Complete Basis Set¶
Code author: Lori A. Burns, Daniel G. A. Smith and Peter Kraus
Section author: Lori A. Burns and Peter Kraus
The psi4.cbs()
function described below is
powerful but complicated, requiring many options. For most common
calculations, a shorthand can be accessed directly though
psi4.energy()
, psi4.gradient()
, etc. For example,
a MP2 single-point DT extrapolation can be accessed through the first item
below more conveniently than the equivalent second or third items.
energy('mp2/cc-pv[dt]z')
energy(cbs, corl_wfn='mp2', corl_basis='cc-pv[dt]z')
energy(cbs, cbs_metadata=[{"wfn": "hf", "basis": "cc-pvtz"}, {"wfn": "mp2", "basis": "cc-pv[dt]z"}])
A CCSD(T) DT coupled-cluster correction atop a TQ MP2 extrapolation geometry optimization can also be accessed through the first item below more conveniently than the equivalent second and third items.
optimize('mp2/cc-pv[tq]z + D:ccsd(t)/cc-pvdz')
optimize(cbs, corl_wfn='mp2', corl_basis='cc-pv[tq]z', delta_wfn='ccsd(t)', delta_basis='cc-pvdz')
optimize(cbs, cbs_metadata=[{"wfn": "hf", "basis": "cc-pvqz"}, {"wfn": "mp2", "basis": "cc-pv[tq]z"}, {"wfn": "ccsd(t)", "basis": "cc-pvdz"}])
Many examples can be found at cbs-xtpl-energy, cbs-xtpl-gradient, cbs-xtpl-opt, cbs-xtpl-freq, cbs-xtpl-func, cbs-xtpl-wrapper, cbs-xtpl-dict.
- psi4.cbs(name[, scf_basis, scf_scheme, corl_wfn, corl_basis, corl_scheme, delta_wfn, delta_wfn_lesser, delta_basis, delta_scheme, delta2_wfn, delta2_wfn_lesser, delta2_basis, delta2_scheme, cbs_metadata])[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'
andscf_basis
keywords to be specified for reference-step only jobs andname
andcorl_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 tocorl_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 Extrapolation Schemes for all available schemes.
- Parameters
scf_scheme (Callable) –
\(\Rightarrow\)
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 inpsi4.driver.driver_cbs.scf_basis
,scf_xtpl_helgaker_2()
if two valid basis sets present inscf_basis
, andxtpl_highest_1()
otherwise.corl_scheme (Callable) –
\(\Rightarrow\)
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 incorl_basis
andxtpl_highest_1()
otherwise.delta_scheme (Callable) –
\(\Rightarrow\)
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 indelta_basis
andxtpl_highest_1()
otherwise.delta2_scheme (Callable) –
\(\Rightarrow\)
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 indelta2_basis
andxtpl_highest_1()
otherwise.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()
andscf_xtpl_helgaker_3()
.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.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.
Combined interface
- Parameters
cbs_metadata (List[Dict]) –
\(\Rightarrow\) 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)
Note
As of October 2018, only two explicit `deltaN_[wfn,basis,scheme]`
sets of options are active; if more delta functions are required, use the `cbs_metadata`
interface. Also, temporarily extrapolations are performed on differences of target and scf total energies, rather than on correlation energies directly. This doesn’t affect the extrapolated values of the particular formulas defined here (though it does affect the betas, which are commented out), but it is sloppy and temporary and could affect any user-defined corl extrapolations.
Output¶
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 / aug-cc-pvqz for SCF TOTAL ENERGY
mp2 / aug-cc-pvtz for MP2 CORRELATION ENERGY
mp2 / aug-cc-pvqz for MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvdz for CCSD(T) CORRELATION ENERGY
ccsd(t) / aug-cc-pvtz for CCSD(T) CORRELATION ENERGY
mp2 / aug-cc-pvdz for MP2 CORRELATION ENERGY
mp2 / aug-cc-pvtz for MP2 CORRELATION ENERGY
Enlightened listing of computations required.
