What makes the cylinder-shaped N72 cage stable?

Recent theoretical studies have suggested that the stabilizing factors for large nitrogen cages tend to favor more five-membered rings, more three-membered rings, and cylindrical structures with large numbers of layers. One of the major issues in this study of the all-nitrogen molecule is the determination of what brings about the stabilizing factors. Herein, the cylinder-shaped molecule of N72 (D3d) has been studied in detail. The geometry and energies are examined at B3LYP/cc-pVDZ, and single-point energy calculations at MP2/cc-pVDZ are carried out for the purposes of determining relative thermodynamic stability. Natural bond order (NBO) analysis and atoms in molecules (AIM) analysis are applied to investigate the bonding properties of the cage molecule. The major result of this study is the identification of intramolecular interactions, whether it is at B3LYP/cc-pVDZ or at MP2/cc-pVDZ, as the dominant stabilizing factor for the large all-nitrogen cage. The length of the cylinder-shaped molecule is about 2.2 nm. N72 (D3d) might be one novel nanomaterial which is environment friendly, and as a beeline nanotube or a beeline "nano-bar", it is expected to impact a wide range of applications.     

From planes to cluster: The design of polynitrogen molecules

Polynitrogen compounds are a class of promising green high‐energy‐density materials. Using three‐membered to six‐memberd nitrogen rings, called all‐nitrogen building blocks, a series of two dimensional (planar) to three dimensional (cluster) polynitrogen molecules can be built. Small‐angle strain of small nitrogen rings and noncovalent interaction between neighboring nitrogen atoms leads to cage strain, and cage strain energy can be used to describe the stability of polynitrogen molecules theoretically. Density functional theory B3LYP/6‐31g(d,p) was used to optimize geometrical configurations and second‐order perturbation theory MP2/6‐311g(d,p) was applied to calculate single point energies of polynitrogen and other related compounds. Homodesmotic reactions were designed to compute cage strain energies of polynitrogen molecules and average bond energies of their N? N bonds. Some strategies were proposed to enhance the stability of polynitrogen molecules. This work provides theoretical evidence for the stability prediction of some nanomaterials (e.g., nanotube). © 2014 Wiley Periodicals, Inc.     

B24N24团簇的结构与稳定性

采用密度泛函理论,在B3LYP/6-31G^*水平下,对B₂₄N₂₄笼状团簇的12种异构体进行了优化,并对它们的几何构型、化学键性质、振动光谱和稳定性进行了探讨.研究表明:具有S₈对称的含有2个八元环、8个四元环和16个六元环的结构h是B₂₄N₂₄笼状团簇最稳定的异构体,只存在B-N键,而无N-N和B-B键.含有五元环结构的稳定性最低.B-B和N-N键对的数目越多,结构的稳定性越低.12种异构体的稳定性顺序为h＞a＞b＞I＞g＞l＞c＞k＞j＞d＞e＞f.     

Structure and stability of tube and cage Ge60H60

A tube Ge(60)H(60) isomer in D(5d) symmetry with fused five-membered rings located at the ends of the tube is more stable than the fullerene-like I(h) cage isomer at the B3LYP/cc-pVDZ level of theory. Introducing endo Ge-H bonds increases the stability of both cage and tube isomers. The most stable tube isomer can admit six endo Ge-H bonds. The cage isomer can admit 10-12 endo Ge-H bonds (H(10)@Ge(60)H(50) and H(12)@Ge(60)H(48)), and they also represent the most stable Ge(60)H(60) isomers. The stability order and structural patterns of Ge(60)H(60) are the same as those found for the corresponding Si(60)H(60) isomers. Moreover, it is found that the 6-31G(d,p) basis set fails to predict the relative energies of the Ge(60)H(60) isomers and the Ge(6)H(6) isomers.     

富勒烯C_(36)等电子体C_(34)BN异构体的结构及其相对稳定性理论研究

用半经验的AM1和MNDO方法优化了富勒烯C_(36)的等电子体C_(34)BN所有可能 异构体的构型,分析了各异构体相对稳定性与杂原子取代位置间的关系。另外,比 较了C_(36)碳笼上同位置地取代杂原子形成的C_34BN,C_(34)B_2和C_(34)N_2间的 电子结构,并分析了C_(34)BN最稳定异构体的振动模型。结果表明以C_(36):A (D_(6h))为母体形成的最稳定C_(34)BN异构体对应于碳笼赤道位置六元环中1,4- 取代产物,而以C_(36):B(D_(2d))为母体形成的最稳定C_(34)BN异构体对应于碳笼 近赤道位置的1,2-取代产物.C_(34)BN各异构体的稳定性可能主要由体系的共轭性 质决定。前线轨道能级表明B,N原子取代所得异构体的氧化-还原活性按以下顺序 递增：C_(34)B_2相似文献   

