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Keyword XRAY

This keyword activates an x-ray absorption or emission spectrum calculation.
Options:
XAS / XES ALPHA=$<$MO1$>$-$<$MO2$>$AA
XAS Request an x-ray absorption spectrum calculation. This is the default.
XES Request an x-ray emission spectrum calculation.
ALPHA=$<$MO1$>$-$<$MO2$>$ Specifies $\alpha$ molecular orbital range from integer $<$MO1$>$ to $<$MO2$>$ for XES.
BETA=$<$MO1$>$-$<$MO2$>$ Specifies $\beta$ molecular orbital range from integer $<$MO1$>$ to $<$MO2$>$ for XES.
TOL=$<$Real$>$ Cutoff tolerance for (extended) XAS basis set orthogonalization. Default is $10^{-6}$.
With the XAS option the calculation of x-ray absorption spectra are requested. By default, the core-hole is specified as a fractionally-occupied molecular orbital with the MOMODIFY (see 4.4.4) keyword. Usually a half-core-hole (transition potential) is used for the spectrum calculation [42,252]. The following input yields a $1s$ oxygen XAS for water: 

 MOMODIFY 1 0
 1 0.5
 PRINT MOS
 XRAY XAS
 SCFTYPE UKS
 VXCTYPE BLYP
 AUXIS (GEN-A2*)
 BASIS (IGLO-III)
 #
 AUGMENT
 O (XAS-I)
 #
 GEOMETRY Z-MATRIX ANGSTROM
 O                                 8    15.999400
 H   1  R                          1     1.007940
 H   1  R   2  A            RAD    1     1.007940
 #
 VARIABLES
 R          0.97344553
 A          104.736377

Note the half-core-hole definition with MOMODIFY and the augmentation of the basis set (see 4.3.2) for the XAS calculation. For reliable spectra the augmentation basis is needed at least on the core-excited atom. Otherwise the sampling of the continuum and Rydberg states will be too coarse. The half-core-hole can be verified from the $\alpha$ MO printing, 

  ALPHA MO COEFFICIENTS OF CYCLE 9
                                1          2          3          4  
                           -19.8771    -1.1772    -0.7189    -0.5834

                             0.5000     1.0000     1.0000     1.0000

     1    1   O    1s        0.1649    -0.0372     0.0000     0.0139
     2    1   O    2s        0.3151    -0.0818     0.0000     0.0303
     3    1   O    3s        0.4328    -0.1554     0.0000     0.0601
     4    1   O    4s        0.2189    -0.0896     0.0000     0.0312
     5    1   O    5s        0.0141     0.3718     0.0000    -0.1410
     6    1   O    6s       -0.0051     0.4611     0.0000    -0.2163
     7    1   O    7s       -0.0015     0.1289    -0.0001    -0.1647
     :    :   :     :         :          :          :          :

    36    2   H    1s        0.0000     0.0449     0.0688     0.0391
    37    2   H    2s        0.0004     0.0876     0.1587     0.0922
    38    2   H    3s        0.0019     0.0285     0.1328     0.0830
    39    2   H    4s       -0.0002     0.0008     0.0120     0.0093
     :    :   :     :         :          :          :          :    

    46    3   H    1s        0.0000     0.0449    -0.0688     0.0391
    47    3   H    2s        0.0004     0.0876    -0.1587     0.0922
    48    3   H    3s        0.0019     0.0285    -0.1327     0.0830
    49    3   H    4s       -0.0002     0.0008    -0.0119     0.0093
     :    :   :     :         :          :          :          :    ,

after SCF convergence. The XAS output, employing the basis set augmentation, is given in the property output section of deMon.out as: 

    TRANSITION           TRANSITION MOMENTS

   NO.    E[eV]   STRENGTH       X          Y          Z

     1    536.10   0.0059     0.0167     0.0000     0.0129
     2    538.09   0.0132     0.0193     0.0000    -0.0251
     3    539.25   0.0016    -0.0087     0.0003    -0.0067
     4    539.30   0.0021     0.0002     0.0126     0.0001
     5    539.69   0.0007     0.0056     0.0000     0.0044
     6    539.99   0.0011     0.0056     0.0000    -0.0073
     7    540.22   0.0000     0.0007     0.0000     0.0005
     8    540.25   0.0002     0.0002    -0.0038     0.0002
     9    540.25   0.0002     0.0032     0.0002     0.0025
    10    540.28   0.0003    -0.0003     0.0044    -0.0002
    11    540.28   0.0002     0.0030     0.0005     0.0022
    12    540.28   0.0001     0.0013     0.0000    -0.0019
    13    540.30   0.0000     0.0000     0.0000     0.0000
     :       :      :          :          :          : 
     :       :      :          :          :          :

