Communication: The role of the positivity N-representability conditions in natural orbital functional theory (original) (raw)
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The intrapair electron correlation in natural orbital functional theory
2013
A previously proposed [M. Piris, X. Lopez, F. Ruipérez, J. M. Matxain, and J. M. Ugalde, J. Chem. Phys. 134, 164102 (2011)] formulation of the two-particle cumulant, based on an orbital-pairing scheme, is extended here for including more than two natural orbitals. This new approximation is used to reconstruct the two-particle reduced density matrix (2-RDM) constrained to the D, Q, and G positivity necessary conditions of the N-representable 2-RDM. In this way, we have derived an extended version of the Piris natural orbital functional 5 (PNOF5e). An antisymmetrized product of strongly orthogonal geminals with the expansion coefficients explicitly expressed by the occupation numbers is also used to generate the PNOF5e. The theory is applied to the homolytic dissociation of selected diatomic molecules: H 2 , LiH, and Li 2 . The Bader's theory of atoms in molecules is used to analyze the electron density and the presence of non-nuclear maxima in the case of a set of light atomic clusters: Li 2 , Li + 3 , Li 2+ 4 , and H + 3 . The improvement of PNOF5e over PNOF5 was observed by visualizing the electron densities. © 2013 AIP Publishing LLC.
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.
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.
The one-electron picture in the Piris natural orbital functional 5 (PNOF5
The natural orbital functional theory provides two complementary representations of the one-electron picture in molecules, namely, the natural orbital (NO) representation and the canonical orbital (CO) representation. The former arises directly from the optimization process solving the corresponding Euler equations, whereas the latter is attained from the diagonalization of the matrix of Lagrange multipliers obtained in the NO representation. In general, the one-particle reduced-density matrix (1-RDM) and the Lagrangian cannot be simultaneously brought to the diagonal form, except for the special Hartree-Fock case. The 1-RDM is diagonal in the NO representation, but not the Lagrangian, which is only a Hermitian matrix. Conversely, in the CO representation, the Lagrangian is diagonal, but not the 1-RDM. Combining both representations we have the whole picture concerning the occupation numbers and the orbital energies. The Piris natural orbital functional 5 leads generally to the localization of the molecular orbitals in the NO representation. Accordingly, it provides an orbital picture that agrees closely with the empirical valence shell electron pair repulsion theory and the Bent's rule, along with the theoretical valence bond method. On the other hand, the equivalent CO representation can afford delocalized molecular orbitals adapted to the symmetry of the molecule. We show by means of the extended Koopmans' theorem that the one-particle energies associated with the COs can yield reasonable principal ionization potentials when the 1-RDM remains close to the diagonal form. The relationship between NOs and COs is illustrated by several examples, showing that both orbital representations complement each other.
The Journal of Chemical Physics, 2012
The Piris natural orbital functional, PNOF5, has been used to predict vertical ionization potentials of a selected set of 30 organic and inorganic spin-compensated molecules by means of the extended Koopmans' theorem. Electron affinities of 10 selected radicals have also been estimated as the inverse of the ionization potentials of the anionic species, calculated at the experimental geometries of the neutral radicals. The basis set limit effects have been assessed by inspecting the data obtained for the Dunning's basis set series cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5). The performance of the PNOF5 is established by carrying out a statistical analysis of the mean absolute errors (MAEs) with respect to the experiment values. The calculated PNOF5 ionization potentials and electron affinities agree satisfactorily with the corresponding experimental data, with MAEs smaller than 0.5 eV.