Quantum crystallography: From the intersection to the union of crystallography and quantum mechanics

Fast quantum crystallography

“…Properties of considerable current interest are the total molecular electron density and the total molecular electrostatic potential (ESP), V, of large macromolecules of biological and nanotechnological interest. KEM has been shown to be capable of delivering electron densities sampled at bond and ring critical points in addition to the complete localization-delocalization matrix [99,100] of a graphene nanoribbon. [33] The method has been extended to estimate electric field-induced changes in the properties (ie, response properties) of a finite graphene flake.…”

“…Later, Jayatilaka developed an alternative approach to constrain wavefunctions to simultaneously minimize the energy of the system and generate densities that are consistent with the observed structure factors . Originally, QCr may have been considered as the intersection between quantum mechanics and traditional experimental diffraction crystallography (X‐ray [in direct or momentum space], neutron, and electron), a view that has been enlarged in recent years to a more encompassing definition as a union of quantum mechanics and traditional crystallography . Presently, QCr is practiced by a variety of researchers in a variety of methodologies, both experimental and theoretic …”

“…[13][14][15] Originally, QCr may have been considered as the intersection between quantum mechanics and traditional experimental diffraction crystallography (X-ray [in direct or momentum space], neutron, and electron), [16] a view that has been enlarged in recent years to a more encompassing definition as a union of quantum mechanics and traditional crystallography. [17] Presently, QCr is practiced by a variety of researchers in a variety of methodologies, both experimental and theoretic. [4] Here is a suggestion, obvious but also of some importance.…”

“…A plethora of approaches have been devised to get around this scaling bottleneck. [8,17,23,[25][26][27][28]30, A common strategy in these approaches is the partitioning of the large system into computationally tractable fragments followed by a recombination whether in Hilbert space or in direct space to reconstruct the properties of the large difficultly calculable system. KEM shares with other methods the fragmentation of a large system into smaller pieces that are then recombined after being subjected to quantum chemical calculations.…”

“…[69] It is beyond the scope of this article to review all these methods and, instead, it will limit itself to the KEM. [8,17,23,[25][26][27][28]30] Most crystal structures are brought to final resolution based upon a model equivalent to a sum of n spherical atomic electron densities (the independent atom model (IAM)). The IAM molecular density is, hence, expressed as:…”