A three-state effective Hamiltonian for symmetric cationic diarylmethanes

Abstract

Comparison of density functionals for energy and structural differences between the high-[ 5 T 2g :(t 2g ) 4 (e g ) 2 ] and low-[ 1 A 1g :(t 2g ) 6 (e g ) 0 ] spin states of iron (II) We analyze the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are bridge-substituted derivatives of Michler's Hydrol Blue. We use a four-electron, threeorbital complete active space self-consistent field and multi-state multi-reference perturbation theory model to calculate a three-state diabatic effective Hamiltonian for each dye in the series. We exploit an isolobal analogy between the active spaces of the self-consistent field solutions for each dye to represent the electronic structure in a set of analogous diabatic states. The diabatic states can be identified with the bonding structures in classical resonance-theoretic models of cyanine dyes. We identify diabatic states with opposing charge and bond-order localization, analogous to the classical resonance structures, and a third state with charge on the bridge. While the left-and right-charged structures are similar for all dyes, the structure of the bridge-charged diabatic state, and the Hamiltonian matrix elements connected to it, change significantly across the series. The change is correlated with an inversion of the sign of the charge carrier on the bridge, which changes from an electron pair to a hole as the series is traversed.

A two-state model of twisted intramolecular charge-transfer in monomethine dyes

“…These projections are described within the four-electron, three-orbital model of the electronic structure that we use. 49,98,111 The bonding energy itself is a consequence of mixing between covalent and ionic states on the bonds 112,113 (cf. Figure 1).…”

“…Equation (2.1)) is because both the energy and the dipole moments of the diabatic states are modulated by their projection on the "ionic" configurations associated with the bridge bonds. These projections are described within the fourelectron, three-orbital model of the electronic structure that we use [49,98,111]. The bonding energy itself is a consequence of mixing between covalent and ionic states on the bonds [112,113] (c.f.…”

Canonical-ensemble state-averaged complete active space self-consistent field (SA-CASSCF) strategy for problems with more diabatic than adiabatic states: Charge-bond resonance in monomethine cyanines

“…Cases have recently been highlighted for diabatic states with respect to displacements along a reaction coordinate 33 and states diabatic with respect to a substituent parameter. 34 In such cases, it may be practically impossible to obtain a wellbehaved microcanonical SA-CASSCF ensemble with enough support to resolve all the relevant diabatic states. If Γ does not have support on the complete CAS-CI Hilbert space (i.e., if M < N), one can only resolve diabatic states to within a least-squares block-diagonalization transformation consistent with the structure of the support ofΓ.…”

“…If Γ does not have support on the complete CAS-CI Hilbert space (i.e., if M < N), one can only resolve diabatic states to within a least-squares block-diagonalization transformation consistent with the structure of the support ofΓ. 24,35 This approach has been used in previous work to generate three-state diabatic Hamiltonians for symmetric cationic diarylmethanes 34 and green fluorescent protein chromophores. 36 A result from quantum information theory says that the Shannon entropy is always minimized in the adiabatic representation.…”

“…The ground state geometry has been discussed previously. 34,[60][61][62] The weights were determined self-consistently as a canonical distribution over the six-dimensional Hilbert space of configurations of active electrons. Equilibration of the SA-CASSCF weights was implemented using an iterative loop in 's internal scripting language, wherein the a priori weights of each SA-CASSCF calculation were calculated using state energies from the previous calculation, and the process was iterated to convergence.…”