Supramolecular Isomers of Metal-Organic Frameworks Derived from a Partially Flexible Ligand with Distinct Binding Motifs

Article abstract of DOI:10.1021/acs.cgd.5b01307

Three novel metal-organic frameworks (MOFs) were isolated upon reacting heterofunctional ligand 4-(pyrimidin-5-yl)benzoic acid (4,5-pmbc) with mixed valence Cu(I,II) under solvothermal conditions. X-ray crystal structural analysis reveals that the first c

Full text of DOI:10.1021/acs.cgd.5b01307

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Article
Supramolecular Isomers of Metal-Organic Frameworks Derived
from a Partially Flexible Ligand with Distinct Binding Motifs
Rasha G. AbdulHalim, Aleksander Shkurenko, Mohamed H Alkordi, and Mohamed Eddaoudi
Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.5b01307 • Publication Date (Web): 04 Jan 2016
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Supramolecular Isomers of Metal-Organic Frameworks
Derived from a Partially Flexible Ligand with Distinct Binding
Motifs
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Rasha G. AbdulHalim, Aleksander Shkurenko, Mohamed H. Alkordi, and Mohamed Eddaoudi*
Functional Materials Design, Discovery & Development Research Group (FMD3), Advanced Membranes & Porous Materials Center,
Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900,
Kingdom of Saudi Arabia
ABSTRACT: Three novel metal-organic frameworks (MOFs) were isolated upon reacting
ligand 4-(pyrimidin-5-yl)benzoic acid (4,5-pmbc) with mixed valence Cu(I,II) under solvothermal conditions.
X-ray crystal structural analysis reveals that the first compound is layered structure composed of one type of
inorganic building block, dinuclear paddlewheel [Cu2(O2C–)4], which are linked through 4,5-pmbc ligands.
The two other supramolecular isomers are composed of the same Cu(II) dinuclear paddlewheel and dinuclear
a
heterofunctional
a
a
Cu2I2 cluster, which are linked via the 4,5-pmbc linkers to yield two different 3-periodic frameworks with
underlying topologies related to lvt and nbo. The observed structural diversity in these structures is due to the
distinct coordination modes of the two coordinating moieties (the carboxylate group on the phenyl ring and the
N-donor atoms from the pyrimidine moiety).
nation of the two requisite building blocks for the formation of a
Introduction
hexagon, namely a bent ligand (120° angle) with a linear bridging
component, was reported by Stang.12 Similarly, discrete metallo-
Metal-organic frameworks (MOFs) are a thriving class of func-
supramolecular hexagons based on pyrimidines (e.g. pyrimi-
dine, 2-hydroxypyrimidine, 2,4-dihydroxypyrimidine,
tional solid-state materials that have attracted considerable atten-
tion due to their modular nature1 and accessible pore system for
potential use in various key applications, such as catalysis,2 lumi-
nescence,3 gas storage and separation.4
2-aminopyrimdines) have been reported by Navarro et al.13
Inspired by the aforementioned discrete assemblies, we opted to
use an in-house synthesized pyrimidine-based ligand (H2-4,5-
pmbc: 4-(pyrimidyl-5-yl)benzoic acid) and explore its potential
in directing the assembly of extended frameworks based on hex-
agonal supramolecular building units. The 4,5-pmbc is a multi-
functional ligand encompassing one carboxylate group and two
aromatic N-donors centers, offering several coordination modes
as depicted in Scheme 1.
In this particular burgeoning class of periodic solids, there has
been noticeable efforts and progress toward designing periodic
functional structures with desired geometrical attributes and
chemical properties for targeted applications.5 This route has be-
come reasonably feasible with the implementation of the molecu-
lar building block (MBB) approach, where organic and inorganic
MBBs with given geometry and directionality (e.g., triangles,
squares, etc.) are targeted and pre-selected prior the assembly
process.6 Markedly, The assembly of preprogrammed MBBs al-
lows the formation of discrete supramolecules of variable geome-
tries, as evidenced by the myriad of metallo-supramolecular poly-
gons, cages and polyhedra.7 Perceptively, targeting structures
based on the assembly of metallamacrocycles, especially supra-
molecular hexagons, is of particular interest due to the plausible
prospective to mimic biological systems.8-9
These binding modes include bis-monodentate and bidentate co-
ordination modes for the carboxylate moiety; whereas, the pyrim-
idyl nitrogen coordinates in a monodentate mode. Scheme 1 (a-c)
shows the likely modes of coordination when reacting this ligand
with a Cu(II) metal source prompting the formation of a Cu(II)
paddlewheel (bis-monodentate coordination) at the carboxylate
functionality. Scheme 1 (d-f) depicts the relatively less plausible
bidentate coordination mode for the Cu(II) centers.
