The access to analytical second derivatives of Time-Dependent Density Functional Theory (TD-DFT) excitation energies [1] is a required step toward a number of interesting applications. One of the most notable among these application is the accurate simulation of vibrationally resolved electronic spectra using potential energy surfaces for both the ground and excited state which include anharmonic corrections [2]. From the formal point of view TD-DFT second derivatives provide a general framework which includes TD-DFT in the Tamm-Dancoff approximation (TD-DFT-TDA), Time-Dependent Hartree-Fock (TD-HF) and Configuration Interaction with Single excitations (CIS).In this contribution we describe a general, robust and efficient implementation of analytical TD-DFT second derivatives. The main elements of generality are the applicability to both closed and open-shell systems, the proper inclusion of the effect of frozen occupied and frozen virtual orbitals and the accurate simulation of solvation effects using the Polarizable Continuum Model (PCM) in its most general Integral Equation Formalism (IEF) version [3]. We discuss the issues related to the robust evaluation of the exchange-correlation functional fourth derivatives which are required by the formalism. In particular we focus on the limits imposed by standard double-precision arithmetic and the techniques used to validate a double-precision implementation by means of tools for arbitrary precision computations. Finally, we discuss efficiency considerations by showing the advantages of using integral-direct methods as much as possible and the rearrangements required to minimize both the number of contractions with integrals and integral derivatives, and the work involved in the transformation of various quantities between atomic and molecular orbital basis.[1] A. Liu, W. Liang, J. Chem. Phys., 2011, 135, 184111.[2] V. Barone, J. Chem. Phys. 2005, 122, 014108[3] F. Lipparini, G. Scalmani, B. Mennucci, E. Cances, M. Caricato, M.J. Frisch, J. Chem. Phys, 2010, 133, 014106.

On the analytical second derivatives of the excited state energy in the framework of Time-Dependent Density Functional Theory

248th National Meeting (2014)

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