Gauge invariance is a fundamental symmetry connectedto chargeconservation and is widely accepted as indispensable for any electronicstructure method. Hence, the gauge variance of the time-dependentkinetic energy density & tau; used in many meta-generalized gradientapproximations (MGGAs) to the exchange-correlation (XC) functionalpresents a major obstacle for applying MGGAs within time-dependentdensity functional theory (TDDFT). Replacing & tau; by the gauge-invariantgeneralized kinetic energy density & tau; significantly improvesthe accuracy of various functionals for vertical excitation energies[R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependenceof the resulting current-MGGAs (cMGGAs) on the paramagnetic currentdensity gives rise to new exchange-correlation kernels and hyper-kernelsignored in previous implementations of quadratic and higher-orderresponse properties. Here we report the first implementation of cMGGAsand hybrid cMGGAs for excited-state gradients and dipole moments,as well as an extension to quadratic response properties includingdynamic hyperpolarizabilities and two-photon absorption cross sections.In the first comprehensive benchmark study of MGGAs and cMGGAs fortwo-photon absorption cross sections, the M06-2X functional is foundto be superior to the GGA hybrid PBE0. Additionally, two case studiesfrom the literature for the practical prediction of nonlinear opticalproperties are revisited and potential advantages of hybrid (c)-MGGAscompared to hybrid GGAs are discussed. The effect of restoring gaugeinvariance varies depending on the employed MGGA functional, the typeof excitation, and the property under investigation: While some individualexcited-state equilibrium structures are significantly affected, onaverage, these changes result in marginal improvements when comparedagainst high-level reference data. Although the gauge-variant MGGAquadratic response properties are generally close to their gauge-invariantcounterparts, the resulting errors are not bounded and significantlyexceed typical method errors in some of the cases studied. Despitethe limited effects seen in benchmark studies, gauge-invariant implementationsof cMGGAs for excited-state properties are desirable from a fundamentalperspective, entail little additional computational cost, and arenecessary for response properties consistent with cMGGA linear responsecalculations such as excitation energies.
