Output generated from ' print "final vectors analysis" ' does not appear to be normalised


Just Got Here
I have amended the code in src/ddscf/movecs_pr_anal.F so that a more complete wavefunction is printed in the log file. I am now printing anything with a coefficient greater than 0.01 (the default value was set as 0.15 with a maximum of 10 basis functions output).

I have noticed that for some vectors summing the square of the basis function coefficients does not sum to 1.0 (or close to 1.0 as I am still ignoring terms below 0.01). In some cases this sum is less than 0.5. Could you please advise whether there may be an issue with the final vectors analysis.

The changes I have made to movecs_pr_anal are shown in the snippets below identified by "jdt42". I don't think my changes have introduced a bug as the top items agree with the output from the default settings. An example output is also pasted in below. I can supply the amended file and output files if required.

Many thanks

Jon

Change 1 to over-ride default threshold .....

110  continue
do i = ilo, ihi
c
           call ga_get(g_vecs, 1, nbf, i, i, dbl_mb(k_vecs), 1)
c
c Identify significant coefficients and sort by size
c
           n = 0
c cur_thresh = thresh
c jdt42: to override the default threshold of 0.15
           cur_thresh = 0.01d0
111 do j = 0, nbf-1
if (abs(dbl_mb(k_vecs+j)).ge.cur_thresh) then
int_mb(k_list + n) = j
n = n + 1
endif
enddo


Change 2 to eliminate the restriction to only 10 basis functions
           
22 format(1x,2(' Bfn. Coefficient Atom+Function ',5x))
write(LuOut,23)
23 format(1x,2(' ----- ------------ ---------------',5x))
c do klo = 0, min(n-1,9), 2
c jdt42: to eliminate the restiction of only 10 bf output
           do klo = 0, min(n-1,(nbf-1)), 2
khi = min(klo+1,n-1)
write(LuOut,2) (
$ int_mb(k_list+k)+1,
$ dbl_mb(k_vecs+int_mb(k_list+k)),
$ (byte_mb(k_tags+int_mb(k_list+k)*16+m),m=0,15),
$ k = klo,khi)
2 format(1x,2(i5,2x,f12.6,2x,16a1,4x))
enddo


An example vector output with all basis function contributions with a coefficient greater than 0.01. The sum of the square of the coefficients is 0.548, the remaining terms below 0.01 do not make up the difference (I have tried lowering the threshold to 0.0001).

Vector   15  Occ=2.000000D+00  E=-1.054512D+00
MO Center= -8.0D-01, 5.1D-01, -4.0D-02, r^2= 1.8D+00
Bfn. Coefficient Atom+Function Bfn. Coefficient Atom+Function
----- ------------ --------------- ----- ------------ ---------------
36 -0.261547 3 N s 17 -0.259538 2 N s
32 -0.252514 3 N s 21 -0.250074 2 N s
77 -0.161915 6 C s 6 -0.145915 1 O s
2 -0.141347 1 O s 16 0.127673 2 N s
31 0.124543 3 N s 47 -0.108267 4 C s
76 0.082512 6 C s 34 -0.076693 3 N py
62 -0.069952 5 C s 48 -0.066961 4 C px
1 0.066766 1 O s 107 -0.064100 8 C s
92 -0.060200 7 C s 4 0.057354 1 O py
96 -0.056720 7 C s 46 0.055405 4 C s
18 0.049977 2 N px 63 0.049236 5 C px
52 0.044419 4 C px 61 0.037371 5 C s
78 -0.037280 6 C px 67 -0.035449 5 C px
109 -0.034766 8 C py 91 0.034132 7 C s
20 -0.033304 2 N pz 106 0.032921 8 C s
93 -0.031074 7 C px 19 0.030821 2 N py
38 -0.030409 3 N py 66 -0.030118 5 C s
110 -0.028708 8 C pz 8 0.027288 1 O py
35 0.026980 3 N pz 97 -0.024668 7 C px
3 0.023663 1 O px 24 -0.022980 2 N pz
94 0.022222 7 C py 39 0.021553 3 N pz
53 0.020166 4 C py 122 -0.017577 9 C s
126 0.017539 9 C s 50 0.017475 4 C pz
152 -0.017242 11 C s 98 0.016903 7 C py
137 -0.016526 10 C s 141 0.015324 10 C s
82 0.014947 6 C px 221 -0.013836 17 H s
30 0.013806 2 N dzz 143 -0.013476 10 C py
216 -0.012655 16 H s 90 0.012262 6 C dzz
119 -0.012147 8 C dyz 226 -0.011741 18 H s
45 0.011158 3 N dzz 88 -0.011135 6 C dyy
79 0.011060 6 C py 33 -0.010922 3 N px
81 -0.010810 6 C s 95 0.010804 7 C pz
113 0.010576 8 C py 123 -0.010347 9 C px

Forum Vet
The molecular orbitals are orthonormal
Jon,
While the eigenvectors are not orthonormal, the molecular orbitals are orthonormal, instead.
Using this property, you can derive that the following product is equal to the identity

C(transpose)*S*C=I

(where C is the Eigenvector matrix, S the Overlap Matrix)


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