The transitions are ordered according to their transition energies. The transition strength [a.u.] is calculated as:


\begin{displaymath} S_{hi} = {2 \over 3} \> (\varepsilon_i - \varepsilon_h) \> {\langle \psi_h \mid {\bf r} \> \, \psi_i \rangle}^2% \end{displaymath} (27)

The transition moment components are given in the last three columns of the above output. This information is also written to the file deMon.xry for further processing with the utility program xray2k. This program convolutes the spectrum and produces output for plotting the results. To improve the absolute energies of the XAS spectrum and place it on an absolute energy scale, it is recommended to calculate explicitly the first core-excited state total energy. For such a calculation we remove a full 1s electron, but only after the occupations are already generated. The excited electron must thus be included as an extra charge (-1) in the molecule. For the water molecule this is the corresponding input: 

 CHARGE -1
 MOMODIFY 1 0
 1 0.0
 SCFTYPE UKS
 VXCTYPE BLYP
 AUXIS (GEN-A2*)
 BASIS (IGLO-III)
 #
 GEOMETRY Z-MATRIX ANGSTROM
 O                                 8    15.999400
 H   1  R                          1     1.007940
 H   1  R   2  A            RAD    1     1.007940
 #
 VARIABLES
 R          0.97344553
 A          104.736377

This yields the following MO occupations after SCF convergence: 

 ALPHA MO COEFFICIENTS OF CYCLE 9
                                1          2    ...      6          7
                           -20.1462    -1.1230  ...  -0.1018    -0.0396

                             0.0000     1.0000  ...   1.0000     0.0000

     1    1   O    1s        0.1660    -0.0396  ...  -0.0143     0.0000
     2    1   O    2s        0.3174    -0.0866  ...  -0.0320     0.0000
     3    1   O    3s        0.4291    -0.1699  ...  -0.0616     0.0000
     4    1   O    4s        0.2214    -0.0798  ...  -0.0349     0.0000
     5    1   O    5s        0.0102     0.4080  ...   0.1954     0.0000
     6    1   O    6s       -0.0020     0.4585  ...   0.1882    -0.0001
     7    1   O    7s        0.0000     0.1112  ...   0.9772     0.0000
     :    :   :     :         :          :       :     :          :

    36    2   H    1s        0.0000     0.0422  ...  -0.0339     0.0388 
    37    2   H    2s        0.0001     0.0807  ...  -0.1164     0.1102
    38    2   H    3s        0.0003     0.0281  ...  -0.3905     0.2107
    39    2   H    4s       -0.0001     0.0006  ...  -0.6048     1.3031
     :    :   :     :         :          :       :     :          :

    46    3   H    1s        0.0000     0.0422  ...  -0.0339    -0.0388
    47    3   H    2s        0.0001     0.0807  ...  -0.1164    -0.1102
    48    3   H    3s        0.0003     0.0281  ...  -0.3903    -0.2108
    49    3   H    4s       -0.0001     0.0006  ...  -0.6053    -1.3029
     :    :   :     :         :          :       :     :          :

The energy difference between this first excited core-state and the ground state is used to shift the origin of the transition potential spectrum, i.e. the first excitation of the above TRANSITION output. A further correction can be introduced by calculating the core ionization potential, here of the O$1s$ orbital in water, and compare with results from experimental x-ray photoelectron spectra (XPS). This offset also corrects for deficiencies in the functional [252,253]. The input for the XPS calculation has the form: 

 MOMODIFY 1 0
 1 0.0
 SCFTYPE UKS
 VXCTYPE BLYP
 AUXIS (GEN-A2*)
 BASIS (IGLO-III)
 #
 GEOMETRY Z-MATRIX ANGSTROM
 O                                 8    15.999400
 H   1  R                          1     1.007940
 H   1  R   2  A            RAD    1     1.007940
 #
 VARIABLES
 R          0.97344553
 A          104.736377

If core-levels are close in energy, like in a water cluster, ECPs (see 4.3.4) can be used to have the relevant core-level uniquely defined. The following shows a water pentamer input for an XAS calculation using this technique: 

