Orbital occupations: electronic configuration, excited states

With the key OCCUPATIONS you can specify in detail the assignment of electrons to MOs

OCCUPATIONS Options
  {irrep orbitalnumbers
  irrep orbitalnumbers
  ...
End }

Occupations

is a general key: it has an argument or a data block. If you want to use both, the continuation code ( &) must be appended at the end of the argument.

Options

May contain Keeporbitals, Smearq, Freeze, or Steep:

Keeporbitals=NKeep

Until SCF cycle Nkeep electrons are assigned to MOs according to the Aufbau principle, using at each cycle the then current orbital energies of the MOs. Thereafter the KeepOrbitals feature is applied. As soon as this is activated the program will on successive SCF cycles assign electrons to the MOs that maximally resemble - in spatial form - those that were occupied in a 'reference cycle number'. The default for Nkeep is 20, except:
a) When orbital occupations for MOs are specified explicitly in the data block of the occupations key, these apply throughout.
b) In a Create run fixed occupations are derived from a database in the program.
c) When electron smearing is explicitly turned on by the user (see the Smearq option below) Nkeep is by default 1,000,000 so the program will 'never' compare the spatial forms of MOs to determine the occupation numbers.
The 'reference cycle number' is by default the previous cycle, which will suppress jumps in the spatial occupations during the SCF development while at the other hand allowing the system to let the more-or-less-frozen configuration relax to self-consistency.

Freeze

Occurrence of this word in the option list specifies that the 'reference cycle number' will be the cycle number on which the KeepOrbitals feature is activated: during all subsequent SCF cycles the program will assign electrons to MOs that resemble the MOs of that specific SCF cycle. This may be used when the MOs of that cycle are already reasonably close to the final ones, and it will suppress unwanted step-by-step charge-transfers from occupied to empty orbitals that are very close in energy. By default this option is not active.

Smearq=Smear1[,Smear2,Smear3,...,Smear10]

SmearN is half the energy width (in hartrees) over which electrons are smeared out over orbitals that lie around the fermi level and that are close in energy. Smearing is a trick that may help when the SCF has problems converging. One should be well aware that the physical meaning of a result obtained with smeared occupations is unclear (to express it mildly). It may be useful to get over a hurdle in a geometry optimization.
By default the initial smear parameter is zero (i.e.: smearing is not applied). It is turned on automatically by the program when SCF convergence is found to be problematic, but only in an optimization-type application (simple optimization, linear transit, transition state) when the geometry is not yet converged.
You can rigorously prohibit any smearing by specifying it explicitly with value zero. More generally: specifying the smear parameter makes the program to apply it always, but always with the input-specified value.
When a comma-delimited list of values is specified, after SCF has converged, the next value from the list is picked and the SCF is continued. This way one can specify a list of gradually decreasing values to get sort of annealing effect. NOTE: No spaces are allowed when specifying a list of values for Smearq.

Steep=Lambda[,Nmax]

The occupation number for each orbitals are updated according to steepest-descent method (Ref: F. W. Averill and G. S. Painter, Phys. Rev. B 46, 2498 (1992)). During an SCF cycle, the occupation number for each new orbital is initially determined by decomposing the old charge density with new orbitals. Then, the occupation numbers are modified so that the total energy of the system will decrease.
The Lambda parameter gives the coefficient for the charge transfer in 1/au unit. The second parameter, Nmax, is an additional limit for the amount of the charge transfer. Nmax would be useful for early steps of cycle when the Lambda parameter gives too large charge transfer. Too small Nmax results in irregular behavior in SCF convergence. In the case of difficult SCF convergence, you should make mixing and Lambda smaller. From our experience, Nmax=0.1 or 0.2 is usually OK.
This method should be used with turning off DIIS method (DIIS N=0), and the choice of the mixing parameter in SCF cycle is also important. This option is especially useful for systems with many quasi-degenerate orbitals around Fermi level. For instance, cluster models of surface systems usually suffer from dangling bonds and should be converged with this method. Note though that slow convergence is an intrinsic feature of this method so one should specify a large limit for the number of SCF cycles, say 500 or even 1000, depending on the cluster size.

irrep

The name of one of the irreducible representations (not a subspecies) of the point group of the system. See the Appendix for the irrep names as they are used in ADF.

orbitalnumbers

A series of one or more numbers: the occupation numbers for one-electron valence orbitals in that irrep. The orbitals are ordered according to their energy eigenvalue; higher states than those listed get an occupation number zero.

