# EM and RM methods

### From FEFF

The Equation of Motion (EM) and Recursion Method (RM) require additional input to be given in the file ‘spring.inp’. This file cannot currently be produced from the JFEFF GUI. The file defines the force fields for feff. First, feff searches for all similar bonds and angles in the material, creates complete lists of all bond stretches and angle bends, and then, based on the force field and geometry of the structure, calculates the cartesian force field matrix and scales it with the atomic masses, thus obtaining the dynamical matrix. Finally, the DW factors are calculated from the dynamical matrix.

The file ‘feff.inp’ has the same CARD-based structure as the master input file ‘feff.inp’. For example, the ‘spring.inp’ file for zinc tetraimidazole looks like this.

* 13-atom model of zinc tetraimidazole * res wmax dosfit acut ￼VDOS 0.02 1 1.2 3 PRINT 5 STRETCHES * i j k_ij dR_ij[%] 0 2 110. 2. 1 2 626. 5. ANGLES * i j k ktheta dtheta[%] 2 0 5 37. 10. 1 2 3 2590. 10.

The corresponding ‘feff.inp’ file contains the DEBYE card:

DEBYE 300. 0. 1 * T T_Debye 2=Equation of Motion Method

The CARDs for the ‘spring.inp’ file are: VDOS, PRINT, STRETCHES, and ANGLES.

## Contents |

## VDOS

res wmax dosfit [acut] Standard

This card is needed only for EM runs and is optional - if it is omitted, default values are used. The card is ignored for RM runs. The keywords in the VDOS card define the integration parameters used in the VDOS calculation. Here res is the VDOS spectral resolution width (default res = 0.05, i.e. 5% of the bandwidth). The smaller this number, the more fine structure is present in the spectrum and the longer the computation time. Finer resolution is usually helpful for mode analysis in small molecules. The next keyword, res, is a multiplication factor used to increase the maximum frequency to which the VDOS is calculated. dosfit is a real positive number governing how much of the low frequency part of the VDOS is to be fitted to Debye-like behavior, A.ω2. If it is equal to 0 then no fitting will be applied. The higher the number, the more of the VDOS will be fitted. The default value is dosfit = 1 (about 10% of the total width). This parameter is useful for elimination of low frequency ”noise” and zero-frequency modes. Finally, acut is the time integration cutoff parameter. It rarely needs to be changed (usually in cases of very small open molecular structures). The higher this number, the longer the computation time. The acut keyword is optional; the default value is acut = 3.

* res wmax dosfit acut VDOS 0.02 1 1.2 3

[iprdos] Standard

If using the EM method, the PRINT card makes feff write files ‘prdenNNNN.dat’ containing projected VDOS for selected scattering paths. Here iprdos specifies that such files will be written for the first iprdos paths in the paths list. If using the RM method, the PRINT card makes feff write a file ‘s2_rm1.dat’ containing first tier results. The keyword iprdos is ignored in this case.

PRINT 5 * print files prden0001.dat - prden0005.dat

## STRETCHES

[i j k ij dR ij] Standard

Required for EM and RM runs. It is followed by the list of bond stretching force constants. Here i and j are atomic indices (as in the file ‘geom.dat’; the absorber has index 0), and k ij is a single central force constant characterizing the interaction between atoms i and j in units of 10^2mdyn/ ̊A2 or N/m. One should include as many distinct bonds in the list as possible and then the code will search for the similar ones and assign them the same force constant. The last parameter in each row, dR ij, is the tolerance in the bond length when searching for similar bonds and is measured in percentage points. For example, if dR ij = 5 then all bonds between pairs of atoms with the same potentials as i and j and with bond length within 5% of Rij will be assigned the same stretching force constant k ij.

STRETCHES * i j k_ij dR_ij[%] 0 2 110. 2. 1 2 626. 5.

## ANGLES

[i j k ktheta dtheta] Standard

Similar to STRETCHES, but optional in most cases. This card allows one to include θijk angle bending force constants kijk in the calculation. The force constants are in units of θ 10^2mdyn ̊A/rad2. Here dtheta is tolerance in the angle value when searching for similar angles. Sometimes it is useful to include this card in order to avoid zero-frequency modes.

ANGLES * i j k ktheta dtheta[%] 2 0 5 37. 10. 1 2 3 2590. 10.

**Output files**
All σj2 values in the output files are given in units of ̊A2, all frequencies are in units of THz, and all reduced masses are in atomic units. The output files from a EM calculation include:

• ‘s2_em.dat’ Contains σj2 for each scattering path in ‘paths.dat’.

• ‘prdenNNN.dat’ which contains projected VDOS for selected scattering paths (as indicated by the PRINT card).

The output files from a RM calculation include:

• ‘s2_rm2.dat’ Contains σj2 for each scattering path in ‘paths.dat’ calculated using the second tier approximation.

• ‘s2_rm1.dat’ Contains σj2 for each scattering path in ‘paths.dat’ calculated using the first tier approximation.

Further details can be found on pp. 98 of Anna Poiarkova’s thesis

**Examples**

These examples can also be found in the ‘examples’ folder of the feff90 distribution. First we present a ‘spring.inp’ example for a 177-atom cluster of a Cu crystal. Here only a single central force constant between the first nearest neighbors is taken into account. Similar input files can be constructed for other fcc structures, e.g. Pt, Al, etc.

* Cu crystal, single central force constant VDOS 0.03 0.5 1 PRINT 3 STRETCHES 0 1 27.9 2.

As a second example we show the ‘spring.inp’ file for a 147-atom cluster of c-Ge crystal. The force constants used here were fitted to phonon dispersion curves. Similar output files can be constructed for other diamond-type lattices, e.g. Si, C, etc.

* c-Ge crystal VDOS 0.02 0.7 0. 3. PRINT 6 STRETCHES 01 103.58 2. 0 5 5.81 2. 020 -1.08 2. 030 -0.30 2. ANGLES 1 0 2 31.45 2.

The output files for these examples can be found in the ‘examples’ folder of the feff90 distribution. They are also discussed in pp. 100-104 of Anna Poiarkova’s thesis.