Physical meaning of the natural orbitals: Analysis of exactly solvable models (original) (raw)
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Quantal density functional theory of excited states: Application to an exactly solvable model
International Journal of Quantum Chemistry, 2001
The quantal density functional theory (Q‐DFT) of excited states is the description of the physics of the mapping from any bound nondegenerate excited state of Schrödinger theory to that of the s‐system of noninteracting Fermions with equivalent density ρk(r), energy Ek, and ionization potential Ik. The s‐system may either be in an excited state with the same configuration as in Schrödinger theory or in a ground state with a consequently different configuration. The Q‐DFT description of the s‐system is in terms of a conservative field ℱk(r), whose electron‐interaction ℰee(r) and correlation‐kinetic 𝒵(r) components are separately representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and correlation‐kinetic effects, respectively. The sources of these fields are expectations of Hermitian operators taken with respect to the system wavefunction. The local electron‐interaction potential vee(r) of the s‐system, representative of all the many‐bod...
The positivity conditions for the N-representability of the reduced density matrices are considered to propose a new natural orbital functional. The Piris reconstruction functional, which is based on an explicit form of the two-particle cumulant ͑⌬ , ⌸͒ is used to reconstruct the two-particle reduced density matrix. A new approach for ⌸ matrix, satisfying rigorously D, Q, and G necessary conditions, leads to Piris Natural Orbital Functional 4 ͑PNOF4͒. The theory is applied to the dissociation of selected diatomic molecules. The equilibrium distances, dipole moments, harmonic frequencies, anharmonicity constants, and binding energies of the considered molecules are presented. The values we have obtained are very accurate results comparing with the experimental data.
Journal of chemical theory and computation, 2014
In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including ...
Density Functional Theory with Fractional Orbital Occupations
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H 2 and N 2 , and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.
Excited-state density functional theory
Journal of Physics: Conference Series, 2012
Starting with a brief introduction to excited-state density functional theory, we present our method of constructing modified local density approximated (MLDA) energy functionals for the excited states. We show that these functionals give accurate results for kinetic energy and exchange energy compared to the ground state LDA functionals. Further, with the inclusion of GGA correction, highly accurate total energies for excited states are obtained. We conclude with a brief discussion on the further direction of research that include the construction of correlation energy functional and exchange potential for excited states. III. EXCITED-STATE FUNCTIONAL OBTAINED BY SPLITTING k-SPACE When energy functionals constructed for ground states are applied to excited states, the results obtained are not accurate [11-14]. To obtain functionals for excited states, we need to incorporate some more information about the excited state in addition to its density. For most of the ground-state functionals local density approximation (LDA)
Communications: Accurate description of atoms and molecules by natural orbital functional theory
The spin-conserving density matrix functional theory is used to propose an improved natural orbital functional. The Piris reconstruction functional, PNOF, which is based on an explicit form of the two-particle cumulant ͑⌬ , ⌳͒ satisfying necessary positivity conditions for the two-particle reduced density matrix, is used to reconstruct the latter. A new approach ⌳ ͑3͒ , as well as an extension of the known ⌬ ␣ to spin-uncompensated systems lead to PNOF3. The theory is applied to the calculation of the total energies of the first-and second-row atoms ͑H-Ne͒ and a number of selected small molecules. The energy differences between the ground state and the lowest-lying excited state with different spin for these atoms, and the atomization energies of the considered molecules are also presented. The obtained values agree remarkably well with their corresponding both CCSD͑T, full͒ and experimental values.
Physical Review A, 2003
The quantal density-functional theory ͑Q-DFT͒ of nondegenerate excited-states maps the pure state of the Schrödinger equation to one of noninteracting fermions such that the equivalent excited state density, energy, and ionization potential are obtained. The state of the model S system is arbitrary in that it may be in a ground or excited state. The potential energy of the model fermions differs as a function of this state. The contribution of correlations due to the Pauli exclusion principle and Coulomb repulsion to the potential and total energy of these fermions is independent of the state of the S system. The differences are solely a consequence of correlation-kinetic effects. Irrespective of the state of the S system, the highest occupied eigenvalue of the model fermions is the negative of the ionization potential. In this paper we demonstrate the state arbitrariness of the model system by application of Q-DFT to the first excited singlet state of the exactly solvable Hookean atom. We construct two model S systems: one in a singlet ground state (1s 2), and the other in a singlet first excited state (1s2s). In each case, the density and energy determined are equivalent to those of the excited state of the atom, with the highest occupied eigenvalues being the negative of the ionization potential. From these results we determine the corresponding Kohn-Sham density-functional theory ͑KS-DFT͒ ''exchangecorrelation'' potential energy for the two S systems. Further, based on the results of the model calculations, suggestions for the KS-DFT of excited states are made.
The Quantified NTO Analysis for the Electronic Excitations of Molecular Many-Body Systems
We show that the origin of electronic transitions of molecular many-body systems can be investigated by a quantified natural transition orbitals (QNTO) analysis and the electronic excitations of the total system can be mapped onto a standard orbitals set of a reference system. We further illustrate QNTO on molecular systems by studying the origin of electronic transitions of DNA moiety, thymine and thymidine. This QNTO analysis also allows us to assess the performance of various functionals used in time-dependent density functional response theory.
Exploring foundations of time-independent density functional theory for excited states
Journal of Physics B: Atomic, Molecular and Optical Physics, 2006
Based on the work of Görling and that of Levy and Nagy, density-functional formalism for many Fermionic excited-states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that the knowledge of the ground-state density is a must to fix the mapping from an excited-state density to the external potential. This is the excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the ground-state density the density of the excited-state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn-Sham system is defined by comparing it's non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.
A natural orbital functional for multiconfigurational states
The Journal of Chemical Physics, 2011
An explicit formulation of the Piris cumulant λ ( , ) matrix is described herein, and used to reconstruct the two-particle reduced density matrix (2-RDM). Then, we have derived a natural orbital functional, the Piris Natural Orbital Functional 5, PNOF5, constrained to fulfill the D, Q, and G positivity necessary conditions of the N -representable 2-RDM. This functional yields a remarkable accurate description of systems bearing substantial (near)degeneracy of one-particle states. The theory is applied to the homolitic dissociation of selected diatomic molecules and to the rotation barrier of ethylene, both paradigmatic cases of near-degeneracy effects. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms. PNOF5 predicts a barrier of 65.6 kcal/mol for the ethylene torsion in an outstanding agreement with Complete Active Space Second-order Perturbation Theory (CASPT2). The obtained occupation numbers and pseudo one-particle energies at the ethylene transition state account for fully degenerate π orbitals. The calculated equilibrium distances, dipole moments, and binding energies of the considered molecules are presented. The values obtained are accurate comparing those obtained by the complete active space self-consistent field method and the experimental data.