Theoretical studies on structures and reactivities of organocuprate(I) and organocopper(III) species

Systematic evaluation of method and basis set on the structure and energetics of organocuprate(I) and organocopper(III) species has been carried out. Various structures of organocuprate(I) and organocuprate(III) complexes were optimized with the HF, MP2, and B3LYP methods, and compared with the structures determined by X-ray crystallography (i.e., Me(2)Cu(I)(-), (CF(3))(4)Cu(III)(-)). Both the MP2 and B3LYP methods reasonably reproduce the X-ray structures while the HF method does not. Using larger basis set and incorporating the relativistic effects for Cu afford the best results. In the studies on the energetics of a Libond;Cu cluster model (Me(2)CuLi. LiCl) and Me(3)Cu model with the MP2, MP3, MP4DQ, MP4SDQ, CCSD(T), and B3LYP methods, the B3LYP method gives energetics similar to those obtained with the CCSD(T) method with much less cost, and hence, is judged to be the best practical method. The studies have shown that B3LYP method with the basis set incorporating the relativistic effective core potentials for Cu and the 6-31G* basis set for the rest is the theoretical method that is the most cost-effective for the studies of the structure and energetics of organocuprate(I) and organocopper(III) species.     

Hydrogen peroxide clusters: the role of open book motif in cage and helical structures

Hartree-Fock (HF) calculations using 6-31G*, 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets show that hydrogen peroxide molecular clusters tend to form hydrogen-bonded cyclic and cage structures along the lines expected of a molecule which can act as a proton donor as well as an acceptor. These results are reiterated by density functional theoretic (DFT) calculations with B3LYP parametrization and also by second-order M?ller-Plesset perturbation (MP2) theory using 6-31G* and 6-311++G(d,p) basis sets. Trends in stabilization energies and geometrical parameters obtained at the HF level using 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are similar to those obtained from HF/6-31G* calculation. In addition, the HF calculations suggest the formation of stable helical structures for larger clusters, provided the neighbors form an open book structure.     

A coupled-cluster study of the structure and vibrational spectra of pyrazole and imidazole

Harmonic force fields were calculated at the corresponding optimized geometries for pyrazole and imidazole at the HF, B3LYP, MP2, CCSD and CCSD(T) levels using the 6-31G* basis set and at the HF and B3LYP levels using the cc-pVTZ basis set. The agreement between the calculated and experimental geometries by the CCSD and CCSD(T) methods was generally similar to that obtained with the B3LYP and MP2 methods. The force fields were scaled using one-scale-factor (1SF), 3SF and 7SF scaling schemes. The scale factors were varied with respect to the experimental frequencies. Using 7SF scaling, the root-mean-square (RMS) deviation of the calculated frequencies from the experimental frequencies by the HF, B3LYP, MP2, CCSD and CCSD(T) methods and the 6-31G* basis set was 16, 7, 13, 11 and 11 cm(-1), respectively. This shows that the B3LYP method is preferred for force field calculations over the perturbative MP2, CCSD and CCSD(T) methods. Using 1SF scaling, the CCSD(T) scale factor was 0.931, the highest among the five methods used but close to that obtained with the B3LYP method and the cc-pVTZ basis set with lower RMS deviation.     

Tautomeric and conformational properties of malonamic acid methyl ester, NH2C(O)-CH2-C(O)OCH3: electron diffraction and quantum chemical study

The tautomeric and conformational properties of malonamic acid methyl ester, NH2C(O)-CH2-C(O)OCH3, have been investigated by means of gas-phase electron diffraction (GED) and quantum chemical calculations (HF, B3LYP, and MP2 approximations with different basis sets up to 6-311++G(3df,pd)). Both quantum chemistry and GED at 360(8) K result in the existence of a single diketo conformer in the gas phase. According to GED refinement, this conformer possesses an (ac, sc) conformation with dihedral angles C-C-C(NH2)=O of 140.3(3.0) degrees and C-C-C(OCH3)=O of 31.1(7.2) degrees. The experimental geometric parameters are reproduced very closely by MP2 and B3LYP methods with large basis sets.     