For degenerate representations such as the 2-dimensional E-representations or the 3-dimensional T-representations, you must give the total occupation, i.e. the sum over the partner representations; adf assigns each partner an occupation equal to the appropriate fraction of what appears here.

In an unrestricted calculation, two sequences of numbers must be specified for each irrep; the sequences are separated by a double slash (//). The first set of numbers is assigned to the spin-α orbitals, the second set to the spin-β orbitals. Note that this is not meaningful in an unrestricted Spin-Orbit coupled calculation using the (non-)collinear approximation, where one should use one sequence of occupation numbers for each irrep.

Notes about the occupations data block:

• When specifying electron configurations, all valence electrons in the calculation must be explicitly assigned to MOs
  and the block form of the OCCUPATIONS keyword must be used.
  In this context the concept valence electrons and hence valence orbitals is not necessarily identical
  to what you may normally assume to be the valence space of an atom or molecule.
  The meaning of valence is here strictly defined as whatever electrons are outside the frozen core.
  It depends therefore on the level of frozen core approximation applied in the calculation.
  This traces back to the Create runs in which the basic atoms were generated that are now used to build the molecule.
• When for some irrep there is a rather long list of occupation numbers, corresponding to
  consecutive fully occupied states, you can combine these numbers and enter their sum instead:
  adf knows the maximum occupation for an irrep, and when you put a larger number the program will split it up.
  For instance, if you give for the p-representation (in a single atom calculation):
  P 17 3
  adf will interpret this as
  P 6 6 5 3
  i.e. the occupation number 17 is interpreted as denoting two fully occupied p-shells and the remaining five
  electrons in the next higher shell.
  This example also illustrates how to specify an excited state: here we have defined a hole in the third p-shell.
• Fractional occupation numbers in input are allowed. For a discussion of the interpretation of
  fractional occupation numbers see [103]. The program even allows you (technically) to use a non-integer
  total number of electrons, whatever the physical meaning of such a calculation is.
• The data block of occupations is not parsed (see the section Interpretation of Input below).
  The program does not replace expressions by their value and it does not recognize constants or functions
  defined with the define key.
• In a Frequencies run the symmetry used internally in the program is nosym, irrespective of any Schönfliess
  symbol in the input file. As a consequence the program will recognize only the A representation
  (the only irrep in nosym), but not the representations belonging to the input point group symmetry.
  (The symmetry in the equilibrium geometry, defined by the input Schönfliess symbol, is used to enhance
  efficiency and stability in the construction of the matrix of Force constants).

Notes about the occupations options:

• When occupation numbers are explicitly defined via the block form of the OCCUPATIONS keyword,
  the Smearq option cannot be used.
• The aufbau principle does not determine or adjust the distribution of electrons over spin-α versus spin-β
  in an unrestricted calculation. This aspect is controlled by the key CHARGE and by any explicit occupations in
  the data block of occupations.
• When occupation numbers are not specified and no Smearing is specified either,
  the program will turn on smearing automatically when the SCF has serious convergence problems, in an attempt
  to overcome those problems, but only in a geometry optimization (including transition state, linear transit, etc.).
  If such happens the program restores the original situation (no smearing) at the start of each new SCF.
  In automatic smearing the smear parameter is initiated at 0.01 hartree and may be varied (by the program)
  between 0.001 and 0.1 hartree. The automatic use of smearing by the program can be
  prohibited by explicitly setting the smear option with value zero (Smearq=0).
• Smearing cannot be used in combination with the keeporbitals option.
  This option therefore also turns of automatic smearing in troublesome SCF 's during an optimization.