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Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium–Ligand Bonds
Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D e and bond length r e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15–0.19. For the single-reference methods, Kohn–Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D e and r e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core–valence terms; this results in highly accurate dissociation energies and good bond lengths. In conclusion, averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.
Bond-length dependence of attosecond ionization delays in O 2 arising from electron correlation to a shape resonance
We experimentally and theoretically demonstrate that electron correlation can cause the bond-length sensitivity of a shape resonance to induce an unexpected vibrational state–dependent ionization delay in a nonresonant channel. This discovery was enabled by a high-resolution attosecond-interferometry experiment based on a 400-nm driving and dressing wavelength. The short-wavelength driver results in a 6.2–electron volt separation between harmonics, markedly reducing the spectral overlap in the measured interferogram. We demonstrate the promise of this method on O 2 , a system characterized by broad vibrational progressions and a dense photoelectron spectrum. We measure a 40-attosecond variation of the photoionization delays over the X 2 Π g vibrational progression. Multichannel calculations show that this variation originates from a strong bond-length dependence of the energetic position of a shape resonance in the b 4 Σ$^{-}_{g}$ channel, which translates to the observed effects through electron correlation. The unprecedented energy resolution and delay accuracies demonstrate the promise of visible-light–driven molecular attosecond interferometry.
Bond length alternation of π -conjugated polymers predicted by the Fermi–Löwdin orbital self-interaction correction method
π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi–Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller–Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).
Flexibility of oxygen sublattice and hydrogen bond length predict proton mobility in ternary metal oxides
Discovery of fast proton conductors is important for advancing clean energy technologies. This requires a better understanding of proton migration mechanisms. While structural and chemical traits of ternary metal oxides have been related to proton migration barriers, lattice dynamical effects have not been resolved quantitatively. Here, in this work, we introduce a phonon-based dynamic descriptor, termed ‘‘thermal O…O fluctuation,’’ quantifying the flexibility of donor-acceptor oxide-ion pairs. This enables direct comparison of O-sublattice flexibility across diverse metal oxides. Using regression models, we ranked physical descriptors as predictors of proton mobility, finding that H-bond length and thermal O…O fluctuation were the strongest descriptors. Further analysis revealed a critical O…O spacing of 2.4 A˚ at the transition state, which is easier to reach by more flexible donor-acceptor pairs, enabling facile proton transfer. Our results demonstrate oxygen sublattice flexibility as a dynamic descriptor and provide guiding principles for enhancing proton mobility in ternary metal oxides.
Unusual Changes of C−H Bond Lengths in Chiral Zinc Complexes Induced by Noncovalent Interactions
In order to better understand the effect of non-covalent weak interactions on molecules, we have explored a variety of weak interactions, such as improper H-bonding (HB), tetrel bonds (TBs) and halogen bonds, in fluorinated chiral zinc complexes. High resolution neutron diffraction studies revealed a methylene carbon-hydrogen bond elongation and shortening due to TB and improper HB interactions, respectively. To show the accumulative effects of multiple weak interactions on the C-H bond, three types of tetrel bonds have been carefully examined. We have also shown how C-H bond elongation can be easily offset by forming an improper HB with the H atom from this C-H bond. Non-covalent interaction and electrostatic potential analysis investigations have been used to affirm the nature of the interactions based on density functional theory (DFT) and other related calculations.
