CC calculations diverge on small systems

Hello,
I’ve come across cases where CCSD calculations on fairly small molecules diverge wildly, and the calculations end up with MP2 energies. For example, SP on acetone is fine with cc-pVDZ but not with cc-pVTZ.

Am I doing something wrong or is it just the way things are?

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 Please cite Q-Chem as follows:
 Y. Shao et al., Mol. Phys. 113, 184-215 (2015)
 DOI: 10.1080/00268976.2014.952696

 Q-Chem 5.4.0 for Intel X86 EM64T Linux

 Parts of Q-Chem use Armadillo 9.800.1 (Horizon Scraper).
 http://arma.sourceforge.net/

 Q-Chem begins on Fri Aug 12 15:14:19 2022  

Host: 
0

     Scratch files written to /somepath/
Processing $rem in /somepath/qchem.20210325/config/preferences:
Processing $rem in  /somepath/:
Core orbitals will be frozen

Checking the input file for inconsistencies... 	...done.

--------------------------------------------------------------
User input:
--------------------------------------------------------------
$rem
 METHOD CCSD(T)
 JOBTYPE SP
 BASIS cc-pVTZ
$end

$molecule
0 1
  C   -2.50154040248934      1.94130075676444     -0.02248358320146
  O   -1.38277650374024      2.39049754028746     -0.01198270966319
  C   -2.81848423251740      0.62291698877755     -0.67970279571791
  C   -3.65209505348638      2.66878046299721      0.62371531767802
  H   -3.30363620087669      3.59656976406576      1.06677387032028
  H   -4.10959097717150      2.04207559163931      1.39023291904063
  H   -4.42500431777946      2.88017266963735     -0.11629234959823
  H   -1.91633754071756      0.19214490436456     -1.10295330529289
  H   -3.56329502268127      0.76358654290276     -1.46408231118147
  H   -3.25032974854015     -0.06538522143640      0.04790494761624
$end
--------------------------------------------------------------
 ----------------------------------------------------------------
             Standard Nuclear Orientation (Angstroms)
    I     Atom           X                Y                Z
 ----------------------------------------------------------------
    1      C      -2.5015404025     1.9413007568    -0.0224835832
    2      O      -1.3827765037     2.3904975403    -0.0119827097
    3      C      -2.8184842325     0.6229169888    -0.6797027957
    4      C      -3.6520950535     2.6687804630     0.6237153177
    5      H      -3.3036362009     3.5965697641     1.0667738703
    6      H      -4.1095909772     2.0420755916     1.3902329190
    7      H      -4.4250043178     2.8801726696    -0.1162923496
    8      H      -1.9163375407     0.1921449044    -1.1029533053
    9      H      -3.5632950227     0.7635865429    -1.4640823112
   10      H      -3.2503297485    -0.0653852214     0.0479049476
 ----------------------------------------------------------------
 Nuclear Repulsion Energy =         119.96460455 hartrees
 There are       16 alpha and       16 beta electrons
 Requested basis set is cc-pVTZ
 There are 76 shells and 204 basis functions
 Total memory of 2000 MB is distributed as follows: 
   MEM_STATIC is set to 192 MB
   QALLOC/CCMAN JOB total memory use is  1808 MB
 Warning: actual memory use might exceed 2000 MB

 Total QAlloc Memory Limit   2000 MB
 Mega-Array Size       188 MB
 MEM_STATIC part       192 MB

                       Distance Matrix (Angstroms)
             C (  1)   O (  2)   C (  3)   C (  4)   H (  5)   H (  6)
   O (  2)  1.205620
   C (  3)  1.506827  2.373067
   C (  4)  1.506843  2.373049  2.565027
   H (  5)  2.137699  2.511579  3.482551  1.085595
   H (  6)  2.142837  3.085956  2.822340  1.090693  1.780629
   H (  7)  2.142427  3.083150  2.827285  1.090728  1.780544  1.752573
   H (  8)  2.137621  2.511505  1.085622  3.482522  4.268773  3.801129
   H (  9)  2.143021  3.083844  1.090771  2.827817  3.807683  3.174916
   H ( 10)  2.142995  3.085888  1.090717  2.822877  3.801427  2.642265
             H (  7)   H (  8)   H (  9)
   H (  8)  3.806889
   H (  9)  2.653115  1.780289
   H ( 10)  3.175395  1.780543  1.752497
 
