Functionalities of ESCF and EGRAD

ESCF and EGRAD are designed as efficient tools for response and excited state calculations on large molecules. ESCF serves to compute the following properties for HF and KS reference states:

• Eigenvalues of the electronic Hessian (stability analysis)
• Frequency-dependent polarizabilities and optical rotations
• Vertical electronic excitation energies
• Transition moments, oscillator and rotatory strengths of electronic excitations
  $\Rightarrow$ mathend000# UV-VIS and CD spectra

Spin-restricted closed-shell and spin-unrestricted ground states (except for stability analysis) are supported. The RI-$J$ mathend000# approximation in conjunction with LDA and GGA functionals is implemented for all properties. Excitation energies and transition moments can be computed either within the full time-dependent HF (TDHF) or time-dependent DFT (TDDFT) formalisms or within the Tamm-Dancoff approximation (TDA).

Excited state first order properties can be evaluated analytically using EGRAD. They include:

• Gradients of the excited state energy with respect to nuclear positions
  $\Rightarrow$ mathend000# Excited state equilibrium structures (JOBEX), adiabatic excitation energies, emission spectra
• Exited state densities $\Rightarrow$ mathend000# Charge moments, population analysis
• Excited state force constants by numerical differentiation of gradients (using the script NUMFORCE)

Moreover, analytical gradients of static and frequency-dependent polarizabilities are available from EGRAD. Together with vibrational normal modes from the AOFORCE or NUMFORCE they are used to calculate vibrational Raman intensities.

Again, ground states may be spin-restricted closed-shell or spin-unrestricted, RI-$J$ mathend000# is available, and either full TDDFT/TDHF or the TDA can be used. For further details we refer to a recent review [71].