Summary for "Calculation on biradical"

From: <acp37 -8 at 8- rs1.rrz.Uni-Koeln.DE>
Subject: Summary for "Calculation on biradical"
Date: Tue, 29 Aug 1995 15:33:48 +0200 (MST)
 Dear netters,
  some days ago I posted a question about calculations on a biradical. The
 original posting and the answers are attached.
  Thanks to all who responded!
  Thorsten Koch
 The original question:
 Dear netters,
  At the moment I am doing ab initio calculations on
 1,5-Dehydronaphthalin, so it is supposed to be a biradical. It is an
 isomer to a ordinary closed-shell molecule which I am interested in. So
 to compare the energies of the molecules, I am interested in the
 singlet-groundstate of the biradical.
  But this doesn't seem to be a trivial problem. It was no problem at all
 to get the wavefunction for the triplet state. So I optimized the
 geometry for the triplet state and tried to get some singlet
 wavefunctions for this geometry.
  Here is what I got:
  1. UHF, 6-31G*, mult=3 : E=-382.059168, <S**2>=2.2470 (2.0346 after
 annihilation of first spin contaminant)
  2. UHF, 6-31G*, mult=1 : E=-381.906022, <S**2>=0.0000
  This result was the same as the result with RHF. Especially the spin
 desity was zero everywhere. So I thought that this wouldn't be a proper
 description of a biradical.
  3. UHF, 6-31G*, mult=1, GUESS=mix
  This calculation didn't converge at all.
  4. In fact I was able to get another singlet state wavefunction. The
 only way to get it was from a stability analysis and optimization from the
 wavefunction obtained with 2. The result was: E=-382.086893,
 <S**2>=2.2807 (8.1431 after annihilation of the first spin contaminant)
 At least the spin density gave two unpaired electrons with different spin
 at the right carbons.
  Because dft is known to give lower spin contaminations, I tried it this way:
  5. UHF, 6-31G*/B3LYP, mult=3 : E=-384.510256, <S**2>=2.0136 (1.9996)
  6. UHF, 6-31G*/B3LYP, mult=1 : E=-384.484437, <S**2>=0.000
  Again the same result as with RHF, spin density zero everywhere.
  7. UHF, 6-31G*/B3LYP, mult=1, GUESS=mix : E=-384.518499, <S**2>=0.9392
 (0.1510 after annihilation) This calculation had no difficulties to converge.
  ROHF calculations for the singlet states always gave the same
 wavefunction as for RHF calculations.
  So there are a couple of questions:
  a) Why is it so difficult to get a UHF singlet wavefunktion for a normal
 biradical?
  b) Can I rely on the energies obtained when the spin contamination is
 about 1.0 (Point 7.)? This is especially problematic because I want to
 compare it to the energiy of a closed-shell isomer. Since I got this
 results with 6-31G*/B3LYP it seems to be the best I can get...
 Is a geometry optimization sensible in this case?
  c) What can I say about the wavefunction of point 4.? The spin
 contamination is about 2.3 before annihilation (not a very small value
 for a singlet ;-) and about 8.1 AFTER annihilation of the first spin
 contaminant. I have no idea what this should mean!
  d) Am I right when I think that the spin density of a system with to
 unpaired electrons in the sigma frame separated far enough from
 another should exhibit these two electrons at the carbons they are
 attached to?
 e) Having all these problems in mind: Which way should I go to determine
 the energiy of the singlet ground state?
 Sorry for this somewhat lengthy question, but I'll summarize the
 responses, when there is interest :-)
 -----------------------------------------------------------------------
 The answers:
 From: Steve Gwaltney <gwaltney -8 at 8- qtp.ufl.edu>
 Your molecule sounds like an open-shell singlet.  If it is, you need
 two determinants to describe the wavefunction.  Thus, any Hartree-Fock
 calculation will fail.  What you need is a MCSCF calculation, or some
 other way to deal with two determinantal wavefunction.
 Steve
 From: Christopher J Cramer <cramer -8 at 8- maroon.tc.umn.edu>
 >  a) Why is it so difficult to get a UHF singlet wavefunktion for a normal
 > biradical?
 >
    Because an open-shell singlet is a two-configuration wavefunction. It
 requires an MCSCF approach to do it properly. The S^2=1 calculations are for
 so-called 50:50 wavefunctions (half singlet, half triplet).
 >  b) Can I rely on the energies obtained when the spin contamination is
 > about 1.0 (Point 7.)? This is especially problematic because I want to
 > compare it to the energiy of a closed-shell isomer. Since I got this
 > results with 6-31G*/B3LYP it seems to be the best I can get...
 > Is a geometry optimization sensible in this case?
