10.18. mcscf — Multi-configurational self-consistent field

The mcscf implements orbital optimization for MCSCF and CASSCF. 1-step (combined orbital and wavefunction optimization) and 2-step algorithms (alternating orbital and wavefunction optimization) are available. Different kinds of active space solvers can be used with this module.

For example, a simple CASCI calculation can be run as:

import pyscf

mol = pyscf.M(
    atom = 'O 0 0 0; O 0 0 1.2',
    basis = 'ccpvdz',
    spin = 2)

myhf = mol.RHF().run()

# 6 orbitals, 8 electrons
mycas = myhf.CASCI(6, 8).run()

and a simple CASSCF can be run as:

import pyscf

 mol = pyscf.M(
     atom = 'O 0 0 0; O 0 0 1.2',
     basis = 'ccpvdz',
     spin = 2)

 myhf = mol.RHF().run()

 # 6 orbitals, 8 electrons
 mycas = myhf.CASSCF(6, 8).run()

The CASSCF orbital optimization is general and can be combined with many different solvers, such as DMRG and selected CI solvers. Optimized orbitals are stored in the attribute mycas.mo_coeff.

10.18.1. Examples

Relevant examples examples/mcscf/00-simple_casci.py examples/mcscf/00-simple_casscf.py examples/mcscf/01-for_expensive_fci.py examples/mcscf/03-natural_orbital.py examples/mcscf/04-density_matrix.py examples/mcscf/10-define_cas_space.py examples/mcscf/11-casscf_with_uhf_uks.py examples/mcscf/12-c2_triplet_from_singlet_hf.py examples/mcscf/13-load_chkfile.py examples/mcscf/13-restart.py examples/mcscf/14-project_init_guess.py examples/mcscf/15-state_average.py examples/mcscf/15-state_specific.py examples/mcscf/15-transition_dm.py examples/mcscf/16-density_fitting.py examples/mcscf/17-approx_orbital_hessian.py examples/mcscf/18-o2_spatial_spin_symmetry.py examples/mcscf/18-spatial_spin_symmetry.py examples/mcscf/19-frozen_core.py examples/mcscf/20-change_symmetry.py examples/mcscf/21-active_space_symmetry.py examples/mcscf/21-nosymhf_then_symcasscf.py examples/mcscf/22-x2c.py examples/mcscf/23-local_spin.py examples/mcscf/33-make_init_guess examples/mcscf/34-init_guess_localization.py examples/mcscf/40-customizing_hamiltonian.py examples/mcscf/41-mcscf_custom_df_hamiltonian.py examples/mcscf/41-state_average.py examples/mcscf/42-compare_cas_space.py examples/mcscf/43-avas.py examples/mcscf/43-dmet_cas.py examples/mcscf/44-mcscf_active_space_hamiltonian.py examples/mcscf/50-casscf_then_dmrgscf.py examples/mcscf/50-casscf_with_selected_ci.py examples/mcscf/50-cornell_shci_casscf.py examples/mcscf/50-dmrgscf_with_block.py examples/mcscf/51-o2_triplet_by_various_fci.py examples/mcscf/60-uhf_based_ucasscf.py examples/mcscf/61-rcas_vs_ucas examples/mcscf/70-casscf_hot_tuning.py examples/mcscf/70-casscf_optimize_scheduler.py

CASCI and CASSCF

When using results of this code for publications, please cite the following paper: “A general second order complete active space self-consistent-field solver for large-scale systems”, Q. Sun, J. Yang, and G. K.-L. Chan, Chem. Phys. Lett. 683, 291 (2017).

Simple usage:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol).run()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> cas_list = [5,6,8,9] # pick orbitals for CAS space, 1-based indices
>>> mo = mcscf.sort_mo(mc, mf.mo_coeff, cas_list)
>>> mc.kernel(mo)[0]
-109.007378939813691

mcscf.CASSCF() or mcscf.CASCI() returns a proper instance of CASSCF/CASCI class. There are some parameters to control the CASSCF/CASCI method.

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to restore the natural orbital during CASSCF optimization. Default is not.

canonicalizationbool

Whether to canonicalize orbitals. Default is True.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

By replacing this fcisolver, you can easily use the CASCI/CASSCF solver with other FCI replacements, such as DMRG, QMC. See dmrgscf and fciqmcscf.

The Following attributes are used for CASSCF

conv_tolfloat

Converge threshold. Default is 1e-7

conv_tol_gradfloat

Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat

The step size for orbital rotation. Small step size is prefered. Default is 0.03. (NOTE although the default step size is small enough for many systems, it happens that the orbital optimizor crosses the barriar of local minimum and converge to the neighbour solution, e.g. the CAS(4,4) for C2H4 in the test files. In these systems, adjusting max_stepsize, max_ci_stepsize and max_cycle_micro, max_cycle_micro_inner and ah_start_tol may be helpful)

>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.max_stepsize = .01
>>> mc.max_cycle_micro = 1
>>> mc.max_cycle_macro = 100
>>> mc.max_cycle_micro_inner = 1
>>> mc.ah_start_tol = 1e-6
max_ci_stepsizefloat

The max size for approximate CI updates. The approximate updates are used in 1-step algorithm, to estimate the change of CI wavefunction wrt the orbital rotation. Small step size is prefered. Default is 0.01.

max_cycle_macroint

Max number of macro iterations. Default is 50.

max_cycle_microint

Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 3 steps should be enough. Default is 2.

max_cycle_micro_innerint

Max number of steps for the orbital rotations allowed for the augmented hessian solver. It can affect the actual size of orbital rotation. Even with a small max_stepsize, a few max_cycle_micro_inner can accumulate the rotation and leads to a significant change of the CAS space. Depending on systems, increasing this value migh reduce the total number of macro iterations. The value between 2 - 8 is preferred. Default is 4.

frozenint or list

If integer is given, the inner-most orbitals are excluded from optimization. Given the orbital indices (0-based) in a list, any doubly occupied core orbitals, active orbitals and external orbitals can be frozen.

ah_level_shiftfloat, for AH solver.

Level shift for the Davidson diagonalization in AH solver. Default is 0.

ah_conv_tolfloat, for AH solver.

converge threshold for Davidson diagonalization in AH solver. Default is 1e-8.

ah_max_cyclefloat, for AH solver.

Max number of iterations allowd in AH solver. Default is 20.

ah_lindepfloat, for AH solver.

Linear dependence threshold for AH solver. Default is 1e-16.

ah_start_tolflat, for AH solver.

In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 1e-4.

ah_start_cycleint, for AH solver.

In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 3.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep can improve the accuracy of CASSCF optimization, but slow down the performance.

