Communication: Chemical bonding in carbon dimer isovalent series from the natural orbital functional theory perspective

Int J of Quantum Chemistry

Ugalde

2014

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The natural orbital functional (NOF) theory is briefly reviewed. The meaning of the top-down and bottom-up approaches for the construction of a NOF is analyzed. A particular reconstruction of the two-particle reduced density matrix (2-RDM) based on the cumulant expansion is discussed. The cumulant is expressed by two auxiliary matrices, which are constrained to certain bounds due to the N-representabilty conditions of the 2-RDM. Appropriate forms of these matrices lead to different implementations known in the literature as PNOFi (i 5 1-5). The strengths and weaknesses of PNOF5 are assessed. Its main strength is its ability to deal with the intrapair electron correlation at a reasonable computational cost. Its main limitation is the absence of the interpair electron correlation. The inclusion of the missing correlation via a multiconfigurational perturbation theory is shortly described. The growing interest in methods based on NOF theory points to a promising future in this field.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Perspective on natural orbital functional theory

Int J of Quantum Chemistry

Ugalde

2014

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“…It is useful therefore, that such approximations should satisfy known constraints. Examples include [21] REVIEW WWW.Q-CHEM.ORG 60) and…”

Section: Correlation Aspects As Consequences Of the Pauli Potentialmentioning

confidence: 99%

“…[54][55][56] The one-electron picture provided by PNOF5 is really very appealing since its orbitals agree closely with the orbitals provided by the valence bond method and with those obtained by a standard molecular orbital calculation. [57][58][59][60] PNOF5 is probably the first NOF obtained by both bottom-up and top-down methods. [49,61] This result is remarkable since the functional N-representability problem is solved, which implies that PNOF5 can be derived from a wavefunction that is antisymmetric in N particles.…”

Section: The Functional Pnof5(n C )mentioning

confidence: 99%

Chemical and ionization potentials: Relation via the Pauli potential and NOF theory

Int J of Quantum Chemistry

March

2015

Hartree-Fock (HF) theory makes the prediction that for neutral atoms the chemical potential (l) is equal to minus the ionization potential (I). This has led us to inquire whether this intimate relation is sensitive to electron correlation. We present here therefore some discussion of the predictions for neutral atoms and atomic ions, and some homonuclear diatomic molecules. An account of fairly recent progress in obtaining the HF ionization potentials for the isoelectronic series of He, Be, Ne, Mg, and Ar-like atomic ions is first considered. The 1=Z expansion for total non-relativistic energy of atomic ions evokes that l52I is not very sensitive to the introduction of electron correlation. The connection between l and I for neutral atoms via the Pauli potential (V P ) is then examined. We focus on the relation of V P to more recent advances in density functional theory (DFT) plus low-order density matrix theory. In this context, the example of nonrelativistic Be-like atomic ions is treated. Afterward, we introduce the bosonized equation for the density amplitude ffiffiffi q p , which emphasizes the major role that plays dT W =dq in DFT. For spherical atomic densities, the bosonized potential argument strongly suggests also that l52I remains valid in the presence of electron correlation. Finally, numerical estimates of l and I from natural orbital functional (NOF) theory are presented for neutral atoms ranging from H to Kr. The predicted vertical I by means of the extended Koopmans' theorem are in good agreement with the corresponding experimental data. However, the NOF theory of l lowers the experimental values considerably as we approach to noble gas atoms though oscillatory behavior is in evidence. V C 2015 Wiley Periodicals, Inc. DOI: 10.1002/qua.25039 Ionization Potential and Asymptotic Large r Behavior of Ground-State Density of Spherical AtomsIt seems natural to begin this review relating to advances in density functional theory (DFT) with some account of fairly recent progress in obtaining the ground-state electron density q r ð Þ in some spherical atoms. Then, the nonrelativistic twoelectron He-like series of atomic ions with atomic number Z affords an appropriate starting point.Large r behavior of q r ð Þ in terms of I and Z It is well-known [1] that, in atomic units (a.u.), the ground-state density of rare gas atoms with spherical electron density q r ð Þ falls off at sufficiently large r as where I is the ionization potential. For sufficiently large Z, the expressions for constants n and A were found by March and Pucci [2] based on the early work of Schwartz, [3] namely, n % 2ð3=4ÞZ 21 and A5ð2Z 3 =pÞ½12ð3=4ZÞlnZ1OðZ 21 Þ . However, a more general relationship between n and I for arbitrary atomic number Z can be obtained using the DFT for the He-like series of atomic ions. [4] Consider V(r) is the one-body potential of DFT, then the constant chemical potential equation reads [5] l5 dT s q ½ dq 1V r ð Þwhere T s q ½ is the single-particle kinetic energy functional. While T s is still unknown for gener...

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confidence: 99%

PNOF5 calculations based on the “thermodynamic fragment energy method”: C n H2n+2 (n = 1, 10) and (FH) n (n = 1, 8) as test cases

López

2015

Theor Chem Acc

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be comparable to accurate quantum chemistry methods in many cases [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. So far this is the only natural orbital functional (NOF) that has been obtained by top-down and bottom-up methods [19]. In the bottom-up method, the functional was generated by progressive inclusion of known necessary N-representability conditions on the 2-RDM, whereas the top-down method was used through reducing the energy expression generated from an N-particle wavefunction to a functional of the occupation numbers and natural orbitals [5]. In the case of PNOF5, this wavefunction is an antisymmetrized product of strongly orthogonal geminals (APSGs), with the expansion coefficients explicitly expressed by the occupation numbers [20,21].The idea of a function of this type dates back to the early fifties [22,23] and is inspired by the valence bond theory [24,25]; in fact, PNOF5 can also be considered as a type of GVB-PP method with fixed signs for the expansion coefficients of the corresponding determinants. Many scientists have worked actively in the field of strongly orthogonal geminals, and one of them is Professor Péter R. Surján to whom is dedicated this Festschrift. Indeed, an excellent review summarizing the evolution of the geminal theory up to 1999 can be found at his work [26]. An overview of geminal-based perturbative techniques for describing electron correlation was given recently [27].Consequently, PNOF5 is an orbital-pairing approach that takes into account most of the non-dynamical effects, but also an important part of the dynamical electron correlation corresponding to the intrapair (intrageminal) interactions. The existence of a generating wavefunction confirms that PNOF5 is strictly N-representable, i.e., the 2-RDM is derived from a function that is antisymmetric in N-particles [28]. Moreover, it demonstrates the size extensivity and size consistency of PNOF5, which is an inherent property to the generating singlet-type APSG wavefunction [29,30]. AbstractThe performance of the "thermodynamic fragment energy method" (FEM) in the context of natural orbital functional theory (NOFT) in its PNOF5 implementation is assessed. Two test cases are considered: the linear chains C n H 2n+2 (n = 1, 10) and the hydrogen-bonded (FH) n (n = 1, 8) clusters. Calculations show a fast convergence of the PNOF5-FEM method, which allows the treatment of extended system at a fractional cost of the whole calculation. We show that this type of methodologies could expand the range of systems achievable by NOFT due to the significant reduction in the computational cost.