Merge pull request #1648 from athomps/add_w_l_orientorder
Add w l orientorder
This commit is contained in:
Axel Kohlmeyer
@ -19,6 +19,8 @@ keyword = {cutoff} or {nnn} or {degrees} or {components}
|
||||
{cutoff} value = distance cutoff
|
||||
{nnn} value = number of nearest neighbors
|
||||
{degrees} values = nlvalues, l1, l2,...
|
||||
{wl} value = yes or no
|
||||
{wl/hat} value = yes or no
|
||||
{components} value = ldegree :pre
|
||||
|
||||
:ule
|
||||
@ -27,7 +29,8 @@ keyword = {cutoff} or {nnn} or {degrees} or {components}
|
||||
|
||||
compute 1 all orientorder/atom
|
||||
compute 1 all orientorder/atom degrees 5 4 6 8 10 12 nnn NULL cutoff 1.5
|
||||
compute 1 all orientorder/atom degrees 4 6 components 6 nnn NULL cutoff 3.0 :pre
|
||||
compute 1 all orientorder/atom wl/hat yes
|
||||
compute 1 all orientorder/atom components 6 :pre
|
||||
|
||||
[Description:]
|
||||
|
||||
@ -48,7 +51,7 @@ neighbors of the central atom.
|
||||
The angles theta and phi are the standard spherical polar angles
|
||||
defining the direction of the bond vector {rij}.
|
||||
The second equation defines {Ql}, which is a
|
||||
rotationally invariant scalar quantity obtained by summing
|
||||
rotationally invariant non-negative amplitude obtained by summing
|
||||
over all the components of degree {l}.
|
||||
|
||||
The optional keyword {cutoff} defines the distance cutoff
|
||||
@ -63,7 +66,7 @@ specified distance cutoff are used.
|
||||
|
||||
The optional keyword {degrees} defines the list of order parameters to
|
||||
be computed. The first argument {nlvalues} is the number of order
|
||||
parameters. This is followed by that number of integers giving the
|
||||
parameters. This is followed by that number of non-negative integers giving the
|
||||
degree of each order parameter. Because {Q}2 and all odd-degree order
|
||||
parameters are zero for atoms in cubic crystals (see
|
||||
"Steinhardt"_#Steinhardt), the default order parameters are {Q}4,
|
||||
@ -71,7 +74,20 @@ parameters are zero for atoms in cubic crystals (see
|
||||
= sqrt(7/3)/8 = 0.19094.... The numerical values of all order
|
||||
parameters up to {Q}12 for a range of commonly encountered
|
||||
high-symmetry structures are given in Table I of "Mickel et
|
||||
al."_#Mickel.
|
||||
al."_#Mickel, and these can be reproduced with this compute
|
||||
|
||||
The optional keyword {wl} will output the third-order invariants {Wl}
|
||||
(see Eq. 1.4 in "Steinhardt"_#Steinhardt) for the same degrees as
|
||||
for the {Ql} parameters. For the FCC crystal with {nnn} =12,
|
||||
{W}4 = -sqrt(14/143).(49/4096)/Pi^1.5 = -0.0006722136...
|
||||
|
||||
The optional keyword {wl/hat} will output the normalized third-order
|
||||
invariants {Wlhat} (see Eq. 2.2 in "Steinhardt"_#Steinhardt)
|
||||
for the same degrees as for the {Ql} parameters. For the FCC crystal
|
||||
with {nnn} =12, {W}4hat = -7/3*sqrt(2/429) = -0.159317...The numerical
|
||||
values of {Wlhat} for a range of commonly encountered high-symmetry
|
||||
structures are given in Table I of "Steinhardt"_#Steinhardt, and these
|
||||
can be reproduced with this keyword.
|
||||
|
||||
The optional keyword {components} will output the components of the
|
||||
normalized complex vector {Ybar_lm} of degree {ldegree}, which must be
|
||||
@ -82,7 +98,7 @@ particles, as discussed in "ten Wolde"_#tenWolde2.
|
||||
|
||||
The value of {Ql} is set to zero for atoms not in the
|
||||
specified compute group, as well as for atoms that have less than
|
||||
{nnn} neighbors within the distance cutoff.
|
||||
{nnn} neighbors within the distance cutoff, unless {nnn} is NULL.
|
||||
|
||||
The neighbor list needed to compute this quantity is constructed each
|
||||
time the calculation is performed (i.e. each time a snapshot of atoms
|
||||
@ -108,6 +124,12 @@ This compute calculates a per-atom array with {nlvalues} columns,
|
||||
giving the {Ql} values for each atom, which are real numbers on the
|
||||
range 0 <= {Ql} <= 1.
|
||||
|
||||
If the keyword {wl} is set to yes, then the {Wl} values for each
|
||||
atom will be added to the output array, which are real numbers.
|
||||
|
||||
If the keyword {wl/hat} is set to yes, then the {Wl_hat}
|
||||
values for each atom will be added to the output array, which are real numbers.
|
||||
|
||||
If the keyword {components} is set, then the real and imaginary parts
|
||||
of each component of (normalized) {Ybar_lm} will be added to the
|
||||
output array in the following order: Re({Ybar_-m}) Im({Ybar_-m})
|
||||
@ -130,7 +152,8 @@ hexorder/atom"_compute_hexorder_atom.html
|
||||
[Default:]
|
||||
|
||||
The option defaults are {cutoff} = pair style cutoff, {nnn} = 12,
|
||||
{degrees} = 5 4 6 8 10 12 i.e. {Q}4, {Q}6, {Q}8, {Q}10, and {Q}12.
