Time-dependent density functional (TDDFT) is an extension of density functional theory to time-dependent potentials. TDDFT is a computationally more feasible approximation to compute excitation energies, compared to approaches based on many-body techniques. The accuracy of TDDFT is restricted by the limitations of the exchange-correlation kernels beyond the Random Phase Approximation that are commonly in use. Dynamical contributions can be improved when frequency-dependence is included, but in addition to frequency-dependence a sophisticated spatial nonlocality of the kernel is also required. In this work a dynamic model exchange-correlation kernel, the MCP07 based on exact constraints, is introduced. The dynamic MCP07 exchange-correlation kernel predicts a static charge-density wave at low densities and delivers excellent quality correlation energies for the ground state, while it predicts a plausible finite plasmon lifetime at all wavevectors for the first time within TDDFT.<br/>The attractive features of the dynamic MCP07 kernel can be further exploited for gaining more insight about strong correlation. Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin-densities or total densities. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge density waves at non-zero wavevector. Familiar examples are the unobservable but revealing symmetry breaking in stretched H<sub>2 </sub>and the observable symmetry breaking in antiferromagnetic solids. The example discussed here is the static charge-density wave/Wigner crystal phase of a low density ( rs~=69) jellium. TDDFT is used to show quantitatively that the static charge density wave is a soft plasmon-like excitation.<br/>The MCP07 kernel has a potential impact on optical spectroscopy. Our work reveals the large role of the frequency model for the optical limit. Work along this direction will be also discussed.

Multiple role of frequency-dependent model kernels beyond the random phase approximation: Static correlation, charge density wave and optical absorption

ACS Spring 2022

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