# 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 " "