 MOMODIFY 1 0
 1 0.5
 XRAY XAS
 BASIS (TZVP)
 O1 (IGLO-III)
 O2 (RECP6|SD)
 SCFTYPE UKS MAX=20 TOL=0.100E-04
 VXCTYPE PBE
 AUGMENTATION
 O1 (XAS-I)
 ERIS DIRECT TOL=1.0E-8
 #
 # Pentamer geometry
 #
 GEOMETRY CARTESIAN ANGSTROM
 O1      0.000000      0.000000      0.000000
 O2      2.264218      1.270427     -1.048492
 O2     -0.236014      0.380416      2.763979
 O2     -2.323588      1.242303     -0.947429
 O2     -0.113699     -2.602651     -1.026294
 H      -0.081064     -1.025238     -0.277800
 H      -0.036255      0.134954      1.127393
 H      -0.909319     -3.125997     -0.746222
 H       0.695861     -3.190749     -0.803055
 H       0.617200      0.800843      3.188623
 H      -0.994919      0.919704      3.110267
 H      -3.037164      0.667781     -0.585638
 H      -1.475886      0.786984     -0.720841
 H       1.514773      0.710601     -0.705452
 H       3.110268      0.796835     -0.730599

The isolated core-level of O1 can be easily identified (first MO) in the corresponding MO output: 

 ALPHA MO COEFFICIENTS OF CYCLE 10


                                1          2          3          4   ...
                           -19.7860    -1.0776    -1.0646    -1.0562 ...

                             0.5000     1.0000     1.0000     1.0000 ...

     1    1   O    1s        0.1647    -0.0327     0.0133     0.0133 ...
     2    1   O    2s        0.3162    -0.0718     0.0293     0.0292 ...
     3    1   O    3s        0.4323    -0.1375     0.0560     0.0558 ...
     4    1   O    4s        0.2183    -0.0774     0.0319     0.0319 ...
     5    1   O    5s        0.0146     0.3176    -0.1315    -0.1317 ...
     6    1   O    6s       -0.0061     0.4356    -0.1739    -0.1716 ...
     7    1   O    7s        0.0065     0.0788    -0.0343    -0.0351 ...
     :    :   :     :         :          :          :          :      :
     :    :   :     :         :          :          :          :      :

With the XES option the calculation of x-ray emission spectra is requested. The core levels are specified with the ALPHA and BETA options of the XRAY keyword. Since the ground state is used we can compute spectra for all relevant core-levels in one calculation so a range of orbitals is specified. This range can include only one orbital as shown in the following input example for the first $\alpha$ MO XES of water: 

 SCFTYPE UKS
 VXCTYPE PBE BASIS
 XRAY XES ALPHA=1-1
 BASIS (IGLO-III)
 H Read
 1   0   3
        14.9588900000        0.0349460000
         2.2563909000        0.2347270000
         0.5112084000        0.8137573000
 2   0   1
         0.1219492000        1.0000000000
 3   0   1
         0.0360000000        1.0000000000
 2   1   1
         1.1000000000        1.0000000000
 AUXIS (GEN-A4*)
 #
 GEOMETRY CARTESIAN ANGSTROM
 O       0.00000000    0.00000000    0.20476407
 H       0.66694680    0.00000000   -0.39124903
 H      -0.66694680    0.00000000   -0.39124903

Here the relevant O 1s level is the lowest in energy, but this depends on the system. The specification is by way of orbital number so that in more complicated cases a ground state calculation should be done first to find the relevant orbital(s). The corresponding XES output is given in the property output section of deMon.out and reads for this example as: 

 XES CALCULATION FOR MO #: 1
 
 IONIZATION POTENTIAL = 510.08 EV
 
    TRANSITION           TRANSITION MOMENTS
   
   NO.    E[eV]    STRENGTH      X          Y          Z
   
     2    483.78   0.4311     0.0000     0.0000    -0.0152
     3    496.73   5.3353     0.0513     0.0000     0.0000
     4    500.29   5.5736     0.0000     0.0000     0.0519
     5    502.75   7.2973     0.0000     0.0589     0.0000

This information is also written to the file deMon.xry for further processing with the utility program xray2k. The emission energies are obtained from orbital energy differences and lack effects of relaxation (most important for the inner-shell). An improved absolute energy can be obtained by computing the difference between the IP for the core and for the HOMO and use that to place the transition with highest energy. This assumes that relaxation effects in the valence are similar, which is not necessarily the case [254].

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Next: Keyword NMR Up: Molecular Property Control Previous: Keyword NONCOLLINEAR   Contents