Least Empirical DFT Calculations for Diatomic Dissociations

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Discussion Overview

The discussion revolves around the search for less empirical density functional theory (DFT) calculations for diatomic dissociations. Participants explore the nature of DFT functionals, their empirical aspects, and the suitability of various methods for calculating dissociation processes in diatomic molecules.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks DFT calculations that are less empirical than those typically found in literature, questioning the availability of such studies.
  • Another participant notes that while DFT is fundamentally ab initio, it still relies on approximations for electron-exchange functions, making it impossible to be entirely free of empirical functions.
  • Concerns are raised about the applicability of DFT approximations like LDA and GGA for diatomic molecules, suggesting they may not perform well compared to methods like CCSDT.
  • Some participants identify certain functionals as more empirical than others, indicating that LDA, PBE, and TPSS are considered more first-principles, while others like B3LYP involve empirical fitting.
  • There is a discussion on the limitations of DFT in accurately describing dissociation processes, particularly due to the single-determinant nature of Kohn-Sham DFT and its inability to capture the necessary correlation for dissociation.
  • A participant expresses difficulty in finding specific LDA/GGA calculations for diatomic dissociation and considers conducting their own calculations using TURBOMOLE.
  • Another participant suggests that while MP2 calculations also face challenges, they can still be useful for certain dissociation-related analyses, such as potential energy surfaces around equilibrium.
  • There is mention of the potential for using MP2 to calculate atomization energies, which may be beneficial for benchmarking electronic structure methods.

Areas of Agreement / Disagreement

Participants express a range of views on the effectiveness of DFT and other methods for diatomic dissociation, with no consensus on the best approach. There is acknowledgment of the limitations of various functionals and methods, but no agreement on a definitive solution or approach.

Contextual Notes

Limitations include the dependence on the choice of functional and the inherent challenges of single-reference methods in accurately describing dissociation processes. The discussion highlights the need for careful consideration of the methods used in computational studies.

Morberticus
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A somewhat strange request. I have come across this paper:

http://jcp.aip.org/resource/1/jcpsa6/v98/i7/p5648_s1

It lists hybrid DFT results for dissociation calculations. I am looking for DFT calculations that are not as phenomenological, but can't seem to find any in the literature. Are there DFT calculations out there with less empirical functionals/less fitting to experiment? Or should I just fire up my own DFT calculations with, say Turbomole to acquire "dumb" DFT results?
 
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DFT calculations are by default ab initio. However, it is impossible to know exact electron-exchange function(Thus DFT can not be entirely without empirical functions). Many approximation exists and you have to find the one that suits you best. Usually the latest ones are more accurate. e.g. LDA, LSDA, GGA etc.
 
Thanks for the info,

I think I remember the LDA approximation. Would I be right in assuming all of these approximations more or less assume some level of uniformity in electron distribution, and would therefore all be unsuitable for diatomic molecules?

* By unsuitable, I mean poor compared to, say CCSDT, when it comes to dissociation.
 
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Yes, DFT won't describe well e.g. van der Waals forces between the separating atoms.
 
There are some functionals which are truly first principles (e.g., LDA, PBE, TPSS). Other functionals are more empirical, or not really functionals at all (e.g., LYP itself, B3LYP, the full Minnesota set, everything containing Hartree-Fock exchange). Could we ask what you are looking for? I guess if you actually intent to calculate diatomic dissociations, CCSD(T) or higher coupled-cluster methods (for the around-equilibrium region and the dissociated atoms) or MRCI (for the dissociation process itself or for excited states) would be more suitable than any DFT, empirical or not.
 
cgk said:
There are some functionals which are truly first principles (e.g., LDA, PBE, TPSS). Other functionals are more empirical, or not really functionals at all (e.g., LYP itself, B3LYP, the full Minnesota set, everything containing Hartree-Fock exchange). Could we ask what you are looking for? I guess if you actually intent to calculate diatomic dissociations, CCSD(T) or higher coupled-cluster methods (for the around-equilibrium region and the dissociated atoms) or MRCI (for the dissociation process itself or for excited states) would be more suitable than any DFT, empirical or not.

