Multistate Density Functional Theory for Effective Diabatic Electronic Coupling

Abstract

Multistate density functional theory (MSDFT) is presented to estimate the effective transfer integral associated with electron and hole transfer reactions. In this approach, the charge-localized diabatic states are defined by block localization of Kohn–Sham orbitals, which constrain the electron density for each diabatic state in orbital space. This differs from the procedure used in constrained density functional theory that partitions the density within specific spatial regions. For a series of model systems, the computed transfer integrals are consistent with experimental data and show the expected exponential attenuation with the donor–acceptor separation. The present method can be used to model charge transfer reactions including processes involving coupled electron and proton transfer.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

“…3,56 The second term in eq 4 is a transition density contribution. 3,18,50,51,56,67 Note that both exchange and static correlation are included in the first term, whereas only dynamic correlation is in the second term. 18 We then approximated the second term of eq 4 by an overlap-weighted average of the KS correlation energies for the two interacting states 50,51 $$V_c^{\text{TDF}}false[{\rho }_{\mathit{\text{AB}}}false(\mathrm{boldr}false)false]\approx \frac{\lambda }{2}{S}_{\mathit{\text{AB}}}false(E_c^{\text{KS}}false[{\rho }_A^{\text{ms}}false(\mathrm{boldr}false)false]+E_c^{\text{KS}}false[{\rho }_B^{\text{ms}}false(\mathrm{boldr}false)false]false)$$ where λ is unity in the present work (in later work this parameter or functional could be optimized to fit experimental results), where S AB is the overlap integral ⟨Ψ A |Ψ B ⟩, and where $E_c^{\text{KS}}$ specifies the correlation energy in the corresponding diagonal matrix element (as obtained from the exchange-correlation functional).…”

“…We have found that the PBE and PBE0 functionals perform well with the MSDFT method, especially for charge transfer processes. 51,86 …”

“…3,56 The use of BLMO or block-localized Kohn−Sham (BLKS) orbitals reduces a large number of valence bond configurations to a manageable number; only those critical to a given system are retained in a way analogous to the spin-coupled valence bond theory. 64,65 This method has been extended to density functional theory, in which case it is called multistate density functional theory (MSDFT), 18,50,51,66,67 and this is the method that is used in the present work.…”

“…68 MSDFT does not suffer from electron-transfer contamination of diabatic states found in spatial localization of density, and there is little-to-no dependency on the amount of HF-exchange used. 51 …”

Efficient Constrained Density Functional Theory Implementation for Simulation of Condensed Phase Electron Transfer Reactions

“…For |H ab |, these include the generalized Mulliken Hush (GMH) method, 14,15 localization and block diagonalization methods, [15][16][17][18][19][20][21] and constrained density functional theory (CDFT). [22][23][24] A more exhaustive list of methods can be found in literature 5,25-33 and we refer the interested readers to these and references therein for a comparison of the different approaches.…”