Constraint-based wave vector and frequency dependent exchange-correlation kernel of the uniform electron gas

Abstract

According to time-dependent density functional theory, the exact exchange-correlation kernel f xc (n, q, ω) for wave vector q and frequency ω determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n = 3/(4π r 3 s ). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static (ω = 0) limit, we modify the model of Constantin and Pitarke to recover at small q the known second-order gradient expansion, and to correct its approach to the large q limit. For all ω at q = 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex ω. Scaling relations are identified. We then combine these ingredients, damping out the ω dependence at large q. Away from q = 0 and ω = 0, the correlation contribution to the kernel becomes dominant over exchange, even at r s = 4. The resulting correlation energies for 1 r s 10 from integration over imaginary ω are essentially exact. The plasmon pole of the density response function is found by analytic continuation of f xc to ω just below the real axis, and the resulting plasmon lifetime at r s = 4 is found for q < k F . A static charge-density wave is found for r s > 69, and shown to be associated with softening of the plasmon mode.

Accurate total energies from the adiabatic-connection fluctuation-dissipation theorem

“…neglecting the frequency dependence in the exact xc kernel, but otherwise retaining its nonlocal spatial structure when solving the Dyson equation of linear response time-dependent DFT (this was also the case for the HEG in Refs. [52,93]). The exact kernel f xc [n] is shown to exhibit little change within the ω interval that contains the majority of the ground-state correlation energy.…”

First-principles wavevector- and frequency-dependent exchange-correlation kernel for jellium at all densities

“…The root finding algorithm stopped either when no roots could be found, or when [6] Re ω p (q) = 1 2…”

“…This is more rigorous than the procedure used in Ref. [6], which used a Taylor series about u 0 , and varied u and v. That procedure assumes the low-order Taylor series about u 0 also has validity for u = u 0 , which cannot be the case generally.…”

“…Figure 4 of Ref. [6] shows that h adequately models this frequency dependence, however h can be improved. We propose a simple modification to the MCP07 h(X) function…”

“…In this work, we will use Hartree atomic units, = m e = e 2 = 1, for all quantities and numerical coefficients, unless noted otherwise. The modified Constantin-Pitarke 2007 (MCP07) [6] kernel is constructed as an interpolation between static f xc (q, ω = 0) and long-wavelength dynamic f xc (q = 0, ω) limits,…”