Hi,

It's literally a couple of lines I'm looking for, regarding a report I'm writing. The trouble is every paper I come across simply says "It is well known that LDA et al are poor for dissociation", without any explicit reference to a study (presumably because the poor quality of LDA/GGA for such problems is textbook at this stage, like F=ma). What I am looking for specifically is a set of LDA/GGA calculations for diatomic dissociation (I.e. C2 N2 O2 etc.). I could do them myself with TURBOMOLE, but I guess that's not kosher if they have been previously published.
 
Morberticus said:
It's literally a couple of lines I'm looking for, regarding a report I'm writing. The trouble is every paper I come across simply says "It is well known that LDA et al are poor for dissociation", without any explicit reference to a study (presumably because the poor quality of LDA/GGA for such problems is textbook at this stage, like F=ma). What I am looking for specifically is a set of LDA/GGA calculations for diatomic dissociation (I.e. C2 N2 O2 etc.). I could do them myself with TURBOMOLE, but I guess that's not kosher if they have been previously published.

Oh, I see. Well, doing them yourself would be fine, in my opinion. The problem here is, however, not the functionals, but the fact that "real DFT" (i.e., Kohn-Sham with semi-local functionals) is for all practical purposes a slightly hacked up Hartree-Fock. The HF exchange is replaced by the approximate DFT exchange-correlation, but the truth is that this does not do anything regarding the principal limitations of a single-determinant descriptions of the wave function. With the practical approximations made, KS still requires a single-determinant description of the full system to be somewhat reasonable.

A semi-local functional will thus never be able to dissociate a real molecule, simply because the process requires more than one determinant for a qualitatively correct description (e.g., to dissociate singlet H2 in a continuous, non-symmetry broken process process, the dissociated end result must be two entangled H atoms which are coupled in an open-shell singlet form, and this requires two determinants).

In short: This problem is inherited from Hartree-Fock, and Kohn-Sham-DFT is not different enough from it to make a difference (at least not with "functionals" which do not involve actually calculating a correlated wave function in order to determine the "functional" values).
 
Me again with another silly question (I just can't seem to get the hang of Web of Knowledge)

The last set I need are dissociation calculations using Moller Plesset (Specifically MP2). I realize these also have problems associated with single reference methods (for reasons cgk outlined previously). These calculations seem to be even more elusive.
 
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Morberticus said:
Me again with another silly question (I just can't seem to get the hang of Web of Knowledge)
I can't either :]. You might want to try scholar.google.com . In my opinion, this works much better (it only has some issues with very old papers, for which it does not always get the cross-citations right).
The last set I need are dissociation calculations using Moller Plesset (Specifically MP2). I realize these also have problems associated with single reference methods (for reasons cgk outlined previously). These calculations seem to be even more elusive.
Well, due to the single-reference issue, you will likely only find MP2 calculations of actual dissociation curves in papers which propose some different method---in order to show how MP2 explodes. If you have access to Turbomole (or some other QC program), there is nothing wrong with just making a curve youself and show that it does not work. It is very well known that these problems exist and no one will challenge you if you do not cite an explicit MP2 calculation which has been done before on some system (or if you like, just cite the purple book[1] on problems of single-reference methods).

[1] Helgaker, Joergensen, Olsen - Molecular electronic structure theory

Note, however, that there are still some dissociation-related things that can be done with MP2 (or other single-reference methods): You can calculate
- the entire potential energy surface for weakly bound complexes (i.e., systems involving only non-covalent bonding),
- the potential energy surface around the equilibrium (i.e., where the molecule is still single-referency) for covalently bonded molecules
- the individual atoms (They are usually fine with high-spin references).

With the equilibrium PES and the individual atoms, you can calculate dissociation energies/atomization energies. But not the dissociation process itself. If you are interested in atomization energies (i.e., just the end results of the dissociation process), these often are used in the benchmarking of electronic structure methods. For example, in http://dx.doi.org/10.1063/1.2889388 , atomization energies are used to test explicitly correlated open-shell MP2. But if you just look for papers citing the G2/97 paper or similar things, you will find many of them.
 

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