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Re^2: Number of states in XMCQDPT2

Maksim Shundalau
m.shundalau@gmail.com

Dear Igor,

I thank you for your answer, but I think that the problem lies elsewhere.
At the CAS level of theory I calculate singlets and triplets together. At the XMCQDPT2 I have TWO DIFFERENT calculations with TWO DIFFERENT effective Hamiltonians (for singlets and for triplets).
For example, if I take 10 and 10 states for singlets and triplets, I have for singlets:

*** XMC-QDPT2 ENERGIES ***
-----------------------------------------------------------------------
STATE                       1ST ORDER                       2ND ORDER
1     E(MCSCF)=   -261.677105329713     E(MP2)=   -262.669376620520
2     E(MCSCF)=   -261.424716215710     E(MP2)=   -262.666212340027
3     E(MCSCF)=   -261.407702388902     E(MP2)=   -262.648775553937
4     E(MCSCF)=   -261.397971587503     E(MP2)=   -262.642175973039
5     E(MCSCF)=   -261.357555431463     E(MP2)=   -262.557674735242
6     E(MCSCF)=   -261.350462737843     E(MP2)=   -262.483099692591
7     E(MCSCF)=   -261.287008744978     E(MP2)=   -262.431768066747
8     E(MCSCF)=   -261.245424936527     E(MP2)=   -262.413558691544
9     E(MCSCF)=   -261.177968460496     E(MP2)=   -262.401800020580
10     E(MCSCF)=   -261.076974499620     E(MP2)=   -262.393379265201
-----------------------------------------------------------------------

and for triplets:

*** XMC-QDPT2 ENERGIES ***
-----------------------------------------------------------------------
STATE                       1ST ORDER                       2ND ORDER
1     E(MCSCF)=   -261.677467336572     E(MP2)=   -262.650249860133
2     E(MCSCF)=   -261.422736915199     E(MP2)=   -262.648363483054
3     E(MCSCF)=   -261.412278358189     E(MP2)=   -262.647654388601
4     E(MCSCF)=   -261.379098420900     E(MP2)=   -262.641941065948
5     E(MCSCF)=   -261.371330821571     E(MP2)=   -262.556120121286
6     E(MCSCF)=   -261.352101462186     E(MP2)=   -262.430043338552
7     E(MCSCF)=   -261.350894460654     E(MP2)=   -262.429204328369
8     E(MCSCF)=   -261.285325773895     E(MP2)=   -262.413817400139
9     E(MCSCF)=   -261.281298497540     E(MP2)=   -262.407448792218
10     E(MCSCF)=   -261.245207039554     E(MP2)=   -262.396032593288
-----------------------------------------------------------------------

One can see that singlets and triplets lie in the different energy intervals, and I think that their contributions will be different.

For 30 and 30 states I have for singlets:

*** XMC-QDPT2 ENERGIES ***
-----------------------------------------------------------------------
STATE                       1ST ORDER                       2ND ORDER
1     E(MCSCF)=   -261.677105329716     E(MP2)=   -262.664827084210
2     E(MCSCF)=   -261.424716215681     E(MP2)=   -262.655108390912
3     E(MCSCF)=   -261.407702389013     E(MP2)=   -262.648871226260
4     E(MCSCF)=   -261.397971587331     E(MP2)=   -262.647641207390
5     E(MCSCF)=   -261.357555431425     E(MP2)=   -262.562002285147
6     E(MCSCF)=   -261.350462737544     E(MP2)=   -262.521468427837
7     E(MCSCF)=   -261.287008744553     E(MP2)=   -262.516814152587
8     E(MCSCF)=   -261.245424936052     E(MP2)=   -262.515688777728
9     E(MCSCF)=   -261.177968460058     E(MP2)=   -262.485727816582
10     E(MCSCF)=   -261.076974499547     E(MP2)=   -262.448472021454
11     E(MCSCF)=   -261.071636924763     E(MP2)=   -262.445527831057
12     E(MCSCF)=   -261.061965988333     E(MP2)=   -262.426980938173
13     E(MCSCF)=   -261.061867648851     E(MP2)=   -262.425780165295
14     E(MCSCF)=   -261.058318432591     E(MP2)=   -262.409979543733
15     E(MCSCF)=   -260.947131439454     E(MP2)=   -262.363605462445
16     E(MCSCF)=   -260.939212649675     E(MP2)=   -262.351319907394
17     E(MCSCF)=   -260.937331966072     E(MP2)=   -262.349316225763
18     E(MCSCF)=   -260.900825307545     E(MP2)=   -262.322552390167
19     E(MCSCF)=   -260.900287274093     E(MP2)=   -262.296210503329
20     E(MCSCF)=   -260.882238086740     E(MP2)=   -262.294632829723
21     E(MCSCF)=   -260.866868419423     E(MP2)=   -262.290450640511
22     E(MCSCF)=   -260.863521956935     E(MP2)=   -262.281366420658
23     E(MCSCF)=   -260.862570729350     E(MP2)=   -262.272658271511
24     E(MCSCF)=   -260.846913749707     E(MP2)=   -262.247134701686
25     E(MCSCF)=   -260.819718841643     E(MP2)=   -262.240637702006
26     E(MCSCF)=   -260.799447977765     E(MP2)=   -262.233250085423
27     E(MCSCF)=   -260.797853874460     E(MP2)=   -262.163451256534
28     E(MCSCF)=   -260.765642203021     E(MP2)=   -262.144550793186
29     E(MCSCF)=   -260.758728140288     E(MP2)=   -262.080540322113
30     E(MCSCF)=   -260.756647137717     E(MP2)=   -262.079221112841
-----------------------------------------------------------------------

and for triplets:

