Density functional theory (DFT) owes its success primarily to affording high efficiency in the calculations, combined with quite reasonable accuracy. However, existing functionals show larger errors at geometries further away from the equlibrium geometry, particularly towards bond dissociation. Complete ground state energy surfaces are still a challenge.Excited state surfaces are even much more problematic: although time-dependent density functional theory (TDDFT) in its adiabatic approximation has enabled vertical excitation energy calculations at equilibrium geometry with quite decent accuracy, it completely fails at elongated bond distances (e.g. twice equilibrium bond distance) in the following cases: 1) single excitation from bonding to corresponding antibonding orbital (erroneously going to zero) [1]; 2) excited states with considerable double excitation character [2] (which is the case in most excited states at long bond distances); 3) charge transfer excitations. Adiabatic TDDFT is not reliable for excited state surfaces and cannot be used for e.g. dynamics on excited state surfaces. Density MATRIX functional theory, using the one-particle reduced density matrix (1RDM) is in principle able to overcome these deficiencies. We will present the pysical concepts behind 1RDMFT [3], which employs functionals of both the natural orbitals (NOs) and occupation numbers (ONs). We will show that both ground state surfaces and excited state surfaces (with adiabatic TD-1RDMFT) can become nearly perfect if an accurate functional is available [4,5].Linear response theory applied to the one-particle reduced density matrix (1RDM) affords a formalism, that, within the adiabatic approximation, yields the excitation energies with a single diagonalization of the (inverse) density matrix - density matrix response matrix. [3] We will demonstrate that the size of this diagonalization problem can be reduced to only slightly larger than the one of TDDFT, while still yielding essentially accurate solutions for all the failure cases of TDDFT mentioned above. [4] 1. K. J. H. Giesbertz, E. J. Baerends, Chem. Phys. Lett. 461  (2008) 3382. K. J. H. Giesbertz, E. J. Baerends, O. V. Gritsenko, Phys. Rev. Lett. 101  (2008) 0330043. M. A. Buijse, E. J. Baerends, Molec. Phys. 100  (2002) 4014. K. J. H. Giesbertz, O. V. Gritsenko and E. J. Baerends, Phys. Rev. Lett. 105  (2010) 013002; J. Chem. Phys. 133  (2010) 1741195. K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 2012 , 136, 094104.

Beyond DFT: Density MATRIX functional theory for ground state and excited state energy surfaces

248th National Meeting (2014)

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