# Curse of the nano-Hartree

5 years 1 week ago #538
by Nike

Replied by

*Nike*on topic*Curse of the nano-Hartree*
Dear Mihaly,

Thanks for replying so fast!

1) Perhaps MOLPRO is also using the AO Fock Matrix, because it agrees with CFOUR to ~1 nHartree. The ROHF in MOLPRO was converged with an energy tolerance of 1e-16 ( here ), so the SCF cannot really be converged any better, and the AO Fock Matrix is probably yielding the correct MO Fock matrix and correct correlation energies to sub-nHartree precision.

With CFOUR the SCF was converged using SCF_CONV=10, which can be achieved with 14,372 iterations, with "largest density difference" being only: 0.9669940548D-10. The energy was converged to 0.1 pHartree at iteration 14, and the next 14,000 iterations were just jiggling around the orbitals until the largest density difference went below 10^-10:

This makes me think that converging the SCF in CFOUR won't be able to change very much.

I tried to converge with the largest density difference being < 10^-11, but after 49060 iterations I gave up.

The reason why I didn't post the ROHF results with CFOUR was because it *looks* like the energy doesn't agree with MOLPRO and MRCC, but actually this is because of the Bohr -> Angstrom conversion in CFOUR:

I thought that a difference of 0.0000006 Bohr would not make a difference, but actually if I use MOLPRO's geometry of 7.880,157,968,027,6825 Bohr, we get perfect agreement between CFOUR and MOLPRO at ROHF level:

So actually the 25 pHartree difference between MOLPRO and MRCC at ROHF level might not have anything to do with the Boys function (why would it?), it might be because of the 0.00000001 Bohr difference in geometry due to using difference conversion factors. This was something that I never would have expected, especially for such a shallow state like Li2,1^3\Sigma_u^+, which has only a -333cm-1 depth and an r_e = 4.17 Angstroms.

Anyway, based on the convergence I've shown for the CFOUR ROHF with SCF_CONV=10, do you still think the difference in MO Fock Matrix can yield a 9 nano-Hartree difference in CCSD? This is 1000 times bigger than the difference between CFOUR's ROHF at iteration 14 and iteration 14,000.

49060 iterations was not enough to get convergence with SCF_CONV=11, so maybe we just have to compare the MO Fock matrices somehow. A Root Mean Square difference between matrix elements with SCF_CONV=10, 9, 8..., along with differences in CCSD for those cases might show how much a small change in matrix elements changes the CCSD energy. This would tell us if SCF_CONV=11 will help or not. Is it possible to do this somehow? Otherwise I might guess that there might be some truncation happening when writing the fort.55 just as there was in ovirt.f, but perhaps you have already checked that.

3) Thank you for looking into the AO-MO transformation performance!

With best wishes!!

Nike

Thanks for replying so fast!

1) Perhaps MOLPRO is also using the AO Fock Matrix, because it agrees with CFOUR to ~1 nHartree. The ROHF in MOLPRO was converged with an energy tolerance of 1e-16 ( here ), so the SCF cannot really be converged any better, and the AO Fock Matrix is probably yielding the correct MO Fock matrix and correct correlation energies to sub-nHartree precision.

With CFOUR the SCF was converged using SCF_CONV=10, which can be achieved with 14,372 iterations, with "largest density difference" being only: 0.9669940548D-10. The energy was converged to 0.1 pHartree at iteration 14, and the next 14,000 iterations were just jiggling around the orbitals until the largest density difference went below 10^-10:

```
14 -14.864012799596406 0.3904492329D-04
14371 -14.864012799596448 0.2061507832D-07
14372 -14.864012799596420 0.9669940548D-10
```

This makes me think that converging the SCF in CFOUR won't be able to change very much.

I tried to converge with the largest density difference being < 10^-11, but after 49060 iterations I gave up.

