From:	Carolina Reyes <creyes &$at$& cgl.ucsf.edu>
Date:	Thu, 15 May 1997 13:12:52 -0700 (PDT)
Subject:	Re: CCL:G:Summary: Chemical Softness by DFT

PLEASE LET YOUR COLLEAGUE KNOW THAT IF S/HE IS GOING TO ACCESS EMAIL IN A
LAB ENVIRONMENT, THEY NEED TO CLOSE THEIR MAIL SESSION AFTERWARD.  NO ONE
IS IN TOO MUCH OF A RUSH TO PROTECT THEIR PRIVATE AND RESEARCH
CORRESPONDENCE.  THANKS FOR YOUR ASSISTANCE IN POINTING THIS OUT TO YOUR
FRIEND.



On Thu, 15 May 1997, Jerry C.C. Chan wrote:

> Dear CCLers,
>
> 	Thanks are due to all who response to my questions concerning
> the chemical hardness.  I am happy that many experienced CCLers did share
> with me their valuable expertise.
>
> Sincere thanks,
> Jerry
>
> > 	Last week I posted a question concerning the determination of
> > chemical hardness (or softness) of the metal centre of a TM complexes.
> > Maybe the way I asked the question was not specific enough, I just
> > received two mails asking for the summary.  So I try to write down my
> > thinking explicitly and hope that someone in the net, who could not
> > tolerate the naiveness or even mistakes of my post, would kindly comment
> > on it.  I will summarize.
> >
> > I want to determine the chemical hardness of the metal centre of a charged
> > TM complexes.  The method that comes to my mind is to do a HF calculation
> > and get the MO spectrum.  Based on the Koopmans' theorem the hardness of
> > the complexes would be (E_LUMO - E_HOMO)/2.
> >
> > Even my thinking is correct, HF calculation seems to be unreliable for TM
> > complexes and correlated methods are usually very expensive.  Therefore
> > last time I enquired the possibility of using DFT methods as an
> > alternative although Koopman's theorem does not hold for KS orbitals.
> >
> > By the way, I have heard that Fukui function is somehow related to the
> > chemical hardness but I don't have the recipe.
>
>
> ++++++++++++++++++++++++++++++++
> Stefan Fau 
> Pascal HEBANT 
> Xavier Assfeld 
> Hogue, Pat (AZ76) 
>
> R.G. Parr and W. Yang, "Density-Functional Theory of Atoms and
> Molecules" (Oxford University Press, 1989, New York).
>
> Ian Fleming, "Frontier Orbitals and Organic Chemical Reactions"
>
> "Hardness and softness in Density Functional Theory in Chemical Hardness",
> K.D. Sen Ed., Coll. Structure and Bonding 80, (Springer-Verlag, Berlin,
> 1993).
>
> R.G. Pearson:				J.Am. Chem. Soc. 85, 3533 ('63)
> N.K. Ray, L. Samuels, R.G. Parr: 	J.Chem. Phys. 70, 3680 ('79)
> M.S. Gopinathan, M.A. Whitehead:   	Isr. J. Chem. 19, 209 ('80)
> J.P. Perdew, R.G. Parr, M. Levy, J.L. Balduz:
>                                      	Phys. Rev. Lett. 49, 1691 ('82)
> R.G. Parr, R.G. Pearson:           	J. Am. Chem. Soc 105, 7512 ('83)
> R.F. Nalewajski:                   	J. Am. Chem. Soc. 106, 944 ('84)
> R.G. Parr, W. Yang:                	J. Am. Chem. Soc. 106, 4049 ('84)
> W. Yang, W.J. Mortier:             	J. Am. Chem. Soc. 108, 5708 ('86)
> R.G. Pearson:                      	J. Chem. Ed. 64, 561 ('87)
> A.R. Orsky, M.A. Whitehead:        	Can. J. Chem. 65, 1970 ('87)
> M. Berkowitz, R.G. Parr:           	J. Chem. Phys. 88, 2554 ('88)
> R.G. Parr, P.K. Chattaraj:         	J. Am. Chem. Soc. 113, 1854 ('91)
> P.K. Chattaraj, H. Lee, R.G. Parr: 	J. Am. Chem. Soc. 113, 1855 ('91)
> D. Datta, S.N. Singh:              	JCS Dalton Trans. 1541, ('91)
> J. Cioslowski, S.T. Mixon:         	J. Am. Chem. Soc. 115, 1084 ('93)
> J. Cioslowski & B.B. Stefanov: 		J. Chem. Phys. 99, 5151 ('93)
> R.G. Pearson:				Acc. Chem. Res. 26, 250 ('93)
> P.K. Chattaraj, P.v.R. Schleyer:   	J. Am. Chem. Soc. 116, 1067 ('94)
> F. Mendez, J.L. Gasquez:           	J. Am. Chem. Soc. 116, 9298 ('94)
> W. Kohn, A.D. Becke, R.G. Parr: 	J. Phys. Chem. 100, 12974 ('96)
>
> +++++++++++++++++++++++++++++++++++++++++
> From: Liang Lou 
>
> There is an equivalence in DFT calculations which is called Slater's
> transition state method. In this method, the EA and IP are approximated by
> the values of an halfly occupied orbital. For example, for IP, you put
> +0.5e on the molecule and run a full SCF. Then you check the eigenvalue
