Local spin: A treatment beyond single determinant wave functions

Generalized spin σ-SCF method

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3-7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Extraction of local spin-coupled states by second quantized operators

We present a methodology for analyzing chemical bonds embedded in the electronic wave function of molecules, especially in terms of spin correlations or so-called "local spin." In this paper, based on biorthogonal second quantization, the spin correlation functions of molecules are naturally introduced, which enables us to extract local singlet and local triplet elements from the wave function. We also clarify the relationship between these spin correlations and traditional chemical concepts, i.e., resonance structures. Several chemical reactions, including the intramolecular radical cyclization and the formation of preoxetane, are demonstrated to verify the analysis method numerically.

Local spin and open quantum systems: clarifying misconceptions, unifying approaches

The theory of open quantum systems (OQSs) is applied to partition the squared spin operator into fragment (local spin) and interfragment (spin-coupling) contributions in a molecular system.

Quantum entanglement in carbon–carbon, carbon–phosphorus and silicon–silicon bonds

We present a quantum entanglement analysis to dissect the bond orders in polyatomic molecules.

Topology of the electron density in open-shell systems

This work describes the decomposition of the electron density field of open-shell molecular systems into physically meaningful contributions. The new features that the open-shell nature of the wave function introduces into these fields are topologically studied and discussed, showing the charge concentration and depletion regions within the system. The localized character (field concentration only close to the nuclear positions of the system) or the nonlocalized character (concentration in other regions of the system) is used to study the reliability of the Lewis model of bonding to describe chemical bonding phenomenon in open-shell systems. Numerical examples are reported for molecular systems at a correlated level of approximation, in the single-double configuration interaction wave function approach.