The Application Of Multi-State Density Functional Theory In Electron Transfer

Electron transfer（ET）reactions are ubiquitous in nature,for instance,the mitochondrial aerobic respiration and a myriad of redox processes in proteins,etc.Most of the theoretical studies of ET are based on the Marcus model,one of the parameters,V₁₂,is the electronic coupling between the electron donor and the receptor,which also is a key characteristic that controls the rate of ET.In theory,the electronically localized donor and acceptor configurations,also called diabatic states,should be defined,but because diabatic states are not uniquely defined,result in the complexity of computing the electronic coupling.Therefore,it is receiving wide attention of the reserchers.Multi-state density functional theory（MSDFT）is presented to provides a convenient way to estimate the electronic coupling.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.In this paper,a previous well-defined HAB11 database including 11π-conjugated organic charge transfer systems will be restudied to illustrate the performence of our MSDFT method.First,we compared the potential energy surface of reactants at different separated distances,and the conditions for the study of the ET reaction are finally confirmed,that is,only the proper separated distances between the reactants and the the charge delocalized state should be well-defined,the reasonableness of the calculation of V₁₂will be ensured.Then the values of electron coupling computed using MSDFT for 11π-conjugated organic systems were compared with ab inito methods（including MRCI,CASPT2 and NEVPT2）,two methods can correctly calculate V₁₂,and the value is very close,the results confirm that the functional for the off-diagonal Hamiltonian matrix element H₁₂ can be used to estimate the electronic coupling for charge transfer reactions.In addition,MSDFT has high accuracy in computing V₁₂ based on the"two state model",with the mean umsigned error（MUE）of electronic coupling from the two approaches to be 17.0 meV and 15.2 meV,respectively,already provide chemically accurate estimates for electronic coupling.Last,we examined the effect of functionals in MSDFT,three different Hartree-Fock exchange-correlation functions denoted as PBE,PBE0 and PBEC,corresponding to 0%,25%and 100%Hartree-Fock exchange,respectively,were used for comparison.We found that three functionals（PBE,PBE0and PBEC）predict the electronic coupling in the same order of magnitude,while the values are slightly decreased as the increasing of Hartree-Fock exchange fraction and the separated distances of reactants,MUEs in V₁₂ using MSDFT about 23.1 meV,21.0meV and 17.0 meV corresponding to PBE,PBE0 and PBEC,respectively,suggest that there is no significant dependence on the percentage of Hartree-Fock exchange in the MSDFT calculations.And PBEC with 100%of Hartree-Fock exchange is the best choice for MSDFT to estimate electronic coupling in practice.In conclusion,MSDFT method provides a effective and accurate way to estimate the electronic coupling.We hope MSDFT can widely used in the study of ET for more complex systems in the future.