Bond Length Alternation and Internal Dynamics in Model Aromatic Substituents of Lignin
In this report broadband microwave spectra were recorded over the 2-18 GHz frequency range for a series of four model aromatic components of lignin; namely, guaiacol (ortho-methoxy phenol, G), syringol (2,6-dimethoxy phenol, S), 4-methyl guaiacol (MG), and 4-vinyl guaiacol (VG), under jet-cooled conditions in the gas phase. Using a combination of 13 C isotopic data and electronic structure calculations, distortions of the phenyl ring by the substituents on the ring are identified. In all four molecules, the r C(1)-C(6) bond between the two substituted C-atoms lengthens, leading to clear bond alternation that reflects an increase in the phenyl ring resonance structure with double bonds at r C(1)-C(2) , r C(3)-C(4) and r C(5)-C(6) . Syringol, with its symmetric methoxy substituents, possesses a microwave spectrum with tunneling doublets in the a-type transitions associated with H-atom tunneling. These splittings were fit to determine a barrier to hindered rotation of the OH group of 1975 cm -1 , a value nearly 50% greater than that in phenol, due to the presence of the intramolecular OH…OCH 3 H-bonds at the two equivalent planar geometries. In 4-methyl guaiacol, methyl rotor splittings are observed and used to confirm and refine an earlier measurement of the three-fold barrier V 3 = 67 cm -1 . Finally, 4-vinyl guaiacol shows transitions due to two conformers differing in the relative orientations of the vinyl and OH groups.
Disentangling the role of bond lengths and orbital symmetries in controlling $T_c$ of optimally doped YBa 2 Cu 3 O 7
Optimally doped YBa 2 Cu 3 O 7 (YBCO) has a high critical temperature, at 92 K. It is largely believed that Cooper pairs form in YBCO and other cuprates because of spin fluctuations, but the issue and the detailed mechanism are far from settled. In the present work, we employ a state-of-the-art first-principles ability to compute both the low- and high-energy spin fluctuations in optimally doped YBCO. We benchmark our results against recent inelastic neutron scattering and resonant inelastic x-ray scattering measurements. Further, we use strain as an external parameter to modulate the spin fluctuations and superconductivity. We disentangle the roles of barium-apical oxygen hybridization, interlayer coupling, and orbital symmetries by applying an idealized strain, and also a strain with a fully relaxed structure. We show that shortening the distance between Cu layers is conducive to enhanced Fermi surface nesting, which increases spin fluctuations and drives up $T_c$. However, when the structure is fully relaxed, electrons flow to the $d_{z^2}$ orbital as a consequence of a shortened Ba-O bond, which is detrimental for superconductivity.
Syntheses, solution behavior, and computational bond length analyses of trifluoromethyl and perfluoroethyl cuprate salts
Heteroleptic cuprate salts of the form [X-Cu-Y][(SIMes) 2 Cu] (SIMes = 1,3-dimesitylimidazolin-2-ylidene, X and Y = permutations of Cl, CF 3 , C 2 F 5 ) were generated by equilibrating mixtures of [(SIMes)Cu-X] and [(SIMes)Cu-Y] in CD 2 Cl 2 solvent. Here, the solubility features of the cuprates relative to the neutral species permitted the structural characterizations of new cuprates, including the first example of a mixed fluoroalkylated cuprate [(CF 3 )Cu(C 2 F 5 )][(SIMes) 2 Cu]. Computational studies (DFT and CCSD(T)) of fluoroalkylated cuprates generate Cu-C distances that are shorter than those in hydrocarbon analogues – a trend that in some cases may conflict with crystallographically determined values.
N-Heterocyclic Carbene to Actinide d-Based π-bonding Correlates with Observed Metal–Carbene Bond Length Shortening Versus Lanthanide Congeners
Not Available
Atomistic insight into the ferroelastic post-stishovite transition by high-pressure single-crystal X-ray diffraction
Abstract The post-stishovite transition is a classic pseudo-proper typed ferroelastic transition with a symmetry-breaking spontaneous strain. This transition has been studied using high-pressure spontaneous strains, optic modes, and elastic moduli (Cij) based on the Landau modeling, but its atomistic information and structural distortion remain poorly understood. Here we have conducted synchrotron single-crystal X-ray diffraction measurements on stishovite crystals up to 75.3 GPa in a diamond-anvil cell. Analysis of the data reveals atomic positions, bond lengths, bond angles, and variations of SiO6 octahedra across the transition at high pressure. Our results show that the O coordinates split at ~51.4 GPa, where the apical and equatorial Si-O bond lengths cross over, the SiO6 octahedral distortion vanishes, and the SiO6 octahedra start to rotate about the c axis. Moreover, distortion mode analysis shows that an in-plane stretching distortion (GM1+ mode) occurs in the stishovite structure at high pressure while a rotational distortion (GM2+ mode) becomes dominant in the post-stishovite structure. These results are used to correlate with elastic moduli and Landau parameters (symmetry-breaking strain e1–e2 and order parameter Q) to provide atomistic insight into the ferroelastic transition. When the bond lengths of two Si-O bonds are equal due to the contribution from the GM1+ stretching mode, C11 converges with C12, and the shear wave VS1[110] polarizing along [110] and propagating along [110] vanishes. Values of e1–e2 and Q are proportional to the SiO6 rotation angle from the occurrence of the GM1+ rotational mode in the post-stishovite structure. Our results on the pseudo-proper type transition are also compared with that for the proper type in albite and improper type in CaSiO3 perovskite. The symmetry-breaking strain, in all these types of transitions, arises as the primary effect from the structural angle (such as SiO6 rotation or lattice constant angle) and its relevant distortion mode in the low-symmetry ferroelastic phase.
