Showing papers on "Dihedral angle published in 2021"
TL;DR: In this paper, molecular dynamics simulations were carried out to understand the mechanical and energy storage properties of bisphenyl-A diglycidyl ether cured with isophorone diamine, a thermoset shape memory polymer with both excellent shape memory and stress memory properties.
35 citations
TL;DR: A series of axially chiral 1,1'-binaphthyls with trialkylsiloxy (OSiR3 ) groups were synthesized in this article, and the neat liquids showed circularly polarized luminescence (CPL).
Abstract: A series of axially chiral 1,1'-binaphthyls with trialkylsiloxy (OSiR3 ) groups were synthesized. Among them, 1 a-c possessing OSiR3 groups at the 7,7'-positions and methyl groups at the 2,2'-positions were liquids at room temperature, and the neat liquids showed circularly polarized luminescence (CPL) (R=Bu; Φfl,liquid =0.21, |glum,liquid |=1.6×10-3 ). The |glum,liquid | value is the highest of pure liquids. These compounds remained liquid over a broad range of temperatures, down to -50 °C. Time-dependent DFT calculations indicated that in the excited state, the binaphthyls adopt a transoid conformation with a small angle between the electric and magnetic transition dipole moments (θμ,m =77°), which is a key factor in their CPL activity. The best binaphthyl dihedral angle in the excited state is approximately 110°.
26 citations
23 citations
TL;DR: In this article, the authors used STM breaking junction and shell-isolated nanoparticle-enhanced Raman spectroscopy technique to probe electron transport and adsorption geometries of pyridyl molecules at Au(111).
Abstract: Clarifying interfacial electronic effects on molecular adsorption is of great significance in many chemical and biochemical processes but remains a challenge. Here, we have successfully used STM breaking junction and shell-isolated nanoparticle-enhanced Raman spectroscopy technique to probe electron transport and adsorption geometries of pyridyl molecules at Au(111). Modifying Au(111) surface with 1-butyl-3-methylimidazolium cation-containing ionic liquids (ILs) decreases surface electron density and stabilizes a vertical orientation of pyridine through nitrogen atom σ-bond interactions, resulting in uniform adsorption configurations for forming molecular junctions. Furthermore, fine modulation from vertical, tilted, to flat, is achieved on adding water to ILs, leading to a new peak around 1633 cm -1 ascribed to CC stretching mode of adsorbed pyridyl ring and 316% modulation of single-molecule conductance. Combining with DFT calculation reveals that the dihedral angle between adsorbed pyridyl ring and surface decreases with increasing surface electronic density, which enhances electron-donation from surface to pyridyl ring.
20 citations
TL;DR: In this article, the relationship between asymmetric/asymmetric molecule structure and the performance of the oligomers were investigated using the density functional theory (DFT) and time-dependent DFT calculations.
Abstract: Asymmetric molecule strategy is considered an effective method to achieve high power conversion efficiency (PCE) of polymer solar cells (PSCs). In this paper, nine oligomers are designed by combining three new electron-deficient units (unitA)—n1, n2, and n3—and three electron-donating units (unitD)—D, E, and F—with their π-conjugation area extended. The relationships between symmetric/asymmetric molecule structure and the performance of the oligomers are investigated using the density functional theory (DFT) and time-dependent density functional theory (TD–DFT) calculations. The results indicate that asymmetry molecule PEn2 has the minimum dihedral angle in the angle between two planes of unitD and unitA among all the molecules, which exhibited the advantages of asymmetric structures in molecular stacking. The relationship of the values of ionization potentials (IP) and electron affinities (EA) along with the unitD/unitA π-extend are revealed. The calculated reorganization energy results also demonstrate that the asymmetric molecules PDn2 and PEn2 could better charge the extraction of the PSCs than other molecules for their lower reorganization energy of 0.180 eV and 0.181 eV, respectively.
17 citations
TL;DR: In this paper, a compact electron donor-acceptor dyads were prepared, in which the orientation and distance between the two subunits were varied by direct connection or with intervening phenyl linker.
