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Register a new userPotential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
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In this work we show the advantages of using the Coulomb-hole plus screened-exchange (COHSEX) approach in the calculation of potential energy surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and partial self-consistent $GW$ approaches, such as eigenvalue-self-consistent $GW$ and quasi-particle self-consistent $GW$, the COHSEX approach yields smooth potential energy surfaces without irregularities and discontinuities. Moreover, we show that the ground-state potential energy surfaces (PES) obtained from the Bethe-Salpeter equation, within the adiabatic connection fluctuation dissipation theorem, built with quasi-particle energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance. When self-consistent COHSEX quasi-particle energies and orbitals are used to build the BSE equation the results become independent of the starting point. We show that self-consistency worsens the total energies but improves the equilibrium distances with respect to BSE@COHSEX@HF. This is mainly due to changes in the screening inside the BSE.
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We report unphysical irregularities and discontinuities in some key experimentally-measurable quantities computed within the GW approximation of many-body perturbation theory applied to molecular systems. In particular, we show that the solution obtained with partially self-consistent GW schemes depends on the algorithm one uses to solve self-consistently the quasi-particle (QP) equation. The main observation of the present study is that each branch of the self-energy is associated with a distinct QP solution, and that each switch between solutions implies a significant discontinuity in the quasiparticle energy as a function of the internuclear distance. Moreover, we clearly observe ripple effects, i.e., a discontinuity in one of the QP energies induces (smaller) discontinuities in the other QP energies. Going from one branch to another implies a transfer of weight between two solutions of the QP equation. The case of occupied, virtual and frontier orbitals are separately discussed on distinct diatomics. In particular, we show that multisolution behavior in frontier orbitals is more likely if the HOMO-LUMO gap is small.
We obtain the quantized momentum eigenvalues, $P_n$, together with space-like coherent eigenstates for the space-like counterpart of the Schru007fodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They can achieve a sub-1 kcal/mol accuracy with respect to reference data and can be used in studies of chemical dynamics. Their construction and a few typical examples are briefly summarized in the present contribution.
We consider the energy spectrum of emitted electrons in $beta$-decay. Exact Coulomb Dirac wave functions describing the $beta$-electron in the Coulomb field of the daughter nucleus are used. Further, the improved wave functions which include the screening of the Coulomb field due to the atomic electron cloud are also used. Thus, the interaction between the $beta$-electron and the field due to the daughter atom is treated within a nonperturbative approach. Are shown the modifications due to the screening on the $beta$ spectra and shown that those effects are very important. In addition, are addressed the contributions to the $beta$ spectra due to the exchange terms and shown that the corresponding effects can be substantial. Higher orders arising from the multipole expansion are considered. A comparison of the theoretical results obtained in this work has been made with recent experimental data and a very good agreement was observed.
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, and neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.
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