Partial Atomic Charge in GAMESS
Unfortunately GAMESS does not support any other than the named population analyses. 

You will need to use a different program. For that matter I suggest MultiWFN, which comes with a variety of different population analyses and is still in active development. From the website:


  Population analysis. Hirshfeld, VDD, Mulliken, Löwdin, Modified MPA (including three methods: SCPA, Stout &amp; Politzer, Bickelhaupt), Becke, ADCH (Atomic dipole moment corrected Hirshfeld), CHELPG, Merz-Kollmann and AIM methods are supported.


The currently developed version MultiWFN 3.4 should be able to even read GAMESS output directly as stated in the update log:


  GAMESS-US output file now can be used as input file (not comprehensively tested, currently only single point task at HF/DFT level is formally supported). The suffix of output file should be changed to .gms so that Multiwfn can properly recognize it


As a workaround for older versions, and a reliable way to import this data, you can export a .wfn file with GAMESS. I will give a brief summary for this, since I am still using MultiWFN 3.3.8. From the corresponding manual:


  For example, the wavefunction represented by GTFs is enough for Hirshfeld population, so you can use .fch/.molden/.31~.40/.wfn/.wfx file as input, but .pdb, .xyz, .chg, .cub and .grd files do not carry any wavefunction information hence cannot be used.


As I have previously stated, .wfn files are technically outdated, especially when it comes to larger basis sets. However, for the time being, they are our only option to make it work.

I am using GAMESS version % DEC 2014 (R1) and the following input to demonstrate the procedure. I am using a Linux environment, so you might have to adjust this guide accordingly.


 $CONTRL SCFTYP=RHF            ! Restricted calculation.
         RUNTYP=OPTIMIZE       ! Geometry optimisation.
         COORD=ZMT             ! Z-matix specifies coordinates.
         AIMPAC=.TRUE.         ! Requests wfn file to be written.
         $END
 $BASIS  GBASIS=STO NGAUSS=3   ! STO-3G minimal basis
         $END
 $GUESS  GUESS=HUCKEL          ! Start with Hückel MO.
         $END
! Following group contains molecule specification.
! Blank lines are important.
 $DATA
Water
Cnv  2

O
H  1 rOH
H  1 rOH  2 aHOH

rOH=1.09
aHOH=110.0
 $END



Note that the indentations before the keywords are important. ! indicates a comment. Any additional output will be written to the punch file. This is dependent on how you set up GAMESS, but it normally is located in ~/scr/&lt;rootfilename&gt;.dat.

To extract the .wfn file you can use the following little script, or extract it manually from the .dat file.


#Script to extract wfn file from GAMESS dat (punch) file
#! /bin/bash

[ ! -z $1 ] &amp;&amp; inputfile="$1" || exit 1
outputfile="${inputfile%.*}.wfn"

startpattern="----- TOP OF INPUT FILE FOR BADER'S AIMPAC PROGRAM -----"
endpattern="----- END OF INPUT FILE FOR BADER'S AIMPAC PROGRAM -----"

sed "/$startpattern/,/$endpattern/!d;//d" "$inputfile" &gt; "$outputfile"


This should give you the following .wfn file for analysis:


