Accuracy of two-particle<i>N</i>-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

Fosso-Tande, Jacob; Nascimento, Daniel R.; DePrince, A. Eugene

doi:10.1080/00268976.2015.1078008

Cited by 36 publications

(62 citation statements)

References 49 publications

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“…In this picture, an antiferromagnetic ground state of the acene molecules evolves [14] . Similar deviations of NOONs were observed in a number of other studies with related approaches (v2RDM‐based CAS), [121, 136–139] and different Hamiltonians, including MR‐AQCC, [15] TAO‐DFT, [114, 115] and pp‐RPA‐B3LYP [116] …”

Section: Theoretical Studiessupporting

confidence: 83%

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

Tönshoff

Bettinger

2020

Chemistry A European J

105

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Acenes, consisting of linearly fused benzene rings, are an important fundamental class of organic compounds with various applications. Hexacene is the largest acene that was synthesized and isolated in the 20th century. The next largest member of the acene family, heptacene, was observed in 2007 and since then significant progress in preparing acenes has been reported. Significantly larger acenes, up to undecacene, could be studied by means of low‐temperature matrix isolation spectroscopy with in situ photolytic generation, and up to dodecacene by means of on‐surface synthesis employing innovative precursors and highly defined crystalline metal surfaces under ultrahigh vacuum conditions. The review summarizes recent experimental and theoretical advances in the area of acenes that give a significantly deeper insight into the fundamental properties and nature of the electronic structure of this fascinating class of organic compounds.

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Section: Theoretical Studiessupporting

confidence: 83%

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

Tönshoff

Bettinger

2020

Chemistry A European J

105

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“…We believe this behavior stems from an inconsistency in the description of different S and L states in v2RDM methods in general. For example, for linear chains of hydrogen atoms, we have found [18] that large-S states are more well-constrained than low-S states. That effect, combined with an apparent complementary effect regarding the relative descrip- tion of large-L and small-L states, results in estimates of the absolute energies of the 1 S states that are relatively poor, as compared to estimates of the absolute energies of higher angular momentum states in the same atoms (the absolute energies for all states considered here are tabulated in the Supporting Information).…”

Section: Resultsmentioning

confidence: 96%

Orbital angular momentum constraints in the variational optimization of the two-electron reduced-density matrix

DePrince

2019

Phys. Rev. A

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The direct variational determination of the two-electron reduced-density matrix (2-RDM) is usually carried out under the assumption that the 2-RDM is a real-valued quantity. However, in systems that possess orbital angular momentum symmetry, the description of states with a well-defined, nonzero z-projection of the orbital angular momentum requires a complex-valued 2-RDM. We consider a semidefinite program suitable for the direct optimization of a complex-valued 2-RDM and explore the role of orbital angular momentum constraints in systems that possess the relevant symmetries. For atomic systems, constraints on the expectation values of the square and z-projection of the orbital angular momentum operator allow one to optimize 2-RDMs for multiple orbital angular momentum states. Similarly, in linear molecules, orbital angular momentum projection constraints enable the description of multiple electronic states, and, moreover, for states with a non-zero zprojection of the orbital angular momentum, the use of complex-valued quantities is essential for a qualitatively correct description of the electronic structure. For example, in the case of molecular oxygen, we demonstrate that orbital angular momentum constraints are necessary to recover the correct energy ordering of the lowest-energy singlet and triplet states near the equilibrium geometry. However, care must still be taken in the description of the dissociation limit, as the 2-RDM-based approach is not size consistent, and the size-consistency error varies dramatically, depending on the z-projections of the spin and orbital angular momenta.

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“…The oligoacenes have long been of fundamental interest to chemists due to their semiconducting and optical properties, [54][55][56][57][58][59][60][61][62][63][64] and theoreticians have been studying their singlet-triplet splittings and ground state electronic structures with particular attention to the disputed emergence of a stable, open-shell singlet ground state with increasing acene size. 12,22,54,[65][66][67][68][69][70][71][72][73][74][75][76] In characterizing the ground state, qualitatively different interpretations can arise depending on the degree dynamical correlation included, with recent studies suggesting that pure active-space methods tend to overestimate biradical character in these ground states. [74][75][76][77] An accurate theoretical characterization of the oligoacenes is complicated, however, by (i) strong correlation in the π/π * manifold, (ii) their size, prohibitive for many ab initio methods, and (iii) the large basis sets required for experimental comparisons.…”

Section: The Oligoacenesmentioning

confidence: 99%

A Combined Selected Configuration Interaction and Many-Body Treatment of Static and Dynamical Correlation in Oligoacenes

Schriber

Hannon

et al. 2018

J. Chem. Theory Comput.

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We have combined our adaptive configuration interaction (ACI) [J.B. Schriber and F.A. Evangelista, J. Chem. Phys. 144, 161106 (2016)] with a density-fitted implementation of the second-order perturbative multireference driven similarity renormalization group (DSRG-MRPT2) [K.P. Hannon, C. Li and F.A. Evangelista J. Chem. Phys. 144, 204111 (2016)]. We use ACI reference wave functions to recover static correlation for active spaces larger than the conventional limit of 18 orbitals. The dynamical correlation is computed using the DSRG-MRPT2 to yield a complete treatment of electron correlation. We apply the resulting method, ACI-DSRG-MRPT2, to predict singlet-triplet gaps, metrics of open-shell character, and spin-spin correlation functions for the oligoacene series (2-7 rings). Our computations employ active spaces with as many as 30 electrons in 30 orbitals and up to 1350 basis functions, yielding gaps that are in good agreement with available experimental results. Large bases and reference relaxation lead to a significant reduction in the estimated radical character of the oligoacenes with respect to previous valence-only treatments of correlation effects.

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Accuracy of two-particleN-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

Cited by 36 publications

References 49 publications

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

Orbital angular momentum constraints in the variational optimization of the two-electron reduced-density matrix

A Combined Selected Configuration Interaction and Many-Body Treatment of Static and Dynamical Correlation in Oligoacenes

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