Discrepancies between RIMP2 polarizabilities with FDIF = 0 and FDIF = 1

Questions
#1

I’m interested in RIMP2 polarizabilities. In checking what degree of finite differences would be more efficient, I noticed that the polarizabilities differ considerably for IDERIV = 0 and IDERIV = 1 with my test molecule.

$molecule
  0  1
  C   5.727114     0.043082    -2.433700
  C   4.736299     0.435107    -3.332344
  C   3.396792     0.373527    -2.963082
  C   3.023077    -0.079004    -1.691371
  C   4.021719    -0.477596    -0.801388
  C   5.364763    -0.414901    -1.170690
  C   1.560911    -0.119377    -1.374187
  C   0.865037    -1.339299    -1.308989
  C   1.548310    -2.604650    -1.324547
  C   0.862201    -3.776933    -1.233781
  C  -0.562314    -3.775401    -1.139063
  C  -1.250589    -2.602535    -1.180159
  C  -0.570183    -1.339903    -1.278688
  C  -1.284480    -0.129722    -1.376523
  C  -0.585840     1.089761    -1.306551
  C  -1.259707     2.360121    -1.308149
  C  -0.567360     3.529450    -1.220797
  C   0.857812     3.526435    -1.152279
  C   1.538185     2.349760    -1.200452
  C   0.849468     1.089761    -1.281096
  C  -2.736944    -0.170856    -1.739825
  C  -3.764114     0.342024    -0.944975
  C  -5.090398     0.290560    -1.369596
  C  -5.412115    -0.273764    -2.600085
  C  -4.395667    -0.780564    -3.408006
  C  -3.072908    -0.726706    -2.982054
  H   6.777201     0.090247    -2.720340
  H   5.007425     0.788288    -4.326789
  H   2.621150     0.680322    -3.664223
  H   3.768308    -0.857776     0.183356
  H   6.128406    -0.732367    -0.461396
  H   2.632802    -2.610602    -1.403254
  H   1.399964    -4.724356    -1.233136
  H  -1.095643    -4.717703    -1.027543
  H  -2.336321    -2.603329    -1.113890
  H  -2.343662     2.379298    -1.383649
  H  -1.102466     4.478125    -1.207941
  H   1.394030     4.469085    -1.059106
  H   2.625210     2.343346    -1.159415
  H  -3.543025     0.795970     0.013488
  H  -5.870843     0.699993    -0.729071
  H  -6.448928    -0.313601    -2.932254
  H  -4.632883    -1.216156    -4.378188
  H  -2.279347    -1.118804    -3.617378
  C  -1.996620    -1.605491     2.111274
  C  -2.651833    -0.358289     2.129371
  C  -1.924597     0.808409     2.076869
  C  -0.508722     0.775998     2.030495
  C   0.261543     1.966318     2.012091
  C   1.634660     1.910192     2.012999
  C   2.293110     0.663359     2.040553
  C   1.565479    -0.503848     2.042256
  C   0.147544    -0.471377     2.033208
  C  -0.624673    -1.660580     2.063900
  C   0.055914    -2.985439     2.088087
  O  -0.528312    -4.046457     2.093780
  N   1.446446    -2.934507     2.127773
  C   2.266494    -1.817169     2.100321
  O   3.476022    -1.932390     2.121655
  C  -0.420817     3.289162     2.023743
  O   0.161663     4.351237     1.989878
  N  -1.812014     3.239835     2.091686
  C  -2.631146     2.119802     2.075518
  O  -3.840680     2.227327     2.049871
  H  -2.557693    -2.537058     2.142982
  H  -3.736906    -0.299246     2.183244
  H   2.196109     2.841862     2.006908
  H   3.379052     0.608882     2.071249
  H   1.922145    -3.831985     2.140706
  H  -2.287461     4.137487     2.082502
$end
$rem
  JOBTYPE    Polarizability
  IDERIV     0 # or 1
  METHOD     RIMP2
  BASIS      cc-pVDZ
  AUX_BASIS  RIMP2-cc-pVDZ
  RI_J       True
  occ_RI_K   True
  SYMMETRY   False
  SYM_IGNORE True
  MEM_TOTAL  120000
  MEM_STATIC 100
  THRESH     14
$end

The output without the IDERIV keyword altogether (finite-difference 2nd derivatives with analytic first derivatives) is:

