8. mcscf — Multiconfigurational selfconsistent field¶
CASCI and CASSCF
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, 1based 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.
 verbose
: int Print level. Default value equals to
Mole.verbose
. max_memory
: float or int Allowed memory in MB. Default value equals to
Mole.max_memory
. ncas
: int Active space size.
 nelecas
: tuple of int Active (nelec_alpha, nelec_beta)
 ncore
: int or tuple of int Core electron number. In UHFCASSCF, it’s a tuple to indicate the different core eletron numbers.
 natorb
: bool Whether to restore the natural orbital during CASSCF optimization. Default is not.
 canonicalization
: bool Whether to canonicalize orbitals. Default is True.
 fcisolver
: an instance ofFCISolver
The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHFCASSCF. 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 = 1e7For 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
andfciqmcscf
.
The Following attributes are used for CASSCF
 conv_tol
: float Converge threshold. Default is 1e7
 conv_tol_grad
: float Converge threshold for CI gradients and orbital rotation gradients. Default is 1e4
 max_stepsize
: floatThe 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 = 1e6 max_ci_stepsize
: float The max size for approximate CI updates. The approximate updates are used in 1step algorithm, to estimate the change of CI wavefunction wrt the orbital rotation. Small step size is prefered. Default is 0.01.
 max_cycle_macro
: int Max number of macro iterations. Default is 50.
 max_cycle_micro
: int 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_inner
: int 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.
 frozen
: int or list If integer is given, the innermost orbitals are excluded from optimization. Given the orbital indices (0based) in a list, any doubly occupied core orbitals, active orbitals and external orbitals can be frozen.
 ah_level_shift
: float, for AH solver. Level shift for the Davidson diagonalization in AH solver. Default is 0.
 ah_conv_tol
: float, for AH solver. converge threshold for Davidson diagonalization in AH solver. Default is 1e8.
 ah_max_cycle
: float, for AH solver. Max number of iterations allowd in AH solver. Default is 20.
 ah_lindep
: float, for AH solver. Linear dependence threshold for AH solver. Default is 1e16.
 ah_start_tol
: flat, 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 1e4.
 ah_start_cycle
: int, 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
andah_start_cycle
can affect the accuracy and performance of CASSCF solver. Lowerah_conv_tol
andah_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 = 1e10 >>> mc.ah_conv_tol = 1e5 >>> mc.kernel() 109.044401898486001 >>> mc.ah_conv_tol = 1e10 >>> mc.kernel() 109.044401887945668 chkfile
: str Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.
Saved results
 e_tot
: float Total MCSCF energy (electronic energy plus nuclear repulsion)
 ci
: ndarray CAS space FCI coefficients
 converged
: bool, for CASSCF only It indicates CASSCF optimization converged or not.
 mo_energy: ndarray,
 Diagonal elements of general Fock matrix
 mo_coeff
: ndarray, 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 inplace convert the orbitals
8.1. CASSCF active space solver¶
8.1.1. DMRG solver¶
8.1.2. FCIQMC solver¶
8.1.3. Stateaverage FCI solver¶
8.1.4. Stateaverage with mixed solver¶
8.2. Symmetry broken¶
8.3. Initial guess¶
8.4. Canonical orbitals¶
There are two relevant parameters for orbital canonicalization. They are
mc.canonicalization
and mc.natorb
(assuming the MCSCF object is mc
).
In the CASCI/CASSCF calculations, the resultant orbitals are stored in the
attribute mc.mo_coeff
. These orbitals may be identical or partially
identical to the initial orbitals, depending on the values of
mc.canonicalization
and mc.natorb
.
mc.canonicalization
controls whether the resultant CASCI/CASSCF orbitals
are canonicalized with respect to the general Fock matrix. General Fock matrix
is defined as
\(\gamma\) is the total density matrix which is the summation of doubly
occupied core density matrix and correlated density matrix in active space.
If mc.canonicalization
is enabled, the CASCI/CASSCF program will call
the mc.canonicalize()
function to diagonalize the core and external space
wrt the general Fock matrix. The eigenvalues of the core and external subspace
are stored in attribute mc.mo_energy
.
By default, mc.canonicalization
is enabled because the canonicalized
MCSCF orbitals can simplify the algorithm of MRPT methods.
mc.natorb
controls whether the CASCI/CASSCF active space orbitals are
transformed to natural orbitals of 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 and it is important for the MCSCF solver.
Generally, the value of mc.natorb
does not affect (the default) FCI
solver because an independent CASCI calculation following a previous MCSCF
calculation should give the same solutions no matter mc.natorb
is enabled
or not. But this is not true for some external large active space solvers such
as DMRG, selected CI methods. The CASCI calculation may produce different
answers depending on the value of mc.natorb
. Therefore, it is
recommended to disable mc.natorb
in your calculation.
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
andmc.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
andmc.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
andmc.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
andmc.natorb = True
mc.mo_coeff
are completely different to the input orbitals.
There is another parameter mc.sorting_mo_energy
which may affect the
ordering of MCSCF orbitals when mc.canonicalization
or mc.natorb
is enabled. Generally, the 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).
This ordering may not be held if point group symmetry is enabled in the
calculation. When a system has high spatial symmetry and point group symmetry
is enabled, each SCF orbital will be assigned to an irreducible representation
label. In the MCSCF calculation and the canonicalization, the irreducible
representation label of the orbitals will not be changed. They are always the
same to the symmetry labels of the input orbitals. Although the orbitals
are still ordered within each irreducible representation, the orbital energies
(or occupancies) for all orbitals are not strictly sorted. Setting
mc.sorting_mo_energy = Trye
(though not recommended) can force the orbitals
to be sorted regardless whether the point group symmetry is enabled. In certain
scenario, you may want to enable mc.natorb
and mc.sorting_mo_energy
.
examples/dmrg/31cr2_scan/cr2scan.py
provides one example that you need to
enable the two parameters. In that example, the dissociation curve of Cr dimer
was scanned by heatbath selectedCI method in which the active space of
selectedCICASSCF was gradually enlarged in a series of CASSCF calculations.
Since the selectedCI algorithm depends on the initial single determinant, the
orbital ordering do have matters to the final CASSCF results. Thus
mc.natorb
and mc.sorting_mo_energy
have to be enabled to make
sure that the each selectedCI starts from the similar initial reference for
each point on the dissociation curve. At some critical points, the difference
in the orbital ordering in the active space can lead to discontinuous potential
energy curve.
8.5. Program reference¶
8.5.1. CASCI¶