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()
-109.044401887945668
chkfilestr

Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

Saved results

e_totfloat

Total MCSCF energy (electronic energy plus nuclear repulsion)

cindarray

CAS space FCI coefficients

convergedbool, for CASSCF only

It indicates CASSCF optimization converged or not.

mo_energy: ndarray,

Diagonal elements of general Fock matrix

mo_coeffndarray, for CASSCF only

Optimized CASSCF orbitals coefficients Note the orbitals are NOT natural orbitals by default. There are two inbuilt methods to convert the mo_coeff to natural orbitals. 1. Set .natorb attribute. It can be used before calculation. 2. call .cas_natorb_ method after the calculation to in-place convert the orbitals

10.18.2. CASSCF active space solver

10.18.2.1. DMRG solver

10.18.2.2. FCIQMC solver

10.18.2.3. State-average FCI solver

10.18.2.4. State-average with mixed solver

10.18.3. Symmetry broken

10.18.4. Initial guess

10.18.5. Canonical orbitals

Orbital canonicalization are controlled by parameters mc.canonicalization and mc.natorb (assuming the MCSCF object is mc). The order of orbitals are affected by the parameter mc.sorting_mo_energy.

  • canonicalization: This flag canonicalizes orbitals in core and external space using general Fock matrix.

  • natorb: Transforms active orbitals using 1-particle density matrices.

  • sorting_mo_energy: Sort orbitals based on the diagonal elements of the general Fock matrix.

  • Enabling natorb or sorting_mo_energy may slightly change the total energy of DMRG solver or selected CI solver.

General Fock matrix is defined as

\[\begin{split}\mathbf{F} &= \mathbf{h}_{core} + \mathbf{J} - \mathbf{K} \\ J_{pq} &= \sum_{rs} (pq|rs) \gamma_{sr} \\ K_{pq} &= \sum_{qr} (pq|rs) \gamma_{qr} \\\end{split}\]

\(\gamma\) is the total density matrix which includes the doubly occupied core density matrix and correlated density matrix in active space.

If mc.canonicalization is enabled, CASCI/CASSCF will call the mc.canonicalize() function to diagonalize orbitals in core space and external space. Orbitals in active space are not changed if merely setting mc.canonicalization. In the attribute mc.mo_energy, eigenvalues of general Fock matrix for core and external subspaces are stored in the corresponding sub-sectors. The sector of active space in mc.mo_energy stores the expectation value of general Fock \(\langle \phi|F|\phi\rangle\). By default, mc.canonicalization is enabled because the canonicalized MCSCF orbitals can simplify the implementations of MRPT (NEVPT2) methods.

mc.natorb controls whether the CASCI/CASSCF active space orbitals are transformed to natural orbitals w.r.t. the correlated density matrix. When this parameter is enabled, the natural orbitals will be stored in the active part of the attribute mc.mo_coeff and the CI coefficients mc.ci (if applicable) will be transformed accordingly. By default mc.natorb is disabled because natural orbitals may not be favored by total energy for an arbitrary CI solver. We make this default value to ensure that a CASCI calculation followed by a CASSCF calculation (e.g. DMRG-CASSCF then DMRG-CASCI) produces results same to the CASSCF results. The CASCI calculation may produce different The value of mc.natorb does not affect (the default) FCI solver. But this is not true for external large active space solvers such as DMRG, selected CI methods. It is recommended to disable mc.natorb in these calculations.

Following presents what the mc.mo_coeff would be like for different combinations of mc.canonicalization and mc.natorb in a CASCI calculation:

  • mc.canonicalization = False and mc.natorb = False:

The resultant orbitals mc.mo_coeff are identical to the input orbitals. If the CASCI was initialized with a RHF calculation, mc.mo_coeff points to RHF orbitals.

  • mc.canonicalization = True and mc.natorb = False:

Core part and external part of mc.mo_coeff are canonicalized orbitals, which diagonalize the core and external blocks of general Fock matrix. The orbitals in active space are identical to the active orbitals in the input.

  • mc.canonicalization = False and mc.natorb = True

Core and external part of mc.mo_coeff are identical to the core and external part of the input orbitals. Active space orbitals are transformed to the natural orbitals of the correlated density matrix.

  • mc.canonicalization = True and mc.natorb = True

mc.mo_coeff are completely different to the input orbitals.

Please note that elements of mc.mo_energy may not be sorted ascendantly. Parameter mc.sorting_mo_energy can affect the ordering of MCSCF orbitals when :attr:`mc.canonicalization` or :attr:`mc.natorb` is enabled.

By default, canonical orbitals in the core and external space are sorted by the orbital energies (from low to high) and the natural orbitals in the active space are sorted by natural occupations (from large to small). If point group symmetry is enabled in the calculation, canonical orbitals are sorted within each symmetry sector only (rather than the entire core or external space). Irreducible representation labels (can be accessed via mc.mo_coeff.orbsym) are assigned to orbitals in the initial guess and they will not be changed in the MCSCF optimization and the subsequent canonicalization procedure. Setting mc.sorting_mo_energy (though not recommended) can force the orbitals to be sorted against energy (or occupations in active space) regardless whether the point group symmetry is used.

In certain scenario, you may want to enable both mc.natorb and mc.sorting_mo_energy. examples/dmrg/31-cr2_scan/cr2-scan.py provides one example that needs both parameters. In that example, the dissociation curve of Cr dimer was scanned using heat-bath selected-CI method in which the active space of selected-CI-CASSCF was gradually enlarged in a series of CASSCF calculations. Since the selected-CI algorithm depends on the initial single determinant, the orbital ordering does matter to the final CASSCF results. mc.natorb and mc.sorting_mo_energy have to be enabled to make sure that the each selected-CI starts from the similar initial reference at each point on the dissociation curve. Without these settings, the differences in the orbital ordering can lead to discontinuous potential energy curve.

10.18.6. Program reference

10.18.6.1. CASCI

class pyscf.mcscf.casci.CASCI(mf_or_mol, ncas, nelecas, ncore=None)[source]
Args:
mf_or_molSCF object or Mole object

SCF or Mole to define the problem size.

ncasint

Number of active orbitals.

nelecasint or a pair of int

Number of electrons in active space.

