Subject: Replies to Bader analysis of CO

From: [email-masked] (Miquel Sol�)
Date: Fri, 17 Feb 1995 15:45:35 +0100

Dear CCLers,

Many thanks to all who replied to my question.
For all who may be interested in the conditions of the calculations, the r(C-O)
bond length in CO molecule was taken as 1.128 A. The results yield a
charge on the oxygen atom of -0.0145 au, while the dipole moment is 0.1024 D.
For the LiF molecule the r(Li-F) was 1.564 A, the charge on fluorine atom 
-0.6478 au and the dipole moment -6.4895 D. Further, the value of the density 
in the bond critical point (bcp) is 0.4829 au in CO and 0.0722 au in LiF.
Probably, the main conclusion is that the mere value of the laplacian 
in the bond critical point is not enough to define ionicity or covalency 
and that one should look also the shape of the laplacian in larger 
regions around the bcp, as well as the value of the electron density
in the bcp. 

My post was:

>An electronic analysis of the CO and LiF systems using the generalized 
>density from a QCISD/6-311++G** wavefunction yields a value for the laplacian
>of the density of 0.8328 au for CO and 0.7389 au for LiF. Could this mean,
>from a Bader analysis point of view, that CO is more ionic than LiF !!??
>Shoud the positive value of the laplacian (charge depletion) mean that the C-O 
>bond in CO molecule is ionic?.
>
>           If there is enough interest, I shall summarize the responses
>that I get on the net.
>
>           Thanks in advance,
>
>                       Miquel Sola
>                      	Institut de Quimica Computacional
>			Universitat de Girona
>			Voice: +34.72.41.83.62
>			FAX:   +34.72.41.83.61
>			World Wide Web: http://stark.udg.es
>			e-mail: [email-masked]
>				[email-masked]

Answers:

From: [email-masked]

Miquel,
  A positive value of the Laplacian at a 'bond crt. pt'
does not neccessarily mean that the bond is an ionic
bond.  It simply means that the density is locally
depleted.  Other types of interactions can give you
a positive value of the Laplacian as well.. eg H-bond.
The positive values have been correlated with 'closed-
shell' interactions which include ionic bonds.  Out of
curiousity,  how does your dipole moment stack up in both
cases?  Just to get an idea of the general charge
distribution.
  Take care... hope this helps.
     Ken Edgecombe
     Dept. of Chem.
     Queen's Univ.
     Kingston, ON

From: [email-masked] (Steven Bachrach)

>the laplacian
>of the density of 0.8328 au for CO and 0.7389 au for LiF. Could this mean,
>from a Bader analysis point of view, that CO is more ionic than LiF !!??

Well, suprising as it may seem, this is probably a correct conclusion!
If you calculate the charge on C and O in CO, my recollection is that the
values are soemthing like +1.2 and -1.2 respectively. The charge on Li and
F in LiF is probably something like +0.95 and -0.95, respectively. So which
is more ionic?

Finally, I don't think that Bader ever suggested that the values of the laplacian are interpretable in this way. All he indicated was that if the laplacian
is positive that this indicates a preponderance of ionic character in the bond
and a negative value indicates a mainly covalent character. I actually had a
long and heated argument with Bader many years ago about this and just what
the laplacian really means. I personally have my doubts about interpreting the
laplacian in terms of ionic/covalent character.

Steve

Steven Bachrach				
Department of Chemistry
Northern Illinois University
DeKalb, Il 60115			Phone: (815)753-6863
[email-masked]			Fax:   (815)753-4802

>From [email-masked] Thu Feb 16 00:09:37 1995

Dear Miguel,

I'm not absolutely sure about this, but I would suspect more negative
values for the laplacian at least for CO. Your are right: positive
values should indicate a more inionic interaction. I carried out 
calculations on organolithium compounds, and the laplacian at the
bond critical point for the C-Li bond was usually in the area of +0.2,
Li-F interactions in these molecules were about +0.3. May be there is
a bug in the program? 
G. Frenking from Marburg pointed me to the fact that the energy density
(H(rc)) at the bond critical point is a better measure for the covalency
of the respective bond. H(rc) is defined as the sum of kinetic energy
density (G(rc)) and potential energy density (V(rc)). For covalent bonds
it is always negative, whereas ionic, H-bond and vdW interactions have
positive densities! ref. D. Cremer, E. Kraka, Croat. Chem. Acta 1984,57,
1259.
Furtheron Cioslowski in Tallahassee calculates degrees of ionicity starting
>from the Bader integrations (J. Cioslowski, S.T. Mixon, JACS 1991,113,4142.