class
pyscf.mcscf.casci.
CASCI
(mf_or_mol, ncas, nelecas, ncore=None)[source]¶  Args:
 mf_or_mol : SCF object or Mole object
 SCF or Mole to define the problem size.
 ncas : int
 Number of active orbitals.
 nelecas : int or a pair of int
 Number of electrons in active space.
 Kwargs:
 ncore : int
 Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.
 Attributes:
 verbose : int
 Print level. Default value equals to
Mole.verbose
.  max_memory : float or int
 Allowed memory in MB. Default value equals to
Mole.max_memory
.  ncas : int
 Active space size.
 nelecas : tuple of int
 Active (nelec_alpha, nelec_beta)
 ncore : int or tuple of int
 Core electron number. In UHFCASSCF, it’s a tuple to indicate the different core eletron numbers.
 natorb : bool
 Whether to restore the natural orbital in CAS space. Default is not. Be very careful to set this parameter when CASCI/CASSCF are combined with DMRG solver because this parameter changes the orbital ordering which DMRG relies on.
 canonicalization : bool
 Whether to canonicalize orbitals. Default is True.
 sorting_mo_energy : bool
 Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.
 fcisolver : an instance of
The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHFCASSCF. 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 = 1e7
For more details of the parameter for FCISolver, See
fci
.
FCISolver
Saved results
 e_tot : float
 Total MCSCF energy (electronic energy plus nuclear repulsion)
 e_cas : float
 CAS space FCI energy
 ci : ndarray
 CAS space FCI coefficients
 mo_coeff : ndarray
 When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1particle 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_energy : ndarray
 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.CASCI(mf, 6, 6) >>> mc.kernel()[0] 108.980200816243354