Nitrogen containing heterocycles have been employed in supra-
molecular chemistry to target and assemble diverse structures
ranging from molecular rings, layered structures to 3-D metal
organic frameworks. In particular, pyrimidine based ligands were
used successively to construct discrete polygons as well as ex-
tended frameworks.10 It is worth mentioning that the deliberate
synthesis of a particular MOF with a precise and intricate topolo-
gy starting from simple MBBs is often challenging. Potentially,
this could be attributed to the lack of control over the coordination
modes of the metal ions and/or the flexibility of the ligand11.
Scheme 1 (b and e) depict the case when the nitrogen donor
groups on the pyrimidine remain uncoordinated leading preferen-
tially to the formation of discrete 0-periodic molecular coordina-
tion compounds.
In Scheme 1 (c and f), a 120° angle enclosed by the carboxylate
group and the coordinated nitrogen atom in the pyrimidine ring is
similar to that observed in isophthalic acid. In this regard, the
isophthalate acts as a two connected bent linker bridging the
[Cu2(O2C–)4] paddlewheel MBBs to either sustain squares or
triangles to form a square grid lattice or a Kagomé layer14 respec-
tively. Finally, in Scheme 1 (a and d) the second nitrogen on the
Our primary objective was to isolate an extended MOF enclosing
hexagonal supramolecular building units. Noticeably, the combi-
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pyrimidine ring can bridge the clusters and thus potentially pro-
Our envisioned strategy to construct 3-periodic MOFs encompass-
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mote the formation of a 3-periodic structure based on linked hex-
agonal polygons.
ing hexagonal supramolecular building units using the heterofunc-
tional ligand H2-4,5-pmbc in combination with Cu(I) and Cu(II),
under various solvothermal reaction conditions, had permitted the
formation of a layered structure 1 and two supramolecular isomers
2 and 3 with lvt and nbo underlying topologies, respectively.
The combination of MBBs with multidentate ligands has proved
to be an efficient pathway for targeting 2-D and 3-D MOFs, in-
cluding supramolecular isomers. One of the most employed and
targeted inorganic MBB is the well-known dinuclear paddle-
wheel type cluster [M2(O2C–)4]. This MBB can be easily targeted
through the use of carboxylate based ligands and divalent transi-
tion metals (Cu, Zn, etc.) under mild solvothermal reaction condi-
tions15. Examples include edge-transitive layers (square grid or
Kagomé) synthesized from dicarboxylate based ligands. Inclusion
of bifunctional N-donor based ligands (e.g. 4,4′-bipyridine) in the
synthesis allows linking these layers via a “pillaring strategy” by
connecting the axial (apical) position of the paddlewheel
clusters.16
Experimental Section
Preparations: All materials and solvents were used as received
from Aldrich Chemical Co. and Fischer Scientific, respectively,
without further purifications.
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Single-crystal X-ray diffraction data was collected using Bruker
X8 PROSPECTOR APEX2 CCD diffractometer (Cu K =
1.54178 Å. Crystallographic data and structural refinements of 1,
2 and 3 are summarized in Table S1. Powder X-ray diffraction
(PXRD) measurements were performed on a PANalytical X’Pert
PRO MPD X-ray diffractometer at 45 kV, 40 mA for Cu K ( =
1.5418 Å). PXRD measurements were performed on DMF
washed samples for 1, 2 and 3, as shown in Figures S4, S5 and
S6. High resolution dynamic thermal gravimetric analysis (TGA)
were performed under a continuous N2 flow and recorded on a TA
Instrument Hi-Res TGAQ500 thermal gravimetric analyzer. TGA
experiments were performed on a DMF washed samples for 1, 2
and 3 under N2 and at a heating rate of 5°C min-1, as shown in
Figures S1, S2 and S3.