 A cutoff of  1.0D-14 yielded   2888 shell pairs
 There are     21028 function pairs (     26828 Cartesian)
 Smallest overlap matrix eigenvalue = 6.92E-04

 Scale SEOQF with 1.000000e-01/1.000000e-01/1.000000e-01

 Standard Electronic Orientation quadrupole field applied
 Nucleus-field energy     =     0.0000000178 hartrees
 Guess from superposition of atomic densities
 Warning:  Energy on first SCF cycle will be non-variational
 SAD guess density has 32.000000 electrons

 -----------------------------------------------------------------------
  General SCF calculation program by
  Eric Jon Sundstrom, Paul Horn, Yuezhi Mao, Dmitri Zuev, Alec White,
  David Stuck, Shaama M.S., Shane Yost, Joonho Lee, David Small,
  Daniel Levine, Susi Lehtola, Hugh Burton, Evgeny Epifanovsky,
  Bang C. Huynh
 -----------------------------------------------------------------------
 Hartree-Fock
 A restricted SCF calculation will be
 performed using DIIS
 SCF converges when DIIS error is below 1.0e-08
 ---------------------------------------
  Cycle       Energy         DIIS error
 ---------------------------------------
    1    -193.0667059155      3.54e-02  
    2    -191.9342292412      4.34e-03  
    3    -191.9930514987      3.35e-03  
    4    -192.0323358565      4.44e-04  
    5    -192.0342265997      1.31e-04  
    6    -192.0344244091      5.23e-05  
    7    -192.0344632660      2.28e-05  
    8    -192.0344692676      6.38e-06  
    9    -192.0344698169      1.11e-06  
   10    -192.0344698327      3.40e-07  
   11    -192.0344698338      5.08e-08  
   12    -192.0344698339      7.30e-09  Convergence criterion met
 ---------------------------------------
 SCF time:   CPU 79.03s  wall 80.00s 
 SCF   energy in the final basis set =     -192.0344698339
 Total energy in the final basis set =     -192.0344698339


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

   CCMAN2: suite of methods based on coupled cluster
           and equation of motion theories.

   Components:
   * libvmm-1.3-trunk
     by Evgeny Epifanovsky, Ilya Kaliman.
   * libtensor-2.5-trunk
     by Evgeny Epifanovsky, Michael Wormit, Dmitry Zuev, Sam Manzer, 
        Ilya Kaliman.
   * libcc-2.5-trunk
     by Evgeny Epifanovsky, Arik Landau, Tomasz Kus, Kirill Khistyaev, 
        Dmitry Zuev, Prashant Manohar, Xintian Feng, Anna Krylov, 
        Matthew Goldey, Alec White, Thomas Jagau, Kaushik Nanda, 
        Anastasia Gunina, Alexander Kunitsa, Joonho Lee.

   CCMAN original authors:
   Anna I. Krylov, C. David Sherrill, Steven R. Gwaltney,
   Edward F. C. Byrd (2000)
   Sergey V. Levchenko, Lyudmila V. Slipchenko, Tao Wang,
   Ana-Maria C. Cristian (2003)
   Piotr A. Pieniazek, C. Melania Oana, Evgeny Epifanovsky (2007)
   Prashant Manohar (2009)

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


 Allocating and initializing 1808MB of RAM...
 Calculation will run on 1 core.


 Occupation and symmetry of molecular orbitals

 Point group: C1 (1 irreducible representation).

