### relativistic corrections to the shielding

Posted:

**19 Nov 2013, 09:55**It appears that there is a bug in relativistic corrections to the shielding. The final printouts are

Paramagnetic Corrections

------------------------

Second Order Singlets. Total Value : 2.95230 [ppm]

Second Order Triplets. Total Value : 37.83090[ppm]

Total Paramagnetic Corrections : 40.78320 [ppm]

Diamagnetic Corrections :

--------------------------

First Order Singlets. Total Value : -27.19241 [ppm]

Second Order Singlets. Total Value : 7.39426 [ppm]

Total Diamagnetic Corrections : -19.79815 [ppm]

Total Relativistic Corrections :

--------------------------------

Sum of corrections : 41.99929 [ppm]

which is clearly NOT the sum.

==============================================

I can see that when we get to the tensor averages in abalresc.F we have:

DO i=1, 3

SGP1T = SGP1T + LRFCZK(i,i) + LRSDZK(i,i)+LRFCBS(i,i)+LRSDBS(i,i)

SGP1S = SGP1S + LRLKIN(i,i) + LRPSOK(i,i)

SGD0S = SGD0S + LRFCAV(i,i) + LRDIAK(i,i) + LRANGP(i,i)

SGD1S = SGD1S + LRDIAD(i,i) + LRDIAM(i,i)

relall= relall + SGD0S + SGD1S + SGP1S + SGP1T

ENDDO

If I read it correctly, the four individual terms are OK - each diagonal tensor

component is fine, considered once. However, in "relall" the first tensor component of each term

will be counted three times, the second twice, and the third once

(e.g. for i=2 SGP1T becomes the sum (1.1)+(2.2) and it is added to relall which

already included the (1,1) contribution)

I have moved the line

"relall= relall + SGD0S + SGD1S + SGP1S + SGP1T"

after the ENDDO and I obtain in the above example

Sum of corrections : 20.98505 [ppm]

which is the sum of the two computed terms.

and best regards,

Michal Jaszunski

Paramagnetic Corrections

------------------------

Second Order Singlets. Total Value : 2.95230 [ppm]

Second Order Triplets. Total Value : 37.83090[ppm]

Total Paramagnetic Corrections : 40.78320 [ppm]

Diamagnetic Corrections :

--------------------------

First Order Singlets. Total Value : -27.19241 [ppm]

Second Order Singlets. Total Value : 7.39426 [ppm]

Total Diamagnetic Corrections : -19.79815 [ppm]

Total Relativistic Corrections :

--------------------------------

Sum of corrections : 41.99929 [ppm]

which is clearly NOT the sum.

==============================================

I can see that when we get to the tensor averages in abalresc.F we have:

DO i=1, 3

SGP1T = SGP1T + LRFCZK(i,i) + LRSDZK(i,i)+LRFCBS(i,i)+LRSDBS(i,i)

SGP1S = SGP1S + LRLKIN(i,i) + LRPSOK(i,i)

SGD0S = SGD0S + LRFCAV(i,i) + LRDIAK(i,i) + LRANGP(i,i)

SGD1S = SGD1S + LRDIAD(i,i) + LRDIAM(i,i)

relall= relall + SGD0S + SGD1S + SGP1S + SGP1T

ENDDO

If I read it correctly, the four individual terms are OK - each diagonal tensor

component is fine, considered once. However, in "relall" the first tensor component of each term

will be counted three times, the second twice, and the third once

(e.g. for i=2 SGP1T becomes the sum (1.1)+(2.2) and it is added to relall which

already included the (1,1) contribution)

I have moved the line

"relall= relall + SGD0S + SGD1S + SGP1S + SGP1T"

after the ENDDO and I obtain in the above example

Sum of corrections : 20.98505 [ppm]

which is the sum of the two computed terms.

and best regards,

Michal Jaszunski