# ESP-fitted charges and dipole contraints (cont...relatively long)

``` Thanks for the several comments I've received regarding the use of the
dipole moment as a constraint when fitting the esp to atom-centered
point-charges, but I'm not yet convinced that there is anything
"wrong"
with DM-constrained esp-fits.
As several respondents have pointed out, the dipole moment depends on your
choice of coordinate system, but once you've made that choice for the
semiemp. (or ab initio) calc of the esp, you can define a dipole moment in
this coord. system, so why not constrain the point charges (which are
centered on atoms with coords in the same system) to reproduce that dipole
moment?
A different choice of coord system would give a different dipole moment,
but then the atoms would have different coords as well. It's not obvious to
me that fitting the new esp, constrained to reproduce the new dipole
moment, wouldn't produce the same set of point charges.  In fact, a
more-mathematically inclined colleague here suggests that the derived set
of point charges is probably independent of coordinate system ("because the
matrix you get for the least-squares fitting is invertible"??)
The use of point charges in many in-house and (all?) commercial mol.
modeling tools is widespread and has obvious appeal, but also important
limitations.  I guess a valid question to ask is why would one want to use
a calculated dipole moment in the point-charge derivation? There seems to
me to be two main reasons:
(i) because you have an experimental observable with which to verify your
calcs. (but only if the molecule is neutral), and
(ii) because it's not obvious that the set of point-charges you get by
esp-fitting is unique, and any extra constraint is likely to reduce the
number of possible sets.  This argument could be used to constrain with
higher order multipoles I guess.
As a matter of interest, when the check on dipole moment constraint for
charged systems is disabled in the Mopac6 code, the following set of
AM1-esp derived charges is available for comparison (GNORM=0.01, PRECISE
keywords).
The ESP and point-charge calc. x, y, z-dipole moment components are also shown.
Mulliken           ESP                  ESP
no DM contraint      with DM constraint
NH4+              N  -0.094          N  -0.600            N  -0.600
DHf=150.581 kcal  HN +0.274          HN +0.400            HN +0.400
rrms 0.0010          rrms 0.0010
D=0.00,0.00,0.00   D=0.00,0.00,0.00     D=0.00,0.00,0.00
CH3.NH3+          N  -0.059          N  -0.184            N -0.716
DHf=148.748 kcal  HN +0.262          HN +0.312            HN +0.54
C  -0.204          C  -0.329            C  +0.19
HC +0.159          HC +0.192            HC -0.034
rrms 0.0080          rrms 0.1293
D=0.81,1.12,1.86   D=-0.42,-0.58,-0.96  D=0.80,1.12,1.86
(CH3)2.NH2+       N  -0.028          N  +0.067            N  -0.060
DHf=149.215 kcal  HN +0.254          HN +0.287            HN +0.400
C  -0.200          C  -0.489            C  -0.295
HC +0.153          HC +0.211,+0.229     HC +0.097,+0.230
rrms 0.0076          rrms 0.1043
D=0.91,1.25,0.00   D=-0.73,-1.00,0.00   D=0.91,1.25,0.00
(CH3)3.NH+        N  +0.004          N  +0.287            N  +0.392
DHf=151.997 kcal  HN +0.250          HN +0.292            HN +0.329
C  -0.196          C  -0.587,-0.60      C  -0.56,-0.63
HC +0.148          HC +0.237,+0.25      HC +0.18,+0.25
rrms 0.0045          rrms 0.0636
D=0.85,0.00,0.00   D=-0.94,0.00,0.00    D=0.85,0.00,0.00
(CH3)4N+          N  +0.030          N  +0.509            N  +0.509
DHf=157.156 kcal  C  -0.187          C  -0.62             C  -0.62
HC +0.143          HC +0.246            HC +0.246
rrms 0.0042          rrms 0.0042
D=0.00,0.00,0.00   D=0.00,0.00,0.00     D=0.00,0.00,0.00
For those of you who are still here (it took longer to type this thing than
(1) most obvious - esp-fits are numerically more precise (except for the
tetrahedral examples) if DM constraint is not used.  Whether the fits are
"better" in a chemical sense is a moot point.
(2) Unconstrained esp-derived atom-centered charges follow the poor old
Mulliken charges in the organic chemist's spirit of the methyl group being
an electron pusher.  Magnitudes are much larger though.
(3) Intriguingly, DM-constrained esp-derived point charges also follow this
trend - with the glaring exception of Me2NH2+ (N is "too negative" and
C is
"too positive").
(4) Does anyone else think it suspicious that every non-zero
point-charge-derived dipole-moment-component in the Unconstrained fits, is
the *opposite* sign to the corresponding esp-derived components?? Could
this be due to a change of coordinate system in the bowels of Mopac, or is
this just a coincidence?
The dipole-constrained Me2NH2+ fit is "poor", but all things are
relative,
as the corresponding table for the non-protonated, neutral amines shows:
Mulliken            ESP                 ESP
no DM contraint     with DM constraint
NH3                N  -0.396           N  -0.807           N  -1.130
DHf=-7.283 kcal    HN +0.132           HN +0.269           HN +0.378
rrms 0.0594         rrms 0.4098
D=0.63,0.88,-1.50   D=0.44,0.63,-1.07   D=0.63,0.88,-1.50
CH3.NH2            N  -0.352           N  -0.708           N  -0.835
DHf=-7.381 kcal    HN +0.143           HN +0.280           HN +0.323
C  -0.129           C  +0.018           C  +0.031
HC +0.03,+0.08      HC +0.00,+0.62      HC +0.05
rrms 0.205          rrms 0.4525
D=0.46,-0.73,-1.22  D=0.26,-0.48,-0.79  D=0.46,-0.73,-1.22
(CH3)2.NH          N  -0.308           N  -0.448           N  -0.518
DHf=-5.626 kcal    HN +0.153           HN +0.292           HN +0.316
C  -0.125           C  -0.262           C  -0.243
HC +0.04,+0.08      HC +0.09 to +0.14   HC +0.10 to +0.13
rrms 0.2403         rrms 0.4536
D=0.35,-0.65,-0.99  D=0.20,-0.39,-0.58  D=0.35,-0.65,-0.99
(CH3)3.N           N  -0.267           N  -0.098           N  -0.136
DHf=-1.710 kcal    C  -0.118           C  -0.419,-0.455    C  -0.38,-0.45
HC +0.04,+0.08      HC +0.14 to +0.17   HC +0.14 to +0.17
rrms 0.2054         rrms 0.4095
D=0.28,-0.50,-0.85  D=0.15,-0.27,-0.46  D=0.28,-0.50,-0.85
In this table, all the fits (constrained or not) are "very poor", but
I
suspect that many people wanting point charges would use these anyway! (so
why not use dipole-contrained charges for charged species in the first
table!!)
Some food for thought...
----
Alan Arnold                          |  e-mail: apa { *at * } pop.cc.adfa.oz.au
Chem. Department,University College  |  voice : +61 6 268 8080
Australian Defence Force Academy     |  fax   : +61 6 268 8002
CANBERRA  ACT 2601 Australia         |
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