Hope this helps

John

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Dept. of Chemistry                         Phone: (403) 220 3232
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>From [email-masked] Thu Feb 16 03:36:38 1995

Your calculation for LiF is of course for an isolated molecule in the gas phase
..... Li(+) is EXTREMELY electrophilic in the gas phase, and would be expected
to have almost as great a "pull" on a pair of electrons as a fluorine nucleus,
so your result is not chemically surprising at all. CO is another story. Its
dipole moment is almost zero: 0.04 Debyes, if I remember correctly, and any
calculation should show this. I'll take a look through Bader's recent book on
his doctrines, and see if I can come up with an answer !
 Check the gas phase electron affinities of Li(+) and F. The electron affinity
of a fluorine atom in the gas phase (no stabilisation by hydrogen bonding) is
surprisingly low.

>From [email-masked] Thu Feb 16 09:11:40 1995

  Dear Miquel,

  With all my respect to the laplacian of the density and the Bader analysis,
which is the conductivity of a solution of CO in water? And the same question
for a solution of LiCl in water. Is the CO dissociated in C(2+) and O(2-) in
solution?
  Sorry for joking with your problem. I know that the true question is why
the Bader analysis gives this bizarre result for these molecules, but I cannot
resist to give the "experimentalist" point of view, which is often hard to
find in the CCL.
  Best regards,

  Jose Ignacio

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>From [email-masked] Thu Feb 16 10:36:54 1995

Dear Miquel,

Although I do not know exactly the reason for such behaviour of the
electron density Laplacian in CO molecule, I have some comments to
this subject:

1. Positive values of the Laplacian are typical of C-O multiple bonds
   as well as of C-F and some other bonds which are normally treated
   as covalent. The most famous example is F2 where the bond is defi-
   nitely purely covalent. Probably the positive Laplacian can occur
   in "electron-rich" molecules.
2. The Bader's topological theory does not state that the bonds with
   the positive Laplacian are ionic ones. Bader distinguishes between
   covalent and "closed-shell" interactions. The latter include ionic,
   donor-acceptor, and van der Waals interactions.
3. It is quite incorrect to compare the absolute values of the Lapla-
   cian in the bonds formed by different atoms (one cannot say whether
   LiF is more or less ionic than CO)
4. There exists another criterion of covalency suggested by Cremer and
   Kraka. Namely, a bond is to be considered as covalent, if the elec-
   tronic energy density is negative. In CO molecule this is the case.
   I would not like to discuss whether or not the Cremer-Kraka's cri-
   terion is better than Bader's one.
5. I have repeated you calculation (QCISD/6-311++G**) of CO molecule
   at C-O separation of 1 angstroem using Gaussian92 followed by Ba-
   der's EXTREME program and obtained the value of the electron den-
   sity Laplacian at the (3,-1) critical point as much as +2.837au.
   Thus, either in my or in you calculation something is wrong.

                              Yours sincerely,
                         Sergei Vyboishchikov
                         FB Chemie der Universitaet Marburg
                         Hans-Meerwein-Strasse
                         D-35032 Marburg, Germany
                         E-Mail: [email-masked]

>From [email-masked] Thu Feb 16 11:12:29 1995

Miquel,
       If i understand the Bader Analysis correctly a positive value
of the Laplacian does indicate ionic character. However the magnitude
of the charge density at the bond critical point must also be considered.
For LiF i would expect that the charge density is much smaller at the bcp 
than in the corresponding CO bond and that this indicates an ionic LiF bond whereas 
the positive value for the CO indicates a strongly polar, covalent bond.
Classification of bonds may also be performed using the energy density
at the bond critical point, as discussed by Cremer and Gauss, JACS, 107, 1985,
p.3800.
  I would be very interested in any other replies you receive on the subject.

                            Cheers,
                                   David.

>From [email-masked] Thu Feb 16 11:49:02 1995

FTP
Hello Miquel,

I suppose that you should analyse larger region around the 
BCP. The analysis of gradient trajectories would help.
I think you will find strange behaviour inside the
CO electron density near to the critical point.
Try acetilene too.

