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gengrp.f90
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gengrp.f90
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!
! ParaGauss, a program package for high-performance computations of
! molecular systems
!
! Copyright (C) 2014 T. Belling, T. Grauschopf, S. Krüger,
! F. Nörtemann, M. Staufer, M. Mayer, V. A. Nasluzov, U. Birkenheuer,
! A. Hu, A. V. Matveev, A. V. Shor, M. S. K. Fuchs-Rohr, K. M. Neyman,
! D. I. Ganyushin, T. Kerdcharoen, A. Woiterski, A. B. Gordienko,
! S. Majumder, M. H. i Rotllant, R. Ramakrishnan, G. Dixit,
! A. Nikodem, T. Soini, M. Roderus, N. Rösch
!
! This program is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License version 2 as
! published by the Free Software Foundation [1].
!
! This program is distributed in the hope that it will be useful, but
! WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
! General Public License for more details.
!
! [1] http://www.gnu.org/licenses/gpl-2.0.html
!
! Please see the accompanying LICENSE file for further information.
!
!=====================================================================
! Public interface of module
!=====================================================================
subroutine gengrp(group,igroup,iorder,elem,namele,ncsco,fcsco)
!-------------------------------------------------------------------
!
! Purpose:
! identifies the group by number in the canonical ordering used in
! the tables of Altmann and Herzig and generates the quaternionic
! representation of the group elements and their name
!
! author: N. Roesch, Theoretische Chemie, TU Muenchen
! version: 07.05.95
!
!== Interrupt of public interface of module =====================
!-------------------------------------------------------------------
! Modifications
!-------------------------------------------------------------------
!
! Modification (Please copy before editing)
! Author: ...
! Date: ...
! Description: ...
!
!-------------------------------------------------------------------
!------------ Modules used -----------------------------------------
use type_module, only: i4_kind,r8_kind
implicit none
!== Interrupt end of public interface of module =================
!------------ Declaration of formal parameters ---------------------
character(len=4), intent(in) :: group
! group name of the group
integer(kind=i4_kind),intent(in) :: iorder,igroup
! iorder order of the group
real(kind=r8_kind),intent(out) :: elem(5,iorder)
! elem quaternionic parameters of the group elements
character(len=8),intent(out) :: namele(iorder)
! namele conventional names of the group elements
integer(kind=i4_kind),intent(out) :: ncsco(3), fcsco(3)
! ncsco indicates the class operator used to generated the
! characters; for the numbering, see subroutine gencls
! a negative value indicates an non-ambivalent class,
! whence real and imaginary parts will be used as
! separate operators
! fcsco coefficient for the linear combination of class
! operators
!===================================================================
! End of public interface of module
!===================================================================
!------------ Declaration of local constants --------------------
integer(kind=i4_kind), parameter :: modnum=1, nptgrp=75, ngrpar=304