Evolution of lone pair of excess electrons inside molecular cages with the deformation of the cage in e2@C60F60 systems

For unusual e(2)@C(60)F(60)(I(h), D(6h), and D(5d)) cage structures with two excess electrons, it is reported that not only the lone pair in singlet state but also two single excess electrons in triplet state can be encapsulated inside the C(60)F(60) cages to form single molecular solvated dielectrons. The interesting relationship between the shape of the cage and the spin state of the system has revealed that ground states are singlet state for spherical shaped e(2)@C(60)F(60)(I(h)) and triplet states for short capsular shaped e(2)@C(60)F(60)(D(6h)) and long capsular shaped e(2)@C(60)F(60)(D(5d)), which shows a spin evolution from the singlet to triplet state with the deformation of the cage from spherical to capsular shape. For these excess electron systems, the three ground state structures have large vertical electron detachment energies (VDEs (I) of 1.720-2.283 eV and VDEs (II) of 3.959-5.288 eV), which shows their stabilities and suggests that the large C(60)F(60) cage is the efficient container of excess electrons.     

Structures and kinetic stabilities of the possible complexes of mononuclear Ni and (N2)x (x = 1-4)

Ab initio and density functional theory (DFT) methods have been applied to study the structures and kinetic stabilities of the possible products of the reactions of mononuclear nickel with (N(2))(x) (x = 1-4). Energy analyses show that end-on bound Ni(N(2))(x) (x = 1-4) complexes are preferred to side-on and N(4) bound ones. Several decomposition and isomerization pathways for Ni(N(2))(x) (x = 2-4) were investigated at the B3LYP/6-31G level of theory. The present study suggests that besides the four experimentally assigned complexes (NiN(2) (C(infinity)(v)), Ni(N(2))(2) (D(infinity)(h)), Ni(N(3))(2) (D(3)(h)), and Ni(N(2))(4) (T(d))), another two complexes (Ni(N(2))(4) (C(2)(v)) and Ni(N(2))(4) (D(4)(d))) are likely to be kinetically stable, while other complexes may be kinetically unstable with barrier heights of less than 30 kcal/mol. The present study also suggests that side-on bound N(2) ligand is ready to transform into the end-on bound one, while N(4) ligand is hard to transform into side-on or end-on bound N(2) ligand.     

Ab initio theoretical studies on N_(28),B_4N_(24),B_(12)N_(16), and B_(16)N_(12) with T_d symmetry

Structures, energies and vibrational frequencies have been calculated for hollow cage clusters N28, B4N24, B12N16, and B16N12 with Td symmetry using ab initio quantum mechanical methods at the RHF/3-21G level. Each species is predicted to be both chemically and kinetically stable. Skeletal polyhedrons of all considered boron nitride hollow cage clusters are constructed from 5- and 6-membered rings.     

多体展开势能函数在碳族元素原子簇研究中的应用(Ⅳ)──Si9─Si16原子簇的分子结构与稳定性

多体展开势能函数研究表明,Si₄-Si₁₆原子簇分子间的结构衍生关系为:依次增加一个二配位或三配位的表面原子,分子表面被四元蝶形环Si₄(D_2d)所覆盖;Si_n(n=5-16)结构中多含有Si₅(D_3h)、Si₆(D_2d)区域结构单元,笼状Si₁₀及Si₁₆的表面原子均为三配位或三配位以上,预计Si₅、Si₆、Si₁₀及Si₁₆是硅原子簇碎片化产物分布中丰度较高的序列;在这一范围内的分子结构呈与晶体硅结构(金刚石)无关的密堆积,最高配位数为5,在小于半球的立体角内形成六配位的硅中心,使该簇合物在能量上不稳定。     

Functionalized nanodiamonds part I. An experimental assessment of diamantane and computational predictions for higher diamondoids

