Quantum Chemical Study of CnAl2^± （n=1～10） Clusters： Structure and Stability

Geometries, electronic structures and vibrational frequencies of CnAl2± clusters have been investigated by using the B3LYP-DFT method in the range of n = 1～10. At the B3LYP/6-311G level, the ground state structures of CnAl2± clusters are planar or linear with terminal aluminum atom. In these structures, the C–C bonds are alternately changed between double and triple. The changing magnitude of the averaged bond length decreases with the increase of cluster size. The energetic analysis showed that CnAl2± clusters with even n are more stable than those with odd n.     

Structures and Aromaticity of Planar XY2Z （X = Li,K, Y - P,As and Z = C,Si, Ge） Clusters

Clusters XY2Z species are theoretically investigated with density functional theory （DFT） method. The results show that for LiP2C, LiAs2Ge and KAs2C species, the C2v isomer is the most stable planar structure, while for other species the Cs isomer is the most stable planar structure at the B3LYP/6-311＋G＊ level. Wiberg Bond Index （WBI） and Nucleus-Independent Chemical Shift （NICS） values indicate the existence of delocalization in stable planar structures. A detailed Molecular Orbital （MO） analysis further reveals that planar isomers of these species have strong aromatic character, which strengthens the structural stability and makes them closely connect with the concept of aromaticity.     

Theoretical Study on the Stable Structures and Aromaticities for Pnictogen Dianionic Sb4^2-, Bi4^2-, and （SbBi）2^2- Clusters

Through the theoretical calculation of structural optimization, vibrational frequencies and atomization energies with one method of density functional theory （B3LYP） and two post- Hartree-Fock approaches （MP2, CCSD（T））, several stable isomers for new three pnictogen dianionic Sb4^2-, Bi4^2-, and （SbBi）2^2- species were determined. For two homoatomic Sb4^2- and Bi4^2- species, there are three stable isomers： square （D4h）, roof-shaped （C2v-1）, and C2v-2 structure with the square isomer being the ground state. For the heteroatomic dian- ionic （SbBi）2^2- species, there are also three stable isomers： rhombus （D2h）, roof-shaped （C1）, and C2v structures with the rhombic isomer being the ground state. The calculated NICS values show that nucleus-independent chemical shifts （NICS） values of roof-shaped isomers for Sb4^2-, Bi4^2-, and （SbBi）2^2- species are all negative, consequently indicating that these roof-shaped isomers possess aromaticities. NICS values for the planar ring isomers are all positive, suggesting that these three planar ring isomers have antiaromatic characters. The aromaticity for the two stable roof-shaped and square isomers are preliminarily explained and discussed with MO analysis.     

Structures, relative stability and dissociation of [Si,N,C,O]2+isomers

Fifteen isomers of [Si,N,C,O]2+ system are obtained at UB3LYP/6-311G(d) and UCCSD(T)/6-311+G(2df) (single-point) levels. The analyses are made for predicting the structures of optimized isomers, while ionic fragments with lower energies are suggested. The calculatedresults indicate that linear isomer SiNCO2+(2П) is thermodynamically the most stable species in [Si,N,C,O]2+ system, followed by linear SiOCN2+ (2П), SiCNO2+ (2П), and SiC(NO) (2A") with NCO three-membered ring. The order of stability of several kinetically stable isomers is SiNCO2 >SiCNO2+ (2П)>SiOCN2+ >SiC(NO)2+>OSiNC2+ (2П). The obtained results by analyzing the isomerizations and ionic fragment patterns show that the signal peaks of [Si,N,C,O]2+ are attributed to the contribution of linear SiNCO2+ species, which is metastable and can dissociate to the ionic fragments in the mass spectrometry experiments.     

Crystal structures and electronic properties of BaC_2 isomers by theoretical study based on DFT

Band structures and electronic properties of two BaC2 isomers were calculated by using density func-tional theory(DFT) properly.The ionic bond features are all typical between cation(Ba) and anion clusters(C2) in both structures of the isomers.However,a much stronger covalent bond exists in anion clusters which can be seen by inspecting the electron distribution contour that has a dull bell like shape between two carbon atoms.The shortest distance between Ba2 and C22? and the bond length in anion clusters are different in these isomers of BaC2,which are 0.2945 nm and 0.1185 nm for the structure with the I4/mmm space group and 0.2744 and 0.1136 nm with the C2/c type,respectively.Band structures were clarified by combining the DOS to indicate the ionic bonding features more clearly.Population analysis provided further evidence on these ideas.Thermodynamical calculation results reveal that the transition temperature of these two polymorphs of BaC2 locates near 132 K,which is consistent with the recent experimental results.     