The use of Cu(I) complexes is particularly attractive because of
their promising optical properties and the readily occurrence of
various MBBs derived from copper halides (CuX).17 CuX reacts
readily with nitrogen-donor ligands as a result of the soft-soft
bonding preference generating diverse geometries with various
[CunIn] structural motifs.18 These motifs range from Cu2I2 rhom-
boid square dimers,19 triangular Cu3I3 clusters, cubane-like or
chair like [Cu4I4] tetramers,20 hexagonal Cu6I6 clusters21, ladder-
like or ribbon like [Cu2I2]n chains,22 zigzag23 [CuI]n or [Cu3I4]n
chains24 and [CuI]n layers.25 Among the various clusters acting as
connecting nodes, dimeric and tetrameric units are the most ob-
served clusters.26
Synthesis of 4-(pyrimidin-5-yl)benzoic acid (H2-4,5-pmbc).
This compound was prepared according to our previously report-
ed procedure.6 In a Schlenk tube under argon atmosphere,
a mixture of 5-bromopyrimidine (8 mmol, 1.272 g), 4-
ethoxycarbonylphenylboronic acid (9 mmol, 1.746 g),
[1,1′-bis(diphenylphosphino) ferrocene] dichloropalladium(II)
(0.2 mmol, 0.146 g),
2-dicyclohexylphosphino-2′,6′-
dimethoxybiphenyl (0.4 mmol, 0.168 g), finely grinded K3(PO4)
(14 mmol, 3 g), and 18-crown-6 ether (3.7 mmol, 1 g) in
a mixture of degassed THF (20 mL) and EtOH (5 mL) was pre-
pared and reacted at 85°C for 24 h. The reaction mixture was then
filtered through celite. The residue was subjected to column
chromatography (10% to 40% EtOAc in hexane) to yield colorless
needles (1.7 g, 7.45 mmol, 93% yield). Hydrolysis of the ester
was accomplished by stirring the solid with 10 equivalents of
NaOH in a mixture of THF/EtOH/water 1:1:1 kept at 60°C for
24h, followed by acidification using 1N HCl, extraction in
EtOAc, drying over Na2SO4 and stand for crystallization (white
solid, 80% yield). NMR data match those reported earlier.27 13C
NMR (DMSO-d6, 150MHz): δ = 155.0, 154.9, 132.4, 132.1,
130.0, 129.8, 127.2, 127.0. 1H NMR (DMSO-d6, 600MHz): δ =
9.20 (s, 1H), 9.19 (s, 1H), 8.06 (d, J = 8.4, 2H), 7.91 (d, J = 7.8,
2H) ppm.
Synthesis of [Cu2(C11H7N2O2)4]∙(CH3CN)2 (1)
Cu(NO3)2∙2.5H2O (5.8 mg, 0.025 mmol) and H2-4,5-pmbc
(10 mg, 0.05 mmol) were added to a 3 mL solution of
N,N′-dimethylformamide (DMF) and 1 mL acetonitrile (CH3CN)
in a 20 mL scintillation vial, heated at 85°C for 48 h, and cooled
to room temperature. The as-synthesized blue rod-like crystals are
insoluble in water and common organic solvents.
Synthesis of [(Cu2I2)Cu2(C11H7N2O2)4]∙(DMF)7.4 (H2O)4.6 (2)
CuI (4.76 mg, 0.025 mmol) and H2-4,5-pmbc (10 mg, 0.05 mmol)
were added to a 3 mL solution of DMF and 1 mL of CH3CN in
a 20 mL scintillation vial, heated to 85°C for 48 h, and cooled to
room temperature. The as-synthesized green hexagon-like crystals
are insoluble in water and common organic solvents.
Scheme 1. (a-f) Noted coordination modes of 4,5-pmbc. 1 is
composed of (a) and (c), 2 and 3 of (a) and (b) types of coordina-
tion modes. Color code (C = grey, O = red, N = blue; lime balls
representing the metal ion)
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Figure 1. Crystal Structure of 1: (a) octahedral coordination environment around the paddlewheel; (b) polyhedral representation of 1 re-
vealing the intercalation of terminal ligands into the channels; (c) the 2-D layers locked through π-π interactions (illustrated by the dotted
lines); (d) highlights one layer; (e) schematic representation of sql topology. Color code (C = grey, O = red, N = blue).