|
||||
{degrees} = 5 4 6 8 10 12 i.e. {Q}4, {Q}6, {Q}8, {Q}10, and {Q}12,
|
||||
{wl} = no, {wl/hat} = no, and {components} off
|
||||
|
||||
:line
|
||||
|
||||
|
||||
91
examples/steinhardt/in.bcc
Normal file
91
examples/steinhardt/in.bcc
Normal file
@ -0,0 +1,91 @@
|
||||
# Steinhardt-Nelson bond orientational order parameters for BCC
|
||||
|
||||
variable rcut equal 3.0
|
||||
|
||||
boundary p p p
|
||||
|
||||
atom_style atomic
|
||||
neighbor 0.3 bin
|
||||
neigh_modify delay 5
|
||||
|
||||
# create geometry
|
||||
|
||||
lattice bcc 1.0
|
||||
region box block 0 3 0 3 0 3
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
|
||||
mass 1 1.0
|
||||
|
||||
# LJ potentials
|
||||
|
||||
pair_style lj/cut ${rcut}
|
||||
pair_coeff * * 1.0 1.0 ${rcut}
|
||||
|
||||
# 14 neighbors, perfect crystal
|
||||
|
||||
compute qlwlhat all orientorder/atom degrees 6 2 4 6 8 10 12 nnn 14 wl/hat yes
|
||||
compute avql all reduce ave c_qlwlhat[1] c_qlwlhat[2] c_qlwlhat[3] c_qlwlhat[4] c_qlwlhat[5] c_qlwlhat[6]
|
||||
compute avwlhat all reduce ave c_qlwlhat[7] c_qlwlhat[8] c_qlwlhat[9] c_qlwlhat[10] c_qlwlhat[11] c_qlwlhat[12]
|
||||
|
||||
thermo_style custom step temp epair etotal c_avql[*] c_avwlhat[*]
|
||||
|
||||
run 0
|
||||
|
||||
# check Q_l values
|
||||
|
||||
print " "
|
||||
print "*******************************************************************"
|
||||
print " "
|
||||
print "Comparison with reference values of Q_l "
|
||||
print " [Table I in W. Mickel, S. C. Kapfer,"
|
||||
print " G. E. Schroeder-Turkand, K. Mecke, "
|
||||
print " J. Chem. Phys. 138, 044501 (2013).]"
|
||||
print " "
|
||||
|
||||
variable q2ref equal 0.0
|
||||
variable q4ref equal 0.036
|
||||
variable q6ref equal 0.511
|
||||
variable q8ref equal 0.429
|
||||
variable q10ref equal 0.195
|
||||
variable q12ref equal 0.405
|
||||
|
||||
variable q2 equal c_avql[1]
|
||||
variable q4 equal c_avql[2]
|
||||
variable q6 equal c_avql[3]
|
||||
variable q8 equal c_avql[4]
|
||||
variable q10 equal c_avql[5]
|
||||
variable q12 equal c_avql[6]
|
||||
|
||||
print "q2 = $(v_q2:%10.6f) delta = $(v_q2-v_q2ref:%10.4f)"
|
||||
print "q4 = $(v_q4:%10.6f) delta = $(v_q4-v_q4ref:%10.4f)"
|
||||
print "q6 = $(v_q6:%10.6f) delta = $(v_q6-v_q6ref:%10.4f)"
|
||||
print "q8 = $(v_q8:%10.6f) delta = $(v_q8-v_q8ref:%10.4f)"
|
||||
print "q10 = $(v_q10:%10.6f) delta = $(v_q10-v_q10ref:%10.4f)"
|
||||
print "q12 = $(v_q12:%10.6f) delta = $(v_q12-v_q12ref:%10.4f)"
|
||||
|
||||
# check W_l_hat values
|
||||
|
||||
print " "
|
||||
print "Comparison with reference values of W_l_hat"
|
||||
print " [Table I in P. Steinhardt, D. Nelson, and M. Ronchetti, "
|
||||
print " Phys. Rev. B 28, 784 (1983).]"
|
||||
print " "
|
||||
|
||||
variable w4hatref equal 0.159317
|
||||
variable w6hatref equal 0.013161
|
||||
variable w8hatref equal -0.058455
|
||||
variable w10hatref equal -0.090130
|
||||
|
||||
variable w4hat equal c_avwlhat[2]
|
||||
variable w6hat equal c_avwlhat[3]
|
||||
variable w8hat equal c_avwlhat[4]
|
||||
variable w10hat equal c_avwlhat[5]
|
||||
|
||||
print "w4hat = $(v_w4hat:%10.6f) delta = $(v_w4hat-v_w4hatref:%10.6f)"
|
||||
print "w6hat = $(v_w6hat:%10.6f) delta = $(v_w6hat-v_w6hatref:%10.6f)"
|
||||
print "w8hat = $(v_w8hat:%10.6f) delta = $(v_w8hat-v_w8hatref:%10.6f)"
|
||||
print "w10hat = $(v_w10hat:%10.6f) delta = $(v_w10hat-v_w10hatref:%10.6f)"
|
||||
print " "
|
||||
print "*******************************************************************"
|
||||
print " "
|
||||
88
examples/steinhardt/in.fcc
Normal file
88
examples/steinhardt/in.fcc
Normal file
@ -0,0 +1,88 @@
|
||||
# Steinhardt-Nelson bond orientational order parameters for FCC
|
||||
|
||||
variable rcut equal 3.0
|
||||
|
||||
boundary p p p
|
||||
|
||||
atom_style atomic
|
||||
neighbor 0.3 bin
|
||||
neigh_modify delay 5
|
||||
|
||||
# create geometry
|
||||
|
||||
lattice fcc 1.0
|
||||
region box block 0 3 0 3 0 3
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
|
||||
mass 1 1.0
|
||||
|
||||
# LJ potentials
|
||||
|
||||
pair_style lj/cut ${rcut}
|
||||
pair_coeff * * 1.0 1.0 ${rcut}
|
||||
|
||||
# 12 neighbors, perfect crystal
|
||||
|
||||
compute qlwlhat all orientorder/atom wl/hat yes
|
||||
compute avql all reduce ave c_qlwlhat[1] c_qlwlhat[2] c_qlwlhat[3] c_qlwlhat[4] c_qlwlhat[5]
|
||||
compute avwlhat all reduce ave c_qlwlhat[6] c_qlwlhat[7] c_qlwlhat[8] c_qlwlhat[9] c_qlwlhat[10]
|
||||
|
||||
thermo_style custom step temp epair etotal c_avql[*] c_avwlhat[*]
|
||||
|
||||
run 0
|
||||
|
||||
# check Q_l values
|
||||
|
||||
print " "
|
||||
print "*******************************************************************"
|
||||
print " "
|
||||
print "Comparison with reference values of Q_l "
|
||||
print " [Table I in W. Mickel, S. C. Kapfer,"
|
||||
print " G. E. Schroeder-Turkand, K. Mecke, "
|
||||
print " J. Chem. Phys. 138, 044501 (2013).]"
