf
    • hf
    • mp2
    • mp2.5
    • mp3
    • mp4(sdq)
    • mp4
    • mpn
    • omp2
    • omp2.5
    • omp3
    • olccd
    • lccd
    • lccsd
    • cepa(0)
    • cepa(1)
    • cepa(3)
    • acpf
    • aqcc
    • qcisd
    • cc2
    • ccsd
    • fno-ccsd
    • bccd
    • cc3
    • qcisd(t)
    • ccsd(t)
    • fno-ccsd(t)
    • bccd(t)
    • cisd
    • cisdt
    • cisdtq
    • cin
    • fci
    • mrccsd
    • mrccsd(t)
    • mrccsdt
    • mrccsdt(q)
Parameters:
  • name (str) –

    'scf' || 'ccsd' || etc.

    First argument, usually unlabeled. Indicates the computational method for the correlation energy, unless only reference step to be performed, in which case should be 'scf'. Overruled if stage_wfn keywords supplied.

  • scf_wfn (str) –

    \(\Rightarrow\) 'scf' \(\Leftarrow\) || 'c4-scf' || etc.

    Indicates the energy method for which the reference energy is to be obtained. Generally unnecessary, as ‘scf’ is the scf in PSI4 but can be used to direct lone scf components to run in PSI4 or Cfour in a mixed-program composite method.

  • corl_wfn (str) –

    'mp2' || 'ccsd(t)' || etc.

    Indicates the energy method for which the correlation energy is to be obtained. Can also be specified with name or as the unlabeled first argument to the function.

  • delta_wfn (str) –

    'ccsd' || 'ccsd(t)' || etc.

    Indicates the (superior) energy method for which a delta correction to the correlation energy is to be obtained.

  • delta_wfn_lesser (str) –

    \(\Rightarrow\) corl_wfn \(\Leftarrow\) || 'mp2' || etc.

    Indicates the inferior energy method for which a delta correction to the correlation energy is to be obtained.

  • delta2_wfn (str) –

    'ccsd' || 'ccsd(t)' || etc.

    Indicates the (superior) energy method for which a second delta correction to the correlation energy is to be obtained.

  • delta2_wfn_lesser (str) –

    \(\Rightarrow\) delta_wfn \(\Leftarrow\) || 'ccsd(t)' || etc.

    Indicates the inferior energy method for which a second delta correction to the correlation energy is to be obtained.

  • Basis Sets
    Currently, the basis set set through set commands have no influence on a cbs calculation.
Parameters:
  • scf_basis (basis string) –

    \(\Rightarrow\) corl_basis \(\Leftarrow\) || 'cc-pV[TQ]Z' || 'jun-cc-pv[tq5]z' || '6-31G*' || etc.

    Indicates the sequence of basis sets employed for the reference energy. If any correlation method is specified, scf_basis can default to corl_basis.

  • corl_basis (basis string) –

    'cc-pV[TQ]Z' || 'jun-cc-pv[tq5]z' || '6-31G*' || etc.

    Indicates the sequence of basis sets employed for the correlation energy.

  • delta_basis (basis string) –

    'cc-pV[TQ]Z' || 'jun-cc-pv[tq5]z' || '6-31G*' || etc.

    Indicates the sequence of basis sets employed for the delta correction to the correlation energy.

  • delta2_basis (basis string) –

    'cc-pV[TQ]Z' || 'jun-cc-pv[tq5]z' || '6-31G*' || etc.

    Indicates the sequence of basis sets employed for the second delta correction to the correlation energy.

  • Schemes
    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, 'xtpl_highest_1', which uses the best basis set available. See sec:cbs_xtpl for all available schemes.
Parameters:
  • scf_scheme (function) –

    \(\Rightarrow\) xtpl_highest_1 \(\Leftarrow\) || scf_xtpl_helgaker_3 || etc.

    Indicates the basis set extrapolation scheme to be applied to the reference energy. Defaults to scf_xtpl_helgaker_3() if three valid basis sets present in scf_basis, scf_xtpl_helgaker_2() if two valid basis sets present in scf_basis, and xtpl_highest_1() otherwise.

