Revisiting the Electronic Structure of Cobalt-Porphyrin Nitrene and Carbene Radicals with NEVPT2-CASSCF Calculations: Doublet versus Quartet Ground States

Cobalt-porphyrin complexes are established catalysts for carbene and nitrene radical group transfer reactions. The key carbene, mono- and bis-nitrene radical complexes coordinated to [Co(TPP)] (TPP = tetraphenylporphyrin) have previously been investigat-ed with a variety of experimental techniques and supporting (single-reference) DFT calculations that indicated doublet (S = ½) ground states for all three species. In this contribution we revisit their electronic structures with multireference NEVPT2-CASSCF calculations to investigate possible multireference contributions to the ground state wavefunctions. The carbene ([Co^III(TPP)(•CHCO₂Et)]) and mono-nitrene ([Co^III(TPP)(•NNs)]) radical complexes were confirmed to have uncomplicated doublet ground states, although a higher carbene or nitrene radical character and a lower Co‒C/N bond order was found in the NEVPT2-CASSCF calculations. Supported by EPR analysis and spin counting, paramagnetic molar susceptibility determination and NEVPT2-CASSCF calculations, we report that the cobalt-porphyrin bis-nitrene complex ([Co^III(TPP•)(•NNs)₂]) has a quartet (S = 3/2) spin ground state, with a thermally assessable multireference & multideterminant ‘broken-symmetry’ doublet spin excited state. A spin flip on the porphyrin-centered unpaired electron allows for interconversion between the quartet and broken-symmetry doublet spin states, with an approximate 10- and 200-fold higher Boltzmann population of the quartet at room tempera-ture or 10 K, respectively.<br>

Revisiting the Electronic Structure of Cobalt-Porphyrin Nitrene and Carbene Radicals with NEVPT2-CASSCF Calculations: Doublet versus Quartet Ground States

Cobalt-porphyrin complexes are established catalysts for carbene and nitrene radical group transfer reactions. The key carbene, mono- and bis-nitrene radical complexes coordinated to [Co(TPP)] (TPP = tetraphenylporphyrin) have previously been investigat-ed with a variety of experimental techniques and supporting (single-reference) DFT calculations that indicated doublet (S = ½) ground states for all three species. In this contribution we revisit their electronic structures with multireference NEVPT2-CASSCF calculations to investigate possible multireference contributions to the ground state wavefunctions. The carbene ([Co^III(TPP)(•CHCO₂Et)]) and mono-nitrene ([Co^III(TPP)(•NNs)]) radical complexes were confirmed to have uncomplicated doublet ground states, although a higher carbene or nitrene radical character and a lower Co‒C/N bond order was found in the NEVPT2-CASSCF calculations. Supported by EPR analysis and spin counting, paramagnetic molar susceptibility determination and NEVPT2-CASSCF calculations, we report that the cobalt-porphyrin bis-nitrene complex ([Co^III(TPP•)(•NNs)₂]) has a quartet (S = 3/2) spin ground state, with a thermally assessable multireference & multideterminant ‘broken-symmetry’ doublet spin excited state. A spin flip on the porphyrin-centered unpaired electron allows for interconversion between the quartet and broken-symmetry doublet spin states, with an approximate 10- and 200-fold higher Boltzmann population of the quartet at room tempera-ture or 10 K, respectively.<br>

Understanding of the C–H stretch region of infra-red spectroscopy: an analysis of the final state wavefunctions

The nature of wavefunctions associated with the final states in the CH stretch region of several medium sized molecules are analysed.

Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem

The earlier treatments of the Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We present here a full solution avoiding those problems. The complete set of Fock states is obtained, together with the corresponding explicit wavefunctions and their inner product integrals free from any divergence problem and with Lorentz symmetry fully maintained without additional constraints imposed. By a simple choice of the pseudo-unitary representation of the underlying symmetry group, motivated from the perspective of the Minkowski spacetime as a representation for the Lorentz group, we obtain the natural non-unitary Fock space picture commonly considered, although not formulated and presented in the careful details given here. From a direct derivation of the appropriate basis state wavefunctions of the finite-dimensional irreducible representations of the Lorentz symmetry, the relation between the latter and the Fock state wavefunctions is also explicitly shown. Moreover, the full picture, including the states with a non-positive norm, may give a consistent physics picture as a version of Lorentz covariant quantum mechanics. The probability interpretation for the usual von Neumann measurements is not a problem, as all wavefunctions restricted to a definite value for the `time’ variable are just like those of the usual time independent quantum mechanics. A further understanding from a perspective of the dynamics from the symplectic geometry of the phase space is shortly discussed.

Induced Representation Method in the Theory of Electron Structure and Superconductivity

It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. The technique is extended on projective representations in the case of nonsymmorphic space groups and examples of applications for topological superconductors UPt3 and Sr2RuO4 are considered.

The application of light front holographic QCD to B physics

Light front holography is a formalism developed by Brodsky and de Téramond in which analytic forms for the hadronic bound state wavefunctions can be obtained. We have used the holographic light front wavefunctions thus obtained to calculate the distribution amplitudes of the light vector mesons ρ and K∗. As a result, we are able to calculate the form factors for B → ρ, K∗ transitions as well as ΛQCD/mb contributions in radiative B(s) → (ρ, K∗)γ decays. We compare our predictions to the available experimental data.