|
||||
print " "
|
||||
|
||||
variable q4ref equal 0.190
|
||||
variable q6ref equal 0.575
|
||||
variable q8ref equal 0.404
|
||||
variable q10ref equal 0.013
|
||||
variable q12ref equal 0.600
|
||||
|
||||
variable q4 equal c_avql[1]
|
||||
variable q6 equal c_avql[2]
|
||||
variable q8 equal c_avql[3]
|
||||
variable q10 equal c_avql[4]
|
||||
variable q12 equal c_avql[5]
|
||||
|
||||
print "q4 = $(v_q4:%10.6f) delta = $(v_q4-v_q4ref:%10.4f)"
|
||||
print "q6 = $(v_q6:%10.6f) delta = $(v_q6-v_q6ref:%10.4f)"
|
||||
print "q8 = $(v_q8:%10.6f) delta = $(v_q8-v_q8ref:%10.4f)"
|
||||
print "q10 = $(v_q10:%10.6f) delta = $(v_q10-v_q10ref:%10.4f)"
|
||||
print "q12 = $(v_q12:%10.6f) delta = $(v_q12-v_q12ref:%10.4f)"
|
||||
|
||||
# check W_l_hat values
|
||||
|
||||
print " "
|
||||
print "Comparison with reference values of W_l_hat"
|
||||
print " [Table I in P. Steinhardt, D. Nelson, and M. Ronchetti, "
|
||||
print " Phys. Rev. B 28, 784 (1983).]"
|
||||
print " "
|
||||
|
||||
variable w4hatref equal -0.159316
|
||||
variable w6hatref equal -0.013161
|
||||
variable w8hatref equal 0.058454
|
||||
variable w10hatref equal -0.090128
|
||||
|
||||
variable w4hat equal c_avwlhat[1]
|
||||
variable w6hat equal c_avwlhat[2]
|
||||
variable w8hat equal c_avwlhat[3]
|
||||
variable w10hat equal c_avwlhat[4]
|
||||
|
||||
print "w4hat = $(v_w4hat:%10.6f) delta = $(v_w4hat-v_w4hatref:%10.6f)"
|
||||
print "w6hat = $(v_w6hat:%10.6f) delta = $(v_w6hat-v_w6hatref:%10.6f)"
|
||||
print "w8hat = $(v_w8hat:%10.6f) delta = $(v_w8hat-v_w8hatref:%10.6f)"
|
||||
print "w10hat = $(v_w10hat:%10.6f) delta = $(v_w10hat-v_w10hatref:%10.6f)"
|
||||
print " "
|
||||
print "*******************************************************************"
|
||||
print " "
|
||||
106
examples/steinhardt/in.icos
Normal file
106
examples/steinhardt/in.icos
Normal file
@ -0,0 +1,106 @@
|
||||
# Steinhardt-Nelson bond orientational order parameters for icosahedral cluster
|
||||
# W_6_hat is sensitive to icosohedral order
|
||||
|
||||
variable rcut equal 1.2 # a bit bigger than LJ Rmin
|
||||
variable rcutred equal 0.75 # a bit bigger than 1/sqrt(2)
|
||||
|
||||
# create a perfect fcc crystallite
|
||||
|
||||
atom_style atomic
|
||||
boundary s s s
|
||||
lattice fcc 1.0 # neighbors at LJ Rmin
|
||||
region box block 0 2 0 2 0 2
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
mass 1 1.0
|
||||
|
||||
region centralatom sphere 1 1 1 0.0 side in
|
||||
group centralatom region centralatom
|
||||
|
||||
region mysphere sphere 1 1 1 ${rcutred} side out
|
||||
delete_atoms region mysphere
|
||||
|
||||
# LJ potential
|
||||
|
||||
pair_style lj/cut 100.0
|
||||
pair_coeff * * 1.0 1.0 100.0
|
||||
|
||||
# define output for central atom
|
||||
|
||||
compute qlwlhat all orientorder/atom wl/hat yes cutoff ${rcut} nnn NULL
|
||||
compute avql centralatom reduce ave c_qlwlhat[1] c_qlwlhat[2] c_qlwlhat[3] c_qlwlhat[4] c_qlwlhat[5]
|
||||
compute avwlhat centralatom reduce ave c_qlwlhat[6] c_qlwlhat[7] c_qlwlhat[8] c_qlwlhat[9] c_qlwlhat[10]
|
||||
variable q6 equal c_avql[2]
|
||||
variable w6hat equal c_avwlhat[2]
|
||||
|
||||
compute mype all pe/atom
|
||||
compute centralatompe centralatom reduce ave c_mype
|
||||
|
||||
# gently equilibrate the crystallite
|
||||
|
||||
velocity all create 0.001 482748
|
||||
fix 1 all nve
|
||||
neighbor 0.3 bin
|
||||
neigh_modify every 1 check no delay 0
|
||||
timestep 0.003
|
||||
thermo_style custom step temp epair etotal c_centralatompe v_q6 v_w6hat
|
||||
thermo 10
|
||||
|
||||
run 10
|
||||
|
||||
# quench to icosehedral cluster
|
||||
|
||||
minimize 1.0e-10 1.0e-6 100 1000
|
||||
|
||||
# check Q_l values
|
||||
|
||||
print " "
|
||||
print "*******************************************************************"
|
||||
print " "
|
||||
print "Comparison with reference values of Q_l "
|
||||
print " [Table I in W. Mickel, S. C. Kapfer,"
|
||||
print " G. E. Schroeder-Turkand, K. Mecke, "
|
||||
print " J. Chem. Phys. 138, 044501 (2013).]"