The structures, strain energies, and enthalpies of formation of diamantane 1, triamantane 2, isomeric tetramantanes 3-5, T(d)-pentamantane 6, and D(3d)-hexamantane 7, and the structures of their respective radicals, cations, as well as radical cations, were computed at the B3LYP/6-31G* level of theory. For the most symmetrical hydrocarbons, the relative strain (per carbon atom) decreases from the lower to the higher diamondoids. The relative stabilities of isomeric diamondoidyl radicals vary only within small limits, while the stabilities of the diamondoidyl cations increase with cage size and depend strongly on the geometric position of the charge. Positive charge located close to the geometrical center of the molecule is stabilized by 2-5 kcal mol(-1). In contrast, diamondoid radical cations preferentially form highly delocalized structures with elongated peripheral C-H bonds. The effective spin/charge delocalization lowers the ionization potentials of diamondoids significantly (down to 176.9 kcal mol(-1) for 7). The reactivity of 1 was extensively studied experimentally. Whereas reactions with carbon-centered radicals (Hal)(3)C(*) (Hal=halogen) lead to mixtures of all possible tertiary and secondary halodiamantanes, uncharged electrophiles (dimethyldioxirane, m-chloroperbenzoic acid, and CrO(2)Cl(2)) give much higher tertiary versus secondary selectivities. Medial bridgehead substitution dominates in the reactions with strong electrophiles (Br(2), 100 % HNO(3)), whereas with strong single-electron transfer (SET) acceptors (photoexcited 1,2,4,5-tetracyanobenzene) apical C(4)-H bridgehead substitution is preferred. For diamondoids that form well-defined radical cations (such as 1 and 4-7), exceptionally high selectivities are expected upon oxidation with outer-sphere SET reagents.     

C24和B12N12团簇的结构与稳定性

本文采用量子化学密度泛函理论的B3LYP/6-31G*方法,对C24和B12N12团簇的12种异构体进行了优化,并对它们的几何构型、振动频率、核独立化学位移(NICS)和结合能进行了理论探讨, 比较了C24和B12N12团簇结构的稳定性。研究表明:C24团簇的最稳定几何构型为类石墨结构d,B12N12团簇的最稳定结构为4/6笼状结构g。C24异构体的稳定性大小顺序为d > b > f > c > a > e。B12N12团簇异构体稳定性大小顺序为a > f> c> d > e >b。     

One and two hydrogen molecules in the large cage of the structure II clathrate hydrate: quantum translation-rotation dynamics close to the cage wall

We have performed a rigorous theoretical study of the quantum translation-rotation (T-R) dynamics of one and two H2 and D2 molecules confined inside the large hexakaidecahedral (5(12)6(4)) cage of the sII clathrate hydrate. For a single encapsulated H2 and D2 molecule, accurate quantum five-dimensional calculations of the T-R energy levels and wave functions are performed that include explicitly, as fully coupled, all three translational and the two rotational degrees of freedom of the hydrogen molecule, while the cage is taken to be rigid. In addition, the ground-state properties, energetics, and spatial distribution of one and two p-H2 and o-D2 molecules in the large cage are calculated rigorously using the diffusion Monte Carlo method. These calculations reveal that the low-energy T-R dynamics of hydrogen molecules in the large cage are qualitatively different from that inside the small cage, studied by us recently. This is caused by the following: (i) The large cage has a cavity whose diameter is about twice that of the small cage for the hydrogen molecule. (ii) In the small cage, the potential energy surface (PES) for H2 is essentially flat in the central region, while in the large cage the PES has a prominent maximum at the cage center, whose height exceeds the T-R zero-point energy of H2/D2. As a result, the guest molecule is excluded from the central part of the large cage, its wave function localized around the off-center global minimum. Peculiar quantum dynamics of the hydrogen molecule squeezed between the central maximum and the cage wall manifests in the excited T-R states whose energies and wave functions differ greatly from those for the small cage. Moreover, they are sensitive to the variations in the hydrogen-bonding topology, which modulate the corrugation of the cage wall.     

The induced magnetic field in cyclic molecules

The response of a molecule to an applied external magnetic field can be evaluated by a graphical representation of the induced magnetic field. We have applied this technique to four representative, cyclic organic molecules, that is, to aromatic (C(6)H(6), D(6h)), anti-aromatic (C(4)H(4), D(2h)) and non-aromatic (C(4)H(8), D(4h), and C(6)H(12), D(3d)) molecules. The results show that molecules that contain a pi system possess a long-range magnetic response, while the induced magnetic field is short-range for molecules without pi systems. The induced magnetic field of aromatic molecules shields the external field. In contrast, the anti-aromatic molecules increase the applied field inside the ring. Aromatic, anti-aromatic, and non-aromatic molecules can be characterized by the appearance of the magnetic response. We also show that the magnetic response is directly connected to nucleus-independent chemical shifts (NICS).     