Improved Predictive Tools for Structural Properties of Metal–Organic Frameworks
The accurate determination of structural parameters is necessary to understand the electronic and magnetic properties of metal–organic frameworks (MOFs) and is a first step toward accurate calculations of electronic structure and function for separations and catalysis. Theoretical structural determination of metal-organic frameworks is particularly challenging because they involve ionic, covalent, and noncovalent interactions, which must be treated in a balanced fashion. Here, we apply a diverse group of local exchange-correlation functionals (PBE, PBEsol, PBE-D2, PBE-D3, vdW-DF2, SOGGA, MN15-L, revM06-L, SCAN, and revTPSS) to a broad test set of MOFs to seek the most accurate functionals to study various structural aspects of porous solids, in particular to study lattice constants, unit cell volume, two types of pore size characteristics, bond lengths, bond angles, and torsional angles). The recently developed meta functionals revM06-L and SCAN, without adding any molecular mechanics terms, are able to predict more accurate structures than previously recommended functionals, both those without molecular mechanics terms (PBE, PBEsol, vdW-DF2, and revTPSS) and those with them (PBE-D2 and PBE-D3). To provide a broader test, these two functionals are also tested for lattice constants and band gaps of unary, binary, and ternary semiconductors.
Materials Data on Te2As2SI6(OF6)2 by Materials Project
AsTeF4(AsF3)2AsTeIF5As3Te3SO6I13F25AsSI2F3OIS1SI2Te2OI4F4TeIF crystallizes in the triclinic P1 space group. The structure is one-dimensional and consists of one ctk7c3725 molecule; two trifluoroarsine molecules; one AsSI2F3 cluster; one AsTeF4 cluster; one AsTeIF5 cluster; one OIS1 cluster; one Te2OI4F4 cluster; one TeIF cluster; and one As3Te3SO6I13F25 ribbon oriented in the (1, 0, 0) direction. In the AsSI2F3 cluster, As5+ is bonded in a distorted T-shaped geometry to three F1- atoms. There is one shorter (1.77 Å) and two longer (1.78 Å) As–F bond length. S2- is bonded in a 3-coordinate geometry to two I and one F1- atom. There are one shorter (2.41 Å) and one longer (2.42 Å) S–I bond lengths. The S–F bond length is 3.11 Å. There are two inequivalent I sites. In the first I site, I is bonded in a single-bond geometry to one S2- atom. In the second I site, I is bonded in a single-bond geometry to one S2- atom. There are three inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one As5+ and one S2- atom. In the third F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the AsTeF4 cluster, As5+ is bonded in a distorted T-shaped geometry to three F1- atoms. There is two shorter (1.76 Å) and one longer (1.82 Å) As–F bond length. Te4+ is bonded in a distorted linear geometry to two F1- atoms. There are one shorter (1.96 Å) and one longer (2.60 Å) Te–F bond lengths. There are four inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the third F1- site, F1- is bonded in a distorted bent 120 degrees geometry to one As5+ and one Te4+ atom. In the fourth F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the AsTeIF5 cluster, As5+ is bonded in a distorted T-shaped geometry to three F1- atoms. There are a spread of As–F bond distances ranging from 1.75–1.91 Å. Te4+ is bonded in a 2-coordinate geometry to one I and three F1- atoms. The Te–I bond length is 2.86 Å. There are a spread of Te–F bond distances ranging from 1.91–2.39 Å. I is bonded in a 1-coordinate geometry to one Te4+ atom. There are five inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the third F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the fourth F1- site, F1- is bonded in a 2-coordinate geometry to one As5+ and one Te4+ atom. In the fifth F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the OIS1 cluster, S2- is bonded in a distorted single-bond geometry to one O2- and one I atom. The S–O bond length is 1.47 