mp2 / aug-cc-pvqz for MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvdz for CCSD(T) CORRELATION ENERGY
ccsd(t) / aug-cc-pvtz 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 / aug-cc-pvqz * -1.11916375 SCF TOTAL ENERGY
mp2 / aug-cc-pvqz * -0.03407997 MP2 CORRELATION ENERGY
scf / aug-cc-pvdz -1.11662884 SCF TOTAL ENERGY
mp2 / aug-cc-pvdz * -0.02881480 MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvdz * -0.03893812 CCSD(T) CORRELATION ENERGY
ccsd / aug-cc-pvdz -0.03893812 CCSD CORRELATION ENERGY
scf / aug-cc-pvtz -1.11881134 SCF TOTAL ENERGY
mp2 / aug-cc-pvtz * -0.03288936 MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvtz * -0.04201004 CCSD(T) CORRELATION ENERGY
ccsd / aug-cc-pvtz -0.04201004 CCSD CORRELATION ENERGY
----------------------------------------------------------------------------------
==> Stages <==
----------------------------------------------------------------------------------
Stage Method / Basis Wt Energy [H] Scheme
----------------------------------------------------------------------------------
scf scf / aug-cc-pvqz 1 -1.11916375 highest_1
corl mp2 / aug-cc-pv[tq]z 1 -0.03494879 corl_xtpl_helgaker_2
delta ccsd(t) / aug-cc-pv[dt]z 1 -0.04330347 corl_xtpl_helgaker_2
delta mp2 / aug-cc-pv[dt]z -1 -0.03460497 corl_xtpl_helgaker_2
----------------------------------------------------------------------------------
==> CBS <==
----------------------------------------------------------------------------------
Stage Method / Basis Energy [H] Scheme
----------------------------------------------------------------------------------
scf scf / aug-cc-pvqz -1.11916375 highest_1
corl mp2 / aug-cc-pv[tq]z -0.03494879 corl_xtpl_helgaker_2
delta ccsd(t) - mp2 / aug-cc-pv[dt]z -0.00869851 corl_xtpl_helgaker_2
total CBS -1.16281105
----------------------------------------------------------------------------------
Extrapolation Schemes¶
- psi4.driver.driver_cbs.xtpl_highest_1(functionname, zHI, valueHI, verbose=True, **kwargs)[source]¶
Scheme for total or correlation energies with a single basis or the highest zeta-level among an array of bases. Used by
cbs()
.- Parameters
- Returns
Returns \(E_{total}^{\infty}\) which is equal to valueHI.
- Return type
Notes
\[E_{total}^X = E_{total}^{\infty}\]
- psi4.driver.driver_cbs.scf_xtpl_helgaker_2(functionname, zLO, valueLO, zHI, valueHI, verbose=True, alpha=None)[source]¶
Extrapolation scheme using exponential form for reference energies with two adjacent zeta-level bases. Used by
cbs()
.- Parameters
functionname (
str
) – Name of the CBS component.zLO (
int
) – Lower zeta level.valueLO (
float
) – Lower value used for extrapolation.zHI (
int
) – Higher zeta level. Should be equal to zLO + 1.valueHI (
float
) – Higher value used for extrapolation.alpha (
Optional
[float
]) – Overrides the default \(\alpha = 1.63\)verbose (bool) –
- Returns
Returns \(E_{total}^{\infty}\), see below.
- Return type
Notes
The extrapolation is calculated according to 1: \(E_{total}^X = E_{total}^{\infty} + \beta e^{-\alpha X}, \alpha = 1.63\)
References
- 1
Halkier, Helgaker, Jorgensen, Klopper, & Olsen, Chem. Phys. Lett. 302 (1999) 437-446, DOI: 10.1016/S0009-2614(99)00179-7
- psi4.driver.driver_cbs.scf_xtpl_truhlar_2(functionname, zLO, valueLO, zHI, valueHI, verbose=True, alpha=None)[source]¶
Extrapolation scheme using power form for reference energies with two adjacent zeta-level bases. Used by
cbs()
.- Parameters
functionname (
str
) – Name of the CBS component.zLO (
int
) – Lower zeta level.valueLO (
float
) – Lower value used for extrapolation.zHI (
int
) – Higher zeta level. Should be equal to zLO + 1.valueHI (
float
) – Higher value used for extrapolation.alpha (
Optional
[float
]) – Overrides the default \(\alpha = 3.4\)verbose (bool) –
- Returns
Returns \(E_{total}^{\infty}\), see below.
- Return type
Notes
The extrapolation is calculated according to 2: \(E_{total}^X = E_{total}^{\infty} + \beta X^{-\alpha}, \alpha = 3.4\)
References
- 2
Truhlar, Chem. Phys. Lett. 294 (1998) 45-48, DOI: 10.1016/S0009-2614(98)00866-5
- psi4.driver.driver_cbs.scf_xtpl_karton_2(functionname, zLO, valueLO, zHI, valueHI, verbose=True, alpha=None)[source]¶
Extrapolation scheme using root-power form for reference energies with two adjacent zeta-level bases. Used by
cbs()
.- Parameters
functionname (
str
) – Name of the CBS component.zLO (
int
) – Lower zeta level.valueLO (
float
) – Lower value used for extrapolation.zHI (
int
) – Higher zeta level. Should be equal to zLO + 1.valueHI (
float
) – Higher value used for extrapolation.alpha (
Optional
[float
]) – Overrides the default \(\alpha = 6.3\)verbose (bool) –
- Returns
Returns \(E_{total}^{\infty}\), see below.