  Polarizability tensor      [a.u.]
    535.8718944     -5.3164273     -1.5560359
     -5.1698965    459.7066554      3.7842880
     -1.7296264      4.5412992    265.1572981
  Principal components       [a.u.]
    265.0759217    459.4065762    536.2533500
  Isotropic polarizability   [a.u.]
    420.2452826
  Anisotropic polarizability [a.u.]
    242.0981584
  Polarizability tensor      [angstrom^3]
     79.4080220     -0.7878132     -0.2305807
     -0.7660996     68.1214981      0.5607736
     -0.2563042      0.6729511     39.2922577
  Principal components       [angstrom^3]
     39.2801990     68.0770309     79.4645479
  Isotropic polarizability   [angstrom^3]
     62.2739259
  Anisotropic polarizability [angstrom^3]
     35.8752457
  Orientation
      0.0053662      0.0697297     -0.9975515
     -0.0192929      0.9973874      0.0696144
      0.9997995      0.0188721      0.0066975

The output with IDERIV = 0 is:

  Polarizability tensor      [a.u.]
    543.3315613     -2.0648542     -1.4926101  
     -2.0648542    600.1016815     12.9597777
     -1.4926101     12.9597777    370.1676203 
  Principal components       [a.u.]
    369.4286101    543.2624799    600.9097731  
  Isotropic polarizability   [a.u.]  
    504.5336210
  Anisotropic polarizability [a.u.]
    208.7162590
  Polarizability tensor      [angstrom^3]
     80.5134306     -0.3059798     -0.2211820
     -0.3059798     88.9258945      1.9204409 
     -0.2211820      1.9204409     54.8531820
  Principal components       [angstrom^3]
     54.7436720     80.5031938     89.0456413
  Isotropic polarizability   [angstrom^3]
     74.7641690 
  Anisotropic polarizability [angstrom^3]
     30.9285586 
  Orientation
      0.0079041     -0.9992751      0.0372389
     -0.0560217     -0.0376241     -0.9977204 
      0.9983983      0.0057999     -0.0562785

Will do the test of doing the finite differences manually but figured I’d bring it up.

~ Juan

#2

I’ve tried to come up with a simpler example and am running into the following situation. For the Ne atom, using the cc-pV5Z basis and no RI approximation of any kind, the HF polarizability gives exactly the same results with IDERIV 0, 1, and 2

$molecule
  0  1
  Ne
$end

$rem
  JOBTYPE    Polarizability
  IDERIV     0 # or 1, or 2
  METHOD     HF
  BASIS      cc-pV5Z
  SCF_ALGORITHM   DIIS_GDM
  SCF_CONVERGENCE 10
  MAX_SCF_CYCLES  200
  SYMMETRY   False
  SYM_IGNORE True
  MEM_TOTAL  120000
  MEM_STATIC 500
  THRESH     14
$end

Results:

  Polarizability tensor      [a.u.]
      1.7593768      0.0000000      0.0000000
      0.0000000      1.7593768      0.0000000
      0.0000000      0.0000000      1.7593768
  Principal components       [a.u.]
      1.7593768      1.7593768      1.7593768
  Isotropic polarizability   [a.u.]
      1.7593768
  Anisotropic polarizability [a.u.]
      0.0000001

with MP2 and IDERIV = 0

$molecule
  0  1
  Ne
$end

$rem
  JOBTYPE    Polarizability
  IDERIV     0
  METHOD     MP2
  BASIS      cc-pV5Z
  SCF_ALGORITHM   DIIS_GDM
  SCF_CONVERGENCE 10
  MAX_SCF_CYCLES  200
  SYMMETRY   False
  SYM_IGNORE True
  MEM_TOTAL  120000
  MEM_STATIC 500
  THRESH     14
$end

the result is

  Polarizability tensor      [a.u.]
      0.0000398      0.0000398      0.0001393
      0.0000398      0.0000796      0.0000398
      0.0001393      0.0000398      0.0000199
  Principal components       [a.u.]
     -0.0001098      0.0000526      0.0001965
  Isotropic polarizability   [a.u.]
      0.0000464
  Anisotropic polarizability [a.u.]
      0.0002655
  Polarizability

and with IDERIV = 1 the result is

  Polarizability tensor      [a.u.]
     -0.0000000     -0.0000000     -0.0000000
     -0.0000000      0.0000000      0.0000000
     -0.0000000     -0.0000000      0.0000000
  Principal components       [a.u.]
     -0.0000000      0.0000000      0.0000000
  Isotropic polarizability   [a.u.]
      0.0000000
  Anisotropic polarizability [a.u.]
      0.0000000

The MP2 results don’t agree very well with each other and the results are very wrong.