Help me understand HF Exchange

I work through Szabo Ostlund and on page 88 (2.3.7 Pseude-Classical Interpretation of Determinantal Energies) it says that "The exchange Interactions between electrons with parallel spin are not real physical interactions but a convenient way of representing the energy of a system described by a single determinant. The physical interaction between two electrons [...] does not depend on the spin of the electrons"
This is the part where they introduce the idea that the energy of a single determinant can be summed up with H, J and K Terms.

Now consider a single determinant with two spacial orbitals. Both are occupied with one electron each. In case 1), both electrons have the same spin. In case 2), both electrons have opposite spins.

From Chemical knowledge I know that 1) is singulet and 2) is triplet and energy wise the triplet state is lower in energy. This is measurable.

Now the theory with this "adding up H, J and K terms to get determinantal energies" also predicts the same as:

Energy of 1) = H11 + H22 + J12

Energy of 2) = H11 + H22 + J12 - K12

So the - K12 lowers the energy of the triplet state which we measured and therefore proved correct.

But on the other hand Szabo Ostlund says that this exchange interaction is not physical.

How can this be not physical if we can measure it and the theory correctly predicts the relative energies of those two determinants?

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u/LWJ_ — 13 days ago

ORCA data/directory structure

Doing Computations creates many files and doing many calculations can lead to quite messy file structures. Additionally I was told by some redittor on a comment of mine that copy pasting values (like energies etc.) out of output files into tables is bad practice and leads to shitty SI tables due to mistakes. Unfortunately he did not elaborate further therefore I ask in here.

How do you organize stuff? How do you name stuff? How do you process your data?

I am interested in directory structures, input and geometry naming and, well, data processing.

I tend to name my geometries either A-Z or 1-10 and for optimized geometries I add an "of" so I know that it is optimized and checked with frequency analysis. Example: Aof.xyz

For Inputs I only do single points or geometry optimizations. The Input name starts with a geometry name (e.g. A) then some identifier which varies frequently and then either "of" for !Opt Freq or "s" for single point. I think that this practice needs an upgrade.

And for data processing I basically look through the .out file either with notepad++ (find all function) or with "$grep -H "Final Gibbs" *.out" and copy paste that stuff into an excel sheet and work from there. I think that this practice also needs an upgrade but I don't know how to improve.

Thank you for every piece of advice. You can even send me lit or forum posts etc. I will gladly read everything and I am open to using python or other programs.

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u/LWJ_ — 1 month ago

Need help for a CBS extrapolation

Hi. I need help with a CBS extrapolation. Can't ask anyone for help bc nobody I know can help me. Therefore:

I did DLPNO-CCSD(T1) calculations with orca (see sull inputs below). My system is a C-C dimer which breaks into two identical C radicals and I want to benchmark the electronic reaction energy.

I used cc-pVDZ and cc-pVTZ (Edit: removed typo) basis sets for the extrapolation and will extrapolate SCF energy (parameter 4.42; exponential fit) and correlation energy (parameter 2.46; polynomial fit) separately. I will use the formulas and fitting parameters of

Frank Neese, Edward F. Valeev; Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?. J. Chem. Theory Comput. 11 January 2011; 7 (1): 33–43. https://doi.org/10.1021/ct100396y.

Now to the problem. I did the calculations with ORCA (input see below) and when I checked if E(SCF)+E(CCSD)+E(T)=E(final single point) I found that the value was off by -0.03378. It seems that for the MDCI ORCA did not use the final SCF energy but a "reference energy" which is exactly -0.03378 off of the SCF energy. (SCF energy: -585.730392772957; E(0) of the MDCI: -585.696614349) My LLM of choice could not sufficiently explain, where this comes from. The whole ORCA output file does not contain this exact value (I searched for 0.03378 and -0.03378).

Now to the questions:

  1. What is this energy difference? Why is it here and where does it come from?
  2. Which correlation energy should I use for the extrapolation? I would choose E(CCSD)+E(T) (values see below).
  3. Which SCF energy should I use for the extrapolation? I would have used the "reference energy" E(0) which was used in the MDCI (values see below).

