Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

Abstract

In this article, we demonstrate that a first-order spin penalty scheme can be efficiently applied to the Slater determinant based Full-CI Quantum Monte Carlo (FCIQMC) algorithm, as a practical route toward spin purification. Two crucial applications are presented to demonstrate the validity and robustness of this scheme: the 1 Δ g ← 3 Σ g vertical excitation in O 2 and key spin gaps in a [Mn 3 (IV) O 4 ] cluster. In the absence of a robust spin adaptation/purification technique, both applications would be unattainable by Slater determinant based ground state methods, with any starting wave function collapsing into the higher-spin ground state during the optimization. This strategy can be coupled to other algorithms that use the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver, including the Stochastic Generalized Active Space, the similarity-transformed FCIQMC, the tailored-CC, and second-order perturbation theory approaches. Moreover, in contrast to the GUGA-FCIQMC technique, this strategy features both spin projection and total spin adaptation, making it appealing when solving anisotropic Hamiltonians. It also provides spin-resolved reduced density matrices, important for the investigation of spin-dependent properties in polynuclear transition metal clusters, such as the hyperfine-coupling constants.

FCIQMC-Tailored Distinguishable Cluster Approach: Open-Shell Systems

“…However, even in such rather single-reference problems, a combination of coupled cluster or distinguishable cluster with FCIQMC (or alternatively, with higher-order coupled-cluster methods) provides a way for a systematic improvement of the results beyond a perturbative triples correction. We are currently working on extending the tailored methods to strongly correlated open-shell systems that usually require spin-broken reference determinants, and for which our recently developed spin-purification technique for FCIQMC 108 will be essential.…”

Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory

“…Therefore, although the current implementation employs a determinant-based expansion, this spin contamination will still occur using a linear combination of all configuration state functions with ⟨ Ŝ z ⟩ = 0 rather than a determinant-based expansion. Spin contamination could be avoided explicitly by including a spin-penalty function or if the CASSCF wave function is constructed from a linear combination of CSFs with the desired ⟨ Ŝ 2 ⟩ value. − …”

Magnetic Interactions in a [Co(II)3Er(III)(OR)4] Model Cubane through Forefront Multiconfigurational Methods

“…Correlation effects outside the active space are commonly described via perturbation theory approaches, such as CASPT2 64,65 or, more recently, via the computationally inexpensive MCPDFT approach. 66,73−75 Notably, in this work CASPT2 has only been coupled to the small CAS (12,12) wave functions, for which the conventional CASSCF (12,12) procedure and related higher order density matrices are available. For larger active space calculations higher-order density matrices are currently unavailable for practical calculations, thus limiting the applicability of PT2 approaches to large active space reference wave functions.…”