The reason why I didn't post the ROHF results with CFOUR was because it *looks* like the energy doesn't agree with MOLPRO and MRCC, but actually this is because of the Bohr -> Angstrom conversion in CFOUR:

```
2014 CODATA: 1 Angstrom = 1/0.529,177,210,67(12) Bohr (4.17 Ang = 7.880,157,943,159,143 Bohr)
MOLPRO: 1 Angstrom = 1/0.529,177,209 Bohr (4.17 Ang = 7.880,157,968,027,6825 Bohr)
MRCC: 1 Angstrom = 1/0.529,177,20859 Bohr (4.17 Ang = 7.880,157,974,133,132 Bohr)
CFOUR: 1 Angstrom = 1/0.529,177,249 Bohr (4.17 Ang = 7.880,157,372,374,11 Bohr)
```

I thought that a difference of 0.0000006 Bohr would not make a difference, but actually if I use MOLPRO's geometry of 7.880,157,968,027,6825 Bohr, we get perfect agreement between CFOUR and MOLPRO at ROHF level:

```
CFOUR with 7.880,157,372,374 Bohr: -14.864,012,799,596
CFOUR with 7.880,157,968,027 Bohr: -14.864,012,797,989
MOLPR with 7.880,157,968,027 Bohr: -14.864,012,797,989
```

So actually the 25 pHartree difference between MOLPRO and MRCC at ROHF level might not have anything to do with the Boys function (why would it?), it might be because of the 0.00000001 Bohr difference in geometry due to using difference conversion factors. This was something that I never would have expected, especially for such a shallow state like Li2,1^3\Sigma_u^+, which has only a -333cm-1 depth and an r_e = 4.17 Angstroms.

Anyway, based on the convergence I've shown for the CFOUR ROHF with SCF_CONV=10, do you still think the difference in MO Fock Matrix can yield a 9 nano-Hartree difference in CCSD? This is 1000 times bigger than the difference between CFOUR's ROHF at iteration 14 and iteration 14,000.

49060 iterations was not enough to get convergence with SCF_CONV=11, so maybe we just have to compare the MO Fock matrices somehow. A Root Mean Square difference between matrix elements with SCF_CONV=10, 9, 8..., along with differences in CCSD for those cases might show how much a small change in matrix elements changes the CCSD energy. This would tell us if SCF_CONV=11 will help or not. Is it possible to do this somehow? Otherwise I might guess that there might be some truncation happening when writing the fort.55 just as there was in ovirt.f, but perhaps you have already checked that.

3) Thank you for looking into the AO-MO transformation performance!

With best wishes!!

Nike

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5 years 1 day ago - 5 years 1 day ago #548
by Nike

Replied by

*Nike*on topic*Curse of the nano-Hartree*
Greetings,

I have not been able to get SCF to converge in CFOUR with "largest density difference" smaller than 1e-11 with 49060 iterations, and I don't think it will be possible since it took 14,372 iterations to get it to become smaller than 1e-10. But I can live with the 9 nH difference this seems to cause from the MO integrals giving the wrong MO Fock matrix.

However at ROHF level for the Li atom, I'm getting a rather large error in MRCC vs MOLPRO for 6Z, and it's relevant compared to the size of our discrepancy with experiment. For some reason 5Z and 7Z are perfectly fine.

For the Li2 molecule, this huge discrepancy doubles in size:

Clearly there's more than just Boys function error in the 6Z case, so I compared the basis set exponents and contraction coefficients but I really so no difference in them (MOLPRO was copied and pasted from the output file and MRCC should have been taken from the MOLDEN file but it was in scientific notation so to make it easier to compare I just took the numbers from the GENBAS file):

Actually now I have directly compared the exponents and contraction coefficients from the MOLPRO output with the MOLDEN file generated in MRCC and after putting the two into arrays, Matlab says the two arrays are the same: isequal(MRCC,molpro) gives a value of 1. So unfortunately the basis sets seem to be exactly the same. The 1's and 0's for the contraction coefficients in the GENBAS are correct, and the likewise the numbers at the top of the GENBAS describing how many exponents and contraction coefficients.

I cannot imagine any other reason why the 6Z results are so much worse than the 5Z and 7Z ones, apart from maybe one code being more prone to errors due to linear dependencies in the basis set (but I think this would hurt the 7Z results more than the 6Z results and this isn't the case here).

The discrepancy is relevant on the scale of our discrepancy with experiment.

After adding an X2C+SFDC+Breit correction of 0.255cm-1 to each De value, we get, before any CBS extrapolations:

1) -333.58 cm-1 (FCIest./aCV7Z) -> Discrepancy with expt = 0.07 cm-1

2) -333.59 cm-1 (FCIest./aCV6Z) -> Discrepancy with expt = 0.06 cm-1

3) -333.65 cm-1 (empirical with finite-mass effects removed)

4) -333.74 cm-1 (FCIest./aCV5Z) -> Discrepancy with expt = 0.09cm-1

But the 125 nHartree difference between ROHF/MRCC and ROHF/MOLPRO is 0.025cm-1 which is more than 40% the size of the 0.06cm-1 discrepancy with experiment.