Analysis of polyaddition levels in i-Sc3NC80

Using the density functional method, the stabilities of highly hydrogenated and fluorinated [80]fullerenes, both empty and containing the Sc3N molecule, have been calculated. Addition of 44 atoms to i-Sc3NC80 is predicted to be most favorable due to the formation of six octahedrally located benzenoid rings, while addition of up to 52 atoms (consistent with preliminary fluorination data) gives a structure stabilized by the presence of four benzenoid rings. The most stable isomers at this addition level have been determined and the relative stabilities of a number of C80H52, C80F52, and i-Sc3NC80H52 species calculated. The hydrogenation of the i-Sc3NC80 has been computed to be more difficult than the corresponding partner, C80. From the geometrical point of view, the Sc3N molecule is planar in the parent [80]fullerene but is calculated to be pyramidal in some of the hydrogenated/fluorinated derivatives. Moreover, in these it has fixed locations due to orbital interactions arising from deformation of the cage and the presence of localized double bonds.     

On the viability of small endohedral hydrocarbon cage complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, AND X@C16H16

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H(+), H, He, Ne, Ar, Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,+,2+)) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C(4)H(4), T(d)()) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C(8)H(8), O(h)()) and bicyclo[2.2.2]octane (C(8)H(14), D(3)(h)()) minima are limited to encapsulating species smaller than Ne and Na(+). Despite its intermediate size, adamantane (C(10)H(16), T(d)()) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li(0,+), Be(0,+,2+), Na(0,+), and Mg(2+). In contrast, the truncated tetrahedrane (C(12)H(12), T(d)()) encapsulates fewer species, while the D(4)(d)() symmetric C(16)H(16) hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg(+) species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C-C bonding and C-H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E(endo)) to the sum of their isolated components (E(inc) = E(endo) - E(cage) - E(x)) and to their exohedral isomer energies (E(isom) = E(endo) - E(exo)). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E(isom) is always exothermic), Be(2+)@C(10)H(16) (T(d)(); -235.5 kcal/mol), Li(+)@C(12)H(12) (T(d)(); 50.2 kcal/mol), Be(2+)@C(12)H(12) (T(d)(); -181.2 kcal/mol), Mg(2+)@C(12)H(12) (T(d)(); -45.0 kcal/mol), Li(+)@C(16)H(16) (D(4)(d)(); 13.3 kcal/mol), Be(+)@C(16)H(16) (C(4)(v)(); 31.8 kcal/mol), Be(2+)@C(16)H(16) (D(4)(d)(); -239.2 kcal/mol), and Mg(2+)@C(16)H(16) (D(4)(d)(); -37.7 kcal/mol) are relatively stable as compared to experimentally known He@C(20)H(20) (I(h)()), which has an E(inc) = 37.9 kcal/mol and E(isom) = -35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.     

Stability and magnetic properties of transition metal atoms endohedral BnNn (n=12-28) cages

First-principles calculations have been conducted to systemically investigate the stability and magnetic properties of 3d and 4d transitional-metal (TM) atoms doped in the BnNn (n=12,16,20,24,28) cages. Among those cages, the B24N24 is the optimal one for encapsulating 3d and 4d TM atoms according to the computed heat of formation. Inside B24N24 cage, 3d and 4d TM dopants belonging to the same group in the Periodic Table exhibit similar magnetic behaviors. Most of the 3d and 4d TM atoms remain magnetic after doped in the B24N24 cage except for Ni, Zr, and Pd. The magnitudes of the remaining moments for 3d (except for Sc, Ti, and V) and 4d dopants are reduced from those of free atoms. The energy gaps are localized at the doped transition metal atoms. Encapsulations of two TM atoms inside the B24N24 cage were also considered.     

Confirmation of the "long-lived" tetra-nitrogen (N4) molecule using neutralization-reionization mass spectrometry and ab initio calculations

Tetra-nitrogen (N(4)), which has been the subject of recent controversy [Cacace, d. Petris, and Troiani, Science 295, 480 (2002); Cacace, Chem. Eur. J. 8, 3839 (2002); Nguyen et al., J. Phys. Chem. A 107, 5452 (2003); Nguyen, Coord. Chem. Rev. 244, 93 (2003)] as well as of great theoretical interest, has been prepared from the N(4) (+) cation and then detected as a reionized gaseous metastable molecule with a lifetime exceeding 0.8 micros in experiments based on neutralization-reionization mass spectrometry. Moreover, we have used the nature of the charge-transfer reaction which occurs between a beam of fast N(4) (+) ions (8 keV translational energy) and various stationary gas targets to identify the vertical neutralization energy of the N(4) (+) ion. The measured value, 10.3+/-0.5, most closely matches that of the lowest energy azidonitrene (4)N(4) (+)C(s)((4)A(')) ion, resulting in the formation of the neutral bound azidonitrene (3)N(4)C(s)((3)A(")). Neutralization of the global minimum (2)N(4) (+)D( infinity h)((2)Sigma(u) (+)) ion leads to a structure 166 kJ mol(-1) above the dissociation products [N(2)((1)Sigma(g) (+))+N(2)((1)Sigma(g) (+))]; moreover, it was not possible to find a minimum on the (1)N(4) neutral potential energy surface for a covalently bonded structure. Ab initio calculations at the G3, QCISD/6-31G(d), and MP2/AUG-cc-pVTZ levels of theory have been used to determine geometries and both vertical neutralization energies of ions (doublet and quartet) and ionization energies of neutrals (singlet and triplet). In addition, we have also described in detail the EI ion source for the Ottawa VG ZAB mass spectrometer [Holmes and Mayer, J. Phys. Chem. A 99, 1366 (1995)] which was modified for high-pressure use, i.e., for the production of dimer and higher number cluster ions.     

