7.10. CP-SCF Options

The coupled perturbed self-consistent field (CP-SCF) equations have to be solved in many cases, such as when second derivative properties (e.g. vibrational frequencies, polarizability, NMR shielding, indirect spin-spin coupling, hyperfine coupling, g-tensor) or the MP2 relaxed density (in this case they are referred to as Z-vector equations) are calculated. They are a set of linear equations generally expressed as

\[\mathbf A \mathbf U^x = \mathbf B^x,\]

where \(\mathbf U^x\) is the vector of solutions for perturbation \(x\), the right-hand side (RHS) matrix \(\mathbf B^x\) is perturbation-specific and the left-hand side (LHS) matrix \(\mathbf A\) is perturbation-independent and contains, among other terms, the two-electron repulsion integrals \(\left(ij\vert ab\right)\) and \(\left(ia\vert jb\right)\). The equations are solved iteratively and the LHS is reassembled at every step, while the RHS does not change. The generation and transformation of the two-electron integrals are therefore the most time-consuming parts of the CP-SCF solution.

The ORCA module which solves these equations accepts several options given below with their default values:

%method
  Z_Solver     Pople # (default) Use the Pople algorithm to solve the equations
               DIIS  # Use the DIIS algorithm
               CG    # Use the conjugate gradient algorithm
  Z_Tol        1e-3  # Convergence tolerance for the residual norm. 
                     # Default is 1e-5 for VeryTightOpt
                     # and varies from 3e-3 to 3e-6 from LooseSCF to ExtremeSCF
  Z_MaxIter    128   # Maximum number of iterations
  Z_MaxDIIS    12    # Maximum number of DIIS vectors
  Z_Shift      0.3   # Level shift for DIIS
  Z_GridXC     1     # XC angular grid used for the LHS
  Z_IntAccXC   3.467 # XC radial grid accuracy used for the LHS
  Z_GridX      1     # COSX angular grid used for the LHS
  Z_IntAccX    3.067 # COSX radial grid accuracy used for the LHS
  Z_GridX_RHS  2     # COSX grid used for the RHS of MP2 Z-vector eqs (see below)
  Z_COSX_Alg   0     # (default) choose the best COSX algorithm automatically
               1     # better prescreening, more efficient for few densities
               2     # uses more memory, more efficient for many densities
end

Since ORCA 6, the same settings are used for all electric response property calculations as well as for CIS/TD-DFT gradients and relaxed densities. For convenience, the keywords in the %elprop input block are still available but they modify the same internal variables as those in %method. For magnetic response properties, the solver and convergence tolerance are set separately in %eprnmr, because the convergence behavior of the magnetic response CP-SCF equations is sometimes different.

%elprop
  Solver     # Alias, see: %method Z_Solver
  Tol        # Alias, see: %method Z_Tol
  MaxIter    # Alias, see: %method Z_MaxIter
  MaxDIIS    # Alias, see: %method Z_MaxDIIS
  LevelShift # Alias, see: %method Z_Shift
end

%eprnmr
  Solver     # Solver for magnetic response, see options at: %method Z_Solver
  Tol        # Convergence tolerance for magnetic response
  MaxIter    # Alias, see: %method Z_MaxIter
  MaxDIIS    # Alias, see: %method Z_MaxDIIS
  LevelShift # Alias, see: %method Z_Shift
end

The keywords Z_GridX and Z_IntAccX are applicable if the RIJCOSX approximation is chosen for the treatment of two-electron integrals. They determine the angular and radial COSX integration grids, as discussed in section Changing TD-DFT, CP-SCF and Hessian grids. Analogously, the keywords Z_Grid and Z_IntAcc determine the integration grid for DFT XC functionals.

Integrals on the RHS are evaluated differently for different perturbations - refer to sections Using the RI Approximation for Hartree-Fock and Hybrid DFT (RIJCOSX), EPR and NMR properties, RIJCOSX-RI-MP2 Gradients, and MP2 and RI-MP2 Second Derivatives and RI-MP2 and Double-Hybrid DFT Response Properties for SCF-level gradients, EPR/NMR calculations with GIAOs, MP2 gradients, and MP2 second derivatives, respectively. For MP2 Z-vector equations, the RIJCOSX Fock-response terms in the RHS are evaluated with the COSX grid specified by Z_GridX_RHS. Note that it is used differently to Z_GridX: instead, it selects one of the three grids used in the SCF (see Sections Using the RI Approximation for Hartree-Fock and Hybrid DFT (RIJCOSX), COSX Grid and Convergence Issues, and Details on the numerical integration grids for details) and it is not recommended to change the default value of 2.

If the RIJONX or RIJK approximation is used in the SCF, the same is also employed in the CP-SCF. Note, however, that the RI-K approximation is not efficient for these terms.