    • xtpl_highest_1
    • scf_xtpl_helgaker_3
    • scf_xtpl_helgaker_2
    • scf_xtpl_truhlar_2
    • scf_xtpl_karton_2
  • corl_scheme (function) –

    \(\Rightarrow\) xtpl_highest_1 \(\Leftarrow\) || corl_xtpl_helgaker_2 || etc.

    Indicates the basis set extrapolation scheme to be applied to the correlation energy. Defaults to corl_xtpl_helgaker_2() if two valid basis sets present in corl_basis and xtpl_highest_1() otherwise.

    • xtpl_highest_1
    • corl_xtpl_helgaker_2
  • delta_scheme (function) –

    \(\Rightarrow\) xtpl_highest_1 \(\Leftarrow\) || corl_xtpl_helgaker_2 || etc.

    Indicates the basis set extrapolation scheme to be applied to the delta correction to the correlation energy. Defaults to corl_xtpl_helgaker_2() if two valid basis sets present in delta_basis and xtpl_highest_1() otherwise.

    • xtpl_highest_1
    • corl_xtpl_helgaker_2
  • delta2_scheme (function) –

    \(\Rightarrow\) xtpl_highest_1 \(\Leftarrow\) || corl_xtpl_helgaker_2 || etc.

    Indicates the basis set extrapolation scheme to be applied to the second delta correction to the correlation energy. Defaults to corl_xtpl_helgaker_2() if two valid basis sets present in delta2_basis and xtpl_highest_1() otherwise.

    • xtpl_highest_1
    • corl_xtpl_helgaker_2
  • scf_alpha (float) –

    \(\Rightarrow\) 1.63 \(\Leftarrow\)

    Overrides the default alpha parameter used in the listed SCF extrapolation procedures. Has no effect on others, including xtpl_highest_1() and scf_xtpl_helgaker_3().

    • scf_xtpl_helgaker_2()
    • scf_xtpl_truhlar_2()
    • scf_xtpl_karton_2()
  • corl_alpha (float) –

    \(\Rightarrow\) 3.00 \(\Leftarrow\)

    Overrides the default alpha parameter used in the listed corl_xtpl_helgaker_2() correlation extrapolation to the corl stage. The supplied alpha does not impact delta or any further stages.

    • corl_xtpl_helgaker_2()
  • delta_alpha (float) –

    \(\Rightarrow\) 3.00 \(\Leftarrow\)

    Overrides the default alpha parameter used in the listed corl_xtpl_helgaker_2() correlation extrapolation for the delta correction. Useful when delta correction is performed using smaller basis sets for which a different alpha might be more appropriate.

    • corl_xtpl_helgaker_2()
  • Combined interface
Parameters:cbs_metadata (list of dicts) –

\(\Rightarrow\) autogenerated from above keywords \(\Leftarrow\) || [{"wfn": "hf", "basis": "cc-pv[TQ5]z"}] || etc.

This is the interface to which all of the above calls are internally translated. The first item in the array is always defining the SCF contribution to the total energy. The required items in the dictionary are:

  • `wfn`: typically `HF`, which is subsumed in correlated methods anyway.
  • `basis`: basis set, can be in a bracketed form (eg. `cc-pv[tq]z`)
Other supported arguments for the first dictionary are:
  • `scheme`: scf extrapolation scheme function, by default it is worked out from the number of basis sets (1 - 3) supplied as `basis`.
  • `alpha`: alpha for the above scheme, if the default is to be overriden
  • `options`: if special options are required for a step, they should be entered as a dict here. If some options should be used for both parts of the stage, they should be entered in both `options` and `options_lo`. This is helpful for calculating all electron corrections in otherwise frozen core calculations, or relativistic (DKH) Hamiltionian corrections for otherwise nonrelativistic.
  • `options_lo`: special options for lower method in a given stage. This is useful to calculate a direct stage in an otherwise density-fitted calculation, or similar.
  • `treatment`: treat extrapolation stage as `scf` or `corl`, by default only the first stage is `scf` and every later one is `corl`.
  • `stage`: tag for the stage used in tables.
The next items in the `cbs_metadata` array extrapolate correlation. All of the above parameters

are available, with only the `wfn` and `basis` keywords required. Other supported parameters are:

