Subject: Summary: UHF vs ROHF in semiempirical calc's of radical cations

From: <[email-masked]>
Date: Tue, 08 Nov 1994 15:56:15 -0400 (EDT)

Dear CCl'ers,
As promised I hereby send you the summary of all responses I received on my 
questions about the use of ROHF versus UHF in semiempirical calculations of
radical cations. This summary starts with the original posting, followed by the
responses.
A big THANKS to all those who responded!

                                              Han Zuilhof

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Original posting:

Subj:	ROHF versus UHF in semiempirical calc.'s of radical cations

Dear CCl'ers,

Semiempirical programs such as MOPAC allow the properties of radicals
and radical ions to be calculated with both the Restricted Open-shell
Hartree-Fock method (ROHF) and the Unrestricted Hartree-Fock (UHF) methods.
I want to calculate reactionpaths for nucleophilic attack on a series of
radical cations.

Does anyone know of 
1) any apriori reasons why one method might be preferred over the other in 
such calculations?
2) literature data in which the performance of the ROHF and UHF methods 
for the study of radical cations is compared directly?

Please report directly to me, and I'll summarize to the net.
Thanks in advance,
                    Han Zuilhof

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A very informative answer, dealing with many issues came from 
prof. Thomas Bally:

From:	IN%"[email-masked]"  2-NOV-1994 08:02:49.67
To:	IN%"[email-masked]"
CC:	
Subj:	RHF vs. UHF

Dear Mr. Zuilhof,

You were asking on CCL about using UHF vs.RHF for calculating the attack of
nucleophiles on radical cations.

The question of UHF vs. RHF is a thorny one and it becomes thornier when
you go to semiempirical methods, even if you disregard for the moment the
problems posed by spin contamination which I will address below.

By allowing alpha and beta-electrons to occupy different spatial MO's (which is
the essence of the UHF model) you take into account a special form of electron
correlation called "spin polarization" which expresses itself experimentally in
negative hyperfine coupling constants in ESR spectra and is hence a physical
phenomenon. However, the UHF model has a tendency to overestimate the extent of
spin polarization which results in an overestimation of the stability of
systems where spin polarization is important (for example systems containing
allylic radical moieties such as they occur quite often in radical ions) if
compared to systems where this effect is less important.

In semiempirical methods, electron correlation effects are already "absorbed"
somehow in the parameters and therefore, in systems with high spin polariza-
tion, you count some of these twice in semiempirical UHF calculations. As a
consequence, the stability of systems where spin polarization is important (see
above) is often *absurdly* overestimated by semiempirical methods.

On the other hand, if you do RHF (I suppose you are referring to the "half-
electron" method which is used rather than the "real" Roothaan ROHF method in
Dewar's modelsbut this makes no difference), you artificially suppress spin
polarization entirely (it cannot occur if alpha and bete-electrons are
constrained to occupy pairwise the same spatial MO's). Hence the stability of
systems where this is important (see above) is *underestimated* with this
model.

To this you have to add the problem of "high-spin contamination" in UHF
wavefunctions which are not eigenfunctions of the S**2 operator and hence
cannot be classified as singlets, doublets, triplets. Most decent programs will
tell you about the *expectation value* of a UHF wavefunction with regard to
S**2 (usually called <S**2>) and the deviation of this expectation value from
the value for a pure singlet(=0), doublet (=0.75), triplet (=2.75) etc. tells
you how far you have gone astray from pure spin states in your calculation. As
a rule of thumb, a UHF wavefunction is acceptable if <S**2> deviates less than
0.1 from the "correct" value. You will find that this deviation is often
exceeded, especially in systems with high spin polarization.

So what can you do? Unfortunately I cannot give you a good answer. Due to the
above-mentioned problems and some other shortcomings of semiempirical methods
(problems with small rings) I have personally all but given up semiempirical
calculations on radical ions and switched to ab-initio based methods which have
become quite affordable with the advent of modern workstations. On the other
hand you may get away with semiempirical methods for large systems if

  (a)  You do have cases where spin polarization is unimportant
       (i.e. if the difference between UHF and RHF heats of formation
       is, say, less than 5 kcal/mol)

  (b)  If the <S**2> values for doublets are <0.85.

