Contents
Navigation:
ISA and GDMA Multipoles
Obtaining molecular multipole moments using CamCASP and GDMA.
To learn how to reduce the multipole moments created using methods described here see the guide on Mulfit.
References
A. J. Misquitta, A. J. Stone and F. Fazeli, 'Distributed multipoles from a robust basis-space implementation of the iterated stockholder atoms procedure', J. Comp. Theor. Chem., 10, 5405-5418 (2014).
A. J. Stone, 'Distributed Multipole Analysis: Stability for large basis sets', J. Comp. Theor. Chem., 1, 1128-1132 (2005).
ISA multipoles
The ISA (iterative stockholder atoms) approach put forward by Lillestolen and Wheatley has proved to be a fantastic way for calculating all sorts of molecular properties that rely on a molecular partitioning in to atom-like domains. The ISA domains are formally very similar to those from Hirshfeld partitioning, except that the reference atoms (taken to be the neutral, free-atoms in the Hirshfeld approach) are obtained iteratively in the ISA. This is important as the iterative procedure allows the pro-atoms to respond to the molecular environment, leading to a significantly better agreement with chemical and physical ideas, and, for us perhaps even more importantly, to significantly superior convergence for the distributed multipoles calculated using this method.
If you'd like to read more on this, see this paper that we have published in JCTC 2014.
Here we will look into how CamCASP is used to calculate BS-ISA (the 'BS' = Basis-Space) moments. This calculation is not a standard CamCASP calculation, but it is fairly easy to perform, nevertheless.
Cluster input file for CamCASP 5.9 and older
Here's an example Cluster input file for an ISA calculation:
Title CH4 : PBE0/AC Global Units Bohr Degrees Overwrite Yes End Molecule CH4 I.P. 0.4634 a.u. ! Vibrationally averaged geom. C 6.0 0.0000000000 0.0000000000 0.0000000000 Type C H1 1.0 0.0000000000 2.0770357780 0.0000000000 Type H H2 1.0 1.6958926074 -0.6923452530 0.9791240615 Type H H3 1.0 -1.6958926074 -0.6923452530 0.9791240615 Type H H4 1.0 0.0000000000 -0.6923452530 -1.9582481041 Type H End Run-Type Properties Molecule CH4 ! Basis aQZ Aux-basis aQZ Spherical ISA-Aux set2 ! File-prefix CH4_aQZ ! Functional PBE0 AC CS00 Kernel ALDA+CHF SCFcode NWChem ! #include ../isa-display ! End Finish
The important changes are
The Basis sets: The main basis is defined normally, but the auxiliary basis is defined to use spherical GTOs. Additionally, the ISA-Aux set2 command causes the s-functions in the auxiliary basis to be replaced by a special set designed for the ISA. See the CamCASP User's Guide for more details.
The commands needed to perform an ISA calculation are included in the file isa-display. The #include statement reads them in. A copy of the isa-display file can be found here.
Cluster input file for CamCASP 6.0.x (dev)
ISA commands have changed in CamCASP 6.0.x. At the time of writing this the code has not been released. If you do not have the code, use the example shown above.
Title CH4 properties PBE0/AC
Global
Units Bohr Degrees
Overwrite Yes
End
Molecule CH4
I.P. 0.4634 a.u.
! Vibrationally averaged geom.