as_scanner
(mc)¶ 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
(mc, 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 effecitve Fock matrix. Effective Fock matrix is built with oneparticle density matrix (see also
mcscf.casci.get_fock()
). For stateaverage CASCI/CASSCF object, the canonicalized orbitals are based on the stateaverage 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/QMCMCSCF 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
 orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If the point group symmetry is not available in the system, the orbitals are always sorted. When the point group symmetry is available, sort=False will keep the symmetry label of input orbitals and only sort the orbitals in each symmetry block while sort=True will reorder all orbitals in each subspace and the symmetry labels may be changed.
 cas_natorb (bool): Whether to transform the active orbitals to natual
 orbitals
 casdm1 (ndarray): 1particle 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 stateaverage CASCI/CASCF calculation, this results in a set of canonicalized orbitals of stateaverage 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 effecitve Fock matrix. Effective Fock matrix is built with oneparticle density matrix (see also
mcscf.casci.get_fock()
). For stateaverage CASCI/CASSCF object, the canonicalized orbitals are based on the stateaverage 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/QMCMCSCF 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
 orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If the point group symmetry is not available in the system, the orbitals are always sorted. When the point group symmetry is available, sort=False will keep the symmetry label of input orbitals and only sort the orbitals in each symmetry block while sort=True will reorder all orbitals in each subspace and the symmetry labels may be changed.
 cas_natorb (bool): Whether to transform the active orbitals to natual
 orbitals
 casdm1 (ndarray): 1particle 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 stateaverage CASCI/CASCF calculation, this results in a set of canonicalized orbitals of stateaverage 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
 Args:
 mc : a CASSCF/CASCI object or RHF object
 Kwargs:
 sort : bool
 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
 Args:
 mc : a CASSCF/CASCI object or RHF object
 Kwargs:
 sort : bool
 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:
 shift : float
 Energy penalty for states which have wrong spin
 ss : number
 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:
 shift : float
 Energy penalty for states which have wrong spin
 ss : number
 S^2 expection value == s*(s+1)

get_h1cas
(casci, mo_coeff=None, ncas=None, ncore=None)¶ CAS sapce oneelectron hamiltonian
 Args:
 casci : a CASSCF/CASCI object or RHF object
 Returns:
 A tuple, the first is the effective oneelectron 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 oneelectron hamiltonian
 Args:
 casci : a CASSCF/CASCI object or RHF object
 Returns:
 A tuple, the first is the effective oneelectron hamiltonian defined in CAS space, the second is the electronic energy from core.

get_h2cas
(mo_coeff=None)[source]¶ Computing active space twoparticle 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 2electron integrals.

get_h2eff
(mo_coeff=None)[source]¶ Computing active space twoparticle 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 2electron integrals.

h1e_for_cas
(casci, mo_coeff=None, ncas=None, ncore=None)¶ CAS sapce oneelectron hamiltonian
 Args:
 casci : a CASSCF/CASCI object or RHF object
 Returns:
 A tuple, the first is the effective oneelectron 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]¶ Oneparticle density matrix in AO representation