Gabor

Gabor I. Csonka		        Budapest University of Technology
Tel/FAX: (361) 463.18.35	Inorganic Chemistry Dept. Ch. Bldg
[email-masked] 		H-1111, Bp. Szent Gellert ter 4
http://www.fsz.bme.hu/bme/chemical/csonka.html

>From [email-masked] Thu Feb 16 15:26:08 1995

	Hola Miquel,

	Creo que el libro de Bader (Atoms in Molecules. A Quantum Theory)
        puede serte util para aclarar tu cuestion. Si mal no recuerdo,
	en el libro se seganala que las propiedades de la densidad elec-
	tronica en los puntos criticos de enlace, no son directamente
	comparables para enlaces constiudos por diferentes pares de atomos.
	Asi, la magnitud de la densidad electronica de enlace para un C-S
	no puede comparase con el valor correspondiente en un enlace C-C
	por ejemplo, para poder decir "quien es mas fuerte que quien".
        (La teoria no puede respaldar ese tipo de afirmaciones, aunque
	luego el mismo Bader sin ir mas lejos compare distintos enlaces
	de puente de H en base al valor de rho(critico) de un modo
	"empirico").
	Ademas, la circunstancia de que el enlace C-O, C-S, presente
	valores positivos de la Laplaciana, del tipo de los compuestos
	ionicos LiF, tambien es tratada por Bader. Estos enlaces, C-O,
	son covalente-polares, implicando una parcial transferencia
	de carga entre los atomos implicados, de resultas del cual
	la energia cinetica predomina en la region de enlace. De todos
	modos, que se trata de una interaccion covalente tambien
	se puede poner de manifiesto mediante un mapa de la Laplaciana
	sobre la region de enlace. En dicho mapa se observa que la densidad
	electronica de C y O se deforma claramente en la region de enlace,
	mientas que para el caso de compuestos ionicos, lo que se observa
	es que la laplaciana es practicamente esferica ("dos bolitas")
	en torno a los atomos en cuestion. Supongo tambien, que si has
	calculado las cargas atomicas de Bader para el caso del CO y el LiF,
	tambien tendras otro criterio para distinguir ambos casos. 
        Supongo que en el libro de Bader (cap 7, si  mal no recuerdo) podras
	encontrar detalladamente este tipo de discusion, acerca de la
        caracterizacion de interacciones atomicas de distintos tipos
	a partir de las propiedades de los puntos criticos de enlace.
	Asimismo, la densidad de energia en el punto critico puede ser otra
	magnitud que diferencie ambos enlaces.(Esta tecnica ya no es de
	Bader, sino de D. Cremer y E. Kraka y esta expuesta en un par 
	de articulos de agno 1984, en JACS y Angewandte..)

	Bueno, no se si estos comentarios te pueden servir de algo,...
	Hasta luego,...

		Dimas Suarez
		e-mail: [email-masked]

>From [email-masked] Thu Feb 16 17:47:22 1995
        Reply to:   RE>CCL:Bader analysis of CO
Miquel:

You should read the section(s) in Richard Bader's book (at least) on this
matter.

I do not believe that there is any correlation, per se, between the mag-
nitude of the Laplacian and any chemical notion of 'covalency/ionicity'.

The Laplacian is simply the trace of the Hessian of Rho; at the bond-
critical point, you look at it as the sum of the 3 eigenvalues (of that
Hessian) and conclude: is the sum of the transverse curvatures greater in 
magnitude than the longitudinal curvature?

You should note, as follows, there are two 'extremes' of behaviour of the
charge density in 'interatomic' regions:  "shared" interactions (typically
between covalently bound atoms) in which the Laplacian is _usually_ negative; 
"closed shell" interactions (like noble-gas vdW dimers and
'ionic' systems) in which it is _invariably_ positive.

In between there are so-called "intermediate" cases, like CO (in fact most
C=O and C=S bonds) in which the interaction is "shared" but the Laplacian
is +ve.  You have to also look at the magnitude of  Rho itself which is 
usually around 10^-1 a.u. for "shared" interactions.  The reason for the 
sign of the Laplacian in these intermediate cases is that the location of 
the 'bond critical point' is close to the "VSCC" (Valence shell charge
concentration) of one of the atoms - see Bader's book.

The point is that you have to look at the _whole_ picture; in the Theory
of Atoms in Molecules, it is often not useful to draw drastic conclusions
>from single numbers.  Many people are guilty of that and misinter-
pretations are legion.

