# DM methods

### From FEFF

**syntax**

To calculate Debye-Waller factors from a dynamical matrix (or matrix of force constants or Hessian matrix) using the Lanczos recursive algorithm, the following syntax is required in ‘feff.inp’ :

DEBYE Temp Debye_Temp [DW_Opt [dymFile DMDW_Order DMDW_Type DMDW_Route]]

where:

• Temp Temperature at which the DW factors are calculate

• Debye Temp Debye Temperature of the material

• DW Opt The model used to calculate the DW factors - here, DW opt = 5

• dymFile Name of the dynamical matrix information file. The default value is ‘feff.dym’

• DMDW Order Lanczos recursion order to be used in the calculation. The default value is 2. Well converged results are usually obtained for DM DW Order = 6 − 10. For small size systems, these values might be too large. As a rule of thumb, DMDWOrder should be less than 3∗(Numberofatoms)−6. Some paths, within systems with high symmetry, might require a lower DMDW Order. The user should always check convergence.

• DMDW Type Type of DW calculation. The possible values are: 0 Parallel s2 (default)

• DMDW Route Which paths to use in the **dmdw** module. These paths do not affect the path selection in the XAS calculations, they are used for the generation of an input file for the independent dmdw module. The possible values are: 0 Skip **dmdw** module (default) 1 All SS paths from absorber 2 Same as 1 + all DS paths from absorber 3 Same as 2 + all TS paths from absorber 11 All SS paths 12 Same as 1 + all DS paths 13 Same as 2 + all TS paths

**Examples**

A typical FEFF input file that uses ab initio DW factors in a XANES calculation looks as follows:

EDGE K 1.0 CONTROL 111111 SCF 4.000 XANES 4.000 FMS 6.000 DEBYE 500.0 1073.0 5 feff.dym 6 0 1 POTENTIALS 0 8 O 1 1 H ATOMS 0.00000 0.00000 0.00000 0 O 0.00000 0 0.96141 -0.12674 0.00000 1 H 0.96972 1 -0.12674 0.96141 0.00000 1 H 0.96972 2 END

This input calculates the XANES O K edge spectrum of a single water molecule. If an EXAFS calculation is required, the same DEBYE card parameters apply, but the XANES card should be subtituted by the EXAFS card. It uses ab initio DW factors at 500K and a dynamical matrix stored in the file ‘feff.dym’. The number of Lanczos recursion iterations is set to 6, the type of DW calculation is to calculate parallel σ2, and it asks that all single scattering paths from the absorber be calculated independently in the dmdw module. When feff reads this ‘feff.inp’ file, it will create another input file ‘dmdw.inp’:

6 1 500.000 500.000 0 feff.dym 1 2 1 0 3.20

The first line gives the number of Lanczos iterations. The second defines the temperature, in this case a grid with a single point. The third defines the type of DW calculation and the fourth the name of the dynamical matrix file. The fifth line declares that the input contains a single path descriptor, which is included in the next line. This descriptor defines all single scattering paths from the absorber that are less than 3.2 Bohr long.

The dynamical matrix file ‘feff.dym’ for this calculation looks like this:

1 3 8 1 1 15.994915 1.007825 1.007825 0.00000000 0.00000000 0.00000000 1.81679640 -0.23950080 0.00000240 -0.23950080 1.81679640 0.00000240 1 1 5.398996E-01 -1.171079E-01 5.031484E-07 -1.171079E-01 5.399060E-01 9.690730E-07 5.031484E-07 9.690730E-07 -1.841479E-03 1 2 # next 3 lines omitted here for brevity 1 3 # and again ... 2 1 2 2 2 3 3 1 3 2 3 3 5.501607E-02 -7.712230E-02 -1.185055E-07 -7.712230E-02 5.034998E-01 8.548785E-07 -1.185055E-07 8.548785E-07 -8.715942E-04

The user must obtain this file using another program, for example, Gaussian or ABINIT. Given these files ‘feff.inp’ and ‘feff.dym’, feff calculates a XANES spectrum including the Debye-Waller factors derived from the given dynamical matrix.

Additional technical information about the calculation of ab initio Debye-Waller factors is provided in the Appendix.