[molpro-user] What is the definition of "Couls-En" and natural orbital energy in molpro?

[cong.wang]

Dear everyone,

 Hi!

 I have a question about the printed HF and CASSCF orbital in Molpro,
namely  "Couls-En" and natural orbital energy.

This is the input file modified from an example case in molpro

***********************************
geometry={o;h1,o,r;h2,o,r,h1,theta}   !Z-matrix geometry input
r=1 ang                               !bond length
theta=104                             !bond angle

gprint,orbitals

hf                                    !do scf calculation
multi                                 !do full valence casscf
******************************************************


In the output file, the HF orbital part gives

****************
 !RHF STATE 1.1 ENERGY                -76.021457977362
 Nuclear energy                         8.80260377
 One-electron energy                 -122.44570201
 Two-electron energy                   37.62164027
 Virial quotient                       -1.00243551
 !RHF STATE 1.1 DIPOLE MOMENT           0.00000000     0.00000000     0.82747571
 Dipole moment /Debye                   0.00000000     0.00000000     2.10309571

 ELECTRON ORBITALS
 =================


 Orb  Occ    Energy  Couls-En    Coefficients

                                 1 1s      1 1s      1 1s      1 2pz
  1 2pz     1 3d0     1 3d2+    2 1s      2 1s      2 2pz
                                 2 2py

 1.1   2   -20.5581  -53.5392  1.000323  0.001854 -0.001396
0.002396 -0.001722 -0.000007 -0.000044 -0.000049  0.000635  0.000557
                               0.000616

 2.1   2    -1.3166   -9.1121 -0.006727  0.879681 -0.099595
0.103848 -0.054753  0.001253 -0.002689  0.424771 -0.196973 -0.027520
                              -0.048485

 3.1   2    -0.5597   -7.3877  0.002198 -0.289707 -0.170278
0.787685  0.005679  0.017393 -0.004598  0.499690 -0.180259  0.008448
                              -0.044423

                                 1 2px     1 2px     1 3d1+    2 2px

 1.2   2    -0.4906   -7.5595  0.922090  0.072589  0.017639  0.041534

                                 1 2py     1 2py     1 3d1-    2 1s
  2 1s      2 2py     2 2pz

 1.3   2    -0.6762   -7.2256  0.706430 -0.090110  0.025373
0.767604 -0.245293 -0.032944 -0.045257

****************

What is the definition of "Couls-En" ?


Then in the natural orbital of CASSCF part,



****************
 NATURAL ORBITALS
 ================

 Orb     Occ        Energy       Coefficients

                                 1 1s      1 1s      1 1s      1 2pz
  1 2pz     1 3d0     1 3d2+    2 1s      2 1s      2 2pz
                                 2 2py

 1.1  2.00000   -20.470020     0.998682 -0.056548 -0.002160
0.023813  0.001386  0.000526 -0.000058 -0.005603  0.005218  0.002348
                               0.001759

 2.1  1.99887    -1.174619     0.058228  0.895999  0.012497
-0.341357 -0.046719 -0.008524  0.000140  0.074622 -0.065989 -0.027176
                              -0.016371

 3.1  1.97579    -0.779968     0.001853  0.245582 -0.214310
0.718893 -0.037541  0.015237 -0.005740  0.668721 -0.259855 -0.004549
                              -0.059350

 4.1  0.02555     0.714455    -0.115528 -0.877379  0.251728
-1.121995  0.602277 -0.016221  0.018564  1.298554 -0.487131  0.050086
                              -0.063457

                                 1 2px     1 2px     1 3d1+    2 2px

 1.2  1.99937    -0.493111     0.922070  0.073035  0.017560  0.040770

                                 1 2py     1 2py     1 3d1-    2 1s
  2 1s      2 2py     2 2pz

 1.3  1.97388    -0.671370     0.714367 -0.107254  0.025685
0.782251 -0.246739 -0.029488 -0.040671

 2.3  0.02654     0.708915    -1.247278  0.508215 -0.029085
1.364846 -0.414257 -0.016361 -0.005323


 Natural orbital dump at molpro section                    2140.2
(Orbital set 2)
**********************

What is the definition of the energy of natural orbital?


Thank you very much
Best regards
Cong Wang
Ph. D. student
Department of Chemistry
Laboratory for Instruction in Swedish
University of Helsinki
A.I. Virtanens plats 1
P.O. Box 55
FI-00014 University of Helsinki
FINLAND