Configuration interaction

Summary

Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, configuration simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), interaction means the mixing (interaction) of different electronic configurations (states). Due to the long CPU time and large memory required for CI calculations, the method is limited to relatively small systems. In contrast to the Hartree–Fock method, in order to account for electron correlation, CI uses a variational wave function that is a linear combination of configuration state functions (CSFs) built from spin orbitals (denoted by the superscript SO), : \Psi = \sum_{I=0} c_{I} \Phi_{I}^{SO} = c_0\Phi_0^{SO} + c_1\Phi_1^{SO} + {...

Official source

https://en.wikipedia.org/wiki/Configuration_interaction

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Cluster perturbation theory. III. Perturbation series for coupled cluster singles and doubles excitation energies

Pablo Jonas Baudin, Jógvan Magnus Olsen

The cluster perturbation series, CPS(D), for coupled cluster singles and doubles excitation energies is considered. It is demonstrated that the second-order model CPS(D-2) is identical to the configuration interaction singles with perturbative doubles, CIS(D) model. The third-order model, CPS(D-3), provides excitation energies of coupled cluster singles and doubles (CCSD) quality in the sense that the difference between CPS(D-3) and CCSD excitation energies is of the same size or smaller than the effect of adding triples corrections to CCSD excitation energies. We further show that the third-order corrections can be efficiently implemented, in particular, when the resolution of the identity approximation is used for integrals. We also show that the CPS(D-3) excitation energies can be determined for system sizes that are far beyond what can be considered in conventional CCSD excitation energy calculations. Published under license by AIP Publishing.

AMER INST PHYSICS2019

In this presentation, we wish to provide an overview of the spectral features for the self-adjoint Hamiltonian of the three-dimensional isotropic harmonic oscillator perturbed by either a single attractive delta-interaction centered at the origin or by a pair of identical attractive delta-interactions symmetrically situated with respect to the origin. Given that such Hamiltonians represent the mathematical model for quantum dots with sharply localized impurities, we cannot help having the renowned article by Bruning, Geyler and Lobanov [1] as our key reference. We shall also compare the spectral features of the aforementioned three-dimensional models with those of the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction in one dimension, fully investigated in [2, 3], given the existence in both models of the remarkable spectral phenomenon called "level crossing". The rigorous definition of the self-adjoint Hamiltonian for the singular double well model will be provided through the explicit formula for its resolvent (Green's function). Furthermore, by studying in detail the equation determining the ground state energy for the double well model, it will be shown that the concept of "positional disorder", introduced in [1] in the case of a quantum dot with a single delta-impurity, can also be extended to the model with the twin impurities in the sense that the greater the distance between the two impurities is, the less localized the ground state will be. Another noteworthy spectral phenomenon will also be determined; for each value of the distance between the two centers below a certain threshold value, there exists a range of values of the strength of the twin point interactions for which the first excited symmetric bound state is more tightly bound than the lowest antisymmetric bound state. Furthermore, it will be shown that, as the distance between the two impurities shrinks to zero, the 3D-Hamiltonian with the singular double well (requiring renormalization to be defined) does not converge to the one with a single delta-interaction centered at the origin having twice the strength, in contrast to its one-dimensional analog for which no renormalization is required. It is worth stressing that this phenomenon has also been recently observed in the case of another model requiring the renormalization of the coupling constant, namely the one-dimensional Salpeter Hamiltonian perturbed by two twin attractive delta-interactions symmetrically situated at the same distance from the origin.

St Petersburg Natl Research Univ Information Technologies, Mech & Optics2016

How Robust Is the Reversible Steric Shielding Strategy for Photoswitchable Organocatalysts?

Raimon Fabregat I De Aguilar-Amat, Simone Gallarati, Théo Pierre Jaffrelot Inizan, Veronika Juraskova

A highly appealing strategy to modulate a catalyst's activity and/or selectivity in a dynamic and noninvasive way is to incorporate a photoresponsive unit into a catalytically competent molecule. However, the description of the photoinduced conformational or structural changes that alter the catalyst's intrinsic reactivity is often reduced to a handful of intuitive static representations, which can struggle to capture the complexity of flexible organocatalysts. Here, we show how a comprehensive exploration of the free energy landscape of N-alkylated azobenzene-tethered piperidine catalysts is essential to unravel the conformational characteristics of each configurational state and explain the experimentally observed reactivity trends. Mapping the catalysts' conformational space highlights the existence of false ON or OFF states that lower their switching ability. Our findings expose the challenges associated with the realization of a reversible steric shielding for the photocontrol of Bronsted basicity of piperidine photoswitchable organocatalysts.

AMER CHEMICAL SOC2022

St Petersburg Natl Research Univ Information Technologies, Mech & Optics2016