Another paper you should look at is Bader and Essen, J. Chem. Phys., 1984.

I also have to ask you: although your numbers look OK to me, you should
check that those values of Del^2 do in fact correspond to the sum of
eigenvalues, if you are using the program "SADD2R" (or "EXTD2R").  E-mail 
me if you think this is a problem.

Richard Bone

__________________________________________________________

Richard G. A. Bone, PhD.
Computational Chemist
Terrapin Technologies, Inc.
South San Francisco
USA

E-mail  [email-masked]

>From [email-masked] Thu Feb 16 18:27:30 1995

	Greetings Miquel:

	You asked about link between the properties of (3,-1) critical
points and the character of bonding; specifically about the sign of the
Laplacian and the 'ionic character' of bonding in LiF and CO.  While its
true that the character of chemical bonding can be summarized by the
properties at the 'bond critical point' (BCP), I think its unwise to treat
the values as magic numbers which tells all about the nature of
interaction between two atoms.  One must take stock of the entire set of 
data to get the correct results from these characterizing properties.

	The rule of thumb is that a low amount of charge AND a positive 
Laplacian signify an ionic interaction.  In the case of LiF vs. CO, the 
magnitude of the Laplacian at the BCP of CO is more positive, but there 
is a good deal more electronic charge than typically found in 'ionic 
bonds' (see Bader and Essen, JCP, 1984).  LiF has the small amount of 
charge typically found in the interatomic region of ionic interactions.

 LITHIUM FLUORIDE HF/6-311++G**      CARBON MONOXIDE HF/6-311++G**

 RHO        7.0078622807E-02         RHO        5.1842212832E-01
 DEL2       7.2110756059E-01         DEL2       1.0834101333E+00

	So, the bonding in CO is not the same as that in LiF, 'ionic'.

---Further ramblings---

	In fact, the case of CO is particularly interesting as the
Laplacian makes clear the seeming contradiction of the different
electronegativities of C & O and the small dipole moment for this system. 
The small dipole moment of CO would lead you to believe that the atoms
were roughly electroneutral, based upon the simple idea that the dipole 
moments is the result of separation of charge.  But then how does one 
reconcile this with the large expected electronegatvities of the two atoms?

	There is a large transfer of charge from C --> O.  But there is
also a large opposing polarization of the remaining charge on the carbon
atom (unlike what one would expect for spherical ions).  It is this large
opposing polarization which produces a large dampening of the dipole
moments, canceling the contribution from charge transfer, and making the
overall dipole nearly zero.  This can be seem in the Laplacian map of CO
in which the valence shell of carbon is polarized away from the direction
of charge transfer, producing a large, relatively diffuse region of charge
concentration (see the cover of Bader's paperback to see the Laplacian of
CO (blue)).  This is why the carbon of CO is so reactive.  

	In addition, the polarization of the carbon valence shell away
>from oxygen is the reason that the Laplacian is positive at the bond
critical point.  The Laplacian map of CO shows that the valence shell of O
reaches almost to the interatomic surface and that the valence shell of
carbon is polarized away from the interatomic surface.  So, it is this 
polarization of C away from O that gives rise to the relatively large 
value of rho at BCP (a 'sort-of' shared interaction) and the larger, 
positive magnitude of the Laplacian.

	Anyway, I think its all pretty interesting...

	Keith

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     Keith E. Laidig 
     Department of Medicinal Chemistry, BG-20,
     University of Washington, Seattle, WA 98195 
     E-Mail: [email-masked]
     Phone: (206) 616-2780 or 685-1000          FAX #: (206) 685-3252
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>From [email-masked] Thu Feb 16 09:28:26 1995

Dear Miquel,
instaed of discussing the Laplacian, it is better to compare the 
energy-density at the bond kritical point (This is the negative K-Value 
in the Bader-output).
For references see:
D. Cremer, E. Kraka, Angew. Chem. 8, 614 (1984) (german edition)
G. Frenking, D. Cremer, Stucture and Bonding 73, Springer Verlag, 
Berlin-Heidelberg (1990)
W. Koch, G. Frenking, J. Gauss, D. Cremer, J. R. Collins, J. Am. Chem. 
Soc. 109 5919 (1987).
I hope this helps, with best regards, 
Andreas Ehlers

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=                   - Vrije Universiteit Amsterdam                        =
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