Å. The S–I bond length is 2.55 Å. O2- is bonded in a single-bond geometry to one S2- atom. I is bonded in a distorted single-bond geometry to one S2- atom. In the Te2OI4F4 cluster, there are two inequivalent Te4+ sites. In the first Te4+ site, Te4+ is bonded in a distorted linear geometry to two I and two F1- atoms. There are one shorter (2.70 Å) and one longer (2.71 Å) Te–I bond lengths. There are one shorter (1.97 Å) and one longer (2.19 Å) Te–F bond lengths. In the second Te4+ site, Te4+ is bonded in a 3-coordinate geometry to one O2- and two F1- atoms. The Te–O bond length is 2.29 Å. There is one shorter (1.92 Å) and one longer (1.95 Å) Te–F bond length. O2- is bonded in a 3-coordinate geometry to one Te4+ and two I atoms. There are one shorter (2.05 Å) and one longer (2.29 Å) O–I bond lengths. There are four inequivalent I sites. In the first I site, I is bonded in a 1-coordinate geometry to one O2- atom. In the second I site, I is bonded in a 1-coordinate geometry to one Te4+ atom. In the third I site, I is bonded in a linear geometry to one O2- and one F1- atom. The I–F bond length is 2.43 Å. In the fourth I site, I is bonded in a distorted single-bond geometry to one Te4+ atom. There are four inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the third F1- site, F1- is bonded in a distorted water-like geometry to one Te4+ and one I atom. In the fourth F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the TeIF cluster, Te4+ is bonded in a distorted single-bond geometry to one I and one F1- atom. The Te–I bond length is 2.69 Å. The Te–F bond length is 1.96 Å. I is bonded in a single-bond geometry to one Te4+ atom. F1- is bonded in a single-bond geometry to one Te4+ atom. In the As3Te3SO6I13F25 ribbon, there are three inequivalent As5+ sites. In the first As5+ site, As5+ is bonded in a distorted trigonal non-coplanar geometry to two O2- and one F1- atom. There is one shorter (1.79 Å) and one longer (1.83 Å) As–O bond length. The As–F bond length is 1.78 Å. In the second As5+ site, As5+ is bonded in a distorted rectangular see-saw-like geometry to one O2- and three F1- atoms. The As–O bond length is 2.19 Å. There are a spread of As–F bond distances ranging from 1.75–1.90 Å. In the third As5+ site, As5+ is bonded in a distorted T-shaped geometry to three F1- atoms. There is two shorter (1.80 Å) and one longer (1.82 Å) As–F bond length. There are three inequivalent Te4+ sites. In the first Te4+ site, Te4+ is bonded in a 3-coordinate geometry to four F1- atoms. There are a spread of Te–F bond distances ranging from 1.92–2.79 Å. In the second Te4+ site, Te4+ is bonded in a 3-coordinate geometry to one O2- and three F1- atoms. The Te–O bond length is 2.06 Å. There are a spread of Te–F bond distances ranging from 1.99–2.87 Å. In the third Te4+ site, Te4+ is bonded in a 3-coordinate geometry to four F1- atoms. There are a spread of Te–F bond distances ranging from 1.91–2.83 Å. S2- is bonded in a trigonal non-coplanar geometry to two I and one F1- atom. There are one shorter (2.40 Å) and one longer (2.44 Å) S–I bond lengths. The S–F bond length is 3.34 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to one As5+ and one I atom. The O–I bond length is 1.86 Å. In the second O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two I atoms. There are one shorter (2.00 Å) and one longer (2.13 Å) O–I bond lengths. In the third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Te4+ and one I atom. The O–I bond length is 1.95 Å. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to one I atom. The O–I bond length is 1.83 Å. In the fifth O2- site, O2- is bonded in a 2-coordinate geometry to one As5+ and one I atom. The O–I bond length is 1.97 Å. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one As5+ and one I atom. The O–I bond length is 2.05 Å. There are thirteen inequivalent I sites. In the first I site, I is bonded in a linear geometry to two F1- atoms. There are one shorter (2.04 Å) and one longer (2.17 Å) I–F bond lengths. In the second I site, I is bonded in a single-bond geometry to one I and one F1- atom. The I–I bond length is 2.98 Å. The I–F bond length is 2.03 Å. In the third I site, I is bonded in a linear geometry to two F1- atoms. There are one shorter (2.03 Å) and one longer (2.38 Å) I–F bond lengths. In the fourth I site, I is bonded in a linear geometry to two F1- atoms. There are one shorter (1.96 Å) and one longer (2.45 Å) I–F bond lengths. In the fifth I site, I is bonded in a single-bond geometry to one O2- atom. In the sixth I site, I is bonded in a 1-coordinate geometry to one S2-, one I, and one F1- atom. The I–F bond length is 3.35 Å. In the seventh I site, I is bonded in a distorted single-bond geometry to one S2- and one F1- atom. The I–F bond length is 2.49 Å. In the eighth I site, I is bonded in a distorted single-bond geometry to one O2- and one F1- atom. The I–F bond length is 3.19 Å. In the ninth I site, I is bonded in a 4-coordinate geometry to one O2- and three F1- atoms. There are a spread of I–F bond distances ranging from 2.00–2.97 Å. In the tenth I site, I is bonded in a T-shaped geometry to one O2- and two F1- atoms. There are one shorter (1.98 Å) and one longer (2.09 Å) I–F bond lengths. In the eleventh I site, I is bonded in a T-shaped geometry to one O2- and two F1- atoms. There are one shorter (1.96 Å) and one longer (2.53 Å) I–F bond lengths. In the twelfth I site, I is bonded in a linear geometry to one O2- and one F1- atom. The I–F bond length is 2.48 Å. In the thirteenth I site, I is bonded in a distorted linear geometry to one O2- and one F1- atom. The I–F bond length is 2.73 Å. There are twenty-five inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one I atom. In the second F1- site, F1- is bonded in a single-bond geometry to one I atom. In the third F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the fourth F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the fifth F1- site, F1- is bonded in a single-bond geometry to one I atom. In the sixth F1- site, F1- is bonded in a distorted single-bond geometry to one I atom. In the seventh F1- site, F1- is bonded in a distorted single-bond geometry to one As5+ and one Te4+ atom. In the eighth F1- site, F1- is bonded in a distorted single-bond geometry to one Te4+ atom. In the ninth F1- site, F1- is bonded in a distorted bent 120 degrees geometry to two I atoms. In the tenth F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the eleventh F1- site, F1- is bonded in a distorted bent 120 degrees geometry to one As5+ and one I atom. In the twelfth F1- site, F1- is bonded in a single-bond geometry to one I atom. In the thirteenth F1- site, F1- is bonded in a distorted water-like geometry to three I atoms. In the fourteenth F1- site, F1- is bonded in a single-bond geometry to one Te4+ and one I atom. In the fifteenth F1- site, F1- is bonded in a single-bond geometry to one As5+ and one I atom. In the sixteenth F1- site, F1- is bonded in a distorted single-bond geometry to one Te4+ and one S2- atom. In the seventeenth F1- site, F1- is bonded in a single-bond geometry to one I atom. In the eighteenth F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the nineteenth F1- site, F1- is bonded in a single-bond geometry to one As5+ atom. In the twentieth F1- site, F1- is bonded in a distorted single-bond geometry to one As5+ and one Te4+ atom. In the twenty-first F1- site, F1- is bonded in a 3-coordinate geometry to one Te4+ and two I atoms. In the twenty-second F1- site, F1- is bonded in a distorted single-bond geometry to one As5+ and one I atom. In the twenty-third F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the twenty-fourth F1- site, F1- is bonded in a single-bond geometry to one Te4+ atom. In the twenty-fifth F1- site, F1- is bonded in a distorted bent 150 degrees geometry to two I atoms.
