2019
DOI: 10.1063/1.5085121
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Complex adiabatic connection: A hidden non-Hermitian path from ground to excited states

Abstract: Processes related to electronically excited states are central in many areas of science, however accurately determining excited-state energies remains a major challenge in theoretical chemistry. Recently, higher energy stationary states of non-linear methods have themselves been proposed as approximations to excited states, although the general understanding of the nature of these solutions remains surprisingly limited. In this Le er, we present an entirely novel approach for exploring and obtaining excited st… Show more

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Cited by 22 publications
(44 citation statements)
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“…52 Each individual h-HF state is given by a di erent branch of a Riemann surface, with Coulson-Fischer points forming isolated exceptional points corresponding to the branch points of the Riemann surface. 52 Signi cantly, we can use this continuous topology of h-HF states to follow solutions around a Coulson-Fischer point by tracing a suitable λ-trajectory in the complex plane. We illustrate this idea by considering the multiple HF solutions of H 2 in a minimal basis set (STO-3G) using two orbitals φ α and φ β parameterised by the complex angle θ,…”
Section: B Moving Past the Coulson-fischer Pointmentioning
confidence: 99%
“…52 Each individual h-HF state is given by a di erent branch of a Riemann surface, with Coulson-Fischer points forming isolated exceptional points corresponding to the branch points of the Riemann surface. 52 Signi cantly, we can use this continuous topology of h-HF states to follow solutions around a Coulson-Fischer point by tracing a suitable λ-trajectory in the complex plane. We illustrate this idea by considering the multiple HF solutions of H 2 in a minimal basis set (STO-3G) using two orbitals φ α and φ β parameterised by the complex angle θ,…”
Section: B Moving Past the Coulson-fischer Pointmentioning
confidence: 99%
“…In contrast, the complex-symmetric inner product x|y C = x y requires complex-symmetric density D (k) = C (k) (C (k) ) and Fock matrices F (k) = (F (k) ) , with energies that are complex in general. e complex-symmetric formulation of HF is used in holomorphic HF theory to ensure solutions exist over all geometries, [13][14][15]17 and for describing resonance phenomena in non-Hermitian approaches. 16 In what follows, we employ the complex-symmetric inner product .|.…”
Section: P T -Symmetry In Hartree-fockmentioning
confidence: 99%
“…(28)]. Stationary points that do not correspond to P T -symmetric states (including the sb-RHF and h-UHF solutions) occur in pairs which are interconverted by the action of P T , and the onset of P T -symmetry breaking coincides with the disappearance of the h-RHF or the sb-UHF solutions at Coulson-Fischer (quasi-exceptional) points 17 in a similar manner to other types of symmetry-breaking in HF theory. [10][11][12]…”
Section: B Complex Orbital Coe Icientsmentioning
confidence: 99%
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“…we have shown that multiple h-HF states form a continuous interconnected manifold in the complex λ-plane. 52 Each individual h-HF state is given by a di erent branch of a Riemann surface, with Coulson-Fischer points forming isolated exceptional points corresponding to the branch points of the Riemann surface. 52 Signi cantly, we can use this continuous topology of h-HF states to follow solutions around a Coulson-Fischer point by tracing a suitable λ-trajectory in the complex plane.…”
Section: B Moving Past the Coulson-fischer Pointmentioning
confidence: 99%