A theoretical study on the origin of pi-facial stereoselectivity in the alkylation of enolates derived from 4-substituted gamma-butyrolactones

The alkylation of 4-methoxymethyl-gamma-butyrolactone enolate with methyl chloride was studied at the B3LYP/6-31+G* level. Conformer search of the free enolate gave 15 unique conformers within 5.39 kcal/mol. The transition structures for both anti- and syn-attacks of methyl chloride on these 15 conformers were located. In all cases, the anti-transition structures are more stable than the corresponding syn-ones. The alkylation of gamma-valerolactone was studied at the MP2, B3LYP, and HF levels of theory with the 6-31+G* basis set in the presence of Li+ and dimethyl ether molecules. Basis set effects were also examined by the comparison of the MP2 results with the 6-31+G*, 6-31+G**, and 6-311+G** basis sets in one case. This study shows that the main source of the anti-selectivity of 4-substituted gamma-butyrolactones is eclipsing strain in the syn-transition structures.     

Quantum-chemical studies of methyl and silyl torsional frequencies and the structures of disilylsulphide and trisilylphosphine

Torsional frequencies of methyl and silyl groups occurring in a range of molecules have been calculated by HF, B3LYP and MP2 methods using several basis sets. Linear correlations between calculated and observed values are derived and used to predict unobserved or dubious frequencies. The current experimental value for the E torsion in trimethylphosphine is questioned. The relative merits of the B3LYP and MP2 methods are explored. MP2 calculations can show wide variation with respect to basis set. In cases where two or more silyl groups are attached to a common atom, as in disilylsulphide (SiH3)2S, disilylmethane (SiH3)2CH2, trisilylmethane (SiH3)3CH and tetrasilylmethane (SiH3)4C, marked differences occur between B3LYP and MP2 estimates. These may be linked to concomitant differences in conformation or potential barrier restraining internal rotation. In disilylmethane the B3LYP results agree much better with experiment than those from the MP2 method. HF and B3LYP calculations for disilylsulphide and trisilylphosphine give normal C2v and C3v equilibrium structures, respectively, but in MP2 structures the silyl groups are twisted through 6-13 degrees yielding C2 and C3 configurations. It may be possible to distinguish between these structures through the observation of isolated SiH stretching frequencies in the spectra of fully deuterated materials. Dispersion forces could contribute to the twisting calculated by the MP2 method. Further studies of the microwave and vibrational spectra of disilylsulphide and trisilylphosphine isotopomers are needed.     

MP2, DFT and ab initio calculations on thioxanthone

Density functional theory (DFT), HF and MP2 calculations have been carried out to investigate thioxanthone molecule using the standard 6-31+G(d,p) basis set. The results of MP2 calculations show a butterfly structure for thioxanthone. The calculated results show that the predicted geometry can well reproduce the structural parameters. The predicted vibrational frequencies were assigned and compared with experimental IR spectra. A good harmony between theory and experiment is found. The theoretical electronic absorption spectra have been calculated using CIS method. ¹³C and ¹H NMR of the title compound have been calculated by means of B3LYP density functional method with 6-31+G(d,p) basis set. The comparison of the experimental and the theoretical results indicate that density functional B3LYP method is able to provide satisfactory results for predicting NMR properties.     

Energetics and structure of glycine and alanine based model peptides: Approximate SCC-DFTB,AM1 and PM3 methods in comparison with DFT,HF and MP2 calculations

We calculate relative energies and geometries of important secondary structural elements for small glycine and alanine based polypeptides containing up to eight residues. We compare the performance of the approximate methods AM1, PM3 and self-consistent charge, density-functional tight-binding (SCC-DFTB) to density-functional theory (DFT), Hartree–Fock (HF) and MP2. The SCC-DFTB is able to reproduce structures and relative energies of various peptide models reliably compared to DFT results. The AM1 and PM3 methods show deficiencies in describing important secondary structure elements like extended, helical or turn structures. The discrepancies between different ab initio (HF, MP2) and DFT (B3LYP) methods for medium sized basis sets (6-31G*) also show the need for higher level calculations, since systematic errors found for small molecules may add up when investigating longer polypeptides.     