C 6.0 0.0000000000 0.0000000000 0.0000000000 Type C
H1 1.0 0.0000000000 2.0770357780 0.0000000000 Type H
H2 1.0 1.6958926074 -0.6923452530 0.9791240615 Type H
H3 1.0 -1.6958926074 -0.6923452530 0.9791240615 Type H
H4 1.0 0.0000000000 -0.6923452530 -1.9582481041 Type H
End
! Show CH4 in PDB format
Run-Type
Properties
Molecule CH4
! In this example the AUX basis is aVTZ+ISAset2 and ATOMAUX is aVQZ+ISAset
Main-Basis aVTZ Type MC
Aux-Basis aVTZ Type MC Cartesian Use-ISA-Basis ( this basis *could* be Spherical )
AtomAux-Basis aVQZ Type MC Spherical Use-ISA-Basis ( this *must* be Spherical )
ISA-Basis set2 Min-S-exp-H = 0.2
( convergence tends to be better with this setting )
Func PBE0 ( other functionals possible, but this is probably the best )
AC CS00 ( [TH | LINEAR | GRAC] [CS00 | MULTIPOLE | LB94] : CS00 with NWChem)
Kernel ALDA+CHF ( not needed for an ISA calculation )
SCF-code NWChem ( DALTON2015, NWCHEM, etc )
! MO-FILE <MOL.movecs> Format ASCII ( Set this to the acutal MO file if available )
File-Prefix CH4 ( change this to something reasonable )
#METHOD isa-A ( this will use the file isa-A from the methods/ directory )
End
FinishSome points:
- We are using four basis sets:
Main-Basis: This is the basis set needed for the molecular orbitals.
Aux-Basis: This is the basis needed for the density-fitting.
AtomAux-Basis: The basis set used for the ISA expansions.
ISA-Basis: This is the s-function part of the Atom-Aux basis that is used for the ISA shape-function expansions.
Run the job
Run the job as usual
runcamcasp.py -q bg --clt CH4-ISA.clt CH4
Outputs
The CamCASP output will be rather long as data for all the ISA iterations will be printed out. The output file will contain four sets of multipole moments:
- Moments calculated based on a density-fitting (DF) partitioning. Do not use these.
- ISA multipole moments. Use these.
- GDMA switch=0 moments (1985 algorithm)
- GDMA switch=4 moments (2005 algorithm)
The first two are included in the output file, but only the last two are actually written out to special *.mom files.
Here are the ISA moments taken from the CamCASP output:
CamCASP ISA moments from output
Begin Multipoles
DF Type ISA
Rank 4
End
Finished reading in the DIST_MOM block
Now for the calculations...
Total moments are computed w.r.t. the origin:
Origin : ( 0.0000, 0.0000, 0.0000) BOHR
! Multipole moments for CH4
! Based on DF-type : ISA
C 0.00000000 0.00000000 0.00000000 Type C Rank 4
-0.408856
-0.000202 -0.000002 -0.000377
0.000484 0.000001 -0.000088 0.000685 -0.000001
0.104779 0.000001 0.088809 -0.082229 -0.000009
0.000004 0.116277
0.185492 -0.000001 0.541383 0.277448 0.000000
0.000000 -0.614966 0.362808 -0.000001
H1 0.00000000 2.07703578 0.00000000 Type H Rank 4
0.102417
-0.000061 0.000000 0.032680
0.008683 0.000000 0.000019 0.015003 0.000000
0.053924 0.000000 -0.106577 -0.041788 0.000000
0.000000 -0.137930
-0.082778 0.000000 -0.007186 -0.124064 0.000000
0.000000 0.008499 -0.164256 0.000000
H2 1.69589261 -0.69234525 0.97912406 Type H Rank 4
0.102242
0.015402 0.026780 -0.010907
0.002756 -0.011373 0.004695 -0.008331 0.008084
-0.057979 0.014050 0.041069 0.085522 -0.124501
0.054163 -0.064681
0.050136 0.095833 -0.046389 -0.041190 0.036058
-0.058609 0.143130 -0.006748 0.097550
H3 -1.69589261 -0.69234525 0.97912406 Type H Rank 4
0.102240
0.015403 -0.026782 -0.010908
0.002755 0.011372 0.004695 -0.008330 -0.008083
-0.057979 -0.014050 0.041069 0.085522 0.124501
-0.054163 -0.064681
0.050135 -0.095833 -0.046389 -0.041190 -0.036058
0.058608 0.143130 -0.006748 -0.097549
H4 0.00000000 -0.69234525 -1.95824810 Type H Rank 4
0.101957
-0.031109 0.000000 -0.011077
-0.013928 0.000000 -0.009349 0.001323 0.000000
-0.115731 0.000000 -0.129307 0.008402 0.000000
0.000000 0.067636
-0.110065 0.000000 -0.180647 0.066106 0.000000
0.000000 0.024363 -0.007363 0.000000
Total molecular moments relative to origin (0,0,0):
0.000000
-0.000013 0.000000 -0.000027
0.000028 -0.000001 0.000028 0.000129 0.000000
-2.013708 0.000000 -1.743219 1.559151 0.000004
-0.000002 -2.248759
1.922123 0.000025 5.736316 2.865968 0.000010
-0.000015 -6.497700 3.793214 0.000026
End of distributed moment moduleThe output is structured the same way as a *.mom file:
ATOM X Y Z Type <ATOM-TYPE> Rank 4 Q00 Q10 Q11c Q11s Q20 Q21c Q21s Q22c Q22s Q30 Q31c Q31s Q32c Q32s Q33c Q33s Q40 ...etc
Coordinates will normally be in Bohr and moments in Atomic Units.