make_rdm1s
(mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs)[source]¶ Oneparticle 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
orCASCI
object mo_coeff : ndarray or a list of ndarray
 Orbitals for CASSCF initial guess. In the UHFCASSCF, it’s a list of two orbitals, for alpha and beta spin.
 caslst : list of int or nested list of int
 A list of orbital indices to represent the CAS space. In the UHFCASSCF, it’s consist of two lists, for alpha and beta spin.
 Kwargs:
 base : int
 0based (Cstyle) or 1based (Fortranstyle) 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.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 effecitve Fock matrix. Effective Fock matrix is built with oneparticle density matrix (see also
mcscf.casci.get_fock()
). For stateaverage CASCI/CASSCF object, the canonicalized orbitals are based on the stateaverage 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/QMCMCSCF 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
 orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If the point group symmetry is not available in the system, the orbitals are always sorted. When the point group symmetry is available, sort=False will keep the symmetry label of input orbitals and only sort the orbitals in each symmetry block while sort=True will reorder all orbitals in each subspace and the symmetry labels may be changed.
 cas_natorb (bool): Whether to transform the active orbitals to natual
 orbitals
 casdm1 (ndarray): 1particle 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 stateaverage CASCI/CASCF calculation, this results in a set of canonicalized orbitals of stateaverage 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
 Args:
 mc : a CASSCF/CASCI object or RHF object
 Kwargs:
 sort : bool
 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 oneelectron Fock matrix in AO representation f = sum_{pq} E_{pq} F_{pq} F_{pq} = h_{pq} + sum_{rs} [(pqrs)(psrq)] DM_{sr}
Ref. Theor. Chim. Acta., 91, 31 Chem. Phys. 48, 157
For stateaverage CASCI/CASSCF object, the effective fock matrix is based on the stateaverage density matrix. To obtain Fock matrix of a specific state in the stateaverage 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/QMCMCSCF 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): 1particle 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 stateaverage CASCI/CASCF calculation, this results in the effective Fock matrix based on the stateaverage 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 oneelectron hamiltonian
 Args:
 casci : a CASSCF/CASCI object or RHF object
 Returns:
 A tuple, the first is the effective oneelectron hamiltonian defined in CAS space, the second is the electronic energy from core.
UCASCI (CASCI with nondegenerated alpha and beta orbitals, typically UHF orbitals)
8.5.2. CASSCF¶

class
pyscf.mcscf.mc1step.
CASSCF
(mf_or_mol, ncas, nelecas, ncore=None, frozen=None)[source]¶  Args:
 mf_or_mol : SCF object or Mole object
 SCF or Mole to define the problem size.
 ncas : int
 Number of active orbitals.
 nelecas : int or a pair of int
 Number of electrons in active space.
 Kwargs:
 ncore : int
 Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.
 Attributes:
 verbose : int
 Print level. Default value equals to
Mole.verbose
.  max_memory : float or int
 Allowed memory in MB. Default value equals to
Mole.max_memory
.  ncas : int
 Active space size.
 nelecas : tuple of int
 Active (nelec_alpha, nelec_beta)
 ncore : int or tuple of int
 Core electron number. In UHFCASSCF, it’s a tuple to indicate the different core eletron numbers.
 natorb : bool
 Whether to restore the natural orbital in CAS space. Default is not. Be very careful to set this parameter when CASCI/CASSCF are combined with DMRG solver because this parameter changes the orbital ordering which DMRG relies on.
 canonicalization : bool
 Whether to canonicalize orbitals. Default is True.
 sorting_mo_energy : bool
 Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.
 fcisolver : an instance of
The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHFCASSCF. 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 = 1e7
For more details of the parameter for FCISolver, See
fci
.
FCISolver
Saved results
 e_tot : float
 Total MCSCF energy (electronic energy plus nuclear repulsion)
 e_cas : float
 CAS space FCI energy
 ci : ndarray
 CAS space FCI coefficients
 mo_coeff : ndarray
 When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1particle 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_energy : ndarray
 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.CASCI(mf, 6, 6) >>> mc.kernel()[0] 108.980200816243354 CASSCF
Extra attributes for CASSCF:
 conv_tol : float
 Converge threshold. Default is 1e7
 conv_tol_grad : float
 Converge threshold for CI gradients and orbital rotation gradients. Default is 1e4
 max_stepsize : float
 The step size for orbital rotation. Small step (0.005  0.05) is prefered. Default is 0.03.
 max_cycle_macro : int
 Max number of macro iterations. Default is 50.
 max_cycle_micro : int
 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_shift : float, for AH solver.
 Level shift for the Davidson diagonalization in AH solver. Default is 1e8.
 ah_conv_tol : float, for AH solver.
 converge threshold for AH solver. Default is 1e12.
 ah_max_cycle : float, for AH solver.
 Max number of iterations allowd in AH solver. Default is 30.
 ah_lindep : float, for AH solver.
 Linear dependence threshold for AH solver. Default is 1e14.
 ah_start_tol : flat, 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_cycle : int, 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
andah_start_cycle
can affect the accuracy and performance of CASSCF solver. Lowerah_conv_tol
andah_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 = 1e10 >>> mc.ah_conv_tol = 1e5 >>> mc.kernel()[0] 109.044401898486001 >>> mc.ah_conv_tol = 1e10 >>> mc.kernel()[0] 109.044401887945668
 chkfile : str
 Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.
 ci_response_space : int
 subspace size to solve the CI vector response. Default is 3.
 callback : function(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.
Saved results
 e_tot : float
 Total MCSCF energy (electronic energy plus nuclear repulsion)
 e_cas : float
 CAS space FCI energy
 ci : ndarray
 CAS space FCI coefficients
 mo_coeff : ndarray
 Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1particle 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_energy : ndarray
 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