!------------ Declaration of local variables --------------------
integer(kind=i4_kind) :: naxis, k, koffst, l, i, &
ncscop(3,nptgrp), fcscop(3,nptgrp)
character(len=36) :: grppar(ngrpar)
logical ::appinv
!
! elements of selected groups, angle/axis/parity coded
! parameter 1 : m/n -> angle = pi*m/n
! parameter 2-4 : unit vector along axis
! coded c -> cos, s -> sin, angle as above,
! special angles in group Oh:
! ct1/2 -> cos of (tetrahedral angle /2),
! sig, rho -> special angles of icosahedral group
! see Altmann & Herzig, Table T75.1,
! but beware of two typos !!!
! 0, 1, 1/2 just what you read
! parameter 5 : + pure rotation, - apply inversion
! parameter 6 : label of group element
!
data (grppar(k), k = 1, 2) /& ! Ci
& '0 0 0 1 + E ', &
& '0 0 0 1 - i ' /
data (grppar(k), k = 3, 4) /& ! Cs
& '0 0 0 1 + E ', &
& '1 0 0 1 - sigh ' /
data (grppar(k), k = 5, 12) / &! D2d
& '0 0 0 1 + E ', &
& '1 0 0 1 + C2 ', &
& '1 1 0 0 + C2,1'' ', &
& '1 0 1 0 + C2,2'' ', &
& '1/2 0 0 1 - S4- ', &
& '1/2 0 0 -1 - S4+ ', &
& '1 c1/4 s1/4 0 - sigd1 ', &
& '1 -s1/4 c1/4 0 - sigd2 ' /
data (grppar(k), k = 13, 24) /& ! D3h
& '0 0 0 1 + E ', &
& '2/3 0 0 1 + C3+ ', &
& '2/3 0 0 -1 + C3- ', &
& '1 1 0 0 + C2,1'' ', &
& '1 -c1/3 s1/3 0 + C2,2'' ', &
& '1 -c1/3 -s1/3 0 + C2,3'' ', &
& '1 0 0 1 - sigh ',&
& '1/3 0 0 1 - S3- ', &
& '1/3 0 0 -1 - S3+ ', &
& '1 0 1 0 - sigv1 ', &
& '1 -s1/3 -c1/3 0 - sigv2 ', &
& '1 s1/3 -c1/3 0 - sigv3 ' /
data (grppar(k), k = 25, 40) / &! D4d
& '0 0 0 1 + E', &
& '1/2 0 0 1 + C4+ ',&
& '1/2 0 0 -1 + C4- ', &
& '1 0 0 1 + C2 ', &
& '1 1 0 0 + C2,1'' ', &
& '1 0 1 0 + C2,2'' ', &
& '1 c1/4 s1/4 0 + C2,3'' ',&
& '1 -s1/4 c1/4 0 + C2,4'' ',&
& '1/4 0 0 1 - S8^3- ',&
& '1/4 0 0 -1 - S8^3+ ',&
& '3/4 0 0 1 - S8- ',&
& '3/4 0 0 -1 - S8+ ', &
& '1 c1/8 s1/8 0 - sigd1 ', &
& '1 -s1/8 c1/8 0 - sigd2 ', &
& '1 s1/8 c1/8 0 - sigd3 ', &
& '1 -c1/8 s1/8 0 - sigd4 ' /
data (grppar(k), k = 41, 60) /& ! D5h
& '0 0 0 1 + E ', &
& '2/5 0 0 1 + C5+ ', &
& '2/5 0 0 -1 + C5- ', &
& '4/5 0 0 1 + C5^2+ ', &
& '4/5 0 0 -1 + C5^2- ', &
& '1 1 0 0 + C2,1'' ', &
& '1 s1/10 c1/10 0 + C2,2'' ', &
& '1 -c1/5 s1/5 0 + C2,3'' ', &
& '1 -c1/5 -s1/5 0 + C2,4'' ', &
& '1 s1/10 -c1/10 0 + C2,5'' ', &
& '1/5 0 0 -1 - S5^2- ', &
& '1/5 0 0 1 - S5^2+ ', &
& '3/5 0 0 -1 - S5- ', &
& '3/5 0 0 1 - S5+ ', &
& '1 0 0 1 - sigh ', &
& '1 0 1 0 - sigv1 ', &
& '1 -c1/10 s1/10 0 - sigv2 ', &
& '1 -s1/5 -c1/5 0 - sigv3 ', &
& '1 s1/5 -c1/5 0 - sigv4 ', &
& '1 c1/10 s1/10 0 - sigv5 ' /
data (grppar(k), k = 61, 84) /& ! D6d
& '0 0 0 1 + E ', &
& '1/3 0 0 1 + C6+ ', &
& '1/3 0 0 -1 + C6- ', &
& '2/3 0 0 1 + C3+ ', &
& '2/3 0 0 -1 + C3- ', &
& '1 0 0 1 + C2 ', &
& '1 1 0 0 + C2,1'' ', &
& '1 -c1/3 s1/3 0 + C2,2'' ', &
& '1 -c1/3 -s1/3 0 + C2,3'' ', &
& '1 0 1 0 + C2,4'' ', &
& '1 -s1/3 -c1/3 0 + C2,5'' ', &
& '1 s1/3 -c1/3 0 + C2,6'' ', &
& '1/6 0 0 1 - S12^5- ', &
& '1/6 0 0 -1 - S12^5+ ', &
& '1/2 0 0 1 - S4- ', &
& '1/2 0 0 -1 - S4+ ', &
& '5/6 0 0 1 - S12- ', &
& '5/6 0 0 -1 - S12+ ', &
& '1 c1/4 s1/4 0 - sigd1 ', &
& '1 -c1/12 s1/12 0 - sigd2 ', &
& '1 s1/12 -c1/12 0 - sigd3 ', &
& '1 -s1/4 c1/4 0 - sigd4 ', &
& '1 -s1/12 -c1/12 0 - sigd5 ', &
& '1 c1/12 s1/12 0 - sigd6 ' /
data (grppar(k), k = 85, 112) /& ! D7h
& '0 0 0 1 + E ', &
& '2/7 0 0 1 + C7+ ', &
& '2/7 0 0 -1 + C7- ', &
& '4/7 0 0 1 + C7^2+ ', &
& '4/7 0 0 -1 + C7^2- ', &
& '6/7 0 0 1 + C7^3+ ', &