|
||||
print " "
|
||||
|
||||
variable q4ref equal 0.0
|
||||
variable q6ref equal 0.663
|
||||
variable q8ref equal 0.0
|
||||
variable q10ref equal 0.363
|
||||
variable q12ref equal 0.585
|
||||
|
||||
variable q4 equal c_avql[1]
|
||||
variable q6 equal c_avql[2]
|
||||
variable q8 equal c_avql[3]
|
||||
variable q10 equal c_avql[4]
|
||||
variable q12 equal c_avql[5]
|
||||
|
||||
print "q4 = $(v_q4:%10.6f) delta = $(v_q4-v_q4ref:%10.4f)"
|
||||
print "q6 = $(v_q6:%10.6f) delta = $(v_q6-v_q6ref:%10.4f)"
|
||||
print "q8 = $(v_q8:%10.6f) delta = $(v_q8-v_q8ref:%10.4f)"
|
||||
print "q10 = $(v_q10:%10.6f) delta = $(v_q10-v_q10ref:%10.4f)"
|
||||
print "q12 = $(v_q12:%10.6f) delta = $(v_q12-v_q12ref:%10.4f)"
|
||||
|
||||
# check W_l_hat values
|
||||
|
||||
print " "
|
||||
print "Comparison with reference values of W_l_hat"
|
||||
print " [Table I in P. Steinhardt, D. Nelson, and M. Ronchetti, "
|
||||
print " Phys. Rev. B 28, 784 (1983).]"
|
||||
print " "
|
||||
|
||||
variable w6hatref equal -0.169754
|
||||
variable w10hatref equal -0.093967
|
||||
|
||||
variable w4hat equal c_avwlhat[1]
|
||||
variable w6hat equal c_avwlhat[2]
|
||||
variable w8hat equal c_avwlhat[3]
|
||||
variable w10hat equal c_avwlhat[4]
|
||||
variable w12hat equal c_avwlhat[5]
|
||||
|
||||
print "w6hat = $(v_w6hat:%10.6f) delta = $(v_w6hat-v_w6hatref:%10.6f)"
|
||||
print "w10hat = $(v_w10hat:%10.6f) delta = $(v_w10hat-v_w10hatref:%10.6f)"
|
||||
print " "
|
||||
print "*******************************************************************"
|
||||
print " "
|
||||
|
||||
@ -43,12 +43,14 @@ using namespace std;
|
||||
#define MY_EPSILON (10.0*2.220446049250313e-16)
|
||||
#endif
|
||||
|
||||
#define QEPSILON 1.0e-6
|
||||
|
||||
/* ---------------------------------------------------------------------- */
|
||||
|
||||
ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg) :
|
||||
Compute(lmp, narg, arg),
|
||||
qlist(NULL), distsq(NULL), nearest(NULL), rlist(NULL),
|
||||
qnarray(NULL), qnm_r(NULL), qnm_i(NULL)
|
||||
qnarray(NULL), qnm_r(NULL), qnm_i(NULL), cglist(NULL)
|
||||
{
|
||||
if (narg < 3 ) error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
|
||||
@ -56,6 +58,8 @@ ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg
|
||||
|
||||
nnn = 12;
|
||||
cutsq = 0.0;
|
||||
wlflag = 0;
|
||||
wlhatflag = 0;
|
||||
qlcompflag = 0;
|
||||
|
||||
// specify which orders to request
|
||||
@ -96,27 +100,39 @@ ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg
|
||||
if (iarg+nqlist > narg)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
qmax = 0;
|
||||
for (int iw = 0; iw < nqlist; iw++) {
|
||||
qlist[iw] = force->numeric(FLERR,arg[iarg+iw]);
|
||||
if (qlist[iw] < 0)
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
qlist[il] = force->numeric(FLERR,arg[iarg+il]);
|
||||
if (qlist[il] < 0)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
if (qlist[iw] > qmax) qmax = qlist[iw];
|
||||
if (qlist[il] > qmax) qmax = qlist[il];
|
||||
}
|
||||
iarg += nqlist;
|
||||
} else if (strcmp(arg[iarg],"wl") == 0) {
|
||||
if (iarg+2 > narg)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
if (strcmp(arg[iarg+1],"yes") == 0) wlflag = 1;
|
||||
else if (strcmp(arg[iarg+1],"no") == 0) wlflag = 0;
|
||||
else error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
iarg += 2;
|
||||
} else if (strcmp(arg[iarg],"wl/hat") == 0) {
|
||||
if (iarg+2 > narg)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
if (strcmp(arg[iarg+1],"yes") == 0) wlhatflag = 1;
|
||||
else if (strcmp(arg[iarg+1],"no") == 0) wlhatflag = 0;
|
||||
else error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
iarg += 2;
|
||||
} else if (strcmp(arg[iarg],"components") == 0) {
|
||||
qlcompflag = 1;
|
||||
if (iarg+2 > narg)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
qlcomp = force->numeric(FLERR,arg[iarg+1]);
|
||||
if (qlcomp <= 0)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
iqlcomp = -1;
|
||||
for (int iw = 0; iw < nqlist; iw++)
|
||||
if (qlcomp == qlist[iw]) {
|
||||
iqlcomp = iw;
|
||||
for (int il = 0; il < nqlist; il++)
|
||||
if (qlcomp == qlist[il]) {
|