> for the one-particle state with an 0.5 occupation number. This gives a
> good estimate of the IP. For EA, charge the molecule with -0.5e. The
> formal explanation of this "transition state" method was given by Janet
> (coauthor of the book "calculation of electronic structure in metals"). It
> is roughly as follows. The total energy of an N-electron system in LDA can
> be written as E=sum[n_k * epsilon_k] + ..., where n_k is the occupation of
> the eigenstate k and epsilon_k is the corresponding eigenvalue.  The
> eigenvalue of the one-particle state k is simply epsilon_k=dE/dn_k. This
> is an equivalence of the koopmans' theorem in LDA. The Slater's transition
> state is a "finite-difference" approximation to the infinitesimal d(n_k).
> The error of this method, from my experience, is in the range between
> 0.1-0.3eV, approximately the same as from a small-delta SCF calculation
> (e.g., dE(EA) = E(N) - E(N+1)).
>
> +++++++++++++++++++++++
> From: Rene Fournier 
>
> > although Koopman's theorem does not hold for KS orbitals.
>    I would not worry about that.  First, Koopman's theorem
> is not so great anyway.  It equates two theoretical constructs:
> the energy difference between the GS and a HYPOTHETICAL excited
> state with orbitals identical to those of the GS on one hand,
> and the difference between the HOMO and LUMO HF orbital energies
> on the other.
>
>    Actually, I would say that Kohn-Sham DFT is THE IDEAL theory
> for your problem.  It has two useful theorems:
>
>   (a) the negative of the KS HOMO energy is equal to the TRUE
> ionization energy of the system (relates a theoretical construct
> to an observable).   CAVEAT: this theorem holds only in the limit
> of an "exact" XC potential.  [ But how could one expect exact
> calculation of observables in any approximate theory anyway?
> At least, in KS-DFT, the framework for exact calculations of
> this kind is there. ]
>
>   (b) the derivative of the KS-DFT energy w.r.t. number of
> electrons, whether the XC is exact or approximate, is precisely
> equal to the energy of the highest partly occupied orbital
> (Janak's theorem)
>
>    The hardness is most conveniently defined as being half the
> second derivative of the energy w.r.t. number of electrons;
> the finite difference approximation to that is (I-A)/2; and
> that in turn can be approximated as (E_LUMO - E_HOMO)/2 .
> Thanks to Janak's theorem, you can get some derivatives (dE/dN)
> simply by looking up orbital energies.
>
>    There is an excellent discussion of hardness and Fukui function in
> Parr and Yang's book "Density-Functional Theory of Atoms and Molecules"
> (Oxford University Press, 1989, New York).
>
>    BTW, the Fukui function is the derivative of the electron
> density at point r w.r.t. total number of electrons, N.  If the
> sum of nuclei charges is M, then:
>
> f(r) is roughly the density associated with the LUMO for N = M+delta
> f(r) is roughly the density associated with the HOMO for N = M-delta
> f(r) is roughly the average of the above two for N=M
>
> ++++++++++++++++++++++++++++++++++++
> From: "N. Sukumar" 
>
> Hardness in DFT is given by the partial second derivative of the energy
> functional with respect to the electron density, at constant external
> potential, ie. (d^{2}E/d\{rho}^2)_v
> See Parr & Yang's book and the references therein for details, including
> relations to the Fukui functional (which is the mixed partial derivative
> of the energy functional with respect to density annd external potential) :
> Robert G. Parr & Weitao Yang, "Density Functional Theory of Atoms and
> Molecules" (Oxford University Press, New York, 1989)
> Jerzy Cioslowski in Florida has done some ab initio (Hartree-Fock level)
> calculations (on small molecules) using the DFT definition of hardness,
> without relying on the Koopman's theorem. Some references are :
> J. Cioslowski & S. T. Mixon, J. Amer. Chem. Soc. 115, 1084 (1993)
> J. Cioslowski & B. B. Stefanov, J. Chem. Phys. 99, 5151 (1993)
> see also references therein (since the above two papers are primarily
> concerned with BOND hardness).
>
> +++++++++++++++++++++++++++++++
> From: Oliver Warschkow  
>
