Some Aspects on the Correlation Problem and Possible Extensions of the Independent‐Particle Model

Löwdin, Per‐Olov

doi:10.1002/9780470143599.ch9

Cited by 98 publications

(12 citation statements)

References 95 publications

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“…This is the famous Löwdin sym- metry dilemma. [175][176][177] Moreover, for these two orbital sets, the TpCCD energies are in good agreement with DOCI (see the supplementary material). Yet, VpCCD is closer to DOCI than TpCCD as already seen in the linear H 4 case [see Sec.…”

Section: B a Strong Correlation Model: The Ring H 4 Moleculesupporting

confidence: 60%

Variational coupled cluster for ground and excited states

Marie,

Kossoski,

Loos

2021

Preprint

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In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes which are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations which may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC (VCC) and we compare it with its (projected) traditional version (TCC) in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H 4 molecule and the continuous deformation of the square H 4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of VpCCD and TpCCD are gauged against their configuration interaction (CI) equivalent, known as doubly-occupied CI (DOCI), for reference Slater determinants made of ground-or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated. I. COUPLED CLUSTER AND STRONG CORRELATIONSingle-reference (SR) coupled-cluster (CC) methods offers a reliable description of weakly correlated systems through a well-defined hierarchy of systematically improvable models. [1][2][3][4][5] On top of this hierarchy stands full CC (FCC), which is equivalent to full configuration interaction (FCI), and consequently provides, at a very expensive computational cost, the exact wave function and energy of the system in a given basis set. Fortunately, more affordable methods have been designed and the popular CCSD(T) method, which includes singles, doubles and non-iterative triples, is nowadays considered as the gold standard of quantum chemistry for ground-state energies and properties. 6,7 Despite its success for weakly correlated systems, it is now widely known that CCSD(T) flagrantly breaks down in the presence of strong correlation as one cannot efficiently describe such systems with a single (reference) Slater determinant. This has motivated quantum chemists to design multi-reference CC (MRCC) methods. [8][9][10][11][12] However, it is fair to say that these methods are computationally demanding and still far from being black-box.Because SRCC works so well for weak correlation, it would be convenient to be able to treat strong correlation within the very same framework. This is further motivated by the fact that one can compensate the poor quality of the reference wave function by simply increasing the maximum excitation degree of the CC expansion. However, this is inevitably associated with a rapid growth of the computational cost, and hence one cannot always afford this brute-force strategy. The development of SR-based methods for strong correlation is ongoing and some of them (usually based on the...

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Section: B a Strong Correlation Model: The Ring H 4 Moleculesupporting

confidence: 60%

Variational coupled cluster for ground and excited states

Marie,

Kossoski,

Loos

2021

Preprint

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“…1). The ACS profile for NGr (15,12) with hydrogen terminated edges presented in Fig. 2a demonstrates a rather significant variation of the quantity over atoms.…”

Section: Chemical Reactivity Of Nanographenesmentioning

confidence: 95%

“…Computed by using UBS HF approach, the spin density distribution over NGr (15,12) atoms with hydrogen-terminated and empty edges is demonstrated in Fig. 3.…”

Section: Magnetism Of Zigzag Edged Nanographenesmentioning

confidence: 99%

“…The first suggestion for using the correlation incompleteness of the UBS solution for practical goals was made thirty years ago [14]. The authors showed that if all electrons spins either are not coupled or have not one direction an extra spin density arises due to Löwdin's symmetry dilemma given rise by unrestricted single-determinant solutions [15]. This is due to spincontamination character of the latter which causes asymmetry of electron density of UHF solution and asymmetric LDA Hamiltonian with different exchange-correlation potentials for spin-up and spin-down orbitals.…”

Section: Introductionmentioning

confidence: 99%

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Chemical reactivity and magnetism of graphene

Sheka

Чернозатонский

2009

Int J of Quantum Chemistry

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“…Finally we remark that electron correlation was central to Per Olov's work and in refs [ 40,57,58 ] the ground work for key aspects of the discussion in this contribution was laid. Also, in his book 59 on linear algebra he discusses the 'mirror theorem'.…”

Section: Condensate Wave Functionsmentioning

confidence: 99%

High-Temperature Superconductivity in Strongly Correlated Electronic Systems

Dunne

Brändas

Cox

2017

Advances in Quantum Chemistry

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In this paper we give a selective review of our work on the role of electron correlation in the theory of high temperature superconductivity. The question of how electronic repulsions might give rise to off-diagonal long range order (ODLRO) in high temperature superconductors is currently one of the key questions in the theory of condensed matter. This paper argues that the key to understanding the occurrence of high temperature superconductivity (HTSC) in cuprates is to be found in the Bohm-Pines Hamiltonian modified to include a polarisable dielectric background. The approach uses reduced electronic density matrices and discusses how these can be used to understand whether ODLRO giving rise to superconductivity might arise from a Bohm-Pines type potential which is comprised of a weak long-range attractive tail and a much stronger short-range repulsive Coulomb interaction. This allows time-reversed electron pairs to undergo a superconducting condensation on alternant Cuprate lattices. Thus, a detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time-reversed pairs of electrons effectively avoid the repulsive hard-core of the inter-electronic Coulomb interaction but reside on average in The alternant cuprate lattice structure is the key to achieving HTSC in cuprates with d x2-y2 symmetry condensate symmetry.

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Some Aspects on the Correlation Problem and Possible Extensions of the Independent‐Particle Model

Cited by 98 publications

References 95 publications

Variational coupled cluster for ground and excited states

Variational coupled cluster for ground and excited states

Chemical reactivity and magnetism of graphene

High-Temperature Superconductivity in Strongly Correlated Electronic Systems

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