DFT Study of Charge Effect on the Odd-even Oscillatory Behavior in Stabilities for Gold Clusters

The comparative study of charge effect on the size-dependence stabilities of gold clusters Aunz(n = 2~12, z = 0/±1) in gas phase is performed at the M06-L/Lanl2 dz level. The lowest-energy structures charged by –1, 0 and +1 are optimized. The result shows that the geometries of the clusters with over 7 atoms tend to be cake-like. From the two- to three-dimensional geometries, the oscillatory behaviors are exhibited in the structural and electronic properties with the most pronounced in energy gap. The amplitude for the positive clusters is bigger than both the neutral and negative clusters. The neutral clusters with even number of even-coordinated atoms are more stable than the neighbors with odd number of even-coordinated atoms, as is completely reversed for the charged clusters. The oscillatory behaviors for the charged clusters are opposite to that for the neutral clusters, as is attributed to the electron-paired effect.     

Theoretical Investigation on the Geometries and Properties of Guanine-BX3 （X = F, Cl） Complex

Geometries and binding energies were predicted at the B3LYP/6-311+G* level for the guanine-BX3 (X = F, Cl) systems and four isomers with no imaginary frequencies have been obtained for both guanine-BF3 and guanine-BCl3, respectively. Single energy calculations using much larger basis sets (6-311+G(2df,p) and aug-cc-pVDZ were carried out as well. It was found that the most stable isomer of guanine-BF3 is BF3 connected to N3 of guanine with the stabilization energy of –19.93 kcal/mol (BSSE corrected), while that of guanine-BCl3 is BCl3 connected to O10 of guanine having stabilization energy of –15.02 kcal/mol at the same level. The analyses for the combining interaction between BX3 and guanine with the atom-in-molecules theory (AIM) and natural bond orbital (NBO) methods have been performed. The results indicated that all the isomers are formed with σ-p type interactions between guanine and BX3, in which pyridine-type nitrogen or carbonyl oxygen or nitrogen atom of amino group offers its lone pair electrons to the empty p orbital of boron atom and the concomitance of charge transfer from guanine to BX3 has occurred. Still, one or two hydrogen bonds exist in some isomers of guanine-BX3 system and contribute to the stability of complex systems. Frequency analysis suggested that the stretching vibration of BX3 undergoes a red shift in complexes. Guanine-BF3 complex is more stable than guanine-BCl3 although the B–Y (Y=N, O) bond distance in the latter is shorter.     

B20N20团簇的结构与稳定性

B3LYP/6-31G* density functional theory calculations have been carried out on the structure and stability of ten B20N20 clusters. It was found that two new proposed isomers with two octagons, twelve hexagons, eight squares in Cab and C2 symmetry were more stable than the isomer with sixteen hexagons and six squares in C2 symmetry which was previously deemed to the most stable by 79.5 and 13.8 kJ/mol respectively. The isomer with two decagons in S10 symmetry is much higher in energy than the most stable structure in C4h symmetry by 637.2 kJ/mol.     

A Density Functional Theory Study of the Hydrates of 2NH_3:H_2SO_4 and Its Implications for the Formation of Atmosphere Particles

Density functional theory was used at the B3LYP/6-311++G(d,p) level of theory to study the hydrates of 2NH3:H2SO4:nH2O for n = 0～4. Neutrals of the most stable clusters, when n = 0 and 1, spontaneously formed and were determined to be hydrogen-bonded molecular complexes of monomeric species. Double ions (clusters containing a NH4+ cation and a HSO4- anion) or even ternary ions (clusters with two NH4+ cations and one SO42- anion) spontaneously formed in the most stable clusters of 2NH3:H2SO4:nH2O (n = 2, 3, 4). The energetics of binding and incremental association was also calculated. Double ions are not energetically favorable until 2NH3:H2SO4:2H2O because of the about equal free energies for forming the neutral (the most stable) and double ion (the second stable) isomers. The free energy of incremental association from free H2O and 2NH3:H2SO4:nH2O has a maximum at n = 2 at room temperature with ΔG ≈ -2 kcal/mol. The comparison of incremental association energies between 2NH3:H2SO4:nH2O, NH3:H2SO4:nH2O and H2SO4:nH2O clusters revealed that NH3 plays an important role in the atmospheric particle nucleation.     

Studies on the Electronic Structures and Spectra of C78（CH2）3

The structures and spectra of 20 possible isomers of C78(CH2)3 have been studied by using AM1,INDO/CIS and DFT methods. The results show that the most stable isomer is 1,2,3,4,5,6-C78(CH2)3 (A) with annulene structures,where three -CH2 groups are added to the 6/6 bonds located at the same hexagon passed by the shortest axis of C78 (C2v). Compared with that of C78 (C2v),the first absorption in the electronic spectrum of C78(CH2)3 (A) is blue-shifted because of its wider LUMO-HOMO energy gap. While the IR frequencies of the C–C bonds on the carbon cage are red-shifted owing to the formation of annulene structures and the extension of the conjugated system. The chemical shifts of the carbon atoms in 13C NMR spectra are moved upfield upon the addition.     