 >
    No, and no. You can adopt the so-called sum method of Ziegler and
 double-the energy difference between the triplet and the 50:50 wavefunction
 to estimate the energy of the open-shell singlet. Although a terrible
 approach at the HF level, comparing UDFT to RDFT seems to be OK for S-T gaps
 (we have several papers on this). However, your B3LYP functional includes HF
 exchange, which will degrade this comparison.
 >  c) What can I say about the wavefunction of point 4.? The spin
 > contamination is about 2.3 before annihilation (not a very small value
 > for a singlet ;-) and about 8.1 AFTER annihilation of the first spin
 > contaminant. I have no idea what this should mean!
 >
    It's garbage.
 >  d) Am I right when I think that the spin density of a system with to
 > unpaired electrons in the sigma frame separated far enough from
 > another should exhibit these two electrons at the carbons they are
 > attached to?
 >
    For the closed-shell singlet, there is probably hybridization and orbital
 splitting. For the open-shell and the triplet, your intuition is right. Much
 of the literature on 1,4-didehydrobenzene discusses these topics.
 > e) Having all these problems in mind: Which way should I go to determine
 > the energiy of the singlet ground state?
 >
    MCSCF is the best approach. Your DFT results are quite curious because
 they indicate the open-shell singlet to be lower in energy than the triplet.
 This is pretty unusual, and I'm not sure I believe it.
    If you would be interested in seeing some of our work on these issues, I'd
 be happy to send you some papers.
 Best regards,
 Chris
 --
 From: Christian Koelle <ck -8 at 8- ws2.theochem.uni-hannover.de>
 >
 > e) Having all these problems in mind: Which way should I go to determine
 > the energiy of the singlet ground state?
 >
 Zwei Wege: einer gut der andere besser:
 1) CI Rechnung. Bei einem Diradikal sollte als aktiver Raum HOMO und LUMO
 ausreichen. Wir benutzen bei unseren Rechnungen mit einer semiempirischen
 Methode die HOMO-LUMO Einfach- und Doppelanregung, wobei die
 Doppelanregung fuer den Singulett entscheidend ist.
 2) MCSCF-Rechnung. Auch hier HOMO und LUMO als aktiver Raum.
 Hoffe geholfen zu haben.
 Gruss
 Christian Koelle
 From: Hans Ueli Suter <husuter -8 at 8- cscs.ch>
 Lieber Herr Koch,
 ich wuerde Ihr Problem unter einem etwas anderen Gesichtspunkt sehen:
 Was Sie effektiv rechnen sind die angeregten Zustaende von ...
 Bei einem Programm wie Gaussian, das keine direkte Symmetriebindung der
 Orbitale kennt ist es natuerlich schwierig diese in der noetigen
 Weise zu besetzen. Wie dem auch sei, das Keyword wuerde lauten
 Guess=Alter und dann am ende des Inputs waeren die Numern vom HOMO und
 vom LUMO einzusetzen, dann wuerde er eben das HOMO einfach besetzen und
 das LUMO einfach, womit Sie das hoffentlich richtige Biradikal haetten.
 Ich war nie in der Lage das auch fuer Dichtefunktionale durchzufuehren,
 aber UHF sollte gehen. Andererseits koennen Sie versuchen mit CIS
 die angeregten Zustaende zu rechnen (Das Biradikal wird auch darunter
 sein). Vom Niveau her ist "CIS" etwa vergleichbar mit HF und nicht mit
 CI.
 Die Resultate sind demzufolge mit Vorsicht zu geniessen. Hier wuerde jetzt
 natuerlich der Hinweis folgen, dass man angeregte Zustaende besser mit ...,
 aber ich spare mir das, sollte eh klar sein. Ich hoffe, dass Ihnen das hilft.
                                    mit freundlichen Gruessen
                                         H.U. Suter
 From: Frank Jensen <frj -8 at 8- dou.dk>
 	Thorsten,
 	UHF wave functions that are spin contaminated to the
 degree you describe are essentially useless, even your triplet
 UHF is pretty bad. The energetics will be all garbage. You need
 a small MCSCF (or equivalently GVB) to get a reasonable zero'th
 order description. For your singlet biradical a [2,2]-CASSCF
 may be OK (or an OSS GVB type wave function which is the same).
 But you won't get any dynamic correlation. To include that you
 need a MRCI, or perhaps a MP2 on top of the MCSCF.
 	Frank
 From: Matthew.Harbowy -8 at 8- tjlus.sprint.com
 Singlet biradicals are no trivial problem. You see, your calculations
 are on the *lowest* singlet, not the biradical. The calculations are
 converging to (what I believe is called) a Renner-Teller distorted
 configuration of the orbitals because it wants to do this
                                                        ------
         U         D
      -------    ------       distorts to
                                                          UD
                                                        ------
 What you want to do is not UHF, where your spins are all crazy mixed up. What
 you want to do is CI, where you can specify exactly what sort of configuration
 you want, and send it on it's merry way. I believe QCISD and CASSCF are the
 methods du jour for these sort of problems.
 matt