Subject: Re: CCL:Non-adiabatic MD: multiple configurations?

From: "Victor Anisimov" <[email-masked]>
Date: Sat, 24 Apr 1999 18:29:17 +0200

Dear Andrew,

Unfortunately I can not read those article you mentioned but it seems to me
there are two general points at this moment to start the discussion.

First, of course there is much sense to attribute HOMO-LUMO gap  in Cl2
molecule to interparticle interactions. When two chlorine atoms in their
ground
states are separated on infinity all energy level are degenerated, of
course,
and correspond to pure chlorine atom levels. When these two atoms become
nearer they begin to interact and this causes breaking of degeneration in
their energy levels. Frankly speaking when such an interaction arises we can
not any more attribute any energy levels of the system of two Cl atoms to
separate pieces. In other words any small interaction turns two independent
Cl atoms into completely new system, a system of two nuclei and 34
electrons.
Energy of ground state of the system is below a sum of energy of two Cl
atoms. Energy of excited state of the system is higher than dissociation
limit. The later is a reason why excitation of Cl2 molecule leads to
dissociation
onto two separate atoms. Energy of ground state and excited state of Cl2 is
a function of inter-nuclei distance. The more distance between Cl nuclei the
less a gap between ground state and excited one. They converge to sum of
ground state energies of isolated Cl atoms on infinity. This diagram
illustrates
that two Cl atoms in their ground state will begin to form Cl2 molecule
without
any external force as only they become to see each other (become to
interact).
Of course, dynamic consideration adds here some additional details.

Second common moment that would be interesting to discuss is a question what
is a goal of configuration interaction methods. Of course everyone uses it
for
more precise description of given state of a system either ground state or
excited one. According to general Hartree-Fock equation each electron of a
system is attributed by separate wave function (MO). Simple total wave
function
of the system is a determinant of such self-consistent molecular orbitals.
This
simplified picture always causes a misunderstanding that to get excited
state we have to put one electron from HOMO onto LUMO. Usually such a
total wave function of excited state will be wrong. The reasons are usually
bad
initial guess and lack of electron correlation. Usually excited state is
more
sensitive to lack of electron correlation therefore even simple description
of
excited state requires applying to configuration interaction methods. A
question
here is why or how configuration interaction takes into account electron
correlation. According to standard Hartree-Fock equation a problem of
electron
correlation is a problem of right chosen wave function. Therefore it is
wrong
to say in general that Hartree-Fock equation does not take into account
electron correlation. Because usually we do not know a priori wave function
of
a system we have to guess it. The simplest guess is a determinant of
molecular
orbitals that is good for rough description of a system but it does not take
into
account those fact that electrons tend to be as much as possible far from
each
other what we call electron correlation. Next better guess (configuration
interaction) of a total wave function is a treatment of a system as
consisting of
different electron configurations where each configuration is constructed
>from
occupying of virtual molecular orbitals. In common but wrong terms we have
to
give a system an ability to occupy excited states (virtual MO's). Why it is
wrong?
Because it is only common slogan of theoreticians embarrassing most of
students and significant part of computational practitioners. In one
determinant
wave function electrons may become very close to each other that is not
good.
To allow them to be as far as possible from each other we have to give them
such a flexibility in wave function. If we look on MO's of hydrogen molecule
we
see that occupied MO concentrates electron density between atomic nuclei and
virtual MO forces electron density to go out of bond region. The later fact
give
us a hint if we will construct total wave function as a special combination
of
occupied and virtual MO's we can give electrons a flexibility to be far from
each other as it is done in configuration interaction (CI) methods.
Therefore CI
(and MCSCF too) methods do not perform electron excitations as people used
to
say to take into account electron correlation but they give electron only
comfortable wave function to feel him better in proximity with other
electrons.

I'm sorry for this long discussion. I guess not every one is happy to read
such long messages in this list. Me too :)

Therefore I have to say thanks for attention and take my seat :)
Victor.

=========================================================================
Victor Anisimov, PhD, Software Researcher - Computational Chemistry
FQS Poland, Palac Pugetow, ul. Starowislna 13-15, 31-038 Krakow, Poland
Email: [email-masked]  Tel.(+48 12) 429 4345  Fax(+48 12) 429 6124
=========================================================================

-----Original Message-----
From: [email-masked] <[email-masked]>
To: [email-masked] <[email-masked]>
Date: 24 àïðåëÿ 1999 ã. 12:26
Subject: CCL:Non-adiabatic MD: multiple configurations?

>I am attempting to repeat the calculations of Gersonde and Gabriel (J.
>Chem. Phys. vol 98 (3), p 2094 (1993)) in which the photodissociation of
>Cl2 in Xe is discussed.
>
>I am attempting to describe the electronic degrees of freedom using a
>simple one particle model (tight binding), but have found a problem which
>I fear is fundamental. Since my background is in DFT, I am not well versed
>in multiple configuration interactions, hence the following question.
>
>Excited states within the model are created by promoting an electron from
>a low lying level to an empty higher lying level. When the interactions
>are weak I believe this is a reasonable description. But when they are
>weak, I suspect the model breaks down.
>
>Consider the Cl2 dimer. It is unstable with respect to dissociation when
>placed into an excited state. Thus, on being excited by a photon the atoms
>begin to separate. As this happens, the HOMO-LUMO splitting decreases
>until they become nearly degenerate. Thus it is no longer possible to
>distinguish the excited from the unexcited states. No transition between
>states is observed to take place. This is a problem should the two atoms
>meet up again some time later as it is not clear what state they should go
>into - ground state or excited state.
>
>I suspect that the root of the problem is that when the HOMO-LUMO
>splitting is very small it no longer makes sense to work with a single
>particle picture - it takes no energy to move between configurations, thus
>they will mix freely.
>
>At this point I get lost. Does this analysis really solve the problem of
>what state the system is in? Or would there still be ambiguity even if
>configurations were allowed to mix?
>
>Cheers,
>
>Andrew
>
>  +----------------------------------------------------+
>   Andrew Horsfield       e-mail: [email-masked]
>     FECIT, 2 Longwalk Road, Stockley Park, Uxbridge,
>          Middlesex UB11 1AB, United Kingdom.
>   phone: +44-(0)181-606-4653  FAX: +44-(0)181-606-4422
>  +----------------------------------------------------+
>