GDMA multipoles
Best to work with an example. Here's the Cluster command file for a GDMA multipole calculation for HCN:
Title HCN molecular properties Global Units Bohr Degrees kJ/mol End Molecule HCN I.P. 13.60 eV Units Angstrom H 1.0000 0.00000000 0.00000000 -1.52104563 C 6.0000 0.00000000 0.00000000 -0.44585114 N 7.0000 0.00000000 0.00000000 0.70975391 End Run-Type Molecule HCN File-Prefix HCN_aTZ Properties DFTCODE DALTON2006 Functional PBE0 Basis aTZ #include ../dma-only Memory 4 GB End Finish
This calculation uses a file dma-only that contains commands for the DMA part of the calculation only. By default CamCASP calculates all sorts of molecular properties (polarizabilities, etc), so we suppress all of that using specific commands contained in dma-only:
CamCASP-commands
BEGIN GRID
Molecule A
Angular 400
Radial 60
END
Begin GDMA
Bohr
! Original DMA
Multipoles
Switch 0.0
Limit 5
Punch DMA_sw0_L5.mom
Start
! Revised DMA
Multipoles
Switch 4.0
Limit 5
Punch DMA_sw4_L5.mom
Start
End
End-CamCASP-commandsThis job can be run using the command:
$ runcamcasp.py --clt HCN.clt HCN_aTZ
To see all the options for runcamcasp.py use runcamcasp.py --help.
After a while you will see the outputs in directory HCN_aTZ. The multipole moments should be in HCN_aTZ/OUT/. If all goes well there will be two multipole moment files:
DMA sw0 : this is the original 1985 DMA algorithm
! HCN
! Basis: aug-cc-pVTZ
H -2.8743594600 Rank 5
0.2677730515
-0.1729485948
-0.0501043708
0.0038900503
-0.0008614651
-0.0202123754
C -0.8425364900 Rank 5
0.3152881314
0.5041632355
-0.5163634872
1.4379616107
-0.7473595714
2.0769049520
N 1.3412404100 Rank 5
-0.5830611829
0.2832706539
-0.3745325169
-1.2378166312
3.4243296572
-6.7990645408and the moments from the newer, 2005, DMA algorithm will be in
! HCN
! Basis: aug-cc-pVTZ
H 0.0000000000 0.0000000000 -2.8743594600 Rank 5
0.1667727889
0.0519443208 0.0000000000 -0.0000000000
0.2213749964 0.0000000000 -0.0000000000 0.0000000000 0.0000000000
-0.1147212899 -0.0000000000 0.0000000000 -0.0000000000 -0.0000000000
-0.0000000000 -0.0000000000
-0.3871377737 -0.0000000000 0.0000000000 0.0000000000 -0.0000000000
0.0000000000 0.0000000000 0.0000045954 0.0000000000
0.7424891191 0.0000000000 -0.0000000000 0.0000000000 0.0000000000
0.0000000000 -0.0000000000 -0.0000004371 -0.0000000000 0.0000000000
-0.0000000000
C 0.0000000000 0.0000000000 -0.8425364900 Rank 5
0.0352352207
0.0043919876 0.0000000000 -0.0000000000
1.0872641596 0.0000000000 -0.0000000000 -0.0000000000 0.0000000000
0.0721604899 0.0000000000 0.0000000000 0.0000000000 0.0000000000
-0.0000000000 -0.0000000000
-0.1138010146 0.0000000000 0.0000000000 0.0000000000 0.0000000000
0.0000000000 0.0000000000 0.0001190378 0.0000000000
-1.0293188776 0.0000000000 -0.0000000000 -0.0000000000 0.0000000000
-0.0000000000 0.0000000000 -0.0000404776 -0.0000000000 0.0000000000
0.0000000000
N 0.0000000000 0.0000000000 1.3412404100 Rank 5
-0.2020069851
-0.4792048831 -0.0000000000 -0.0000000000
0.5941594696 -0.0000000000 0.0000000000 0.0000000000 -0.0000000000
-1.1372026726 0.0000000000 0.0000000000 0.0000000000 -0.0000000000
-0.0000000000 -0.0000000000