||||
iqlcomp = il;
|
||||
break;
|
||||
}
|
||||
if (iqlcomp < 0)
|
||||
if (iqlcomp == -1)
|
||||
error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
iarg += 2;
|
||||
} else if (strcmp(arg[iarg],"cutoff") == 0) {
|
||||
@ -130,8 +146,10 @@ ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg
|
||||
} else error->all(FLERR,"Illegal compute orientorder/atom command");
|
||||
}
|
||||
|
||||
if (qlcompflag) ncol = nqlist + 2*(2*qlcomp+1);
|
||||
else ncol = nqlist;
|
||||
ncol = nqlist;
|
||||
if (wlflag) ncol += nqlist;
|
||||
if (wlhatflag) ncol += nqlist;
|
||||
if (qlcompflag) ncol += 2*(2*qlcomp+1);
|
||||
|
||||
peratom_flag = 1;
|
||||
size_peratom_cols = ncol;
|
||||
@ -151,7 +169,7 @@ ComputeOrientOrderAtom::~ComputeOrientOrderAtom()
|
||||
memory->destroy(qlist);
|
||||
memory->destroy(qnm_r);
|
||||
memory->destroy(qnm_i);
|
||||
|
||||
memory->destroy(cglist);
|
||||
}
|
||||
|
||||
/* ---------------------------------------------------------------------- */
|
||||
@ -166,8 +184,8 @@ void ComputeOrientOrderAtom::init()
|
||||
error->all(FLERR,"Compute orientorder/atom cutoff is "
|
||||
"longer than pairwise cutoff");
|
||||
|
||||
memory->create(qnm_r,qmax,2*qmax+1,"orientorder/atom:qnm_r");
|
||||
memory->create(qnm_i,qmax,2*qmax+1,"orientorder/atom:qnm_i");
|
||||
memory->create(qnm_r,nqlist,2*qmax+1,"orientorder/atom:qnm_r");
|
||||
memory->create(qnm_i,nqlist,2*qmax+1,"orientorder/atom:qnm_i");
|
||||
|
||||
// need an occasional full neighbor list
|
||||
|
||||
@ -183,6 +201,8 @@ void ComputeOrientOrderAtom::init()
|
||||
if (strcmp(modify->compute[i]->style,"orientorder/atom") == 0) count++;
|
||||
if (count > 1 && comm->me == 0)
|
||||
error->warning(FLERR,"More than one compute orientorder/atom");
|
||||
|
||||
if (wlflag || wlhatflag) init_clebsch_gordan();
|
||||
}
|
||||
|
||||
/* ---------------------------------------------------------------------- */
|
||||
@ -274,8 +294,8 @@ void ComputeOrientOrderAtom::compute_peratom()
|
||||
// if not nnn neighbors, order parameter = 0;
|
||||
|
||||
if ((ncount == 0) || (ncount < nnn)) {
|
||||
for (int iw = 0; iw < nqlist; iw++)
|
||||
qn[iw] = 0.0;
|
||||
for (int jj = 0; jj < ncol; jj++)
|
||||
qn[jj] = 0.0;
|
||||
continue;
|
||||
}
|
||||
|
||||
@ -287,6 +307,7 @@ void ComputeOrientOrderAtom::compute_peratom()
|
||||
}
|
||||
|
||||
calc_boop(rlist, ncount, qn, qlist, nqlist);
|
||||
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -403,13 +424,12 @@ void ComputeOrientOrderAtom::select3(int k, int n, double *arr, int *iarr, doubl
|
||||
void ComputeOrientOrderAtom::calc_boop(double **rlist,
|
||||
int ncount, double qn[],
|
||||
int qlist[], int nqlist) {
|
||||
for (int iw = 0; iw < nqlist; iw++) {
|
||||
int n = qlist[iw];
|
||||
|
||||
qn[iw] = 0.0;
|
||||
for(int m = 0; m < 2*n+1; m++) {
|
||||
qnm_r[iw][m] = 0.0;
|
||||
qnm_i[iw][m] = 0.0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for(int m = 0; m < 2*l+1; m++) {
|
||||
qnm_r[il][m] = 0.0;
|
||||
qnm_i[il][m] = 0.0;
|
||||
}
|
||||
}
|
||||
|
||||
@ -433,24 +453,24 @@ void ComputeOrientOrderAtom::calc_boop(double **rlist,
|
||||
expphi_i *= rxymaginv;
|
||||
}
|
||||
|
||||
for (int iw = 0; iw < nqlist; iw++) {
|
||||
int n = qlist[iw];
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
|
||||
qnm_r[iw][n] += polar_prefactor(n, 0, costheta);
|
||||
qnm_r[il][l] += polar_prefactor(l, 0, costheta);
|
||||
double expphim_r = expphi_r;
|
||||
double expphim_i = expphi_i;
|
||||
for(int m = 1; m <= +n; m++) {
|
||||
double prefactor = polar_prefactor(n, m, costheta);
|
||||
for(int m = 1; m <= +l; m++) {
|
||||
double prefactor = polar_prefactor(l, m, costheta);
|
||||
double c_r = prefactor * expphim_r;
|
||||
double c_i = prefactor * expphim_i;
|
||||
qnm_r[iw][m+n] += c_r;
|
||||
qnm_i[iw][m+n] += c_i;
|
||||
qnm_r[il][m+l] += c_r;
|
||||
qnm_i[il][m+l] += c_i;
|
||||
if(m & 1) {
|
||||
qnm_r[iw][-m+n] -= c_r;
|
||||
qnm_i[iw][-m+n] += c_i;
|
||||
qnm_r[il][-m+l] -= c_r;
|
||||
qnm_i[il][-m+l] += c_i;
|
||||
} else {
|
||||
qnm_r[iw][-m+n] += c_r;
|
||||
qnm_i[iw][-m+n] -= c_i;
|
||||
qnm_r[il][-m+l] += c_r;
|
||||
