External DMA: ext


[-]ext   <filename>


The keyword ext define a pathname to a disk file which contains a valid atom centered Distributed Multipole Analysis of the electron density (DMA). It provides PAMoC with an external set of multipole moments either for comparison with moments already available from the idf or to be used in the calculation of electrostatic interaction energies instead of the default moments. In the latter case, the keyword "usedma 8" must be supplied in order to let PAMoC know which DMA to use among the available ones.

The file may contain one or more data input sections (see the manual page on the Data Input). The first section, always needed, is the DMA input section, which is defined by a block of lines like:


The first line of the section must contain the keyword DMA, followed by the specification of the DMA type. The section is terminated either by the end-of-file or by an END line. In the example above, the distribute multipoles are generated by Stone's GDMA program (see below) and are retrieved (included) from the disk file GDMA-print-output-file.

An atom-coordinate input-section is optionally present. The atom coordinates must be given in the same sequence order of the interface data file. PAMoC will check if the atom coordinates in the external-dma data file have the same orientation of those in the interface data file. If this condition is not satisfied, a rotation matrix will be generated and the external moments will be rotated to the IDF orientation.

Instead of atom coordinates, a rotation matrix can be provided to rotate the external moments to the same orientation of the IDF moments, using a specific rotation input section.

External DMA formats accepted by PAMoC


1. - PAMoC

PAMoC prints nuclear center multipole moments using a general format, which may include standard deviations. The same format can be used to enter nuclear centered multipole moments to PAMoC.

DMAs can be in the form of (a) unabridged cartesian tensors, (b) traceless cartesian tensors, and (c) spherical tensors. PAMoC is able to discriminate between unabridged and traceless cartesian tensors, as well as between cartesian and spherical tensors.

Experimental DMAs can be reported with their standard deviations. PAMoC recognizes the presence of standard deviations and will ignore them.

DMAs can be referred to an arbitrary origin and system of orthogonal axes. PAMoC is unable to decide by itself what the origin and orientation of the DMA are, so that they are supposed to be the same as the IDF.

PAMoC is unable to determine by itself which units are in use, so it is assumed that they are the most common (i.e. the standard units: electrons, Debye, Debye-Ang, Debye-Ang2, Debye-Ang3).


This is the format used by the VALRAY code[1Stewart, R. F.; Spackman, M. A.; Flensburg, C.
VALRAY User's Manual (Version 2.1), Carnegie-Mellon University, Pittsburg, and University of Copenhagen, Copenhagen, 2000.
] to specify pseudoatom populations. It consists of a sequence of lines (cards) 76 characters long which are structured as follows:

1-6 POPVAL 8-9 <generic atom label> 12-13 <specific atom label> 14-16 <continuation flag> = 0 for first POPVAL card for this atom > 0 for subsequent cards 17-19 <sequence number for following population value> 20-26 <population value> 27-29 <sequence number> 30-36 <population> ... ... 67-69 <sequence number> 70-76 <population>

and are read/written according to the Fortran FORMAT(A6, 1X, A2, 2X, A2, I3, 6(I3,F7.4).

Only non-zero populations need to be input, along with their sequence number. Populations must be in the sequence

1 monopole PCR 2 monopole PVL 3 monopole PSH 4-6 dipole D1,D2,D3 7-11 quadrupole Q1,Q2,Q3,Q4,Q5 12-18 octupole O1,O2,O3,O4,O5,O6,O7 19-27 hexadecapole H1,H2,H3,H4,H5,H6,H7,H8,H9 28-38 tricontadipole T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11 39-51 hexacontatetrapole S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13 52-66 hectoicosaoctopole I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,I11,I12,I13,I14,I15

For the polarised H atom, populations must be input as 1 and 2, and are assumed to refer to FVAL and FDIPOL from VALDAT. They are generally = 1.0.

In VALRAY the multipole rank can be as high as 7, but PAMoC can deal with multipoles up to rank 4.

3. - GDMA

Anthony Stone introduced the Distributed Multipole Analysis or DMA as "a technique for describing a molecular charge distribution by using local multipoles at a number of sites within a molecule".[2Anthony Stone, University of Cambridge. Website.] He developed a computer program, named GDMA,[3GDMA: Distributed Multipole Analysis of Gaussian wavefunctions.] that carries out distributed multipole analysis of wavefunctions calculated by the Gaussian system of programs[4Gaussian.com | Expanding the limits of computational chemistry] and retrieved from its formatted checkpoint file.[5Structure of the Formatted Checkpoint File.] The distributed multipoles are calculated in terms of wavefunction normalized spherical harmonic tensors. Total molecular multipoles are calculated as well.