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Synthesis of [(Cu2I2)Cu2(C11H7N2O2)4]∙(NMP)6.4 (H2O)2.4 (3)
garded as a partially flexible ligand, where the carboxylate group
and the pyrimidine ring can twist and bend, as shown in Figure 2,
which could lead to the formation of supramolecular isomers
through conformational diversities. In order to target and isolate
these isomers, we slightly changed the reaction conditions; either
by replacing Cu(II) with Cu(I), knowing that Cu(I) can be oxi-
dized into Cu(II), as a mean to control the reaction rate which
resulted in 2, or by mixing both Cu(I) and Cu(II) resulting in 3.
CuI (3 mg, 0.016 mmol), Cu(NO3)2∙3H2O (4 mg, 0.016 mmol)
and H2-4,5-pmbc (6.4 mg, 0.032 mmol) were added to a 2 mL
solution of N-methyl-2-pyrrolidone (NMP), 2 mL CH3CN and
1 mL EtOH in a 20 mL scintillation vial, heated to 85°C for 24 h
and cooled to room temperature. The as-synthesized green crys-
tals are insoluble in water and common organic solvents.
Results and Discussions
A solvothermal reaction between H2-4,5-pmbc and CuI in DMF
yielded 2 in pure phase, featuring the formation of two distinct
clusters based on Cu(I) and Cu(II). The SCXRD analysis of 2
revealed the formation of a 3-periodic MOF that crystallized in
a tetragonal space group I41/a.
Crystals of 1 were isolated by reacting H2-4,5-pmbc in DMF with
Cu(II) under mild conditions. Single-crystal X-ray diffraction
(SCXRD) analysis revealed a layered structure that crystallized in
a monoclinic space group P21/c. The layered structure is con-
structed from dinuclear copper paddlewheel [Cu2(O2C–)4] MBBs,
where the equatorial plane contains four carboxylate groups from
four independent 4,5-pmbc ligands, and the two apical positions
are occupied by nitrogen atoms from the pyrimidyl moieties of
two separate ligands (Figure 1).Two free ligands with trans-
carboxylate groups located in the equatorial plane intercalate into
the voids of the square grids of adjacent layers filling the empty
space (Figure 1a and 1b). Head-to-tail π-π interactions are ob-
served between pyrimidine and phenyl groups with a mean cen-
troid-centroid distance of 3.789(3) Å between adjacent layers.
The resultant structure encloses two distinct types of copper ions
(Cu(I) and Cu(II)), one type of iodide anion and two crystallo-
graphically independent ligands. The overall structure reveals the
formation of two distinct inorganic MBBs with the ligand acting
as a bifunctional-multidentate linker. MBB-1 is based on a dinu-
clear cluster represented by copper iodide rhomboid dimeric units
[Cu2I2].
Topological analysis using TOPOS28 corroborates the exclusion
of the terminal ligands, regarded as no points of extension, as
they are not contributing to the overall resultant network connec-
tivity and net underlying topology. Hence the structure can be
reduced to a 4-connected net where the 4-c nodes [Cu2(O2C–)2(N–
)2] are linked via a bifunctional bent linker to form a 2-periodic
MOF structure with a 4,4-connected sql topology (Figure 1e).
Figure 2. A schematic representation illustrating the twist around
the pyrimidine ring, and the bending angle of the carboxylate
group.
As stated earlier, the ability of the two N-donor groups in the
pyrimidine ring to concurrently participate in a metal coordination
bonding offers potential to augment the connectivity of the
4,5-pmbc ligand and subsequently promote the prospective for-
mation of a 3-periodic MOF structure. The 4,5-pmbc can be re-
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MBB-1 and one MBB-2. The resulting paddlewheel is surrounded
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by 4 La ligands and 2 Lb ligands to yield a 6-connected MBB,
[Cu2(O2C–)4(N–)2]; whereas, two La and two Lb support the for-
mation of the 4-connected MBB, [Cu2I2(N–)4] (Figure 3). The 3-
periodic structure in 2 is sustained by two dinuclear clusters
MBB-1 and MBB-2 that are linked to each other via La and Lb to
form square-like channels that run along c-axis with a pore diame-
ter of 9 Å (Figure 3).
