What is the output format of BasisTable?

[mira42780534]

Dear all,

I am trying to analyze the correlation among basis wave functions and therefore use BasisTable to output the mixing coefficients. However, I could not find any description of the output format in the manual.

Could someone please explain the meaning of each column in the BasisTable output?

According to the direct output of BasisTable, there are two data blocks:

1. Basis Table
2. Mixing Coefficients

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Below are the first 10 lines of the Basis Table:

============Basis Table===========================
#    0    0  0     146
     0    0  0       0   0     0     0   4*8                              4p6                                              4p+4(0)0
     0    0  0       1   5     8     0   4*7.5*1                          4s1.5s1                                          4s+1(1)1.5s+1(1)0
     0    0  0       2   6    12     0   4*7.5*1                          4p5.5p1                                          4p+3(3)3.5p+1(3)0
     0    0  0       3   6    15     0   4*7.5*1                          4p5.5p1                                          4p-1(1)1.5p-1(1)0
     0    0  0       4   7    10     0   4*7.6*1                          4s1.6s1                                          4s+1(1)1.6s+1(1)0
     0    0  0       5   8    16     0   4*7.6*1                          4p5.6p1                                          4p+3(3)3.6p+1(3)0
     0    0  0       6   8    19     0   4*7.6*1                          4p5.6p1                                          4p-1(1)1.6p-1(1)0
     0    0  0       7   9    12     0   4*7.7*1                          4s1.7s1                                          4s+1(1)1.7s+1(1)0
     0    0  0       8  10    20     0   4*7.7*1                          4p5.7p1                                          4p+3(3)3.7p+1(3)0
     0    0  0       9  10    23     0   4*7.7*1                          4p5.7p1                                          4p-1(1)1.7p-1(1)0

At the moment, I can only recognize the configuration labels, but I do not understand the physical or numerical meaning of the other columns.

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The first 10 lines of the Mixing Coefficients block are:

============Mixing Coefficients===================
#    0     0  0  0     145  0.00000000E+00  1.00000E+00
     0     0  0  0       0     0   0     0     0    9.88403977E-01  9.76942422E-01
     0     0  0  0       1    18  11     6    39   -7.07950294E-02  9.81954358E-01
     0     0  0  0       2    17  11     6     0    6.02188165E-02  9.85580664E-01
     0     0  0  0       3    16  11     4   252   -5.89673007E-02  9.89057806E-01
     0     0  0  0       4    15  11     4    84   -5.16327933E-02  9.91723752E-01
     0     0  0  0       5    13  11     2     0    4.43611948E-02  9.93691667E-01
     0     0  0  0       6    12  11     1    65    4.32099569E-02  9.95558768E-01
     0     0  0  0       7    10  11     0     0    2.68189806E-02  9.96278026E-01
     0     0  0  0       8    19  11     7    65    1.88405300E-02  9.96632991E-01
     0     0  0  0       9    14  11     3   140   -1.68033459E-02  9.96915344E-01

For the mixing coefficients, I am not sure about the meaning of any column:

• Which index corresponds to the basis state?
• Which column is the actual mixing coefficient?
• How these coefficients should be interpreted or normalized?

Any clarification or reference to documentation would be greatly appreciated.

[mfgu]

for the basis table,
the line starting with #

1. running index of the totalJ and Parity
2. parity of the state, 0 = even, 1 = odd
3. 2*totalJ
4. total number of states with this symmetry
   then the list of states for this symmetry,
   col 1,2,3 repeats the 3 columns in the header.
5. running index of states within this symmetry
6. running index of the configuration group defined by fac.Config() function.
7. running index of the configurations within the group
8. running index of states within the config
   8, 9, 10, the configuration and state labels, as in FAC energy level output.

for the mixing coefficient table,
the header line stating with #

1. running index of the atomic state
2. running index of the J/P, same as col 1 in the basis table.
3. parity
4. 2*totalJ
5. total number basis states for this atomic state
6. energy of the state relative to ground state in eV
7. sum of all b_i*b_i for the state. b_i is the mixing coef. of the ith component. should be 1.0 if properly normalized
   then comes the list of basis states for this atomic state.
   col 1, 2, 3, 4 are the same as in the header.
8. running index of the basis states for this atomic state
9. index of the basis state within the same symmetry, same as col 4 in basis table
10. config group index, same as col 5 in basis table.
11. config index within group, same as col 6 in basis table
12. state index within the config, same as col 7 in basis table
13. mixing coef of this basis component. the basis states are ordered from large abs(mixing) to small.
14. cummulative sum of b_i*b_i up to this state.