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.
PAMoCPAMoC 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:
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,I15For 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.
GDMAAnthony 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> MULTIPOLES LIMIT 4 SWITCH 0 START FINISH
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.
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:
#!/bin/csh # set EXEDIR = $HOME/bin/CRYSTAL98 date >& glycine-crystal98.ext hostname >>& glycine-crystal98.ext $EXEDIR/scfdir < glycine-crystal98.inp >>& glycine-crystal98.ext $EXEDIR/properties << ENDINPUT >>& glycine-crystal98.ext POLI 4 0 -4 END ENDINPUT 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).
GDMA: Distributed Multipole Analysis of wavefunctions
calculated by the Gaussian system of programs, using the formatted
checkpoint files that they produce.GAUSSIAN package:
https://www.gaussian.com. Accessed 16 April 2019.CRYSTAL”