Structures, stabilities, and electronic and optical properties of C52 fullerene, ions, and metallofullerenes

The 437 classical isomers of fullerene C52 have been studied by PM3, HCTH/3-21G, and B3LYP6-31G(d). C(2):029 with the least number of adjacent pentagons is predicted to be the most stable isomer. The investigations show that both the number of adjacent pentagons and the degree of aromaticity play important roles in the relative stabilities of fullerene isomers. To clarify the relative stabilities of the C52 isomers in a wide range of temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP6-31G(d) level. C(2):029 prevails in a wide temperature range. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and sum-over-states model. The static second-order hyperpolarizability of C(2):029 is 51% larger than that of C60. Furthermore, intensity-dependent refractive index gamma (-omega;omega,omega,-omega) (omega=1.1653 eV) of C(2):029 is 13 times larger than that of C60. The encapsulation of Ca atom in C52 fullerene is exothermic and the metallofullerene Ca-C52 is described as Ca2+-C52(2-).     

Structures, stabilities, and electronic and optical properties of c(58) fullerene isomers, ions, and metallofullerenes.

The 1205 classical isomers of fullerene C58, as well as one quasi-fullerene C58 isomer with a heptagonal ring (labeled as Cs:hept) have been investigated by the quantum chemical methods PM3, HCTH/3-21G, and B3LYP/6-31G(d). Isomer C3v:0001, which has the lowest number of adjacent pentagons, is predicted to be the most stable isomer, but the quasi-fullerene isomer Cs:hept is only 2.50 kcal mol-1 higher in energy. Systematic investigations of the electronic properties of C3v:0001 and Cs:hept find that the C3v:0001 isomer has high vertical electron affinity (3.19 eV). The nucleus-independent chemical shifts (NICS) value at the center of Cs:hept (-5.1 ppm) is more negative than that of C60 (-2.8 ppm). The NICS value at the center of the heptagonal ring in Cs:hept (-2.5 ppm) indicates weakly aromatic character. In contrast, the C58(6-) and C58(8-) ions of the C3v:0001 and Cs:hept geometries possess large aromatic character, with NICS values between -14.0 and -26.2 ppm. To clarify the thermodynamic stabilities of C58 isomers at different temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. The C3v:0001 isomer prevails in a wide range of temperatures, and the Cs:hept isomer is also an important component around 2800 K. The IR spectra of C58 isomers are simulated to facilitate experimental identification of different isomers. In addition, the electronic spectra and the second-order hyperpolarizabilities are predicted by ZINDO and the sum-over-states model. The static second-order hyperpolarizability of the C3v:0001 isomer is 96.5 % larger than that of C60, and its second-order hyperpolarizabilities at external field frequencies are at least nine times larger than those of C60.     

Structures, stabilities, electronic, and optical properties of C64 fullerene isomers, anions (C64(2-) and C64(4-)), metallofullerene Sc2@C64, and Sc2C2@C64

The 3465 classical isomers of C(64) fullerene have been investigated by quantum chemical methods PM3, and the most stable isomers have been refined with HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-311G(d)//B3LYP/6-31G(d) level. C(64)(D(2):0003) with the lowest e(55) (e(55) = 2), the number of pentagon-pentagon fusions, is predicted to be the most stable isomer and it is followed by the C(64)(C(s):0077) and C(64)(C(2):0103) isomers within relative energy of 20.0 kcal/mol. C(64)(D(2):0003) prevails in a wide temperature range according to energy analysis with entropy contribution at B3LYP/6-31G(d) level. The simulated IR spectra and electronic spectra help to identify different fullerene isomers. All the hexagons in the isomers with e(55) = 2 display local aromaticity. The relative stabilities of C(64) isomers change with charging in ionic states. Doping also affects the relative stabilities of fullerene isomers as demonstrated by Sc(2)@C(64)(D(2):0003) and Sc(2)@C(64)(C(s):0077). The bonding of Sc atoms with C(64) elongates the C-C bond of two adjacent pentagons and enhances the local aromaticity of the fullerene cages. Charging, doping, and derativization can be utilized to isolate C(64) isomers through differentiating the electronic and steric effects.     