Abstract: Anthracene-naphthalimide (An-NI) compact electron donor-acceptor dyads were prepared, in which the orientation and distance between the two subunits were varied by direct connection or with intervening phenyl linker. Efficient intersystem crossing (ISC) and long triplet state lifetime (ΦΔ =92 %, τT =438 μs) were observed for the directly connected dyads showing a perpendicular geometry (81°). This efficient spin-orbit charge transfer ISC (SOCT-ISC) takes 376 fs, inhibits the direct charge recombination (CR) to ground state (1 CT→S0 , takes 3.04 ns). Interestingly, efficient SOCT-ISC for dyads with intervening phenyl linker (ΦΔ =40 % in DCM) was also observed, although the electron donor and acceptor adopt almost coplanar geometry (dihedral angle: 15°). Time-resolved electron paramagnetic resonance (TREPR) spectroscopy shows that the electron spin polarization of the triplet state, i. e. the electron spin selectivity of ISC, is highly dependent on the dihedral angle and the linker. For the dyads showing weaker coupling between the donor and acceptors, the charge separation and the intramolecular triplet energy transfer are inhibited at 80 K (frozen solution), because both the 3 An and 3 NI states were observed and the ESP are same as compared to the native anthracene and naphthalimide, which unravel their origin. The dyads were used as triplet photosensitizers for triplet-triplet annihilation upconversion (TTA UC). High UC quantum yield (ΦUC =12.9 %) as well as a large anti-Stokes shift (0.72 eV) was attained by excitation into the CT absorption band.
15 citations
TL;DR: In this article, it was shown that changes in conformation associated with the three dihedral angles are not infrequent; a number of events are observed during the course of the simulations allowing for a straightforward estimate of the kinetic parameters.
Abstract: The central OCCO dihedral of the ethylene glycol (EG) molecule exists in both trans and gauche geometries in the liquid The presence of the trans conformer had been inferred from the Raman spectra by interpreting the occurrence of bands in the Raman spectra that were absent in the infrared as evidence for inversion symmetry and hence the trans conformation The validity of this interpretation is questionable as not all conformations of the EG molecule, where the OCCO dihedral is trans, possess inversion symmetry We show here that the resolution of the apparent paradox is intimately related to the conformation and dynamics of not just the central OCCO but also the two terminal dihedrals of the EG molecule Using ab initio molecular dynamics simulations, we show that changes in conformation associated with the three dihedral angles are not infrequent; a number of events are observed during the course of the simulations allowing for a straightforward estimate of the kinetic parameters More importantly, these parameters allow us to address and resolve the problems in interpreting the Raman spectra and consequently relate molecular conformation to the Raman spectrum of the EG molecule in the liquid state
12 citations
TL;DR: In this article, an azobenzene unit is intentionally introduced through atomically precise side functionalization at the central ring of the terphenyl, which is reversibly isomerized between trans and cis forms by either electric or optical stimuli.
Abstract: Charge transport in a single-molecule junction is extraordinarily sensitive to both the internal electronic structure of a molecule and its microscopic environment. Two distinct conductance states of a prototype terphenyl molecule are observed, which correspond to the bistability of outer phenyl rings at each end. An azobenzene unit is intentionally introduced through atomically precise side-functionalization at the central ring of the terphenyl, which is reversibly isomerized between trans and cis forms by either electric or optical stimuli. Both experiment and theory demonstrate that the azobenzene side-group delicately modulates charge transport in the backbone via a single-molecule stereoelectronic effect. We reveal that the dihedral angle between the central and outer phenyl ring, as well as the corresponding rotation barrier, is subtly controlled by isomerization, while the behaviors of the phenyl ring away from the azobenzene are hardly affected. This tunability offers a new route to precisely engineer multiconfigurational single-molecule memories, switches, and sensors.
12 citations
TL;DR: In this paper, the cycloaddition reaction of azide-alkyne derivatives with glucopyranose azide 2a,b was catalyzed via Cu(I) to afford the corresponding acetylated 1,2,3-triazole N-glycoside derivatives.
12 citations
TL;DR: The chirality of 1,1′-binaphthol (BINOL) is due to the restricted rotation between two naphthalene rings, and its skeletal structure of binaphthyl unit can be further modified by choosing functionalize as discussed by the authors.
Abstract: Chirality of 1,1′-binaphthol (BINOL) is due to the restricted rotation between two naphthalene rings, and its skeletal structure of binaphthyl unit can be further modified by choosing functionalize...
12 citations
TL;DR: In this article, the title compound, C10H10FNO3, is synthesized efficiently, and its structure is confirmed by the SC-XRD technique, which indicates that two crystallographically different molecules are present in the asymmetric unit.
