Energy Decomposition Analysis for Interactions of Radicals: Theory and Implementation at the MP2 Level with Application to Hydration of Halogenated Benzene Cations and Complexes between CO₂^–· and Pyridine and Imidazole

Abstract

To study intermolecular interactions involving radicals at the correlated level, the Energy Decomposition Analysis scheme for Second-Order Møller-Plesset Perturbation Theory based on Absolutely Localized Molecular Orbitals (ALMO-MP2-EDA) is generalized to unrestricted and restricted open-shell MP2. The benefit of restricted open-shell MP2 is that it can provide accurate binding energies for radical complexes where density functional theory can be error prone due to delocalization errors. As a model application, the open-shell ALMO-MP2-EDA is applied to study the first solvation step of halogenated benzene radical cations, where both halogen and hydrogen bonded isomers are possible. We determine that the lighter halogens favor the hydrogen-bonded form, while the iodine-substituted species prefers halogen bonding due to larger polarizability and charge transfer at the halogen. As a second application, relevant to the activation of CO 2 in photoelectrocatalysis, complexes of CO 2 −• interacting with both pyridine and imidazole are analyzed with ALMO-MP2-EDA. The results reveal the importance of charge transfer into the π * orbital of the heterocycle in controlling the stability of the carbamate binding mode, which is favored for pyridine, but not for imidazole.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis

“…ALMO-EDA-I has been extended to excited states (35,36), as well as to ground states using second-order Møller-Plesset perturbation theory (MP2). (37,38,39) While successful and quite widely used, BLW-EDA and ALMO-EDA-I lack useful basis set limits for the POL and CT terms, (40,41,42) and rely on the use of an AO basis. These challenges motivated the developments described in the following section.…”

“…These include the generalization from ground state to excited state exciplexes and excimers (35,36), and the development of an EDA-based fingerprint to characterize single chemical bonds (114,115). We have also limited our scope to describing DFT-based EDA, although there has been progress in developing an analogous ALMO-EDA to treat intermolecular interactions described by second-order Møller-Plesset perturbation theory (37,38,39). There are also a range of opportunities for further development of the ALMO-EDA approach.…”

Probing radical–molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals

“…The desired electronic wavefunction given by the polarized fragment orbitals is retained in the resulting fragment orbitals in most cases, thanks to the stepwise manner of handling these orbital rotations. The recent extension of ALMO-MP2-EDA to RO orbitals also adopted the PtD approach, 40 where the resemblance between the polarized and depolarized fragment orbitals was ensured via MOM as in the present paper.…”

“…[33][34][35][36][37] Besides DFT-based approaches, extensions of wavefunction theory (WFT)-based EDA schemes to open-shell systems have also been achieved, including the recently developed local energy decomposition (LED) analysis under the quasi-restricted 38 domain-based local pair natural orbital (DLPNO) framework 21 and the extension of absolutely localized molecular orbital (ALMO)-EDA to restricted openshell second-order Møller-Plesset perturbation theory (ROMP2) 39 by some of us. 40 In this paper, we present the recent development and applications of ALMO-EDA for studying radical-molecule interactions, i.e., the interactions between open-shell and closedshell species. The original ALMO-EDA scheme partitions a total interaction energy into frozen interaction (FRZ), polarization (POL), and charge-transfer (CT) contributions, 41 and it was extended to treat systems involving radicals by Horn et al 35 Recent years have seen the development of an improved, second-generation ALMO-EDA scheme, 42 which has addressed two limitations of the original approach: (i) the use of fragment electrical response functions (FERFs) 43 allows for a useful basis set limit for the separation of POL and CT contributions;…”

“…Other notable recent advances in ALMO-EDA include the extensions for treating bonded interactions 53,54 and interactions involving excited electronic states, 55,56 as well as developments for the use of correlated wavefunction methods. 40,57,58 The initial supersystem state in the ALMO-EDA procedure, the frozen wavefunction, is typically constructed via a concatenation of fragment orbitals that are optimized in isolation. 41 The same choice was made by many other popular supermolecular approaches, such as the EDA-NOCV (natural orbitals for chemical valence) method 24,59,60 and the blocklocalized wavefunction (BLW)-EDA.…”