In order to describe the underlying topology of 2 and 3, it is note-
worthy to briefly introduce secondary building units (SBUs) as
the geometrical entity representing the points of extension of the
molecular building blocks (MBBs). From the viewpoint of an
underlying topology,29 2 can be simplified as follows. In 2, when
all coordination sites are considered as points of extension, the
connecting nodes becomes as such: MBB-1 coordinating to 6
ligands, forming a 6-c node representing an octahedral building
unit, as shown in Figure S7 (a) and (b). The rhomboid dimeric
unit [Cu2I2(N–)4] can be viewed as a 4-c node (Figure S7 (c) and
(d)). La represents a 3-c node, Figure S7 (e) and (f). Hence the
overall topology of 2 is a new (3,4,6)-connected net with a transi-
tivity of [3443], Figure S9.
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Compound 3 crystalizes in the hexagonal space group R-3. Crys-
tals of 3 were obtained under similar reaction conditions to 2 upon
the addition of a Cu(II) source. Similar MBBs are observed,
MBB-1 containing a paddlewheel forming a 6-c node with an
octahedral building unit as all the coordination sites of the dimeric
clusters are occupied. In addition, a 4-c rhomboid dimer Cu2I2
cluster is also isolated, along with both modes of coordination of
the 4,5-pmbc, La and Lb. Noticeably, the aromatic rings (phenyl
and pyrimidyl) twisted out of plane with dihedral angles of 47.5°
(1) and 46.1° (1) for La and Lb respectively. The topological anal-
ysis of 3 has been subjected to similar analysis followed for 2. By
accounting for all points of extension, a new (3,4,6)-c net was
derived with a transitivity of [3432], Figure S11.
Figure 3. Coordination environments surrounding MBB-1 and
MBB-2: 4-connected [Cu2I2(N–)4], MBB-1 (to the right). 6-
connected paddlewheel [Cu2(O2C–)4(N–)2], MBB-2 (to the left).
Color code (Cu(I) = bright green, Cu(II) = sea green, I = brown).
Each Cu(I) has a tetrahedral coordination geometry with two co-
ordination sites occupied by two nitrogen atoms from two sepa-
rate ligands and the remaining sites coordinated to two iodide
anions. The two Cu(I) centers are bridged via two iodide anions,
balancing the charge, and affording a dinuclear cluster with
Cu(I)∙∙∙Cu(I) distance of 2.537(2) Å. MBB-2 is the conventional
dinuclear cluster with two Cu(II) ions, [Cu2(O2C–)4(N–)2] with
Cu(II)∙∙∙Cu(II) distance of 2.608(2) Å. It is to note that there is a
significant twist between the phenyl ring and the pyrimidyl ring
with dihedral angles of 37.5° (3) and 44.0° (3) for La and Lb re-
spectively. Each Cu(II) displays a square pyramidal coordination
geometry with four oxygen atoms from four distinct carboxylates
and one N-donor from the pyrimidine moiety. The two crystallo-
graphic independent ligands show different coordination modes
represented by La and Lb (Figure 3). La acting as a tritopic linker,
as shown in Figure 3, where the two N-atoms from the pyrimidine
moiety coordinate to two distinct MBBs and the carboxylate
group being occluded into the paddlewheel. On the other hand, Lb
with only one of its nitrogen atoms coordinating acts as a bridging
linker. Two of the trans-Lb ligands coordinate through carbox-
ylate groups in a bis-monodentate fashion and contribute to the
formation of the dinuclear copper paddlewheel [Cu2(O2C–)4]
MBB, while the associated pyrimidine moieties coordinate via
only one nitrogen and promote the formation of the second inor-
ganic MBB, [Cu2I2(N–)4].
To better understand structures 2 and 3, we opted to assess the
intrinsic roles of each MBB in the associated structures. Close
examination of the respective MBBs connectivity revealed that
the rhomboid dimer [Cu2I2(N–)4] can be deliberately omitted in
the topological analysis and still retain the 3-periodic overall
structure. Resultantly, the connectivity of this structure can be
simplified by means of the following attributes: La can be regard-
ed as a 2-c node bridging two paddlewheels (Figure S8 (c) and (d)
and Lb as a terminal ligand upon discounting the [Cu2I2(N–)4]
(Figure 4, S8 (a)). Subsequently, the resultant connectivity of the
paddlewheel differs from the common square SBU, [Cu2(O2C–)4],
and can be regarded as a lozenge SBU, [Cu2(O2C–)2(N–)2], when
the points of extension are joined together, namely the two car-
boxylate C-atoms of La and the two pyrimidyl N-atoms (at the
apical position) (Figure S8). Noticeably, the simplified structure
can be viewed as a 3-periodic network based on 4-c nodes bridged
via ditopic linker, resulting in a 4-connected net based on the lvt
underlying topology, Figure S10.