                           A     All 
 -------------------------------------
 All molecular orbitals:
  - Alpha                  204   204 
  - Beta                   204   204 
 -------------------------------------
 Alpha orbitals:
  - Frozen occupied        4     4   
  - Active occupied        12    12  
  - Active virtual         188   188 
  - Frozen virtual         0     0   
 -------------------------------------
 Beta orbitals:
  - Frozen occupied        4     4   
  - Active occupied        12    12  
  - Active virtual         188   188 
  - Frozen virtual         0     0   
 -------------------------------------

 Import integrals:   CPU 0.00 s  wall 0.00 s

 Import integrals:   CPU 116.02 s  wall 122.26 s

 MP2 amplitudes:   CPU 0.64 s  wall 1.45 s

Running a double precision version
           CCSD T amplitudes will be solved using DIIS.

           Start     Size      MaxIter   EConv     TConv     
           3         7         100       1.00e-06  1.00e-04  
 ------------------------------------------------------------------------------
           Energy (a.u.)   Ediff      Tdiff       Comment
 ------------------------------------------------------------------------------
          -192.77459996                           
     1    -179.83594822   1.29e+01   3.25e+01     Step took 04.31.
     2    1.2697265e+04   1.29e+04   5.82e+04     
     3    2.6704471e+16   2.67e+16   2.81e+11     
     4   -5.9672497e+12   2.67e+16   2.67e+11     Switched to DIIS steps.
     5    2.4276428e+11   6.21e+12   1.27e+10     
     6    1.3898991e+09   2.41e+11   8.80e+08     
     7    1.8375754e+08   1.21e+09   5.76e+07     
     8    3.9242982e+06   1.80e+08   1.54e+07     
     9    4.1174153e+05   3.51e+06   2.20e+06     
    10    5.5193096e+18   5.52e+18   5.73e+12     
    11    2.7372574e+19   2.19e+19   1.10e+12     
    12    6.0228464e+17   2.68e+19   4.93e+12     
    13    1.0621670e+17   4.96e+17   1.36e+12     
    14    9.6868592e+15   9.65e+16   4.47e+11     
    15    3.3377559e+15   6.35e+15   4.85e+10     
    16    7.2118731e+16   6.88e+16   3.58e+11     
    17    3.5806286e+46   3.58e+46   1.02e+32     
    18    -192.77459996   3.58e+46   1.02e+32     
    19    -192.77459996   0.00e+00   0.00e+00     
 ------------------------------------------------------------------------------
          -192.77459996                           CCSD T converged.

End of double precision

WARNING: YOUR (T) CALCULATION MAY RUN OUT OF MEMORY
REDUCE CC_MEMORY OR USE CC_BACKEND=XM IF THIS HAPPENS

----------------------------------------
libpt (c) 2016-2019 Ilya Kaliman
Fast Coupled Cluster Triples Corrections
https://github.com/ilyak/libpt
----------------------------------------

 Starting (T) calculation...
 Using double precision libpt code
 Running restricted (T) code
 Using 1 integral batch

 (T) calculation completed in 777.93 sec
 (T) energy is -0.0333959097

 SCF energy                 = -192.03446983
 MP2 energy                 = -192.77459996
 CCSD correlation energy    =   -0.74013013
 CCSD total energy          = -192.77459996
 CCSD(T) correlation energy =   -0.03339591
 CCSD(T) total energy       = -192.80799587

 CCSD  T1^2 = 0.0000  T2^2 = 0.2148  Leading amplitudes:

 Amplitude    Orbitals with energies

 Amplitude    Orbitals with energies
 -0.0522       15 (A) A      15 (A) B    ->    18 (A) A      18 (A) B     
              -0.4886       -0.4886            0.1487        0.1487       
  0.0522       15 (A) A      15 (A) B    ->    18 (A) B      18 (A) A     
              -0.4886       -0.4886            0.1487        0.1487       
  0.0522       15 (A) B      15 (A) A    ->    18 (A) A      18 (A) B     
              -0.4886       -0.4886            0.1487        0.1487       
 -0.0522       15 (A) B      15 (A) A    ->    18 (A) B      18 (A) A     
              -0.4886       -0.4886            0.1487        0.1487       

 CCSD calculation:   CPU 3670.66 s  wall 7621.90 s

 Total ccman2 time:   CPU 3793.29 s  wall 7753.64 s

 
 --------------------------------------------------------------
 
                    Orbital Energies (a.u.)
 --------------------------------------------------------------
 
