arXiv subjects

Evert Jan Baerends

Publications and source records attributed to Evert Jan Baerends.

6 recordsLinked to original sources

arXiv2022

Reply to Comment on "Self-Consistent-Field Method for Correlated Many-Electron Systems with an Entropic Cumulant Energy", arXiv2202.05532v1

Recently we proposed an information entropy based method for electronic structure calculations within the density-matrix functional theory(DMFT) (Phys. Rev. Lett. 128, 013001), dubbed as $i$-DMFT. Comments have been raised regarding the accuracy of the one-particle density-matrix compared to that from the wave function, and the universality of the functional. We address these questions and the problematic case of HeH$^+$.

quant-ph↗

arXiv2022

Chemical potential, derivative discontinuity, fractional electrons, jump of the Kohn-Sham potential, atoms as thermodynamic open systems, and other (mis)conceptions of the density functional theory of electrons in molecules

Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier $μ= \partial E/\partial N$ in the Euler-Lagrange variational equation for the ground state density as the chemical potential of the electrons. We first discuss why the Lagrange multiplier in this case is an arbitrary constant and therefore cannot be a physical characteristic of an atom or molecule. The switching of the energy derivative ("chemical potential") from $-I$ to $-A$ when the electron number crosses the integer, called integer discontinuity or derivative discontinuity, is not physical but only occurs when the nonphysical noninteger electron systems and the corresponding energy and derivative $\partial E/\partial N$ are chosen in a specific discontinuous way. The question is discussed whether in fact the thermodynamical concept of a chemical potential can be defined for the electrons in such few-electron systems as atoms and molecules. The conclusion is that such systems lack important characteristics of thermodynamic systems and do not afford the definition of a chemical potential. They also cannot be considered as analogues of the open systems of thermodynamics that can exchange particles with an environment (a particles bath or other members of a Gibbsian ensemble). Thermodynamical (statistical mechanical) concepts like chemical potential, open systems, grand canonical ensemble etc. are not applicable to a few electron system like an atom or molecule. A number of topics in DFT are critically reviewed in the light of these findings: jumps in the Kohn-Sham potential when crossing an integer number of electrons, the band gap problem, the deviation-from-straight-lines error, the role of ensembles in DFT.

physics.chem-ph↗

arXiv2022

Secondary kinetic peak in the Kohn-Sham potential and its connection to the response step

We consider a prototypical 1D model Hamiltonian for a stretched heteronuclear molecule and construct individual components of the corresponding KS potential, namely: the kinetic, the N - 1, and the conditional potentials. These components show very special features, such as peaks and steps, in regions where the density is drastically low. Some of these features are quite well known, whereas others, such as a secondary peak in the kinetic potential or a second bump in the conditional potential, are less or not known at all. We discuss these features building on the analytical model treated in J. Chem. Theory Comput. 14, 4151 (2018). In particular, we provide an explanation for the underlying mechanism which determines the appearance of both peaks in the kinetic potential and elucidate why these peaks delineate the region over which the plateau structure, due to the N - 1 potential, stretches. We assess the validity of the Heitler-London Ansatz at large but finite internuclear distance, showing that, if optimal orbitals are used, this model is an excellent approximation to the exact wavefunction. Notably, we find that the second natural orbital presents an extra node very far out on the side of the more electronegative atom.

physics.chem-ph↗

arXiv2019

On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem

The relation between the derivative of the energy with respect to occupation number and the orbital energy, $\partial E/\partial n_i = ε_i$, was first introduced by Slater for approximate total energy expressions such as Hartree-Fock and exchange-only LDA, and his derivation holds for hybrid functionals as well. We argue that Janak's extension of this relation to (exact) Kohn-Sham density functional theory is not valid. The reason is the nonexistence of systems with noninteger electron number, and therefore of the derivative of the total energy with respect to electron number, $\partial E/\partial N$. How to handle the lack of a defined derivative $\partial E/\partial N$ at the integer point, is demonstrated using the Lagrange multiplier technique to enforce constraints. The well-known straight-line behavior of the energy as derived from statistical physical considerations [J.P. Perdew, R. G. Parr, M. Levy and J.J. Balduz, Phys. Rev. Lett. 49, 1691 (1982)] for the average energy of a molecule in a macroscopic sample ("dilute gas") as a function of average electron number is not a property of a single molecule at $T=0$. One may choose to represent the energy of a molecule in the nonphysical domain of noninteger densities by a straight-line functional, but the arbitrariness of this choice precludes the drawing of physical conclusions from it.

physics.chem-ph↗

arXiv2018

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

It is known that the asymptotic decay of the electron density outside a molecule is informative about its first ionization potential. 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 [Mol. Phys. 114 (2016) 1086]. 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 etxernal 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.

physics.chem-ph↗

arXiv2014

Response calculations based on an independent particle system with the exact one-particle density matrix: polarizabilities

Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [Phys. Rev. Lett. 105, 013002 (2010), J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit ($ω\to0$), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H$_2$ and compare the performance of two different two-electron functionals: the phase-including Löwdin-Shull functional and the density matrix form of the Löwdin-Shull functional.

physics.chem-ph↗