Kwargs:
ncoreint

Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:
verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbital in active space. Be cautious of this parameter when CASCI/CASSCF are combined with DMRG solver or selected CI solver because DMRG and selected CI are not invariant to the rotation in active space. False by default.

canonicalizationbool

Whether to canonicalize orbitals. Note that canonicalization does not change the orbitals in active space by default. It only diagonalizes core and external space of the general Fock matirx. To get the natural orbitals in active space, attribute natorb need to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat

Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat

CAS space FCI energy

cindarray

CAS space FCI coefficients

mo_coeffndarray

When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray

Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray

Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
Gradients(*args, **kwargs)

Non-relativistic restricted Hartree-Fock gradients

ao2mo(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

as_scanner()

Generating a scanner for CASCI PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total CASCI energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters of MCSCF object are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mf = scf.RHF(gto.Mole().set(verbose=0))
>>> mc_scanner = mcscf.CASCI(mf, 4, 4).as_scanner()
>>> mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.1'))
>>> mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.5'))
canonicalize(mo_coeff=None, ci=None, eris=None, sort=False, cas_natorb=False, casdm1=None, verbose=3, with_meta_lowdin=True)

Canonicalized CASCI/CASSCF orbitals of effecitive Fock matrix and update CI coefficients accordingly.

Effective Fock matrix is built with one-particle density matrix (see also mcscf.casci.get_fock()). For state-average CASCI/CASSCF object, the canonicalized orbitals are based on the state-average density matrix. To obtain canonicalized orbitals for an individual state, you need to pass “casdm1” of the specific state to this function.

Args:

mc: a CASSCF/CASCI object or RHF object

Kwargs:
mo_coeff (ndarray): orbitals that span the core, active and external

space.

ci (ndarray): CI coefficients (or objects to represent the CI

wavefunctions in DMRG/QMC-MCSCF calculations).

eris: Integrals for the MCSCF object. Input this object to reduce the

overhead of computing integrals. It can be generated by mc.ao2mo() method.

sort (bool): Whether the canonicalized orbitals are sorted based on

the orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If point group symmetry is not available in the system, orbitals are always sorted. When point group symmetry is available, sort=False will preserve the symmetry label of input orbitals and only sort the orbitals in each symmetry sector. sort=True will reorder all orbitals over all symmetry sectors in each subspace and the symmetry labels may be changed.

cas_natorb (bool): Whether to transform active orbitals to natual

orbitals. If enabled, the output orbitals in active space are transformed to natural orbitals and CI coefficients are updated accordingly.

casdm1 (ndarray): 1-particle density matrix in active space. This

density matrix is used to build effective fock matrix. Without input casdm1, the density matrix is computed with the input ci coefficients/object. If neither ci nor casdm1 were given, density matrix is computed by mc.fcisolver.make_rdm1() method. For state-average CASCI/CASCF calculation, this results in a set of canonicalized orbitals of state-average effective Fock matrix. To canonicalize the orbitals for one particular state, you can assign the density matrix of that state to the kwarg casdm1.

Returns:

A tuple, (natural orbitals, CI coefficients, orbital energies) The orbital energies are the diagonal terms of effective Fock matrix.

canonicalize_(mo_coeff=None, ci=None, eris=None, sort=False, cas_natorb=False, casdm1=None, verbose=None, with_meta_lowdin=True)[source]

Canonicalized CASCI/CASSCF orbitals of effecitive Fock matrix and update CI coefficients accordingly.

Effective Fock matrix is built with one-particle density matrix (see also mcscf.casci.get_fock()). For state-average CASCI/CASSCF object, the canonicalized orbitals are based on the state-average density matrix. To obtain canonicalized orbitals for an individual state, you need to pass “casdm1” of the specific state to this function.

Args:

mc: a CASSCF/CASCI object or RHF object

Kwargs:
mo_coeff (ndarray): orbitals that span the core, active and external

space.

ci (ndarray): CI coefficients (or objects to represent the CI

wavefunctions in DMRG/QMC-MCSCF calculations).

eris: Integrals for the MCSCF object. Input this object to reduce the

overhead of computing integrals. It can be generated by mc.ao2mo() method.

sort (bool): Whether the canonicalized orbitals are sorted based on

the orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If point group symmetry is not available in the system, orbitals are always sorted. When point group symmetry is available, sort=False will preserve the symmetry label of input orbitals and only sort the orbitals in each symmetry sector. sort=True will reorder all orbitals over all symmetry sectors in each subspace and the symmetry labels may be changed.

cas_natorb (bool): Whether to transform active orbitals to natual

orbitals. If enabled, the output orbitals in active space are transformed to natural orbitals and CI coefficients are updated accordingly.

casdm1 (ndarray): 1-particle density matrix in active space. This

density matrix is used to build effective fock matrix. Without input casdm1, the density matrix is computed with the input ci coefficients/object. If neither ci nor casdm1 were given, density matrix is computed by mc.fcisolver.make_rdm1() method. For state-average CASCI/CASCF calculation, this results in a set of canonicalized orbitals of state-average effective Fock matrix. To canonicalize the orbitals for one particular state, you can assign the density matrix of that state to the kwarg casdm1.

Returns:

A tuple, (natural orbitals, CI coefficients, orbital energies) The orbital energies are the diagonal terms of effective Fock matrix.

cas_natorb(mo_coeff=None, ci=None, eris=None, sort=False, casdm1=None, verbose=None, with_meta_lowdin=True)[source]

Transform active orbitals to natrual orbitals, and update the CI wfn accordingly

Args:

mc : a CASSCF/CASCI object or RHF object

Kwargs:
sortbool

Sort natural orbitals wrt the occupancy.

Returns:

A tuple, the first item is natural orbitals, the second is updated CI coefficients, the third is the natural occupancy associated to the natural orbitals.

cas_natorb_(mo_coeff=None, ci=None, eris=None, sort=False, casdm1=None, verbose=None, with_meta_lowdin=True)[source]

Transform active orbitals to natrual orbitals, and update the CI wfn accordingly

Args:

mc : a CASSCF/CASCI object or RHF object

Kwargs:
sortbool

Sort natural orbitals wrt the occupancy.

Returns:

A tuple, the first item is natural orbitals, the second is updated CI coefficients, the third is the natural occupancy associated to the natural orbitals.

fix_spin(shift=0.2, ss=None)

Use level shift to control FCI solver spin.

\[(H + shift*S^2) |\Psi\rangle = E |\Psi\rangle\]
Kwargs:
shiftfloat

Energy penalty for states which have wrong spin

ssnumber

S^2 expection value == s*(s+1)

fix_spin_(shift=0.2, ss=None)[source]

Use level shift to control FCI solver spin.

\[(H + shift*S^2) |\Psi\rangle = E |\Psi\rangle\]
Kwargs:
shiftfloat

Energy penalty for states which have wrong spin

ssnumber

S^2 expection value == s*(s+1)

get_h1cas(mo_coeff=None, ncas=None, ncore=None)

CAS sapce one-electron hamiltonian

Args:

casci : a CASSCF/CASCI object or RHF object

Returns:

A tuple, the first is the effective one-electron hamiltonian defined in CAS space, the second is the electronic energy from core.

get_h1eff(mo_coeff=None, ncas=None, ncore=None)[source]