The 6Z MRCC output is here (we're just comparing ROHF, because the norm goes bad when MRCC tries to do correlation on a basis set this big): github.com/ndattani/AI_ENERGIES/blob/mas..._betterIntegrals.txt

The MOLPRO output is here:

github.com/ndattani/AI_ENERGIES/blob/mas...etterConvergence.txt

Is there anything else that might be causing this big discrepancy for the 6Z case?

With best wishes!

Nike Dattani

I have not been able to get SCF to converge in CFOUR with "largest density difference" smaller than 1e-11 with 49060 iterations, and I don't think it will be possible since it took 14,372 iterations to get it to become smaller than 1e-10. But I can live with the 9 nH difference this seems to cause from the MO integrals giving the wrong MO Fock matrix.

However at ROHF level for the Li atom, I'm getting a rather large error in MRCC vs MOLPRO for 6Z, and it's relevant compared to the size of our discrepancy with experiment. For some reason 5Z and 7Z are perfectly fine.

```
aug-cc-pCV5Z (< 1 pico-Hartree Boys function error):
-------------------------------------------------------------
ROHF/MRCC (canonical) -7.432 722 692 551 (default)
ROHF/MRCC (semi-can) -7.432 722 692 551 (default)
ROHF/MOLPRO: -7.432 722 692 551 (itol=18,scftol=16)
-------------------------------------------------------------
aug-cc-pCV6Z (62,000 pico-Hartree Boys function error ??):
-------------------------------------------------------------
ROHF-MRCC (semi-can) -7.432 726 059 513 (itol=18, scftol=13)
ROHF-MRCC (canonical) -7.432 726 059 513 (itol=18, scftol=13)
ROHF-MOLRPO -7.432 726 121 753 (itol=18, scftol=16)
-------------------------------------------------------------
aug-cc-pCV7Z (3 pico-Hartree Boys function error):
-------------------------------------------------------------
ROHF/MRCC (semi-can) -7.432 726 687 162
ROHF/MRCC (canonical) -7.432 726 687 162
ROHF/MOLRPO -7.432 726 687 159
```

For the Li2 molecule, this huge discrepancy doubles in size:

```
aug-cc-pCV5Z (25 pico-Hartree Boys function error):
-------------------------------------------------------------
ROHF/MRCC -14.864 012 797 964 (itol=18,scftol=14)
ROHF/MOLPRO -14.864 012 797 989 (itol=18,scftol=16)
-------------------------------------------------------------
aug-cc-pCV6Z (125,000 pico-Hartree Boys function error ??):
-------------------------------------------------------------
ROHF/MRCC (semi-can) -14.864 019 536 409 (itol=18, scftol=13)
ROHF/MRCC (canonical) -14.864 019 536 410 (itol=18, scftol=13)
ROHF/MOLPRO -14.864 019 661 611 (itol=18, scftol=16)
-------------------------------------------------------------
aug-cc-pCV7Z (28 pico-Hartree Boys function error):
-------------------------------------------------------------
ROHF/MRCC (semi-can) -14.864 020 697 720 (default settings)
ROHF/MRCC (canonical) -14.864 020 697 720 (default settings)
ROHF/MOLPRO -14.864 020 697 748 (itol=18,scftol=16)
```

