Driven by the interest in frequency-dependent molecular properties, theoretical spectroscopy and intermolecular interactions, the development of ab initio, in particular coupled-cluster, methods for the theoretical description of the interaction of molecules with oscillating (i.e. time-dependent) fields has become a central topic of our research. The basis of this work is a modern formulation of response theory based on a time-dependent Lagrangian, which provides a general handle for the description of a physical system interacting with time-dependent external fields in approximate wavefunction models. Most our work in this field has been carried out in collaboration with group of Poul Jørgensen at Århus University and other developers of the Dalton program and is included in the coupled-cluster response code which is part of Dalton. Our work in this field has been concerned with

• the implementation of the approximate coupled-cluster singles, doubles and triples model CC3 for frequency-dependent first and second hyperpolarizabilities, which allows now highly accurate calculations of these nonlinear optical properties

  • Frequency-dependent polarizabilities

  • Oscillator strengths

  • Hyperpolarizabilities

  • Cauchy Moments

• the development of a coupled-cluster response program which employs an explicitly correlated R12 or F12 ansatz for the wavefunction to increase the accuracy and/or reduce the computational costs for such calculations. This work was carried out in collaboration with Wim Klopper and coworkers (Institute of Physical Chemistry, University of Karlsruhe and Institute of Nanotechnology, Forschungszentrum Kalrsruhe) as a project of the DFG priority program 1145 "Modern and universal first-principles methods for many-electron systems in chemistry and physics".

  • The CC2-R12 model for vertical excitation energies

  • Frequency-dependent nonlinear optical properties with CCSD(R12)

  • Structures and harmonic vibrational frequencies for excited states with CCSD(R12) and CCSD(F12)

  • Highly accurate CCSD(R12) and CCSD(F12) optical response properties

  • A review on: Recent Advances in Explicitly Correlated Coupled-Cluster Response Theory for Excited States and Optical Properties

During the last fifteen years, an efficient formulation of ADC(2), a propagator method which is based on the same ground-state wavefunction as MP2, has been developed in our group. The ADC(2) method, in combination with resolution-of-identity approximation, provides the same accuracy for excitation energies as RI-CC2, but has about four times lower computational costs for calculation of gradients. Moreover, thanks to its compactness and Hermetian formulation, nowadays RI-ADC(2) turns into the single-reference method of choice for studying excited state dynamics of small and medium sized chromophores if its computational cost is affordable.

• The excitation energies and gradients for CIS(D∞) and ADC(2)

In recent years and in an undergoing (collaborative) project (with group of Ove Christiansen and Jacob Kongsted), the ADC(2) and CC2 methods have been coupled with a post-SCF formulation of QM/MM polarizable embedding and the continuum conductor-like solvation model (COSMO) approaches to simulate photo-isomerization mechanisms and linear and non-linear optical spectra of chromophores in complex molecular environments, e.g. solvents, bio- and supermolecular complexes, etc.

• PERI-CC2: A Polarizable Embedded RI-CC2 Method

• Two-Photon Absorption PERI-CC2

• Algebraic Diagrammatic Construction for the Polarization Propagator PE-ADC(2)

• COSMO-RI-ADC(2) excitation energies and excited state gradients

Exemplarily, in a collaboration with the physical chemistry group of Patrick Nürnberger, these methods are combined to elucidate the photochemistry of the linear triazene compound, berenil, and its ultrafast fluorescent up-conversion and transient absorption spectra.

• Ultrafast Dynamics of a Triazene