CAS sapce one-electron hamiltonian

Args:

casci : a CASSCF/CASCI object or RHF object

Returns:

A tuple, the first is the effective one-electron hamiltonian defined in CAS space, the second is the electronic energy from core.

get_h2cas(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

Note It is different to get_h2eff when df.approx_hessian is applied, in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

get_h2eff(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

Note It is different to get_h2cas when df.approx_hessian is applied. in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

get_jk(mol, dm, hermi=1, with_j=True, with_k=True, omega=None)[source]

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays

A density matrix or a list of density matrices

Kwargs:
hermiint

Whether J, K matrix is hermitian

0 : not hermitian and not symmetric
1 : hermitian or symmetric
2 : anti-hermitian
vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

with_jboolean

Whether to compute J matrices

with_kboolean

Whether to compute K matrices

omegafloat

Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)
get_veff(mol=None, dm=None, hermi=1)[source]

Hartree-Fock potential matrix for the given density matrix

Args:

mol : an instance of Mole

dmndarray or list of ndarrays

A density matrix or a list of density matrices

Kwargs:
dm_lastndarray or a list of ndarrays or 0

The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.

vhf_lastndarray or a list of ndarrays or 0

The reference HF potential matrix.

hermiint

Whether J, K matrix is hermitian

0 : no hermitian or symmetric
1 : hermitian
2 : anti-hermitian
vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True
h1e_for_cas(mo_coeff=None, ncas=None, ncore=None)

CAS sapce one-electron hamiltonian

Args:

casci : a CASSCF/CASCI object or RHF object

Returns:

A tuple, the first is the effective one-electron hamiltonian defined in CAS space, the second is the electronic energy from core.

kernel(mo_coeff=None, ci0=None, verbose=None)[source]
Returns:

Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients.

They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy

make_rdm1(mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs)[source]

One-particle density matrix in AO representation

make_rdm1s(mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs)[source]

One-particle density matrices for alpha and beta spin on AO basis

sort_mo(caslst, mo_coeff=None, base=1)[source]

Pick orbitals for CAS space

Args:

casscf : an CASSCF or CASCI object

mo_coeffndarray or a list of ndarray

Orbitals for CASSCF initial guess. In the UHF-CASSCF, it’s a list of two orbitals, for alpha and beta spin.

caslstlist of int or nested list of int

A list of orbital indices to represent the CAS space. In the UHF-CASSCF, it’s consist of two lists, for alpha and beta spin.

Kwargs:
baseint

0-based (C-style) or 1-based (Fortran-style) caslst

Returns:

An reoreded mo_coeff, which put the orbitals given by caslst in the CAS space

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> cas_list = [5,6,8,9] # pi orbitals
>>> mo = mc.sort_mo(cas_list)
>>> mc.kernel(mo)[0]
-109.007378939813691
state_average(weights=(0.5, 0.5))[source]

State average over the energy. The energy funcitonal is E = w1<psi1|H|psi1> + w2<psi2|H|psi2> + …

Note we may need change the FCI solver to

mc.fcisolver = fci.solver(mol, False)

before calling state_average_(mc), to mix the singlet and triplet states

MRH, 04/08/2019: Instead of turning casscf._finalize into an instance attribute that points to the previous casscf object, I’m going to make a whole new child class. This will have the added benefit of making state_average and state_average_ actually behave differently for the first time (until now they both modified the casscf object inplace). I’m also going to assign the weights argument as a member of the mc child class because an accurate second-order CASSCF algorithm for state-averaged calculations requires that the gradient and Hessian be computed for CI vectors of each root individually and then multiplied by that root’s weight. The second derivatives computed by newton_casscf.py need to be extended to state-averaged calculations in order to be used as intermediates for calculations of the gradient of a single root in the context of the SA-CASSCF method; see: Mol. Phys. 99, 103 (2001).

state_average_(weights=(0.5, 0.5))[source]

State average over the energy. The energy funcitonal is E = w1<psi1|H|psi1> + w2<psi2|H|psi2> + …

Note we may need change the FCI solver to

mc.fcisolver = fci.solver(mol, False)

before calling state_average_(mc), to mix the singlet and triplet states

MRH, 04/08/2019: Instead of turning casscf._finalize into an instance attribute that points to the previous casscf object, I’m going to make a whole new child class. This will have the added benefit of making state_average and state_average_ actually behave differently for the first time (until now they both modified the casscf object inplace). I’m also going to assign the weights argument as a member of the mc child class because an accurate second-order CASSCF algorithm for state-averaged calculations requires that the gradient and Hessian be computed for CI vectors of each root individually and then multiplied by that root’s weight. The second derivatives computed by newton_casscf.py need to be extended to state-averaged calculations in order to be used as intermediates for calculations of the gradient of a single root in the context of the SA-CASSCF method; see: Mol. Phys. 99, 103 (2001).

state_specific_(state=1)[source]

For excited state

Kwargs:

state : int 0 for ground state; 1 for first excited state.

pyscf.mcscf.casci.as_scanner(mc)[source]

Generating a scanner for CASCI PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total CASCI energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters of MCSCF object are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mf = scf.RHF(gto.Mole().set(verbose=0))
>>> mc_scanner = mcscf.CASCI(mf, 4, 4).as_scanner()
>>> mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.1'))
>>> mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.5'))
pyscf.mcscf.casci.canonicalize(mc, mo_coeff=None, ci=None, eris=None, sort=False, cas_natorb=False, casdm1=None, verbose=3, with_meta_lowdin=True)[source]

Canonicalized CASCI/CASSCF orbitals of effecitive Fock matrix and update CI coefficients accordingly.

Effective Fock matrix is built with one-particle density matrix (see also mcscf.casci.get_fock()). For state-average CASCI/CASSCF object, the canonicalized orbitals are based on the state-average density matrix. To obtain canonicalized orbitals for an individual state, you need to pass “casdm1” of the specific state to this function.

Args:

mc: a CASSCF/CASCI object or RHF object

Kwargs:
mo_coeff (ndarray): orbitals that span the core, active and external

space.

ci (ndarray): CI coefficients (or objects to represent the CI

wavefunctions in DMRG/QMC-MCSCF calculations).

eris: Integrals for the MCSCF object. Input this object to reduce the

overhead of computing integrals. It can be generated by mc.ao2mo() method.

sort (bool): Whether the canonicalized orbitals are sorted based on

the orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If point group symmetry is not available in the system, orbitals are always sorted. When point group symmetry is available, sort=False will preserve the symmetry label of input orbitals and only sort the orbitals in each symmetry sector. sort=True will reorder all orbitals over all symmetry sectors in each subspace and the symmetry labels may be changed.

cas_natorb (bool): Whether to transform active orbitals to natual

orbitals. If enabled, the output orbitals in active space are transformed to natural orbitals and CI coefficients are updated accordingly.

casdm1 (ndarray): 1-particle density matrix in active space. This

density matrix is used to build effective fock matrix. Without input casdm1, the density matrix is computed with the input ci coefficients/object. If neither ci nor casdm1 were given, density matrix is computed by mc.fcisolver.make_rdm1() method. For state-average CASCI/CASCF calculation, this results in a set of canonicalized orbitals of state-average effective Fock matrix. To canonicalize the orbitals for one particular state, you can assign the density matrix of that state to the kwarg casdm1.

