Ionization potentials and conditional amplitudes

Hunter, Geoffrey

doi:10.1002/qua.560090839

Cited by 36 publications

(46 citation statements)

References 11 publications

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“…In molecules, the external potential v ext (r) goes to zero at large distance like −Z/r, with Z representing the total charge of all nuclei and r the distance from the barycenter of nuclear charge. In this case, according to equations (1) and (2), the asymptotic (|r| → ∞) decay of n(r) and ψ k (r) is (with r = |r|)…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The eigenvalue in equation (1) [1,2] is the first ionization potential, I 0 = E N −1 0 − E N 0 , and the occupied KS orbitals reproduce the density, N k |ψ k (r)| 2 = n(r). For the derivation of equation (1) it is essential to assume that the ground-state, interacting, N -electron wavefunction is real [2]. When this is not the case, an additional vector potential appears in the left-hand-side of equation (1), as in the exact factorization approach put forward by Gross and coworkers [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we further investigate this issue focussing on the effective potential v eff (r) appearing in equation (1), which is related to the functional derivative of the von Weizsäcker kinetic energy functional [12],…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Gori‐Giorgi

Baerends

2018

Eur. Phys. J. B

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Abstract. It is known that the asymptotic decay (|r| → ∞) of the electron density n(r) outside a molecule is informative about its first ionization potential I0. It has recently become clear that the special circumstance that the Kohn-Sham (KS) highest-occupied molecular orbital (HOMO) has a nodal plane that extends to infinity may give rise to different cases for the asymptotic behavior of the exact density and of the exact KS potential [P. Gori-Giorgi et al., Mol. Phys. 114, 1086(2016]. Here we investigate the consequences of such a HOMO nodal plane for the effective potential in the Schrödinger-like equation for the square root of the density, showing that for atoms and molecules it will usually diverge asymptotically on the plane, either exponentially or polynomially, depending on the coupling between Dyson orbitals. We also analyze the issue in the external harmonic potential, reporting an example of an exact analytic density for a fully interacting system that exhibits a different asymptotic behavior on the nodal plane.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Gori‐Giorgi

Baerends

2018

Eur. Phys. J. B

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“…Solving the problem by direct accessing n(r), [68][69][70][71][72][73] however, frequently leads to equations that, albeit conceptually important, are not convenient for computational purposes.…”

Section: Kohn-sham Equationsmentioning

confidence: 99%

Electronic properties of complex interfaces and nanostructures

Medeiros

2015

Linköping Studies in Science and Technology. Dissertations

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To my grandmother, minha veinha. AbstractThis thesis investigates the structural and electronic properties of graphene, polyaromatic hydrocarbon (PAH) molecules, and other carbon-based materials, when interacting with metallic surfaces, as well as under the influence of different types of perturbations. Density functional theory, incorporating van der Waals interactions, has been employed.PAH molecules can, with gradual accuracy, be considered as approximations to an infinite graphene layer. A method to estimate the contributions to the binding energies and net charge transfers from different types of carbon atoms and CH groups in graphene-and PAH-metal systems has been generalized. In this extended method, the number and the nature of the functional groups is determined using a first-principles approach, rather than intuitively or through empirical considerations. Relationships between charge transfers, interface dipole moments and work functions in such systems are explored.Although the electronic structure of physisorbed graphene keeps most of the features of freestanding graphene, the use of large supercells in calculations makes it difficult to resolve the changes introduced in the band structures of such materials. In this thesis, this was the initial motivation for the development of a method to perform the Brillouin zone unfolding of band structures. This method, as initially developed, is shown to be of general use for any periodic structure, and is even further generalized -through the introduction of the unfolding density operator -to tackle the unfolding of the eigenvalues of any arbitrary operator, with both scalar as well as spinor eigenstates.A combined experimental and theoretical investigation of the self-assembly of a binary mixture of 4,9-diaminoperylene-quinone-3,10-diimine (DPDI) and 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) molecules on Ag(111) is presented. The DFT calculations performed here allow for the investigation of the interplay between molecule-molecule and molecule-surface interactions in the network.Besides the main results mentioned above, this thesis also incorporates a study of silicon-metal nanostructures, as well as an investigation of the use of hybrid v vi graphene-graphane structures as prototypes for atomically precise design in nanoelectronics. Populärvetenskaplig sammanfattningI denna avhandling undersöks strukturella och elektroniska egenskaper hos grafen, polycykliska aromatiska kolväten (PAH) och andra kolbaserade material, i situationer då dessa växelverkar med metallytor eller utsätts för olika slags störningar. Undersökningarna är baserade på s.k. täthetsfunktionalteori (DFT) och tar hänsyn till van der Waals-interaktioner.Polycykliska aromatiska kolväten kan, med gradvis noggrannhet, anses representera grafen med oändlig utsträckning. I avhandlingen har en metod för att uppskatta bidragen till bindningsenergier och laddningsöverföringar från olika kolatomer hos grafen-och PAH-metallsystem generaliserats på ett sådant sätt att antalet och karakt...

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Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

Giarrusso,

Gori‐Giorgi,

Agostini

2024

ChemPhysChem

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We generalize the definitions of local scalar potentials named vkin and vN−1, which are relevant to properly describe phenomena such as molecular dissociation with density‐functional theory, to the case in which the electronic wavefunction corresponds to a complex current‐carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non‐interacting electrons is showcased together with its associated circulation, giving rise to a non‐vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born‐Oppenheimer approximation are also discussed.

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Ionization potentials and conditional amplitudes

Cited by 36 publications

References 11 publications

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Electronic properties of complex interfaces and nanostructures

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

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