硼碳团簇BnC2 (n＝1～6)的理论研究

应用密度泛函理论在B3LYP/6-311＋G(d)水平上研究了硼碳团簇B_nC₂ (n＝1～6)的几何结构、生长机制和相对稳定性. 计算结果表明, 对于n＝2～6的簇, 平面多环状构型为最稳定的结构, 其中C原子分布于环的顶点、有尽可能多的三配位硼原子和尽可能多的B—C键. 碳原子作为杂原子倾向掺杂于团簇的顶点位置, 它的掺杂不改变硼团簇的主体结构. 与平面多环状结构相比, 随着簇尺寸的增大, 三维结构和线性链结构更不稳定. 在低能线性结构中, C原子位于链两侧的第二个位置. 计算的碎片分裂能、递增键能以及HOMO-LUMO能隙表明, B₄C₂为幻数簇.     

AlmN(m=2～9)团簇结构与稳定性的DFT研究

用密度泛涵理论(DFT)的B3LYP方法在6-31G*水平上对AlmN(m =2～9)团簇的几何构型、电子结构、振动频率等性质进行了理论研究.给出了以Alm团簇作为设计AlmN类结构的母体，考虑在不同位置上结合N原子的结构，可以较快找到AlmN类团簇基态结构的一种方法.通过对基态结构的几何参数分析发现， m＜4的结构只存在Al－N键； m≥4的结构, Al－N键和Al－Al键共存.对基态结构的绝热电离能讨论结果表明，只存在Al－N键的Al2N和Al3N团簇较稳定.     

Experimental and theoretical studies on carbon-nitrogen clusters C2nN7-

C(2n)N7(-) cluster ions are produced by laser ablating on the K(3)[Fe(CN)6] sample. DFT calculations have been performed for these cluster anions. Various isomeric structures of these clusters are optimized and their energies are compared to find the most stable isomers. The most stable structure for C8N7(-) is similar to that of adenine by theoretical calculation, which is in agreement with the collision-induced dissociation (CID) experimental results. With the increasing even numbers of C atoms from 8 to 16, the N atoms in the double-ring structure are gradually substituted by C atoms from the six-membered ring to the five-membered ring. All these C(2n)N7(-) (n = 3-9) clusters exhibit planar aromatic characters. The energy difference and incremental binding energy analyses show that C(2n)N7(-) (n = 4-8) clusters are more stable than C6N7(-) and C18N7(-), which are consistent with the observed mass spectrum.     

杂富勒烯的电子结构与性质关系的研究──Ⅱ.C_(57)X_3,C_(56)X_4(X=B、N、P)的位置异构体

用 CNDO／2方法在 586微机上计算了 C57X3C56X4（X=B、N、P）的 234个位置异构体的电子结构。在C57X3（X=B、N、P）位置异构体中，C57X3（1，2，9）（X=B、N、P）分别是最稳定的。对于C56X4（X=B、N、P）位置异构体，C56B4（1，2，9，8），C56N4（1，2，9，12）和C56P4（1，2，9，12）分别是最稳定的，但稳定性都比C60差。其氧化或还原性都比 C60好，将它们和 C60比较，与 X相距一个或两个键的 C原子电荷密度增加或减少较多，其余电或亲核反应性增加；X与 X，X与 C原子之间 Wiberg Order都减少较多，其键的强度削弱；邻近杂原子的 C与 C原子之间 Wiberg Order减少或增加很少，其键的强度稍有削弱或增强。     

全金属负离子团簇Ga42-、In42-芳香性的磁特征与多重芳香性

The optimized geometries, frequencies, and total electronic energies of two all-metal dianionic clusters Ga42- , In42- are calculated at the B3LYP, B3PW91, and MP2 levels of theory. There are two stable structures for each Ga42- , In42- species. For Ga42- , In42- species the square isomers are the most stable. On the basis of these computed stable structures we focus on two magnetic properties: magnetic susceptibility anisotropy and nucleus-independent chemical shift (NICS) for the square planar Ga42- , In42- isomers, which are calculated with B3LYP and HF methods. The computed results of NICS show that the square planar Ga42- , In42- isomers possess strong aromaticity. The detailed molecular orbital analysis for the two isomers further reveals that the two square planar Ga42- , In42- isomers have multiple-fold aromaticity: one delocalized π MOs and two delocalized σ MOs, which play important role in explaining the special stability of these all-metal square clusters.     