Returns:

A tuple, (natural orbitals, CI coefficients, orbital energies) The orbital energies are the diagonal terms of effective Fock matrix.

pyscf.mcscf.casci.cas_natorb(mc, mo_coeff=None, ci=None, eris=None, sort=False, casdm1=None, verbose=None, with_meta_lowdin=True)[source]

Transform active orbitals to natrual orbitals, and update the CI wfn accordingly

Args:

mc : a CASSCF/CASCI object or RHF object

Kwargs:
sortbool

Sort natural orbitals wrt the occupancy.

Returns:

A tuple, the first item is natural orbitals, the second is updated CI coefficients, the third is the natural occupancy associated to the natural orbitals.

pyscf.mcscf.casci.get_fock(mc, mo_coeff=None, ci=None, eris=None, casdm1=None, verbose=None)[source]

Effective one-electron Fock matrix in AO representation f = sum_{pq} E_{pq} F_{pq} F_{pq} = h_{pq} + sum_{rs} [(pq|rs)-(ps|rq)] DM_{sr}

Ref. Theor. Chim. Acta., 91, 31 Chem. Phys. 48, 157

For state-average CASCI/CASSCF object, the effective fock matrix is based on the state-average density matrix. To obtain Fock matrix of a specific state in the state-average calculations, you can pass “casdm1” of the specific state to this function.

Args:

mc: a CASSCF/CASCI object or RHF object

Kwargs:
mo_coeff (ndarray): orbitals that span the core, active and external

space.

ci (ndarray): CI coefficients (or objects to represent the CI

wavefunctions in DMRG/QMC-MCSCF calculations).

eris: Integrals for the MCSCF object. Input this object to reduce the

overhead of computing integrals. It can be generated by mc.ao2mo() method.

casdm1 (ndarray): 1-particle density matrix in active space. Without

input casdm1, the density matrix is computed with the input ci coefficients/object. If neither ci nor casdm1 were given, density matrix is computed by mc.fcisolver.make_rdm1() method. For state-average CASCI/CASCF calculation, this results in the effective Fock matrix based on the state-average density matrix. To obtain the effective Fock matrix for one particular state, you can assign the density matrix of that state to the kwarg casdm1.

Returns:

Fock matrix

pyscf.mcscf.casci.h1e_for_cas(casci, mo_coeff=None, ncas=None, ncore=None)[source]

CAS sapce one-electron hamiltonian

Args:

casci : a CASSCF/CASCI object or RHF object

Returns:

A tuple, the first is the effective one-electron hamiltonian defined in CAS space, the second is the electronic energy from core.

pyscf.mcscf.casci.kernel(casci, mo_coeff=None, ci0=None, verbose=3)[source]

CASCI solver

pyscf.mcscf.casci_symm.CASCI

alias of pyscf.mcscf.casci_symm.SymAdaptedCASCI

class pyscf.mcscf.casci_symm.SymAdaptedCASCI(mf_or_mol, ncas, nelecas, ncore=None)[source]
kernel(mo_coeff=None, ci0=None, verbose=None)[source]
Returns:

Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients.

They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy

sort_mo_by_irrep(cas_irrep_nocc, cas_irrep_ncore=None, mo_coeff=None, s=None)[source]

Select active space based on symmetry information. See also pyscf.mcscf.addons.sort_mo_by_irrep()

UCASCI (CASCI with non-degenerated alpha and beta orbitals, typically UHF orbitals)

pyscf.mcscf.ucasci.CASCI

alias of pyscf.mcscf.ucasci.UCASCI

class pyscf.mcscf.ucasci.UCASCI(mf_or_mol, ncas, nelecas, ncore=None)[source]
ao2mo(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

cas_natorb(mo_coeff=None, ci0=None)[source]

Transform active orbitals to natrual orbitals, and update the CI wfn accordingly

Args:

mc : a CASSCF/CASCI object or RHF object

Kwargs:
sortbool

Sort natural orbitals wrt the occupancy.

Returns:

A tuple, the first item is natural orbitals, the second is updated CI coefficients, the third is the natural occupancy associated to the natural orbitals.

cas_natorb_(mo_coeff=None, ci0=None)[source]

Transform active orbitals to natrual orbitals, and update the CI wfn accordingly

Args:

mc : a CASSCF/CASCI object or RHF object

Kwargs:
sortbool

Sort natural orbitals wrt the occupancy.

Returns:

A tuple, the first item is natural orbitals, the second is updated CI coefficients, the third is the natural occupancy associated to the natural orbitals.

get_h1cas(mo_coeff=None, ncas=None, ncore=None)

CAS sapce one-electron hamiltonian for UHF-CASCI or UHF-CASSCF

Args:

casci : a U-CASSCF/U-CASCI object or UHF object

get_h1eff(mo_coeff=None, ncas=None, ncore=None)[source]

CAS sapce one-electron hamiltonian for UHF-CASCI or UHF-CASSCF

Args:

casci : a U-CASSCF/U-CASCI object or UHF object

get_h2cas(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

Note It is different to get_h2eff when df.approx_hessian is applied, in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

get_h2eff(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

Note It is different to get_h2cas when df.approx_hessian is applied. in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

get_veff(mol=None, dm=None, hermi=1)[source]

Hartree-Fock potential matrix for the given density matrix

Args:

mol : an instance of Mole

dmndarray or list of ndarrays

A density matrix or a list of density matrices

Kwargs:
dm_lastndarray or a list of ndarrays or 0

The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.

vhf_lastndarray or a list of ndarrays or 0

The reference HF potential matrix.

hermiint

Whether J, K matrix is hermitian

0 : no hermitian or symmetric
1 : hermitian
2 : anti-hermitian
vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True
h1e_for_cas(mo_coeff=None, ncas=None, ncore=None)

CAS sapce one-electron hamiltonian for UHF-CASCI or UHF-CASSCF

Args:

casci : a U-CASSCF/U-CASCI object or UHF object

kernel(mo_coeff=None, ci0=None)[source]
Returns:

Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients.