Clearly there's more than just Boys function error in the 6Z case, so I compared the basis set exponents and contraction coefficients but I really so no difference in them (MOLPRO was copied and pasted from the output file and MRCC should have been taken from the MOLDEN file but it was in scientific notation so to make it easier to compare I just took the numbers from the GENBAS file):

```
MOLPRO: MRCC:
======= =======
s 103207.000000 0.000004 0.000001 103207.00000 0.000004 0.000001
s 15664.800000 0.000029 0.000005 15664.80000 0.000029 0.000005
s 3600.840000 0.000149 0.000023 3600.84000 0.000149 0.000023
s 1026.350000 0.000627 0.000098 1026.35000 0.000627 0.000098
s 335.925000 0.002274 0.000355 335.92500 0.002274 0.000355
s 121.409000 0.007358 0.001159 121.40900 0.007358 0.001159
s 47.337200 0.021450 0.003373 47.33720 0.021450 0.003373
s 19.630900 0.055599 0.008978 19.63090 0.055599 0.008978
s 8.547060 0.124328 0.020423 8.54706 0.124328 0.020423
s 3.853030 0.228994 0.040705 3.85303 0.228994 0.040705
s 1.780350 0.323811 0.064625 1.78035 0.323811 0.064625
s 0.837931 1.000000 0.837931 0.000000 0.000000
s 0.390527 1.000000 0.390527 0.000000 0.000000
s 0.097776 1.000000 0.097776 0.000000 0.000000
s 0.044933 1.000000 0.044933 0.000000 0.000000
s 0.020602 1.000000 0.020602 0.000000 0.000000
s 0.006100 1.000000 0.006100 0.000000 0.000000
s 49.390700 1.000000 49.390700 0.000000 0.000000
s 26.340100 1.000000 26.340100 0.000000 0.000000
s 14.047200 1.000000 14.047200 0.000000 0.000000
s 7.491400 1.000000 7.491400 0.000000 0.000000
s 3.995100 1.000000 3.995100 0.000000 0.000000
p 32.644300 0.000229 32.644300 0.000229
p 7.758170 0.001768 7.758170 0.001768
p 2.461690 0.007560 2.461690 0.007560
p 0.869615 0.023322 0.869615 0.023322
p 0.327205 1.000000 0.327205 0.000000
p 0.134815 1.000000 0.134815 0.000000
p 0.059995 1.000000 0.059995 0.000000
p 0.028101 1.000000 0.028101 0.000000
p 0.013320 1.000000 0.013320 0.000000
p 0.003900 1.000000 0.003900 0.000000
p 51.457700 1.000000 51.457700 0.000000
p 23.052200 1.000000 23.052200 0.000000
p 10.327000 1.000000 10.327000 0.000000
p 4.626300 1.000000 4.626300 0.000000
p 2.072500 1.000000 2.072500 0.000000
d 0.825300 1.000000 0.825300
d 0.437300 1.000000 0.437300
d 0.231700 1.000000 0.231700
d 0.122800 1.000000 0.122800
d 0.065000 1.000000 0.065000
d 0.034500 1.000000 0.034500
d 34.914700 1.000000 34.914700
d 15.004700 1.000000 15.004700
d 6.448300 1.000000 6.448300
d 2.771200 1.000000 2.771200
f 0.679100 1.000000 0.679100
f 0.358800 1.000000 0.358800
f 0.189500 1.000000 0.189500
f 0.100100 1.000000 0.100100
f 0.052900 1.000000 0.052900
f 23.047600 1.000000 23.047600
f 8.994200 1.000000 8.994200
f 3.509900 1.000000 3.509900
g 0.419900 1.000000 0.419900
g 0.230900 1.000000 0.230900
g 0.127000 1.000000 0.127000
g 0.069900 1.000000 0.069900
g 15.913400 1.000000 15.913400
g 5.499300 1.000000 5.499300
h 0.337100 1.000000 0.337100
h 0.183500 1.000000 0.183500
h 0.099900 1.000000 0.099900
h 10.203500 1.000000 10.203500
i 0.292700 1.000000 0.292700
i 0.146200 1.000000 0.146200
```

Actually now I have directly compared the exponents and contraction coefficients from the MOLPRO output with the MOLDEN file generated in MRCC and after putting the two into arrays, Matlab says the two arrays are the same: isequal(MRCC,molpro) gives a value of 1. So unfortunately the basis sets seem to be exactly the same. The 1's and 0's for the contraction coefficients in the GENBAS are correct, and the likewise the numbers at the top of the GENBAS describing how many exponents and contraction coefficients.

I cannot imagine any other reason why the 6Z results are so much worse than the 5Z and 7Z ones, apart from maybe one code being more prone to errors due to linear dependencies in the basis set (but I think this would hurt the 7Z results more than the 6Z results and this isn't the case here).

The discrepancy is relevant on the scale of our discrepancy with experiment.

After adding an X2C+SFDC+Breit correction of 0.255cm-1 to each De value, we get, before any CBS extrapolations:

1) -333.58 cm-1 (FCIest./aCV7Z) -> Discrepancy with expt = 0.07 cm-1

2) -333.59 cm-1 (FCIest./aCV6Z) -> Discrepancy with expt = 0.06 cm-1

3) -333.65 cm-1 (empirical with finite-mass effects removed)

4) -333.74 cm-1 (FCIest./aCV5Z) -> Discrepancy with expt = 0.09cm-1

But the 125 nHartree difference between ROHF/MRCC and ROHF/MOLPRO is 0.025cm-1 which is more than 40% the size of the 0.06cm-1 discrepancy with experiment.