Theoretical investigation of C56 fullerene isomers and related compounds

All the 924 classical isomers of fullerene C(56) have been investigated by PM3, and some most stable isomers are refined with HCTH/3-21G and B3LYP6-31G(d) methods. D(2):003 with the least number of adjacent pentagons is predicted to be the most stable isomer at B3LYP/6-31G(d) level, while C(s):022 and C(2):049 possess nearly degenerate energies with relative energies of 0.03 and 3.90 kcal/mol, respectively. However, as to dianionic C(56)(2-) fullerene, C(2v):011 is predicted to be the most stable isomer. Investigations also show that the encapsulation of Ca atom in C(56) fullerene is exothermic and the metallofullerenes Ca@C(56) can be described as Ca(2+)@C(56)(2-). The computed relative stabilities show that the D(2):003 behaves more thermodynamically stable than other isomers in a wide temperature interval, and C(2v):011 should also be an important component. The electronic isomerization of C(56) (C(2v):011) and C(50) (D(5h):002) indicates that this phenomenon might be rather general in fullerenes and causes different properties, thus bringing about new possible applications of fullerenes. The static second-order hyperpolarizabilities of the three most stable isomers are slightly larger than that of C(60).     

Search for suitable approximation methods for fullerene structure and relative stability studies: case study with C50

Local density approximation (LDA), several popular general gradient approximation (GGA), hybrid module based density functional theoretical methods: SVWN, BLYP, PBE, HCTH, B3LYP, PBE1PBE, B1LYP, and BHandHLYP, and some nonstandard hybrid methods are applied in geometry prediction for C60 and C70. HCTH with 3-21G basis set is found to be one of the best methods for fullerene structural prediction. In the predictions of relative stability of C50 isomers, PM3 is an efficient method in the first step for sorting out the most stable isomers. HCTH with 3-21G predicts very good geometries for C50, similar to the performance of B3LYP6-31G(d). The gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital from the predictions of all the density functional theory methods has the following descending order: E(gap)(half-and-half hybrid)>E(gap)(B3LYP)>E(gap)(HCTH)(GGA)>E(gap)(SVWN)(LDA).     

The conversion among various B4C clusters: a density functional theoretical study

Geometry optimizations and vibration frequencies of B4C clusters were performed with Becke-3LYP method using 6-31G(d) basis set. We have found 14 stable isomers, and the most stable structure among them is the five-member ring containing two three-member boron rings. We also analyzed these stable isomers in detail, and the results show that the structures containing three-member boron rings are predominant in energy for B4C clusters. In terms of MO and NBO analysis, the three-centered bond and the pi-electron delocalization play an important role in stabilizing the planar five-member rings of these B4C clusters. Our calculations suggest that isomer4 can be converted into isomer7 with only an energy barrier of 0.31 kJ mol(-1) at the B3LYP/6-311G+(3df) level. Although the planar structures of the five-member rings (isomers12-14) can be converted with each other, the conversions of isomer14 to isomer13 and isomer13 to isomer12 have high-energy barriers of 70.99 and 68.51 kJ mol(-1) at the B3LYP/6-31G(d) level, respectively.     

Searching for stable hept-C62X2 (X = F, Cl, and Br): structures and stabilities of heptagon-containing C62 halogenated derivatives

To determine the geometries of the most stable hept-C(62)X(2) (X = F, Cl, and Br) isomers, all 967 possible hept-C(62)F(2) isomers have been orderly optimized using AM1, HF/STO-3G, B3LYP/3-21G, and B3LYP/6-31G* methods, and chlorofullerenes and bromofullerenes, which are isostructural with five most stable hept-C(62)F(2) isomers, were regarded as candidates of the most stable isomer, and optimized at the B3LYP/6-31G* level. The results reveal that 2,9- and 9,62-hept-C(62)X(2) (X = F, Cl, and Br) are the two most stable isomers with slight energy difference. The halogenation releases strain energy of hept-C(62), and all halogenated fullerenes are more chemically stable than hept-C(62) with lower E(HOMO) and higher E(LUMO). All five most stable hept-C(62)X(2) (X = F, Cl, and Br) isomers are energetically favorable, and their thermodynamic stability decreases along with the increase of sizes of addends. Only hept-C(62)F(2) isomers show high thermodynamic stability, and they are potentially synthesized in experiments. 59,62-squ-C(62)X(2) (X = F, Cl, and Br) were computed for comparison, and they are found to be more stable than their heptagon-containing isomers.     

