STRUCTURE AND STABILITY OF MONOCYCLIC $({\rm CH})_{4-n} ({\rm BL})_{n}^{2-}$(L = CO, N2, CS) DIANIONS AND THEIR DILITHIUM COMPLEXES

2008 ◽  
Vol 07 (04) ◽  
pp. 595-606
Author(s):  
HAI-SHUN WU ◽  
XIAO-FANG QIN ◽  
HAIJUN JIAO
Keyword(s):  
Ground State ◽  
Negative Charge ◽  
Chemical Shifts ◽  
Ground States ◽  
Membered Ring ◽  
Triplet States ◽  
Structure And Stability ◽  
Ring Carbon ◽  
Carbon Centers ◽  
Electrostatic Stabilization

Structure and stability of monocyclic [Formula: see text] dianions ( L = CO , N 2, CS ) with 6π-electrons, which are isolobal with cyclobutadiene dianion [Formula: see text], have been investigated at the B3LYP and CCSD(T) levels of theory. ( CH )3( BL )2- have non-planar singlet ground states. [Formula: see text] have planar singlet ground states, while [Formula: see text] isomers have folded four-membered central rings. Both [Formula: see text] and [Formula: see text] have planar ground states, the ground state of [Formula: see text] has a six-membered ring with two bridging and one terminal CS. Both [Formula: see text] and [Formula: see text] have reduced aromaticity compared to [Formula: see text] as indicated by the less negative nucleus independent chemical shifts (NICS) values. The mono-, di- and trisubstituted ( CH )3( BL )2-, [Formula: see text], and [Formula: see text] also have reduced aromaticity, while the 1,3-substituted [Formula: see text] have positive NICS values due to the localization of the negative charge at the ring carbon centers. In addition, the electrostatic stabilization of Li + in favor of the singlet or triplet states depends on the nature of their structures.

scholarly journals Exploitation of Baird Aromaticity and Clar’s Rule for Tuning the Triplet Energies of Polycyclic Aromatic Hydrocarbons

Chemistry ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 532-549
Author(s):  
Felix Plasser
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Excited States ◽  
Aromatic Hydrocarbons ◽  
Density Functional ◽  
Materials Science ◽  
Chemical Shifts ◽  
Qualitative Description ◽  
Triplet States ◽  
Excitation Energies ◽  
Polycyclic Aromatic

Polycyclic aromatic hydrocarbons (PAH) are a prominent substance class with a variety of applications in molecular materials science. Their electronic properties crucially depend on the bond topology in ways that are often highly non-intuitive. Here, we study, using density functional theory, the triplet states of four biphenylene-derived PAHs finding dramatically different triplet excitation energies for closely related isomeric structures. These differences are rationalised using a qualitative description of Clar sextets and Baird quartets, quantified in terms of nucleus independent chemical shifts, and represented graphically through a recently developed method for visualising chemical shielding tensors (VIST). The results are further interpreted in terms of a 2D rigid rotor model of aromaticity and through an analysis of the natural transition orbitals involved in the triplet excited states showing good consistency between the different viewpoints. We believe that this work constitutes an important step in consolidating these varying viewpoints of electronically excited states.

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.

Excitation of triplet states of ScII from ground state scandium atoms

1992 ◽  
Vol 56 (1) ◽  
pp. 9-13
Author(s):  
A. N. Kuchenev ◽  
Yu. M. Smirnov
Keyword(s):  
Ground State ◽  
Triplet States

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.

scholarly journals Exploitation of Baird Aromaticity and Clar's Rule for Tuning the Triplet Energies of Polycyclic Aromatic Hydrocarbons

2021 ◽  
Author(s):  
Felix Plasser
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Excited States ◽  
Aromatic Hydrocarbons ◽  
Density Functional ◽  
Materials Science ◽  
Chemical Shifts ◽  
Qualitative Description ◽  
Triplet States ◽  
Excitation Energies ◽  
Polycyclic Aromatic

Polycyclic aromatic hydrocarbons (PAH) are a prominent substance class with a variety of applications in molecular materials science. Their electronic properties crucially depend on the bond topology in ways that are often highly non-intuitive. Here, we study, using density functional theory, the triplet states of four PAHs based on the biphenylene motif finding dramatically different triplet excitation energies for closely related isomeric structures. These differences are rationalised using a qualitative description of Clar sextets and Baird quartets, quantified in terms of nucleus independent chemical shifts, and represented graphically through a recently developed method for visualising chemical shielding tensors (VIST). These results are further interpreted in terms of a 2D rigid rotor model of aromaticity and through an analysis of the natural transition orbitals involved in the triplet excited states showing good consistency between the different viewpoints. We believe that this work constitutes an important step in consolidating these varying viewpoints of electronically excited states.

scholarly journals A 195Pt NMR study on zero-magnetic-field splitting and the phosphorescence properties in the excited triplet states of cyclometalated platinum(ii) complexes

2020 ◽  
Vol 49 (19) ◽  
pp. 6363-6367
Author(s):  
Soichiro Akagi ◽  
Sho Fujii ◽  
Noboru Kitamura
Keyword(s):  
Magnetic Field ◽  
Metal Complexes ◽  
Chemical Shifts ◽  
Zero Magnetic Field ◽  
Triplet States ◽  
Field Splitting ◽  
Excited Triplet ◽  
Nmr Chemical Shifts ◽  
Nmr Study ◽  
Excited Triplet States

The strength of zero-magnetic-field splitting in the excited triplet states of metal complexes is reflected in the metal NMR chemical shifts.

scholarly journals Non-local to local transition for ground states of fractional Schrödinger equations on $$\mathbb {R}^N$$

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Bartosz Bieganowski ◽  
Simone Secchi
Keyword(s):  
Ground State ◽  
Ground States ◽  
Ground State Solution ◽  
State Solution ◽  
Local Problem ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Fractional Schrödinger Equations ◽  
Non Local ◽  
Local Transition

Abstract We consider the nonlinear fractional problem $$\begin{aligned} (-\Delta )^{s} u + V(x) u = f(x,u)&\quad \hbox {in } \mathbb {R}^N \end{aligned}$$ ( - Δ ) s u + V ( x ) u = f ( x , u ) in R N We show that ground state solutions converge (along a subsequence) in $$L^2_{\mathrm {loc}} (\mathbb {R}^N)$$ L loc 2 ( R N ) , under suitable conditions on f and V, to a ground state solution of the local problem as $$s \rightarrow 1^-$$ s → 1 - .

SEPARATION OF INITIAL AND FINAL STATE CONTRIBUTIONS TO CHEMICAL SHIFTS IN TERMS OF A POTENTIAL MODEL

1994 ◽  
Vol 01 (04) ◽  
pp. 469-472 ◽  
Author(s):  
R.J. COLE ◽  
P. WEIGHTMAN
Keyword(s):  
Charge Transfer ◽  
Ground State ◽  
Potential Model ◽  
Chemical Shifts ◽  
Free Atom ◽  
Core Hole ◽  
Final State ◽  
State Charge ◽  
Elemental Solid

A recently developed potential model facilitates the separation of initial and final state contributions to chemical shifts in terms of ground state charge transfer and differences in core hole screening charge. The model is applied to the free atom to elemental solid shifts of the elements Na, Mg, Si, and Zn.

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