Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes

Abstract

Quantum-chemical multi-configurational methods are required for a proper description of static electron correlation, a phenomenon inherent to the electronic structure of molecules with multiple (near-)degenerate frontier orbitals. Here, we review how a property of these frontier orbitals, namely the entanglement entropy is related to static electron correlation. A subset of orbitals, the so-called active orbital space is an essential ingredient for all multi-configurational methods. We proposed an automated selection of this active orbital space, that would otherwise be a tedious and error prone manual procedure, based on entanglement measures. Here, we extend this scheme to demonstrate its capability for the selection of consistent active spaces for several excited states and along reaction coordinates.

Complete active space analysis of a reaction pathway: Investigation of the oxygen–oxygen bond formation

“…Another approach has been based on the orbital entanglement method, [ 66,67 ] which has been used for the consistent selection of orbital active spaces along reaction coordinates and applied to isomerization [ 53 ] and Diels–Alder reactions. [ 68,69 ] The entanglement measure, however, may not be provided in commonly used programs and up to 4‐electron reduced density matrix elements are required to derive the two‐orbital reduced density matrix.…”

Automated Construction of Molecular Active Spaces from Atomic Valence Orbitals

“…We expect that normally the simple d-electron AVAS will be sufficient to qualitatively represent In the presence of such effects it may be warranted to combine AVAS with either one of several methods of constructing approximate FCI wave functions in large active spaces (vide infra), or with the entanglement-based active-space construction procedure of Reiher and coworkers. 26,34 In the simplest case of suspected complex metal-ligand interactions in a single-metal complex, one might, for example, first create an AVAS by including as target AOs both the d-electrons of the transition metal, as well as all ligand AOs suspected to play an important role (e.g., all ligand valence AOs from the first coordination sphere, or all p z -orbtials of a large π-system coordinated to the metal atom). In practice, the active space created from this choice will frequently be too large for an accurate quantitative multi-reference calculation including dynamic correlation.…”

“…For example, correlated occupation numbers can be estimated from unrestricted Hartree-Fock 28,29 or Kohn-Sham calculations or from correlated calculations, such as MP2 30,31 or approximate DMRG calculations. 27,[32][33][34] Nonetheless, while these existing automated approaches are advancements from typical ad hoc active space constructions, there is still room for further improvement. For example, an obvious drawback of the above procedures is that they all require a non-trivial preliminary calculation: either a correlated calculation must be performed, or a suitable broken symmetry solution must be found.…”

Quantum information-based analysis of electron-deficient bonds

“…These include density matrix renormalization group (DMRG) method 35,36 , which variationally optimizes wave functions in the form of matrix product states (MPS). 37 Other important examples represent characterization of electron correlation into its static (strong) and dynamic contributions 9 , automatic (black-box) selection of the active spaces 1, 6,17,23,24,38 , or the self-adaptive tensor network states with multi-site correlators 25 , all of which harness single-and two-orbital entanglement entropies. Last but not least, correlation measures based on the single-and two-orbital entanglement entropies have also been employed for the purposes of bond analysis 10,20 .…”