qnm_i[il][-m+l] -= c_i;
|
||||
}
|
||||
double tmp_r = expphim_r*expphi_r - expphim_i*expphi_i;
|
||||
double tmp_i = expphim_r*expphi_i + expphim_i*expphi_r;
|
||||
@ -461,30 +481,110 @@ void ComputeOrientOrderAtom::calc_boop(double **rlist,
|
||||
}
|
||||
}
|
||||
|
||||
double fac = sqrt(MY_4PI) / ncount;
|
||||
double normfac = 0.0;
|
||||
for (int iw = 0; iw < nqlist; iw++) {
|
||||
int n = qlist[iw];
|
||||
// convert sums to averages
|
||||
|
||||
double facn = 1.0 / ncount;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for(int m = 0; m < 2*l+1; m++) {
|
||||
qnm_r[il][m] *= facn;
|
||||
qnm_i[il][m] *= facn;
|
||||
}
|
||||
}
|
||||
|
||||
// calculate Q_l
|
||||
// NOTE: optional W_l_hat and components of Q_qlcomp use these stored Q_l values
|
||||
|
||||
int jj = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
double qnormfac = sqrt(MY_4PI/(2*l+1));
|
||||
double qm_sum = 0.0;
|
||||
for(int m = 0; m < 2*n+1; m++) {
|
||||
qm_sum += qnm_r[iw][m]*qnm_r[iw][m] + qnm_i[iw][m]*qnm_i[iw][m];
|
||||
// printf("Ylm^2 = %d %d %g\n",n,m,
|
||||
// qnm_r[iw][m]*qnm_r[iw][m] + qnm_i[iw][m]*qnm_i[iw][m]);
|
||||
}
|
||||
qn[iw] = fac * sqrt(qm_sum / (2*n+1));
|
||||
if (qlcompflag && iqlcomp == iw) normfac = 1.0/sqrt(qm_sum);
|
||||
|
||||
for(int m = 0; m < 2*l+1; m++)
|
||||
qm_sum += qnm_r[il][m]*qnm_r[il][m] + qnm_i[il][m]*qnm_i[il][m];
|
||||
qn[jj++] = qnormfac * sqrt(qm_sum);
|
||||
}
|
||||
|
||||
// output of the complex vector
|
||||
// TODO:
|
||||
// 1. [done]Need to allocate extra memory in qnarray[] for this option
|
||||
// 2. [done]Need to add keyword option
|
||||
// 3. [done]Need to caclulate Clebsch-Gordan/Wigner 3j coefficients
|
||||
// (Can try getting them from boop.py first)
|
||||
// 5. [done]Compare to bcc values in /Users/athomps/netapp/codes/MatMiner/matminer/matminer/featurizers/boop.py
|
||||
// 6. [done]I get the right answer for W_l, but need to make sure that factor of 1/sqrt(l+1) is right for cglist
|
||||
// 7. Add documentation
|
||||
// 8. [done] run valgrind
|
||||
// 9. [done] Add Wlhat
|
||||
// 10. Update memory_usage()
|
||||
// 11. Add exact FCC values for W_4, W_4_hat
|
||||
|
||||
// calculate W_l
|
||||
|
||||
if (wlflag) {
|
||||
int idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
double wlsum = 0.0;
|
||||
for(int m1 = 0; m1 < 2*l+1; m1++) {
|
||||
for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
|
||||
int m = m1 + m2 - l;
|
||||
double qm1qm2_r = qnm_r[il][m1]*qnm_r[il][m2] - qnm_i[il][m1]*qnm_i[il][m2];
|
||||
double qm1qm2_i = qnm_r[il][m1]*qnm_i[il][m2] + qnm_i[il][m1]*qnm_r[il][m2];
|
||||
wlsum += (qm1qm2_r*qnm_r[il][m] + qm1qm2_i*qnm_i[il][m])*cglist[idxcg_count];
|
||||
idxcg_count++;
|
||||
}
|
||||
}
|
||||
qn[jj++] = wlsum/sqrt(2*l+1);
|
||||
}
|
||||
}
|
||||
|
||||
// calculate W_l_hat
|
||||
|
||||
if (wlhatflag) {
|
||||
int idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
double wlsum = 0.0;
|
||||
for(int m1 = 0; m1 < 2*l+1; m1++) {
|
||||
for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
|
||||
int m = m1 + m2 - l;
|
||||
double qm1qm2_r = qnm_r[il][m1]*qnm_r[il][m2] - qnm_i[il][m1]*qnm_i[il][m2];
|
||||
double qm1qm2_i = qnm_r[il][m1]*qnm_i[il][m2] + qnm_i[il][m1]*qnm_r[il][m2];
|
||||
wlsum += (qm1qm2_r*qnm_r[il][m] + qm1qm2_i*qnm_i[il][m])*cglist[idxcg_count];
|
||||
idxcg_count++;
|
||||
}
|
||||
}
|
||||
// Whats = [w/(q/np.sqrt(np.pi * 4 / (2 * l + 1)))**3 if abs(q) > 1.0e-6 else 0.0 for l,q,w in zip(range(1,max_l+1),Qs,Ws)]
|
||||
if (qn[il] < QEPSILON)
|
||||
qn[jj++] = 0.0;
|
||||
else {
|
||||
double qnormfac = sqrt(MY_4PI/(2*l+1));
|
||||
double qnfac = qnormfac/qn[il];
|
||||
qn[jj++] = wlsum/sqrt(2*l+1)*(qnfac*qnfac*qnfac);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Calculate components of Q_l, for l=qlcomp
|
||||
|
||||
if (qlcompflag) {
|
||||
int j = nqlist;
|
||||
for(int m = 0; m < 2*qlcomp+1; m++) {
|
||||
qn[j++] = qnm_r[iqlcomp][m] * normfac;
|
||||
qn[j++] = qnm_i[iqlcomp][m] * normfac;
|
||||
int il = iqlcomp;
|
||||
int l = qlcomp;
|
||||
if (qn[il] < QEPSILON)
|
||||
for(int m = 0; m < 2*l+1; m++) {
|
||||
qn[jj++] = 0.0;