Cyclic vinyl p-tolyl sulfilimines as chiral dienophiles: theoretical study on the stereoselectivity, Lewis acid catalysis, and solvent effects in their Diels-Alder reactions

The theoretical study reported in the present work deals with chiral cyclic vinyl sulfilimines and their reactivity as dienophiles in [4 + 2] cycloaddition reactions, using B3LYP/6-31G(d)//AM1 and B3LYP/6-31G(d)//B3LYP/6-31G(d) model chemistries. Consideration of Lewis acid catalysis, illustrated by BF(3), decreases the activation energies of the cycloaddition process while the charge transfer from the diene to the sulfilimine is augmented. The [4 + 2] cycloaddition reactions of sulfilimines with both furan and cyclopentadiene occur in the gas phase with endo stereoselectivity, which is more pronounced with the latter diene. Endo-exo energy differences in the gas phase with the B3LYP/6-31+G(d)//B3LYP/6-31+G(d), B3LYP/6-31G(d)//B3LYP/6-31G(d), and B3LYP/6-31G(d)//AM1 model chemistries are almost the same. Solvent effects are responsible for the inversion of the stereoselectivity in the reactions of sulfilimines with furan because of the great difference in the dipole moments in endo and exo approaches.     

Conformational stability, vibrational assignmenents, barriers to internal rotations and ab initio calculations of 2-aminophenol (d 0 and d3)

The Raman (3700-100 cm(-1)) and infrared (4000-400 cm(-1)) spectra of solid 2-aminophenol (2AP) have been recorded. The internal rotation of both OH and NH2 moieties produce ten conformers with either Cs or C1 symmetry. However, the calculated energies as well as the imaginary vibrational frequencies reduce rotational isomerism to five isomers. The molecular geometry has been optimized without any constraints using RHF, MP2 and B3LYP levels of theory at 6-31G(d), 6-311+G(d) and 6-31++G(d,p) basis sets. All calculations predict 1 (cis; OH is directed towards NH2) to be the most stable conformation except RHF/6-31++G(d,p) basis set. The 1 (cis) isomer is found to be more stable than 8 (trans; OH is away from the NH2 moiety and the NH bonds are out-of-plane) by 1.7 kcal/mol (598 cm(-1)) as obtained from MP2/6-31G(d) calculations. Aided by experimental and theoretical vibrational spectra, cis and trans 2AP are coexist in solution but cis isomer is more likely present in the crystalline state. Aided by MP2 and B3LYP frequency calculations, molecular force fields, simulated vibrational spectra utilizing 6-31G(d) basis set as well as normal coordinate analysis, complete vibrational assignments for HOC6H4NH2 and DOC6H4ND2 have been proposed. Furthermore, we carried out potential surface scan, to determine the barriers to internal rotations of NH2 and OH groups. All results are reported herein and compared with similar molecules when appropriate.     

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。     

Energetic preferences for alpha,beta versus beta,gamma unsaturation

Density functional theory has been applied at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level to examine the energetics of alpha,beta- versus beta,gamma-unsaturation for some common organic functional groups. Specifically, the relative stabilities of allyl-X (H2C=CHCH2X) and 1-propenyl-X (H3CCH=CHX) isomers have been computed for X = methyl, vinyl, phenyl, formyl, acetyl, methoxy, methylthio, methylsulfinyl, methylsulfonyl, sulfamoyl, and methoxysulfonyl, and the results are compared to available experimental data. The intrinsic preference of 3 kcal/mol for the 1-propenyl isomer when X = CH3 is exceeded by 2-4 kcal/mol for first-row conjugating groups, but it is not met for the sulfur-containing groups. In particular, alpha,beta-unsaturation is favored by less than 1 kcal/mol for the sulfone and sulfonamide analogues, while it is preferred by 8 kcal/mol for the vinyl-substituted case. Detailed structural results and torsional energy profiles are also reported.     

Comparison studies of fullerenes C72, C74, C76 and C78 by tight-binding Monte Carlo and quantum chemical methods

From C₇₂ to C₇₈, the top 20 low-energy isomers screened out from all isomers of each fullerene are optimized and computed by tight-binding Monte Carlo (TBMC), semi-empirical PM3, and ab initio B3LYP/6-31G*//HF/3-21G methods. The comparison results show that the TBMC method can efficiently optimize the structures and correctly predicate the low energy isomers. The relative energies computed by TBMC are in good agreement with the high-lever B3LYP calculation results. Our TBMC and B3LYP results show that the most energetically favorable structure of C₇₂ is not an isomer satisfying the isolated pentagon rule (IPR), which is different with the result by PM3. The symmetry of the most stable IPR isomer tends to low as the fullerene becomes large and several non-isolated-pentagon structures are found to have low symmetries and low energies close to the most stable isomer.     