as_scanner
(mc)¶ 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_h2cas
(mo_coeff=None)[source]¶ Computing active space twoparticle 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 2electron integrals.

get_h2eff
(mo_coeff=None)[source]¶ Computing active space twoparticle 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 2electron 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

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=1e07, conv_tol_grad=None, ci0=None, callback=None, verbose=3, dump_chk=True)[source]¶ quasinewton CASSCF optimization driver

pyscf.mcscf.mc1step_symm.
CASSCF
¶ alias of
SymAdaptedCASSCF

class
pyscf.mcscf.mc1step_symm.
SymAdaptedCASSCF
(mf_or_mol, ncas, nelecas, ncore=None, frozen=None)[source]¶  Args:
 mf_or_mol : SCF object or Mole object
 SCF or Mole to define the problem size.
 ncas : int
 Number of active orbitals.
 nelecas : int or a pair of int
 Number of electrons in active space.
 Kwargs:
 ncore : int
 Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.
 Attributes:
 verbose : int
 Print level. Default value equals to
Mole.verbose
.  max_memory : float or int
 Allowed memory in MB. Default value equals to
Mole.max_memory
.  ncas : int
 Active space size.
 nelecas : tuple of int
 Active (nelec_alpha, nelec_beta)
 ncore : int or tuple of int
 Core electron number. In UHFCASSCF, it’s a tuple to indicate the different core eletron numbers.
 natorb : bool
 Whether to restore the natural orbital in CAS space. Default is not. Be very careful to set this parameter when CASCI/CASSCF are combined with DMRG solver because this parameter changes the orbital ordering which DMRG relies on.
 canonicalization : bool
 Whether to canonicalize orbitals. Default is True.
 sorting_mo_energy : bool
 Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.
 fcisolver : an instance of
The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHFCASSCF. 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 = 1e7
For more details of the parameter for FCISolver, See
fci
.
FCISolver
Saved results
 e_tot : float
 Total MCSCF energy (electronic energy plus nuclear repulsion)
 e_cas : float
 CAS space FCI energy
 ci : ndarray
 CAS space FCI coefficients
 mo_coeff : ndarray
 When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1particle 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_energy : ndarray
 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.CASCI(mf, 6, 6) >>> mc.kernel()[0] 108.980200816243354 CASSCF
Extra attributes for CASSCF:
 conv_tol : float
 Converge threshold. Default is 1e7
 conv_tol_grad : float
 Converge threshold for CI gradients and orbital rotation gradients. Default is 1e4
 max_stepsize : float
 The step size for orbital rotation. Small step (0.005  0.05) is prefered. Default is 0.03.
 max_cycle_macro : int
 Max number of macro iterations. Default is 50.
 max_cycle_micro : int
 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_shift : float, for AH solver.
 Level shift for the Davidson diagonalization in AH solver. Default is 1e8.
 ah_conv_tol : float, for AH solver.
 converge threshold for AH solver. Default is 1e12.
 ah_max_cycle : float, for AH solver.
 Max number of iterations allowd in AH solver. Default is 30.
 ah_lindep : float, for AH solver.
 Linear dependence threshold for AH solver. Default is 1e14.
 ah_start_tol : flat, 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_cycle : int, 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
andah_start_cycle
can affect the accuracy and performance of CASSCF solver. Lowerah_conv_tol
andah_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 = 1e10 >>> mc.ah_conv_tol = 1e5 >>> mc.kernel()[0] 109.044401898486001 >>> mc.ah_conv_tol = 1e10 >>> mc.kernel()[0] 109.044401887945668
 chkfile : str
 Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.
 ci_response_space : int
 subspace size to solve the CI vector response. Default is 3.
 callback : function(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.
Saved results
 e_tot : float
 Total MCSCF energy (electronic energy plus nuclear repulsion)
 e_cas : float
 CAS space FCI energy
 ci : ndarray
 CAS space FCI coefficients
 mo_coeff : ndarray
 Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1particle 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_energy : ndarray
 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

