Hartree-Fock and DFT Calculations

DSCF and GRAD are modules for energy and gradient calculations at the Hartree-Fock (HF) and density functional theory (DFT) levels which use an efficient semi-direct SCF algorithm. Calculation of the Coulomb and HF exchange terms is based on the conventional method employing four-center two-electron repulsion integrals (ERI's). These modules should be used for HF and DFT calculations with exchange-correlation functionals including HF exchange contribution, e.g. B3-LYP. All functionalities are implemented for closed-shell RHF and open-shell UHF reference wavefunctions.

The most important special features of the DSCF and GRAD modules are:

• Selective storage of the most time consuming and frequently used integrals. The integral storage is controlled by two threshold parameters, $thize and $thime, related to integral size and computational cost.
• Efficient convergence acceleration techniques for energy calculations. They include standard methods for convergence acceleration (DIIS), which reduce the number of SCF iterations needed as well as methods to reduce the effort within each iteration when the calculation is almost converged (integral prescreening and differential density scheme).

RIDFT and RDGRAD are modules for very efficient calculation of energy and gradient at the DFT level using pure functionals, i.e. without the HF exchange term [41]. Both programs employ the Resolution of the Identity approach for computing the electronic Coulomb interaction (RI-$J$). This approach expands the molecular electron density in a set of atom-centered auxiliary functions, leading to expressions involving three-center ERI's only. This usually leads to a more than a tenfold speedup compared to the conventional method based on four-center ERI's (for example the DSCF module).

The most important special features of the RIDFT and RDGRAD modules are:

• A very efficient semi-core algorithm for energy calculation. The most expensive three-center integrals are kept in memory which significantly reduces the computational time for small and middle sized molecules. The amount of stored integrals is controlled by simply specifying the amount of free memory using the keyword $ricore.
• Multipole accelerated RI for Coulomb (MARI-J) linear scaling ($O(N)$) method for large molecules. It significantly reduces calculation times for molecules with more than 1000-2000 basis functions.

All algorithms implemented in DSCF, GRAD, RIDFT, and RDGRAD modules can exploit molecular symmetry for all finite point groups. Typically, the CPU time is proportional to $1/{N_G}$, where $N_G$ is the order of the nuclear exchange group. Another important feature is a parallel implementation using the MPI interface.

Additionally DSCF and RIDFT modules include the following common features:

• An UHF implementation [42] with automatic generation of optimal start vectors by solving the HF instability equations [43] in the AO basis (see the keyword $scfinstab for detailed information).
• Occupation number optimization using (pseudo-Fermi) thermal smearing.

RI-techniques can also be used for the Hartree-Fock exchange part of the Fock matrix (RI-HF). This is done by the ridft-module, if the keyword $rik is found in the control file. In this case ridft performs a Hartree-Fock-SCF calculation using the RI- approximation for both $J$ and $K$, if suitable auxiliary basis sets (which differ from that used for fitting of the Coulomb part only) are specified. This is efficient only for comparably large basis sets like TZVPP, cc-pVTZ and larger.