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/usr/share/psi4/samples/fd-freq-energy/test.in is in psi4-data 1:1.1-5.

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#! SCF STO-3G finite-difference frequencies from energies

molecule h2o {
  symmetry c1
  O
  H 1 0.9894093
  H 1 0.9894093 2 100.02688
}

set {
  basis sto-3g
  d_convergence 11
  scf_type pk
}

# Test against Analytic second derivatives from PSI3. #TEST
anal_freqs = psi4.Vector(3)  #TEST
anal_freqs.set(0, 0, 2170.045) #TEST
anal_freqs.set(0, 1, 4140.001) #TEST
anal_freqs.set(0, 2, 4391.065) #TEST

# PSI3 3-point formula:  #TEST
# A1 force constants     #TEST
#  0.3546775  -0.2277549 #TEST
# -0.2277549   0.4721543 #TEST
#                        #TEST
# B2 force constant      #TEST
#  0.7296851             #TEST

# Frequencies by 3-pt formula in C1 point group.
set { points 3 }
set findif {print 3}

scf_e, scf_wfn = frequencies('scf', dertype=0, return_wfn=True)

fd_freqs = scf_wfn.frequencies()                                                         #TEST
compare_vectors(anal_freqs, fd_freqs, 1,                                                 #TEST
 "Analytic vs. Finite-difference (3-pt.) frequencies from energies to 0.1 cm^-1 (C1) ")  #TEST


## Frequencies by 5-pt formula in C1 point group.
#molecule h2o {
#  symmetry c1
#  O
#  H 1 0.9894093
#  H 1 0.9894093 2 100.02688
#}
#
#set { points 5 }
#
#frequencies('scf',dertype=1)
#
#fd_freqs = psi4.wavefunction().frequencies()                                            #TEST
#compare_vectors(anal_freqs, fd_freqs, 3,                                                  #TEST
# "Analytic vs. Finite-difference (5-pt.) frequencies from energies to 0.001 cm^-1 (C1) ") #TEST
#
#clean()
#
## Frequencies by 3-pt formula in C2v.
#molecule h2o {
#  O
#  H 1 0.9894093
#  H 1 0.9894093 2 100.02688
#}
#
#set { points 3 }
#
#frequencies('scf',dertype=1)
#
#fd_freqs = psi4.wavefunction().frequencies()                                           #TEST
#compare_vectors(anal_freqs, fd_freqs, 1,                                                 #TEST
# "Analytic vs. Finite-difference (3-pt.) frequencies from energies to 0.1 cm^-1 (C2v) ") #TEST
#
## Frequencies by 5-pt formula in C2v.
#molecule h2o {
#  O
#  H 1 0.9894093
#  H 1 0.9894093 2 100.02688
#}
#
#set { points 5 }
#
#frequencies('scf',dertype=1)
#
#fd_freqs = psi4.wavefunction().frequencies()                                             #TEST
#compare_vectors(anal_freqs, fd_freqs, 3,                                                   #TEST
# "Analytic vs. Finite-difference (5-pt.) frequencies from energies to 0.001 cm^-1 (C2v) ") #TEST
#
## Frequencies by 5-pt formula for A1 irrep only.
#molecule h2o {
#  O
#  H 1 0.9894093
#  H 1 0.9894093 2 100.02688
#}
#
#set { points 5 }
#
#a1_freqs = psi4.Vector(2)          #TEST
#a1_freqs.set(0, 0, anal_freqs[0])    #TEST
#a1_freqs.set(0, 1, anal_freqs[1])    #TEST
#
#frequencies('scf', dertype=1, irrep=1)
#
#fd_freqs = psi4.wavefunction().frequencies()                                #TEST
#compare_vectors(a1_freqs, fd_freqs, 3, "A1 frequencies only (5-pt. formula)") #TEST
#
#del a1_freqs #TEST
#
#clean()
#
## Frequencies by 5-pt formula for B2 irrep only.
#molecule h2o {
#  O
#  H 1 0.9894093
#  H 1 0.9894093 2 100.02688
#}
#
#set { points 5 }
#
#b2_freqs = psi4.Vector(1)       #TEST
#b2_freqs.set(0, 0, anal_freqs[2]) #TEST
#
#frequencies('scf', dertype=1, irrep=4)
#
#fd_freqs = psi4.wavefunction().frequencies()                                #TEST
#compare_vectors(b2_freqs, fd_freqs, 3, "B2 frequencies only (5-pt. formula)") #TEST
#
#del b2_freqs   #TEST
#del anal_freqs #TEST
#clean()