# Development:Multiconfiguration SCF

### From NWChem

# MCSCF

The NWChem multiconfiguration SCF (MCSCF) module can currently perform complete active space SCF (CASSCF) calculations with at most 20 active orbitals and about 500 basis functions.

MCSCF STATE <string state> ACTIVE <integer nactive> ACTELEC <integer nactelec> MULTIPLICITY <integer multiplicity> [SYMMETRY <integer symmetry default 1>] [VECTORS [[input] <string input_file default file_prefix.movecs>] [swap <integer vec1 vec2> ...] \ [output <string output_file default input_file>] \ [lock] [HESSIAN (exact||onel)] [MAXITER <integer maxiter default 20>] [THRESH <real thresh default 1.0e-4>] [TOL2E <real tol2e default 1.0e-9>] [LEVEL <real shift default 0.1d0>] END

Note that the ACTIVE, ACTELEC, and MULTIPLICITY directives are required. The symmetry and multiplicity may alternatively be entered using the STATE directive.

## ACTIVE -- Number of active orbitals

The number of orbitals in the CASSCF active space must be specified using the ACTIVE directive.

E.g.,

active 10

The input molecular orbitals (see the vectors directive in MCSCF Vectors and SCF Vectors) must be arranged in order

- doubly occupied orbitals,
- active orbitals, and
- unoccupied orbitals.

## ACTELEC -- Number of active electrons

The number of electrons in the CASSCF active space must be specified using the the ACTELEC directive. An error is reported if the number of active electrons and the multiplicity are inconsistent.

The number of closed shells is determined by subtracting the number of active electrons from the total number of electrons (which in turn is derived from the sum of the nuclear charges minus the total system charge).

## MULTIPLICITY

The spin multiplicity must be specified and is enforced by projection of the determinant wavefunction.

E.g., to obtain a triplet state

multiplicity 3

## SYMMETRY -- Spatial symmetry of the wavefunction

This species the irreducible representation of the wavefunction as an integer in the range 1--8 using the same numbering of representations as output by the SCF program. Note that only Abelian point groups are supported.

E.g., to specify a *B*_{1} state when using the *C*_{2v} group

symmetry 3

## STATE -- Symmetry and multiplicity

The electronic state (spatial symmetry and multiplicity) may alternatively be specified using the conventional notation for an electronic state, such as ^{3}*B*_{2} for a triplet state of *B*_{2} symmetry. This would be accomplished with the input

state 3b2

which is equivalent to

symmetry 4 multiplicity 3

## VECTORS -- Input/output of MO vectors

Calculations are best started from RHF/ROHF molecular orbitals (see SCF), and by default vectors are taken from the previous MCSCF or SCF calculation. To specify another input file use the VECTORS directive. Vectors are by default output to the input file, and may be redirected using the output keyword. The swap keyword of the VECTORS directive may be used to reorder orbitals to obtain the correct active space.

The LOCK keyword allows the user to specify that the ordering of orbitals will be locked to that of the initial vectors, insofar as possible. The default is to order by ascending orbital energies within each orbital space. One application where locking might be desirable is a calculation where it is necessary to preserve the ordering of a previous geometry, despite flipping of the orbital energies. For such a case, the LOCK directive can be used to prevent the SCF calculation from changing the ordering, even if the orbital energies change.

Output orbitals of a converged MCSCF calculation are canonicalized as follows:

- Doubly occupied and unoccupied orbitals diagonalize the corresponding blocks of an effective Fock operator. Note that in the case of degenerate orbital energies this does not fully determine the orbtials.
- Active-space orbitals are chosen as natural orbitals by diagonalization of the active space 1-particle density matrix. Note that in the case of degenerate occupations that this does not fully determine the orbitals.

## HESSIAN -- Select preconditioner

The MCSCF will use a one-electron approximation to the orbital-orbital Hessian until some degree of convergence is obtained, whereupon it will attempt to use the exact orbital-orbital Hessian which makes the micro iterations more expensive but potentially reduces the total number of macro iterations. Either choice may be forced throughout the calculation by specifying the appropriate keyword on the HESSIAN directive.

E.g., to specify the one-electron approximation throughout

hessian onel

## LEVEL -- Level shift for convergence

The Hessian used in the MCSCF optimization is by default level shifted by 0.1 until the orbital gradient norm falls below 0.01, at which point the level shift is reduced to zero. The initial value of 0.1 may be changed using the LEVEL directive. Increasing the level shift may make convergence more stable in some instances.

E.g., to set the initial level shift to 0.5

level 0.5

## PRINT and NOPRINT

Specific output items can be selectively enabled or disabled using the print control mechanism with the available print options listed in the table below.

MCSCF Print Options | Option | Class | Synopsis |

ci energy | default | CI energy eigenvalue | |

fock energy | default | Energy derived from Fock matrices | |

gradient norm | default | Gradient norm | |

movecs | default | Converged occupied MO vectors | |

trace energy | high | Trace Energy | |

converge info | high | Convergence data and monitoring | |

precondition | high | Orbital preconditioner iterations | |

microci | high | CI iterations in line search | |

canonical | high | Canonicalization information | |

new movecs | debug | MO vectors at each macro-iteration | |

ci guess | debug | Initial guess CI vector | |

density matrix | debug | One- and Two-particle density matrices |