The 6Z MRCC output is here (we're just comparing ROHF, because the norm goes bad when MRCC tries to do correlation on a basis set this big): github.com/ndattani/AI_ENERGIES/blob/mas..._betterIntegrals.txt

The MOLPRO output is here:

github.com/ndattani/AI_ENERGIES/blob/mas...etterConvergence.txt

Is there anything else that might be causing this big discrepancy for the 6Z case?

With best wishes!

Nike Dattani

Last edit: 5 years 1 day ago by Nike.

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5 years 1 day ago #551
by kallay

Best regards,

Mihaly Kallay

Replied by

*kallay*on topic*Curse of the nano-Hartree*
Nike,

Can you please post the GENBAS file with the aug-cc-pCV6Z basis you use?

Can you please post the GENBAS file with the aug-cc-pCV6Z basis you use?

Best regards,

Mihaly Kallay

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5 years 1 day ago #552
by Nike

Replied by

*Nike*on topic*Curse of the nano-Hartree*
Dear Mihaly,

Here is the GENBAS file I used, which contains the basis named "LI:aCV6Z-KOPUT":

github.com/ndattani/AI_ENERGIES/blob/master/GENBAS

With best wishes!

Nike

Here is the GENBAS file I used, which contains the basis named "LI:aCV6Z-KOPUT":

github.com/ndattani/AI_ENERGIES/blob/master/GENBAS

With best wishes!

Nike

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5 years 1 day ago #555
by kallay

Best regards,

Mihaly Kallay

Replied by

*kallay*on topic*Curse of the nano-Hartree*
Dear Nike,

I have tested the 6Z calculation with all the integral algorithms implemented in mrcc. I have also run the calculation with cfour. I am getting -7.432 726 059 511 in every case. So something might be wrong with your molpro calculation.

I have tested the 6Z calculation with all the integral algorithms implemented in mrcc. I have also run the calculation with cfour. I am getting -7.432 726 059 511 in every case. So something might be wrong with your molpro calculation.

Best regards,

Mihaly Kallay

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5 years 1 day ago - 5 years 1 day ago #556
by Nike

Replied by

*Nike*on topic*Curse of the nano-Hartree*
Dear Mihaly,

Thank you so much for taking the time to test it.

The agreement with CFOUR seems good indication that MOLPRO might be the problem.

MOLPRO had a lower energy at iteration 4, and then never went up:

From github.com/ndattani/AI_ENERGIES/blob/mas...-cc-pCV6Z/MOLPRO.txt:

All I told it to do was converge integrals to 1e-18 and energy to 1e-16:

geometry={Li}

gthresh,oneint=1e-18,twoint=1e-18

THRESH,ENERGY=1d-16

wf,charge=0,spin=1

rhf

I will check with the MOLPRO developers.

With best wishes!

Nike

Thank you so much for taking the time to test it.

The agreement with CFOUR seems good indication that MOLPRO might be the problem.

MOLPRO had a lower energy at iteration 4, and then never went up:

From github.com/ndattani/AI_ENERGIES/blob/mas...-cc-pCV6Z/MOLPRO.txt:

```
IT DDIFF GRAD ENERGY 2-EL.EN. DIIS ORB.
1 0.0D+0 0.0D+00 -7.43042075 4.450025 0 start
2 0.0D+0 0.8D-03 -7.43214903 4.508094 1 diag,B
3 0.1D-2 0.4D-03 -7.43272528 4.560007 2 diag,B
4 0.1D-2 0.2D-04 -7.43272612 4.561845 3 diag,B
5 0.7D-4 0.2D-05 -7.43272612 4.561833 4 diag,B
6 0.4D-5 0.2D-06 -7.43272612 4.561833 5 diag,B
7 0.6D-6 0.4D-07 -7.43272612 4.561833 6 fixocc
8 0.1D-6 0.3D-08 -7.43272612 4.561833 7 diag,B
9 0.2D-7 0.3D-09 -7.43272612 4.561833 8 diag,B
10 0.2D-8 0.2D-10 -7.43272612 4.561833 0 orth
```

All I told it to do was converge integrals to 1e-18 and energy to 1e-16:

geometry={Li}

gthresh,oneint=1e-18,twoint=1e-18

THRESH,ENERGY=1d-16

wf,charge=0,spin=1

rhf

I will check with the MOLPRO developers.

With best wishes!

Nike

Last edit: 5 years 1 day ago by Nike.

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