-0.7446501643 0.0000000000 -0.0000000000 0.0000000000 0.0000000000
0.0000000000 -0.0000000000 0.0000409239 -0.0000000000
4.2454184167 -0.0000000000 -0.0000000000 -0.0000000000 0.0000000000
0.0000000000 -0.0000000000 -0.0001231820 0.0000000000 0.0000000000
-0.0000000000We will normally use the latter as they are usually more appropriate when large, diffuse basis sets are used.
Using MULFIT to transform multipoles
Instruction for this can be found on a separate page.
ISA with Cartesian auxiliary basis set
Warning
This calculation can only be performed using CamCASP 6.0.010 and later. At present, this is a developer's version only.
The ISA as described above is restricted to auxiliary basis sets that use spherical GTOs. This leads to a loss in accuracy. Here we explain how Cartesian GTOs may be used in the auxiliary basis set.
ISA algorithm : A
The ISA A-algorithm can be used directly with the mixed, Cartesian/Spherical basis set. To do this you need to define three basis sets for the system:
Basis Main: The main basis (no changes here)
Basis Aux: The auxiliary basis in Cartesian form as in a normal properties calculation.
Basis Atom-Aux: The atomic basis set that will be used for the ISA. This must use spherical GTOs.
The rest of the commands are identical to a standard ISA calculation. The code automatically used the Atom-Aux basis for the ISA expansions and the Aux basis for the density and transition-density expansions. Here is an example of how this works:
Example : ISA A with Cartesian GTOs in Aux : H$_2$O
MOLECULE H2OA at 0.0 0.0 0.0
Charge 0
Echo No
Hessian format SAPT2006
MO-file H2O_aQZ-A-asc.movecs format ASCII-2
IP 0.463800 a.u.
Basis Main
Spherical
Units Bohr
Format GAMESS
O 8.0 0.00000000 0.00000000 0.00000000 TYPE O
#include-camcasp basis/gamess_us/aug-cc-pVQZ/O
---
H1 1.0 -1.45365196 0.00000000 -1.12168732 TYPE H
#include-camcasp basis/gamess_us/aug-cc-pVQZ/H
---
H2 1.0 1.45365196 0.00000000 -1.12168732 TYPE H
#include-camcasp basis/gamess_us/aug-cc-pVQZ/H
---
End
Basis Aux
Cartesian
Units Bohr
Format TURBOMOLE
O 8.0 0.00000000 0.00000000 0.00000000 TYPE O
Limit G
#include-camcasp basis/auxiliary/aug-cc-pVQZ/O
---
H1 1.0 -1.45365196 0.00000000 -1.12168732 TYPE H
Limit G
#include-camcasp basis/auxiliary/aug-cc-pVQZ/H
---
H2 1.0 1.45365196 0.00000000 -1.12168732 TYPE H
Limit G
#include-camcasp basis/auxiliary/aug-cc-pVQZ/H
---
End
Basis Atom-Aux
Spherical
Units Bohr
Format TURBOMOLE
O 8.0 0.00000000 0.00000000 0.00000000 TYPE O
Limit G
#include-camcasp basis/auxiliary/ISA/set2/O
Symmetry Exclude = S
#include-camcasp basis/auxiliary/aug-cc-pVQZ/O
---
H1 1.0 -1.45365196 0.00000000 -1.12168732 TYPE H
Limit Min-S-exp 0.2
Limit G
#include-camcasp basis/auxiliary/ISA/set2/H
Symmetry Exclude = S
#include-camcasp basis/auxiliary/aug-cc-pVQZ/H
---
H2 1.0 1.45365196 0.00000000 -1.12168732 TYPE H
Limit Min-S-exp 0.2
Limit G
#include-camcasp basis/auxiliary/ISA/set2/H
Symmetry Exclude = S
#include-camcasp basis/auxiliary/aug-cc-pVQZ/H
---
End
ENDComments:
The //Limit// commands in the Atom-Aux definition are optional. I used them to prevent the hydrogen atom shape-functions from going negative.