*** XMC-QDPT2 ENERGIES ***
-----------------------------------------------------------------------
STATE                       1ST ORDER                       2ND ORDER
1     E(MCSCF)=   -261.677467336573     E(MP2)=   -262.654083846240
2     E(MCSCF)=   -261.422736915806     E(MP2)=   -262.653265539279
3     E(MCSCF)=   -261.412278358707     E(MP2)=   -262.648304114864
4     E(MCSCF)=   -261.379098421442     E(MP2)=   -262.648127316962
5     E(MCSCF)=   -261.371330822110     E(MP2)=   -262.584515910929
6     E(MCSCF)=   -261.352101463680     E(MP2)=   -262.558824510546
7     E(MCSCF)=   -261.350894462307     E(MP2)=   -262.436002170858
8     E(MCSCF)=   -261.285325775641     E(MP2)=   -262.428495934141
9     E(MCSCF)=   -261.281298499281     E(MP2)=   -262.426761523750
10     E(MCSCF)=   -261.245207041357     E(MP2)=   -262.421963057847
11     E(MCSCF)=   -261.185251020882     E(MP2)=   -262.413996783130
12     E(MCSCF)=   -261.099741312200     E(MP2)=   -262.401036874001
13     E(MCSCF)=   -261.095932349753     E(MP2)=   -262.372825498208
14     E(MCSCF)=   -261.095199811925     E(MP2)=   -262.363547305445
15     E(MCSCF)=   -261.077182795536     E(MP2)=   -262.345708355947
16     E(MCSCF)=   -261.045831371041     E(MP2)=   -262.341998919423
17     E(MCSCF)=   -261.037001604898     E(MP2)=   -262.338765683535
18     E(MCSCF)=   -260.986096084652     E(MP2)=   -262.336175193009
19     E(MCSCF)=   -260.970504809476     E(MP2)=   -262.326520191372
20     E(MCSCF)=   -260.953834738864     E(MP2)=   -262.302975938659
21     E(MCSCF)=   -260.930468059888     E(MP2)=   -262.300922500423
22     E(MCSCF)=   -260.927506378889     E(MP2)=   -262.289594157038
23     E(MCSCF)=   -260.902625698348     E(MP2)=   -262.277853276837
24     E(MCSCF)=   -260.878635540109     E(MP2)=   -262.268828319223
25     E(MCSCF)=   -260.870555344468     E(MP2)=   -262.266066055734
26     E(MCSCF)=   -260.866711639703     E(MP2)=   -262.257206346321
27     E(MCSCF)=   -260.863948383487     E(MP2)=   -262.172040193340
28     E(MCSCF)=   -260.861468622304     E(MP2)=   -262.144226911284
29     E(MCSCF)=   -260.806654554042     E(MP2)=   -262.142572031784
30     E(MCSCF)=   -260.805557844229     E(MP2)=   -262.113701530678
-----------------------------------------------------------------------

At CAS I get E(triplet)-E(singlet) = -80 cm-1;
at CAS/XMCQDPT2(10,10) deltaE = 4198 cm-1;
at CAS/XMCQDPT2(20,20) deltaE = 2778 cm-1;
at CAS/XMCQDPT2(30,30) deltaE = 2357 cm-1.

How many triplets and singlets should I take in the XMCQDPT2 procedure: the same and very large numbers or the different numbers but in the same energy intervals?

Kind regards,
Maksim Shundalau.

On Sat Dec 24 '16 9:00pm, Igor Polyakov wrote
---------------------------------------------
>Hello, Maksim

>I'm not Alex, but I'll try to help. First of all, CASSCF state order is not guaranteed to be the correct one=)
>Larger effective Hamiltonian dimension should yield more correct results, however for big systems it is simply impractical (high computational effort) to calculate Heff for more than 10-20 states. 2x2 seems to be a bit extreme in the low end because higher states (up to 5 or even more sometimes) can be of influence to the lowest ones. I would recommend to conduct a single large calculation to see the "EIGENVECTORS OF THE EFFECTIVE HAMILTONIAN".
>For example for one of my systems:
>                      1          2          3          4          5

>               *******************************************************

>    1            -0.996755  -0.063006  -0.025667   0.000488   0.007272
>    2             0.068939  -0.930901  -0.324050   0.023948   0.052243
>    3             0.002769   0.257066  -0.672227   0.680566  -0.104661
>    4             0.004256   0.225480  -0.647910  -0.704316   0.166305
>    5             0.013621   0.100592   0.148076   0.039046   0.262885
>    6            -0.004291  -0.005923  -0.014240  -0.189029  -0.930557
>    7            -0.005277   0.019798   0.006718  -0.032537   0.111529
>    8             0.036419  -0.043997  -0.013186  -0.042064  -0.102410
>    9            -0.008000  -0.005780   0.016341   0.009414   0.020153
>   10            -0.008890   0.003653   0.006373  -0.004601  -0.015154

>This means that to correctly describe state 3 it is crucial to include state 4. This can also be seen in the CAS-CI states, states 3 and 4 share some large weighted CSF-S

>Best regards, Igor

>On Fri Dec 23 '16 5:37pm, Maksim Shundalau wrote
>------------------------------------------------
>>Dear Alex,
>>
>>
>>Let's pretend that I calculated two lower states (triplet and singlet) of transient molecule (or radical) at the CASSCF level of theory. I get triplet as a ground state and singlet is only a few tens of cm-1 higher than the triplet.
>>How many triplets and singlets should I take in the XMCQDPT2 procedure to get the same sequence of states and trust the results? If I take 2 and 2 (or 10 and 10), I have triplet higher than singlet. Should I take 3 and 2 (or 5 and 2, for example) for triplet and singlet, respectively?
>>
>>
>>Kind regards,
>>Maksim Shundalau.
>>

Mon Dec 26 '16 1:18pm