Many-Electron Densities and Reduced Density MatricesJerzy Cioslowski Springer Science & Business Media, 2012/12/06 - 301 ページ Science advances by leaps and bounds rather than linearly in time. I t is not uncommon for a new concept or approach to generate a lot of initial interest, only to enter a quiet period of years or decades and then suddenly reemerge as the focus of new exciting investigations. This is certainly the case of the reduced density matrices (a k a N-matrices or RDMs), whose promise of a great simplification of quantum-chemical approaches faded away when the prospects of formulating the auxil iary yet essential N-representability conditions turned quite bleak. How ever, even during the period that followed this initial disappointment, the 2-matrices and their one-particle counterparts have been ubiquitous in the formalisms of modern electronic structure theory, entering the correlated-level expressions for the first-order response properties, giv ing rise to natural spinorbitals employed in the configuration interaction method and in rigorous analysis of electronic wavefunctions, and al lowing direct calculations of ionization potentials through the extended Koopmans'theorem. The recent research of Nakatsuji, Valdemoro, and Mazziotti her alds a renaissance of the concept of RDlvls that promotes them from the role of interpretive tools and auxiliary quantities to that of central variables of new electron correlation formalisms. Thanks to the economy of information offered by RDMs, these formalisms surpass the conven tional approaches in conciseness and elegance of formulation. As such, they hold the promise of opening an entirely new chapter of quantum chemistry. |
目次
| 1 | |
Some Theorems on Uniqueness and Reconstruc | 19 |
The Reconstruction | 25 |
References | 31 |
On Calculating Approximate and Exact Density | 57 |
The Fundamental Optimization Theorem | 64 |
Minimizing the Dispersion | 76 |
References | 84 |
Density Matrix Functional Theory | 165 |
Numerical Implementation of a Natural Orbital Functional | 178 |
Exact Density Functional Theory DFT | 192 |
Improving on The Local Density Approximation | 200 |
Functional Nrepresentability in Density | 209 |
Nrepresentability of Functionals of the OneParticle Density | 220 |
Conclusions | 227 |
ElectronPair Functions as a Tool for Understanding | 239 |
The Correlated Density Equation | 94 |
A Geminal Equation Derived from the DE | 102 |
DET for OpenShell Systems | 109 |
Critical Questions Concerning Iterative Solution | 117 |
Reduced Density Matrices 42 ཡུཊྛོ | 124 |
The Correspondence between 2A and the SecondOrder | 125 |
The Role of the Nrepresentability Conditions in the | 132 |
Cumulants and the Contracted Schrödinger | 139 |
Reconstruction of RDMS | 145 |
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多く使われている語句
2-matrix approximation atoms attractors cage point calculations Chem Chemistry Cioslowski coefficients configuration configuration interaction contracted Schrödinger convex set correlation cage corresponding Coulomb hole critical circle cumulant density equation Density Functional Theory Density Matrices eigenvalue electron correlation electron-electron electron-pair elements equivalent Erdahl exact exchange-correlation expansion expectation value Fermi hole follows formula given by Eq ground ground-state Hamiltonian Hartree-Fock Hermitian interaction intracule and extracule intracule densities J. P. Perdew k-density k-spectrum Lett linear matrix representation Mazziotti method minimizer molecules momentum space N-particle N-representability conditions Nakatsuji Neumann density obtained occupation numbers one-particle operator p₁(r pair density PE(R Phys pi(u potential properties quantum r₁ RDMs reconstruction Reduced Density Matrices representable region Rosina RTMs satisfies Schrödinger equation second-order Slater determinant solution spin spin-orbitals TCSE theorem tion two-particle Valdemoro variational vector wave function Yasuda