The Application Of Multistate Density Functional Theory In Carbonyl Complexes And Radicals Systems

Several different systems including carbonyl complexes and radicals have been theoretical studied and analyzed by using the multistate density functional theory which is based on the framework of valence bond theory,describing the effectiveness of the multistate density functional theory method.The main research contents are summarized as follows:1.The energy decomposition and vibrational frequency analysis of charge-transfer interactions between metals and ligands in carbonyl complexesThe energy decomposition and vibrational frequency analysis have been presented to quantify theσ-dative,ligand-to-metal forward charge transfer（CT）and theπ-conjugative,metal-to-ligand backward charge delocalization on a series of isoelectronic transition-metal carbonyl complexes M（CO）₆,including M=Ti^2-,V^-,Cr,Mn⁺and Fe²⁺.Although the qualitative features of these energy terms are understood,well-defined quantitative studies have been scarce.In all complexes,the overall binding stabilization can be attributed to CT effects,with opposing trends betweenσ-donation andπ-back bonding that follows an order of Ti^2-（4.4）>V^-（2.6）>Cr（1.5）>Mn⁺（1.1）>Fe²⁺（0.5）inπ-to-σCT ratio.Consistent with early findings,electrostatic and Pauli exchange effects play a key role inσ-donation,resulting in blue shifts in ligand vibrational frequency in the complex geometries.Excluding chemical bonding interactions between the CO ligand and the metal fragments in the energy decomposition analysis,we found that loosely bound electrostatic complexes can be formed at a longer metal-to-ligand distance due to the exponential decay of Pauli exchange.These electronic and energetic features are mirrored in the vibrational frequency shifts induced by different factors.Among the various energy decomposition method,the block-localized wavefunction energy decomposition method has the advantage of defining the hypothetical electron-localized state self-consistently.Morover,this method has the geometry optimization capability.The present investigation may help stimulate the use of energy decomposition techniques to understand the structure and activity of metal catalysts using multistate density functional theory.2.Kinetic isotope effect study of the hydrogen atom abstraction of the hydrocarbons by Phthalimide N-oxyl（PINO）radicalThe hydrogen atom abstraction of the Phthalimide N-oxyl（PINO）radical and a series of hydrocarbons which have different C-H bond dissociation energies（BDEs）have been studied in this part.It is difficult to quantify the actual mechanism of these reactions by traditional methods.In this work,we use multistate density functional theory（MS-DFT）,in which the electron and proton diabatic configurations can be constructed through block-localized wave function（BLW）theory,to distinct hydrogen atom transfer（HAT）and concerted proton-electron transfer（CPET）.Based on these two theories,we determine the mechanism of this type of reaction as HAT before the transition state,the concerted HAT-CPET after the transition state.Based on this mechanism,the transition state theory with small tunneling corrections（SCT）was used to calculate rate constants and kinetic isotope effects（KIEs）.The observed KIEs are much larger than unity values,and have a maximum value.It was found that this abnormal tendency is related to tunneling,which is influenced by imaginary frequency and tunneling distance.The large imaginary frequency and short tunneling distance result in large KIE.We think this kind of methods can be applied into more radical systems,especially reactions involving proton and electron transfer.3.Minimal active space for diradicals using multistate density functional theoryThe work of this part explores the electronic structure as well as the reactivity of singlet diradicals,making use of multistate density functional theory（MS-DFT）.In particular,we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases.This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn-Sham density functional theory.In addition,molecular fragment,i.e.,block-localized Kohn-Sham orbitals,are optimized separately for each determinant,proving a variational diabatic representation of valence bond-like states,which are subsequently used in nonorthogonal state interactions（NOSIs）.The computational procedure and its performance are illustrated on some prototypical diradical species.It is shown that NOSI calculations in MS-DFT can be used to model bond dissociation and hydrogen-atom transfer reactions,employing a minimal number of configuration state functions as the basis states.For p-and s-types of diradicals,the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state.Such a diabatic representation may be useful to define reaction coordinates for electron transfer,proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.This method provides a new and simpler idea for the study of other diradical systems.