Although the Aux and Atom-Aux basis sets place atoms on the same sites, this need not be the case.
To get the best mutlipole moments combine this calculation with an ISA-GRID multipole moment calculation:
Begin Multipoles Molecule H2OA DF Type ISA-GRID Rank 4 End
Important
Although the ISA A-algorithm typically leads to charge conservation issues of magnitude something like $10^{-3}e$, when the ISA-GRID partitioning algorithm is used, these vanish and charge is conserved.
Here are the multipole moments obtained using this method:
! Multipole moments for H2OA
! Based on DF-type : ISA-GRID
O 0.00000000 0.00000000 0.00000000 Type O Rank 4
-0.841982
0.191034 -0.000042 -0.000000
0.003255 0.000050 -0.000000 0.426891 0.000000
-0.107414 0.000003 -0.000000 0.074719 0.000000
0.000553 0.000000
-0.295681 0.001011 -0.000000 0.288788 0.000000
-0.002832 0.000000 -0.071186 -0.000000
H1 -1.45365196 0.00000000 -1.12168732 Type H Rank 4
0.420938
0.006258 -0.027575 -0.000000
0.002940 0.005508 0.000000 0.031273 0.000000
0.008032 -0.016349 0.000000 -0.021900 0.000000
-0.009186 0.000000
-0.015407 -0.002128 0.000000 0.026073 0.000000
0.002988 -0.000000 -0.026605 -0.000000
H2 1.45365196 0.00000000 -1.12168732 Type H Rank 4
... related to H1 by symm...
Total molecular moments relative to origin (0,0,0):
-0.000064
-0.740846 -0.000000 -0.000000
0.070726 0.000000 -0.000000 2.168801 0.000000
1.998676 0.000000 -0.000000 -4.322235 -0.000000
0.000000 0.000000
-4.732613 0.000000 -0.000000 6.354305 0.000000
-0.000000 0.000000 3.932732 -0.000000
ISA algorithm : A+DF
This algorithm cannot be used directly because we cannot combine the ISA matrices and the DF matrices: one will use spherical GTOs and the other Cartesian GTOs. Instead we can obtain this solution as follows.
There are a few steps needed for such a calculation:
- First perform an A+DF ISA calculation (A+DF generally leads to the highest accuracy) using the standard ISA route with spherical GTOs in the auxiliary basis. One nice feature of A+DF is that we can impose charge conservation. The only purpose of this step is to obtain converged ISA shape-functions.
- Next, we use these converged shape-functions in an A-type ISA calculation (no DF here); this time with a Cartesian auxiliary basis set, and with spherical GTOs in the Atom-Aux basis. This is a RESTART of the ISA, so the shape-functions will not change.
- The multipole moments/polarizabilities can now be calculated using the code.
Important
Caveats:
- The ISA shape-functions will not be fully consistent with the density calculated using Cartesian GTOs.
Example: H$_2$O
Here is an example of the above. First, make sure that the ISA solution file is present. This will have the suffix //*.ISA//.
First the partial CamCASP input file for an A+DF ISA calculation. There are only two basis sets defined for this job:
MOLECULE H2OA at 0.0 0.0 0.0
Charge 0
Echo No
Hessian format SAPT2006
MO-file H2O_aQZ-A-asc.movecs format ASCII-2
IP 0.463800 a.u.
