C-Atom

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cymantren
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First name(s): Alfred
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C-Atom

Post by cymantren » 03 Dec 2020, 09:45

Hello developers and Dalton-users,


I want to repeat a simple scf-calculation on the C-atom, but it is not clear to me, how one adjust the different L-values in Dalton.
The C-Atom, with the following configuration has three different states:
(1s^2 2s^2) 2p^2:
^3P, ^1D, ^1S.

So in D2h-sym, there are for the px,y,z orbs, b3u,b2u and b1u.
The ground-state is ^3P and, also according to chap.24 in the manual, I did the input as shown in the appendix. But how one has to treat the other possibillities is not clear to me ?

Knowing how to adjust different L-values, is also important if one wants to calculate different states to a certain configuration of a molecule.

Please help me with this topic.
Thank you!

Best greetings

Alfred
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taylor
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First name(s): Peter
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Re: C-Atom

Post by taylor » 05 Dec 2020, 08:26

For the 3P state your input is correct but you should recognize that this is only one component of a triply (spatially) degenerate state. The pz orbital that would result will not have the same spatial form as the singly occupied px and py. This may not matter to you, of course. To obtain three equivalent p orbitals a fractional occupation of 2/3 of an electron in each p component is required. This can be enforced in some open-shell SCF codes (although a dwindling number as the years go by...) but not in Dalton. An alternative possible with some MCSCF codes (but not Dalton) is to calculate the average of three states, with occupations, pxpy, pxpz, and pypz. This is exactly equivalent to the open-shell SCF calculation with fractional occupation numbers.

For the singlet states the situation is more complex. The 1S state has the configuration (for full spatial symmetry) px^2 + py^2 + pz^2 which obviously has spin multiplicity 1 and symmetry 1 in D2h. But the five components of 1D appear in symmetries 1 (twice), 4, 6, and 7. You can thus run a CASSCF and take out a root in symmetry 4 or 6 or 7 and get a component of a 1D state, but again the three p orbitals will not be equivalent. The components in symmetry 1 will also not have equivalent p orbitals, and both will lie below 1S. So you could try taking the third root in symmetry 1 out of a CASSCF calculation to get your 1S state.

None of this is terribly satisfactory from a symmetry perspective. In general, if one wants orbitals in calculations on atoms or diatomics or other high-symmetry systems the easiest tactic is state-averaged MCSCF as I mentioned above, but this is not available in Dalton.

Best regards
Pete

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Re: C-Atom

Post by cymantren » 07 Dec 2020, 09:53

Dear Mr. Pete Taylor,

thank you for your quick and interesting answer.

You say that I could use SA-state averaging, but one has to use different codes, to perform these kind calculations. But I have to understand throughly what e.g. SA-3 means. Surely more than the averaging of three states and it is interesting to note, that you speak of three components. It's a bit confusing for me, but do you mean the averaging of the three states, namly the ^3P, ^1D, ^1S, or that of the 3 p-states ?
In any way, this topic does not concern that of this forum and therefore I will stop here.

I want to mention that according to Herzberg, there is a connection of atomic and molecular states, which is marvelous for me. In fact, in the case of the C-atom, which has 6 electrons, there should be also a molecule - Li2 - which has similar states.

Finally one last question regarding, which I beg to answer me is concerning : STATES. What do you mean by the term " states", electronic, spectroscopic or molecular states ?
Of course these terms are in conection, but it is not always clear to me, what is meant by "states".

Thank you !


Best regards

Alfred

P.S.:
There are (2S+1)(2L+1) functions which desribe Terms to a certain Electronenconfiguraion. Therefore in the case of ^1D (L=2,S=0) , there are 5 Eigenfunctions.

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