  • `wfn_lo`: the lower method from which the delta correction is to be calculated. By default, it is set to `wfn` from the previous field in the `cbs_metadata` array.
  • `basis_lo`: basis set to be used for the delta correction. By default, it is the same as the `basis` specified above.
  • Others
Parameters:molecule (molecule) –

h2o || etc.

The target molecule, if not the last molecule defined.

Examples:
>>> # [1] replicates with cbs() the simple model chemistry scf/cc-pVDZ: set basis cc-pVDZ energy('scf')
>>> energy(cbs, scf_wfn='scf', scf_basis='cc-pVDZ')
>>> # [2] replicates with cbs() the simple model chemistry mp2/jun-cc-pVDZ: set basis jun-cc-pVDZ energy('mp2')
>>> energy(cbs, corl_wfn='mp2', corl_basis='jun-cc-pVDZ')
>>> # [3] DTQ-zeta extrapolated scf reference energy
>>> energy(cbs, scf_wfn='scf', scf_basis='cc-pV[DTQ]Z', scf_scheme=scf_xtpl_helgaker_3)
>>> # [4] DT-zeta extrapolated mp2 correlation energy atop a T-zeta reference
>>> energy(cbs, corl_wfn='mp2', corl_basis='cc-pv[dt]z', corl_scheme=corl_xtpl_helgaker_2)
>>> # [5] a DT-zeta extrapolated coupled-cluster correction atop a TQ-zeta extrapolated mp2 correlation energy atop a Q-zeta reference (both equivalent)
>>> energy(cbs, corl_wfn='mp2', corl_basis='aug-cc-pv[tq]z', delta_wfn='ccsd(t)', delta_basis='aug-cc-pv[dt]z')
>>> energy(cbs, corl_wfn='mp2', corl_basis='aug-cc-pv[tq]z', corl_scheme=corl_xtpl_helgaker_2, delta_wfn='ccsd(t)', delta_basis='aug-cc-pv[dt]z', delta_scheme=corl_xtpl_helgaker_2)
>>> # [6] a D-zeta ccsd(t) correction atop a DT-zeta extrapolated ccsd cluster correction atop a TQ-zeta extrapolated mp2 correlation energy atop a Q-zeta reference
>>> energy(cbs, corl_wfn='mp2', corl_basis='aug-cc-pv[tq]z', corl_scheme=corl_xtpl_helgaker_2, delta_wfn='ccsd', delta_basis='aug-cc-pv[dt]z', delta_scheme=corl_xtpl_helgaker_2, delta2_wfn='ccsd(t)', delta2_wfn_lesser='ccsd', delta2_basis='aug-cc-pvdz')
>>> # [7] a Q5-zeta MP2 calculation, corrected by CCSD(T) at the TQ-zeta extrapolated level, and all-electron CCSD(T) correlation at T-zeta level
>>> energy(cbs, cbs_metadata=[{"wfn": "hf", "basis": "cc-pv5z"}, {"wfn": "mp2", "basis": "cc-pv[q5]z"}, {"wfn": "ccsd(t)", "basis": "cc-pv[tq]z"}, {"wfn": "ccsd(t)", "basis": "cc-pvtz", "options": {"freeze_core": "False"}}])
>>> # [8] cbs() coupled with database()
>>> TODO database('mp2', 'BASIC', subset=['h2o','nh3'], symm='on', func=cbs, corl_basis='cc-pV[tq]z', corl_scheme=corl_xtpl_helgaker_2, delta_wfn='ccsd(t)', delta_basis='sto-3g')
>>> # [9] cbs() coupled with optimize()
>>> TODO optimize('mp2', corl_basis='cc-pV[DT]Z', corl_scheme=corl_xtpl_helgaker_2, func=cbs)