Analytical Nuclear Gradients of Density-Fitted Dirac–Fock Theory with a 2-Spinor Basis

2013 ◽  
Vol 9 (10) ◽  
pp. 4300-4303 ◽  
Author(s):  
Toru Shiozaki
Keyword(s):  
Spinor Basis

scholarly journals The Second-Order-Polarization-Propagator-Approximation (SOPPA) in a four-component spinor basis

2020 ◽  
Vol 152 (13) ◽  
pp. 134113 ◽  
Author(s):  
Anna Kristina Schnack-Petersen ◽  
Mats Simmermacher ◽  
Elke Fasshauer ◽  
Hans Jørgen Aa. Jensen ◽  
Stephan P. A. Sauer
Keyword(s):  
Second Order ◽  
Polarization Propagator ◽  
Spinor Basis ◽  
Component Spinor

Angular momentum adaptation of spinor basis

2009 ◽  
Vol 28 (S19) ◽  
pp. 69-77
Author(s):  
J. S. Murty ◽  
R. S. Nikam ◽  
C. R. Sarma
Keyword(s):  
Angular Momentum ◽  
Spinor Basis

scholarly journals Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

2021 ◽  
Author(s):  
Sokol Andoni
Keyword(s):  
Tensor Product ◽  
Physical Space ◽  
Cross Product ◽  
Expectation Values ◽  
Spacetime Algebra ◽  
Orientation Space ◽  
Spin Pairs ◽  
The One ◽  
Spinor Basis ◽  
Geometric Picture

Abstract A new representation for spin 1/2 in the even 3D subalgebra of the spacetime algebra (STA) combines in a single geometric object the roles of the standard Pauli spin vector and spin state. It is a vector quantity comprising a gauge phase. In the one-particle case the representation (1) is Hermitian; (2) chiral; (3) reproduces all standard expectation values, including the total one-particle spin modulus ; (4) constrains a spinor basis representing opposite spins to preserve handiness (chirality); (5) the gauge phase allows to explicitly formalize irreversibility in spin measurement. In the two-particle case it (1) identifies entangled spin pairs as having opposite handiness and precise gauge phase relations; (2) doubles the dimensionality of the spin space due to variation of handiness; (3) the four maximally entangled states are naturally derived by pairing spins that are reflections (triplets) and inversions (singlet) of each-other. The cross-product terms in the expression for the squared total spin of two particles can be affected by experiment and they yield the standard expectation values after measurement. Here I directly define and transform spin in 3D orientation space, without invoking concepts like abstract Hilbert space and tensor product as in the standard formulation. The STA formalism allows working with whole geometric objects instead of only components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on lab’ (uncontrolled gauge phase) spin transformations.

scholarly journals Electron correlation effects of the ThO and ThS molecules in the spinor basis. A relativistic coupled cluster study of ground and excited states properties

2018 ◽  
Vol 20 (36) ◽  
pp. 23424-23432 ◽  
Author(s):  
Paweł Tecmer ◽  
Cristina E. González-Espinoza
Keyword(s):  
Detailed Analysis ◽  
Excited States ◽  
Electron Correlation ◽  
Coupled Cluster ◽  
Correlation Effects ◽  
Spectroscopic Parameters ◽  
Electron Correlation Effects ◽  
Spinor Basis

Our study provides a reliable set of spectroscopic parameters and a detailed analysis of the electron correlation effects in the ThO and ThS molecules.

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