On the structure and relative stability of C50 fullerenes

The complete set of 271 classical fullerene isomers of C50 has been studied by full geometry optimizations at the SAM1, PM3, AM1, and MNDO quantum-chemical levels, and their lower energy structures have also been partially computed at the ab initio levels of theory. A D(5h) species, with the least number of pentagon adjacency, is predicted by all semiempirical methods and the HF/4-31G calculations as the lowest energy structure, but the B3LYP/6-31G* geometry optimizations favor a D3 structure (with the largest HOMO-LUMO gap and the second least number of adjacent pentagons) energetically lower (-2 kcal/mol) than the D(5h) isomer. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the HF/4-31G level for the first time. The computed relative-stability interchanges show that the D3 isomer behaves more thermodynamically stable than the D(5h) species within a wide temperature interval related to fullerene formation. According to a newly reported experimental observation, the structural/energetic properties and relative stabilities of both critical isomers (D(5h) and D3) are analyzed along with the experimentally identified decachlorofullerene C50Cl10 of D(5h) symmetry. Some features of higher symmetry C50 nanotube-type isomers are also discussed.     

Mechanistic insights into triterpene synthesis from quantum mechanical calculations. Detection of systematic errors in B3LYP cyclization energies

Most quantum mechanical studies of triterpene synthesis have been done on small models. We calculated mPW1PW91/6-311+G(2d,p)//B3LYP/6-31G* energies for many C30H51O+ intermediates to establish the first comprehensive energy profiles for the cationic cyclization of oxidosqualene to lanosterol, lupeol, and hopen-3beta-ol. Differences among these 3 profiles were attributed to ring strain, steric effects, and proton affinity. Modest activation energy barriers and the ample exothermicity of most annulations indicated that the cationic intermediates rarely need enzymatic stabilization. The course of reaction is guided by hyperconjugation of the carbocationic 2p orbital with parallel C-C and C-H bonds. Hyperconjugation for cations with a horizontal 2p orbital (in the plane of the ABCD ring system) leads to annulation and ring expansion. If the 2p orbital becomes vertical, hyperconjugation fosters 1,2-methyl and hydride shifts. Transition states leading to rings D and E were bridged cyclopropane/carbonium ions, which allow ring expansion/annulation to bypass formation of undesirable anti-Markovnikov cations. Similar bridged species are also involved in many cation rearrangements. Our calculations revealed systematic errors in DFT cyclization energies. A spectacular example was the B3LYP/6-311+G(2d,p)//B3LYP/6-31G* prediction of endothermicity for the strongly exothermic cyclization of squalene to hopene. DFT cyclization energies for the 6-311+G(2d,p) basis set ranged from reasonable accuracy (mPW1PW91, TPSSh with 25% HF exchange) to underestimation (B3LYP, HCTH, TPSS, O3LYP) or overestimation (MP2, MPW1K, PBE1PBE). Despite minor inaccuracies, B3LYP/6-31G* geometries usually gave credible mPW1PW91 single-point energies. Nevertheless, DFT energies should be used cautiously until broadly reliable methods are established.     

Neutral homoaromaticity in some heterocyclic systems

[reaction: see text] Neutral homoaromaticity has been evaluated in heterocyclic systems related to the bicyclo[3.2.1]octane skeleton with replacement of CH(2) at C-2 in bicyclo[3.2.1]octa-3,6-diene with X = BH, AlH, Be, Mg, O, S, PH, NH (12); replacement of CH at C-3 in bicyclo[3.2.1]octa-3,6-dien-2-yl anion with PH, S, NH, O (13); and replacement at C-2 and C-3 with N and O (14). Stabilization energies (SE) are evaluated using density functional theory and homodesmotic equations at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) level for series 12-14. Stabilization energies are compared with diamagnetic susceptibility exaltations, Lambda, CSGT-B3LYP/6-31G(d)//B3LYP/6-31G(d), and nucleus-independent chemical shifts (NICS), GIAO-B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d). Analysis of frontier orbitals and geometries, B3LYP/6-31G(d)//B3LYP/6-31G(d), and proton affinities of 2-azabicyclo[3.2.1]octa-3,6-diene, pyrrole, and related model systems, B3LYP/6-311+G(2d,2p)//B3LYP/6-31G(d), provide complementary evidence supporting the division of the substrates evaluated into antihomoaromatic (12, X = BH, AlH, and Be), nonhomoaromatic (12, X = O, S, NH, PH), and homoaromatic (13, X = S, PH, NH, O and 14 X = ON), with 12 (X = Mg) appearing as transitional between anti- and nonhomoaromatic.     