They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy

make_rdm1(mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs)[source]

One-particle density matrix in AO representation

make_rdm1s(mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs)[source]

One-particle density matrices for alpha and beta spin on AO basis

sort_mo(caslst, mo_coeff=None, base=1)[source]

Pick orbitals for CAS space

Args:

casscf : an CASSCF or CASCI object

mo_coeffndarray or a list of ndarray

Orbitals for CASSCF initial guess. In the UHF-CASSCF, it’s a list of two orbitals, for alpha and beta spin.

caslstlist of int or nested list of int

A list of orbital indices to represent the CAS space. In the UHF-CASSCF, it’s consist of two lists, for alpha and beta spin.

Kwargs:
baseint

0-based (C-style) or 1-based (Fortran-style) caslst

Returns:

An reoreded mo_coeff, which put the orbitals given by caslst in the CAS space

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> cas_list = [5,6,8,9] # pi orbitals
>>> mo = mc.sort_mo(cas_list)
>>> mc.kernel(mo)[0]
-109.007378939813691
pyscf.mcscf.ucasci.h1e_for_cas(casci, mo_coeff=None, ncas=None, ncore=None)[source]

CAS sapce one-electron hamiltonian for UHF-CASCI or UHF-CASSCF

Args:

casci : a U-CASSCF/U-CASCI object or UHF object

pyscf.mcscf.ucasci.kernel(casci, mo_coeff=None, ci0=None, verbose=3)[source]

UHF-CASCI solver

10.18.6.2. CASSCF

class pyscf.mcscf.mc1step.CASSCF(mf_or_mol, ncas, nelecas, ncore=None, frozen=None)[source]
Args:
mf_or_molSCF object or Mole object

SCF or Mole to define the problem size.

ncasint

Number of active orbitals.

nelecasint or a pair of int

Number of electrons in active space.

Kwargs:
ncoreint

Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:
verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbital in active space. Be cautious of this parameter when CASCI/CASSCF are combined with DMRG solver or selected CI solver because DMRG and selected CI are not invariant to the rotation in active space. False by default.

canonicalizationbool

Whether to canonicalize orbitals. Note that canonicalization does not change the orbitals in active space by default. It only diagonalizes core and external space of the general Fock matirx. To get the natural orbitals in active space, attribute natorb need to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat

Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat

CAS space FCI energy

cindarray

CAS space FCI coefficients

mo_coeffndarray

When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray

Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray

Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
CASSCF

Extra attributes for CASSCF:

conv_tolfloat

Converge threshold. Default is 1e-7

conv_tol_gradfloat

Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat

The step size for orbital rotation. Small step (0.005 - 0.05) is prefered. Default is 0.03.

max_cycle_macroint

Max number of macro iterations. Default is 50.

max_cycle_microint

Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 5 steps should be enough. Default is 3.

ah_level_shiftfloat, for AH solver.

Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.

ah_conv_tolfloat, for AH solver.

converge threshold for AH solver. Default is 1e-12.

ah_max_cyclefloat, for AH solver.

Max number of iterations allowd in AH solver. Default is 30.

ah_lindepfloat, for AH solver.

Linear dependence threshold for AH solver. Default is 1e-14.

ah_start_tolflat, for AH solver.

In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 0.2.

ah_start_cycleint, for AH solver.

In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 2.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep might improve the accuracy of CASSCF optimization, but decrease the performance.

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()[0]
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()[0]
-109.044401887945668
chkfilestr

Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

ci_response_spaceint

subspace size to solve the CI vector response. Default is 3.

callbackfunction(envs_dict) => None

callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

scale_restorationfloat

When a step of orbital rotation moves out of trust region, the orbital optimization will be restored to previous state and the step size of the orbital rotation needs to be reduced. scale_restoration controls how much to scale down the step size.

Saved results

e_totfloat

Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat

CAS space FCI energy

cindarray

CAS space FCI coefficients

mo_coeffndarray

Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray

Diagonal elements of general Fock matrix (in mo_coeff representation).

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134
Gradients(*args, **kwargs)

Non-relativistic restricted Hartree-Fock gradients

ao2mo(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

as_scanner()

Generating a scanner for CASSCF PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total CASSCF energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters of MCSCF object (conv_tol, max_memory etc) are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1.2', verbose=0)
>>> mc_scanner = mcscf.CASSCF(scf.RHF(mol), 4, 4).as_scanner()
>>> e = mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.1'))
>>> e = mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.5'))
get_grad(mo_coeff=None, casdm1_casdm2=None, eris=None)[source]

Orbital gradients

get_h2cas(mo_coeff=None)[source]

Computing active space two-particle Hamiltonian.

Note It is different to get_h2eff when df.approx_hessian is applied, in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

get_h2eff(mo_coeff=None)[source]

Computing active space two-particle Hamiltonian.

Note It is different to get_h2cas when df.approx_hessian is applied, in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

kernel(mo_coeff=None, ci0=None, callback=None, _kern=<function kernel>)[source]
Returns:

Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients.

They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy

rotate_mo(mo, u, log=None)[source]

Rotate orbitals with the given unitary matrix

solve_approx_ci(h1, h2, ci0, ecore, e_cas, envs)[source]

Solve CI eigenvalue/response problem approximately

pyscf.mcscf.mc1step.as_scanner(mc)[source]

Generating a scanner for CASSCF PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total CASSCF energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters of MCSCF object (conv_tol, max_memory etc) are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1.2', verbose=0)
>>> mc_scanner = mcscf.CASSCF(scf.RHF(mol), 4, 4).as_scanner()
>>> e = mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.1'))
>>> e = mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.5'))
pyscf.mcscf.mc1step.kernel(casscf, mo_coeff, tol=1e-07, conv_tol_grad=None, ci0=None, callback=None, verbose=3, dump_chk=True)[source]

quasi-newton CASSCF optimization driver

pyscf.mcscf.mc1step_symm.CASSCF

alias of pyscf.mcscf.mc1step_symm.SymAdaptedCASSCF

class pyscf.mcscf.mc1step_symm.SymAdaptedCASSCF(mf_or_mol, ncas, nelecas, ncore=None, frozen=None)[source]
Args:
mf_or_molSCF object or Mole object

SCF or Mole to define the problem size.

ncasint

Number of active orbitals.

nelecasint or a pair of int

Number of electrons in active space.

Kwargs:
ncoreint

Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:
verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbital in active space. Be cautious of this parameter when CASCI/CASSCF are combined with DMRG solver or selected CI solver because DMRG and selected CI are not invariant to the rotation in active space. False by default.

canonicalizationbool

Whether to canonicalize orbitals. Note that canonicalization does not change the orbitals in active space by default. It only diagonalizes core and external space of the general Fock matirx. To get the natural orbitals in active space, attribute natorb need to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat

Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat

CAS space FCI energy

cindarray

CAS space FCI coefficients

mo_coeffndarray

When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray

Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray

Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
CASSCF

Extra attributes for CASSCF:

conv_tolfloat

Converge threshold. Default is 1e-7

conv_tol_gradfloat

Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat

The step size for orbital rotation. Small step (0.005 - 0.05) is prefered. Default is 0.03.

max_cycle_macroint

Max number of macro iterations. Default is 50.

max_cycle_microint

Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 5 steps should be enough. Default is 3.

ah_level_shiftfloat, for AH solver.

Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.

ah_conv_tolfloat, for AH solver.

converge threshold for AH solver. Default is 1e-12.

ah_max_cyclefloat, for AH solver.

Max number of iterations allowd in AH solver. Default is 30.

ah_lindepfloat, for AH solver.

Linear dependence threshold for AH solver. Default is 1e-14.

ah_start_tolflat, for AH solver.

In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 0.2.

ah_start_cycleint, for AH solver.

In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 2.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep might improve the accuracy of CASSCF optimization, but decrease the performance.

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()[0]
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()[0]
-109.044401887945668
chkfilestr

Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

ci_response_spaceint

subspace size to solve the CI vector response. Default is 3.

callbackfunction(envs_dict) => None

callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

scale_restorationfloat

When a step of orbital rotation moves out of trust region, the orbital optimization will be restored to previous state and the step size of the orbital rotation needs to be reduced. scale_restoration controls how much to scale down the step size.

Saved results

e_totfloat

Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat

CAS space FCI energy

cindarray

CAS space FCI coefficients

mo_coeffndarray

Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray

Diagonal elements of general Fock matrix (in mo_coeff representation).

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134
kernel(mo_coeff=None, ci0=None, callback=None, _kern=None)[source]
Returns:

Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients.

They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy

rotate_mo(mo, u, log=None)[source]

Rotate orbitals with the given unitary matrix

sort_mo_by_irrep(cas_irrep_nocc, cas_irrep_ncore=None, mo_coeff=None, s=None)[source]

Select active space based on symmetry information. See also pyscf.mcscf.addons.sort_mo_by_irrep()

UCASSCF (CASSCF without spin-degeneracy between alpha and beta orbitals) 1-step optimization algorithm

pyscf.mcscf.umc1step.CASSCF

alias of pyscf.mcscf.umc1step.UCASSCF

class pyscf.mcscf.umc1step.UCASSCF(mf_or_mol, ncas, nelecas, ncore=None, frozen=None)[source]
ao2mo(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

get_h2cas(mo_coeff=None)[source]

Compute the active space two-particle Hamiltonian.

Note It is different to get_h2eff when df.approx_hessian is applied, in which get_h2eff function returns the DF integrals while get_h2cas returns the regular 2-electron integrals.

get_h2eff(mo_coeff=None)[source]

Computing active space two-particle Hamiltonian.

kernel(mo_coeff=None, ci0=None, callback=None, _kern=<function kernel>)[source]
Returns:

Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients.

They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy

rotate_mo(mo, u, log=None)[source]

Rotate orbitals with the given unitary matrix

solve_approx_ci(h1, h2, ci0, ecore, e_cas)[source]

Solve CI eigenvalue/response problem approximately

MO integrals for UCASSCF methods

10.18.6.3. addons

pyscf.mcscf.addons.cas_natorb(casscf, mo_coeff=None, ci=None, sort=False)[source]

Natrual orbitals in CAS space

pyscf.mcscf.addons.caslst_by_irrep(casscf, mo_coeff, cas_irrep_nocc, cas_irrep_ncore=None, s=None, base=1)[source]

Given number of active orbitals for each irrep, return the orbital indices of active space

Args:

casscf : an CASSCF or CASCI object

cas_irrep_nocclist or dict

Number of active orbitals for each irrep. It can be a dict, eg {‘A1’: 2, ‘B2’: 4} to indicate the active space size based on irrep names, or {0: 2, 3: 4} for irrep Id, or a list [2, 0, 0, 4] (identical to {0: 2, 3: 4}) in which the list index is served as the irrep Id.

Kwargs:
cas_irrep_ncorelist or dict

Number of closed shells for each irrep. It can be a dict, eg {‘A1’: 6, ‘B2’: 4} to indicate the closed shells based on irrep names, or {0: 6, 3: 4} for irrep Id, or a list [6, 0, 0, 4] (identical to {0: 6, 3: 4}) in which the list index is served as the irrep Id. If cas_irrep_ncore is not given, the program will generate a guess based on the lowest CASCI.ncore orbitals.

sndarray

overlap matrix

baseint

0-based (C-like) or 1-based (Fortran-like) caslst

Returns:

A list of orbital indices

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvtz', symmetry=True, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.kernel()
>>> mc = mcscf.CASSCF(mf, 12, 4)
>>> mcscf.caslst_by_irrep(mc, mf.mo_coeff, {'E1gx':4, 'E1gy':4, 'E1ux':2, 'E1uy':2})
[5, 7, 8, 10, 11, 14, 15, 20, 25, 26, 31, 32]
pyscf.mcscf.addons.get_fock(casscf, mo_coeff=None, ci=None)[source]

Generalized Fock matrix in AO representation

pyscf.mcscf.addons.make_rdm1(casscf, mo_coeff=None, ci=None, **kwargs)[source]

One-particle densit matrix in AO representation

Args:

casscf : an CASSCF or CASCI object

Kwargs:
cindarray

CAS space FCI coefficients. If not given, take casscf.ci.

mo_coeffndarray

Orbital coefficients. If not given, take casscf.mo_coeff.

Examples:

>>> import scipy.linalg
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='sto-3g', verbose=0)
>>> mf = scf.RHF(mol)
>>> res = mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> res = mc.kernel()
>>> natocc = numpy.linalg.eigh(mcscf.make_rdm1(mc), mf.get_ovlp(), type=2)[0]
>>> print(natocc)
[ 0.0121563   0.0494735   0.0494735   1.95040395  1.95040395  1.98808879
  2.          2.          2.          2.        ]
pyscf.mcscf.addons.make_rdm1s(casscf, mo_coeff=None, ci=None, **kwargs)[source]

Alpha and beta one-particle densit matrices in AO representation

pyscf.mcscf.addons.map2hf(casscf, mf_mo=None, base=1, tol=0.4)[source]

The overlap between the CASSCF optimized orbitals and the canonical HF orbitals.

pyscf.mcscf.addons.project_init_guess(casscf, init_mo, prev_mol=None)[source]

Project the given initial guess to the current CASSCF problem. The projected initial guess has two parts. The core orbitals are directly taken from the Hartree-Fock orbitals, and the active orbitals are projected from the given initial guess.