Similarly, the topological analysis of structure 3 was subjected to
identical connectivity simplification as applied to structure 2.
Noticeably, the exclusion of the rhomboid dimer didn’t alter the
3-periodic nature of the structure. Consequently, the simplified
structure of 3 can be regarded as a 3-periodic network based on a
4-c nodes SBU, , [Cu2(O2C–)2(N–)2], bridged via ditopic La link-
er, resulting in a 4-connected net based on the nbo underlying
topology, Figure S12.
As for the tritopic ligand, La, apart from the coordination modes
observed in Lb, links both MBBs to a second MBB-1 through the
coordination of the second N-atom on the pyrimidine ring to the
apical position of the paddlewheel. Therefore, La spans through
two 4-connected MBB-1, [Cu2I2(N–)4], and one 6-connected
MBB-2, [Cu2(O2C–)4(N–)2]; whereas, Lb spans through one
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Figure 4. Topological analysis of 2 and 3; (a) La bridging 4-c paddlewheel and Lb acting as terminal ligand (highlighted in turquoise); (b)
and (c) molecular and schematic illustration of 2 and 3 as lvt and nbo, respectively; (d) and (e) View along the c-axis showing square and
hexagonal channels of 2 and 3 respectively.
In summary, we here-in report the isolation of a layered structure
ASSOCIATED CONTENT
Supporting Information
1 and supramolecular isomers 2 and 3 with network structural
differences. We have shown that the concentration of Cu(II) in
solution plays a role in the isolation of 3, which could be driven
by the kinetics of the reaction. In addition, the flexibility of 4,5-
pmbc, allowing both the pyrimidyl group and the carboxylate
group to twist and turn, provides additional degree of freedom in
which the SBUs can be connected to form supramolecular iso-
mers.
PXRD, TGA, structure characterization and crystallographic data.
This material is available free of charge via the Internet at
http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
*Email: mohamed.eddaoudi@kaust.edu.sa
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13. Navarro, J. A. R.; Barea, E.; Galindo, M. A.; Salas, J. M.;
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Romero, M. A.; Quirós, M.; Masciocchi, N.; Galli, S.; Sironi, A.;
Lippert, B. J. Solid State Chem. 2005, 178 (8), 2436-2451.
Notes
The authors declare no competing financial interest.
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14. Moulton, B.; Lu, J.; Hajndl, R.; Hariharan, S.; Zaworotko, M.
J. Angew. Chem. Int. Ed. 2002, 41 (15), 2821-2824.
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15. Zhang, Z.; Wojtas, L.; Zaworotko, M. J. Cryst. Growth Des.
2011, 11 (5), 1441-1445.
ACKNOWLEDGMENT
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This work was supported by the King Abdullah University of
Science and Technology (KAUST)
16. Eubank, J. F.; Wojtas, L.; Hight, M. R.; Bousquet, T.;
Kravtsov, V.; Eddaoudi, M. J. Am. Chem. Soc. 2011, 133 (44),
17532-17535.
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Crystal Growth & Design
For the Table of Content Use Only
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Supramolecular Isomers of Metal-Organic Frameworks
Derived from a Partially Flexible Ligand with Distinct Binding
Motifs
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Rasha G. AbdulHalim, Aleksander Shkurenko, Mohamed H. Alkordi, and Mohamed Eddaoudi*
In the present work, three novel MOFs were isolated upon reacting a heterofunctional ligand 4-(pyrimidin-5-
yl)benzoic acid (4,5-pmbc) with mixed valence Cu(I,II) under solvothermal conditions. The two distinct coordi-
nating moieties in the ligand (carboxylate group and the N-donor atoms) prompted the formation of two 3-
periodic MOFs, supramolecular isomers, with underlying topologies related to lvt and nbo.
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