Perspectives of geminal methods for large molecular systems

Abstract

Geminals are counterparts of two-electron chemical bonds and lone pairs in the realm of wave functions. Antisymmetrized products of geminals provide a solid framework for studies of electron pairing in molecular systems. Natural advantages of geminal wave functions such as the correct description of bond breaking and formation make them a powerful model for electronic structure calculations. The concerted efforts to develop geminal-based methods concentrate on increasing their accuracy and universality. The downside is the high computational cost limiting applications to small and toy systems. In contrast, the inherent local structure of optimal geminals opens pathways to development of methods for large systems. In particular, perspectives for linear scaling and hybrid quantum/classical approaches using geminals are discussed. The same principles are proposed for development of computational schemes for covalently bound and molecular crystals.

Benchmarking ionization potentials using the simple pCCD model

“…58 Although being a simplification, the pCCD model proved to be a low-cost wavefunction ansatz for describing strongly correlated closed-shell molecules. Examples of frequent testing grounds for geminal-based models include the process of bond breaking and formation in small molecules 49,[59][60][61][62][63][64][65][66][67][68][69] or heavy-element-containing compounds featuring actinide 63,[69][70][71][72][73][74] or lanthanide 75 atoms. Despite the growing interest in creating efficient and reliable geminal-based methods to account for various forms of electron correlation effects, 66,70,74,[76][77][78][79][80][81][82][83][84][85][86] orbitalor density-based approaches are still widely employed in computational quantum chemistry.…”

Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry

“…The natural basis, however, does not necessarily constitute the optimal basis in practical calculations. For instance, the AGP model in its natural representation does suffer from sizeconsistency errors, which might vanish in the general AGP ansatz of eqn (7). 23 The singlet-coupled natural APSG ansatz does not predict proper spin coupling of its fragments (vide infra).…”

“…For instance, the bond-breaking/forming process of small molecules is a common testing ground for various geminal-based models. [6][7][8][9][10][11][12][13][14][15] Despite the growing interest in developing efficient and reliable geminal-based methods to account for various types of electron correlation effects, orbital or density-based methods dominate in the computational quantum chemistry community.…”