Vibrational spectra and gas phase structure of N-cyanoimidosulfurous difluoride, NCN=SF2

The vibrational spectra, IR (gas) and Raman (liquid) of N-cyanoimidosulfurous difluoride, NCN=SF2, were recorded, and the molecular structure was determined by gas electron diffraction. The spectra were assigned by comparing the vibrational frequencies with those in related molecules and with calculated (HF, MP2, B3LYP with 6-31G(d) basis sets) values, and a normal coordinate analysis was performed. The molecule possesses a syn conformation (Ctriple bondN syn with respect to the bisector of the SF2 angle). This has been rationalized by orbital interactions of the electron lone pairs of sulfur and nitrogen with the N-C and S-F bonds, respectively, which are antiperiplanar or anticlinal to these lone pairs (anomeric effects). Quantum chemical calculations with the B3LYP and MP2 methods reproduce the experimental structure reasonably well if large basis sets (6-311G(2d,f)) are used.     

Experimental (FTIR and FT-Raman) and ab initio and DFT study of vibrational frequencies of 5-amino-2-nitrobenzoic acid

The FTIR and FT-Raman spectra of 5-amino-2-nitrobenzoic acid (ANB) have been recorded in the region 400-4000cm(-1). The observed frequencies were assigned to different modes of vibrations on the basis of fundamental, combination and overtones. The geometry has been optimized with complete relaxation on the potential energy surface at HF, MP2 and B3LYP level of theories using 6-311++G(d,p) basis set and compared with the crystal data. The possible hydrogen bond interaction has been estimated taking a model compound. Further harmonic vibrational frequency calculations have been carried out at HF and B3LYP levels and the scaled values were in good agreement with majority of the experimental observations. The theoretically constructed spectra coincide satisfactorily with those of experimental spectra.     

Vibrational spectra and gas-phase structure of N-methyl-S,S-bis(trifluoromethyl)sulfimide, CH3N=S(CF3)2

The molecular structure of N-methyl-S,S-bis(trifluoromethyl)sulfimide, CH3N=S(CF3)2, was determined by gas electron diffraction and quantum chemical calculations [B3LYP and MP2 with 6-31+G(2df,p) basis sets]. Furthermore, vibrational spectra, IR (gas) and Raman (liquid), were recorded. These spectra were assigned by comparison with analogous molecules and with calculated frequencies and intensities (HF, B3LYP, and MP2 with 6-311G basis sets). All experimental data and computational methods result in a single conformer with syn orientation of the CH3 group relative to the bisector of the two CF3 groups. The molecule possesses C1 symmetry, slightly distorted from CS symmetry. The N=S bond length in this compound [1.522(10) A] is longer than that in imidosulfur difluorides RN=SF2 [1.476(4) A - 1.487(5) A].     

杂硼原子簇XB6+ (X=C,Si, Ge,Sn, Pb)的稳定性和芳香性

利用从头算MP2方法和密度泛函理论B3LYP和B3PW91方法, 研究了杂硼原子簇XB₆⁺ (X=C, Si, Ge, Sn, Pb)的结构、稳定性及化学键合情况. 对C, Si, Ge, B使用6-311+G(d)基组, 对Sn和Pb使用LANL2DZ赝势基组. 研究结果表明, 具有C_s对称性的假平面XB₆⁺ (X=C, Si, Ge, Sn, Pb)结构是势能面上的全域极小点, 其稳定性要高于C_6v对称性的锥形结构和C₂对称性的假锥形结构. 在B3LYP水平上, 对这些异构体的势能面的极小点进行了自然键轨道(NBO)的分析; 对最稳定构型的最高占据分子轨道(HOMO)和最低空轨道(LUMO)能级差、分子轨道(MO)和核独立化学位移(NICS)进行了计算和讨论. 分析了杂原子和硼原子间、相邻硼原子间的键合情况, 讨论了最稳定构型的芳香性质.     

H3PAuR型单核Au(Ⅰ)配合物的结构和非线性光学系数的量子化学计算比较

采用量子化学ab initio和DFT中的不同方法和基组对H3PAuR型单核Au(Ⅰ)配合物结构和二阶NLO系数进行计算, 探讨不同计算方法和Au基组对计算结果产生的影响. 对计算结果分析表明, 不同计算方法对Au(Ⅰ)配合物结构和二阶NLO系数影响较大, 其中用考虑电子相关效应的DFT-B3LYP和MP2方法优化得到的Au—P配键长比用HF方法的短, 相应的二阶NLO系数比HF方法的大2倍左右; 同一计算方法下, Au基组中d轨道个数增加优化得到的Au—P配键键长减小; 随着Au基组的增大, 前线分子轨道能级差减小, 其中SDD和CEP-121G基组之间的变化更明显. 基组变化对分子二阶NLO系数的影响较小, 多数分子Au取不同基组计算的βμ值相差在10%以内.     

