Subject: wavefunction stability issues

From: Wai-To Chan <[email-masked]>
Date: Fri, 21 Jun 2002 03:46:59 -0400 (EDT)

>Date: Wed, 29 May 2002 18:29:02 +0200
>From: Patrick Bultinck <[email-masked]>

>Dear all,

>Can anybody refer me to a good reference on the different sources of wave
>function instability ? Especially as on how to judge whether a certain post
>SCF calculation will help. Also, it is sometimes stated that wave function
>instability would indicate the necessity of electron correlation. At this
>day and age, only single reference (Hartree-Fock) dynamical electron
>correlation techniques can be used for the larger molecules I am looking
>at. What good is MP2, CC etc. when the reference is not appropriate ?

  I don't think there is a clear-cut answer to your question. 
Switching to a reference UHF wavefunction in the region 
of a PES for a closed-shell system where the RHF wave is unstable towards
spin-symmetry breaking sounds theoretically more rigourous. 
To my knowledge it is not known whether a UHF-based MPn or CCSD(T) method 
would always give more accurate result than if you stick to the unstable
RHF wavefunction. At least from my limited experience
if the degree of distortion of the structure calcluated and its
degree of wavefunction instability are not too high it 
may be prudent to stick with RMP2 or RDFT for 
transition structure optimization to avoid spin 
contamination of the stable UHF wavefunction. 

These two references may be helpful to you:

"Evaluation of S^2 for correlated wavefunctions...." 
Chen and Schlegel, J chem phys, vol 101 (1994) 5957. 

"Spin-contamination of coupled-cluster wave functions"
A Krylov, J chem phys, vol 113 (2000) 6052. 

  The Schlegel paper compares the performances of variuos R and U method 
with full CI on potential curve calculations. It also reports 
the degree of spin-contamination of the correlated wavefunctions that 
allows you to judge which method can best handle an unstable reference
wavefunction. 

>Really, for a good result a technique like mrci would be very interesting,
>but for some systems (and computer resources), even a large CAS+PT is
>impossible. So how to handle this ? Any references ?

    At present analytical gradient is available in neither method. 
It is safe to say that their applications to calculation of 
ground state as an alternate to single-reference method will be 
limited for some time.  You may check out this paper for an example of 
possibly an unusually large-scale CASMP2 calculations on a system 
presumably not amenable to single-reference method. 
I would be delighted to see some comparisons between
CASMP2 and the single-reference BD(T) method in this subject. 

"UDFT and MSCF description of the photochemical Bergman cyclization of enediynes"
Clark, Davidson and Zaleski
JACS, vol 123 (2001) 2650. 

>As a side question: would anybody have any idea what percentage of post-scf
>calculations being done has ever had the stability of its HF reference
>checked ?
 
  Perhaps the real question is how often stability of HF reference is an issue
in studies involving post-scf calculations. In principle 
instability of RHF wavefunction could be solved by using a MCSCF approach
which in practice is not straightforward to apply. My view is
there is not much one can do beyond standard methods in dealing with 
wavefunction instability in the intermediate bond-breaking region. 
Instability of UHF wavefunctions of radicals towards spatial symmetry breaking is 
hardly an overlooked issue. You may find this example of interest

"A detailed study on the symmetry breaking and its effect 
on the potential surface of NO3"
Eisfeld and Morokuma
J chem phys, vol 113 (2000) 5587. 

  This one concerns DFT but is still relevant

"On the performance of density functional theory for
symmetry-breaking problems"
Sherill, Lee and Head-Gordon
Chem phys lett, vol 302 (1999) 425.

    One area where some people may overlook the stability issue concerns
singlet diradicals. This paper convers two previous studies where
use of unstable RDFT wavefunctions lead to erroneous observations. 

J phys chem A, vol 104 (2000) 1748
Grafenstein, Hjerpe, Kraka and Cremer

Wai-To Chan

>Thanks,

>Patrick Bultinck
>Ghent University
>Belgium

---

From: "T. Daniel Crawford" <[email-masked]>
Date: Fri, 21 Jun 2002 11:26:21 -0400 (EDT)

We have done a number of studies directly addressing the question as to how
post-HF methods perform when reference functions are unstable.  My experience
with spatial symmetry breaking is that a strong instability in the MO's
(i.e., a negative eigenvalue in the MO Hessian/stability matrix) is often
not a problem (apart from practical difficulties such as finite-difference
vibrational analyses).  The difficult cases occur when the MO Hessian is
nearly singular, that is, when one of its eigenvalues is close to zero,
regardless of sign.  In such cases, even high-level coupled cluster cases
can give anomolous results --- e.g., vibrational frequencies > 5000 cm-1.

Please see:

@Article{
  author =       "T. D. Crawford and J. F. Stanton and W. D. Allen and
                  H. F. Schaefer",
  title =        "Hartree-Fock orbital instability envelopes in highly
                  correlated single-reference wavefunctions",
  journal =      JCP,
  year =         1997,
  volume =       107,
  number =       24,
  pages =        10626
}

for a detailed theoretical analysis of this.  Also, for a difficult singlet
diradical case:

@Article{
  author =       "T. D. Crawford and E. Kraka and J.F. Stanton and D.
                  Cremer,"
  title =        "Problematic p-Benzyne: Orbital Instabilities, Biradical
                  Character, and Symmetry Breaking",
  journal =      JCP,
  year =         2001,
  volume =       114,
  pages =        "10638-10650"
}

In this above, we applied a wide range of reference functions, including
Brueckner, GVB, RHF, and UHF, to the p-benzyne diradical.

-Daniel

-- 
T. Daniel Crawford                           Department of Chemistry
[email-masked]                                    Virginia Tech
www.chem.vt.edu/chem-dept/crawford    Voice: 540-231-7760  FAX: 540-231-3255
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