import numpy as np
from esipy.tools import format_partition
[docs]def info_no(aom, molinfo):
"""
Prints the initial information for correlated wavefunctions.
:param aom: Atomic Overlap Matrices (AOMs) in the MO basis.
:type aom: list of matrices or str
:param molinfo: Contains the information about the molecule and the calculation.
:type molinfo: dict
"""
aom, occ = aom
partition = format_partition(molinfo["partition"])
print(" -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ")
print(" | Number of Atoms: {}".format(len(aom)))
print(" | Occ. Mol. Orbitals: {}".format(np.shape(aom[0])[0]))
print(" | Wavefunction type: Natural Orbitals")
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"])
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 = np.sum([np.trace(matrix) for matrix in aom])
print(" | Tr(Enter): {:.13f}".format(trace))
print(" ------------------------------------------- ")
[docs]def deloc_no(aom, molinfo):
"""
Population analysis, localization and delocalization indices for correlated wavefunctions.
:param aom: Atomic Overlap Matrices (AOMs) in the MO basis.
:type aom: list of matrices or str
:param molinfo: Contains the information about the molecule and the calculation.
:type molinfo: dict
"""
aom, occ = aom
symbols = molinfo["symbols"]
# Getting the LIs and DIs
difs, dixs, lifs, lixs, N = [], [], [], [], []
print(" ---------------------------------------------------------- ")
print(" | Atom N(Sij) dlocF dlocX locF locX ")
print(" ---------------------------------------------------------- ")
for i in range(len(aom)):
lif = np.trace(np.linalg.multi_dot((occ ** (1 / 2), aom[i], occ ** (1 / 2), aom[i])))
lix = 0.5 * np.trace(np.linalg.multi_dot((occ, aom[i], occ, aom[i])))
lifs.append(lif)
lixs.append(lix)
N.append(np.trace(np.dot(occ, aom[i])))
dlocF = 0
dlocX = 0
for j in range(len(aom)):
if i != j:
dif = np.trace(np.linalg.multi_dot((occ ** (1 / 2), aom[i], occ ** (1 / 2), aom[j])))
dix = 0.5 * np.trace(np.linalg.multi_dot((occ, aom[i], occ, aom[j])))
dlocF += dif
dlocX += dix
difs.append(dif)
dixs.append(dix)
print(" | {:>2} {:>2d} {:8.4f} {:8.4f} {:8.4f} {:8.4f} {:8.4f}".format(
symbols[i], i + 1, N[i], N[i] - lif, dlocX, lif, lix))
print(" ---------------------------------------------------------- ")
print(" | TOT: {:>8.4f} {:>8.4f} {:>8.4f} {:>8.4f} {:>8.4f}".format(
sum(N), sum(N) - sum(lifs), sum(dixs), sum(lifs), sum(lixs)))
print(" ---------------------------------------------------------- ")
print(" ---------------------------------- ")
print(" | Pair DI(F) DI(X) ")
print(" ---------------------------------- ")
for i in range(len(aom)):
for j in range(i, len(aom)):
if i == j:
print(" | {:>2}{:>2}-{:>2}{:>2} {:>8.4f} {:>8.4f}".format(
symbols[i], i + 1, symbols[j], j + 1, lifs[i], lixs[i]))
else:
print(" | {:>2}{:>2}-{:>2}{:>2} {:>8.4f} {:>8.4f}".format(
symbols[i], i + 1, symbols[j], j + 1, 2 * difs[i * len(aom) + j - (i + 1)],
2 * dixs[i * len(aom) + j - (i + 1)]))
print(" ---------------------------------- ")
print(" | TOT: {:>8.4f} {:>8.4f} ".format(np.sum(difs) + np.sum(lifs), np.sum(dixs) + np.sum(lixs)))
print(" | LOC: {:>8.4f} {:>8.4f} ".format(np.sum(lifs), np.sum(lixs)))
print(" | DELOC: {:>8.4f} {:>8.4f} ".format(np.sum(difs), np.sum(dixs)))
print(" ---------------------------------- ")
[docs]def arom_no(rings, molinfo, indicators, mci=False, av1245=False, partition=None, flurefs=None, homarefs=None,
homerrefs=None, ncores=1):
"""
Output for the aromaticity indices for Natural Orbitals calculations. Will use Fulton's approximation.
