Energy-Based Molecular Orbital Localization in a Specific Spatial Region

Abstract

We present a novel energy-based localization procedure able to localize molecular orbitals into predefined spatial regions. The method is defined in a multiscale framework based on the multilevel Hartree–Fock approach. In particular, the system is partitioned into active and inactive fragments. The localized molecular orbitals are obtained maximizing the repulsion between the two fragments. The method is applied to several cases including both conjugated and non-conjugated systems. Our multiscale approach is compared with reference values for both ground-state properties, such as dipole moments, and local excitation energies. The proposed approach is useful to extend the application range of high-level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations.

Fragment Localized Molecular Orbitals

“…In Figure , we report the four most relevant FLMOs contributing to E ex for each studied pair. Note that the computed FLMOs are characterized by a localization spread comparable to what has been reported by the authors in a recent paper . As expected, the top and middle panels show that the interaction between the two aromatic rings (frag 1 and frag 3 ) and both DNA helices is dominated by π–π stacking.…”

“…They are obtained by performing a partial Cholesky decomposition of the total density matrix at each localization step. Such a procedure has recently been detailed by us in ref , in which we also demonstrate that such a partitioning method guarantees the continuity of the potential energy surface (PES), differently from other localization techniques such as Boys . It is worth noting that the methodology here presented is completely general and any partitioning method can be used to obtain the starting MOs.…”

Multilevel Density Functional Theory

“…Therefore, a choice has to be made at this point. In this work, the partitioning is performed by means of Cholesky decomposition of the total density matrix for the active occupied MOs, from which the active density matrix D A is calculated, similarly to what was done in previous works presenting alternative multilevel methods. ,,,, One advantage of this procedure is that it ensures the all active and inactive orbitals are orthogonal and remain so during all the subsequent SCF procedure performed on the active subsystem …”

“…The MLDFT calculation follows this computational protocol: Construction of the initial density matrix by means of superposition of molecular densities, , followed by the diagonalization of the initial Fock matrix. Partitioning of the new density matrix into A and B densities, using Cholesky decomposition for the active occupied orbitals and PAOs for active virtual orbitals. ,,,− ,, We refer the reader to ref for the full details on this partitioning of the density matrix. The inactive density matrix is obtained by subtracting the active density matrix from the total one. Calculation of the constant energy terms and the one-electron contributions due to the inactive density matrix B entering in eqs and . Minimization of the energy defined in eq in the MO basis of the active part A only, until convergence is reached.…”

“…Partitioning of the new density matrix into A and B densities, using Cholesky decomposition for the active occupied orbitals and PAOs for active virtual orbitals. ,,,− ,, We refer the reader to ref for the full details on this partitioning of the density matrix. The inactive density matrix is obtained by subtracting the active density matrix from the total one.…”