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

2021 ◽  
Author(s):  
Nicolaas P. van Leest ◽  
Bas de Bruin
Keyword(s):  
Ground State ◽  
Ground States ◽  
Broken Symmetry ◽  
Transfer Reactions ◽  
Group Transfer ◽  
Cobalt Porphyrin ◽  
Spin Counting ◽  
State Wavefunctions ◽  
Radical Character ◽  
Spin Ground State

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<sup>III</sup>(TPP)(•CHCO<sub>2</sub>Et)]) and mono-nitrene ([Co<sup>III</sup>(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<sup>III</sup>(TPP•)(•NNs)<sub>2</sub>]) 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>

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

2021 ◽  
Author(s):  
Nicolaas P. van Leest ◽  
Bas de Bruin
Keyword(s):  
Ground State ◽  
Ground States ◽  
Broken Symmetry ◽  
Transfer Reactions ◽  
Group Transfer ◽  
Cobalt Porphyrin ◽  
Spin Counting ◽  
State Wavefunctions ◽  
Radical Character ◽  
Spin Ground State

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<sup>III</sup>(TPP)(•CHCO<sub>2</sub>Et)]) and mono-nitrene ([Co<sup>III</sup>(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<sup>III</sup>(TPP•)(•NNs)<sub>2</sub>]) 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>

Accurate ground state wavefunctions for several three-body systems

2009 ◽  
Vol 193 (1-3) ◽  
pp. 147-151 ◽  
Author(s):  
K. V. Rodriguez ◽  
Y. V. Gonzalez ◽  
G. Gasaneo ◽  
L. U. Ancarani ◽  
D. M. Mitnik
Keyword(s):  
Ground State ◽  
Three Body ◽  
State Wavefunctions

scholarly journals LOCALIZATION OF THE NUMBER OF PHOTONS OF GROUND STATES IN NONRELATIVISTIC QED

2003 ◽  
Vol 15 (03) ◽  
pp. 271-312 ◽  
Author(s):  
FUMIO HIROSHIMA
Keyword(s):  
Radiation Field ◽  
Ground State ◽  
Fock Space ◽  
Adjoint Operator ◽  
Ground States ◽  
Electron System ◽  
Number Operator ◽  
Position Variable ◽  
Boson Fock Space ◽  
Quantized Radiation Field

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2 (ℝ3) ⊗ ℱ ≅ L2 (ℝ3; ℱ), where ℱ is the Boson Fock space over L2 (ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to [Formula: see text], where N denotes the number operator of ℱ. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ‖(1 ⊗ Nk/2) ψg (x)‖ℱ ≤ Dk e-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular [Formula: see text] for 0 < β < δ/2 is obtained.

Correlation of the solid-state reactivities of racemic 2,4(6)-di-O-benzoyl-myo-inositol 1,3,5-orthoformate and its 4,4′-bipyridine cocrystal with their crystal structures

2014 ◽  
Vol 70 (11) ◽  
pp. 1040-1045 ◽  
Author(s):  
Majid I. Tamboli ◽  
Vir Bahadur ◽  
Rajesh G. Gonnade ◽  
Mysore S. Shashidhar
Keyword(s):  
Solid State ◽  
Self Assembly ◽  
Transfer Reaction ◽  
Acyl Transfer ◽  
Transfer Reactions ◽  
Group Transfer ◽  
Hydrogen Bonding Interactions ◽  
Benzoyl Group ◽  
The Stability ◽  
Group Migration

Racemic 2,4(6)-di-O-benzoyl-myo-inositol 1,3,5-orthoformate, C21H18O8,(1), shows a very efficient intermolecular benzoyl-group migration reaction in its crystals. However, the presence of 4,4′-bipyridine molecules in its cocrystal, C21H18O8·C10H8N2,(1)·BP, inhibits the intermolecular benzoyl-group transfer reaction. In(1), molecules are assembled around the crystallographic twofold screw axis (baxis) to form a helical self-assembly through conventional O—H...O hydrogen-bonding interactions. This helical association places the reactive C6-O-benzoyl group (electrophile, El) and the C4-hydroxy group (nucleophile, Nu) in proximity, with a preorganized El...Nu geometry favourable for the acyl transfer reaction. In the cocrystal(1)·BP, the dibenzoate and bipyridine molecules are arranged alternately through O—H...N interactions. The presence of the bipyridine molecules perturbs the regular helical assembly of the dibenzoate molecules and thus restricts the solid-state reactivity. Hence, unlike the parent dibenzoate crystals, the cocrystals do not exhibit benzoyl-transfer reactions. This approach is useful for increasing the stability of small molecules in the crystalline state and could find application in the design of functional solids.

scholarly journals Trivial low energy states for commuting Hamiltonians, and the quantum PCP conjecture

2013 ◽  
Vol 13 (5&6) ◽  
pp. 393-429
Author(s):  
Matthew Hastings
Keyword(s):  
Ground State ◽  
Coding Theory ◽  
Energy State ◽  
Ground States ◽  
Coarse Graining ◽  
Quantum Circuit ◽  
Technical Condition ◽  
Two Dimensions ◽  
Low Energy ◽  
Coarse Grained

We consider the entanglement properties of ground states of Hamiltonians which are sums of commuting projectors (we call these commuting projector Hamiltonians), in particular whether or not they have ``trivial" ground states, where a state is trivial if it is constructed by a local quantum circuit of bounded depth and range acting on a product state. It is known that Hamiltonians such as the toric code only have nontrivial ground states in two dimensions. Conversely, commuting projector Hamiltonians which are sums of two-body interactions have trivial ground states\cite{bv}. Using a coarse-graining procedure, this implies that any such Hamiltonian with bounded range interactions in one dimension has a trivial ground state. In this paper, we further explore the question of which Hamiltonians have trivial ground states. We define an ``interaction complex" for a Hamiltonian, which generalizes the notion of interaction graph and we show that if the interaction complex can be continuously mapped to a $1$-complex using a map with bounded diameter of pre-images then the Hamiltonian has a trivial ground state assuming one technical condition on the Hamiltonians holds (this condition holds for all stabilizer Hamiltonians, and we additionally prove the result for all Hamiltonians under one assumption on the $1$-complex). While this includes the cases considered by Ref.~\onlinecite{bv}, we show that it also includes a larger class of Hamiltonians whose interaction complexes cannot be coarse-grained into the case of Ref.~\onlinecite{bv} but still can be mapped continuously to a $1$-complex. One motivation for this study is an approach to the quantum PCP conjecture. We note that many commonly studied interaction complexes can be mapped to a $1$-complex after removing a small fraction of sites. For commuting projector Hamiltonians on such complexes, in order to find low energy trivial states for the original Hamiltonian, it would suffice to find trivial ground states for the Hamiltonian with those sites removed. Such trivial states can act as a classical witness to the existence of a low energy state. While this result applies for commuting Hamiltonians and does not necessarily apply to other Hamiltonians, it suggests that to prove a quantum PCP conjecture for commuting Hamiltonians, it is worth investigating interaction complexes which cannot be mapped to $1$-complexes after removing a small fraction of points. We define this more precisely below; in some sense this generalizes the notion of an expander graph. Surprisingly, such complexes do exist as will be shown elsewhere\cite{fh}, and have useful properties in quantum coding theory.

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