Theoretical study of light-metal tetrahydroborates

Ab initio calculations of the structural, energetic, vibrational, and magnetic characteristics of the lowest-lying structures for isolated molecules and ions of light-metal tetrahydroborates (Li, Na, Be, Mg, and Al) have been performed by the perturbation theory (MP2), quadratic configuration interaction (QCISD(T)), coupled cluster (CCSD(T)), and density functional theory (B3LYP) methods using the 6-31G*, 6-31G**, 6-311+G**, and 6-311++G** basis sets. The trends in the behavior of the structural parameters, the energies of different decomposition pathways, barriers to internal rotation of BH₄ groups, normal mode frequencies, magnetic shielding constants, and spin density distribution (in radicals) have been analyzed in various related series of these compounds. The results obtained by ab initio methods and at the DFT level are compared. The economical approximation B3LYP/6-311++G**//B3LYP/6-311+G** adequately reproduces the results obtained at the higher level of theory CCSD(T)/6-311++G*s*//MP2/6-31G* even though it requires considerably shorter CPU times and smaller amounts of memory.     

Influence of diffuse and polarization functions on the second-order Møller–Plesset optimized dihedral angle of biphenyl

 Using 6-31G and 6-311G basis sets to which diffuse and polarization functions were added in a stepwise fashion (a total of 16 basis sets), Hartree–Fock (HF), MP2 and B3LYP geometry optimizations were performed on biphenyl. With the MP2 method, diffuse functions raise the dihedral angle φ, for example, from 46.3° for 6-31G to 54.1° for 6-311++G, while polarization functions lower it, for example, from 54.1° for 6-311++G to 42.1° for 6-311++G(2d,2p). For a single set of polarization functions, φ(MP2) lies close to or above φ(HF) (44–47°), but for a double set it is below φ(HF) and is close to B3LYP values (38–42°) which show little basis set dependence. The most reliable value for φ, 42.1° [MP2/6-311++G(2d,2p)], is expected to increase slightly by adding more diffuse functions. The corresponding best calculated energy barrier at 0° (coplanar conformation) is 2.83 kcal/mol, much higher than the experimental estimate (1.4 ± 0.5 kcal/mol). The barrier at 90° is 1.82 kcal/mol, in line with the experimental estimate (1.6 ± 0.5 kcal/mol) and with previous theoretical results. Received: 9 September 2002 / Accepted: 15 November 2002 / Published online: 1 April 2003 Correspondence to: Friedrich Grein e-mail: fritz@unb.ca Acknowledgement. The author would like to thank NSERC (Canada) for financial support.     

Advanced conformational energy surfaces for cellobiose**

Energy surfaces imply which molecular shapes are more likely and which are less likely. Therefore, they are valuable for assisting the understanding of the structures involved in biosynthesis and many practical post-harvest exploitations of cellulose. Although usually calculated with molecular mechanics, energy surfaces for the cellobiose fragment of cellulose can now be based on quantum mechanics. This paper presents three sets of energy surfaces. One set is for three analogs of cellobiose that lack hydroxyl groups, calculated based on geometries minimized at the HF/6-31G(d) or B3LYP/6-31G(d) levels. Larger basis sets were also used without further atomic movement. Predictions of experimental crystal structures of cellobiose and related compounds by these gas-phase analogs improved as the analog became sterically more like cellobiose. The second set of maps, for cellobiose itself, gave low HF energies for some experimental structures that had higher energies on the other sets of maps, but they were generally less predictive of the small molecule crystal structure shapes. Finally, AMBER*, a trial version of MM4, and a hybrid B3LYP/6-311++G(d,p)::MM3(96) method all gave similar results, increasing the promise of modeling. These analyses suggest that folding conformations depend on hydrogen bonding to overcome intrinsic strain, and that there may be intrinsic strain for 2-fold shapes in crystalline cellulose, with a maximum of about 1.0 kcal for each mole of cellobiose.     