 Alpha MOs
 -- Occupied --
-20.5410 -11.3281 -11.2327 -11.2327  -1.3880  -1.0431  -0.9685  -0.7409
 -0.6465  -0.6371  -0.6245  -0.5621  -0.5597  -0.5375  -0.4886  -0.4124
 -- Virtual --
  0.1270   0.1487   0.1797   0.2045   0.2068   0.2306   0.2447   0.2694
  0.3273   0.3438   0.3700   0.3868   0.4109   0.4901   0.5032   0.5109
  0.5696   0.5992   0.5994   0.6218   0.6238   0.6303   0.6410   0.6535
  0.6859   0.7370   0.7543   0.7908   0.7950   0.8441   0.8896   0.9056
  0.9763   1.0405   1.0431   1.0495   1.0679   1.1237   1.1441   1.1641
  1.1650   1.1841   1.2176   1.2456   1.2649   1.2814   1.3320   1.3568
  1.3734   1.4482   1.4522   1.4915   1.4973   1.5053   1.5187   1.5227
  1.5497   1.5895   1.6047   1.6182   1.6784   1.7361   1.7707   1.8316
  1.9910   2.0840   2.1223   2.1912   2.4120   2.4162   2.4181   2.4822
  2.5278   2.6022   2.6630   2.6812   2.7460   2.7685   2.7918   2.8736
  2.9020   2.9184   2.9401   3.0532   3.0671   3.0896   3.0916   3.1074
  3.1254   3.1586   3.1835   3.1844   3.2310   3.2752   3.2974   3.3026
  3.3077   3.3643   3.3682   3.4139   3.4291   3.4394   3.4923   3.5383
  3.5718   3.5969   3.6154   3.6392   3.6581   3.7079   3.7291   3.7581
  3.7583   3.8005   3.8094   3.8271   3.8399   3.9712   3.9942   4.0275
  4.0422   4.0828   4.0942   4.1133   4.1319   4.1381   4.1673   4.2170
  4.2330   4.3068   4.3209   4.3505   4.3608   4.3845   4.4161   4.4481
  4.4924   4.5310   4.5330   4.5984   4.6121   4.6294   4.6779   4.7006
  4.7134   4.8914   4.8991   4.9536   5.1147   5.1346   5.1671   5.1816
  5.2904   5.4037   5.4205   5.4411   5.4604   5.4730   5.4969   5.5122
  5.5130   5.5999   5.6108   5.6283   5.6334   5.6689   5.7022   5.7459
  5.7705   5.9240   6.0527   6.1837   6.2090   6.2144   6.2505   6.2806
  6.7566   6.7709   6.9219   6.9650   7.1751   7.3771   7.5486   7.5748
  9.4070  13.7784  14.1467  14.2328
 --------------------------------------------------------------
 
          Ground-State Mulliken Net Atomic Charges

     Atom                 Charge (a.u.)
  ----------------------------------------
      1 C                     0.292977
      2 O                    -0.350614
      3 C                    -0.291884
      4 C                    -0.291788
      5 H                     0.127830
      6 H                     0.096346
      7 H                     0.096469
      8 H                     0.127820
      9 H                     0.096477
     10 H                     0.096368
  ----------------------------------------
  Sum of atomic charges =     0.000000