2',3'-二脱氧-2',3'-二去氢鸟嘌呤核苷构象稳定性的理论研究

采用密度泛函方法在B3LYP/6-31＋G**水平上研究了2',3'-二脱氧-2',3'-二去氢鸟嘌呤核苷分子(D4G)的构象. 分别研究在气相中的孤立分子和一水合物异构体的相对稳定性和异构体之间的相互转变过程, 分析了水分子的参与对D4G异构体的相对稳定性和几何结构参数以及自然电荷的影响. 结果表明, 孤立的D4G分子在气相中存在8种稳定构象, 其中构象d4g-2是所有构象中最稳定的, 气相中D4G主要以d4g-2存在. 气相中各构象的相对稳定性为: d4g-2＞d4g-1＞d4g-5＞d4g-3＞d4g-6＞d4g-4＞d4g-8＞d4g-7. 计算得到的各构象键长和键角数据与实验值接近. 一个水分子的加入对D4G分子的构型参数有所影响, 基本不改变D4G分子各构象的稳定性顺序, 但构象转变的能垒有所提高. 氢键在分子构象中发挥了重要作用.     

2',3'-二脱氧-2',3'-二去氢鸟嘌呤核苷构象稳定性的理论研究

采用密度泛函方法在B3LYP/6-31＋G**水平上研究了2',3'-二脱氧-2',3'-二去氢鸟嘌呤核苷分子(D4G)的构象. 分别研究在气相中的孤立分子和一水合物异构体的相对稳定性和异构体之间的相互转变过程, 分析了水分子的参与对D4G异构体的相对稳定性和几何结构参数以及自然电荷的影响. 结果表明, 孤立的D4G分子在气相中存在8种稳定构象, 其中构象d4g-2是所有构象中最稳定的, 气相中D4G主要以d4g-2存在. 气相中各构象的相对稳定性为: d4g-2＞d4g-1＞d4g-5＞d4g-3＞d4g-6＞d4g-4＞d4g-8＞d4g-7. 计算得到的各构象键长和键角数据与实验值接近. 一个水分子的加入对D4G分子的构型参数有所影响, 基本不改变D4G分子各构象的稳定性顺序, 但构象转变的能垒有所提高. 氢键在分子构象中发挥了重要作用.     

Role of four-membered rings in C32 fullerene stability and mechanisms of generalized Stone-Wales transformation: a density functional theory investigation

Density functional theory (DFT) methods have been applied to study C(32) fullerenes built from four-, five-, and six-membered rings. The relative energies of pure C(32) fullerenes have been evaluated to locate three most stable structures, 32:D(4d) with two squares, 1:D(3) without square and 5:C(s) with one square. Structural analysis reveals that there is a rearrangement pathway between the lowest energy classical isomer 1:D(3) and the lowest energy non-classical isomer 32:D(4d), and 5:C(s) behaves just as an intermediate between them. The kinetic processes of generalized Stone-Wales transformation (GSWT) with four-membered rings have been explored and two distinct reaction mechanisms are determined by all the transition states and intrinsic reaction coordinates with PBE1PBE/6-31G(d) approach for the first time. One mechanism is the concerted reaction with a rotating dimer closed to the cage surface and another is the stepwise reaction with a carbene-like sp(3) structure, whereas the latter is sorted into two paths based on four-membered ring vanishing before or after the formation of the carbene-like structure. It is indicated that there is no absolute preference for any mechanism, which depends on the adaptability of different reactants on the diverse mechanisms. Furthermore, it's found that the interconversion process with the participation of squares is more reactive than the rearrangement between C(60)_I(h) and C(60)_C(2v), implying some potential importance of non-classical small fullerenes in the fullerene isomerization.