& '6/7 0 0 -1 + C7^3- ', &
& '1 1 0 0 + C2,1'' ', &
& '1 c2/7 s2/7 0 + C2,2'' ', &
& '1 -c3/7 s3/7 0 + C2,3'' ', &
& '1 -c1/7 s1/7 0 + C2,4'' ', &
& '1 -c1/7 -s1/7 0 + C2,5'' ', &
& '1 -c3/7 -s3/7 0 + C2,6'' ', &
& '1 c2/7 -s2/7 0 + C27'' ', &
& '1 0 0 1 - sigh ', &
& '5/7 0 0 -1 - S7+ ', &
& '5/7 0 0 1 - S7- ', &
& '3/7 0 0 -1 - S7^2+ ', &
& '3/7 0 0 1 - S7^2- ', &
& '1/7 0 0 -1 - S7^3+ ', &
& '1/7 0 0 1 - S7^3- ', &
& '1 0 1 0 - sigv1 ', &
& '1 -s2/7 c2/7 0 - sigv2 ', &
& '1 -s3/7 -c3/7 0 - sigv3 ', &
& '1 -s1/7 -c1/7 0 - sigv4 ', &
& '1 s1/7 -c1/7 0 - sigv5 ', &
& '1 s3/7 -c3/7 0 - sigv6 ', &
& '1 s2/7 c2/7 0 - sigv7 ' /
data (grppar(k), k = 113, 144) /& ! D8d &
& '0 0 0 1 + E ', &
& '1/4 0 0 1 + C8+ ', &
& '1/4 0 0 -1 + C8- ', &
& '1/2 0 0 1 + C4+ ', &
& '1/2 0 0 -1 + C4- ', &
& '3/4 0 0 1 + C8^3+ ', &
& '3/4 0 0 -1 + C8^3- ', &
& '1 0 0 1 + C2 ', &
& '1 1 0 0 + C2,1'' ', &
& '1 0 1 0 + C2,2'' ', &
& '1 c1/4 s1/4 0 + C2,3'' ', &
& '1 -s1/4 c1/4 0 + C2,4'' ', &
& '1 c1/8 s1/8 0 + C2,5'' ', &
& '1 -s1/8 c1/8 0 + C2,6'' ', &
& '1 s1/8 c1/8 0 + C2,7'' ', &
& '1 -c1/8 s1/8 0 + C2,8'' ', &
& '1/8 0 0 1 - S16^7- ', &
& '1/8 0 0 -1 - S16^7+ ', &
& '3/8 0 0 1 - S16^5- ', &
& '3/8 0 0 -1 - S16^5+ ', &
& '5/8 0 0 1 - S16^3- ', &
& '5/8 0 0 -1 - S16^3+ ', &
& '7/8 0 0 1 - S16- ', &
& '7/8 0 0 -1 - S16+ ', &
& '1 c1/16 s1/16 0 - sigd1 ', &
& '1 -s1/16 c1/16 0 - sigd2 ', &
& '1 s3/16 c3/16 0 - sigd3 ', &
& '1 -c3/16 s3/16 0 - sigd4 ', &
& '1 c3/16 s3/16 0 - sigd5 ', &
& '1 -s3/16 c3/16 0 - sigd6 ', &
& '1 s1/16 c1/16 0 - sigd7 ', &
& '1 -c1/16 s1/16 0 - sigd8 ' /
data (grppar(k), k = 145, 180) /& ! D9h &
& '0 0 0 1 + E ', &
& '2/9 0 0 1 + C9+ ', &
& '2/9 0 0 -1 + C9- ', &
& '4/9 0 0 1 + C9^2+ ', &
& '4/9 0 0 -1 + C9^2- ', &
& '2/3 0 0 1 + C3+ ', &
& '2/3 0 0 -1 + C3- ', &
& '8/9 0 0 1 + C9^4+ ', &
& '8/9 0 0 -1 + C9^4- ', &
& '1 1 0 0 + C2,1'' ', &
& '1 -c1/3 s1/3 0 + C2,2'' ', &
& '1 -c1/3 -s1/3 0 + C2,3'' ', &
& '1 c2/9 s2/9 0 + C2,4'' ', &
& '1 -c1/9 s1/9 0 + C2,5'' ', &
& '1 c4/9 -s4/9 0 + C2,6'' ', &
& '1 c4/9 s4/9 0 + C2,7'' ', &
& '1 -c1/9 -s1/9 0 + C2,8'' ', &
& '1 c2/9 -s2/9 0 + C2,9'' ', &
& '1 0 0 1 - sigh ', &
& '7/9 0 0 -1 - S9+ ', &
& '7/9 0 0 1 - S9- ', &
& '5/9 0 0 -1 - S9^2+ ', &
& '5/9 0 0 1 - S9^2- ', &
& '1/3 0 0 -1 - S3+ ', &
& '1/3 0 0 1 - S3- ', &
& '1/9 0 0 -1 - S9^4+ ', &
& '1/9 0 0 1 - S9^4- ', &
& '1 0 1 0 - sigv1 ', &
& '1 -s1/3 -c1/3 0 - sigv2 ', &
& '1 s1/3 -c1/3 0 - sigv3 ', &
& '1 -s2/9 c2/9 0 - sigv4 ', &
& '1 -s1/9 -c1/9 0 - sigv5 ', &
& '1 s4/9 c4/9 0 - sigv6 ', &
& '1 -s4/9 c4/9 0 - sigv7 ', &
& '1 s1/9 -c1/9 0 - sigv8 ', &
& '1 s2/9 c2/9 0 - sigv9 ' /
data (grppar(k), k = 181, 216) /& ! D10d
& '0 0 0 1 + E ', &
& '1/5 0 0 1 + C10+ ', &
& '1/5 0 0 -1 + C10- ', &
& '2/5 0 0 1 + C5+ ', &
& '2/5 0 0 -1 + C5- ', &
& '3/5 0 0 1 + C10^3+ ', &
& '3/5 0 0 -1 + C10^3- ', &
& '4/5 0 0 1 + C5^2+ ', &
& '4/5 0 0 -1 + C5^2- ', &
& '1 0 0 1 + C2 ', &
& '1 1 0 0 + C2,1'' ', &
& '1 s1/10 c1/10 0 + C2,2'' ', &
& '1 -c1/5 s1/5 0 + C2,3'' ', &
& '1 -c1/5 -s1/5 0 + C2,4'' ', &
& '1 s1/10 -c1/10 0 + C2,5'' ', &
& '1 0 1 0 + C2,6'' ', &
& '1 -c1/10 s1/10 0 + C2,7'' ', &
& '1 -s1/5 -c1/5 0 + C2,8'' ', &
& '1 s1/5 -c1/5 0 + C2,9'' ', &
& '1 c1/10 s1/10 0 + C2,10'' ', &
& '1/10 0 0 1 - S20^9- ', &
& '1/10 0 0 -1 - S20^9+ ', &
& '3/10 0 0 1 - S20^7- ', &