|
||||
qn[jj++] = 0.0;
|
||||
}
|
||||
else {
|
||||
double qnormfac = sqrt(MY_4PI/(2*l+1));
|
||||
double qnfac = qnormfac/qn[il];
|
||||
for(int m = 0; m < 2*l+1; m++) {
|
||||
qn[jj++] = qnm_r[il][m] * qnfac;
|
||||
qn[jj++] = qnm_i[il][m] * qnfac;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
@ -542,3 +642,258 @@ double ComputeOrientOrderAtom::associated_legendre(int l, int m, double x)
|
||||
|
||||
return p;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
assign Clebsch-Gordan coefficients
|
||||
using the quasi-binomial formula VMK 8.2.1(3)
|
||||
specialized for case j1=j2=j=l
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void ComputeOrientOrderAtom::init_clebsch_gordan()
|
||||
{
|
||||
double sum,dcg,sfaccg, sfac1, sfac2;
|
||||
int m, aa2, bb2, cc2;
|
||||
int ifac, idxcg_count;
|
||||
|
||||
idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for(int m1 = 0; m1 < 2*l+1; m1++)
|
||||
for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++)
|
||||
idxcg_count++;
|
||||
}
|
||||
idxcg_max = idxcg_count;
|
||||
memory->create(cglist, idxcg_max, "computeorientorderatom:cglist");
|
||||
|
||||
idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for(int m1 = 0; m1 < 2*l+1; m1++) {
|
||||
aa2 = m1 - l;
|
||||
for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
|
||||
bb2 = m2 - l;
|
||||
m = aa2 + bb2 + l;
|
||||
|
||||
sum = 0.0;
|
||||
for (int z = MAX(0, MAX(-aa2, bb2));
|
||||
z <= MIN(l, MIN(l - aa2, l + bb2)); z++) {
|
||||
ifac = z % 2 ? -1 : 1;
|
||||
sum += ifac /
|
||||
(factorial(z) *
|
||||
factorial(l - z) *
|
||||
factorial(l - aa2 - z) *
|
||||
factorial(l + bb2 - z) *
|
||||
factorial(aa2 + z) *
|
||||
factorial(-bb2 + z));
|
||||
}
|
||||
|
||||
cc2 = m - l;
|
||||
sfaccg = sqrt(factorial(l + aa2) *
|
||||
factorial(l - aa2) *
|
||||
factorial(l + bb2) *
|
||||
factorial(l - bb2) *
|
||||
factorial(l + cc2) *
|
||||
factorial(l - cc2) *
|
||||
(2*l + 1));
|
||||
|
||||
sfac1 = factorial(3*l + 1);
|
||||
sfac2 = factorial(l);
|
||||
dcg = sqrt(sfac2*sfac2*sfac2 / sfac1);
|
||||
|
||||
cglist[idxcg_count] = sum * dcg * sfaccg;
|
||||
idxcg_count++;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
factorial n, wrapper for precomputed table
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
double ComputeOrientOrderAtom::factorial(int n)
|
||||
{
|
||||
if (n < 0 || n > nmaxfactorial) {
|
||||
char str[128];
|
||||
sprintf(str, "Invalid argument to factorial %d", n);
|
||||
error->all(FLERR, str);
|
||||
}
|
||||
|
||||
return nfac_table[n];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
factorial n table, size SNA::nmaxfactorial+1
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
const double ComputeOrientOrderAtom::nfac_table[] = {
|
||||
1,
|
||||
1,
|
||||
2,
|
||||
6,
|
||||
24,
|
||||
120,
|
||||
720,
|
||||
5040,
|
||||
40320,
|
||||
362880,
|
||||
3628800,
|
||||
39916800,
|
||||
479001600,
|
||||
6227020800,
|
||||
87178291200,
|
||||
1307674368000,
|
||||
20922789888000,
|
||||
355687428096000,
|
||||
6.402373705728e+15,
|
||||
1.21645100408832e+17,
|
||||
2.43290200817664e+18,
|
||||
5.10909421717094e+19,
|
||||
1.12400072777761e+21,
|
||||
2.5852016738885e+22,
|
||||
6.20448401733239e+23,
|
||||
1.5511210043331e+25,
|
||||
4.03291461126606e+26,
|
||||
1.08888694504184e+28,
|
||||
3.04888344611714e+29,
|
||||
8.8417619937397e+30,
|
||||
2.65252859812191e+32,
|
||||
8.22283865417792e+33,
|
||||
2.63130836933694e+35,
|
||||
8.68331761881189e+36,
|
||||
2.95232799039604e+38,
|
||||
1.03331479663861e+40,
|
||||
3.71993326789901e+41,
|
||||
1.37637530912263e+43,
|
||||
5.23022617466601e+44,
|
||||
2.03978820811974e+46,
|
||||
8.15915283247898e+47,
|
||||
3.34525266131638e+49,
|
||||
1.40500611775288e+51,
|
||||
6.04152630633738e+52,
|
||||
2.65827157478845e+54,
|
||||
1.1962222086548e+56,
|
||||
5.50262215981209e+57,
|
||||
2.58623241511168e+59,
|
||||
1.24139155925361e+61,
|
||||
6.08281864034268e+62,
|
||||
3.04140932017134e+64,
|
||||
1.55111875328738e+66,
|
||||
8.06581751709439e+67,
|
||||
4.27488328406003e+69,
|
||||
2.30843697339241e+71,
|
||||
1.26964033536583e+73,
|
||||