Abstract: The title compound, C10H10FNO3, also known as [4-((4-fluorophenyl)amino)-4-oxobutanoic acid] (BFAOB), is synthesized efficiently, and its structure is confirmed by the SC-XRD technique, which indicates that two crystallographically different molecules are present in the asymmetric unit. The fluorobenzene ring is oriented at a dihedral angle of 76.09 (9)° and 23.7 (2)° with respect to acetamide moiety in the first and second types of molecule, respectively. A molecular overlay plot is employed to explore the difference between two types of molecules. Strong hydrogen bonding of type N–H…O, O–H…O and comparatively weak hydrogen bonding of type C-H…O stabilize the crystal packing. The titled compound is also characterized by powder XRD. Hirshfeld surface inspection is carried out to explore the non-covalent interactions that are responsible for crystal packing. DFT calculations demonstrate the high stability of BFAOB crystal compound.
TL;DR: In this article, the authors determined the energy distribution of CT states of the TADF emitter TPSA in frozen toluene at 77 K by the measurement of time-resolved spectra in the full time range (1 ns to 30 s).
Abstract: Reverse intersystem crossing (RISC) rate of a thermally activated delayed fluorescence (TADF) molecule is sensitive to the energy alignment of the singlet charge-transfer state (1CT), triplet charge-transfer state (3CT), and locally excited triplet state (3LE). However, the energy distribution of the charge-transfer states originating from the conformational distribution of TADF molecules in a solid matrix inevitably generated during the preparation of a solid sample due to the rotatable donor-acceptor linkage is rarely considered. Moreover, the investigation of the energy distribution of the 3CT state is both theoretically and experimentally difficult due to the triplet instabilities of time-dependent density functional (TD-DFT) calculations and difficulties in phosphorescence measurements, respectively. As a result, the relationships between conformational distribution, configurations of excited state transition orbitals, and excited state energies/dynamics have not been clearly explained. In this work, we determined the energy distribution of CT states of the TADF emitter TPSA in frozen toluene at 77 K by the measurement of time-resolved spectra in the full time range (1 ns to 30 s) of emission including prompt fluorescence, TADF, 3CT phosphorescence, and 3LE phosphorescence. We obtained the energy band of CT states where 1CT and 3CT states are distributed in the range of 2.85-3.00 and 2.64-2.96 eV, respectively. We tested various global hybrid and long-range corrected functionals for the TD-DFT calculation of 3CT energy of TPSA and found that only the M11 functional shows consistent results without triplet instability. We performed TD-DFT with the M11* functional optimized for a robust dihedral angle scan of 3CT states without triplet instability and reproduced the energy band structure obtained from the experiment. Through TD-DFT and experimental investigations, it is estimated that the dihedral angles of donor-acceptor (θD-A) and acceptor-linker (θA) of TPSA in frozen toluene lie within the range 70° ≤ θD-A ≤ 90° and 0° ≤ θA ≤ 30° respectively. Our results show that the dihedral angle distribution must be considered for further investigation of the photophysics of TADF molecules and the development of stable and efficient TADF emitters.
TL;DR: In this article, the largest substituent variations on amidinate ligands bring delicate changes of CrN4 coordination in a family of chromium(II) complexes with the common formula of Cr(RNC(CH3)NR)2, where R = iPr (1), Cy (2), Dipp (Dipp = 2, 6-diisopropylphenyl) (3), and tBu (4).
Abstract: Systematic substituent variations on amidinate ligands bring delicate changes of CrN4 coordination in a family of chromium(II) complexes with the common formula of Cr(RNC(CH3)NR)2, where R = iPr (1), Cy (2), Dipp (Dipp = 2, 6-diisopropylphenyl) (3), and tBu (4). With the largest substituent group, 4 shows the largest distortion of the N4 coordination geometry from square-planar to seesaw shape, which leads to its field-induced single-molecule magnet (SMM) behavior. This is an indication that 4 has the strongest axial magnetic anisotropy and/or optimized magnetic relaxation process. Combined with high-frequency/field electron paramagnetic resonance (HF-EPR) experiments and ab initio calculations, we deduce that the smallest energy gap between ground 4Ψ0 and the first excited 4Ψ1 orbitals in 4 contributes the most to its strongest magnetic anisotropy. Moreover, the lower E value of 4 ensures its being a field-induced SMM. Specifically, the D and E values were found to be correlated to the dihedral angle between the ΔN1CrN2 and ΔN3CrN4 triangles, indicating that distortion from ideal square-planar geometry to the seesaw help increase axial magnetic anisotropy and suppress the transversal part. Thus, the study on this system not only expands the family of Cr(II)-based SMMs but also contributes to a deeper understanding of magneto-structural correlation in four-coordinate Cr(II) SMMs.