& '3/10 0 0 -1 - S20^7+ ', &
& '1/2 0 0 1 - S4- ', &
& '1/2 0 0 -1 - S4+ ', &
& '7/10 0 0 1 - S20^3- ', &
& '7/10 0 0 -1 - S20^3+ ', &
& '9/10 0 0 1 - S20- ', &
& '9/10 0 0 -1 - S20+ ', &
& '1 c1/4 s1/4 0 - sigd1 ', &
& '1 -s3/20 c3/20 0 - sigd2 ', &
& '1 -c1/20 -s1/20 0 - sigd3 ', &
& '1 -s1/20 -c1/20 0 - sigd4 ', &
& '1 c3/20 -s3/20 0 - sigd5 ', &
& '1 -s1/4 c1/4 0 - sigd6 ' /
data (grppar(k), k= 217,220) / &
& '1 -c3/20 -s3/20 0 - sigd7 ', &
& '1 s1/20 -c1/20 0 - sigd8 ', &
& '1 c1/20 -s1/20 0 - sigd9 ', &
& '1 s3/20 c3/20 0 - sigd10 ' /
data (grppar(k), k = 221, 244) /& ! O
& '0 0 0 1 + E ', &
& '1 1 0 0 + C2x ', &
& '1 0 1 0 + C2y ', &
& '1 0 0 1 + C2z ', &
& '2/3 ct/2 ct/2 ct/2 + C3,1+ ', &
& '2/3 -ct/2 -ct/2 ct/2 + C3,2+ ', &
& '2/3 ct/2 -ct/2 -ct/2 + C3,3+ ', &
& '2/3 -ct/2 ct/2 -ct/2 + C3,4+ ', &
& '2/3 -ct/2 -ct/2 -ct/2 + C3,1- ', &
& '2/3 ct/2 ct/2 -ct/2 + C3,2- ', &
& '2/3 -ct/2 ct/2 ct/2 + C3,3- ', &
& '2/3 ct/2 -ct/2 ct/2 + C3,4- ', &
& '1/2 1 0 0 + C4x+ ', &
& '1/2 0 1 0 + C4y+ ', &
& '1/2 0 0 1 + C4z+ ', &
& '1/2 -1 0 0 + C4x- ', &
& '1/2 0 -1 0 + C4y- ', &
& '1/2 0 0 -1 + C4z- ', &
& '1 c1/4 s1/4 0 + C2a'' ', &
& '1 -s1/4 c1/4 0 + C2b'' ', &
& '1 s1/4 0 c1/4 + C2c'' ', &
& '1 0 -c1/4 -s1/4 + C2d'' ', &
& '1 c1/4 0 -s1/4 + C2e'' ', &
& '1 0 -s1/4 c1/4 + C2f'' ' /
data (grppar(k), k = 245, 274) /& ! I
& '0 0 0 1 + E ', &
& '2/5 csig 0 ssig + C5,1+ ', &
& '2/5 -csig 0 ssig + C5,2+ ', &
& '2/5 0 ssig csig + C5,3+ ', &
& '2/5 0 -ssig csig + C5,4+ ', &
& '2/5 ssig csig 0 + C5,5+ ', &
& '2/5 ssig -csig 0 + C5,6+ ', &
& '2/5 -csig 0 -ssig + C5,1- ', &
& '2/5 csig 0 -ssig + C5,2- ', &
& '2/5 0 -ssig -csig + C5,3- ', &
& '2/5 0 ssig -csig + C5,4- ', &
& '2/5 -ssig -csig 0 + C5,5- ', &
& '2/5 -ssig csig 0 + C5,6- ', &
& '4/5 csig 0 ssig + C5,1^2+ ', &
& '4/5 -csig 0 ssig + C5,2^2+ ', &
& '4/5 0 ssig csig + C5,3^2+ ', &
& '4/5 0 -ssig csig + C5,4^2+ ', &
& '4/5 ssig csig 0 + C5,5^2+ ', &
& '4/5 ssig -csig 0 + C5,6^2+ ', &
& '4/5 -csig 0 -ssig + C5,1^2- ', &
& '4/5 csig 0 -ssig + C5,2^2- ', &
& '4/5 0 -ssig -csig + C5,3^2- ', &
& '4/5 0 ssig -csig + C5,4^2- ', &
& '4/5 -ssig -csig 0 + C5,5^2- ', &
& '4/5 -ssig csig 0 + C5,6^2- ', &
& '2/3 ct/2 ct/2 ct/2 + C3,1+ ', &
& '2/3 -ct/2 -ct/2 ct/2 + C3,2+ ', &
& '2/3 ct/2 -ct/2 -ct/2 + C3,3+ ', &
& '2/3 -ct/2 ct/2 -ct/2 + C3,4+ ', &
& '2/3 -srho 0 crho + C3,5+ ' /
data (grppar(k) , k=275,304) / &
& '2/3 0 crho -srho + C3,6+ ', &
& '2/3 crho -srho 0 + C3,7+ ', &
& '2/3 srho 0 crho + C3,8+ ', &
& '2/3 0 crho srho + C3,9+ ', &
& '2/3 crho srho 0 + C3,10+ ', &
& '2/3 -ct/2 -ct/2 -ct/2 + C3,1- ', &
& '2/3 ct/2 ct/2 -ct/2 + C3,2- ', &
& '2/3 -ct/2 ct/2 ct/2 + C3,3- ', &
& '2/3 ct/2 -ct/2 ct/2 + C3,4- ', &
& '2/3 srho 0 -crho + C3,5- ', &
& '2/3 0 -crho srho + C3,6- ', &
& '2/3 -crho srho 0 + C3,7- ', &
& '2/3 -srho 0 -crho + C3,8- ', &
& '2/3 0 -crho -srho + C3,9- ', &
& '2/3 -crho -srho 0 + C3,10- ', &
& '1 1 0 0 + C2a ', &
& '1 0 1 0 + C2b ', &
& '1 0 0 1 + C2c ', &
& '1 c1/5 s1/10 1/2 + C2d ', &
& '1 1/2 -c1/5 -s1/10 + C2e ', &
& '1 s1/10 1/2 -c1/5 + C2f ', &
& '1 s1/10 1/2 c1/5 + C2g ', &
& '1 1/2 -c1/5 s1/10 + C2h ', &
& '1 c1/5 s1/10 -1/2 + C2i ', &
& '1 -s1/10 1/2 c1/5 + C2j ', &
& '1 -c1/5 s1/10 -1/2 + C2k ', &
& '1 -1/2 -c1/5 s1/10 + C2l ', &
& '1 -c1/5 s1/10 1/2 + C2m ', &
& '1 -s1/10 1/2 -c1/5 + C2n ', &
& '1 -1/2 -c1/5 -s1/10 + C2o ' /
!