Update (from comments): The ORCA Compound script git repository has a extrapolate_ep1 script where it clearly says they use the SCF energy. But they have another one where they clearly state that they use the E(0) (so this adjusted reference energy which is the core of my original comment). I tried both and the extrapolation with E(0) makes much more sense bc with the SCF energy the values are all over the place and the reaction energies turned from +30 kcal/mol to like -7 kcal/mol. Now with the E(0) extrapolation energies are waay more reasonable. I will find out if they are good if I see the results of the TZ QZ test extrapolation for 1-2 of my examples. Due to spin contamination (<S^2> of between 1.4 and 2.2 over 5 different molecules) I reran my calculations with !UKS wB97X-V DLPNO-CCSD(T1). This means the DLPNO step get's the better KS-DFT orbitals which eliminated spin contamination (now <S^2> is 0.753). Now the Energy difference between SCF and E(0) is 3.59 Eh which makes totally sense as the SCF energy is from DFT and the E(0) is from the HF step done before the DLPNO. This now makes me sure that using the E(0) is the right thing to do. Why is there a difference in E(0) and SCF energy when only using the HF DLPNO? patonlab (comment) suggested that the HF SCF energy is calculated with UHF orbitals but the DLPNO E(0) is with QRO (quasi restricted orbitals) and a big difference in those energies hint to spin contamination. I can neither confirm nor deny this (as I am a beginner) but I want to mention this here for future people to read.

Examples for a radical monomer calculation:

Total SCF Energy:

----------------
TOTAL SCF ENERGY
----------------

Total Energy       :       -585.73039277295754 Eh          -15938.53429 eV
...

Correlation energy part 1 (CCSD iterations):

--- The CCSD iterations have converged ---

E(0)                                       ...   -585.696614349
E(CORR)(strong-pairs)                      ...     -1.982761334
E(CORR)(weak-pairs)                        ...     -0.002944788
E(CORR)(corrected)                         ...     -1.985706122
E(TOT)                                     ...   -587.682320471
Singles norm &lt;S|S&gt;**1/2                    ...      0.154748668 ( 0.062079079, 0.092669589)
T1 diagnostic                              ...      0.018629550
&lt;S**2&gt;(linearized)                         ...      0.7533235 (ideal value:      0.7500000)

Correlation energy part 2 (triples correction):

Triples Correction (T)                     ...     -0.086625089
    alpha-alpha-alpha ... -0.002628018 (  3.0%)
    alpha-alpha-beta  ... -0.041032413 ( 47.4%)
    alpha-beta -beta  ... -0.040372285 ( 46.6%)
    beta -beta -beta  ... -0.002592373 (  3.0%)
Final correlation energy                   ...     -2.072331210
E(CCSD)                                    ...   -587.682320471
E(CCSD(T))                                 ...   -587.768945560

ORCA Input for a radical monomer:

!UHF DLPNO-CCSD(T1) cc-pVDZ cc-pVDZ/C TightPNO

%scf
  maxiter 1000
end

%pal
  nprocs 12
end

%maxcore 8500

*xyzfile 0 2 a0of.xyz

ORCA Input for a closed shell dimer:

!DLPNO-CCSD(T1) cc-pVDZ cc-pVDZ/C TightPNO

%mdci
  UseFullLMP2Guess false
end

%scf
  maxiter 1000
end

%pal
  nprocs 12
end

%maxcore 8500

*xyzfile 0 1 A0of.xyz

Feel free to criticize my input files and point out bad practices. I like to learn and improve. And thanky for the help :)

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u/LWJ_ — 2 months ago

Isn't it all just solved with a simple model comparison?

Title. We have model A) flat earth and model B) round earth. We go a step away from reality and just compare a round object and a flat object rotating (we see the rotation) with some randomly scattered (but fixed) lights in the background. What's the biggest difference between those two models? For the observer on the flat earth there is one point where all the fixed lights rotate around. For the observer on the round earth there are two points were all the fixed lights rotate around. The moment you have two different points were all the fixed lights rotate around, you cannot be flat anymore. Those two conditions are mutually exclusive. This is our prediction from our simple model and now we look for clues in reality. And Tada. No flat earth.
How do we convince people that the earth is in fact round? Angles from the surface to those two points.
When the flat earthers say: Earth does not rotate, the stars do. Ask them where the difference is. Movement is relative.

How can anyone possible argue against that?

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u/LWJ_ — 4 months ago

Isn't it all just solved with a simple model comparison?