The recommended procedure for using the program is to construct a small data file of the following form:

DENSITY <density-type>
FILE <checkpointfile>
   LIMIT 4

The keywords shown in uppercase may be typed in upper, lower or mixed case. The initial DENSITY command is optional; the default is to read the SCF density matrix from the checkpoint file. Any other density matrix that appears in the checkpoint file may be specified. The LIMIT subcommand specifies the highest multipole rank. In GDMA, limit can be as high as rank 10, but PAMoC can deal with multipoles up to rank 4. The SWITCH command selects the algorithm to be used. A value of 0 requires that the original nearest-site allocation algorithm is used, as set out in references [6Stone, A. J. Chem. Phys. Lett. 1981, 83, 233.], [7Stone, A. J.; Alderton, M. Molec. Phys. 1985, 56, 1047.], and [8 Stone, A. J. The Theory of Intermolecular Forces, (Oxford University Press, Oxford, 2013), 2nd edn.] This algorithm is both exact and very fast, because it uses an exact and very efficient Gauss-Hermite quadrature. Overlap densities involving compact basis functions (those with large ζ) are well localized in space, and their allocation to the nearest multipole site is entirely satisfactory. On the other hand, overlap densities of diffuse primitive functions (those with small ζ) could extend to some extent over several atoms. In this case a 3D grid-based quadrature, like that proposed by Becke,[9Becke, A. D. J. Chem. Phys. 1988, 88, 2547-2553.] would be more appropriate. Of course this appoach is very much slower, because it is necessary to use a fine grid, and even with a fine grid it is not exact. Version 2 of the GDMA program[10Stone, A. J. J. Chem. Theory Comput. 2005, 1, 1128-1132.] uses this method to calculate the multipole contributions arising from the overlap of diffuse primitive functions. Actually, the program can use both methods. If the sum of exponents ζa + ζb for a pair of primitive functions χa and χb is greater than a switch value Z, the grid-based analysis is used, and otherwise the original DMA method is used. A value of 4 is recommended by the GDMA user's manual. A value of 1 would switch to the Becke's partitioning scheme for most pairs of primitive functions.

4. - CRYSTAL print output files

The CRYSTAL package[11CRYSTAL: a computational tool for solid state chemistry and physics.] provides a nuclear-centered multipole expansion of the periodic wave function, based on Mulliken partitioning scheme. Mulliken moments can be used to estimate molecule-molecule electrostatic interaction energies as well as the electrostatic contribution to the crystal lattice energy. The interface-data-file to PAMoC is the union of the output files produced by the CRYSTAL programs crystal (which calculates a periodic wave-function) and properties (which calculates spherical harmonics multipole moments, using the keyword POLI).

The following shell-script illustrates the procedure:

date                                    >& glycine-crystal98.ext
hostname                               >>& glycine-crystal98.ext
$EXEDIR/scfdir < glycine-crystal98.inp >>& glycine-crystal98.ext
$EXEDIR/properties << ENDINPUT         >>& glycine-crystal98.ext
4  0 -4
date                                   >>& glycine-crystal98.ext

Only a limited number of tests has been made, using versions 1998, 2003 and 2006 of the CRYSTAL package.

CRYSTAL print output files are also recognized by PAMoC as an nterface data file (see keyword idf).

Related Keywords



  1. Stewart, R. F.; Spackman, M. A.; Flensburg, C. VALRAY User's Manual (Version 2.1), Carnegie-Mellon University, Pittsburg, and University of Copenhagen, Copenhagen, 2000.
  2. Anthony Stone, University of Cambridge. Website: http://www-stone.ch.cam.ac.uk/. Accessed 18 Apr 2019.
  3. GDMA: Distributed Multipole Analysis of wavefunctions calculated by the Gaussian system of programs, using the formatted checkpoint files that they produce.
    (a) Website: http://www-stone.ch.cam.ac.uk/pub/gdma/. Accessed 18 Apr 2019.
    (b) Online User's Manual: http://www-stone.ch.cam.ac.uk/documentation/gdma/manual.pdf. Accessed 18 Apr 2019.
  4. “Gaussian.com | Expanding the limits of computational chemistry”
    Website of the GAUSSIAN package: https://www.gaussian.com. Accessed 16 April 2019.
  5. “Structure of the Formatted Checkpoint File”, Jen-Shiang K. Yu, Institute of Bioinformatics and Systems Biology and Dept. of Biological Science and Technology, National Chiao Tung University, Hsinchu, Taiwan. Online resource: http://wild.life.nctu.edu.tw/~jsyu/compchem/g09/g09ur/f_formchk.htm. Accessed 18 Apr 2019.
  6. Stone, A. J. Chem. Phys. Lett. 1981, 83, 233.
  7. Stone, A. J.; Alderton, M. Molec. Phys. 1985, 56, 1047.
  8. Stone, A. J. The Theory of Intermolecular Forces, (Oxford University Press, Oxford, 2013), 2nd edn.
  9. Becke, A. D. J. Chem. Phys. 1988, 88, 2547-2553.
  10. Stone, A. J. J. Chem. Theory Comput. 2005, 1, 1128-1132.
  11. (a) “Quantum‐mechanical condensed matter simulations with CRYSTAL
    Dovesi, R.; Erba, A.; Orlando, R.; Zicovich‐Wilson, C. M.; Civalleri, B.; Maschio, L.; Rérat, M.; Casassa, S.; Baima, J.; Salustro. S; Kirtman, B. Wiley Interdisciplinary Reviews: Computational Molecular Science (WIREs Comput. Mol. Sci.) 2018, 8, 4, e1360. DOI: 10.1002/wcms.1360.
    (b) “CRYSTAL17 User's Manual” R. Dovesi, V. R. Saunders, C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N. M. Harrison, I. J. Bush, P. D’Arco, M. Llunell, M. Causà, Y. Noël, L. Maschio, A. Erba, M. Rerat and S. Casassa (University of Torino, Torino, 2017).
    (c) “CRYSTAL: a computational tool for solid state chemistry and physics.” Website: http://www.crystal.unito.it/. Accessed 19 Apr 2019.