Water
GAUSSIAN              5 MOL ORBITALS     21 PRIMITIVES        3 NUCLEI
  O    1    (CENTRE  1)   0.00000000  0.00000000 -0.14560943  CHARGE =  8.0
  H    2    (CENTRE  2)  -1.43257773  0.00000000  1.05592484  CHARGE =  1.0
  H    3    (CENTRE  3)   1.43257773  0.00000000  1.05592484  CHARGE =  1.0
CENTRE ASSIGNMENTS    1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  3  3
CENTRE ASSIGNMENTS    3
TYPE ASSIGNMENTS      1  1  1  1  1  1  2  2  2  3  3  3  4  4  4  1  1  1  1  1
TYPE ASSIGNMENTS      1
EXPONENTS  1.3070932E+02 2.3808866E+01 6.4436083E+00 5.0331513E+00 1.1695961E+00
EXPONENTS  3.8038896E-01 5.0331513E+00 1.1695961E+00 3.8038896E-01 5.0331513E+00
EXPONENTS  1.1695961E+00 3.8038896E-01 5.0331513E+00 1.1695961E+00 3.8038896E-01
EXPONENTS  3.4252509E+00 6.2391373E-01 1.6885540E-01 3.4252509E+00 6.2391373E-01
EXPONENTS  1.6885540E-01
MO  1                     OCC NO =   2.00000000 ORB. ENERGY = -20.25158070
  4.22735195E+00  4.08851077E+00  1.27421022E+00 -6.18804850E-03  8.27701479E-03
  6.24678653E-03  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  6.97684832E-03  4.38722945E-03  6.95010854E-04
 -1.54630881E-03 -1.49552256E-03 -4.66089059E-04 -1.54630881E-03 -1.49552256E-03
 -4.66089059E-04
MO  2                     OCC NO =   2.00000000 ORB. ENERGY =  -1.25754111
 -9.93961353E-01 -9.61316148E-01 -2.99600254E-01 -2.02173727E-01  2.70423693E-01
  2.04092795E-01  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  2.05800516E-01  1.29412887E-01  2.05011755E-02
  4.30889918E-02  4.16737970E-02  1.29879022E-02  4.30889918E-02  4.16737970E-02
  1.29879022E-02
MO  3                     OCC NO =   2.00000000 ORB. ENERGY =  -0.59384261
  0.00000000E+00  0.00000000E+00  0.00000000E+00 -0.00000000E+00  0.00000000E+00
  0.00000000E+00  1.02654522E+00  6.45519180E-01  1.02261083E-01  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00
 -1.24405583E-01 -1.20319664E-01 -3.74983838E-02  1.24405583E-01  1.20319664E-01
  3.74983838E-02
MO  4                     OCC NO =   2.00000000 ORB. ENERGY =  -0.45973131
 -4.42352599E-01 -4.27824176E-01 -1.33334109E-01 -1.28843153E-01  1.72338126E-01
  1.30066155E-01  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00 -1.26642108E+00 -7.96359559E-01 -1.26156734E-01
 -8.17262213E-02 -7.90420432E-02 -2.46339524E-02 -8.17262213E-02 -7.90420432E-02
 -2.46339524E-02
MO  5                     OCC NO =   2.00000000 ORB. ENERGY =  -0.39261686
  0.00000000E+00  0.00000000E+00  0.00000000E+00 -0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00  1.67545020E+00
  1.05356804E+00  1.66902879E-01  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00
END DATA
RHF      ENERGY =      -74.9659012162   VIRIAL(-V/T)  =   2.00600297


You can now use this file and load it with MultiWFN. After the start-up process you should find the key values printed to the screen like this (I abridged it a little bit):


 Multiwfn -- A Multifunctional Wavefunction Analyzer (for Linux)
 Version 3.3.8, release date: 2015-Dec-1
[...]
 System energy:     -74.965901216200 Hartree,   Virial ratio:  2.00600297
 Total/Alpha/Beta electrons:     10.0000      5.0000      5.0000
 Net charge:     0.00000    Expected multiplicity:    1
 The number of orbitals:     5,  Atoms:      3,  GTFs:     21
 This is restricted close-shell single-determinant wavefunction
 Title line of this file: Water
 Formula: H2 O1
 Molecule weight:        18.01528

 Loaded water-sto3g.wfn successfully!

                    ------------ Main function menu ------------
[...]
 7 Population analysis
[...]


You may now choose 7 and enter the following menu:


                 ============== Population analysis ==============
 0 Return
 1 Hirshfeld population
 2 Voronoi deformation density (VDD) population
 10 Becke atomic charge with atomic dipole moment correction
 11 Atomic dipole corrected Hirshfeld population (ADCH)
 12 CHELPG ESP fitting charge
 13 Merz-Kollmann (MK) ESP fitting charge
 14 AIM charge


Follow the guidance of the manual and the on-screen instructions to produce the required charges. For comparison here are the computed Hirshfeld charges, written to water-sto3g.chg with the following command sequence 7; 1; 1; y.


  O     0.000000    0.000000   -0.077053   -0.296017
  H    -0.758088    0.000000    0.558771    0.147959
  H     0.758088    0.000000    0.558771    0.147959


The element identifier is followed by the Cartesian coordinates, which are followed by the charges.

In principle all other implemented charges are equally as easy to compute. Keep in mind, that basin based charges (e.g. AIM) need more computing power and depend heavily on molecule and basis set size.

Apart from this procedure, you can obtain natural charges with the NBO6 program, which conveniently interfaces with GAMESS. Unfortunately you have to buy it.