Args:

casscf : an CASSCF or CASCI object

init_mondarray or list of ndarray

Initial guess orbitals which are not orth-normal for the current molecule. When the casscf is UHF-CASSCF, the init_mo needs to be a list of two ndarrays, for alpha and beta orbitals

Kwargs:
prev_molan instance of Mole

If given, the inital guess orbitals are associated to the geometry and basis of prev_mol. Otherwise, the orbitals are based of the geometry and basis of casscf.mol

Returns:

New orthogonal initial guess orbitals with the core taken from Hartree-Fock orbitals and projected active space from original initial guess orbitals

Examples:

import numpy
from pyscf import gto, scf, mcscf
mol = gto.Mole()
mol.build(atom='H 0 0 0; F 0 0 0.8', basis='ccpvdz', verbose=0)
mf = scf.RHF(mol)
mf.scf()
mc = mcscf.CASSCF(mf, 6, 6)
mo = mcscf.sort_mo(mc, mf.mo_coeff, [3,4,5,6,8,9])
print('E(0.8) = %.12f' % mc.kernel(mo)[0])
init_mo = mc.mo_coeff
for b in numpy.arange(1.0, 3., .2):
    mol.atom = [['H', (0, 0, 0)], ['F', (0, 0, b)]]
    mol.build(0, 0)
    mf = scf.RHF(mol)
    mf.scf()
    mc = mcscf.CASSCF(mf, 6, 6)
    mo = mcscf.project_init_guess(mc, init_mo)
    print('E(%2.1f) = %.12f' % (b, mc.kernel(mo)[0]))
    init_mo = mc.mo_coeff
pyscf.mcscf.addons.sort_mo(casscf, mo_coeff, caslst, base=1)[source]

Pick orbitals for CAS space

Args:

casscf : an CASSCF or CASCI object

mo_coeffndarray or a list of ndarray

Orbitals for CASSCF initial guess. In the UHF-CASSCF, it’s a list of two orbitals, for alpha and beta spin.

caslstlist of int or nested list of int

A list of orbital indices to represent the CAS space. In the UHF-CASSCF, it’s consist of two lists, for alpha and beta spin.

Kwargs:
baseint

0-based (C-style) or 1-based (Fortran-style) caslst

Returns:

An reoreded mo_coeff, which put the orbitals given by caslst in the CAS space

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> cas_list = [5,6,8,9] # pi orbitals
>>> mo = mc.sort_mo(cas_list)
>>> mc.kernel(mo)[0]
-109.007378939813691
pyscf.mcscf.addons.sort_mo_by_irrep(casscf, mo_coeff, cas_irrep_nocc, cas_irrep_ncore=None, s=None)[source]

Given number of active orbitals for each irrep, construct the mo initial guess for CASSCF

Args:

casscf : an CASSCF or CASCI object

cas_irrep_nocclist or dict

Number of active orbitals for each irrep. It can be a dict, eg {‘A1’: 2, ‘B2’: 4} to indicate the active space size based on irrep names, or {0: 2, 3: 4} for irrep Id, or a list [2, 0, 0, 4] (identical to {0: 2, 3: 4}) in which the list index is served as the irrep Id.

Kwargs:
cas_irrep_ncorelist or dict

Number of closed shells for each irrep. It can be a dict, eg {‘A1’: 6, ‘B2’: 4} to indicate the closed shells based on irrep names, or {0: 6, 3: 4} for irrep Id, or a list [6, 0, 0, 4] (identical to {0: 6, 3: 4}) in which the list index is served as the irrep Id. If cas_irrep_ncore is not given, the program will generate a guess based on the lowest CASCI.ncore orbitals.

sndarray

overlap matrix

Returns:

sorted orbitals, ordered as [c,..,c,a,..,a,v,..,v]

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvtz', symmetry=True, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.kernel()
>>> mc = mcscf.CASSCF(mf, 12, 4)
>>> mo = mc.sort_mo_by_irrep({'E1gx':4, 'E1gy':4, 'E1ux':2, 'E1uy':2})
>>> # Same to mo = sort_mo_by_irrep(mc, mf.mo_coeff, {2: 4, 3: 4, 6: 2, 7: 2})
>>> # Same to mo = sort_mo_by_irrep(mc, mf.mo_coeff, [0, 0, 4, 4, 0, 0, 2, 2])
>>> mc.kernel(mo)[0]
-108.162863845084
pyscf.mcscf.addons.spin_square(casscf, mo_coeff=None, ci=None, ovlp=None)[source]

Spin square of the UHF-CASSCF wavefunction

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='O 0 0 0; O 0 0 1', basis='sto-3g', spin=2, verbose=0)
>>> mf = scf.UHF(mol)
>>> res = mf.scf()
>>> mc = mcscf.CASSCF(mf, 4, 6)
>>> res = mc.kernel()
>>> print('S^2 = %.7f, 2S+1 = %.7f' % mcscf.spin_square(mc))
S^2 = 3.9831589, 2S+1 = 4.1149284
pyscf.mcscf.addons.state_average(casscf, weights=(0.5, 0.5), wfnsym=None)[source]

State average over the energy. The energy funcitonal is E = w1<psi1|H|psi1> + w2<psi2|H|psi2> + …

Note we may need change the FCI solver to

mc.fcisolver = fci.solver(mol, False)

before calling state_average_(mc), to mix the singlet and triplet states

MRH, 04/08/2019: Instead of turning casscf._finalize into an instance attribute that points to the previous casscf object, I’m going to make a whole new child class. This will have the added benefit of making state_average and state_average_ actually behave differently for the first time (until now they both modified the casscf object inplace). I’m also going to assign the weights argument as a member of the mc child class because an accurate second-order CASSCF algorithm for state-averaged calculations requires that the gradient and Hessian be computed for CI vectors of each root individually and then multiplied by that root’s weight. The second derivatives computed by newton_casscf.py need to be extended to state-averaged calculations in order to be used as intermediates for calculations of the gradient of a single root in the context of the SA-CASSCF method; see: Mol. Phys. 99, 103 (2001).

pyscf.mcscf.addons.state_average_(casscf, weights=(0.5, 0.5))[source]

Inplace version of state_average

pyscf.mcscf.addons.state_average_mix(casscf, fcisolvers, weights=(0.5, 0.5))[source]

State-average CASSCF over multiple FCI solvers.

pyscf.mcscf.addons.state_average_mix_(casscf, fcisolvers, weights=(0.5, 0.5))[source]

Inplace version of state_average

pyscf.mcscf.addons.state_specific(casscf, state=1, wfnsym=None)

For excited state

Kwargs:

state : int 0 for ground state; 1 for first excited state.

pyscf.mcscf.addons.state_specific_(casscf, state=1, wfnsym=None)[source]

For excited state

Kwargs:

state : int 0 for ground state; 1 for first excited state.