Pros and Cons of the Bethe–Salpeter Formalism for Ground-State Energies

Abstract

The combination of the many-body Green's function GW approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density-functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems. The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuationdissipation theorem (ACFDT). Here, we study the topology of the ground-state potential energy surfaces (PES) of several diatomic molecules near their equilibrium bond length. Thanks to comparisons with state-of-art computational approaches (CC3), we show that ACFDT@BSE is surprisingly accurate, and can even compete with lower-order coupled cluster methods (CC2 and CCSD) in terms of total energies and equilibrium bond distances for the considered systems. However, we sometimes observe unphysical irregularities on the groundstate PES in relation with difficulties in the identification of a few GW quasiparticle energies.

Spin-Conserved and Spin-Flip Optical Excitations from the Bethe–Salpeter Equation Formalism

“… 171 − 174 Besides this, G 0 W 0 @UHF and ev GW @UHF yield similar quasiparticle energies, while G 0 W 0 allows us to avoid rather laborious iterations as well as the significant additional computational effort of ev GW . 44 , 69 , 169 In the following, all linear response calculations are performed within the TDA to ensure consistency between the spin-conserved and spin-flip results. Finally, the infinitesimal η is set to 100 meV for all calculations.…”

Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism

“…is the expectation value of Ŝ 2 for the reference configuration, the first term corresponding to the exact value of Ŝ 2 , and (p σ |q σ ) = φ p σ (r)φ q σ (r)dr (44) are overlap integrals between spin-up and spin-down orbitals.…”

“…97 for spin-conserved and spin-flip excitations, and are functions of the vectors X m and Y m as well as the orbital overlaps defined in Eq. (44).…”

“…This is left for future work. However, it is worth mentioning that, for the present (small) molecular systems, Hartee-Fock is usually a good starting point, 44,69,171 although improvements could certainly be obtained with starting orbitals and energies computed with, for example, optimally-tuned range-separated hybrid functionals. [172][173][174][175] Besides, G 0 W 0 @UHF and evGW@UHF yield similar quasiparticle energies, while G 0 W 0 allows us to avoid rather laborious iterations as well as the significant additional computational effort of evGW.…”

“…11 Originally developed in the framework of nuclear physics, 13 and popularized in condensed-matter physics, [14][15][16] one of the new emerging method in the computational chemistry landscape is the Bethe-Salpeter equation (BSE) formalism 10,13,17-22 a) Electronic mail: loos@irsamc.ups-tlse.fr from many-body perturbation theory 23,24 which, based on an underlying GW calculation to compute accurate charged excitations (i.e., ionization potentials and electron affinities) and the dynamically-screened Coulomb potential, 25,26 is able to provide accurate optical (i.e., neutral) excitations for molecular systems at a rather modest computational cost. 10,22,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] Most of BSE implementations rely on the so-called static approximation, 22,39,41,45 which approximates the dynamical (i.e., frequency-dependent) BSE kernel by its static limit. Like adiabatic time-dependent density-functional theory (TD-DFT), [46][47][48][49] the static BSE formalism is plagued by the lack of double (and higher) excitations, which are, for example, ubiquitous in conjugated molecules like polyenes [50][51]…”