Computation of Molecular Electron Affinities Using an Ensemble Density Functional Theory Method

Abstract

Computation of the electron attachment energies (electron affinities) was implemented in connection with an ensemble density functional theory (eDFT) method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method. With the use of the extended Koopmans' theorem the electron affinities and the respective Dyson orbitals are obtained directly for the neutral molecule; thus avoiding the necessity to compute the ionized system. Together with the EKT-SSR method for ionization potentials, which was developed earlier, EKT-SSR for electron affinities completes the implementation of the EKT-SSR formalism, which can now be used for obtaining electron detachment as well as the electron attachment energies of molecules in the ground and excited electronic states. The extended EKT-SSR method was tested in the calculation of several closed-shell molecules. For the molecules in the ground states, the EKT-SSR energies of Dyson's orbitals are virtually identical to the energies of the unoccupied orbitals in the usual single-reference spinrestricted Kohn-Sham calculations. For the molecules in the excited states, EKT-SSR predicts increase of the most positive electron affinity by approximately the amount of the vertical excitation energy. The electron affinities of a number of diradicals were calculated with EKT-SSR and compared with the available experimental data. With the use of a standard density functional (BH&HLYP) the EKT-SSR electron affinities deviate on average by ca. 0.2 eV from the experimental data. It is expected that the agreement with the experiment can be improved by designing density functionals parameterized for ionization energies.

Cu2+-modified MOF as laccase-mimicking material for colorimetric determination and discrimination of phenolic compounds with 4-aminoantipyrine

“…The LUMO orbital energy has a strong affinity for electrons and electron acceptor properties. The smaller the value, the easier the nucleophilic reaction occurs [29][30][31]. In this work, we used the B3LYP function to calculate the HOMO and LUMO molecular orbitals and energy level potentials of phenol and its derivatives [32].…”

Recent advances in ensemble density functional theory and linear response theory for strong correlation

“…24,26,80 Equation ( 17) was derived 24,26,80 by the application of the Slater-Condon rules to a system of nearly noninteracting electrons followed by integration with respect to the electron-electron interaction strength. 26 The described SSR(2,2) method provides an accurate description of the ground and the lowest excited singlet states for a wide class of molecular systems, for example, diradicals, 93,94 extended π-conjugated molecules, 95 charge transfer complexes,, 68,96,97 and so on. The method has the ability of properly and accurately describing the conical intersections between the ground and excited electronic states 24,28 ; the ability, which the standard TD-DFT methodology lacks.…”

“…Both matrices, D X k and e W X k , depend on the orbital response contribution and require solving the coupled-perturbed REKS (CP-REKS) equations. 99,100 Using these matrices, the ionization energies of the ground and excited states can be calculated 93,94,99 by invoking the extended Koopmans' theorem. [101][102][103] The REKS(4,4) 80,81 and the SSR(4,4) 27 methods are formulated in the space of many more electronic configurations; the latter arise within the active space of four electrons in four active orbitals.…”

“…[108][109][110] Using the relaxed density matrix and the Lagrangian matrix employed in the SSR analytic energy gradient Equation ( 18), the Dyson orbitals, their norms, and the respective electron binding energies can be easily obtained. The EKT-SSR approach 93,94 is capable of providing the information necessary to simulate theoretically the photoelectron spectra (PES) and the time-resolved PES (TRPES). 36,38…”

“…To be able to describe the TRPE spectrum, it is necessary to calculate the ionization energies of the molecule together with the respective probabilities of ionization. These tasks can be fulfilled by the EKT-SSR method, 93,94 which enables computation of the ionization energies and probabilities (see Equations ( 19) and ( 20)) simultaneously with computing the total energy, the nuclear gradient, and the nonadiabatic coupling needed for on-the-fly NAMD simulation.…”