# Different results from MP2 calculations on same geometry in ORCA

I am trying to do a segmented potential energy scan around a dihedral for a molecule. I have optimized the geometry to a minima, and the scan runs from [-180, 180] in steps of two points at a time.

This is the input file that I used to calculate the energies at $$\phi = 170$$ and $$\phi = 160$$. The initial coordinates for $$\phi = 170$$ was obtained from the previous scan of $$\phi \rightarrow [180, 170]$$.

! Opt MP2 6-31g* PAL4
%geom Scan
D 5 0 1 2 = 170, 160, 2
end
end
*xyz 0 1
C   -0.01296114269949      0.94440242563597     -0.29053248441691
C    1.20359520080223      1.00137801653345      0.29786516905158
C    2.43657224093117      1.07558212649403     -0.46404217200734
C    3.67272330832435      0.98117376597373      0.06277543031523
H   -0.10490902371364      1.11202620979905     -1.36291570524297
N   -1.22131071498263      0.67701537644153      0.34966432355423
H    1.28397084032817      0.83321545027387      1.37307026220526
H    2.33425017243896      1.20438753874106     -1.54294877796397
H    3.82735652201142      0.85397587500326      1.13084169769749
H    4.55938381385145      1.02098202753128     -0.56055815416925
H   -1.12997794903088      0.20498190250356      1.24205069378367
H   -1.92086326826118      0.23860928506914     -0.23528028280703
*


As expected, the calculation of $$\phi = 170$$ completed in a single step (since it was already optimized in the last step). However, the energies that I obtained are different in both the cases.

 180.00000000 -210.60870348
170.00000000 -210.60703037
===========================
170.00000000 -210.60703059
160.00000000 -210.60380225


What can be the reason for this difference? I know that the difference is in the 7th and 8th decimal places, but I would ideally like them to be same.

• I cannot unfortunately use a better basis set because I am parameterizing this for CHARMM FF, and this is the recommended level of theory and basis set. Apr 19 at 13:44

Using ORCA 5.0.4, I ran calculations based on the input file provided. As is, the orca.relaxscanact.dat list:

 180.00000000 -210.60870333
170.00000000 -210.60703035
###########################
170.00000000 -210.60703059
160.00000000 -210.60380225


I compared the nuclear repulsion energies (ENN) for the two relevant/final 170Â° structures and found:

154.428728248405
################
154.432470546304


which suggests that the relevant geometry optimizations started at different structures.

In the light of these results, I made the convergence tolerances more conservative (input file):

# ... snip
%geom
convergence tight
Scan
D 5 0 1 2 = 180, 170, 2
end
end
# snip ...


which yielded

 180.00000000 -210.60870351
170.00000000 -210.60703076
###########################
170.00000000 -210.60703076
160.00000000 -210.60380252


For completeness, the '170Â°' ENN are:

154.433928524878
################
154.434477456670


so there is some deviation cancellation. The increase in computational time was around 20%, though that number does not extrapolate well to larger systems. Note that the convergence tight line can be substituted for more detailed (and tighter still) control of the geometry optimization criteria, though overdoing it leads to geometries flipping back and forth in my experience. If one is looking for curves to fit potentials, one may be better off running the curves forwards and backwards to use average results.

Have you confirmed that the geometries for each are exactly the same? If the second calculation took a single step, its possible it moved the geometry very slightly. ORCA's default convergence criteria for geometry optimizations includes a condition that the energies between steps should not differ by more than $$1\times10^{-6}$$ Hartree. So as far as at least the energy criteria is concerned, structures with energies differing by $$1\times10^{-6}$$ would also qualify as a minimum.

In general, when a QM program converges a geometry to a minimum, its not likely to be converging it to the exact/true local minimum for your level of theory. Rather, it is converging to one structure among many subtly different structures which all meet the convergence criteria for the optimizer. If the program chooses reasonable convergence criteria, these structures should be qualitatively and, for most use cases, even quantitatively consistent in terms of their properties.

Of course, there are some properties which depend more sensitively on the geometry and in those cases you may want to use even more stringent convergence criteria to ensure you are "close enough" to the true local minimum. But even in this case, you are just shrinking the acceptable convergence region and in practice you can never reduce it a single point representing the true/exact local minimum.

You have a difference of 0.22 micro-hartrees between your two runs of the calculation:

Phi [radians]  Energy [hartrees]
=================================
170.00000000  -210.607030 37
170.00000000  -210.607030 59


In electronic structure calculations, this can be considered unacceptable, even when comparing across completely different codes, for example the data below from the AI_ENERGIES database is for FCI/CCSDT calculations with aug-cc-pCV5Z for a Li atom using three different codes that were written by completely different people (with the default settings in all cases), notice that the energies all agree to within 1 nano-hartree:

CCSDT-CFOUR:          -7.477431654 745
FCI-MRCC:             -7.477431654 427
FCI-MOLPRO:           -7.477431653 828


However, ORCA was not designed for micro-hartree precision. It was designed for milli-hartree precision, and the discrepancy between your two energies is in a digit 4 orders of magnitude away from anything that would matter to an ORCA user (there's better software available for free such as , , , , , , , , etc. for high-precision quantum chemistry).

Your difference in MP2 energies is likely because your SCF energies are different, or because the integrals were slightly different in the two cases. If you do find that the SCF energies are different in the nano-hartree digit and you're curious about the reason, I suggest that you ask a question with a title such as "Why are my SCF energies different in these two calculations" and ensure that you have provided the output files for both cases (the input file is really not enough to answer this type of question).

• "However, ORCA was not designed for micro-hartree precision." Citation or retraction needed. As a former Dev of ORCA, I find the statement offensive. Apr 19 at 5:43
• +1 on @TAR86 from a current ORCA developer. Some functionalities of ORCA may be designed for milli-hartree accuracy, but apart from methods that use random number generators, ORCA certainly achieves better than micro-hartree reproducibility for single point energies. And it's highly inappropriate to compare the energy difference of the end points of a dihedral scan to the precision of atomic calculations; the former comes from both wavefunction difference and geometry difference, but the latter only comes from the wavefunction. This gives readers a wrong idea of how much error is acceptable. Apr 19 at 8:11
• @TAR86 may I say "citation needed" for the claim that ORCA was designed for micro-hartree precision? I believe that here's not going to be a citation that says that ORCA was not designed for micro-hartree precision, just as there is not going to be a citation that says that ORCA was designed for micro-hartree precision. Apr 19 at 11:26
• @wzkchem5 "ORCA certainly achieves better than micro-hartree reproducibility for single point energies" that seems to contradict what was found by the OP of this question! About atomic vs molecular calculations: in the link that I provided, you can see that three completely different codes (MRCC, CFOUR, MOLPRO) are agreeing to each other within 0.1 micro-Hartree for a molecule with 500+ orbitals, despite CFOUR having an incorrect bohr to angstrom conversion factor built into it. Generally a 0.2 uH discrepancy is considered unacceptable in MOLPRO and CFOUR. For ORCA it's the default. Apr 19 at 11:46
• @NikeDattani-NoFreeTime You are the first one to claim anything about whether ORCA was designed for micro-hartree precision, so the burden of proof is on you. Apr 20 at 11:25