Materials Data on KMg2As2H31O23 by Materials Project
(K2Mg3As2(H11O12)2)2(MgAs2H23O18)2(H2)9(H2O)8 crystallizes in the triclinic P-1 space group. The structure is two-dimensional and consists of five hydrogen molecules; four water molecules; one MgAs2H23O18 ribbon oriented in the (-1, 1, 0) direction; and one K2Mg3As2(H11O12)2 sheet oriented in the (0, 0, 1) direction. In the MgAs2H23O18 ribbon, Mg2+ is bonded in an octahedral geometry to six O2- atoms. There are four shorter (2.00 Å) and two longer (2.30 Å) Mg–O bond lengths. As5+ is bonded in a 2-coordinate geometry to one H1+ and three O2- atoms. The As–H bond length is 1.77 Å. There are a spread of As–O bond distances ranging from 1.74–2.46 Å. There are twelve inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a linear geometry to two equivalent As5+ atoms. In the second H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.06 Å) and one longer (1.43 Å) H–O bond length. In the third H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.04 Å) and one longer (1.51 Å) H–O bond length. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the fifth H1+ site, H1+ is bonded in a distorted single-bond geometry to one O2- atom. The H–O bond length is 1.01 Å. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.70 Å) H–O bond length. In the seventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the eighth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the tenth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the eleventh H1+ site, H1+ is bonded in a distorted single-bond geometry to two O2- atoms. There is one shorter (1.02 Å) and one longer (1.59 Å) H–O bond length. In the twelfth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. There are nine inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to one Mg2+ and two H1+ atoms. In the second O2- site, O2- is bonded in a single-bond geometry to one H1+ and one O2- atom. The O–O bond length is 1.47 Å. In the third O2- site, O2- is bonded in a 1-coordinate geometry to one Mg2+, two H1+, and one O2- atom. The O–O bond length is 1.51 Å. In the fourth O2- site, O2- is bonded in a bent 120 degrees geometry to one As5+ and one H1+ atom. In the fifth O2- site, O2- is bonded in a distorted water-like geometry to one As5+ and one O2- atom. In the sixth O2- site, O2- is bonded in a distorted water-like geometry to three H1+ atoms. In the seventh O2- site, O2- is bonded in a distorted single-bond geometry to one Mg2+, one H1+, and one O2- atom. In the eighth O2- site, O2- is bonded in a water-like geometry to one As5+ and two H1+ atoms. In the ninth O2- site, O2- is bonded in a 3-coordinate geometry to three H1+ atoms. In the K2Mg3As2(H11O12)2 sheet, K1+ is bonded in a 5-coordinate geometry to one H1+ and four O2- atoms. The K–H bond length is 2.56 Å. There are a spread of K–O bond distances ranging from 2.61–2.77 Å. There are two inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded in a distorted octahedral geometry to six O2- atoms. There are a spread of Mg–O bond distances ranging from 2.01–2.14 Å. In the second Mg2+ site, Mg2+ is bonded in a square co-planar geometry to four O2- atoms. There are two shorter (1.98 Å) and two longer (2.04 Å) Mg–O bond lengths. As5+ is bonded in a distorted trigonal non-coplanar geometry to three O2- atoms. There are a spread of As–O bond distances ranging from 1.74–1.92 Å. There are eleven inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the third H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the fourth H1+ site, H1+ is bonded in a distorted linear geometry to one K1+ and two O2- atoms. There is one shorter (1.05 Å) and one longer (1.53 Å) H–O bond length. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.74 Å) H–O bond length. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.97 Å. In the seventh H1+ site, H1+ is bonded in a distorted linear geometry to two O2- atoms. There is one shorter (1.01 Å) and one longer (1.62 Å) H–O bond length. In the eighth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the tenth H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.04 Å) and one longer (1.52 Å) H–O bond length. In the eleventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.01 Å. There are twelve inequivalent O2- sites. In the first O2- site, O2- is bonded in a water-like geometry to two H1+ atoms. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Mg2+, one As5+, and one H1+ atom. In the third O2- site, O2- is bonded in a distorted single-bond geometry to one As5+ and two H1+ atoms. In the fourth O2- site, O2- is bonded in a water-like geometry to two H1+ atoms. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to one K1+, one As5+, and one O2- atom. The O–O bond length is 1.44 Å. In the sixth O2- site, O2- is bonded in a distorted single-bond geometry to one Mg2+, one H1+, and one O2- atom. The O–O bond length is 1.50 Å. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to one Mg2+ and two H1+ atoms. In the eighth O2- site, O2- is bonded in a distorted water-like geometry to one Mg2+ and one O2- atom. The O–O bond length is 1.37 Å. In the ninth O2- site, O2- is bonded in a 1-coordinate geometry to one K1+, one Mg2+, and one O2- atom. In the tenth O2- site, O2- is bonded in a 4-coordinate geometry to two Mg2+, one H1+, and one O2- atom. In the eleventh O2- site, O2- is bonded in a 1-coordinate geometry to one K1+, one Mg2+, and two H1+ atoms. In the twelfth O2- site, O2- is bonded in a water-like geometry to one K1+ and two H1+ atoms.
Materials Data on Na3AsH22S2O13 by Materials Project
Na3AsH22S2O13 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded to six O2- atoms to form a mixture of corner and face-sharing NaO6 octahedra. The corner-sharing octahedral tilt angles are 57°. There are a spread of Na–O bond distances ranging from 2.37–2.52 Å. In the second Na1+ site, Na1+ is bonded to six O2- atoms to form face-sharing NaO6 octahedra. There are two shorter (2.36 Å) and four longer (2.41 Å) Na–O bond lengths. As5+ is bonded in a distorted tetrahedral geometry to two S2- and two equivalent O2- atoms. There are one shorter (2.18 Å) and one longer (2.19 Å) As–S bond lengths. Both As–O bond lengths are 1.74 Å. There are twelve inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a distorted linear geometry to two O2- atoms. There is one shorter (1.02 Å) and one longer (1.61 Å) H–O bond length. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.97 Å. In the third H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.97 Å. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.74 Å) H–O bond length. In the seventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the eighth H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.01 Å) and one longer (1.69 Å) H–O bond length. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the tenth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the eleventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the twelfth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a single-bond geometry to one As5+ atom. In the second S2- site, S2- is bonded in a single-bond geometry to one As5+ atom. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms. In the second O2- site, O2- is bonded in a distorted water-like geometry to one Na1+ and two H1+ atoms. In the third O2- site, O2- is bonded in a distorted water-like geometry to one Na1+ and two H1+ atoms. In the fourth O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms. In the fifth O2- site, O2- is bonded in a distorted water-like geometry to two equivalent Na1+ and two H1+ atoms. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to one As5+ and three H1+ atoms. In the seventh O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms.