> You have asked about hardness/softness calculations.
> I dont have any experiences in such calculations myself,
> but there is a recent review by Kohn, Becke and Parr
> (J.Phys.Chem (1996), 100, 12974) where hardness,softness
> and fukui-functions in the framework of DFT are discussed.
> The explicit expression given in there (eq.3.4) is
>
>      hardness = (del mu / del N) at const. V
>
> where mu is the chemical potential (or fermi leve Ef)
> of the system. So, it probably boils down to running a
> two DFT calculations on the system with slightly
> (that is fractionally) different number of electrons and
> to see how the HOMO orbital energy (or Ef if you use
> a Fermi-Dirac orbital occupation scheme) changes. Well, that
> would be my guess how to do it. You are right in
> that you are probably better off in doing DFT instead of
> HF on TM systems and according to the review, concepts
> like hardness,softness etc are quite natural to DFT.
>
> +++++++++++++++++++++++++++++
> From: "Jack A. Smith"  peabody.sct.ucarb.com>
>
>   I think a good reference for you would be "Density Functional Theory of
> Atoms and Molecules" by Parr and Yang (Oxford Press, 1989), particularly
> chapters 4 & 5.  You'll see that the KS orbitals of DFT are actually more
> directly related to the chemical potential, hardness, Fukui functions, etc.
> than canonical HF orbitals [Grand Canonical HF, on the other hand, can be
> viewed as a natural extension of HF to DFT which includes proper exchange
> (see J. Linderberg, IJQC 12:supp 1, p267) but no extra correlation, and
> whose orbitals allow similar interpretation as do KS orbitals].
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
> From: Liang Lou 
>
> > Thank you very much for your reply.  Since I always work on closed shell
> > system, I would like to know if I understand your suggestion correctly:
> >
> > If I have a +3 TM complexes, in G94 I can simply change the the charge
> > from +3 to +3.5 and the multiplicity from 1 to 2 and then do a DFT
> > calculation.  No special keywords are needed.  Repeat the calculation
> > with the charge of +2.5.  I may have difficulties to get the SCF
> > convergence for these +3.5 and +2.5 systems but using vshift should be
> > able to solve it (though I don't have any experience on it).
>
> As far as I know, Gaussian is not particularly strong for metals,
> especially in the sense of the efficiency of basis sets. Other DFT program
> packages could do better (with either highly optimized Gaussian bases or
> Slater type bases, or numerical bases).  I guess the level shifting would
> result in artificial values for orbital energy near the separation of HOMO
> and LUMO.  When calculating electron removal energies, IP and EA, the
> system always changes spin multiplicity and there are always associated
> uncertainties. Usually, the orbital energy values do not change in the
> first few decimal places after he total energy has converged to under,
> say, 10**(-4). Therefore, higher convergence of total energy will not
> affect comparing with experiment.
>
>
>
>
> -------This is added Automatically by the Software--------
> -- Original Sender Envelope Address: chan "-at-" uni-muenster.de
> -- Original Sender From: Address: chan { *at * } uni-muenster.de
> CHEMISTRY : at : www.ccl.net: Everybody | CHEMISTRY-REQUEST : at : www.ccl.net:
Coordinator
> MAILSERV &$at$& www.ccl.net: HELP CHEMISTRY or HELP SEARCH | Gopher:
www.ccl.net 73
> Anon. ftp: www.ccl.net   | CHEMISTRY-SEARCH ( ( at ) ) www.ccl.net -- archive
search
>              Web: http://www.ccl.net/chemistry.html
>
>


Similar Messages
05/15/1997:  Summary: Chemical Softness by DFT 
10/04/1993:  DFT
03/27/1996:  meaning of eigenvalues in dft
08/01/1996:  Re: CCL:M:Heat of formation calculation using MOPAC.
12/11/1995:  Summary: Koopmans' Theorem and Neglect of Bond in CAChe MOPAC Input
08/01/1995:  Spin contamination, effect on energy and structure.
02/14/1995:  Warning - possibly undelivered mail.
02/04/1995:  Summary: DFT and H
12/16/1994:  Spin contamination & AM1 "ROHF" versus UHF
03/11/1996:  Law of conservation of difficulty: violations.


Raw Message Text