- Return type
Notes
The extrapolation is calculated according to 3: \(E_{total}^X = E_{total}^{\infty} + \beta e^{-\alpha\sqrt{X}}, \alpha = 6.3\)
References
- 3
Karton, Martin, Theor. Chem. Acc. 115 (2006) 330-333, DOI: 10.1007/s00214-005-0028-6
- psi4.driver.driver_cbs.scf_xtpl_helgaker_3(functionname, zLO, valueLO, zMD, valueMD, zHI, valueHI, verbose=True, alpha=None)[source]¶
Extrapolation scheme for reference energies with three adjacent zeta-level bases. Used by
cbs()
.- Parameters
functionname (
str
) – Name of the CBS component.zLO (
int
) – Lower zeta level.valueLO (
float
) – Lower value used for extrapolation.zMD (
int
) – Intermediate zeta level. Should be equal to zLO + 1.valueMD (
float
) – Intermediate value used for extrapolation.zHI (
int
) – Higher zeta level. Should be equal to zLO + 2.valueHI (
float
) – Higher value used for extrapolation.verbose (bool) –
- Returns
Returns \(E_{total}^{\infty}\), see below.
- Return type
Notes
The extrapolation is calculated according to 4: \(E_{total}^X = E_{total}^{\infty} + \beta e^{-\alpha X}, \alpha = 3.0\)
References
- 4
Halkier, Helgaker, Jorgensen, Klopper, & Olsen, Chem. Phys. Lett. 302 (1999) 437-446, DOI: 10.1016/S0009-2614(99)00179-7
- psi4.driver.driver_cbs.corl_xtpl_helgaker_2(functionname, zLO, valueLO, zHI, valueHI, verbose=True, alpha=None)[source]¶
Extrapolation scheme for correlation energies with two adjacent zeta-level bases. Used by
cbs()
.- Parameters
functionname (
str
) – Name of the CBS component.zLO (
int
) – Lower zeta level.valueLO (
float
) – Lower value used for extrapolation.zHI (
int
) – Higher zeta level. Should be equal to zLO + 1.valueHI (
float
) – Higher value used for extrapolation.alpha (
Optional
[float
]) – Overrides the default \(\alpha = 3.0\)verbose (bool) –
- Returns
Returns \(E_{total}^{\infty}\), see below.
- Return type
Notes
The extrapolation is calculated according to 5: \(E_{corl}^X = E_{corl}^{\infty} + \beta X^{-alpha}\)
References
- 5
Halkier, Helgaker, Jorgensen, Klopper, Koch, Olsen, & Wilson, Chem. Phys. Lett. 286 (1998) 243-252, DOI: 10.1016/S0009-2614(99)00179-7
Aliases¶
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/psi4/driver/aliases.py
(source location) or psi4/lib/psi4/driver/aliases.py
(installed
location). No recompilation is necessary after defining an alias. Some
existing examples are below.
- psi4.driver.aliases.sherrill_gold_standard(func, label, **kwargs)[source]¶
Function to call the quantum chemical method known as ‘Gold Standard’ in the Sherrill group. Uses
cbs()
to evaluate the following expression. Two-point extrapolation of the correlation energy performed according tocorl_xtpl_helgaker_2()
.\[E_{total}^{\text{Au\_std}} = E_{total,\; \text{SCF}}^{\text{aug-cc-pVQZ}} \; + E_{corl,\; \text{MP2}}^{\text{aug-cc-pV[TQ]Z}} \; + \delta_{\text{MP2}}^{\text{CCSD(T)}}\big\vert_{\text{aug-cc-pVTZ}}\]>>> # [1] single-point energy by this composite method >>> energy('sherrill_gold_standard')
>>> # [2] finite-difference geometry optimization >>> optimize('sherrill_gold_standard')
>>> # [3] finite-difference geometry optimization, overwriting some pre-defined sherrill_gold_standard options >>> optimize('sherrill_gold_standard', corl_basis='cc-pV[DT]Z', delta_basis='3-21g')
- psi4.driver.aliases.allen_focal_point(func, label, **kwargs)[source]¶
Function to call Wes Allen-style Focal Point Analysis. JCP 127 014306. Uses
cbs()
to evaluate the following expression. SCF employs a three-point extrapolation according toscf_xtpl_helgaker_3()
. MP2, CCSD, and CCSD(T) employ two-point extrapolation performed according tocorl_xtpl_helgaker_2()
. CCSDT and CCSDT(Q) are plain deltas. This wrapper requires Kallay’s MRCC code.\[E_{total}^{\text{FPA}} = E_{total,\; \text{SCF}}^{\text{cc-pV[Q56]Z}} \; + E_{corl,\; \text{MP2}}^{\text{cc-pV[56]Z}} \; + \delta_{\text{MP2}}^{\text{CCSD}}\big\vert_{\text{cc-pV[56]Z}} \; + \delta_{\text{CCSD}}^{\text{CCSD(T)}}\big\vert_{\text{cc-pV[56]Z}} \; + \delta_{\text{CCSD(T)}}^{\text{CCSDT}}\big\vert_{\text{cc-pVTZ}} \; + \delta_{\text{CCSDT}}^{\text{CCSDT(Q)}}\big\vert_{\text{cc-pVDZ}}\]>>> # [1] single-point energy by this composite method >>> energy('allen_focal_point')
>>> # [2] finite-difference geometry optimization embarrasingly parallel >>> optimize('allen_focal_point', mode='sow')