! For each group, ncscop denotes the classes making up a CSCO and
! fcscop provides the coefficient in the linear combination of the
! class operators. A negative number indicates a non-ambivalent
! class whence the real and the imaginary part will be used as
! separate class operators. The list of the classes will be
! generated in subroutine gencls.
!
data ((ncscop(i,k), i = 1,3), k = 1, 18) &
& / 1, 0, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0,&
& -2, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, &
& -4, 0, 0, -6, 0, 0, -8, 0, 0,-10, 0, 0,-12, 0, 0,-14, 0, 0 /
data ((fcscop(i,k), i = 1,3), k = 1, 18) &
& / 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,&
& 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, &
& 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 /
data ((ncscop(i,k), i = 1,3), k = 19, 36) &
& /-16, 0, 0,-18, 0, 0,-20, 0, 0, 2, 3, 0, 3, 0, 0, 2, 4, 0, &
& 2, 4, 0, 2, 5, 0, 2, 5, 0, 2, 6, 0, 2, 6, 0, 2, 7, 0, &
& 2, 3, 5, 3, 4, 0, 2, 4, 6, 2, 4, 7, 2, 5, 7, 2, 5, 6 /
data ((fcscop(i,k), i = 1,3), k = 19, 36) &
& / 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 2, 1, 0,&
& 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 2, 0, 2, 1, 0, 2, 1, 0, &
& 6, 2, 1, 1, 1, 0, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1 /
data ((ncscop(i,k), i = 1,3), k = 37, 54) &
& / 2, 6, 8, 2, 6, 7, 2, 7, 9, 2, 4, 6, 4, 5, 0, 4, 6, 0, &
& 6, 7, 0, 7, 8, 0, 8, 9, 0, 9,10, 0, 10,11, 0, 11,12, 0, &
& 12,13, 0, 2, 3, 0, 3, 0, 0, 2, 4, 0, 2, 4, 0, 2, 5, 0 /
data ((fcscop(i,k), i = 1,3), k = 37, 54) &
& / 2, 2, 1, 2, 1, 1, 4, 2, 1, 2, 1, 1, 2, 1, 0, 2, 1, 0,&
& 3, 1, 0, 2, 1, 0, 4, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, &
& 2, 1, 0, 2, 1, 0, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0 /
data ((ncscop(i,k), i = 1,3), k = 55, 72) &
& / 2, 5, 0, 2, 6, 0, 2, 6, 0, 2, 7, 0, 2, 4, 0, 2, 3, 0, &
& -2, 4, 0, -2, 5, 0, -2,10, 0, -2, 7, 0, -2, 8, 0, -2, 9, 0, &
& -2,10, 0, -2,11, 0, 5, 0, 0, -3, 0, 0, 5, 6, 0, -3, 5, 0 /
data ((fcscop(i,k), i = 1,3), k = 55, 72) &
& / 2, 1, 0, 2, 2, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0,&
& 1, 5, 0, 2, 5, 0, 2, 5, 0, 2, 5, 0, 2, 5, 0, 2, 5, 0, &
& 2, 5, 0, 2, 5, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 5, 0 /
data ((ncscop(i,k), i = 1,3), k = 73, 75) &
& / 5, 0, 0, 2, 5, 0, 2, 5, 6 /
data ((fcscop(i,k), i = 1,3), k = 73, 75) &
& / 1, 0, 0, 2, 1, 0, 2, 1, 1 /
!
! FIXME: for some reason the subroutine suplab() is called
! with uninitialized names of elements from intent(out)
! array namele(:) as input, this seems to lead to some
! artifacts. Initialize them to empty strings as a workaround:
!
do i = 1, size(namele)
namele(i) = " "
enddo
appinv = .false.
!
! selects proper subgroup or supplement with inversion etc.
