7.10 Restricted Active Space Spin-Flip (RAS-SF) and Configuration Interaction (RAS-CI)

The restricted active space spin-flip (RAS-SF) is a special form of configuration interaction that is capable of describing the ground and low-lying excited states with moderate computational cost in a single-reference formulation,^{143, 1072, 78, 148} including strongly correlated systems. The RAS-SF approach is essentially a much lower computational cost alternative to Complete Active Space SCF (CASSCF) methods. RAS-SF typically works by performing a full CI calculation within an active space that is defined by the half-occupied orbitals of a restricted open shell HF (ROHF) reference determinant. In this way the difficulties of state-specific orbital optimization in CASSCF are bypassed. Single excitations into (hole) and out of (particle) the active space provide state-specific relaxation instead. Unlike most CI-based methods, RAS-SF is size-consistent, as well as variational, and, the increase in computational cost with system size is modest for a fixed number of spin flips. Beware, however, for the increase in cost as a function of the number of spin-flips is exponential! RAS-SF has been shown to be capable of tackling multiple low-lying electronic states in polyradicals and reliably predicting ground state multiplicities. ^{143, 77, 1071, 147, 1072, 78}

RAS-SF can also be viewed as one particular case of a more general RAS-CI family of methods. For instance, instead of defining the active space via spin-flipping as above, initial orbitals of other types can be read in, and electronic excitations calculated this way may be viewed as a RAS-EE-CI method (though size-consistency will generally be lost). Similar to EOM-CC approaches (see Section 7.8), other target RAS-CI wave functions can be constructed starting from any electronic configuration as the reference and using a general excitation-type operator. For instance, one can construct an ionizing variant that removes an arbitrary number of particles that is RAS-$n$IP-CI. An electron-attaching variant is RAS-$n$EA-CI.¹⁴⁸

Q-Chem features two versions of RAS-CI code with different, complementary, functionality. One code (invoked by specifying CORRRELATION = RASCI) has been written by David Casanova;¹⁴⁸ below we will refer to this code as RASCI1. The second implementation (invoked by specifying CORRRELATION = RASCI2) is primarily due to Paul Zimmerman;¹⁰⁷² we will refer to it as RASCI2 below.

The RASCI1 code uses an integral-driven implementation (exact integrals) and spin-adaptation of the CI configurations which results in a smaller diagonalization dimension. The current Q-Chem implementation of RASCI1 only allows for the calculation of systems with an even number of electrons, with the multiplicity of each state being printed alongside the state energy. Shared memory parallel execution decreases compute time as all the underlying integrals routines are parallelized.

The RASCI2 code includes the ability to simulate closed and open shell systems (i.e., even and odd numbers of electrons), fast integral evaluation using the resolution of the identity (RI) approximation, shared memory parallel operation, and analysis of the $⟨S^2⟩$ values and natural orbitals. The natural orbitals are stored in the QCSCRATCH directory in a folder called “NOs” in MolDen-readable format. Shared memory parallel is invoked as described in Section 2.8. A RASCI2 input requires the specification of an auxiliary basis set analogous to RI-MP2 computations (see Section 6.6.1). Otherwise, the active space as well as hole and particle excitations are specified in the same way as in RASCI1.

Note:  Because RASCI2 uses the RI approximation, the total energies computed with the two codes will be slightly different; however, the energy differences between different states should closely match each other.