Laboratory for theoretical studies of electronic structure and spectroscopy of open-shell and electronically excited species.

## Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets
Natural orbitals are often used in quantum chemistry to achieve a more compact representation of
correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual-virtual
block of the state density matrix instead of the canonical Hartree-Fock molecular orbitals
results in smaller errors when the same fraction of virtual orbitals is frozen.
This strategy, termed frozen natural orbitals (FNO) approach,
has been successfully used to reduce the cost of state-specific
coupled-cluster (CC) calculations, such as ground-state CC, as well as some multi-state
methods, i.e., EOM-IP-CC (equation-of-motion CC method for ionization potentials).
This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip), which
has been developed to describe certain multi-configurational wave-functions within the single-reference
framework. In contrast to EOM-IP-CCSD, which describes open-shell target states by using a
closed-shell
reference, EOM-SF-CCSD relies on high-spin open-shell references (triplets, quartets, etc).
Consequently, straightforward application of FNOs computed for an open-shell reference
leads to an erratic behavior of the EOM-SF-CC energies and properties,
which can be attributed to an inconsistent
truncation of the alpha and beta orbital spaces.
A general solution to problems arising in the EOM-CC calculations utilizing open-shell references,
termed OSFNO (open-shell FNO), is proposed.
The OSFNO algorithm first identifies corresponding orbitals
by means of singular value decomposition (SVD) of
the overlap matrix of the alpha and beta molecular orbitals and determines virtual orbitals
corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state
density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve
the spin purity of the open-shell orbital subspace to the extent allowed by the original
reference thus facilitating a safe truncation of the virtual space.
The performance of the OSFNO approximation in combination with different choices of reference
orbitals is benchmarked for a set of diradicals and triradicals.
For a set of di-copper single-molecule magnets, a conservative truncation criterion corresponding to a
two-fold reduction of the virtual space in a triple-zeta basis
leads to errors of 5-18 cm ## Related Research |