TL;DR: In this paper, the influence factors on the heat transfer of polydimethylsiloxane (PDMS), a kind of thermal interface materials (TIMs), were analyzed.
TL;DR: In this paper, the 1,2,7,8-tetra-hydro-iso-quinoline ring system has a twist-boat conformation, with Cremer-Pople parameters QT = 0.367, QT θ = 117.3, and φ = 327.3.
Abstract: In the title compound, C28H21N3O, the 1,2-dihydropyridine ring of the 1,2,7,8-tetrahydroisoquinoline ring system is planar as expected, while the cyclohexa-1,3-diene ring has a twist-boat conformation, with Cremer–Pople parameters QT = 0.367 (2) A, θ = 117.3 (3)° and φ = 327.3 (4)°. The dihedral angles between the best planes through the isoquinoline ring system and the three phenyl rings are 81.69 (12), 82.45 (11) and 47.36 (10)°. In the crystal, molecules are linked via N—H⋯O and C—H⋯N hydrogen bonds, forming a three-dimensional network. Furthermore, the crystal packing is dominated by C—H⋯π bonds with a strong interaction involving the phenyl H atoms. The role of the intermolecular interactions in the crystal packing was clarified using Hirshfeld surface analysis, and two-dimensional fingerprint plots indicate that the most important contributions to the crystal packing are from H⋯H (46.0%), C⋯H/H⋯C (35.1%) and N⋯H/H⋯N (10.5%) contacts.
TL;DR: In this article, a new type of distorted nanographene was designed and synthesized by Diels-Alder and Scholl reactions that contains one dibenzobistetracene (DBT, 1) core and two end-capping corannulene units.
Abstract: We have designed and synthesized a new type of distorted nanographene by Diels-Alder and Scholl reactions that contains one dibenzobistetracene (DBT, 1) core and two end-capping corannulene units. Single-crystal X-ray diffraction analyses demonstrate that nanographene 1 contains two [5] helicene subunits with a dihedral angle of 62°, consequently leading to the distorted DBT core. In addition, the photophysical properties and (non)aromaticity of 1 were investigated by the absorption and emission spectra in combination with theoretical calculations.
TL;DR: In this paper, the chemical structure of 6-formylvisnagin with cyanoacetic acid in dry pyridine has been determined by the elemental analysis and spectral data, and individual emulation characteristics of compound (2, MOFCA) were accomplished by DFT, and TD-DFT/B3LYP, at 6-311 ++ G (d, p).
TL;DR: Using density functional theory in combination with Green's functional formalism, quantum transport through molecular junctions containing pyrimidine units characterized by a permanent dipole moment is studied and can be useful in understanding the role of polar self-assembled monolayers in interface engineering.
TL;DR: In this paper, a series of benzohydrazide/benzoic acid derivatives were synthesized and subjected to solid-state characterization by NMR spectroscopic measurements, which revealed that naphthalene frameworks are close to planarity and the dihedral angle between the mean plane of the naphalene ring system and the phenyl ring is 2.26(7) and 78.87(8)° for 4a and 5a, respectively.
TL;DR: In this paper, the melting point of room temperature ionic liquids is explained in terms of the presence of bulky, low symmetry and flexible ions, with the first two factors related to the lattice energy while an entropic effect is attributed to the latter.
Abstract: The low melting point of room temperature ionic liquids is usually explained in terms of the presence of bulky, low symmetry and flexible ions, with the first two factors related to the lattice energy while an entropic effect is attributed to the latter. By means of molecular dynamics simulations, the melting points of 1-ethyl-3-methylimidazolium hexafluorophosphate and 1-decyl-3-methyl-imidazolium hexafluorophosphate were determined and the effect of the molecular flexibility over the melting point was explicitly computed by restraining the rotation of dihedral angles in both the solid and the liquid phase. The rotational flexibility over the bond between the ring and the alkyl chain affects the relative ordering of the anions around the cations and results in substantial effects over both the enthalpy and the entropy of melting. For the other dihedral angles of the alkyl group, the contributions are predominantly entropic and an alternating behavior was found. The flexibility of some dihedral angles has negligible effects on the melting point, while others can lead to differences in the melting point as large as 20 K. This alternating behavior is rationalized by the different probabilities of conformation defects in the crystal.
