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We discuss some strategies for extending recent geminal-based methods to open-shells by replacing the geminal-creation operators with more general composite boson creation operators, and even creation operators that mix fermionic and bosonic components. We also discuss the utility of symmetry-breaking and restoration, but using a projective (not a variational) approach. Both strategies—either together or separately—give a pathway for extending geminals-based methods to open shells, while retaining the computational efficiency and conceptual simplicity of existing geminal product wavefunctions. [ABSTRACT FROM AUTHOR]

We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented. [ABSTRACT FROM AUTHOR]

[Display omitted] • A unifying framework for multi-determinant wavefunctions is developed. • Mathematical requirements for wavefunction ansätze to be size-consistent are derived. • New wavefunction ansatze are proposed, e.g. the determinant ratio wavefunction form. • Geminal-product wavefunctions are generalized. We present a Flexible Ansatz for N-body Configuration Interaction (FANCI) that includes any multideterminant wavefunction. This ansatz is a generalization of the Configuration Interaction (CI) wavefunction, where the coefficients are replaced by a specified function of certain parameters. By making an appropriate choice for this function, we can reproduce popular wavefunction structures like CI, Coupled-Cluster, Tensor Network States, and geminal-product wavefunctions. The universality of this framework suggests a programming structure that allows for the easy construction and optimization of arbitrary wavefunctions. Here, we will discuss the structures of the FANCI framework and its implications for wavefunction properties, particularly accuracy, cost, and size-consistency. We demonstrate the flexibility of this framework by reconstructing popular wavefunction ansätze and modifying them to construct novel wavefunction forms. FANCI provides a powerful framework for exploring, developing, and testing new wavefunction forms. [ABSTRACT FROM AUTHOR]