Electronic Configuration
The next few keys can be used to specify the electronic configuration. If
you don't specify any such keys, certain defaults will apply. In principle, the
program will (by default) attempt to find the lowest-energy spin-restricted
(one-determinant) state. If SCF convergence is problematic the program may wind
up at an excited state, by which (in this context) we mean a one-determinant
state with a higher energy than some other one-determinant state with the same
net spin polarization. In worse cases the program may fail to converge to any
state at all. It is good practice to always verify which configuration
you actually have computed.
When you specify a particular configuration and/or net charge and/or net
spin-polarization of the system, the program will try to compute accordingly,
even if the data have no physical or chemical meaning. The program has no
knowledge about the existence of materials and will simply try to carry out
what you tell it to do.
Specifies that spin-a
and spin-b MOs may be spatially different and may have different occupation
numbers. The default (absence of the key) is spin-restricted. The key has no
argument.
The unrestricted mode roughly doubles the computational effort. The actual
numbers of spin-a and spin-b electrons respectively are controlled by the keys
CHARGE and OCCUPATIONS.Not e carefully, that using only the keyword
UNRESTRICTED, without either CHARGE or OCCUPATIONS (or both) would not result
in any spin polarization. This implies that you would effectively perform a
spin-restricted calculation, but with increased computational effort.
Therefore, the program will check that in an unrestricted calculation at least
one of the keys CHARGE and OCCUPATIONS is applied.
The unrestricted feature is equivalent with, in ab-initio terminology,
(Spin-)Unrestricted-Hartree-Fock (UHF); the N-particle wavefunction is a single
determinant and not necessarily an eigenfunction of the spin operator
S2.
A restricted calculation implies that the (spatial) orbitals and
the occupation numbers are identical for spin-a and spin-b.
The Fock operator, both in an unrestricted and in a restricted run, commutes
with the spin operator Sz, but not (unless accidentally) with
S2. The obtained one-determinant wave function may for instance be a
mixture of a singlet and a triplet state.
The expectation value of S2 is not computed in ADF.
Note: implementation of an evaluation of S2 is not quite trivial.
DFT is essentially a one-particle formalism, so the S-operator for the
N-particle system has to be written out in single-particle operators [67].
Molecules that have been calculated using the unrestricted formalism cannot be
employed as fragments. ADF will abort when you attach the TAPE21 result file
from an unrestricted calculation as a fragment file.
A fair approximation to a computation with unrestricted fragments can be
achieved with the key FRAGOCCUPATIONS. See also the Examples.
The
net charge of the molecule and the net spin polarization can be controlled with
the key CHARGE.
- NetQ
- The net total charge of the molecule
- ab
- The net total spin
polarization: the number of spin-a electrons in excess of spin-b electrons.
Specification is only meaningful in a spin-unrestricted
calculation.
If the key is used, the first value in the argument is
assigned to netQ, the net total charge, and the second to ab. If the key is not
used at all, default values apply. The default for the net total charge is the
sum of fragment charges: not necessarily neutral!! The fragment charges
are the net total charges that were used in the fragment runs; this information
is stored in the fragment files.
The default spin polarization is zero.
An unrestricted calculation with ab=0 (for instance by not specifying CHARGE at
all) is in fact a restricted run: it should give exactly the same as the
restricted calculation, but it will use more CPU time.
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 one or more of the
following:
- 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=Smear
- Smear 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. - 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 the 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-a orbitals, the second set to the spin-b
orbitals.
Notes about the OCCUPATIONS data block:
- If the block form of OCCUPATIONS is used all valence electrons
that you want to use in the calculation must explicitly be assigned to MOs: any
MOs that are not mentioned in the data block will be empty (except the frozen
core orbitals).
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 [68].
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:
- If occupation numbers are explicitly defined (the block form is used), the
Smearq option cannot be used.
- The aufbau principle does not determine or adjust the distribution of
electrons over spin-a versus spin-b 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.
The
contents of the data block of OCCUPATIONS,
if used, defines the total number of valence electrons and hence the net total
charge. In an unrestricted run it also defines the net spin polarization. If
the key CHARGE
is also used, the program will check that both specifications are consistent.
We
strongly recommend to employ this and always specify the net total charge and
spin polarization with CHARGE whenever explicit occupation numbers are supplied
with OCCUPATIONS, to that the program will check that your occupation numbers
result in the total charge and spin polarization that you have in mind.
In
Create mode occupation numbers are predefined (see Appendix 2 Elements of the
Periodic Table), and these are applied unless you specify occupations in input
yourself. Conceivably this may result in a non-aufbau configuration. In Create
mode the program always operates as if OCCUPATIONS were set in input.
Pseudopotentials
are not supported. The frozen core approximation is automatic in a normal
(Fragment mode) calculation and is defined by the basic atomic fragments. The
data file used in the Create run specifies the frozen core for the atom, which
is then used in all molecules that incorporate that atomic fragment.