TL;DR: It can be assumed that interaction of TPhTCl molecule with metal cluster results in orientation ordering of the benzene rings, and the formation of weak hydrogen bonds and the rearrangement of the Benzene rings to form a complex with negatively charged parts of other molecules were proven by ESP maps.
TL;DR: In this article, the authors describe the synthesis and characterization of a trinuclear Ni(II) Schiff base complex of formula [Ni3(L)2NCS)2(OAc)2 (CH3OH)2] (1) where HL is the 1 : 1 condensation product of 2-picolylamine and o-vanillin.
Abstract: We describe the synthesis and characterization of a new trinuclear Ni(II) Schiff base complex of formula [Ni3(L)2(NCS)2(OAc)2(CH3OH)2] (1) where HL is the 1 : 1 condensation product of 2-picolylamine and o-vanillin. The crystal structure of complex 1 shows that the two terminal Ni(II) ions are connected to the central one through a phenoxido- and a syn–syn acetato bridge, giving rise to a very bent configuration in the Ni3-core. Magnetic susceptibility measurements show the presence of a weak antiferromagnetic coupling with J = −3.22(2) cm−1. We also report a magneto-structural correlation, performed with all the magnetically characterized Ni(II) trimers with similar bridges, showing a linear dependence between the J value and the dihedral angle (θ) between the planes containing the Ni–O–Ni and the carboxylate bridges. The super-exchange interaction is investigated by extensive density functional calculations within the broken symmetry approximation which show good agreement with the experimental data. The analysis of the spin density distribution and the shape of the magnetically active single occupied molecular orbitals (SOMO) provide a mechanism of exchange coupling through the bridging groups.
TL;DR: In this article, the authors employed sensitive fluorescence depolarization kinetics by following picosecond time-resolved fluorescence anisotropy decays to directly capture the essential dynamical features of intrinsically disordered α-synuclein (α-syn) site-specifically labeled with thiol-active fluorophores.
Abstract: Intrinsically disordered proteins (IDPs) do not autonomously fold into well-defined three-dimensional structures and are best described as a heterogeneous ensemble of rapidly interconverting conformers. It is challenging to elucidate their complex dynamic signatures using a single technique. In this study, we employed sensitive fluorescence depolarization kinetics by following picosecond time-resolved fluorescence anisotropy decays to directly capture the essential dynamical features of intrinsically disordered α-synuclein (α-syn) site-specifically labeled with thiol-active fluorophores. By utilizing a long-lifetime (≥10 ns) anisotropic label, we were able to discern three distinct rotational components of α-syn. The subnanosecond component represents the local wobbling-in-cone motion of the fluorophore, whereas the slower (∼1.4 ns) component corresponds to the short-range backbone dynamics governed by collective torsional fluctuations in the Ramachandran Φ-Ψ dihedral space. This backbone dihedral rotational time scale is sensitive to the local chain stiffness and slows down in the presence of an adjacent proline residue. We also observed a small-amplitude (≤10%) slower rotational correlation time (6-10 ns) that represents the long-range correlated dynamics involving a much longer segment of the polypeptide chain. These intrinsic dynamic signatures of IDPs will provide critical mechanistic underpinnings in a mosaic of biophysical phenomena involving internal friction, allosteric interactions, and phase separation.
TL;DR: In this article, the twisting angle tuning effect induced by the intramolecular hydrogen bond on the charge transport through their single-molecule junctions was investigated, and it was shown that the presence of strong inter-atomic hydrogen bonds promoted the planarization of the molecular structure without additional transmission channels, offering a new strategy for controlling molecular switches via tuning the molecular twisting.
TL;DR: In this paper, the authors calculate the Hugoniot relations of polyurea and investigate the atomic-scale energy change, the related chain conformation evolution and the hydrogen bond dissociation of polyuresa under high-speed shock.