B28N28笼的稳定性及笼中四元环间键联类型对笼稳定性的影响

采用密度泛函方法对四、六元环组成的所有可能的的23个笼状B28N28结构进行了理论计算和拓扑学特性研究, 用三个指标N4x4(x=0, 1, 2)来描述相邻四元环间的键联类型, 结果发现B28N28笼的相对能量随N4x4值的增大而增大, 且N404对稳定性的影响起主导作用. 这一简单的拓扑学标准可以给出所有四六结构B28N28异构体的大致能量顺序, 并从ISR结构中挑选出能量较低的结构, 因此有望用于挑选大尺寸氮化硼团簇的热力学稳定结构.     

Clusters of hydrated methane sulfonic acid CH3SO3H.(H2O)n (n = 1-5): a theoretical study

Ab initio and density functional methods have been used to examine the structures and energetics of the hydrated clusters of methane sulfonic acid (MSA), CH3SO3H.(H2O)n (n = 1-5). For small clusters with one or two water molecules, the most stable clusters have strong cyclic hydrogen bonds between the proton of OH group in MSA and the water molecules. With three or more water molecules, the proton transfer from MSA to water becomes possible, forming ion-pair structures between CH3SO3- and H3O+ moieties. For MSA.(H2O)3, the energy difference between the most stable ion pair and neutral structures are less than 1 kJ/mol, thus coexistence of neutral and ion-pair isomers are expected. For larger clusters with four and five water molecules, the ion-pair isomers are more stable (>10 kJ/mol) than the neutral ones; thus, proton transfer takes place. The ion-pair clusters can have direct hydrogen bond between CH3SO3- and H3O+ or indirect one through water molecule. For MSA.(H2O)5, the energy difference between ion pairs with direct and indirect hydrogen bonds are less than 1 kJ/mol; namely, the charge separation and acid ionization is energetically possible. The calculated IR spectra of stable isomers of MSA.(H2O)n clusters clearly demonstrate the significant red shift of OH stretching of MSA and hydrogen-bonded OH stretching of water molecules as the size of cluster increases.     

TiN12团簇的合成研究

以高纯氮气为载气,通过532nm的激光轰击由Ti、BN粉末混合压制成的样品,生成了钛氮团簇,确定了最稳定钛氮团簇的组成为TiN12。以四氟化钛和三甲基叠氮硅烷为原料,在液氮冷却下开展了钛氮团簇的化学法合成,对所得产物进行了IR、NMR表征,确定其结构为Ti(N3)4。用密度泛函理论(DFT)对TiN12的结构进行了优化,发现存在一种Ti(N3)4形式的具有对称的正四面体结构的稳定构型,这与化学法合成的TiN12的IR和NMR谱相符。不过,仍需进一步确定激光轰击法和化学合成法产生的TiN12是否具有相似的结构。     

[Ca(NH2)2]n (n＝1～5)团簇的密度泛函理论研究

用密度泛函理论(DFT)的杂化密度泛函B3LYP方法在6-31G*基组水平上对[Ca(NH2)2]n (n＝1～5)团簇各种可能的构型进行几何结构优化, 预测了各团簇的最稳定结构. 并对最稳定结构的振动特性、成键特性、电荷特性等进行了理论研究. 结果表明: 团簇易形成环状结构, 以金属Ca原子团簇作为骨架, NH2基结合在金属团簇骨架上, 并主要是Ca—N成键和Ca—Ca成键. 团簇中Ca—N键长为0.225～0.257 nm, Ca—Ca键长为0.312～0.354 nm, N—H键长为0.102～0.103 nm, H—N—H键角为102.9°～104.2°; 团簇中Ca原子的自然电荷在1.657e～1.720e之间, N原子的自然电荷在－1.543e～－1.592e之间, H原子的自然电荷在0.349e～0.367e之间, Ca原子和NH2基之间相互作用呈现较强的离子性;对比团簇和晶体的结构及IR谱表明, NH2基在团簇和晶体中的结构基本一致.     

Structure and stability of (TiO2)n, (SiO2)n, and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] clusters

Structures, energetics, and vibrational spectra are investigated for small pure (TiO(2))(n), (SiO(2))(n), and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] oxide clusters by density functional theory (DFT). The BP86/ATZP level of theory is employed to obtain constitutional isomers of the oxide clusters. In accordance with previous studies, our calculations show three-dimensional compact structures are preferred for pure (TiO(2))(n) with oxo-stabilized higher hexavalent states, and linear chain structures are favored for pure (SiO(2))(n) with tetravalent states. However, the herein theoretically first reported mixed Ti(m)Si(n-m)O(2n) oxide clusters prefer either three-dimensional compact or linear chain structures depending upon the stoichiometry of the compound. Vibrational analysis of the important modes of some highly stable structures is provided. Coupled-cluster single and double excitation (with triples) [CCSD(T)] computed energy gaps for the TiO(2) dimers compare well with results from previous study. Excitation energies are computed by use of time-dependent (TD) DFT and equation-of-motion coupled-cluster calculations with singles and doubles (EOM-CCSD) for the most stable isomers.