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Complete Active Space Self-Consistent Field (CASSCF)

The Complete Active Space Self-Consistent Field (CASSCF) method is one of the most widely used multiconfigurational quantum chemistry methods for studying molecules with complicated electronic structures.

Unlike Hartree–Fock (RHF), which represents the electronic wavefunction using a single Slater determinant, CASSCF constructs the wavefunction as a linear combination of many electronic configurations. This enables it to accurately describe systems where several electronic configurations contribute significantly to the molecular wavefunction.

CASSCF is particularly useful for

  • electronically excited states,
  • bond breaking and bond formation,
  • near-degenerate electronic states,
  • conical intersections,
  • photochemical reactions,
  • transition metal complexes,
  • and strongly correlated molecules.

The method simultaneously optimizes

  • the molecular orbitals, and
  • the configuration interaction (CI) coefficients,

making it considerably more accurate than methods such as CIS for multiconfigurational systems.

Why Do We Need CASSCF?

The previous tutorial introduced Configuration Interaction Singles (CIS), which describes excited states using only single-electron excitations from a Hartree–Fock reference.

Although CIS is computationally efficient, it has several limitations:

  • only single excitations are included,
  • electron correlation is treated approximately,
  • orbitals remain fixed during the calculation,
  • double and higher excitations are neglected.

For many molecules, particularly near avoided crossings or conical intersections, these approximations become inadequate.

CASSCF overcomes these limitations by allowing multiple electronic configurations to contribute to the wavefunction while simultaneously optimizing the molecular orbitals.

The Complete Active Space

The defining feature of CASSCF is the active space.

Instead of allowing every electron to occupy every molecular orbital (which would be prohibitively expensive), only a carefully selected subset of orbitals participates in the multiconfigurational treatment.

The molecular orbitals are divided into three groups:

          Virtual Orbitals
      -------------------------
        Secondary (Empty)

      -------------------------
          Active Orbitals

      -------------------------
        Inactive (Doubly Occupied)

          Core Orbitals
  • Inactive orbitals remain doubly occupied.
  • Active orbitals allow all possible occupations consistent with the chosen spin and symmetry.
  • Secondary orbitals remain unoccupied.

Every possible electron distribution within the active orbitals is included in the wavefunction, giving the method its name:

Complete Active Space

Choosing an Active Space

Selecting an appropriate active space is the most important step in a CASSCF calculation.

A good active space should include

  • orbitals involved in chemical bonding,
  • orbitals participating in electronic excitations,
  • partially occupied orbitals,
  • orbitals identified from a previous CIS calculation.

Throughout this tutorial we will demonstrate systematic procedures for selecting active spaces using RHF and CIS results.

Learning Objectives

After completing this tutorial, you should be able to

  • understand why CASSCF is required,
  • select an appropriate active space,
  • prepare a GAMESS CASSCF input,
  • interpret the output,
  • understand state averaging,
  • understand orbital optimization,
  • use CASSCF results for XMCQDPT and diabatization.

  • Download Input

    Complete GAMESS input used in this tutorial.

    CASSCF Input

  • Download Output

    Complete output file discussed below.

    CASSCF Output