Abstract: The purpose of this paper is to calculate the Hugoniot relations of polyurea; also to investigate the atomic-scale energy change, the related chain conformation evolution and the hydrogen bond dissociation of polyurea under high-speed shock.,The atomic-scale simulations are achieved by molecular dynamics (MD). Both non-equilibrium MD and multi-scale shock technique are used to simulate the high-speed shock. The energy dissipation is theoretically derived by the thermodynamic and the Hugoniot relations. The distributions of bond length, angle and dihedral angle are used to characterize the chain conformation evolution. The hydrogen bonds are determined by a geometrical criterion.,The Hugoniot relations calculated are in good agreement with the experimental data. It is found that under the same impact pressure, polyurea with lower hard segment content has higher energy dissipation during the shock-release process. The primary energy dissipation way is the heat dissipation caused by the increase of kinetic energy. Unlike tensile simulation, the molecular potential increment is mainly divided into the increments of the bond energy, angle energy and dihedral angle energy under shock loading and is mostly stored in the soft segments. The hydrogen bond potential increment only accounts for about 1% of the internal energy increment under high-speed shock.,The simulation results are meaningful for understanding and evaluating the energy dissipation mechanism of polyurea under shock loading, and could provide a reference for material design.
TL;DR: In this article, the authors present an equivalent geometric condition to the maximum angle condition for tetrahedrons, which ensures that we can obtain an error estimation, even on certain kinds of anisotropic tetrahedral structures.
Abstract: For a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant C that is smaller than π. Then, it is said to satisfy the maximum angle condition with the constant C. The maximum angle condition is important in the error analysis of Lagrange interpolation on tetrahedrons. This condition ensures that we can obtain an error estimation, even on certain kinds of anisotropic tetrahedrons. In this paper, using two quantities that represent the geometry of tetrahedrons, we present an equivalent geometric condition to the maximum angle condition for tetrahedrons.
TL;DR: In this paper, a series of 3,7-diphenyl-1,5-dioctyl derivatives bearing various substituents (i.e., OCH3, CH3, H, F, and Cl) in the end-capping phenyl rings were designed and synthesized.
Abstract: To elucidate the origin of high charge carrier mobility in bis-lactam compounds with twisted geometries, we designed and synthesized a series of 3,7-diphenyl-1,5-dioctyl-1,5-naphthyridine-2,6-dione (NTDP) derivatives bearing various substituents (i.e., OCH3, CH3, H, F, and Cl) in the end-capping phenyl rings. Despite the distinct dihedral angle between the 1,5-naphthyridine-2,6-dione (NTD) core and the end-capping groups, all of the derivatives formed rigid molecular structures and the delocalized highest occupied molecular orbitals (HOMOs), which could lead to high charge transport properties. Among the derivatives, the fluorinated NTDP molecule (NTDP-F) exhibited the highest hole mobility of 0.54 cm2 V−1 s−1 in vacuum-deposited organic field-effect transistors (OFETs) due to the strong intermolecular interaction, high crystallinity, and two-dimensional (2D) terrace-like morphology in the thin-film. Furthermore, the twisted geometry of NTDP-F allowed facile solution processability resulting in a high hole mobility of up to 0.27 cm2 V−1 s−1 in solution-processed OFETs.
TL;DR: In this article, the authors showed that the total crystal net energy is the main factor in determining the molecular conformations even if the molecular conformation has a higher energy in the gaseous phase.
Abstract: A specially designed new compound, 5,5′-bis(4-hydroxyphenyl)-2,2′-dihydroxy-1,1′-biphenyl, can crystallize in different crystallographic systems. The molecule adopts the C-conformation for the torsion angle of around 60° and the T-conformation for the angle of around 130°, which differ in energy by ∼0.8 kJ mol−1. Theoretical studies for the gaseous phase show that the C-conformer has a lower energy. However, crystallization experiments show that the most stable crystal structure consists of only the energetically less stable T-conformer. On the other hand, fast crystal growth at low temperature and crystal growth after milling both lead to the formation of metastable crystals in which the studied molecule adopts the C-conformation. Our study shows that the total crystal net energy is the main factor in determining the molecular conformations even if the molecular conformation has a higher energy in the gaseous phase.
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TL;DR: In this article, it was shown that the ADM mass in general relativity can be expressed as the limit of the total mean curvature plus the total defect of dihedral angle of the boundary of large Riemannian polyhedra.
Abstract: We show that the concept of the ADM mass in general relativity can be understood as the limit of the total mean curvature plus the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also express the $n$-dimensional mass as a suitable integral of geometric quantities that determine the $(n-1)$-dimensional mass.