:param rings: Contains the indices of the atoms in the rings.
:type rings: list of lists
:param molinfo: Contains the information about the molecule and the calculation.
:type molinfo: dict
:param indicators: Contains the aromaticity indicators.
:type indicators: class
:param mci: If True, the MCI is computed.
:type mci: bool, optional
:param av1245: If True, the AV1245 is computed.
:type av1245: bool, optional
:param partition: Contains the name of the partition.
:type partition: str, optional
:param flurefs: Contains the custom references for the FLU aromaticity index.
:type flurefs: dict, optional
:param homarefs: Contains the custom references for the HOMA aromaticity index.
:type homarefs: dict, optional
:param homerrefs: Contains the custom references for the HOMER aromaticity index.
:type homerrefs: dict, optional
:param ncores: Number of cores to use in the MCI calculation. By default, 1.
:type ncores: int, optional
"""
print(" | Fulton index used for the calculation of aromaticity indicators ")
if partition == "iao":
print(" | WARNING: IAOs transformation matrix is built upon the HF instance")
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 molinfo:
symbols = molinfo["symbols"]
partition = molinfo["partition"]
else:
raise NameError(" 'molinfo' not found. Check input")
if not isinstance(rings[0], list):
rings = [rings]
# Looping through each of the rings
for ring_index, ring in enumerate(rings):
print(" ----------------------------------------------------------------------")
print(" |")
print(" | Ring {} ({}): {}".format(ring_index + 1, len(ring), " ".join(str(num) for num in ring)))
print(" |")
print(" ----------------------------------------------------------------------")
if homarefs is not None:
print(" | Using HOMA references provided by the user")
else:
print(" | Using default HOMA references")
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))
if homerrefs:
print(" | ")
print(" | Found custom HOMER references 'alpha' and 'r_opt'. Computing")
print(" | HOMER {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].homer))
print(" ----------------------------------------------------------------------")
print(" | BLA {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].bla))
print(" | BLAc {} = {:>.6f}".format(ring_index + 1, indicators[ring_index].bla_c))
print(" ----------------------------------------------------------------------")
print(" ----------------------------------------------------------------------")
print(" | Current version does not allow FLU for correlated wavefunctions")
print(" ----------------------------------------------------------------------")
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 = indicators[ring_index].pdi_list
print(" | DI ({:>2} -{:>2} ) = {:.4f}".format(ring[0], ring[3], pdi_list[0]))
print(" | DI ({:>2} -{:>2} ) = {:.4f}".format(ring[1], ring[4], pdi_list[1]))
print(" | DI ({:>2} -{:>2} ) = {:.4f}".format(ring[2], ring[5], pdi_list[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 = indicators[ring_index].av1245_list
av1245_pairs = [(ring[i % len(ring)], ring[(i + 1) % len(ring)], ring[(i + 3) % len(ring)],
ring[(i + 4) % len(ring)])
for i in range(len(ring))]
for j in range(len(ring)):
print(" | {} {} - {} {} - {} {} - {} {} | {:>6.4f}".format(
str(ring[j]).rjust(2), symbols[av1245_pairs[j][0] - 1].ljust(2),
str(ring[(j + 1) % len(ring)]).rjust(2), symbols[av1245_pairs[j][1] - 1].ljust(2),
str(ring[(j + 3) % len(ring)]).rjust(2), symbols[av1245_pairs[j][2] - 1].ljust(2),
str(ring[(j + 4) % len(ring)]).rjust(2), symbols[av1245_pairs[j][3] - 1].ljust(2),
av1245_list[(ring[j] - 1) % len(ring)]))
print(" | AV1245 {} = {:.4f}".format(ring_index + 1, indicators[ring_index].av1245))
print(" | AVmin {} = {:.4f}".format(ring_index + 1, indicators[ring_index].avmin))
print(" ---------------------------------------------------------------------- ")
iring_total = indicators[ring_index].iring
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_total = indicators[ring_index].mci
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 {} = {:.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_total = indicators[ring_index].mci
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 {} = {:.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(" ---------------------------------------------------------------------- ")