Title. We have model A) flat earth and model B) round earth. We go a step away from reality and just compare a round object and a flat object rotating (we see the rotation) with some randomly scattered (but fixed) lights in the background. What's the biggest difference between those two models? For the observer on the flat earth there is one point where all the fixed lights rotate around. For the observer on the round earth there are two points were all the fixed lights rotate around. The moment you have two different points were all the fixed lights rotate around, you cannot be flat anymore. Those two conditions are mutually exclusive. This is our prediction from our simple model and now we look for clues in reality. And Tada. No flat earth.
How do we convince people that the earth is in fact round? Angles from the earch surface to those two points. Roughly on the equator you could see both points simultaneously (when you are high enough in the air). On both poles you only see one (they are distinct because they have different patterns). And on (roughly) 45° Latitude you have (roughly) 45° from earth surface to this rotation point.

How can anyone possible argue against that? And this is easily testable. Just set up a nighttime camera and watch the stars. Or even better go to the equator and film both rotation points simultaneously.

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u/LWJ_ — 4 months ago

Isn't it all just solved with a simple model comparison?

Title. We have model A) flat earth and model B) round earth. We go a step away from reality and just compare a round object and a flat object rotating (we see the rotation) with some randomly scattered (but fixed) lights in the background. What's the biggest difference between those two models? For the observer on the flat earth there is one point where all the fixed lights rotate around. For the observer on the round earth there are two points were all the fixed lights rotate around. The moment you have two different points were all the fixed lights rotate around, you cannot be flat anymore. Those two conditions are mutually exclusive. This is our prediction from our simple model and now we look for clues in reality. And Tada. No flat earth.
How do we convince people that the earth is in fact round? Angles from the surface to those two points.
When the flat earthers say: Earth does not rotate, the stars do. Ask them where the difference is. Movement is relative.

How can anyone possible argue against that?

(I posted this exact same comment without the "When the flat earthers say: ..." line in a flat earth subreddit and I got muted and banned without any message. Do you think I offended them in any way? Did I violate rules? (GlobeEarth_Polite; A community to politely debate the nature of Earth; only 1 Rule: "Be polite")

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u/LWJ_ — 4 months ago

Ich will mich persönlich verändern, habe aber nach 4-7 Tagen keine Lust mehr darauf. Wie kann ich diesen Mangel an Motivation überwinden?

Siehe Titel.

Kontext: Ich habe 10 Jahre meines Leben nichts anderes gemacht, als Schule und Youtube konsumieren. Da ich bei meinen Eltern gelebt habe, war ich gefühlt nie einkaufen, hab gefühlt nie gekocht, und Wäsche waschen hab ich auch noch nie. Versteht mich nicht falsch, ich kann das schon machen und ich will das auch machen aber ich finde nie die Motivation dazu, weil Handy und Internet dazu viel zu addictive sind. Ich bin jetzt recht weit mit dem Studium (eine Naturwissenschaft) und versuche das zu ändern. Ich habe eigentlich viel vor und verschwende meine Zeit im Internet (Reddit, Anime/Manga und mobile games. Youtube habe ich mittlerweile schon überwunden und seit letztes Jahr Dezember nicht mehr geschaut). Kurioserweise macht mir das ganze nicht mal spaß aber ich mach's trotzdem, einfach aus Gewohnheit. Das würde ich gerne ändern und genau jetzt ist wieder so ne 4-7 Tage Phase, in der ich richtig was anpacken und verändern will. Mir ist aber aufgefallen, dass ich das schon mehrmals hatte und immer nach eben 4-7 Tagen die Motivation zur Veränderung verloren hab und wieder in alte Muster zurückgefallen bin. Habt ihr Ideen, wie ich das überwinden könnte?

Ich habe einkaufen, kochen und Wäsche waschen als Beispiele benutzt, um zu zeigen, dass ich wirklich nichts nichts neben Schule und Youtube konsumieren gemacht habe. Mittlerweile gehe ich schon einkaufen und koche auch (nur halt irgend nen schund). Außerdem habe ich noch andere Wünsche und träume, die aber dann schon ziemlich viel Persönlichkeit freigeben, weshalb ich auf die nicht weiter eingehen werde.

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u/LWJ_ — 4 months ago