! then decodes and forms quaternionic parameters elem as well as
! label of element from grppar. Where appropriate, supnam is
! called for labels of derived elements (i.e. those generated by
! applying the inversion)
!
if ( igroup.ge.1 .and. igroup.le.10 ) then ! Cn
naxis = iorder ! order of main rotation axis
koffst = 2*naxis*(naxis-1) ! offset in list grppar
do k = 1, iorder
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
else if ( igroup.eq.11 ) then ! Ci
call decdel (grppar(1),elem(1,1))
namele(1) = grppar(1) (29:)
call decdel (grppar(2),elem(1,2))
namele(2) = grppar(2) (29:)
else if ( igroup.eq.12 ) then ! Cs
call decdel (grppar(3),elem(1,1))
namele(1) = grppar(3) (29:)
call decdel (grppar(4),elem(1,2))
namele(2) = grppar(4) (29:)
else if ( igroup.ge.13 .and. igroup.le.21 ) then ! S2n
naxis = iorder/2
koffst = 2*naxis*(naxis-1)
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
if ( mod(naxis,2) .eq. 0 ) then
koffst = koffst + iorder
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,naxis+k))
namele(naxis+k) = grppar(koffst+k) (29:)
end do
else
do k = 1, naxis
do l = 1, 4
elem(l,naxis+k) = elem(l,k)
end do
elem(5,naxis+k) = - elem(5,k)
appinv = .true.
call suplab (namele(k),namele(naxis+k),group,naxis, &
& appinv)
end do
end if
else if ( igroup.ge.22 .and. igroup.le.30 ) then ! Dn
naxis = iorder/2
koffst = 2*naxis*(naxis-1)
do k = 1, iorder
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
if ( naxis .eq. 2 ) then
call suplab (namele(2),namele(2),group,naxis,appinv)
call suplab (namele(3),namele(3),group,naxis,appinv)
call suplab (namele(4),namele(4),group,naxis,appinv)
else if ( mod(naxis,2) .eq. 0 .and. naxis .gt. 2 ) then
do k = 3*naxis/2+1, iorder
call suplab (namele(k),namele(k),group,naxis,appinv)
end do
end if
else if ( igroup.ge.31 .and. igroup.le.39 ) then ! Dnh
naxis = iorder/4
koffst = 2*naxis*(naxis-1)
if ( mod(naxis,2) .eq. 0 ) then
do k = 1, iorder/2
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
appinv = .false.
if ( naxis .eq. 2 ) then
call suplab (namele(2),namele(2),group,naxis,appinv)
call suplab (namele(3),namele(3),group,naxis,appinv)
call suplab (namele(4),namele(4),group,naxis,appinv)
else
do k = 3*naxis/2+1, iorder
call suplab (namele(k),namele(k),group,naxis,appinv)
end do
end if
appinv = .true.
do k = 1, iorder/2
do l = 1, 4
elem(l,iorder/2+k) = elem(l,k)
end do
elem(5,iorder/2+k) = - elem(5,k)
call suplab (namele(k),namele(iorder/2+k),group, &
& naxis,appinv)
end do
else
do k = 1, iorder
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
end if
else if ( igroup.ge.41 .and. igroup.le.49 ) then ! Dnd
naxis = iorder/4
koffst = 2*naxis*(naxis-1)
if ( mod(naxis,2).eq.0 ) then
do k = 1, iorder
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
else
do k = 1, iorder/2
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
do l = 1, 4
elem(l,iorder/2+k) = elem(l,k)
end do
elem(5,iorder/2+k) = - elem(5,k)
appinv = .false.
call suplab (namele(k),namele(iorder/2+k),group,naxis, &
& appinv)
end do
end if
else if ( igroup.ge.50 .and. igroup.le.58 ) then ! Cnv
naxis = iorder/2
koffst = 2*naxis*(naxis-1)
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
if ( mod(naxis,2).eq.0 ) then
koffst = koffst + naxis
appinv = .true.
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,naxis+k))
elem(5,naxis+k) = - elem(5,k)
namele(naxis+k) = grppar(koffst+k) (29:)
call suplab (namele(naxis+k),namele(naxis+k),group, &
& naxis,appinv)
end do
else
koffst = koffst + 3*naxis
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,naxis+k))
namele(naxis+k) = grppar(koffst+k) (29:)
end do
end if
else if ( igroup.ge.60 .and. igroup.le.68 ) then ! Cnh
naxis = iorder/2
koffst = 2*naxis*(naxis-1)
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
if ( mod(naxis,2).eq.0 ) then
koffst = koffst + naxis
appinv = .true.
do k = 1, naxis
do l = 1, 4
elem(l,naxis+k) = elem(l,k)
end do
elem(5,naxis+k) = - elem(5,k)
call suplab (namele(k),namele(naxis+k),group,naxis, &
& appinv)
end do
else
koffst = koffst + 2*naxis
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,naxis+k))
namele(naxis+k) = grppar(koffst+k) (29:)
end do
end if
else if ( igroup.ge.69 .and. igroup.le.73 ) then ! octahedral
koffst = 220
if ( igroup.eq.69 .or. igroup.eq.70 ) then
naxis = iorder ! O or T
else
naxis = iorder/2 ! Oh, Th, Td
end if
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
if ( igroup.eq.71 .or. igroup.eq.72 ) then ! Oh or Th
appinv = .true.
do k = 1, naxis
do l = 1, 4
elem(l,naxis+k) = elem(l,k)
end do
elem(5,naxis+k) = - elem(5,k)
call suplab (namele(k),namele(naxis+k),group,naxis,&
& appinv)
end do
else if ( igroup.eq. 73 ) then ! Td
koffst = koffst + naxis
appinv = .true.
