<i>Methods of Molecular Quantum Mechanics</i>

McWeeny, R.; Sutcliffe, Brian T.; Brink, G. O.

doi:10.1063/1.3022743

Cited by 472 publications

(398 citation statements)

References 0 publications

Supporting

Mentioning

378

Contrasting

Unclassified

Order By: Relevance

“…A restricted Slater determinant is always an eigenfunction of Ŝ z with eigenvalue M S h ¼ ðN a À N b Þh=2. [60,58] If all singly occupied orbitals are either a-or b-spin orbitals, then it is also an eigenfunction of Ŝ 2 with S ¼ |M S |. In all other cases, an eigenfunction of Ŝ 2 can be constructed as a linear combination of (degenerate) determinants in which the same orbitals are singly occupied and which correspond to the same value of M S .…”

Section: Spin-restricted Kohn-sham Dftmentioning

confidence: 99%

“…Such determinants-which can only differ in the spin of the singly occupied orbitals-are degenerate with respect to the noninteracting Hamiltonian of Eq. (60).…”

Section: Spin-restricted Kohn-sham Dftmentioning

confidence: 99%

“…The total electron densities q MS and the spin densities Q MS ðrÞ of these Ŝ z eigenstates are related to each other [60,78,79] : All 2S þ 1 states share the same total electron density, …”

Section: Spin Structure Of the Many-electron Wavefunctionmentioning

confidence: 99%

“…[56,59,60] Then, the N-electron wavefunction depends on N spin coordinates in addition to the N spatial coordinates,…”

Section: Spin Structure Of the Many-electron Wavefunctionmentioning

confidence: 99%

See 3 more Smart Citations

Spin in density‐functional theory

Jacob¹,

Reiher²

2012

Int J of Quantum Chemistry

225

224

View full text Add to dashboard Cite

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. Although density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchangecorrelation energy functional and lead to different exact conditions on this functional. Finally, we suggest possible directions for future developments.

show abstract

Section: Spin-restricted Kohn-sham Dftmentioning

confidence: 99%

“…Such determinants-which can only differ in the spin of the singly occupied orbitals-are degenerate with respect to the noninteracting Hamiltonian of Eq. (60).…”

Section: Spin-restricted Kohn-sham Dftmentioning

confidence: 99%

Section: Spin Structure Of the Many-electron Wavefunctionmentioning

confidence: 99%

“…[56,59,60] Then, the N-electron wavefunction depends on N spin coordinates in addition to the N spatial coordinates,…”

Section: Spin Structure Of the Many-electron Wavefunctionmentioning

confidence: 99%

See 2 more Smart Citations

Spin in density‐functional theory

Jacob¹,

Reiher²

2012

Int J of Quantum Chemistry

225

224

View full text Add to dashboard Cite

show abstract

“…For two-component relativistic calculations, the e-e interaction needs to be transformed to two-component form. In order c −2 , the corresponding terms are well known [2,109]. The leadingorder relativistic corrections to r −1 kl can be written as…”

Section: Many-electron Systemsmentioning

confidence: 99%

Relativistic calculations of magnetic resonance parameters: background and some recent developments

Autschbach

2014

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

show abstract