The grist of the matter is, that you should always do *both* RHF and UHF
calculations. If the results do not differ substantially, both with regard to
geometries and relative energies, you are probably safe (unless you have small
rings, but that's another can of worms).

Don't hesitate to get back to me if you have follow-up questions or if you need
guidance for getting started with ab-initio calculations (of such calculations
are feasible for your systems)..

  thomas bally

P.S. please don't reply to the address from where you got this message (I use
     it exlusively for CCL) but to the one indicated below:

------------------------------------------------------------------------------
|  Prof. Thomas Bally                    |  E-mail:  [email-masked]   |
|  Institute for Physical Chemistry      |                                   |
|  University of Fribourg                |  Tel:     011-41-37 826 489       |
|  Perolles                              |  FAX:     011-41-37 826 488       |
|  CH-1700 FRIBOURG                      |                                   |
|  Switzerland                           |                                   |
------------------------------------------------------------------------------

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Both Serge Pachkovsky and John McKelvey commented that MOPAC/AMPAC etc do not
implement the REAL/CORRECT ROHF method, but rather Dewar's half-electron method:

From:	IN%"[email-masked]"  2-NOV-1994 03:58:29.52
To:	IN%"[email-masked]"
CC:	
Subj:	RE: CCL:ROHF versus UHF in semiempirical calc.'s of radical cations

Dear Han,

In your message to the CCL you write:
> Semiempirical programs such as MOPAC allow the properties of radicals
> and radical ions to be calculated with both the Restricted Open-shell
> Hartree-Fock method (ROHF) and the Unrestricted Hartree-Fock (UHF) methods.
                       ^^^^

This is not exactly true. Semiempirical programs usually implement half-electron
method (and Mopac is not an exception), not ROHF, which is notorious for the
poor SCF convergence properties. Although half-electron method often gives
results one would expect from the exact ROHF treatment (and in some cases is
exactly equivalent to it), there is one important distinction: electronic
energy computed within the half-electron approximation is not variational.

With my best regards,

Serge Pachkovsky.

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Careful...NONE of the semi-empirical methods derived from MOPAC or AMPAC does 
the CORRECT ROHF. They all use a half-electron method of Dewar followed by a 
small C.I. for clean up. Gaussian and GAMESS will do the ROHF for the 
semiempirical methods correctly, I believe.

-- 

John M. McKelvey			email: [email-masked]
Computational Science Laboratory	phone: (716) 477-3335
2nd Floor, Bldg 83, RL
Eastman Kodak Company			
Rochester, NY 14650-2216

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the matter of spin contamination occurring in UHF calculations was adressed
by several people:
Dave Ewing writes:

From:	IN%"[email-masked]"  "DAVID W. EWING (216) 397-4742"
To:	IN%"[email-masked]"
CC:	
Subj:	RE: CCL:ROHF versus UHF in semiempirical calc.'s of radical cations

With ROHF you don't have to worry about spin contamination.

Dave Ewing
John Carroll University
[email-masked]
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and Irene Newhouse wrote:

From:	IN%"[email-masked]"  3-NOV-1994 12:35:15.41
To:	IN%"[email-masked]"
CC:	
Subj:	RE: CCL:ROHF versus UHF in semiempirical calc.'s of radical cations

There are people who are VERY suspicious of ROHF -- people like Andy Holder,
one of the authors of AMPAC v4.  On the other hand, UHF can, especially very
close to the transition state, suffer from 'spin contamination', that is,
states with the wrong spin mix in.  At very stage, SZ**2 is plotted, so that
you can TELL if it's happening.  Which way you do it, depends on if you're
trying to qualitatively describe experiments, or do a thorough theoretical`
investigation.  If the former, I'd try it both ways & be happy if the results
are about the same.  If the latter, all either method is good for is a guess
to plug into ab initio computations!

Good luck!`
Irene Newhouse 
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**   Dr. Han Zuilhof           **  e-mail: [email-masked]  **
**   Department of Chemistry   **  (optional: [email-masked]) **
**   University of Rochester   **                                           **
**   Rochester, NY, 14627      **  Fax:   (716) 473-6889                    **
**   USA                       **  Voice: (716) 275-2219                    **
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**                        "Excite a photochemist!"                          **
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