Introduction
The program dos gives information on the number and character of one-electron levels (molecular orbitals) as a function of the (orbital) energy. The total density of states N(E) is a well known concept in electronic structure theory of infinite systems (crystals). N(E)dE denotes the number of one-electron levels (orbitals) in the infinitesimal energy interval dE. The total density of states (TDOS) at energy E is usually written as
N(E) = ∑i δ(E-εi) (3.3.1)
where the εi denote the one-electron energies. So the integral of N(E) over an energy interval E1 to E2 gives the number of one-electron states in that interval. Usually the δ-functions are broadened to make a graphical representation possible.
When the δ-functions are multiplied by a weight factor that describes some property of the one-electron state φi at energy εi various types of densities-of-states are obtained that provide a graphical representation of the state character (orbital character) as a function of one-electron energy.
In calculations on finite molecules the total density of states as a function of (orbital) energy may also be useful, but the main use of various types of densities-of-states is to provide a pictorial representation of Mulliken populations. The weight factors employed are related to the orbital character determined by means of a Mulliken population analysis per orbital (see below). The program dos, therefore, provides the same information as can be generated by the ADF program (a population analysis per orbital) but dos enables an easy graphical representation and is particularly useful when there are many one-electron levels, for instance in calculations on clusters. You can obtain a simple view of the character of the orbitals in a certain energy range. You can also find out in which orbitals (at which energies) certain basis functions or fragment orbitals give a large contribution, and whether such contributions are bonding, nonbonding or antibonding with respect to particular bonds. Such information is provided by dos in the form of (weighted) density of states values over a user-specified energy range, which can for instance be plotted by gnuplot.
The following options are available for computations by dos:
- TDOS: Total Density of States
- GPDOS: Gross Population Density of States
- OPDOS: Overlap Population Density of States
- PDOS: Projected Density of States
The total density of states (TDOS) has large values at energies where there are many states per energy interval.
The GPDOS (Gross Population based Density Of States) of a function χμ (or a sum of such functions) has large values at energies where this function (these functions) occur(s) in the molecular orbitals.
The PDOS of a function χμ provides similar information, but with the projection of χμ onto the orbital φi as weight factor for the importance of χμ in the orbital φi.
The OPDOS
(Overlap Population based Density Of States) between
χμ
and χν has large
positive values at energies where the interaction between them is bonding, and
negative values where the interaction is antibonding. An example of the use of
these plots is provided in [1].
[1] P.J. van den Hoek, E.J. Baerends, and R.A. van Santen, J. Phys. Chem. 93, 6469 (1989).
We review below the Mulliken population analysis, and then describe the forms of density of states analysis performed by DOS. Finally an input description of DOS is given.