Structural elucidation of nitro-substituted five-membered aromatic heterocycles utilizing GIAO DFT calculations

The GIAO (Gauge Including Atomic Orbitals) DFT (Density Functional Theory) method is applied at the B3LYP/6-31+G(d,p)//B3LYP/6-31+G(d), B3LYP/6-311++G(d,p)//B3LYP/6-31+G(d), B3LYP/6-311+G (2d,p)//B3LYP/6-31+G(d) and B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) levels of theory for the calculation of proton and carbon chemicals shifts and coupling constants for 25 nitro-substituted five-membered heterocycles. Difference (1D NOE) spectra in combination with long-range gHMBC experiments were used as tools for the structural elucidation of nitro-substituted five-membered heterocycles. The assigned NMR data (chemical shifts and coupling constants) for all compounds were found to be in good agreement with theoretical calculations using the GIAO DFT method. The magnitudes of one-bond (1JCH) and long-range (nJCH, n>1) coupling constants were utilized for unambiguous differentiation between regioisomers of nitro-substituted five-membered heterocycles.     

Electrophilic and oxidative chemistry of pyrene and its non-alternant isomers: theoretical (DFT, GIAO-NMR, NICS) study of protonation carbocations and oxidation dications from pyrene, azupyrene (dicyclopenta[ef,kl]heptalene) and dicyclohepta[ed,gh]pentalene

Mono- and diprotonated carbocations and the two-electron oxidation dications derived from parent pyrene and its nonalternant isomers "azupyrene"(dicyclopenta[ef,kl]heptalene)(DCPH) and dicyclohepta[ed,gh]pentalene (DCHP) were studied by DFT at the B3LYP/6-31G(d) level. The most likely site(s) for mono- and diprotonation were determined based on relative arenium ion energies and the structures of the energetically most favored carbocations were determined by geometry optimization. The NMR chemical shifts for the protonated mono- and dications and the oxidation dications were computed by GIAO-NMR at the B3LYP/6-31G(d)//B3LYP/6-31G(d) level and their charge delocalization paths were deduced based on magnitude of the computed [capital Delta][small delta](13)C values and the NPA-derived changes in charges. Relative aromaticity/antiaromaticity in various rings in the energetically favored mono- and dications was estimated via NICS and [capital Delta]NICS. Calculated NMR chemical shift data for and were compared with the available experimental NMR values. The available data on chemical and physical properties of DCPH and DCHP are extremely limited and biological activity data are non-existent. The present study provides the first glance into their carbocations and oxidation dications, while augmenting and reinforcing the previous stable ion data on the pyrenium cations.     

DFT Studies on Thermal Stabilities,Electronic Structures,and ~（13）C Chemical Shifts of C_（24）O_2 Based on Fullerene C_（24）（D_6）

Quantum chemical calculations on some possible equilibrium geometries of C24O2 isomers derived from C24 (D6) and C24O have been performed using density functional theory (DFT) method. The geometric and electronic structures as well as the relative energies and thermal stabilities of various C24O2 isomers at the ground state have been calculated at the B3LYP/6-31G(d) level of theory. And the 1,4,2,5-C24O2 isomer was found to be the most stable geometry where two oxygen atoms were added to the longest carbon-carbon bonds in the same pentagon from a thermodynamic point of view. Based on the optimized neutral geometries, the vertical ionization potential and vertical electron affinity have been obtained. Meanwhile, the vibrational frequencies, IR spectrum, and 13C chemical shifts of various C24O2 isomers have been calculated and analyzed.     

DFT, FT-Raman and FT-IR investigations of 5-o-tolyl-2-pentene

FT-IR and Raman spectra of 5-o-tolyl-2-pentene (OTP) have been experimentally reported in the region of 4000-10 cm(-1) and 4000-100 cm(-1), respectively. The optimized geometric parameters, normal mode frequencies and corresponding vibrational assignments of cis and trans isomers of OTP (C12H16) have been theoretically examined by means of B3LYP hybrid density functional theory (DFT) method together with 6-31G(d) and 6-31++G(d,p) basis sets. Furthermore, reliable vibrational assignments have made on the basis of potential energy distribution (PED) calculated. Comparison between the experimental and theoretical results indicates that density functional B3LYP method is able to provide satisfactory results for predicting vibrational wavenumbers and trans isomer is supposed to be the most stable form of OTP molecule.     

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.