Strong Correlation in Acene Sheets from the Active-Space Variational Two-Electron Reduced Density Matrix Method: Effects of Symmetry and Size

Pelzer, Kenley M.; Greenman, Loren; Gidofalvi, Gergely; Mazziotti, David A.

doi:10.1021/jp2017192

Cited by 94 publications

(128 citation statements)

References 62 publications

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“…Even when the Hamiltonian of interest is not rigorously contained in this class, the associated N -representability conditions, which intrinsically are not constrained by the approximations of perturbation theory, may produce an accurate lower bound on the ground-state energy. Computational experience with the variational calculation of the 2-RDM in atoms and molecules [3,14,15,18,25,26,54,55] shows that sufficiently accurate lower-bound ground-state energies are often produced with (2, q)-positivity conditions where q ≤ 3.…”

Section: Discussionmentioning

confidence: 99%

Significant conditions for the two-electron reduced density matrix from the constructive solution ofNrepresentability

Mazziotti

2012

Phys. Rev. A

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We recently presented a constructive solution to the N -representability problem of the twoelectron reduced density matrix (2-RDM)-a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic N -electron quantum system [D. A. Mazziotti, Phys. Rev. Lett. 108, 263002 (2012)]. In this paper we provide additional details and derive further N -representability conditions on the 2-RDM that follow from the constructive solution. The resulting conditions can be classified into a hierarchy of constraints, known as the (2, q)-positivity conditions where the q indicates their derivation from the nonnegativity of q-body operators. In addition to the known T1 and T2 conditions, we derive a new class of (2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of (2,6)-positivity conditions. The constraints obtained can be divided into two general types: (i) lifting conditions, that is conditions which arise from lifting lower (2, q)-positivity conditions to higher (2, q + 1)-positivity conditions and (ii) pure conditions, that is conditions which cannot be derived from a simple lifting of the lower conditions. All of the lifting conditions and the pure (2, q)-positivity conditions for q > 3 require tensor decompositions of the coefficients in the model Hamiltonians. Subsets of the new N -representability conditions can be employed with the previously known conditions to achieve polynomially scaling calculations of ground-state energies and 2-RDMs of many-electron quantum systems even in the presence of strong electron correlation.

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Section: Discussionmentioning

confidence: 99%

Significant conditions for the two-electron reduced density matrix from the constructive solution ofNrepresentability

Mazziotti

2012

Phys. Rev. A

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“…Recently, linear n-acenes (C 4n+2 H 2n+4 ), containing n linearly fused benzene rings (see Figure 10), have attracted considerable interest in the research community owing to their promising electronic properties [20,21,[45][46][47][48][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124]. The electronic properties of nacenes have been found to be highly dependent on the chain lengths.…”

Section: Electronic Properties Of Linear Acenesmentioning

confidence: 99%

“…Consequently, the experimental singlet-triplet energy gaps (ST gaps) of n-acenes are only available up to pentacene [109][110][111][112]. On the theoretical side, since n-acenes belong to conjugated π-orbital systems, high-level ab initio multi-reference methods, such as the density matrix renormalization group (DMRG) algorithm [115,122], the variational twoelectron reduced density matrix (2-RDM) method [121,124], and other high-level methods [114,[118][119][120], are typically required to capture the essential strong static correlation effects.…”

Section: Electronic Properties Of Linear Acenesmentioning

confidence: 99%

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

Chai

2017

The Journal of Chemical Physics

138

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We propose hybrid schemes incorporating exact exchange into thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] for an improved description of nonlocal exchange effects. With a few simple modifications, global and range-separated hybrid functionals in Kohn-Sham density functional theory (KS-DFT) can be combined seamlessly with TAO-DFT. In comparison with global hybrid functionals in KS-DFT, the resulting global hybrid functionals in TAO-DFT yield promising performance for systems with strong static correlation effects (e.g., the dissociation of H 2 and N 2 , twisted ethylene, and electronic properties of linear acenes), while maintaining similar performance for systems without strong static correlation effects. Besides, a reasonably accurate description of noncovalent interactions can be efficiently achieved through the inclusion of dispersion corrections in hybrid TAO-DFT. Relative to semilocal density functionals in TAO-DFT, global hybrid functionals in TAO-DFT are generally superior in performance for a wide range of applications, such as thermochemistry, kinetics, reaction energies, and optimized geometries.

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“…These molecules are the basic building blocks of polycyclic aromatic hydrocarbons (PAHs), π-conjugated oligomers, and many organic semiconductors and dyes. They embody the basic physics of such systems including the strong correlation effects in aromatic π-systems 84,89,92 and the self-interaction effects introduced by the nitrogen lone pairs. 51,59 Another advantage of these systems is that they are well-characterized experimentally [93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108] and well-studied theoretically by high-level wavefunction and Green's function methods.…”

Section: Introductionmentioning

confidence: 99%

Benchmark ofGWmethods for azabenzenes

et al. 2012

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Many-body perturbation theory in the GW approximation is a useful method for describing electronic properties associated with charged excitations. A hierarchy of GW methods exists, starting from non-self-consistent G 0 W 0 , through partial self-consistency in the eigenvalues (evscGW) and in the Green's function (scGW 0 ), to fully self-consistent GW (scGW). Here, we assess the performance of these methods for benzene, pyridine, and the diazines. The quasiparticle spectra are compared to photoemission spectroscopy (PES) experiments with respect to all measured particle removal energies and the ordering of the frontier orbitals. We find that the accuracy of the calculated spectra does not match the expectations based on their level of selfconsistency. In particular, for certain starting points G 0 W 0 and scGW 0 provide spectra in better agreement with the PES than scGW.

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Strong Correlation in Acene Sheets from the Active-Space Variational Two-Electron Reduced Density Matrix Method: Effects of Symmetry and Size

Cited by 94 publications

References 62 publications

Significant conditions for the two-electron reduced density matrix from the constructive solution ofNrepresentability

Significant conditions for the two-electron reduced density matrix from the constructive solution ofNrepresentability

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

Benchmark ofGWmethods for azabenzenes

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