Basis Main
Spherical
Units Bohr
Format GAMESS
O 8.0 0.00000000 0.00000000 0.00000000 TYPE O
#include-camcasp basis/gamess_us/aug-cc-pVQZ/O
---
H1 1.0 -1.45365196 0.00000000 -1.12168732 TYPE H
#include-camcasp basis/gamess_us/aug-cc-pVQZ/H
---
H2 1.0 1.45365196 0.00000000 -1.12168732 TYPE H
#include-camcasp basis/gamess_us/aug-cc-pVQZ/H
---
End
Basis Aux
Spherical
Units Bohr
Format TURBOMOLE
O 8.0 0.00000000 0.00000000 0.00000000 TYPE O
Limit G
#include-camcasp basis/auxiliary/ISA/set2/O
Symmetry Exclude = S
#include-camcasp basis/auxiliary/aug-cc-pVQZ/O
---
H1 1.0 -1.45365196 0.00000000 -1.12168732 TYPE H
Limit Min-S-exp 0.2
Limit G
#include-camcasp basis/auxiliary/ISA/set2/H
Symmetry Exclude = S
#include-camcasp basis/auxiliary/aug-cc-pVQZ/H
---
H2 1.0 1.45365196 0.00000000 -1.12168732 TYPE H
Limit Min-S-exp 0.2
Limit G
#include-camcasp basis/auxiliary/ISA/set2/H
Symmetry Exclude = S
#include-camcasp basis/auxiliary/aug-cc-pVQZ/H
---
End
END
...
...
Begin Stockholder
Molecule H2OA
DF = Drho-C
W-INIT = ONE-GTO ALPHA0 = 1.0
ISA-Algorithm A+DF Zeta = 0.9
DF-PARAMETERS Lambda = 1000.0
Solver LU
Convergence
Convergence-Type W
EPS-Norm = 1.0e-07
EPS-Q = 1.0e-4
Max-Iter = 60
W-Damping = 0.0
W-Mix-Fraction = 0.0 Skip-Iterations = 20
! W-Eps = 0.17 S-Block-Only Couple Switch-On-Eps-Norm = 1.0e-04
W-Eps = 0.17 S-Block-Only Couple Switch-On-Eps-Norm = 0.0
Positive-W Lambda = 0.0001 for Max-Alpha = 2.0 AUTO
Tail-Iterations = 10
End
W-TAILS
Activate at Eps-Norm = 1e-12 or Max-Iter = 100
Func = 1
R1-Multiplier = 2.0
R2-Multiplier = 3.0
Fit-Type = 3
W-Tests
END
End
Begin Multipoles
Molecule H2OA
DF Type ISA-GRID
Rank 4
EndHere are the multipole moment you get for this job:
! Multipole moments for H2OA
! Based on DF-type : ISA-GRID
O 0.00000000 0.00000000 0.00000000 Type O Rank 4
-0.840926
0.191954 -0.000000 -0.000000
0.007819 0.000000 0.000000 0.423913 0.000000
-0.087368 -0.000000 0.000000 0.208861 -0.000000
-0.000000 0.000000
-0.235341 -0.000000 0.000000 0.164563 0.000000
0.000000 -0.000000 -0.090598 -0.000000
H1 -1.45365196 0.00000000 -1.12168732 Type H Rank 4
0.420407
0.005397 -0.029959 -0.000000
0.003387 0.005937 0.000000 0.036881 0.000000
0.007698 -0.007759 0.000000 -0.012025 0.000000
-0.015101 0.000000
-0.006338 0.002302 0.000000 -0.011913 -0.000000
-0.026974 -0.000000 -0.030921 -0.000000
H2 1.45365196 0.00000000 -1.12168732 Type H Rank 4
...same as H1 but rotated...
Total molecular moments relative to origin (0,0,0):
-0.000113
-0.740382 0.000000 -0.000000
0.072814 0.000000 0.000000 2.187225 0.000000
2.037522 -0.000000 -0.000000 -4.232304 -0.000000
0.000000 -0.000000
-4.619601 0.000000 0.000000 6.071613 0.000000
-0.000000 0.000000 4.131253 0.000000Now for the CamCASP A-type ISA calculation that uses the solution of the above in a restart:
H2O_A+DF_3basis.cks (partial listing)
MOLECULE H2OA...