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 spindegeneracy between alpha and beta orbitals) 1step optimization algorithm
MO integrals for UCASSCF methods
8.5.3. 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
orCASCI
object cas_irrep_nocc : list 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_ncore : list 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.  s : ndarray
 overlap matrix
 base : int
 0based (Clike) or 1based (Fortranlike) 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]¶ Oneparticle densit matrix in AO representation
 Args:
 casscf : an
CASSCF
orCASCI
object  Kwargs:
 ci : ndarray
 CAS space FCI coefficients. If not given, take casscf.ci.
 mo_coeff : ndarray
 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='sto3g', 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 oneparticle 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 HartreeFock orbitals, and the active orbitals are projected from the given initial guess.
 Args:
casscf : an
CASSCF
orCASCI
object init_mo : ndarray or list of ndarray
 Initial guess orbitals which are not orthnormal for the current molecule. When the casscf is UHFCASSCF, the init_mo needs to be a list of two ndarrays, for alpha and beta orbitals
 Kwargs:
 prev_mol : an instance of
 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
Mole
 Returns:
 New orthogonal initial guess orbitals with the core taken from HartreeFock 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
orCASCI
object mo_coeff : ndarray or a list of ndarray
 Orbitals for CASSCF initial guess. In the UHFCASSCF, it’s a list of two orbitals, for alpha and beta spin.
 caslst : list of int or nested list of int
 A list of orbital indices to represent the CAS space. In the UHFCASSCF, it’s consist of two lists, for alpha and beta spin.
 Kwargs:
 base : int
 0based (Cstyle) or 1based (Fortranstyle) 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
orCASCI
object cas_irrep_nocc : list 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_ncore : list 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.  s : ndarray
 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 UHFCASSCF 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='sto3g', 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))¶ State average over the energy. The energy funcitonal is E = w1<psi1Hpsi1> + w2<psi2Hpsi2> + ...
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

pyscf.mcscf.addons.
state_average_
(casscf, weights=(0.5, 0.5))[source]¶ State average over the energy. The energy funcitonal is E = w1<psi1Hpsi1> + w2<psi2Hpsi2> + ...
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

pyscf.mcscf.addons.
state_average_mix
(casscf, fcisolvers, weights=(0.5, 0.5))¶ Stateaverage CASSCF over multiple FCI solvers.

pyscf.mcscf.addons.
state_average_mix_
(casscf, fcisolvers, weights=(0.5, 0.5))[source]¶ Stateaverage CASSCF over multiple FCI solvers.

pyscf.mcscf.addons.
state_specific
(casscf, state=1)¶ For excited state
 Kwargs:
 state : int 0 for ground state; 1 for first excited state.