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Complexities of the Molecular Conductance Problem
Published in Sergey Edward Lyshevski, Nano and Molecular Electronics Handbook, 2018
Gil Speyer, Richard Akis, David K. Ferry
The Hartree–Fock theory uses a Slater determinant to describe the many-electron wavefunction. This treatment of correlation and exchange differs greatly from the Fermi liquid treatment commonly used in DFT. This latter treatment has been shown to result in improper bond dissociation calculations, such as those needed in this work [14]. Exact exchange has been proposed to ameliorate the low bandgaps that plague DFT, but it introduces considerably more computation. For example, the VASP group estimates two orders of magnitude more computation time for the exact exchange functionals in VASP5 (scheduled for release in mid-2007 [15]). Other groups describe DC conductance corrections to the exchange and correlation functionals using time-dependent current–density–functional theory [16]. Hartree–Fock methods, on the other hand, have their own shortcomings in the calculation of opposite spin correlations, one of which can be corrected using multiple Slater determinants in the computationally demanding configuration-interaction method [17].
Influence Functional for Interacting Electrons in Disordered Metals
Published in Andrei D. Zaikin, Dmitry S. Golubev, Dissipative Quantum Mechanics of Nanostructures, 2019
Andrei D. Zaikin, Dmitry S. Golubev
Let us now turn to an alternative and somewhat less standard representation of the effective action via the system evolution operators. For the sake of simplicity, we will initially assume that at t < 0, the system of N electrons was prepared in a pure state with the wave function Ψ0(r1, …, rN), which we choose in the form of a Slater determinant constructed from N orthogonal single-electron wave functions ψkj (r), j = 1… N, where the indices kj also include spin orientation and indicate the occupied states chosen from a full infinite set of orthogonal states ψk(r). The wave function in the form of the Slater determinant is fully antisymmetric in accordance with the Pauli principle. It can be conveniently expressed with the aid of electron creation operators akj† in the states ψkj (r), () Ψ0(r1,…,rN)=akN†…ak1†|0〉
Bohmian Pathways into Chemistry: A Brief Overview
Published in Xavier Oriols, Jordi Mompart, Applied Bohmian Mechanics, 2019
Molecular orbital theories [76–78], on the contrary, consider delocalized orbitals covering the whole molecule (molecular orbitals). Thus, the molecular orbital wave function is expressed as a linear combination of atomic orbitals (Slater determinants). These atomic orbitals can be hydrogen-like or Gaussian functions. The basic method within the molecular orbital approach is the Hartree–Fock (HF) method, an ab initio approach based on assuming that φe,N(l) is given by a Slater determinant, which leads to a set of N coupled monoelectronic Schrödinger equations. In these equations, the electron-electron repulsion interactions involved in h^e are accounted for by a mean field interaction (i.e., the averaged action of the N-1 remaining electrons), thus neglecting electron correlation. In those cases where large molecules are considered and the HF method becomes inoperative, one can apply the so-called semiempirical molecular quantum-mechanical methods (e.g., the Hückel and extended Hückel methods or the Pariser–Parr–Pople method), where a simple Hamiltonian plus a set of fitting parameters are used to adjust the experimental data. On the other hand, within the ab initio stream, there are different routes to tackle the problem of the electron correlation, and therefore to improve the HF results, such as the post-Hartree–Fock methods (e.g., configuration interaction, coupled cluster or Møller–Plesset), the multiconfigurational self-consistent field or the multireference configuration interaction.
Partial-wave decomposition of the one-electron properties of the LiH molecule computed with explicitly correlated basis sets
Published in Molecular Physics, 2022
Krzysztof Strasburger, Jerzy Cioslowski
In the conventional methods of quantum chemistry, such as the configuration interaction (CI), that do not suffer from these limitations, the electronic wavefunction is expressed in terms of the Slater determinants built from one-electron functions (spinorbitals). Since reaching the energy error below 1 mhartree (which is often referred to as ‘chemical accuracy’) with those methods is very costly, procedures for extrapolation to complete-basis-set (CBS) limit have been developed. Such extrapolation is usually based upon the assumption that the energy increments due to all the atom-centred basis functions with a given angular momentum quantum number l follow the asymptotics of for sufficiently large l. Initially, this asymptotics has been rigorously proven only for the ground state of the helium atom and its isoelectronic ions [7–11]. However, taking advantage of the recently discovered off-diagonal cusp in the 1-electron reduced density matrix [12], extended proof has been subsequently formulated for all the natural-parity states of atoms, and also for the states of linear molecules [13].
Photoinduced relaxation dynamics of nitrogen-capped silicon nanoclusters: a TD-DFT study
Published in Molecular Physics, 2018
Xiang-Yang Liu, Xiao-Ying Xie, Wei-Hai Fang, Ganglong Cui
In the framework of TD-DFT, the total electronic wave function of an electronically excited state is approximately written as linear combinations of many singly excited Slater determinants where wKia stands for the linear combination coefficient of the Slater determinant ψai for the K electronic state. The Slater determinant is constructed through the electron creation and annihilation operations on the ground-state determinant ψ0. In this situation, nonadiabatic coupling term between states K and J, namely , can be further written as
Autocorrelation of electronic wave-functions: a new approach for describing the evolution of electronic structure in the course of dynamics
Published in Molecular Physics, 2018
Barak Hirshberg, R. Benny Gerber, Anna I. Krylov
For simplicity, here we consider wave-functions represented by a single Slater determinant, i.e. as in the Hartree–Fock approximation or Kohn–Sham density functional theory (DFT) [41]. The formalism can be generalised by using several different strategies, i.e. one can exploit techniques similar to those used to compute overlap between many-body wave-functions in surface-hopping simulations [34] or for analysing the differences between wave-functions computed using different ab initio approaches [31,32]. One can also maintain single-determinantal representation, either by using natural orbitals (which afford compact representation of correlated wave functions with a small number of determinants [42]), or by mapping correlated density to a single Kohn–Sham-like determinant.