The structure and energetics of pyrrolidinones, tetrahydrofuranones, piperidinones, and tetrahydropyranones: a computational study

We have performed high level ab initio quantum chemical calculations for 2- and 3-pyrrolidinone; tetrahydro-2- and -3-furanone; 2-, 3-, and 4-piperidinone; and tetrahydro-2-, -3-, and -4-pyranone. The most stable molecular structures were obtained from DFT calculations using the B3LYP density functional and the 6-31G(d) and 6-311+G(3df,2p) basis sets. The respective enthalpies of formation have been computed by the G3(MP2)//B3LYP composite method and appropriately chosen reactions. The calculated results are in excellent agreement with experimental data reported in the literature.     

Ab initio study of some peroxides. HOOH, CH3OOH and, CH3OOCH3

The geometries of HOOH, CH₃OOH, and CH₃OOCH₃, were optimized with different basis sets (3-21G, 6-31G^*(*) and D95^**) at different levels of theory (HF, MP2, MP4, and CI). HF/3-21G optimizations result in planar trans conformations for all three peroxides. HF/6-31G^** calculations predict skew conformations for HOOH and CH₃OOH, but a planar trans struture for CH₃OOCH₃. For the larger basis set the calculated bond lengths, especially the O-O bonds, are too short. Optimizations for HOOH including electron correlation at the MP2, MP3, MP4, CI, and CCD level improve the agreement for bond lengths and the OOH angle, but result in dihedral angles Which are too large by 3– 8°. In the case of CH₃OOCH₃, similar calculations at the MP2 and CI level predict planar trans structures instead of the experimentally observed skew conformation. On the other hand, MP4 single point calculations at MP2 optimized parameters result in a correct skew structure. For all three peroxides a computationally “economic” method, i.e., single point calculations at MP2 or MP4 level with HF/3-21G optimized parameters, result in close agreement between calculated and experimental structures.     

The geometry of pyrazole: A test for ab initio calculations

Ab initio calculations on the structure of pyrazole have been carried out at different levels of accuracy. At the Hartree-Fock (HF) level, the performance of several basis sets, namely 3-21G, 6-31G, 6-31G**, and 6–311G** was investigated. The influence of electron correlation effects also was studied by carrying out geometry optimizations at the MP2, MP4, and QCISD levels. The performance of a density functional method also was evaluated. We have also investigated the possible influence of the frozen core approximation on the final optimized geometry. Three different statistical analyses were considered in determining which geometry is closest to the experimental microwave geometry—namely Paul Curtin's diagrams, cluster analysis, and multidimensional scaling. From these analyses, we conclude that there is no asymptotic approach to the experimental geometry by increasing the quality of the theoretical model, although, as expected, the more reliable structures are those obtained at the MP2, MP4, and QCISD levels, as well as those obtained by the B3LYP density functional method. We have also found that the values of the rotational constants are a tight criterion to define the quality of a molecular geometry. © 1995 by John Wiley & Sons, Inc.     

Comparison of ab initio and DFT electronic structure methods for peptides containing an aromatic ring: effect of dispersion and BSSE

We establish that routine B3LYP and MP2 methods give qualitatively wrong conformations for flexible organic systems containing pi systems and that recently developed methods can overcome the known inadequacies of these methods. This is illustrated for a molecule (a conformer of the Tyr-Gly dipeptide) for which B3LYP/6-31+G(d) and MP2/6-31+G(d) geometry optimizations yield strikingly different structures [Mol. Phys. 2006, 104, 559-570]: MP2 predicts a folded "closed-book" conformer with the glycine residue located above the tyrosine ring, whereas B3LYP predicts a more open conformation. By employing different levels of theory, including the local electron correlation methods LMP2 (local MP2) and LCCSD(T0) (local coupled cluster with single, double, and noniterative local triple excitations) and large basis sets (aug-cc-pVnZ, n=D, T, Q), it is shown that the folded MP2 minimum is an artifact caused by large intramolecular BSSE (basis set superposition error) effects in the MP2/6-31+G(d) calculations. The B3LYP functional gives the correct minimum, but the potential energy apparently rises too steeply when the glycine and tyrosine residues approach each other, presumably due to missing dispersion effects in the B3LYP calculations. The PWB6K and M05-2X functionals, designed to give good results for weak interactions, remedy this to some extent. The reduced BSSE in the LMP2 calculations leads to faster convergence with increasing basis set quality, and accurate results can be obtained with smaller basis sets as compared to canonical MP2. We propose LMP2 as a suitable method to study interactions with pi-electron clouds.