Materials Data on PrMgSi2 by Materials Project
MgPrSi2 crystallizes in the tetragonal I4_1/amd space group. The structure is three-dimensional. Mg is bonded in a distorted square co-planar geometry to four Si atoms. There are two shorter (2.77 Å) and two longer (2.78 Å) Mg–Si bond lengths. Pr is bonded in a 10-coordinate geometry to ten Si atoms. There are a spread of Pr–Si bond distances ranging from 3.12–3.27 Å. There are eight inequivalent Si sites. In the first Si site, Si is bonded in a 9-coordinate geometry to four equivalent Mg, four equivalent Pr, and one Si atom. There are two shorter (2.77 Å) and two longer (2.78 Å) Si–Mg bond lengths. The Si–Si bond length is 2.33 Å. In the second Si site, Si is bonded in a 9-coordinate geometry to six equivalent Pr and three Si atoms. There are one shorter (2.33 Å) and two longer (2.38 Å) Si–Si bond lengths. In the third Si site, Si is bonded in a 9-coordinate geometry to six equivalent Pr and three Si atoms. Both Si–Si bond lengths are 2.38 Å. In the fourth Si site, Si is bonded in a 9-coordinate geometry to six equivalent Pr and three Si atoms. There are two shorter (3.12 Å) and four longer (3.27 Å) Si–Pr bond lengths. There are one shorter (2.33 Å) and two longer (2.38 Å) Si–Si bond lengths. In the fifth Si site, Si is bonded in a 9-coordinate geometry to four equivalent Mg, four equivalent Pr, and one Si atom. All Si–Pr bond lengths are 3.22 Å. The Si–Si bond length is 2.33 Å. In the sixth Si site, Si is bonded in a 9-coordinate geometry to four equivalent Mg, four equivalent Pr, and one Si atom. All Si–Pr bond lengths are 3.22 Å. In the seventh Si site, Si is bonded in a 9-coordinate geometry to four equivalent Mg, four equivalent Pr, and one Si atom. There are two shorter (2.77 Å) and two longer (2.78 Å) Si–Mg bond lengths. All Si–Pr bond lengths are 3.22 Å. In the eighth Si site, Si is bonded in a 9-coordinate geometry to six equivalent Pr and three Si atoms. There are two shorter (3.12 Å) and four longer (3.27 Å) Si–Pr bond lengths. There are one shorter (2.33 Å) and two longer (2.38 Å) Si–Si bond lengths.
Materials Data on NaSrPH18SO12 by Materials Project
NaSrPH18SO12 crystallizes in the cubic P2_13 space group. The structure is three-dimensional. Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are three shorter (2.45 Å) and three longer (2.48 Å) Na–O bond lengths. Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are six shorter (2.65 Å) and three longer (2.85 Å) Sr–O bond lengths. P5+ is bonded in a distorted tetrahedral geometry to one S2- and three equivalent O2- atoms. The P–S bond length is 2.06 Å. All P–O bond lengths are 1.55 Å. There are six inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a distorted single-bond geometry to two O2- atoms. There is one shorter (1.01 Å) and one longer (1.67 Å) H–O bond length. In the second H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.73 Å) H–O bond length. In the third H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.71 Å) H–O bond length. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. S2- is bonded in a single-bond geometry to one P5+ atom. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a water-like geometry to one Na1+, one Sr2+, and two H1+ atoms. In the second O2- site, O2- is bonded in a distorted water-like geometry to one Na1+, one Sr2+, and two H1+ atoms. In the third O2- site, O2- is bonded in a 1-coordinate geometry to one P5+ and three H1+ atoms. In the fourth O2- site, O2- is bonded in a water-like geometry to one Sr2+ and two H1+ atoms.
Ultrafast Correlation Energy Estimator
A virtually no-cost method is proposed that can compute the correlation energies of general, covalently bonded, organic, and inorganic molecules (including conjugated π-electron systems) with a well-defined dominant Lewis structure at the accuracy of 99.5% of the near-exact values determined by the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] in the complete-basis-set (CBS) limit. This Correlation Energy Per Bond (CEPB) method assigns a partial correlation energy to each bond type (characterized by the identities of the two atoms forming the bond and its integer bond order) and to a lone pair, regardless of the bond length, bond angle, sp-hybridization, π-electron conjugation, ionicity, noncovalent interactions, etc. At its current stage, the method is mainly suitable for near-equilibrium geometries. The correlation energies per bond are determined by a fit to the CCSD(T)/CBS benchmarks. It can neither improve the equilibrium structures nor discern conformers or positional isomers, yet its accuracy for reaction energies rivals that of the second-order Møller–Plesset perturbation theory, which is far more expensive. Its promising performance underscores the possibility that surprisingly compact, chemically intuitive molecular fragments exist into which correlation energies can be partitioned, leading to various ultrafast correlation-energy estimators tailored to different purposes.