Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability

Abstract

Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.

Quantum Crystallography: Current Developments and Future Perspectives

“…[132,133] This enables a" classical" atom-centered crystallographic description and al eastsquaresr efinement of atomicp ositions and thermal parameters using quantum atoms. Coupling HAR with ab initio linear-scaling strategies (e.g.,t echniques based on the transferability of ELMOs) [135,136] would allow considerable progress in this respect. The HAR procedure is iteratively repeated until convergencei sr eached.…”

Electron density learning of non-covalent systems

“…These large scale problems are typically tackled using a more scalable approach that consists of either using linear scaling techniques such as Mezey's molecular electron density LEGO assembler (MEDLA) 33,34 and adjustable density matrix assembler (ADMA), [35][36][37] as well as approaches based on localized molecular orbitals, such as ELMO. [38][39][40][41] Another methodology belonging to this second category involves the use of experimental techniques, such as X-ray diffraction, to probe the electron density and subsequently reconstructing r(r) through multipolar models [42][43][44] and pseudo-atomic libraries, such as ELMAM, [45][46][47][48] ELMAM2, 49,50 UBDB, 51,52 Invarioms 53 and SBFA. 54 While successful, these two methodologies have intrinsic limits: the rst is unable to capture the deformations of the charge density due to intermolecular interactions unless a suitable fragment is generated ad hoc, while the second relies on experimental data and is difficult to extend to thousands of different chemical systems at once.…”

On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

“…Among these techniques, one of the most popular and efficient is the strategy based on the recurrence relations introduced by Obara & Saika (1986), which were also discussed in the context of the Fourier transform operation in a follow-up paper (Obara & Saika, 1988). The Obara-Saika (OS) approach has actually been used very recently to compute structure factors corresponding to quantum chemistry-like electron densities: in XCW methods (Genoni, 2013a,b;Dos Santos et al, 2014;Genoni & Meyer, 2016;Genoni, 2017;Casati et al, 2017) based on the concept of extremely localized molecular orbitals (Stoll et al, 1980;Meyer, Guillot, Ruiz-Lopez & Genoni, 2016a;Meyer, Guillot, Ruiz-Lopez, Jelsch & Genoni, 2016b;Meyer & Genoni, 2018), in the novel X-ray constrained spin-coupled technique (Genoni, Franchini et al, 2018;Genoni et al, 2019), in charge-density investigations of molecular magnets (Thomsen et al, 2019;Gao et al, 2019) and in the study of the capability of the XCW strategy in capturing electron correlation effects on electron density .…”