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,naxis+k))
elem(5,naxis+k) = - elem(5,k)
namele(naxis+k) = grppar(koffst+k) (29:)
call suplab (namele(naxis+k),namele(naxis+k),group, &
& naxis,appinv)
end do
end if
else if ( igroup.eq.74 .or. igroup.eq.75 ) then ! icosahedral
koffst = 244
if ( igroup.eq.74 ) then
naxis = iorder ! I
else
naxis = iorder/2 ! Ih
end if
do k = 1, naxis
call decdel (grppar(koffst+k),elem(1,k))
namele(k) = grppar(koffst+k) (29:)
end do
if ( igroup.eq.75 ) then ! Ih
appinv = .true.
do k = 1, naxis
do l = 1, 4
elem(l,naxis+k) = elem(l,k)
end do
elem(5,naxis+k) = - elem(5,k)
call suplab (namele(k),namele(naxis+k),group,naxis,&
& appinv)
end do
end if
end if
!
do l = 1, 3
ncsco(l) = ncscop (l,igroup)
fcsco(l) = fcscop (l,igroup)
end do
contains
subroutine addinv (namold, namnew)
implicit none
!
! author: N. Roesch, Theoretische Chemie, TU Muenchen
! version: 30.04.95
!
! ... subroutine parameters
character(len=8), intent(in) :: namold
character(len=8), intent(out) :: namnew
!
! renames a rotation as required when the inversion is applied
! based on the representation Cn+, Cn-, Cn^m+, Cn^m- where
! the rotation angle is +-2*pi*m/n. The first two forms are
! used in case of m = 1. E and C2 are treated explicitly
! in subroutine supnam and thus are excluded here. The
! subroutine relies on the ASCII collating sequence.
!
! namold old name
! namnew new name
!
! ... integer
integer possig, poscar, m, n, posnup, next
! ... character
character(len=8) namcha
!
possig = index(namold,'+') + index(namold,'-')
if ( possig .eq. 0 ) then
if (namold(1:1) .eq. 'E' ) then
namcha = 'i'
else if ( namold(1:3) .eq. 'C2 ' ) then
namcha = 'sigh'
end if
else
poscar = index(namold,'^')
if (poscar .eq. 0) then
m = 1
posnup = possig - 1
else
m = ichar(namold(poscar+1:poscar+1)) - 48
posnup = poscar - 1
end if
n = ichar(namold(2:2)) - 48
if ( posnup .eq. 3 ) then
n = n*10 + ichar(namold(3:3)) - 48
end if
!... generate improper rotation and eliminate factors if necessary
m = n - 2*m
n = n*2
if (mod(m,2) .eq. 0) then
m = m/2
n = n/2
end if
if (mod(m,2) .eq. 0) then
m = m/2
n = n/2
end if
namcha = 'S'
if (n .gt. 9) then
namcha(2:2) = char(48+n/10)
namcha(3:3) = char(48+n-(n/10)*10)
next = 4
else
namcha(2:2) = char(48+n)
next = 3
end if
if (m .gt. 1) then
namcha(next:next) = '^'
namcha(next+1:next+1) = char(48+m)
next = next + 2
end if
!... reverse sense of rotation
if (namold(possig:possig) .eq. '+') then
namcha(next:next) = '-'
else
namcha(next:next) = '+'
end if
end if
!
namnew = namcha
!
end subroutine addinv
subroutine decdel (grppar,elem)
implicit none
!
! author: N. Roesch, Theoretische Chemie, TU Muenchen
! version: 30.04.95
!
! ... subroutine parameters
!!$ integer, parameter :: r8_kind = selected_real_kind(15)
character(len=36) grppar
real(r8_kind) :: elem(5)
!
! decodes the group element grppar (given in the data statements
! of subroutine gengrp) and converts angle/axis parameters into
! quaternionic parameters elem:
! cos(phi/2), sin(phi/2)*n1, sin(phi/2)*n2, sin(phi/2)*n3), parity
! The subroutine relies on the ASCII collating sequence.
!
! ... integer
integer k, m, n
! ... real
real(r8_kind) :: angle, phi2, pi
real(r8_kind),parameter ::&
& zero = 0.0_r8_kind,&
& one = 1.0_r8_kind,&
& two = 2.0_r8_kind,&
& three = 3.0_r8_kind,&
& five = 5.0_r8_kind
! ... character
character(len=4) chphi
character(len=5) chang
!
pi = 4.0_r8_kind*atan(1.0_r8_kind)
!
chphi = grppar(1:4)
m = iachar(chphi(1:1)) - 48
if ( chphi(2:2).eq.'/' ) then
if ( chphi(4:4).ne.' ' ) then
n = 10*(iachar(chphi(3:3))-48) + (iachar(chphi(4:4))-48)
else
n = iachar(chphi(3:3)) - 48
endif
else
n = 1
endif
phi2 = ((pi/two) * m) / n
!