7.10998587804863e+74,
|
||||
4.05269195048772e+76,
|
||||
2.35056133128288e+78,
|
||||
1.3868311854569e+80,
|
||||
8.32098711274139e+81,
|
||||
5.07580213877225e+83,
|
||||
3.14699732603879e+85,
|
||||
1.98260831540444e+87,
|
||||
1.26886932185884e+89,
|
||||
8.24765059208247e+90,
|
||||
5.44344939077443e+92,
|
||||
3.64711109181887e+94,
|
||||
2.48003554243683e+96,
|
||||
1.71122452428141e+98,
|
||||
1.19785716699699e+100,
|
||||
8.50478588567862e+101,
|
||||
6.12344583768861e+103,
|
||||
4.47011546151268e+105,
|
||||
3.30788544151939e+107,
|
||||
2.48091408113954e+109,
|
||||
1.88549470166605e+111,
|
||||
1.45183092028286e+113,
|
||||
1.13242811782063e+115,
|
||||
8.94618213078297e+116,
|
||||
7.15694570462638e+118,
|
||||
5.79712602074737e+120,
|
||||
4.75364333701284e+122,
|
||||
3.94552396972066e+124,
|
||||
3.31424013456535e+126,
|
||||
2.81710411438055e+128,
|
||||
2.42270953836727e+130,
|
||||
2.10775729837953e+132,
|
||||
1.85482642257398e+134,
|
||||
1.65079551609085e+136,
|
||||
1.48571596448176e+138,
|
||||
1.3520015276784e+140,
|
||||
1.24384140546413e+142,
|
||||
1.15677250708164e+144,
|
||||
1.08736615665674e+146,
|
||||
1.03299784882391e+148,
|
||||
9.91677934870949e+149,
|
||||
9.61927596824821e+151,
|
||||
9.42689044888324e+153,
|
||||
9.33262154439441e+155,
|
||||
9.33262154439441e+157,
|
||||
9.42594775983835e+159,
|
||||
9.61446671503512e+161,
|
||||
9.90290071648618e+163,
|
||||
1.02990167451456e+166,
|
||||
1.08139675824029e+168,
|
||||
1.14628056373471e+170,
|
||||
1.22652020319614e+172,
|
||||
1.32464181945183e+174,
|
||||
1.44385958320249e+176,
|
||||
1.58824554152274e+178,
|
||||
1.76295255109024e+180,
|
||||
1.97450685722107e+182,
|
||||
2.23119274865981e+184,
|
||||
2.54355973347219e+186,
|
||||
2.92509369349301e+188,
|
||||
3.3931086844519e+190,
|
||||
3.96993716080872e+192,
|
||||
4.68452584975429e+194,
|
||||
5.5745857612076e+196,
|
||||
6.68950291344912e+198,
|
||||
8.09429852527344e+200,
|
||||
9.8750442008336e+202,
|
||||
1.21463043670253e+205,
|
||||
1.50614174151114e+207,
|
||||
1.88267717688893e+209,
|
||||
2.37217324288005e+211,
|
||||
3.01266001845766e+213,
|
||||
3.8562048236258e+215,
|
||||
4.97450422247729e+217,
|
||||
6.46685548922047e+219,
|
||||
8.47158069087882e+221,
|
||||
1.118248651196e+224,
|
||||
1.48727070609069e+226,
|
||||
1.99294274616152e+228,
|
||||
2.69047270731805e+230,
|
||||
3.65904288195255e+232,
|
||||
5.01288874827499e+234,
|
||||
6.91778647261949e+236,
|
||||
9.61572319694109e+238,
|
||||
1.34620124757175e+241,
|
||||
1.89814375907617e+243,
|
||||
2.69536413788816e+245,
|
||||
3.85437071718007e+247,
|
||||
5.5502938327393e+249,
|
||||
8.04792605747199e+251,
|
||||
1.17499720439091e+254,
|
||||
1.72724589045464e+256,
|
||||
2.55632391787286e+258,
|
||||
3.80892263763057e+260,
|
||||
5.71338395644585e+262,
|
||||
8.62720977423323e+264,
|
||||
1.31133588568345e+267,
|
||||
2.00634390509568e+269,
|
||||
3.08976961384735e+271,
|
||||
4.78914290146339e+273,
|
||||
7.47106292628289e+275,
|
||||
1.17295687942641e+278,
|
||||
1.85327186949373e+280,
|
||||
2.94670227249504e+282,
|
||||
4.71472363599206e+284,
|
||||
7.59070505394721e+286,
|
||||
1.22969421873945e+289,
|
||||
2.0044015765453e+291,
|
||||
3.28721858553429e+293,
|
||||
5.42391066613159e+295,
|
||||
9.00369170577843e+297,
|
||||
1.503616514865e+300, // nmaxfactorial = 167
|
||||
};
|
||||
|
||||
|
||||
@ -33,7 +33,7 @@ class ComputeOrientOrderAtom : public Compute {
|
||||
void compute_peratom();
|
||||
double memory_usage();
|
||||
double cutsq;
|
||||
int iqlcomp, qlcomp, qlcompflag;
|
||||
int iqlcomp, qlcomp, qlcompflag, wlflag, wlhatflag;
|
||||
int *qlist;
|
||||
int nqlist;
|
||||
|
||||
@ -55,6 +55,13 @@ class ComputeOrientOrderAtom : public Compute {
|
||||
|
||||
double polar_prefactor(int, int, double);
|
||||
double associated_legendre(int, int, double);
|
||||
|
||||
static const int nmaxfactorial = 167;
|
||||
static const double nfac_table[];
|
||||
double factorial(int);
|
||||
void init_clebsch_gordan();
|
||||
double *cglist; // Clebsch-Gordan coeffs
|
||||
int idxcg_max;
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user