...defined as shown in section on ISA A algorithm. Three basis sets used here.
END
...
...
Begin Stockholder
Molecule H2OA
DF = Drho-C
W-INIT = ONE-GTO ALPHA0 = 1.0
ISA-Algorithm A
DF-PARAMETERS Lambda = 0.0
Solver LU
Convergence
Convergence-Type W
EPS-Norm = 1.0e-07
EPS-Q = 1.0e-4
Max-Iter = 60
W-Damping = 0.0
W-Mix-Fraction = 0.0 Skip-Iterations = 20
! W-Eps = 0.17 S-Block-Only Couple Switch-On-Eps-Norm = 1.0e-04
W-Eps = 0.17 S-Block-Only Couple Switch-On-Eps-Norm = 0.0
Positive-W Lambda = 0.0001 for Max-Alpha = 2.0 AUTO
Tail-Iterations = 10
End
W-TAILS
Activate at Eps-Norm = 1e-12 or Max-Iter = 100
Func = 1
R1-Multiplier = 2.0
R2-Multiplier = 3.0
Fit-Type = 3
W-Tests
END
Restart
File ref-A+DF-2bas/H2OA_atoms.ISA
Tests Yes
Iterate No
End
End
Begin Multipoles
Molecule H2OA
DF Type ISA-GRID
Rank 4
EndNotice we have restarted the ISA from the solution obtained using the A+DF algorithm, but here we define the ISA to be the A-type only.
Here are the multipole moments for this system:
! Multipole moments for H2OA
! Based on DF-type : ISA-GRID
O 0.00000000 0.00000000 0.00000000 Type O Rank 4
-0.840855
0.191891 -0.000000 -0.000000
0.001296 -0.000000 0.000000 0.410826 0.000000
-0.122891 0.000000 0.000000 0.138468 0.000000
0.000000 0.000000
-0.231414 0.000000 0.000000 0.159840 0.000000
-0.000000 -0.000000 -0.132731 -0.000000
H1 -1.45365196 0.00000000 -1.12168732 Type H Rank 4
0.420396
0.005184 -0.029688 -0.000000
0.004736 0.007546 0.000000 0.034914 0.000000
0.008001 -0.015741 0.000000 -0.022386 0.000000
-0.007215 0.000000
-0.014832 -0.006552 0.000000 0.021457 0.000000
-0.004347 -0.000000 -0.042430 -0.000000
H2 1.45365196 0.00000000 -1.12168732 Type H Rank 4
...
Total molecular moments relative to origin (0,0,0):
-0.000064
-0.740846 -0.000000 -0.000000
0.070726 0.000000 0.000000 2.168801 0.000000
1.998676 0.000000 0.000000 -4.322235 -0.000000
0.000000 0.000000
-4.732613 0.000000 0.000000 6.354305 0.000000
-0.000000 -0.000000 3.932732 0.000000
Analysis
For reference, here are the total molecular multipoles obtained directly from the density (no density-fitting!):
Total molecular moments without fitting
Total multipoles
referred to origin at x = 0.000000, y = 0.000000, z = 0.000000
Q00 = 0.000000
|Q1| = 0.740556 Q10 = -0.740556
|Q2| = 2.169405 Q20 = 0.070240 Q22c = 2.168267
|Q3| = 4.696276 Q30 = 1.976820 Q32c = -4.259952
|Q4| = 8.911126 Q40 = -4.731016 Q42c = 6.359787 Q44c = 4.071701You can see that the ISA A and A+DF algorithms give results very similar to these as long as the auxiliary basis is Cartesian. It may be simpler to use the A algorithm with the 3 basis sets defined as shown above. But this is only one example!
ISA with additional sites
Warning
This calculation can only be performed using CamCASP 6.0.010 and later. At present, this is a developer's version only.
Adding extra sites to the ISA expansion is now possible, but as this has not been tested very much, I'll write this tutorial later. If you are interested, ask me.