 -----------------------------------------------------------------
                    Cartesian Multipole Moments
 -----------------------------------------------------------------
    Charge (ESU x 10^10)
                -0.0000
    Dipole Moment (Debye)
         X      -3.0393      Y      -1.2210      Z      -0.0280
       Tot       3.2755
    Quadrupole Moments (Debye-Ang)
        XX     -12.3005     XY      -4.3584     YY     -29.0933
        XZ      -0.0022     YZ       0.2339     ZZ     -24.0680
    Octopole Moments (Debye-Ang^2)
       XXX     161.7354    XXY     -23.3312    XYY      60.2171
       YYY    -149.3542    XXZ       0.1939    XYZ      -0.0416
       YYZ       2.2148    XZZ      64.6704    YZZ     -44.9050
       ZZZ       1.6836
    Hexadecapole Moments (Debye-Ang^3)
      XXXX   -1121.2178   XXXY     299.4455   XXYY    -271.8214
      XYYY     362.8377   YYYY    -691.4699   XXXZ      13.0905
      XXYZ     -12.9406   XYYZ      -0.5437   YYYZ     -22.1880
      XXZZ    -209.1754   XYZZ     121.8206   YYZZ    -121.4931
      XZZZ       8.4686   YZZZ     -29.6475   ZZZZ     -78.8243
 -----------------------------------------------------------------
Archival summary:
1\1\n19\SP\ProcedureUnspecified\BasisUnspecified\136\morgunov\FriAug1217:24:532022FriAug1217:24:532022\0\\#,ProcedureUnspecified,BasisUnspecified,\\0,1\C\O,1,1.20562\C,1,1.50683,2,121.667\H,3,1.08562,1,110.025,2,0.186191,0\H,3,1.09072,1,110.149,2,121.365,0\H,3,1.09077,1,110.147,2,-120.958,0\C,1,1.50684,2,121.664,3,179.858,0\H,7,1.0856,1,110.032,2,-0.222193,0\H,7,1.09069,1,110.136,2,-121.412,0\H,7,1.09073,1,110.102,2,120.932,0\\HF=-192.03447\\@

 Total job time:  7834.65s(wall), 3873.76s(cpu) 
 Fri Aug 12 17:24:53 2022

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I’m not sure whether the observation that E(CCSD) = E(MP2) is actually meaningful, because it’s clear that solution of the CCSD equations didn’t converge and I would not trust anything beyond that point.

When I run this job with Q-Chem 6.0, it fails to run because it demands larger MEM_TOTAL, which isn’t surprising – it’s more surprising that your job runs without setting MEM_TOTAL, but either you’re setting that in local configuration or else the Q-Chem 5.4 settings were different. When I use a large MEM_TOTAL (=100000 but that’s probably overkill for this job), the CCSD equations converge nicely:

          Energy (a.u.)   Ediff      Tdiff       Comment
 ------------------------------------------------------------------------------
          -192.77459996
     1    -192.78182786   7.23e-03   7.72e-01
     2    -192.80218122   2.04e-02   9.56e-02
     3    -192.80214386   3.74e-05   3.57e-02
     4    -192.80406111   1.92e-03   1.24e-02     Switched to DIIS steps.
     5    -192.80473276   6.72e-04   8.50e-03
     6    -192.80475831   2.56e-05   1.56e-03
     7    -192.80475841   9.90e-08   7.30e-04
     8    -192.80475813   2.81e-07   1.94e-04
     9    -192.80475895   8.14e-07   1.02e-04
    10    -192.80475894   4.03e-09   2.38e-05
 ------------------------------------------------------------------------------
          -192.80475894                           CCSD T converged.

It’s not clear to me why your job is behaving differently.

1 Like

Interesting, I didn’t think the program could finish w/o enough memory. I’ll try running with a larger MEM_TOTAL.

Is there any way to estimate how much MEM_TOTAL should be used given the number of atoms/orbitals used?

It’s NBasis^4 double-precision numbers, but note that MEM_TOTAL is measured in Mb. See Q-Chem 4.3 User’s Manual : Memory Options and Parallelization of Coupled-Cluster Calculations

1 Like

I can’t reproduce this either with 5.2.2 or 6.0.0 with mem_total = 2000. Can you repeatably get this divergence?

1 Like

Yes, I can. Also, it turns out our cluster sets up MEM_TOTAL automatically, that’s why it wasn’t an issue for me, and in fact setting MEM_TOTAL=100000 changed nothing. This was all on a qchem installed on Ubuntu 18.04. I’ve just tried a qchem installation on CentOS 8 and I could replicate @jherbert’s output. Maybe there was something wrong with the way we installed qchem on Ubuntu :man_shrugging: