import numpy as np
from esipy.tools import format_partition, find_multiplicity
[docs]def info_unrest(aom, molinfo, nfrags=0):
"""
Prints the information of the calculation for unrestricted wavefunctions.
:param aom: The Atomic Overlap Matrices (AOMs) in the MO basis.
:type aom: list of matrices
:param molinfo: Contains the information of the molecule and the calculation.
:type molinfo: dict
"""
partition = format_partition(molinfo["partition"])
print(" -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ")
print(" | Number of Atoms: {}".format(len(aom[0])-nfrags))
print(" | Occ. Mol. Orbitals: {}({})".format(np.shape(aom[0][0])[0], np.shape(aom[1][0])[0]))
print(" | Wavefunction type: Unrestricted")
print(" | Atomic partition: {}".format(partition.upper() if partition else "Not specified"))
print(" ------------------------------------------- ")
print(" ------------------------------------------- ")
print(" | Method: ", molinfo["calctype"])
if "dft" in molinfo["method"] and molinfo["xc"] is not None:
print(" | Functional: ", molinfo["xc"])
if isinstance(molinfo["basisset"], dict) or isinstance(molinfo["basisset"], list):
print(" | Basis set: GEN")
elif isinstance(molinfo["basisset"], str):
print(" | Basis set: ", molinfo["basisset"].upper())
if isinstance(molinfo["energy"], str):
print(" | Total energy: {}".format(molinfo["energy"]))
else:
print(" | Total energy: {:<13f}".format(molinfo["energy"]))
print(" ------------------------------------------- ")
trace_a = np.sum([np.trace(matrix) for matrix in aom[0]][:len(molinfo["symbols"])])
trace_b = np.sum([np.trace(matrix) for matrix in aom[1]][:len(molinfo["symbols"])])
print(" | Tr(alpha): {:.13f}".format(trace_a))
print(" | Tr(beta) : {:.13f}".format(trace_b))
print(" | Tr(Enter): {:.13f}".format(trace_a + trace_b))
print(" ------------------------------------------- ")
[docs]def deloc_unrest(aom, molinfo, fragmap={}):
"""
Population analysis, localization and delocalization indices for unrestricted, single-determinant calculations.
:param aom: The Atomic Overlap Matrices (AOMs) in the MO basis.
:type aom: list of matrices
:param molinfo: Contains the information of the molecule and the calculation.
:type molinfo: dict
"""
presymbols = molinfo["symbols"]
symbols = presymbols + ["FF"] * (len(aom[0]) - len(presymbols))
# Getting the LIs and DIs
dis_alpha, dis_beta = [], []
lis_alpha, lis_beta = [], []
Nij_alpha, Nij_beta = [], []
for i in range(len(aom[0])):
li_alpha = np.einsum('ij,ji->', aom[0][i], aom[0][i])
li_beta = np.einsum('ij,ji->', aom[1][i], aom[1][i])
lis_alpha.append(li_alpha)
lis_beta.append(li_beta)
Nij_alpha.append(np.trace(aom[0][i]))
Nij_beta.append(np.trace(aom[1][i]))
for j in range(i + 1, len(aom[0])):
diaa = 2 * np.einsum('ij,ji->', aom[0][i], aom[0][j])
dibb = 2 * np.einsum('ij,ji->', aom[1][i], aom[1][j])
dis_alpha.append(diaa)
dis_beta.append(dibb)
print(" ------------------------------------------------------------------- ")
print(" | Atom N(Sij) Na(Sij) Nb(Sij) dloc_a dloc_b ")
print(" ------------------------------------------------------------------- ")
for i in range(len(aom[0])):
print(" | {:>2}{:>2d} {:8.4f} {:8.4f} {:8.4f} {:8.4f} {:8.4f} ".format(
symbols[i], i + 1, Nij_alpha[i] + Nij_beta[i], Nij_alpha[i], Nij_beta[i], Nij_alpha[i] - lis_alpha[i],
Nij_beta[i] - lis_beta[i]))
print(" ------------------------------------------------------------------- ")
Ntota = np.sum(Nij_alpha[:len(presymbols)])
Ntotb = np.sum(Nij_beta[:len(presymbols)])
listota = np.sum(lis_alpha[:len(presymbols)])
listotb = np.sum(lis_beta[:len(presymbols)])
distota = Ntota - listota
distotb = Ntotb - listotb
print(" | TOT: {:8.4f} {:8.4f} {:8.4f} {:8.4f} {:8.4f}".format(Ntota+Ntotb, Ntota, Ntotb, distota, distotb))
print(" ------------------------------------------------------------------- ")
print(" ------------------------------------------- ")
print(" | Pair DI DIaa DIbb ")
print(" ------------------------------------------- ")
for i in range(len(symbols)):
for j in range(i, len(symbols)):
if i == j:
print(" | {:>2}{:>2}-{:>2}{:>2} {:8.4f} {:8.4f} {:8.4f}".format(
symbols[i], str(i + 1).center(2), symbols[j],
str(j + 1).center(2), lis_alpha[i] + lis_beta[i], lis_alpha[i], lis_beta[i]))
else:
dia = 2 * np.einsum('ij,ji->', aom[0][i], aom[0][j])
dib = 2 * np.einsum('ij,ji->', aom[1][i], aom[1][j])
ditot = dia + dib
print(" | {:>2}{:>2}-{:>2}{:>2} {:8.4f} {:8.4f} {:8.4f}".format(
symbols[i], str(i + 1).center(2), symbols[j],
str(j + 1).center(2), ditot, dia, dib))
print(" ------------------------------------------- ")
print(" | TOT: {:>9.4f} {:>9.4f} {:>9.4f} ".format(
Ntota + Ntotb, Ntota, Ntotb))
print(" | LOC: {:>9.4f} {:>9.4f} {:>9.4f} ".format(
listota + listotb, listota, listotb))
print(" | DELOC: {:>9.4f} {:>9.4f} {:>9.4f} ".format(
distota + distotb, distota, distotb))
print(" ------------------------------------------- ")
[docs]def arom_unrest(aom, rings, molinfo, indicators, mci=False, av1245=False, partition=None, flurefs=None, homarefs=None,
homerrefs=None, ncores=1, fragmap=None):
"""
Outputs the aromaticity indices for unrestricted, single-determinant wavefunctions.
:param aom: The Atomic Overlap Matrices (AOMs) in the MO basis.
:type aom: list of matrices
:param rings: List containing the atoms in the ring.
:type rings: list of lists
:param molinfo: Contains the information of the molecule and the calculation.
:type molinfo: dict
:param indicators: Class containing the aromaticity indicators.
:type indicators: class
:param mci: If True, the MCI will be calculated.
:type mci: bool, optional
:param av1245: If True, the AV1245 will be calculated.
:type av1245: bool, optional
:param partition: The atomic partition used in the calculation.
:type partition: str, optional
:param flurefs: Dictionary with custom references for the FLU.
:type flurefs: dict, optional
:param homarefs: Dictionary with custom references for the HOMA.
:type homarefs: dict, optional
:param homerrefs: Dictionary with custom references for the HOMER.
:type homerrefs: dict, optional
:param ncores: Number of cores to use in the MCI calculation. By default, 1.
:type ncores: int, optional
"""
print(" ----------------------------------------------------------------------")
print(" | Aromaticity indices - PDI [CEJ 9, 400 (2003)] ")
print(" | HOMA [Tetrahedron 52, 10255 (1996)]")
print(" | FLU [JCP 122, 014109 (2005)] ")
print(" | Iring [PCCP 2, 3381 (2000)] ")
if mci is True:
print(" | MCI [JPOC 18, 706 (2005)] ")
if av1245 is True:
print(" | AV1245 [PCCP 18, 11839 (2016)] ")
print(" | AVmin [JPCC 121, 27118 (2017)] ")
print(" | [PCCP 20, 2787 (2018)] ")
print(" | For a recent review see: [CSR 44, 6434 (2015)] ")
print(" ----------------------------------------------------------------------")
# Checking where to read the atomic symbols from
if not molinfo:
raise NameError(" 'molinfo' not found. Check input")
symbols = molinfo["symbols"] + ["FF"] * (len(fragmap))
partition = molinfo["partition"]
# Checking if the list rings is contains more than one ring to analyze
if not isinstance(rings[0], list):
rings = [rings]
# Looping through each of the rings
for ring_index, ring in enumerate(rings.copy()):
frag = False
if any(tuple(r) in fragmap for r in ring if isinstance(r, (set, list))):
frag = True
connectivity = None if frag else [symbols[int(i) - 1] for i in ring]
print(" ----------------------------------------------------------------------")
print(" |")
print(" | Ring {} ({}): {}".format(
ring_index + 1, len(ring), " ".join(str(num) for num in ring)))
print(" |")
print(" ----------------------------------------------------------------------")
goodring = ring
ring = list(np.arange(1, len(ring) + 1))
# Starting the calculation of the aromaticity indicators
if homarefs is not None:
print(" | Using HOMA references provided by the user")
else:
print(" | Using default HOMA references")
if frag:
print(" | Could not compute geometric indicators between fragments")
homa = None
else:
homa = indicators[ring_index].homa
if homa is None:
print(" | Connectivity could not match parameters")
else:
print(" | EN {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].en))
print(" | GEO {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].geo))
print(" | HOMA {} = {:>.6f}".format(ring_index + 1, homa))
print(" ----------------------------------------------------------------------")
if find_multiplicity(aom) == "triplet":
print(" | Triplet AOMs. Computing HOMER")
if homerrefs is not None:
print(" | Using HOMER references provided by the user")
else:
print(" | Using the default HOMER references")
print(" | HOMER {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].homer))
print(" ----------------------------------------------------------------------")
if molinfo["geom"] is not None:
bla = indicators[ring_index].bla
if bla is not None:
bla_c = indicators[ring_index].bla_c
print(" | BLA {} = {:>.6f}".format(ring_index + 1, bla))
print(" | BLAc {} = {:>.6f}".format(ring_index + 1, bla_c))
print(" ----------------------------------------------------------------------")
if not frag:
flu = indicators[ring_index].flu
if flu is None:
print(" | Could not compute FLU")
else:
if flurefs is not None:
print(" | Using FLU references provided by the user")
else:
print(" | Using the default FLU references")
print(" | Atoms : {}".format(" ".join(str(atom) for atom in connectivity)))
print(" |")
print(" | *** FLU_ALPHA ***")
print(" | FLU_aa {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].flu_alpha))
print(" |")
print(" | *** FLU_BETA ***")
print(" | FLU_bb {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].flu_beta))
print(" |")
print(" | *** FLU_TOTAL ***")
print(" | FLU {} = {:>.6f}".format(ring_index + 1, flu))
print(" ----------------------------------------------------------------------")
print(" |")
print(" | *** BOA_ALPHA ***")
print(" | BOA_aa {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].boa_alpha))
print(" | BOAc_aa {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].boa_c_alpha))
print(" |")
print(" | *** BOA_BETA ***")
print(" | BOA_bb {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].boa_beta))
print(" | BOAc_bb {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].boa_c_beta))
print(" |")
print(" | *** BOA_TOTAL ***")
print(" | BOA {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].boa))
print(" | BOAc {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].boa_c))
print(" ----------------------------------------------------------------------")
# Printing the PDI
if len(ring) != 6:
print(" | PDI could not be calculated as the number of centers is not 6")
else:
pdi_list_alpha = indicators[ring_index].pdi_list_alpha
pdi_list_beta = indicators[ring_index].pdi_list_beta
print(" |")
print(" | *** PDI_ALPHA ***")
print(" | DIaa ({:>2} -{:>2} ) = {:.4f}".format(ring[0], ring[3], pdi_list_alpha[0]))
print(" | DIaa ({:>2} -{:>2} ) = {:.4f}".format(ring[1], ring[4], pdi_list_alpha[1]))
print(" | DIaa ({:>2} -{:>2} ) = {:.4f}".format(ring[2], ring[5], pdi_list_alpha[2]))
print(" | PDI_alpha {} = {:.4f} ".format(ring_index + 1, indicators[ring_index].pdi_alpha))
print(" |")
print(" | *** PDI_BETA ***")
print(" | DIbb ({:>2} -{:>2} ) = {:.4f}".format(ring[0], ring[3], pdi_list_beta[0]))
print(" | DIbb ({:>2} -{:>2} ) = {:.4f}".format(ring[1], ring[4], pdi_list_beta[1]))
print(" | DIbb ({:>2} -{:>2} ) = {:.4f}".format(ring[2], ring[5], pdi_list_beta[2]))
print(" | PDI_beta {} = {:.4f} ".format(ring_index + 1, indicators[ring_index].pdi_beta))
print(" |")
print(" | *** PDI_TOTAL ***")
print(" | DI ({:>2} -{:>2} ) = {:.4f}".format(ring[0], ring[3], pdi_list_alpha[0] + pdi_list_beta[0]))
print(" | DI ({:>2} -{:>2} ) = {:.4f}".format(ring[1], ring[4], pdi_list_alpha[1] + pdi_list_beta[1]))
print(" | DI ({:>2} -{:>2} ) = {:.4f}".format(ring[2], ring[5], pdi_list_alpha[2] + pdi_list_beta[2]))
print(" | PDI {} = {:.4f} ".format(ring_index + 1, indicators[ring_index].pdi))
print(" ---------------------------------------------------------------------- ")
if av1245 == True:
if len(ring) < 6:
print(" | AV1245 could not be calculated as the number of centers is smaller than 6 ")
else:
av1245_list_alpha = indicators[ring_index].av1245_list_alpha
av1245_list_beta = indicators[ring_index].av1245_list_beta
av1245_pairs, av1245_indices = [], []
for i in range(len(goodring)):
first = fragmap[tuple(goodring[i % len(goodring)])] if isinstance(goodring[i % len(goodring)], set) else goodring[i % len(goodring)]
second = fragmap[tuple(goodring[(i + 1) % len(goodring)])] if isinstance(
goodring[(i + 1) % len(goodring)], set) else goodring[(i + 1) % len(goodring)]
third = fragmap[tuple(goodring[(i + 3) % len(goodring)])] if isinstance(
goodring[(i + 3) % len(goodring)], set) else goodring[(i + 3) % len(goodring)]
fourth = fragmap[tuple(goodring[(i + 4) % len(goodring)])] if isinstance(
goodring[(i + 4) % len(goodring)], set) else goodring[(i + 4) % len(goodring)]
# Create the ring with corresponding symbols
symbs = [
symbols[first - 1] if isinstance(first, int) else symbols[first],
symbols[second - 1] if isinstance(second, int) else symbols[second],
symbols[third - 1] if isinstance(third, int) else symbols[third],
symbols[fourth - 1] if isinstance(fourth, int) else symbols[fourth]
]
av1245_pairs.append(symbs)
av1245_indices.append((first, second, third, fourth))
print(" |")
print(" | *** AV1245_ALPHA ***")
for j in range(len(ring)):
symbs = av1245_pairs[j]
av1245_idx = av1245_indices[j]
print(" | {} {} - {} {} - {} {} - {} {} | {:>6.4f}".format(
str(av1245_idx[0]).rjust(2), symbs[0].ljust(2),
str(av1245_idx[1]).rjust(2), symbs[1].ljust(2),
str(av1245_idx[2]).rjust(2), symbs[2].ljust(2),
str(av1245_idx[3]).rjust(2), symbs[3].ljust(2),
av1245_list_alpha[(av1245_idx[0] - 1) % len(ring)]))
print(" |")
print(" | *** AV1245_BETA ***")
for j in range(len(ring)):
symbs = av1245_pairs[j]
av1245_idx = av1245_indices[j]
print(" | {} {} - {} {} - {} {} - {} {} | {:>6.4f}".format(
str(av1245_idx[0]).rjust(2), symbs[0].ljust(2),
str(av1245_idx[1]).rjust(2), symbs[1].ljust(2),
str(av1245_idx[2]).rjust(2), symbs[2].ljust(2),
str(av1245_idx[3]).rjust(2), symbs[3].ljust(2),
av1245_list_beta[(av1245_idx[0] - 1) % len(ring)]))
print(" | ")
print(" | *** AV1245_TOTAL ***")
for j in range(len(ring)):
symbs = av1245_pairs[j]
av1245_idx = av1245_indices[j]
print(" | {} {} - {} {} - {} {} - {} {} | {:>6.4f}".format(
str(av1245_idx[0]).rjust(2), symbs[0].ljust(2),
str(av1245_idx[1]).rjust(2), symbs[1].ljust(2),
str(av1245_idx[2]).rjust(2), symbs[2].ljust(2),
str(av1245_idx[3]).rjust(2), symbs[3].ljust(2),
av1245_list_alpha[(av1245_idx[0] - 1) % len(ring)]
+av1245_list_beta[(av1245_idx[0] - 1) % len(ring)]))
print(" |")
print(" | AV1245 {} = {:.4f}".format(ring_index + 1, indicators[ring_index].av1245))
print(" | AVmin {} = {:.4f}".format(ring_index + 1, indicators[ring_index].avmin))
print(" ---------------------------------------------------------------------- ")
iring_alpha = indicators[ring_index].iring_alpha
iring_beta = indicators[ring_index].iring_beta
iring_total = iring_alpha + iring_beta
print(" | Iring_alpha {} = {:>6f}".format(ring_index + 1, iring_alpha))
print(" | Iring_beta {} = {:>6f}".format(ring_index + 1, iring_beta))
print(" | Iring {} = {:>6f}".format(ring_index + 1, iring_total))
if iring_total < 0:
print(" | Iring**(1/n) {} = {:>6f}".format(ring_index + 1, -(np.abs(iring_total) ** (1 / len(ring)))))
else:
print(" | Iring**(1/n) {} = {:>6f}".format(ring_index + 1, iring_total ** (1 / len(ring))))
print(" ---------------------------------------------------------------------- ")
if mci == True:
import time
# SINGLE-CORE
if ncores == 1:
if partition is None:
print(" | Partition not specified. Will assume symmetric AOMs")
start_mci = time.time()
mci_alpha = indicators[ring_index].mci_alpha
mci_beta = indicators[ring_index].mci_beta
mci_total = mci_alpha + mci_beta
end_mci = time.time()
time_mci = end_mci - start_mci
print(" | The MCI calculation using 1 core took {:.4f} seconds".format(time_mci))
print(" | MCI_alpha {} = {:>6f}".format(ring_index + 1, mci_alpha))
print(" | MCI_beta {} = {:>6f}".format(ring_index + 1, mci_beta))
print(" | MCI {} = {:>6f}".format(ring_index + 1, mci_total))
# MULTI-CORE
else:
if partition is None:
print(" | Partition not specified. Will assume symmetric AOMs")
start_mci = time.time()
mci_alpha = indicators[ring_index].mci_alpha
mci_beta = indicators[ring_index].mci_beta
mci_total = mci_alpha + mci_beta
end_mci = time.time()
time_mci = end_mci - start_mci
print(" | The MCI calculation using {} cores took {:.4f} seconds".format(ncores, time_mci))
print(" | MCI_alpha {} = {:>6f}".format(ring_index + 1, mci_alpha))
print(" | MCI_beta {} = {:>6f}".format(ring_index + 1, mci_beta))
print(" | MCI {} = {:>6f}".format(ring_index + 1, mci_total))
if mci_total < 0:
print(" | MCI**(1/n) {} = {:>6f}".format(ring_index + 1, -((np.abs(mci_total)) ** (1 / len(ring)))))
else:
print(" | MCI**(1/n) {} = {:>6f}".format(ring_index + 1, mci_total ** (1 / len(ring))))
print(" ---------------------------------------------------------------------- ")