do k = 1, 3
chang = grppar(7*k:7*k+4)
if ( chang.eq.'1/2 ' ) then
elem(k+1) = sin(phi2) / two
else if ( chang.eq.'ct/2 ' ) then
elem(k+1) = sin(phi2) / sqrt(three)
else if ( chang.eq.'1 ' ) then
elem(k+1) = sin(phi2)
else if ( chang.eq.'0 ' ) then
elem(k+1) = zero
else
if ( chang(2:4).eq.'rho' ) then
angle = atan((sqrt(five) + three) / two)
else if ( chang(2:4).eq.'sig' ) then
angle = atan((sqrt(five) + one ) / two)
else
m = iachar(chang(2:2)) - 48
if ( chang(5:5).ne.' ' ) then
n = 10*(iachar(chang(4:4))-48) &
& + (iachar(chang(5:5))-48)
else
n = iachar(chang(4:4)) - 48
endif
angle = (pi * m) / n
end if
if ( chang(1:1).eq.'c' ) then
elem(k+1) = sin(phi2) * cos(angle)
else
elem(k+1) = sin(phi2) * sin(angle)
end if
end if
if ( grppar(7*k-1:7*k-1).eq.'-' ) then
elem(k+1) = -elem(k+1)
end if
end do
!
elem(1) = cos(phi2)
if (grppar(27:27).eq.'-' ) then
elem(5) = -one
else
elem(5) = one
end if
!
end subroutine decdel
subroutine suplab (namold,namnew,group,naxis,appinv)
implicit none
!
! part of the module efm_mo
! author: N. Roesch, Theoretische Chemie, TU Muenchen
! version: 01.05.95
!
! ... subroutine parameters
character(len=8), intent(in) :: namold
character(len=8), intent(out) :: namnew
character(len=4), intent(in) :: group
integer , intent(in) :: naxis
logical , intent(in) :: appinv
!
! supplies additinoal names for group elements not explicitly
! given in the data statements of subroutine gengrp,
! e.g. for all improper rotations. In most cases, the inversion
! is applied automically by subroutine addinv, but E and C2
! are handled explictly. In all cases, the names have been
! chosen to closely follow the tables of Altmann and Herzig.
! The subroutine relies on the ASCII collating sequence.
!
! namold old name
! namnew new name
! group name of the point group
! naxis order of the main axis
! appinv apply inversion (evaluated only for certain groups !)
!
! ... subroutines called
! addinv
! ... integer
integer possig, poscar, n, poskup
! ... character
character(len=8) namcha
character(len=3) kvalue
!
if (group(1:1) .eq. 'S') then ! S2n
!... groups S2n, n even
!... apply inversion to proper rotations
if (namold(1:1) .eq. 'E') then
namcha = 'i '
else
call addinv (namold,namcha)
end if
else if (group(1:2) .eq. 'D2') then ! D2, D2h
!... groups D2, D2h
!... apply inversion to proper rotations, use special names
if (namold(1:3) .eq. 'C2 ') then
namcha = 'C2z'
else if (namold(1:5) .eq. 'C2,1''') then
namcha = 'C2x'
else if (namold(1:5) .eq. 'C2,2''') then
namcha = 'C2y'
else if (namold(1:1) .eq. 'E') then
namcha = 'i'
else if (namold(1:3) .eq. 'C2z') then
namcha = 'sigz'
else if (namold(1:3) .eq. 'C2x') then
namcha = 'sigx'
else if (namold(1:3) .eq. 'C2y') then
namcha = 'sigy'
end if
else if ( group(1:1).eq.'D' .and. naxis.gt.2 .and. &
& mod(naxis,2).eq.0 .and. .not.appinv ) then ! Dn, n>2
!... groups Dn, Dnh and Dnd, n even and n > 2
!... generates the labels for the second class C2,k" of C2 operations
!... besides C2,k'
poscar = index(namold,',')
possig = index(namold,'''')
n = ichar(namold(poscar+1:poscar+1)) - 48
if ( poscar+1 .lt. possig-1 ) then
n = n*10 + ichar(namold(poscar+2:poscar+2)) - 48
end if
n = n - naxis/2
namcha = namold(:poscar)//char(48+n)//"''"
else if ( group(1:1).eq.'D' .and. naxis.gt.2 .and. &
& index(group,'H') .gt. 0 ) then ! Dnh, n>2
!... groups Dnh, n even and n > 2
!... apply inversion to proper rotations, generate labels for the
!... two sets of vertical mirror planes, sigv and sigd
poscar = index(namold,',')
if (poscar .eq. 0 ) then
call addinv (namold,namcha)
else
possig = index(namold,'''')
namcha = 'sig '//namold(poscar+1:poscar+1)
if ( mod(naxis,4) .eq. 0 ) then
if ( possig .gt. 0 ) then
namcha(4:4) = 'V'
else
namcha(4:4) = 'D'
end if
else
if ( possig .gt. 0 ) then
namcha(4:4) = 'D'
else
namcha(4:4) = 'V'
end if
end if
end if
else if ( group(1:1).eq.'D' .and. mod(naxis,2).ne.0 &
& .and. index(group(2:),'D') .gt. 0 ) then ! Dnd, n odd
!... groups Dnd, n odd and n > 2
!... apply inversion to proper rotations, generate labels for the
!... two class of vertical mirror planes, sigd.
poscar = index(namold,',')
if (poscar .eq. 0 ) then
call addinv (namold,namcha)
else
possig = index(namold,'''')
namcha = 'sigd'//namold(poscar+1:poscar+1)
end if
else if ( group(1:1).eq.'C' .and. mod(naxis,2).eq.0 &
& .and. index(group,'V') .gt. 0 ) then ! Cnv, n even
!... groups Cnv, n even
!... generate labels for the two sets of vertical mirror planes,
!... sigvk' and sigvk", C2v is handled explicitly.
if ( naxis .eq. 2 ) then
if ( namold(1:5) .eq. 'C2,1''') then
namcha = 'sigx'